University of Southern California Dissertations and Theses

Seeing the future through the lens of the past: fusing paleoclimate observations and models

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Seeing the future through the lens of the past: fusing paleoclimate observations and models

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Content Se eing the Futur e thr ough the Lens of the Past:
Fusing Pale o climate Obser vations and Mo dels
by
Feng Zhu
A Dissertation P r esente d to the
F A CULT Y OF THE USC GRADU A TE SCHOOL
UNI VERSI T Y OF SOU THERN CALIFORNIA
In Partial Fulfillment of the
Re quir ements for the Degr e e
DOCT OR OF PHILOSOPH Y
( Ge ological Sciences)
A ugust 2021
Cop yright 2021 Feng Zhu
De d ication
This dissertation is de dicate d to the memor y of my grandfather , Genfu Zhu,
who taught me brav er y , determination, and diligence .
ii
A c kno wle dgements
This dissertation w ould not hav e b e en p ossible without the advice , help , supp ort, and encouragement fr om
many p e ople , to whom I w ould like to e xpr ess my sincer e gratitude:
My advisor , Dr . Julien Emile-Geay . Thank y ou for offering me the opp ortunity to pursue a P h.D . in
science , when I was ab out to giv e up other wise; for b eing patient to me and guiding me to the field of pale-
o climatology , when I was ignorant in the early stage; and for supp orting me for confer ences, w orkshops,
summer scho ols, and the opp ortunities to w ork with gr eat r esear chers, which hav e shap e d me a go o d sta-
tus in this field and help e d me a lot for my car e er . Y ou hav e b e en set a go o d e xample of an e xtraor dinar y
scientist and mentor , b eing always enthusiastic and har d-w orking when face d with scientific challenges,
and caring ab out not only my r esear ch, but also my physical and mental health, encouraging me to ke ep
a balance b etw e en study and life . I r eally appr e ciate the time and effort y ou hav e sp ent on p olishing my
writings and pr esentations, and I fe el truly blesse d to hav e learne d so much b e cause of y ou.
My dissertation and qualifying e xam committe es, Dr . Frank Corsetti, Dr . Felip e de Barr os, Dr . William
Frank, and Dr . Richar d Leahy . Thank y ou for y our kindness and time , as w ell as the questions and com-
ments that hav e help e d me to impr o v e . I cannot b e her e without y our supp ort.
My academic collab orators, esp e cially Dr . K e vin Anchukaities, Dr . Gr eg Hakim, Dr . Michael Evans,
and Dr . James Kir chner . Thank y ou for b eing ther e with me , attacking inter esting but challenging scientific
questions together . I appr e ciate y our wisdom and insights, as w ell as the countless e dits of the manuscripts.
It has b e en a fantastic learning e xp erience w orking with y ou.
My labmates, Jun Hu, Deb orah Khider , Michael Erb , and Ale xander James. Thank y ou for the accom-
pany during the days in the lab and the e xp erience y ou hav e taught me ab out b oth science and the daily
life in LA.
Ev er y staff in the department: Cynthia W aite , V ar dui T er-Simonian, John McRane y , K ar en Y oung, John
Y u, Barbara Grubb , Miguel Rincon, Ste v e Lin, and Ale xandra Aloia. Thank y ou for y our timely help all the
time that hav e made my study and r esear ch so much easier .
My friends in the department, esp e cially Haoran Meng, Gen Li, Jun Shao , Xiaop eng Bian, Hengdi Liang,
Sijia Dong, Yifang Cheng, Hongrui Qiu, Lei Qin, Abby Lunstrum, Mark Peaple , Alan Juar ez, and Rachel
K elly . Thank y ou for y our help , accompany , and all the fun w e hav e had these y ears.
My friends far away in space but with each other in heart, esp e cially Jiaqi Cao , Ran Zhang, Pei W ang,
Huaran Liu, Y ang Zhang, and Xiao qing Liu. Thank y ou for y our unconditional supp ort and encouragement
whene v er I felt frustrate d. It is so nice to hav e y our r emote accompany .
Finally , my family . Thank y ou for y our lo v e , supp ort, understanding, and sacrifices these y ears when
I hav e b e en far away fr om home . I am de eply indebte d to y ou.
iii
Contents
De dication ii
A c kno wle dgements iii
List of T ables vii
List of Figur es viii
Abstract xvii
Chapter 1: Intr o duction 1
1.1 Climate Mo dels and Their Evaluati on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scientific questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 The continuum of temp eratur e variability . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 The temp eratur e r esp onse to v olcanic for cing . . . . . . . . . . . . . . . . . . . . . 6
1.2.3 The ENSO r esp onse to v olcanic for cing . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2: The P leisto cene ’s climate continuum in mo dels and obser vations 10
2.1 Intr o duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Completing the Continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Simulating the continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 A tale of tw o r egimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Climate Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 Sp e ctral estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.2 Estimation of scaling e xp onents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Supplementar y Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.1 Data Sour ces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.2 Timeseries P lots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7.3 Sp e ctral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7.4 Distinguishing lo cal, r egional, and global vari ability . . . . . . . . . . . . . . . . . 26
2.7.5 Analysis of P A GES 2k r e cor ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7.6 Analysis of PMIP3 simulations of the last m illennium . . . . . . . . . . . . . . . . . 28
2.7.7 An ideal test of the scaling br eak hyp othesis . . . . . . . . . . . . . . . . . . . . . . 29
2.7.8 W av elet analysis of time-dep endent b oundar y co nditions . . . . . . . . . . . . . . 30
2.7.9 Comparing mo del simulations and obser vationa l r e cor ds o v er similar time spans . 30
iv
Chapter 3: Evaluating the temp eratur e r esp onse to v olcanic for cing 50
3.1 Intr o duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Data and Metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.1 Pale o climate data assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.2 Simulate d and Instrumental T emp eratur e Obser vatio ns . . . . . . . . . . . . . . . . 53
3.2.3 Sup erp ose d ep o ch analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 The Discr epancy and Its Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Spatial co v erage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.3 Biological memor y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.4 Pr o xy system noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.5 Re conciling the discr epancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Supplementar y Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Settings of the LMR frame w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.2 Re constructions using the Northern Hemisphe r e T r e e-Ring Netw ork De v elopment
(N TREND ) netw ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.3 Choice of eruption ke y dates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5.4 Softwar e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter 4: A r e-appraisal of the ENSO r esp onse to v olcanic for cing 77
4.1 Intr o duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 Corals vs T r e e Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 Combining Corals and T r e e Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 A non-stationar y sensitivity? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Effe cts of For cing A symmetr y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7 Metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.7.1 The Last Millennium Reanalysis data assimilati on frame w ork . . . . . . . . . . . . 85
4.7.2 Data Sour ces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.7.3 Sup erp ose d ep o ch analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.7.4 Ranking analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.8 Supplementar y Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.8.1 Cr oss-validation of the last millennium r eanalysis r e constructions . . . . . . . . . 92
4.8.2 T est on typ e I err or in sup erp ose d ep o ch a nalysis . . . . . . . . . . . . . . . . . . . 96
4.8.3 The ENSO r esp onse to v olcanism in PMIP3 and CESM-LME simulations . . . . . . 98
4.8.4 Sensitivity to r e construction season in t he last millennium r eanalysis . . . . . . . . 99
4.8.5 A comparison b etw e en historical SST analyses pr o ducts . . . . . . . . . . . . . . . 99
Chapter 5: Enhancing pale o climate data analysis and r epr o ducible r esear ch 119
5.1 Intr o duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2 Co de design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.3 Usage e xamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.1 Loading pale o climate data fr om a LiPD file . . . . . . . . . . . . . . . . . . . . . . 122
5.3.2 Data pr epr o cessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.2.1 Standar dization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.2.2 Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3.2.3 Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
v
5.3.2.4 Interp olation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.2.5 Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.3.2.6 Coarse-graining via a Gau ssian kernel . . . . . . . . . . . . . . . . . . . 130
5.3.2.7 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.3.2.8 Detr ending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.3.3.1 Corr elation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.3.3.2 Sp e ctral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3.3.3 W av elet analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3.3.4 W av elet coher ence analysis . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.4 Summar y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Chapter 6: Conclusion 147
6.1 Summar y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2 Cav eats and futur e w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.2.1 Structural err ors in climate mo del simulations . . . . . . . . . . . . . . . . . . . . . 149
6.2.2 Pr o xy system mo deling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.2.3 Pr o xy obser vation netw ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.3 Outlo ok . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography 153
vi
List of T ables
2.1 The o v er vie w information of the instrumental obser vations, r eanalysis, r e constructions
base d on pr o xy r e cor ds, and mo del simulations tha t b eing use d in this pap er . . . . . . . . . 13
S2.1 The b oundar y conditions b eing use d in T raCE-21ka, SIM2bl, and DG
ns
. . . . . . . . . . . . 34
S3.1 Last millennium mo del simulations c onsider e d in this study . . . . . . . . . . . . . . . . . 65
4.1 Metadata of the 22 large eruptions sho wn in Figur e 4.2a accor ding to e V olv2k v ersion 3
(T o ohe y and Sigl, 2017). Note that the value 0.0 in the column of Latitude denotes that the
pr e cise eruption latitude is unkno wn but the e v ent is define d as tr opical, and the value
-1.0 in the column of A symmetr y ( hemispheric asymmetr y for tr opical eruptions) denotes
that the e v ent is define d as e xtratr opical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
S4.1 V alidation skill of the LMR-r e con structe d Niño 3.4. . . . . . . . . . . . . . . . . . . . . . . 96
S4.2 Pr obability of accidentally ident ifying significant ENSO r esp onse . . . . . . . . . . . . . . . 97
S4.3 V olcanic for cing applie d in Pale o climate Mo delling Inter comparison Pr oje ct P hase III
(PMIP3, Braconnot et al., 2012) and Community Earth System Mo del Last Millennium
Ensemble simulations ( CESM-LME Otto-Bliesner et al., 2 015). . . . . . . . . . . . . . . . . 99
vii
List of Figur es
1.1 The W orld Mete or ological Organization (WMO ) Global Obser ving System ( GOS).
Sour ce: h t tp : / / w w w . c h a n t h a b u r i . b u u . a c . t h / ~ w i r o t e / m e t / t r o p i c a l / t e x t b o o k_ 2 n d _ e d i t i o n
/navmenu.php_tab_10_page_2.1.0.htm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Major pale o climate data ar chiv es. Sour ce: http://wiki.linked.earth. . . . . . . . . . . 3
1.3 The last millennium r eanalysis (LMR) pale o climate data assimilation (PD A )
frame w ork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 The qualitativ e o v er vie w of the sp e ctrum of climate variability fr om Fig. 1 of
Mitchell (1976), with annotations of p eaks and continuum. . . . . . . . . . . . . . . 5
1.5 Sup erp ose d ep o ch analysis (SEA ) on simulate d and r e constructe d Northern
Hemishpher e (NH) temp eratur e r esp onse to the 12 str ongest v olcanic eruptions
since 1400 CE, r epr o duce d fr om IPCC AR5 Figur e 5.8b (Masson-Delmotte et al.,
2013). For the details of the SEA metho d, se e Chapter 3. . . . . . . . . . . . . . . . . . . . 6
2.1 A sp e ctral estimate of the global-av erage surface temp eratur e variability using
instrumental and pale o climate datasets ( scale d degr e es K elvin), as w ell as pr o xy-
base d r e constructions of surface temp eratur e variability . (HadCRU T4) The Met
Office Hadle y Centr e gridde d dataset of global historical surface temp eratur e anomalies
(Morice et al., 2012). (P A GERS2k/LMR GAST) The Last Millennium Reanalysis frame w ork
(Hakim et al., 2016; T ar dif et al., 2019) applie d to the P A GES2k dataset (P A GES 2k
Consortium, 2017). The thick r e d cur v e denotes the me dian p o w er sp e ctral density (PSD ),
the dark r e d shade d ar ea denotes the inter quartile range , and the light r e d ar ea denotes the
central 95% range , fr om 2.5% to 97.5%. (S16 GAST) The r e construction of global av erage
surface temp eratur e (Sny der , 2016). (Pr obStack) A pr obabilistic P lio cene-P leisto cene stack
of b enthicδ
18
O ( Ahn et al., 2017).β ’s denote the estimate d scaling e xp onents o v er each
appr opriate fr e quency band. Details of their estimation ar e pr esente d in the Metho ds
se ction and SI T e xt 2.7.3. The r egional dataset (E DC) EPICA Dome C Ice Cor e 800K Y r
Deuterium Data and T emp eratur e Estimates ( Jouzel et al., 2007) is include d as a p oint of
comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 The p o w er sp e ctral density (PSD ) of transient mo del simulations. In the upp er
panel,β is estimate d o v er 2-500 yr . The inset plot compar es distributions of the scaling
e xp onents ( estimate d o v er 2-500 yr ) of GAST in P A GES2k-base d LMR vs the PMIP3
simulations. In the lo w er panel, β
CM
is the centennial-to-millennial scale e xp onent
estimate d o v er 400-2000 yr , whileβ
DC
is the de cadal-to-centennial scale e xp onent
estimate d o v er 20-400 yr . The inset plot compates the β values of the mo del simulations
(r e d, gr e en, and blue dots) and that of the obser vations ( gray dots). The gray cur v es
ar e identical as those in Figur e 2.1. Note that cur v es lab ele d ’CESM’ and ’GISS’ ar e the
ensemble av erage of the PSDs of 10 and 3 m emb ers for each mo del, r esp e ctiv ely . . . . . . . 15
viii
2.3 Effe ct of for cings on scaling b ehavior in the T raCE-21ka simulations The full
simulation is for ce d by transient Northern Hemispher e meltwater fluxes (MWF), orbital
for cing ( ORB), changing continental ice she ets (ICE), and transient gr e enhouse gas for cing
( GHG). Conv entions identical to Figur e 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
S2.1 The timeseries of the pr o xy-base d r e constructions, r eanalysis, and instrumental
obser vations. With r esp e ct to P A GES 2k/LMR GAST , the dark r e d shade d ar ea denotes
the inter quartile range , and the light r e d shade d ar ea denotes the central 95% range , fr om
2.5% to 97.5%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
S2.2 The timeseries of the PMIP3 simulations. Note that the cur v es for CESM and GISS
ar e 10 and 3 memb ers r esp e ctiv ely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
S2.3 The timeseries of the deglaciation simulations. . . . . . . . . . . . . . . . . . . . . . . 32
S2.4 (top) The timeseries with length of 2001 along with the delete d 900 p oints, and ( b ottom)
the analytical PSD cur v e along with the PSD estimate fr om W WZ applying on the
une v enly-sample d data and that fr om MTM applying on the cubic-interp olate d and
linear-interp olate d data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
S2.5 The sp e ctra of the global mean surface temp eratur e in the T raCE-21ka full simulation and
the asso ciate d sp e ctra of the av erage temp eratur e of the grid p oints picke d near est to the
corr esp onding obser vation lo cations of the pr o xies use d in LH14 and other tw o arbitrarily
sele cte d lo cations. The short duration pr o xies hav e duration less than 1000 y ears, while
the long duration pr o xies hav e duration longer than 1 000 y ears. . . . . . . . . . . . . . . . 34
S2.6 The sp e ctra of the global mean surface temp eratur e in the (top) T raCE-21ka full simulation,
(middle) DG
ns
, and ( b ottom) SIM2bl simulations, and their asso ciate d sp e ctra of the av erage
temp eratur e of the grid p oints picke d near est to the corr esp onding obser vation lo cations
of the Pr obStack, GAST , and EDC datasets. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
S2.7 The p o w er sp e ctral density of P A GES 2k dataset stratifie d by ar chiv e typ e along
with the distribution of the corr esp onding β
I
and β
D
. The interannual scaling
e xp onentβ
I
is estimate d o v er p erio d of 2-8 y ears, while the de cadal to centennial scaling
e xp onentβ
D
is estimate d o v er p erio d of 20-200 y ears. In the right panel, only the β
values with standar d err or less than or e qual to 0.5 is taken into account. The solid notch
indicates the me dian of β
D
, and the dashe d notch indicates that of β
I
. Note thatβ
I
for
marine se dimentar y r e cor ds is not calculable du e to their limite d temp oral r esolution. . . . 36
S2.8 Maps of scaling e xp onent s estimate d fr om the P A GES 2k phase 2 datasets. The
interannual scaling e xp onent β
I
is estimate d o v er p erio d of 2-8 y ears, while the de cadal
to centennial scaling e xp onent β
D
is estimate d o v er p erio d of 20-200 y ears. The sites in
gray ar e not calculable due to limite d temp oral r esolution and/or length, or the standar d
err or is gr eater than 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
S2.9 Ar chiv e-sp e cific comp osites of the P A GES 2k phase 2 dataset, scale d to HadCRU T4
temp eratur e . The upp er left sho ws all ar chiv es together , while the others stratify the
comp osites by ar chiv e typ e . The time series ar e 10-y ear binne d for the calculation of the
linear corr elation b etw e en the instrumental temp eratur e r e cor ds and the comp osites. The
shade d bars sho w 95% confidence inter vals calculat e d by a b o otstrap pr o ce dur e . . . . . . . 38
ix
S2.10 Sp e ctral estimates of (top) the comp osites of P A GES 2k r e cor ds stratifie d by
ar chiv e typ e and that of the LMR r eanalysis ensemble (50 memb ers); ( b ottom)
one of the CESM last millennium ensemble memb er’s global mean surface
temp eratur e ( o v er time span 850-2005) and r egional mean surface temp eratur e at
P A GES 2k lo cations stratifie d by ar chiv e typ e . The solid dark cur v e is the ensemb le
me dian PSD of LMR. The de cadal and centennial scaling e xp onent β
DC
is estimate d o v er
p erio d 20-300 y ears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
S2.11 The comparison b etw e en the scaling e xp onents of P A GES 2k/LMR G AST an d that
of the PMIP3 simulations o v er time span with or without industrial warming
p erio d. ( left ) Comparison o v er time span with industrial warming p erio d include d.
(right) Comparison o v er time span with industrial warming p erio d e xclude d. The dark r e d
shade d ar ea denotes the inter quartile range of LMR, and the light r e d shade d ar ea denotes
the central 95% range , fr om 2.5% to 97.5%. β s ar e estimate d o v er 2-500 yrs. . . . . . . . . . 40
S2.12 (top) The sp e ctra of the Holo cene temp eratur e pr o xies (253 r e cor ds). The colors denote
differ ent latitudes. Data citations se e the fo otnote in the te xt. ( b ottom) The distribution of
the scaling e xp onent β ’s o v er differ ent p erio ds. The solid notch indicates the me dian of
eachβ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
S2.13 The p o w er sp e ctral density estimations of the timeseries b efor e and after 8 kyr
BP in the T raCE-21ka full simulation. β
S
is estimate d o v er the p erio d of 20-400 yrs,
andβ
L
is estimate d o v er the p erio d of 400-2000 yrs. Note that for the timeseries after 8
kyr BP , w e do not se e a scaling br eak, and β is estimate d o v er p erio ds of 20-2000 yrs. . . . 42
S2.14 W av elet analysis of the T raCE-21ka full simulation. The upp er panel is the timeseries
of the simulation, the main p anel is the wav elet analysis plot, and the right panel is the
corr esp onding p o w er sp e ctral density . β
S
is estimate d o v er the p erio d of 50-300 yrs, and
β
L
is estimate d o v er 300-5000 yrs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
S2.15 (upp er left) The Fano r esonance impulse (I); ( lo w er left) The white noise (W) and that with
the impulse sup erp ose d (W +I); (right) The PSDs of those tw o signals. . . . . . . . . . . . . 43
S2.16 W av elet analysis of the mixe d signal with a Fano r esonance impulse sup erp ose d
onto a white noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yr , and β
L
is
estimate d o v er 20-200 yrs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
S2.17 (upp er left) The Fano r esonance impulse (I); ( lo w er left) The pink noise (I) and that with
the impulse sup erp ose d (P+I); (right) The PSDs of tho se tw o signals. . . . . . . . . . . . . . 44
S2.18 W av elet analysis of the mixe d signal with a Fano r esonance impulse sup erp ose d
onto a pink noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yrs, and β
L
is
estimate d o v er 20-200 yrs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
S2.19 (upp er left) The Gaussian impulse (I); ( lo w er left) The pink noise (I) and that with the
impulse sup erp ose d (P+I); (right) The PSDs of those t w o signals. . . . . . . . . . . . . . . . 45
S2.20 W av elet analysis of the mixe d signal with a Gaussian impulse sup erp ose d onto a
pink noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yrs, and β
L
is estimate d
o v er 20-200 yrs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
S2.21 W av elet analysis of the calculate d summer solstice insolation at 65
◦
N. The
pr e cession and obliquity harmonics ar e e vident, with a much lesser amplitude for the 100
kyr cy cle , as note d in Huyb ers (2006). The upp er panel sho ws the r esult o v er the past 2
my , while the lo w er panel sho ws that o v er the past 20 kyr , in which β is estimate d o v er
100-1000 yrs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
x
S2.22 W av elet analysis of the atmospheric CO
2
for cing use d in DG
ns
simulation
obtaine d fr om the EPICA Dome C ice cor e . β
S
is estimate d o v er the p erio d of
200-1000 yrs, andβ
L
is estimate d o v er 1000-5000 yrs . . . . . . . . . . . . . . . . . . . . . . 47
S2.23 W av elet analysis of the b est estimates of the ice-v olume e quivalent sea-le v el
function ( esl). β is estimate d o v er 400-5000 yrs. . . . . . . . . . . . . . . . . . . . . . . . 48
S2.24 The comparison b etw e en mo del simulations and obser vations in the fr e quency
domain o v er similar t ime spans. Note that the DG
ns
simulation has no o v erlapp e d
time span with LMR and HadCRU T4, and the HadCRU T4 analyze d her e is the annualize d
v ersion so that its magnitude or der w ould b e simila r to that of the mo del simulations. . . . 49
3.1 ( a) Comparison b etw e en the v olcanic for cing ( Gao , Rob o ck, and Ammann, 2008) use d
in the isotop e-enable d Community Earth System Mo del (iCESM) simulation (Ste v enson
et al., 2019; Brady et al., 2019) and the e V olv2k v ersion 3 V olcanic Stratospheric Sulfur
Inje ction (VSSI) compilation (T o ohe y and Sigl, 2017). The triangles denote the sele cte d 6
large e v ents b etw e en 1400 and 1850 CE. ( b) Sup erp ose d ep o ch analysis (SEA ) on simulate d
and r e constructe d temp eratur e r esp onse to the 12 str ongest v olcanic eruptions since 1400
AD , r epr o duce d fr om IPCC AR5 (Masson-Delmotte et al., 2013) Figur e 5.8b . ( c) Sup erp ose d
ep o ch analysis on annual Northern hemispheric mean temp eratur e (NHMT) simulate d
by 9 GCMs (Se ction 3.2.2, T able S1) and LMR r e constructions assimilating the whole
netw ork ( solid black cur v e with shading), the tr e e-ring netw ork ( dashe d br o wn cur v e), the
tr e e-ring width (TRW) netw ork ( solid gr e en cur v e), and the maximum late w o o d density
(MXD ) netw ork ( solid blue cur v e), r esp e ctiv ely . The shading encompasses the 5% and 95%
quantiles of the ensemble , while the cur v es indicate the ensemble me dian ( se e SI T e xt 3.5.1
for details ab out ensemble scheme). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Differ ences b etw e en P A GES 2k TRW and MXD r e cor ds r egar ding ( a, b) spatial
co v erage , ( c, d) seasonality dete cte d by the algorithm use d in T ar dif et al. (2019), and ( e ,
f) biological memor y quantifie d by the partial auto corr elation function (P A CF). ( a) The
spatial co v erage of TRW netw ork. ( c) The optimal seasonality of the TRW netw ork. ( e)
The P A CF of the TRW netw ork. ( b), ( d), and (f) ar e ar e as ( a), ( b), and ( e), r esp e ctiv ely , but
for the MXD netw ork. The color contours in ( a, b) indicate the corr elation b etw e en the
LMR r e constructions and the Berkele y Earth instrumental temp eratur e analysis (Rohde
et al., 2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 SEA in pseudopr o xy e xp eriments, e valuating the impact of ( a) spatial co v erage ,
( b) seasonality , and ( c) biological memor y and noise . ( a) the r e d cur v e denotes
the target, and the dashe d light gr e en cur v e , the solid dark gr e en cur v e , and the solid
light gr e en cur v e indicate the LMR r e construction assimilating 336 pseudo-P A GES2k
TRW r e cor ds o v er the NH, 50 r e cor ds o v er North America, and 50 r e cor ds o v er the NH,
r esp e ctiv ely . ( b) The solid r e d cur v e denotes the annual target, the dashe d r e d cur v e
denotes the b or eal summer target, and the gr e en cur v es indicate the LMR annual and
summer r e constructions assimilating the pseudo-P A GES2k TRW netw ork, r esp e ctiv ely .
( c) The solid r e d cur v e denotes the annual target, and the gr e en cur v es denote the LMR
r e construction assimilating pseudo-P A GES2k TRW as p erfe ct temp eratur e r e cor ders
( dashe d), and temp eratur e smo others ( solid). The case of smo othe d temp eratur e with
adde d Gaussian noise (SNR=0.3) is in dark gr e en. All the r e construction cur v es r efer to
the ensemble me dian ( se e SI T e xt 3.5.1 for details a b out the ensemble design). . . . . . . . 58
xi
3.4 ( a) Same as Figur e 3.1c, after r esolving differ ences in the mo del and pr o xy domains
asso ciate d with seasonality , spatial distribution, and biological memor y . ( b) Same as ( a)
but using the N TREND MXD netw ork. A v ersion of this figur e sho wing each mo del
simulation is available in Figur e S3.9, and one using mor e eruption e v ents is available in
Figur e S3.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
S3.1 Data fr om the P A GES 2k netw ork (P A GES 2k Consortium, 2017) assimilate d in
LMR . ( a) Spatial co v erage by ar chiv e typ e . ( b) T emp oral availability by ar chiv e typ e . . . . 63
S3.2 ( a) The r e constructe d northern hemispher e mean temp eratur e (NHMT) series using the official
LMR implementation (T ar dif et al., 2019) and the lightw eight implementation use d in our study
LMRt (Zhu et al., 2019a), using the same CCSM4 mo del prior (Landrum et al., 2012a) and the
P A GES 2k phase 2 dataset (P A GES 2k Consortium, 2017). ( b) The LMR r e constructe d NHMT
series assimilating the P A GES 2k netw ork, along with its mo del prior , the simulate d NHMT series
fr om the isotop e-enable d Community Earth System Mo del (iCESM, Ste v enson et al., 2019; Brady
et al., 2019). ( c) The corr elation b etw e en the surface temp eratur e simulate d by iCESM and the
instrumental obser vation Berkele y Earth instrumental temp eratur e analysis (Rohde et al., 2013)
o v er 1880 to 2000. ( d) Same as ( b) but for LMR r e construction assimilating the P A GES 2k netw ork.
The symb ols follo w that in Figur e S3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
S3.3 The pseudopr o xy e xp eriments (PPEs) that indicate the impact of spatial co v erage
and seasonality on the corr elation b etw e en r e construction and the pseudo-truth.
( a) The pseudopr o xies ar e generate d as p erfe ct temp eratur e r e cor ders of the annual
temp eratur e simulate d by iCESM, and the whole netw ork is assimilate d. ( b) Same as ( a),
but only 50 r e cor ds o v er North America (NA ) r egion ar e assimilate d. ( c) Same as ( a), but
only 50 r e cor ds o v er Northern H emispher e (NH) ar e assimilate d. ( d) Same as ( a), but the
pseudopr o xies ar e generate d as p erfe ct temp eratur e r e cor ders of the summer temp eratur e
simulate d by iCESM, and summer temp eratur e field is r e constructe d. ( e) Same as ( d), but
annual temp eratur e field is r e constructe d. (f) The corr elation b etw e en annual temp eratur e
and summer temp eratur e simulate d by iCESM. . . . . . . . . . . . . . . . . . . . . . . . . . 65
S3.4 Impact of seasonality on the corr elation b etw e en the r e constructions assimilating the
MXD netw ork and the Berkele y Earth instrumental temp eratur e analysis (Rohde et al.,
2013). ( a) Re constructing annual temp eratur e ( b) Re constructing summer temp eratur e .
Note that b oth e xp eriments use r eal, not pseudo , pr o xies. . . . . . . . . . . . . . . . . . . . 66
S3.5 ( a) The NH TRW comp osites compar e d to the seasonal obser vational temp eratur e , the
Go ddar d Institute for Space Studies ( GISS) Surface T emp eratur e Analysis ( GISTEMP ,
Hansen et al., 2010), at pr o xy lo cales. ( b) Same as ( a), but for MXD . ( c) The comp osite of
the pseudopr o xy that is generate d as temp eratur e smo other with a 5-yr mo ving av erage
filter , compar e d to the iCESM simulate d temp eratur e a t the pr o xy lo cales. . . . . . . . . . . 67
S3.6 The signal-to-noise ra tio (SNR) in TRW (T r e e Rings_WidthPages2) and MXD (T r e e
Rings_W o o dDensity ) r e cor ds dete cte d by the for war d op erator calibration pr o ce dur e ( se e
SI T e xt 3.5.1 for details) that follo ws T ar dif et al. (2019) in LMR, with curate d pr e-define d
seasonal windo ws. Higher SNR indicates mor e fraction of signal can b e e xplaine d by
seasonal temp eratur e and moistur e via bivariate a nd univariate linear r egr ession. . . . . . 68
S3.7 The Northern Hemispher e T r e e-Ring Netw ork De v elopment (N TREND , Wilson et al.,
2016; Anchukaitis et al., 2017). ( a) The spatial co v erage of each pr o xy typ e . ( b) The
temp oral availability of each pr o xy typ e . ( c) The partial auto corr elation function (P A CF)
up to lag-10 for each pr o xy typ e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
xii
S3.8 The comparison b etw e en the mo del simulate d temp eratur e r esp onse and the LMR
r e construction assimilating the whole N TREND netw ork. SEA applie d on the annual
NHMT o v er the whole NH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
S3.9 Similar to Figur e 3.4, but with the r esult of each mo del simulation plotte d out. . . . . . . . 70
S3.10 The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
whole P A GES 2k Netw ork a nd GCM simulations, targeting NHMT . The blue title denotes
the 6 eruption e v ents that ar e sele cte d for SEA in o ur study . . . . . . . . . . . . . . . . . . 71
S3.11 The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
P A GES 2k MXD Netw ork and GCM simulations, targeting mean summer temp eratur e at
pr o xy lo cales. The blue title denotes the 6 eruptio n e v ents that ar e sele cte d for SEA in our
study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
S3.12 The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
N TREND MXD Netw ork and GCM simulations, targeting mean summer temp eratur e at
pr o xy lo cales. The blue title denotes the 6 eruptio n e v ents that ar e sele cte d for SEA in our
study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
S3.13 Same as Figur e 3.4, but SEA takes a ll eruption e v ents liste d in Figur e S3.10. . . . . . . . . . 74
S3.14 ( a) Same as Figur e 3.1c, but using CCSM4 as prior . ( b) Same as Figur e 3.4a, but using
CCSM4 as prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
S3.15 Same as Figur e 3.1c, but using CCSM4 as prior and only sho wing the r e constructions
assimilating the P A GES2k TRW netw ork, with b oth bivariate and univariate for war d
op erator calibration. The comparison indicates that moistur e information do es not
alle viate the issue of lagge d r esp onse to v olcanism in TRW r e cor ds. . . . . . . . . . . . . . 75
S3.16 ( a) Same as Figur e S3.1a, but for pr o xies with start y ear older than or e qual to 1257 AD .
The shap es and colors denote each pr o xy typ e . ( b) A ges of P A GES2k r e cor ds. The shap e is
same as in ( a), while the colors denote differ ent range s of age . . . . . . . . . . . . . . . . . 76
4.1 ( a-c) Spatial v erification of the me dian field of the LMR (Hakim et al., 2016; T ar dif
et al., 2019) r e constructe d b or eal winter (De cemb er-Februar y , DJF) surface temp eratur e
assimilating thr e e sour ces: ( a,d) corals fr om the Ocean2k compilation (Tierne y et al.,
2015) up date d with the latest Palmyra data (De e et al., 2020); ( b ,e) the six b est pr e dictors
fr om Li et al. (2013) ( denote d as Li13b6), and ( c,f) b oth d ata sour ces combine d. V alidation
is p erforme d against the Extende d Re constructe d Sea Surface T emp eratur e , V ersion 5
(ERSST v5) (Huang et al., 20 17) o v er the instrumental p erio d (1881-2 000 CE). The orange
dots denote the lo cation o f the corals, the mint and blue squar es denote the lo cation of
the North American Dr ought Atlas (V ersion 2a) (NAD A, Co ok et al., 2004) and Monso on
A sia Dr ought Atlas (MAD A, Co ok et al., 201 0) sites, the gr e en up war d triangle denotes
the lo cation of the K auri tr e e-ring comp osite (W ahl et al., 2014), and the gr e en do wnwar d
triangle denotes the lo cation of the South America Altiplano (SA Altiplano) tr e e-ring
comp osite (Morales et al., 2012). ( d-f ) T emp oral v erification of the me dian of the LMR
r e constructe d DJF Niño 3.4 series ( color e d cur v es) against the ERSST v5 deriv e d Niño 3.4
( black solid cur v e) o v er the instrumental p erio d (1873-2000 CE). For each r e construction,
dark shading denotes the inter quartile range , and light shading denotes the central 95%
r egion, fr om 2.5% to 97.5%. R=corr elation co efficient, CE=co efficient of efficiency (Nash
and Sutcliffe , 1970). ( g-i) Scatter plot of the data p oints in ( d-f). The gr e y dashe d cur v e
r epr esents the linear r egr ession fitting cur v e . The black and color e d dots denote the data
p oints at y ear 0 and y ear 1 r elativ e to large eruption y ears (1883, 1902, 1913, 1951, 1963,
1982, 1991) as in Li et al. (2013), r esp e ctiv ely . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
xiii
4.2 ( a) The 22 large eruption e v ents define d as the v olcanic stratospheric sulfur inje ction
(VSSI) gr eater than 6 accor ding to e V olv2k v ersion 3 (T o ohe y and Sigl, 2017). 12 e v ents
o v er the y ears when the Palmyra coral r e cor d ( Cobb et al., 2003; Cobb et al., 2013; De e
et al., 2020) is available ar e color e d in black, while other e v ents ar e color e d in gr e y . Se e
T able 4.1 for the details of the metadata. ( b-d) Same as Figur e 4.1d-f, but for the past
millennium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3 ( a-b) Sup erp ose d ep o ch analy sis (SEA ) of the r e constructions LMR ( Corals) and LMR (Li13b6) r egar ding
the 12 e v ents when Palmyra is available . Solid cur v es with dots denote the comp osite mean, and the light
dots denote the Niño 3.4 anomaly at each y ear for each individual e v ent. The light gr e y dashe d cur v es
denote the 1%, 5%, 10%, 90%, 95%, and 99% quantiles of the comp osite means fr om 1000 b o otstrap draws fr om
non-v olcanic y ears (Metho ds). ( c-d) Ranking analysis of the LMR r e constructe d Y ear 0 Niño 3.4 values. The
gr e y shade d ar ea denotes the distribution of the Niño 3.4 anomaly value o v er all non-v olcanic y ears, whose
50%, 80%, 90%, and 95% quantiles ar e denote d by v ertical dot-dashe d cur v es, ser ving as significance le v els
(Metho ds). The v ertical solid lines mark individual v olcanic e v ents; for each, the horizontal axis p osition
denotes the Niño 3.4 anomaly value , and the v ertical axis p osition denotes the r elativ e rank of the Niño 3.4
anomaly value compar e d to all other e v ents. The cir cle/do wnwar d triangle/up war d triangle/diamond marker
r epr esents that a v olcanic e v ent has a Niño 3.4 anomaly value that is b elo w 80%/b etw e en 80-90%/b etw e en
90-95%/ab o v e 95% of that o v er the non-v olcanic y ears. The significance ratio denotes the numb er of e v ents
that ar e ab o v e the 80%, 90%, and 95% significance le v els, r esp e ctiv ely , out of all v olcanic e v ents. ( e-f ) Same as
( c-d), but for the y ear 1 Niño 3.4 values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4 Same as Figur e 4.3, but for LMR ( Corals+Li13b6) r egar ding the 12 e v ents when Palmyra is
available and all the 22 e v ents o v er the past millenniu m. . . . . . . . . . . . . . . . . . . . 91
4.5 ( a) Corr elation co efficient and ( b) co efficient of efficiency b etw e en instrumental
obser vations and r e constructions of De cemb er-Februar y (DJF) Niño 3.4 o v er timespan
1881-2000 CE. Data sour ces include: Extende d Re constructe d Sea Surface T emp eratur e ,
V ersion 5 (ERSST v5, Huang et al., 2017), Bunge and Clarke (2009), Li et al. (2013), the
Pale o Hy dr o dynamics Data A ssimilation pr o duct (PH YD A Steiger et al., 2018), and the
r e constructions of this study LMR ( Corals), LMR (Li13b6), and LMR ( Corals+Li13b6). Note
that Li13 is a No v emb er-Januray (NDJ) r e construction, and its corr elation to NDJ ERSST v5
and NDJ BC09 is 0.76 and 0.75, r esp e ctiv ely , and the co efficient of efficient is 0.47 and 0.5,
r esp e ctiv ely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6 ( a-f ) Timeseries of the six b est pr e dictors fr om Li et al. (2013), including the first tw o
principal comp onents of NAD A and MAD A, the K auri tr e e-ring comp osite (Fo wler et al.,
2008), as w ell as the South American Altiplano tr e e-ring comp osite (Morales et al., 2012),
o v er the past millennium (110 0-2000 CE). ( g-l) Same as in ( a-f), but o v er the instrumental
p erio d (1881-2000 CE). V alidation is p erforme d against the De cemb er-Februar y (DJF)
seasonally av erage d Niño 3.4 calculate d fr om Extende d Re constructe d Sea Surface
T emp eratur e , V ersion 5 (ERSST v5, Huang et al., 2017) o v er the instrumental p erio d
(1881-2000 CE). (m-r ) Scatter plots of the data p oints in ( g-l). The black and color e d dots
denote the data p oints at y ear 0 and y ear 1 of large eruption y ears (1883, 1902, 1913, 1951,
1963, 1982, 1991) as in Li et al. (2013), r esp e ctiv ely . The dashe d gr e y lines denote the linear
r egr ession fitting cur v es. R=corr elation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
xiv
4.7 ( a) The timeseries of the Li et al. (2013) Niño 3.4 r e construction ( denote d as Li13). ( b) SEA
of Li13, comparing the p o ol of all 22 large eruptions define d as V olcanic Explosivity Inde x
(VEI) larger than 4 and the p o ol e xcluding the e v ents o v er the instrumental p erio d after
1850 CE. ( c) Ranking analysis of Li13 with the p o ol of all 22 large eruptions. ( d) Ranking
analysis of Li13 with the p o ol e xcluding the e v ents o v er the instrumental p erio d after 1850
CE. The color denotes the eruption y ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.8 Scatter plots of the r e constructe d y ear 0 and y ear 1 Niño 3.4 anomaly in LMR
( Corals+Li13b6) against VSSI fr om e V olv2k v ersion 3 (T o ohe y and Sigl, 2017) for
tr opical eruption e v ents liste d in T able 4.1, categorize d by ( a, e) A symmetr y b etw e en [0.8,
1.5], ( b , f ) A symmetr y > 1.5, ( c, g) A symmetr y < 0.8 , as w ell as ( d, h) e xtr eme e v ents
with VSSI>20 (1230, 1257, 1458, 1815). The dashe d gr e y lines denote the linear r egr ession
fitting cur v es. R=corr elation co efficient. A symmetr y=hemispheric asymmetr y (NH/SH)
of aer osol spr ead for tr opical eruptions base d o n ratio of Gr e enland to Antar ctic flux. . . . 95
4.9 The timeseries of tr opical av e rage (20S-20N) temp eratur e anomaly , sea surface temp eratur e
(SST) base d Niño 3.4, and r elativ e sea surface temp eratur e (RSST , Kho dri et al., 2017) base d
Niño 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
S4.1 Same as Figur e 4.1, but validation i s p erforme d o v er 1881-1940 CE. . . . . . . . . . . . . . . 100
S4.2 Same as Figur e 4.1, but validation i s p erforme d o v er 1941-2000 CE. . . . . . . . . . . . . . . 101
S4.3 Same as Figur e S4.1, but the LMR r e constructions ar e p erforme d with calibration p erio d
o v er 1941-2000 CE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
S4.4 Same as Figur e S4.2, but the LMR r e constructions ar e p erforme d with calibration p erio d
o v er 1881-1940 CE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
S4.5 Same as Figur e 4.3, but for LMR (Li 13b6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
S4.6 Same as Figur e 4.3, but for LMR ( Corals+Li13b6). . . . . . . . . . . . . . . . . . . . . . . . . 105
S4.7 The thr e e v olcanic for cing sour ces in timeseries: T o ohe y and Sigl (2017), Gao , Rob o ck,
and Ammann (2008), and Cr o wle y et al. (2008). V ertical gr e y cur v es denote the y ears with
r elativ e large for cing values ( > 6, > 20, > 2, r esp e ctiv ely ), among which the consistent
e v ents ( with small temp oral offsets) dete cte d in all of the thr e e sour ces ar e lab ele d with the
y ear . The quantities of the thr e e sour ces ar e global v olcanic stratospheric sulfur inje ction
of eruption, global total stratospheric sulfate aer osol inje ction, and av erage d e xtratr opical
aer osol optical depth, r esp e ctiv ely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
S4.8 Similar to Figur e 4.3, but for mo del simulations with Gao , Rob o ck, and Ammann (2008)
v olcanic for cing applie d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
S4.9 Similar to Fi gur e S4.8, but for mo del simulations with Cr o wle y et al. (2008) v olcanic
for cing applie d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
S4.10 Similar to Figur e S4.8, but the Niño 3.4 anomaly values ar e calculate d base d on r elativ e
sea surface temp eratur e (RSST , Kho dri et al., 2017). . . . . . . . . . . . . . . . . . . . . . . 109
S4.11 Similar to Figur e S4.9, but the Niño 3.4 anomaly values ar e calculate d base d on r elativ e
sea surface temp eratur e (RSST , Kho dri et al., 2017). . . . . . . . . . . . . . . . . . . . . . . 110
S4.12 T r opical av erage temp eratur e (the differ ence b etw e en SST and RSST) in PMIP3 and
CESM-LME simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
S4.13 Same as Figur e 4.2, but with the July-Septemb er ( JAS) seasonally av erage d Extende d
Re constructe d Sea Surface T emp eratur e v5 (ER SST v5, Huang et al., 2017). . . . . . . . . . . 112
xv
S4.14 Same as Figur e 4.2, but with the Octob er-De cemb er ( OND ) seasonally av erage d Extende d
Re constructe d Sea Surface T emp eratur e v5 (ER SST v5, Huang et al., 2017). . . . . . . . . . . 113
S4.15 Same as Figur e 4.1, but for the July -Septemb er ( JAS) r e constructions. . . . . . . . . . . . . 114
S4.16 Same as Figur e 4.1, but for the Oct ob er-De cemb er ( OND ) r e constructions. . . . . . . . . . 115
S4.17 Same as Figur e 4.4, but for the July -Septemb er ( JAS) r e constructions. . . . . . . . . . . . . 116
S4.18 Same as Figur e 4.4, but for the Oct ob er-De cemb er ( OND ) r e constructions. . . . . . . . . . 117
S4.19 Historical SST analyses pr o ducts of De cemb er-Februar y (DJF) Niño 3.4, including a
spatially complete d v ersion of HadCRU T4.6 (V accar o et al., 2021) le v eraging the GraphEM
( Guillot, Rajaratnam, and Emile-Geay , 2015) algorithm, the Extende d Re constructe d Sea
Surface T emp eratur e v5 (ERSST v5, Huang et al., 2017), and the NASA Go ddar d Institute
for Space Studies ( GISS) Surface T emp eratur e Analysis ( G ISTEMP , Hansen et al., 2010). . . 118
5.1 The ar chite ctur e of the Pyleoclim user interface . Color e d squar es r epr esent obje cts
along with the p ositional arguments and ke y w or d arguments. Gr e y he xagons r epr esent
pr o cessing metho ds of the corr esp onding obje ct, while y ello w he xagons r epr esent
visualization metho ds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 A quick visualization of the SST series using the plot() metho d. . . . . . . . . . . . . . . . 123
5.3 A quick visualization of the SST series with the “w eb ” style . . . . . . . . . . . . . . . . . . 124
5.4 A quick o v er vie w of the data using the dashboard() metho d. . . . . . . . . . . . . . . . . . 125
5.5 The standar dize d series obtaine d usi ng the standardize() metho d. . . . . . . . . . . . . . . 126
5.6 The slice d series obtaine d using t he slice () metho d. . . . . . . . . . . . . . . . . . . . . . . 127
5.7 The slice d series with the time axis c onv erte d. . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.8 The anomaly series obtaine d using t he anomaly() metho d. . . . . . . . . . . . . . . . . . . . 128
5.9 The interp olate d series obtaine d u sing the interp() metho d. . . . . . . . . . . . . . . . . . 129
5.10 The binne d series obtaine d using t he bin () metho d. . . . . . . . . . . . . . . . . . . . . . . 130
5.11 The binne d series obtaine d using t he gkernel() metho d. . . . . . . . . . . . . . . . . . . . . 131
5.12 The filter e d series obtaine d using t he filter () metho d. . . . . . . . . . . . . . . . . . . . . 132
5.13 The detr ende d series obtaine d using t he detrend() metho d. . . . . . . . . . . . . . . . . . . 133
5.14 A visualization of the PMIP3 s imulations using the plot() metho d. . . . . . . . . . . . . . 134
5.15 A visualization of the PMIP3 s imulations using the stackplot() metho d. . . . . . . . . . . 135
5.16 A visualization of the ensemble s eries using the plot_envelope() metho d. . . . . . . . . . . 136
5.17 A visualization of the multiple o bser vational series using the stackplot() metho d. . . . . . 138
5.18 A visualization of the multiple s imulation series using the stackplot() metho d. . . . . . . 138
5.19 A visualization of the ensemble o f corr elation co efficients using the plot() metho d. . . . . 140
5.20 The sp e ctral analysis of the obs er vational datasets. . . . . . . . . . . . . . . . . . . . . . . . 141
5.21 The sp e ctral analysis of the degl aciation simulations. . . . . . . . . . . . . . . . . . . . . . 142
5.22 The sp e ctral analysis of the PMI P3 simulations. . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.23 A visualization of the indices u sing the stackplot() metho d. . . . . . . . . . . . . . . . . . 144
5.24 The wav elet analysis of the tw o indices: ( left) the Deseasonalize d All Indian Rainfall Inde x
and (right) the NINO3 inde x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.25 The analysis of the wav elet cohe r ency b etw e en the tw o indices. . . . . . . . . . . . . . . . 145
xvi
Abstract
The fate of humanity and countless other sp e cies dep ends sensitiv ely on the b ehavior of the climate system.
Our b est guess as to this futur e b ehavior comes fr om climate mo del simulations, which span a br oad range
of scenarios. Ho w w ell can w e trust these mo dels?
Le v eraging the l ast millennium r eanalysis (LMR) pale o climate data assimilation (PD A ) frame w ork,
which enables the p o w er of fusing pale o climate obser vations and mo del simulations, this thesis tackles
the question in thr e e parts: The first part inv estigates the continuum of climate variability since the Last
Glacial Maximum ( ab out 21,000 y ears ago), and asks whether mo dels can r epr o duce it. The se cond part
hones in on the Common Era (past 2000 y ears), and e xplor es the causes of disagr e ements b etw e en mo dels
and r e constructions of the global temp eratur e r esp onse to the major for cing – major v olcanic eruptions.
The thir d part considers the El Niño-Southern Oscillation (ENSO ) o v er the same inter val, and e xplor es
endogenous and e xogenous causes for its variations. The r esult of this study will advance not only science
but also the w ell-b eing of so ciety .
The first part has b e en under inv estigation for almost 20 y ears, and most pr e vious studies hav e claime d
that climate mo dels under estimate climate variability compar e d to pr o xy r e cor ds. Such comparison is,
ho w e v er , o v ershado w e d by the spatially and temp orally limite d numb er of available obser vations at their
time . Our study , on the other hand, has utilize d the most compr ehensiv e pr o xy database , and has pr o vide d
e vidence that the curr ent hierar chy of climate mo dels is capable of r epr o ducing the global-mean temp er-
atur e variability that w e se e in obser vations. The r obustness of our r esult has imp ortant implications for
climate pr e dictability o v er the coming centur y .
The se cond part also tackles a long standing question: why do pale o climate r e constructions and cli-
mate mo del simulations disagr e e so much ab out the climate r esp onse to v olcanic eruptions? This question
is imp ortant b e cause v olcanism is the main e xternal for cing to climate system o v er the Common Era. Our
w ork le v erage d pale o climate data assimilation, which is a r e cent endeav or that optimally combines b oth
pale o-obser vations and mo del simulations and helps to constrain the uncertainties fr om b oth sides, and an-
alyze d the leading causes of the discr epancy fr om the tw o sides, and up date d the comparison by accounting
for such causes. The r esult is a much closer agr e ement b etw e en mo del simulations and obser vation-base d
r e c onstructions.
The thir d part studies a topic that is of particular imp ortance to b oth climate science and the so ciety ,
namely , El Niño-Southern Oscillation (ENSO ). It is the leading pattern of y ear-to-y ear climate variability ,
influencing rainfall and temp eratur e not only ar ound the tr opical Pacific, wher e it dw ells, but also the
North Atlantic se ctor and the Eurasian continent via tele conne ctions. Ther efor e , b eing able to pr e dict the
ENSO cy cle , including its phase and amplitude , is a ke y to successful pr e diction of hy dr o climate conditions
xvii
of many r egions with large conse quences for the management of cr ops, wildfir es, air quality , tourism, and
op erations for many industries. For instance , the 1997-98 El Niño e v ent has cause d $2.2 billion damage
in California. Base d on this, the understanding of the r elationship b etw e en ENSO variability and e xternal
for cing (natural and anthr op ogenic) can help us b etter understand climate variability , impr o v e the pr e dic-
tion, and thus lo w er the p otential damage . W e inv estigate d the r elationship b etw e en ENSO and v olcanic
eruptions le v eraging pale o climate data assimilation. A no v el, skillful r e construction of NINO3.4 sea sur-
face temp eratur e o v er the last millennium integra ting the latest pale o climate e vidence is pr o duce d, and
car eful and original analyses of the v olcano-ENSO link ar e p erforme d.
These thr e e lines of inquir y shall pr o vide ke y insights to the climate community and help b etter con-
strain near-term climate pr oje ctions. In addition, these themes sp eak to the notion of climate risk, which
the r einsurance industr y no w estimates as an e xistential thr eat to the w orld e conomy .
xviii
Chapter 1
Intr o duction
1.1 Climate Mo dels and Their Evaluation
Climate change has b e come a thr eat to the fate of humanity and countless other sp e cies. Global warming
leads to ice she et melting and mean sea le v el rise , br eaking the intrinsic balance of the climate system.
Extr eme w eather and climate e v ents o ccur mor e fr e quently in an unstable climate system, causing sig-
nificant damage and casualty to so ciety (Emanuel, 2012 ). It is thus of gr eat imp ortance and urgency for
p olicy-makers to b e pr o vide d with actionable scientific r esults.
Climate pr oje ctions ar e foundational to formulations of climate p olicies, and the de v elopment of cli-
mate mo dels is a cornerstone of obje ctiv e climate pr oje ctions. Mo dern climate mo dels encompass the
simplifie d, mathematical r epr esentation of the r eal-w orld climate system and their numerical and com-
puterize d implementations. The traje ctor y of the r epr esente d system generate d by such mo dels ar e calle d
climate simulations. The histor y of such simulations go es back to the 1920s when Le wis Fr y Richar d-
son conducte d the first unsuccessful attempt of a 6-hour pr e diction of the atmospheric state , le v eraging
human computers and mor e than 6 w e eks (Richar dson and Lynch, 2007 ). It was not until 1950 that Char-
ne y , Fjörtoft, and Neumann ( 1950 ) conducte d the first successful r egional numerical integration of the
bar otr opic v orticity e quation on the first ele ctr onic computer ENIA C (Ele ctr onic Numerical Integrator and
Computer ), thus op ening a ne w chapter for w eather pr e diction. Since then, numerical w eather pr e dic-
tion (N WP) has de v elop e d significantly and has b e come indisp ensable to p e ople ’s daily life and e conomic
activity .
In the meantime , General Cir culation Mo dels ( GCMs) hav e e v olv e d fr om r egional N WP mo dels, to
Global Climate Mo dels (the se cond meaning of the ”GCM” acr onym) with comp onents that emulate not
only the atmospheric pr o cesses but also the o ceanic pr o cesses and other climate-r elate d pr o cesses such as
land-surface pr o cesses and ice-she ets. (W arner , 2011 ).
Mathematically , a mo dern GCM consists of a “ dynamical cor e ” that simulates the ge ophysical fluid dy-
namics using primitiv e e quations, and a colle ction of “physics mo dules” that simulate imp ortant climate-
r elate d physical pr o cesses such as radiativ e transfer , cloud micr ophysics, cumulus conv e ction, using pa-
rameterization schemes (Edwar ds, 2011 ). Numerically , a mo dern GCM also consists of a “grid scheme ” that
implements the spatial discr etizations of the climatic variables under consideration, which determines the
length scales of solvable pr o cesses, and w e call the physical pr o cesses with length scales comparable or
1
smaller than such r esolvable scale “sub-grid” pr o cesses (Rougier and Goldstein, 2014 ). Both sub-grid pr o-
cesses and scientifically not w ell-understo o d pr o cesses cannot b e r esolv e d e xplicitly with such numerical
mo dels, and physically-base d empirical parameterization schemes ar e thus use d for a simplifie d r epr esen-
tation of these pr o cesses. Such parameterization schemes w ould ideally captur e at least the lo w er or der
featur es of the pr o cesses, but ar e subje ct to large uncertainties. In addition, GCMs hav e to b e pr o vide d
with b oundar y conditions (i.e ., for cings) that may b e subje ct to large uncertainty as w ell, contributing to
further uncertainties in the simulations.
Giv en that, the Intergo v ernmental Panel on Climate Change (IPCC) was establishe d in 1988 for p erio dic
assessments of climate change , and the Couple d Mo del Inter comparison Pr oje ct ( CMIP) was launche d in
1989 to compar e and e valuate the output fr om atmospher e-o cean couple d GCMs ( A OGCMs) de v elop e d by
differ ent countries and institutions. Since then, climatologists hav e also r ealize d that to r eliably pr oje ct
the climate for the futur e centuries, it is critical for the same mo dels to simulate climate variability o v er
the past inter vals of Earth’s histor y .
Mor e o v er , the parameterization schemes, one big sour ce of the uncertainty in GCMs, as w ell as other
b e havior of the climate mo dels, ar e c alibrate d and tune d to the pr esent-day climate conditions. Hence the
only p ossible out-of-sample validation of these asp e cts must use such pale o climate constraints.
The idea of pale o climate mo deling thus emerge d. In 2007, the Pale o climate Mo delling Inter comparison
Pr oje ct (PMIP) was launche d, with a fo cus on the comparison b etw e en pale o climate simulations by the
CMIP mo dels, as w ell as mo del e valuation ( or mo del-data comparison), namely the comparison b etw e en
simulations and pr o xy obser vations (non-instrumental obser vational r e cor ds), aiming to b etter understand
the me chanisms of climate change (Braconnot et al., 2012 ). Inde e d, climate mo del e valuation has b e come
one of the central topics of climate science , and it is also a main topic of this thesis.
The target use d to validate climate mo del simulations can b e either instrumental or pale o climate ob-
ser vations. Instrumental obser vations, on the one hand, include dir e ct measur ements of variables such
as temp eratur e , pr essur e , moistur e , and wind sp e e d and dir e ction fr om mete or ological stations, ballo ons,
air craft, buo ys, and ships, as w ell as indir e ct r etrie val data fr om radar and satellites (Figur e 1.1 ). The y can
b e in the form of non-gridde d site data or gridde d r eanalysis data base d on these sour ces.
Pale o climate obser vations, on the other hand, ar e indir e ct (pr o xy ) r e cor ds of the climate signal obtaine d
fr om a variety of ar chiv es such as corals, tr e es, se diments, glacier ice cor es, mollusk shells, sp ele othem,
do cuments, etc. (Figur e 1.2 ). The y ar e non-gridde d site data by natur e , but can r e cor d climate signals o v er
a r egional or e v en global scale dep ending on the typ e and timescale .
Another central topic of climate science is pale o climate r e construction, which combines such pr o xy
obser vations to depict the histor y of climate as accurately as p ossible . Climate mo del simulations can
b e influence d by multiple factors such as for cing, dynamics, and sub-grid physical pr o cesses. Ther efor e ,
the simulate d gridp oint-wise values ar e just one plausible but heavily simplifie d r ealization of the climate
system, instead of a r eliable r e construction of the true histor y . Pr o xy obser vations, on the other hand,
in spite of b eing spatially sparse , r efle ct the obje ctiv e and unique r ealization of the climate , and thus ar e
the principal basis for a r e construction. T raditional pale o climate r e construction appr oaches ar e mainly
statistical, including r egr ession mo dels, which r egr ess climate variables ( e .g., temp eratur e , pr essur e , pr e-
cipitation, and so on) onto pr o xy obser vations ( e .g., Mann, Bradle y , and Hughes, 1998 ; Mann, Bradle y ,
2
Figur e 1.1: The W orld Mete or ological Organization (WMO ) Global Obser ving System ( GOS).
Sour ce: h t tp : / / w w w . c h a n t h a b u r i . b u u . a c . t h / ~ w i r o t e / m e t / t r o p i c a l / t e x t b o o k_ 2 n d _ e d i t i o n / n a v m e n u . p
hp_tab_10_page_2.1.0.htm
Figur e 1.2: Major pale o climate data ar chiv es. Sour ce: http://wiki.linked.earth.
3
and Hughes, 1999 ; Evans, K aplan, and Cane , 2002 ; Co ok et al., 2004 ; Co ok et al., 2010 ; Tingle y et al., 2012 ;
Smer don and Pollack, 2016 ), as w ell as Bay esian hierar chical mo dels, which inv ert the pr o xy-climate r ela-
tion utilizing Bay es’ the or em ( e .g., Tingle y and Huyb ers, 2010a ; Tingle y and Huyb ers, 2010b ; Tingle y and
Huyb ers, 2013 ). Both appr oaches r ely on the co variance structur e b etw e en pr o xies and climate variables
that is estimate d fr om obser vational data o v er a calibration p erio d. A thir d typ e of pale o climate r e con-
struction is base d on pale o climate data assimilation (PD A ) ( e .g., Dirr en and Hakim, 2005 ; Go osse et al.,
2006 ; Ridgw ell et al., 2007 ; Steiger and Hakim, 2016 ; Hakim et al., 2016 ; T ar dif et al., 2019 ). PD A follo ws a
similar idea to the statistical appr oaches, but with a critical differ ence that the pr o xy-climate co variance
matrix is estimate d fr om climate mo del simulations instead of obser vational data, as such spatial multi-
variate r elationship is naturally r eady in mo del simulations and is also subje ct to dynamical constraints.
This idea bridges pr o xy obser vations and mo del simulations.
A r e cent application of PD A is the Last Millennium Reanalysis (LMR, Hakim et al., 2016 ; T ar dif et
al., 2019 ), no v el frame w ork that assimilates pr o xy obser vations to generate multivariate climate r e con-
structions with annual r esolution o v er the Common Era. LMR implemen ts a w ell establishe d assimilation
metho d use d with gr eat success in w eather for e casting, namely the ensemble K alman filter (EnKF , K alman,
1960 ; Ev ensen, 1992 ; Thomas, Hacker , and Anderson, 2009 ; Lakshmivarahan and Stensrud, 2009 ; Zhang
et al., 2010 ), and featur es gr eat scalability: available , temp eratur e-sensitiv e pr o xy obser vations o v er the
Common Era can b e r eadily assimilate d in a mathematically optimal way , which allo ws us to scrutinize
the dynamical structur e of the climate o v er the past 2000 y ears at r egional and global scales for the first
time (Singh et al., 2018 ). Figur e 1.3 illustrates this frame w ork.
In this thesis, w e will le v erage pale o climate data analysis to ols to fuse the latest pale o climate obser va-
tions and mo del simulations for r e constructing climate o v er the Common Era, and r e visit se v eral imp ortant
r esear ch topics r egar ding mo del e valuation and ho w the climate system r esp onds to e xternal for cing.
1.2 Scientific questions
1.2.1 The continuum of temp eratur e variability
The climate system is comple x, nonlinear , and e xhibits multi-scale variability . T o faithfully pr e dict the
climate , mo del simulations must successfully r epr o duce ke y featur es of the climate system. The temp oral
sp e ctrum of obser v e d global surface temp eratur e is one such imp ortant b enchmark.
An early qualitativ e o v er vie w of this sp e ctrum is giv en by Mitchell ( 1976 ) base d on causal me chanisms,
and it sho ws a nearly flat ” continuum” linking p eaks (Figur e 1.4 ). Peaks r epr esent pr o cesses that ar e
deterministic, p erio dic, and thus pr e dictable , such as the annual cy cle and the Milanko vitch cy cles, while
the continuum r epr esents pr o cesses that ar e sto chastic, ap erio dic, and thus unpr e dictable , such as energy
cascades in turbulence . Ab out 30 y ears later , a landmark study Huyb ers and Curr y ( 2006 ) depicte d the
sp e ctrum utilizing the available obser vational data sour ces at that time , and pr op ose d the the or y that the
annual cy cle and Milanko vitch cy cles ar e linke d by the continuum, which app ears to hav e tw o distinct
r egimes with ste ep slop es. This ne w finding implies that the continuum is actually pr e dictable to some
e xtent.
4
Figur e 1.3: The last millennium r eanalysis (LMR) pale o climate data assimilation (PD A ) frame-
w ork.
peaks
continuum
Figur e 1.4: The qualitativ e o v er vie w of the sp e ctrum of climate variability fr om Fig. 1 of Mitchell
( 1976 ), with annotations of p eaks and continuum.
5
Ho w w ell can climate mo dels r epr o duce this continuum? Laepple and Huyb ers ( 2014b ) r ep orte d a
large mismatch b etw e en r egional temp eratur e sp e ctra simulate d by mo dels and those inferr e d fr om pr o xy
obser vations, concluding that climate mo dels se v er ely under estimate lo w-fr e quency climate variability .
This conclusion implies fundamental flaws in climate mo dels.
Since then, considerably mor e pale o climate obser vational datasets and simulations hav e b e en pub-
lishe d. Notably , the LMR r e construction no w pr o vides a ne w outlo ok on de cadal to centennial temp era-
tur e variability , allo wing to r e visit the question: can curr ent climate mo dels corr e ctly r epr o duce the
obser v e d continuum of temp eratur e sp e ctrum accor ding to the latest obser vational e vidence? .
This will b e the obje ct of Chapter 2 .
1.2.2 The temp eratur e r esp onse to v olcanic for cing
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
NH temp. anom. (K)
GCMs
Reconstructions
Figur e 1.5: Sup erp ose d ep o ch analysis (SEA ) on simulate d and r e constructe d Northern Hemish-
pher e (NH) temp eratur e r esp onse to the 12 str ongest v olcanic eruptions since 1400 CE, r epr o-
duce d fr om IPCC AR5 Figur e 5.8b (Masson-Delmotte et al., 2013 ). For the details of the SEA metho d,
se e Chapter 3 .
In addition to the temp eratur e sp e ctrum, climate variability o v er the Common Era has gr eat implica-
tions for the climate of coming de cades, and v olcanic for cing is one of the major for cings o v er this p erio d.
Ther efor e , the climate r esp onse to v olcanic eruptions, including the hemispheric or r egional temp eratur e
r esp onse , as w ell as that of the El Niño Southern Oscillation (ENSO ) phenomenon, is another critical b ench-
mark of mo del p erformance . Inv estigating this r esear ch topic will also giv e insights in assessing the risk
of ge o engine ering solar radiation management schemes, which emulate v olcanic eruptions.
6
Discr epancies b etw e en simulate d and r e constructe d temp eratur e r esp onses to v olcanism ar e a long-
standing pr oblem. The latest assessment r ep ort of the IPCC (Masson-Delmotte et al., 2013 ) (Figur e 1.5 )
summarize d the state of kno wle dge at the time ( e .g., Br ohan et al., 2012 ; D’ Arrigo , Wilson, and Anchukaitis,
2013 ; Schur er et al., 2013 ) and compar e d a colle ction of GCM simulations and pr o xy-base d r e constructions
of the temp eratur e r esp onses to v olcanism, and demonstrate d discr epancies in se v eral asp e cts, including
the amplitude of p eak co oling, the p eak co oling y ear , and the length of the temp eratur e r e co v er y (r eturn
to baseline). This r esult implies uncertainties in either the mo del simulations or the pr o xy-base d r e con-
structions, or b oth.
Mo deling studies (Timmr e ck et al., 2009 ; Timmr e ck, 2012 ; Stoffel et al., 2015b ; LeGrande , T sigaridis,
and Bauer , 2016 ) suggest that the aer osol micr ophysics in CMIP5-era mo dels ar e o v ersimplifie d and can
lead to o v er estimate d temp eratur e r esp onses in simulations, questioning the fidelity of climate mo dels.
In parallel, obser vational studies (Fri tts, 1966 ; St. Ge orge , 2014 ; St Ge orge and A ult, 2014 ; Esp er et al.,
2015 ; Frank et al., 2007 ; Krakauer and Randerson, 2003 ; Zhang et al., 2015 ) demonstrate se v eral issues in
tr e e-ring r e cor ds that could cause distorte d temp eratur e r esp onses in tr e e-ring base d r e constructions. The
LMR PD A frame w ork allo ws us to test some of these the ories with b oth pseudopr o xy e xp eriments
∗
and
r eal-w orld data, and r e visit the scientific question: ho w can the appar ent discr epancy b etw e en the
simulate d and r e constructe d temp eratur e r esp onses to e xplosiv e v olcanism b e r e concile d? This
question will b e tackle d in Chapter 3 .
1.2.3 The ENSO r esp onse to v olcanic for cing
The El Niño Southern Oscillation (ENSO ) r epr esents t he quasi-p erio dic alternation of warm and cold phases
of the tr opical Pacific o cean-atmospher e system. It has a gr eat impact on global w eather conditions and
interannual climate variability (Sarachik and Cane , 2010 ). Ther efor e , b eing able to pr e dict the ENSO cy cle ,
including its phase and amplitude , is a ke y to successful pr e diction of w orldwide hy dr o climate conditions.
Finding r obust pr e dictors of ENSO is thus an imp ortant topic in climate science .
In the 1980s, a trigger me chanism of ENSO by the tr op ospheric aer osols fr om a v olcanic eruption
was pr op ose d (Handler , 1984 ; Schatten et al., 1984 ; Hir ono , 1988 ), implying that v olcanic eruptions could
b e a pr e dictor of ENSO e v ents. This me chanism was later challenge d by successful pr e dictions of ENSO
that did not inv oke v olcanic for cing ( Cane , Zebiak, and Dolan, 1986 ), as w ell as the studies of Nicholls
( 1990 ), Rob o ck and Mao ( 1995 ), Rob o ck and Fr e e ( 1995 ), and Self et al. ( 1997 ), who claime d that no r obust
corr elation could b e found. Since then, the link b etw e en ENSO activity and v olcanic for cing has b e en hotly
debate d. This topic is difficult b e cause large v olcanic eruptions o v er the Common Era ar e – by definition
– rar e e v ents, usuall y not w ell do cumente d, and b e cause characterizations of ENSO activity must r ely on
pr o xy obser vations with limite d availability prior to the instrumental era.
∗
Pseudopr o xies ar e emulations of r eal-w orld pr o xies base d on synthetic data. The idea is to use a mo del simulation as “truth” ,
and generate ” obser vations” of this state base d on pr o cesses that affe ct r eal-w orld climate pr o xies such as bioturbation in se di-
mentar y r e cor ds, seasonal bias in tr e e-ring r e cor ds, and compaction and diffusion in ice cor e r e cor ds. W e call such obser vations
“pseudopr o xies” . Within such a setup , w e hav e b oth the obser vational data and the kno wn truth, with which w e ar e able to test
many scientific ideas, particularly the ability of infer ence metho ds to unco v er the ”truth” base d on these imp er fe ct obser vations.
7
So far , me chanistic studies ( Clement et al., 1996 ; Mann et al., 2005 ; Emile-Geay et al., 2008 ; Ohba et
al., 2013 ; Pr e dybaylo et al., 2017 ; Kho dri et al., 2017 ; McGr egor and Timmermann, 2011 ; Ste v enson et
al., 2017a ; Pausata et al., 2015 ; Ste v enson et al., 2016 ; Ste v enson et al., 2017a ; Pausata et al., 2020 ) hav e
pr op ose d at least fiv e plausible me chanisms that could e xplain ho w v olcanic f or cing may triggers or fav or
El Niño e v ents in the y ear after eruptions. Early tr e e-ring base d obser vational studies ( A dams, Mann, and
Ammann, 2003 ; McGr egor , Timmermann, and Timm, 2010 ; Li et al., 2013 ; W ahl et al., 2014 ; McGr egor
et al., 2020 ) app ear e d to corr ob orate the notion that v olcanic for cing fav ors the triggering of El Niñ o
e v ents. Ho w e v er , coral base d obser vational studies ( Cobb et al., 2003 ; Tierne y et al., 2015 ; De e et al., 2020 )
demonstrate e vidence of a much w eaker – if not ine xistent – linkage .
Ho w should w e r e concile such disparate accounts? With LMR, w e ar e able to compar e the information
obtaine d fr om tr e es and corals separately but in a unifie d frame w ork, and optimally combine those tw o
data sour ces, yielding a no v el and skillful Niño 3.4 r e construction o v er the last millennium that can help
us inv estigate our last big question: is the v olcano-ENSO link statistically r obust base d on the latest
obser vational e vidence? This question will b e tackle d in Chapter 4 .
1.3 Outline of the thesis
The thesis is structur e d as follo ws:
• Chapter 2 - The P leisto cene ’s climate continuum in mo dels and obser vations
• Chapter 3 - Evaluating the temp eratur e r esp onse to v olcanic for cing
• Chapter 4 - A r e-appraisal of the ENSO r esp onse to v olcanic for cing
• Chapter 5 - Enhancing pale o climate data analysis and r epr o ducible r esear ch
• Chapter 6 - Conclusion
In Chapter 2 , w e first up date the study of Huyb ers and Curr y ( 2006 ) with the latest obser vational e vi-
dence , including instrumental obser vations, pr o xy r e cor ds, and the LMR data pr o duct. These obser vational
datasets together depict the temp eratur e sp e ctrum acr oss scales fr om annual to orbital. With this up date d
sp e ctrum, w e e valuate the latest climate mo del simulations with differ ent le v els of comple xities. O v erall,
the most fundamental b enchmark of climate mo dels is p erforme d in this chapter , and climate variability
since the Last Glacial Maximum is scrutinize d.
Chapter 3 fo cuses on climate variability o v er the last millennium, during which v olcanic for cing is the
main for cing. In this chapter , w e first utilize the LMR frame w ork to r epr o duce the discr epancy se en in
Figur e 1.5 . Inspir e d by e xisting studies on the characteristics of tr e e-ring r e cor ds, w e then inv estigate the
impact of such characteristics on the temp eratur e r e construction. A ccor ding to the r esults, w e confirm
the major causes of the discr epancy and inv estigate strategies to account for those factors, after which w e
apply the strategies to the r eal-w orld cases to r esolv e the discr epancy .
In Chapter 4 , w e fo cus on the ENSO r esp onse to v olcanic for cing. A gain, LMR is utilize d as a uni fie d
frame w ork to e valuate the information obtaine d fr om tr e es and corals. That is, w e assimilate tr e e-ring
8
r e c or ds and coral r e cor ds separately , and compar e the r esulting r e constructions to e xplain why discr ep-
ancies r emain in e xisting obser vational studies that ar e base d on tw o differ ent data sour ces. After that, w e
optimally combine those tw o data sour ces within the LMR frame w ork, and pr o duce a no v el and skillful
Niño 3.4 sea surface temp eratur e (SST) r e construction that allo ws us to p erform a car eful analysis on the
v olcano-ENSO link. This chapter illustrates again the p o w er of fusing pale o climate mo del simulations and
pr o xy obser vations with the PD A frame w ork.
Be y ond the scientific questions mentione d ab o v e , this thesis also do cuments an imp ortant effort at
enhancing pale o climate data analysis and r epr o ducible science . Chapter 5 pr esents a no v el Python package
calle d Pyleoclim , on which the analysis in Chapter 2 critically r elies. A s one of the lead designers and
de v elop ers, I discuss the motivations of this package and the philosophy b ehind its co de design, as w ell
as pr esent se v eral typical usage e xamples to sho w ho w this package can help daily scientific r esear ch by
enhancing efficiency and r epr o ducibility .
Chapter 6 pr esents our summar y and conclusions.
9
Chapter 2
The P leisto cene ’s climate continuum in mo dels and
obser vations
Abstract
Climate r e cor ds e xhibit scaling b ehavior with large e xp onents, r esulting in larger fluctuations at longer
timescales. It is unclear whether climate mo dels ar e capable of simulating these fluctuations, which draws
into question their ability to simulate such variability in the coming de cades and centuries. Using the latest
simulations and data syntheses, w e find agr e ement for sp e ctra deriv e d fr om obser vations and mo dels on
timescales ranging fr om interannual to multi-millennial. Our r esults confirm the e xistence of a scaling
br eak b etw e en orbital and annual p eaks, o ccurring ar ound millennial p erio dicities. That b oth simple and
compr ehensiv e o cean-atmospher e mo dels can r epr o duce these featur es suggests that long-range p ersis-
tence is a conse quence of the o ceanic integration of b oth gradual and abrupt climate for cings. The r esult
implies that Holo cene lo w-fr e quency variability is partly a conse quence of the climate system’s integrate d
memor y of orbital for cing. W e conclude that climate mo dels app ear to contain the essen tial physics to
corr e ctly simulate the sp e ctral continuum of global-mean temp eratur e; ho w e v er , r egional discr epancies
r emain unr esolv e d. A critical element of successfully simulating sub-orbital climate variability inv olv es,
w e hyp othesize , initial conditions of the de ep o cean state that ar e consistent with obser vations of the
r e c ent past.
2.1 Intr o duction
A grand challenge for climate science is to accurately simulate lo w-fr e quency variability ( changes o ccur-
ring on scales longer than a fe w y ears). Of particular inter est is the temp oral sp e ctrum of surface tem-
p eratur e , whose p eaks indicate dominant oscillations, and whose continuum describ es energy transfers
b e tw e en scales (Lo v ejo y and Schertzer , 2013 ). This continuum is often characterize d by its scaling e xp o-
nentβ , wher e the p o w er sp e ctral density (PSD ) S and the fr e quencyf satisfy the p o w er law r elationship:
S(f)∝f
−β
(2.1)
Publication Details: Zhu, F ., Emile-Geay , J. , McK ay , N. P ., Hakim, G. J., Khider , D ., A ult, T . R., Steig, E. J., De e , S., & Kir chner ,
J. (2019). Climate mo dels can corr e ctly simulate the continuum of global-av erage temp eratur e variability . Pr o ce e dings of the
National A cademy of Sciences, 201809959. https://doi.org/10.1073/pnas.1809959116
10
The larger the e xp onent, the longer the memor y of past e v ents. A sp e ctral depiction of climate change
dates back to Kutzbach and Br yson ( 1974 ), who inv estigate d Holo cene climate variability in the North
Atlantic se ctor using various r e cor ds, and conne cte d the obser v e d sp e ctral pattern to the thermal inertia
of the o cean and cr y ospher e . T w o y ears later , Mitchell gav e an early qualitativ e o v er vie w of the sp e ctrum
of climate variability base d on causal me chanisms Mitchell ( 1976 ). Later , Pelletier estimate d the PSD of
r egional atmospheric temp eratur e fr om synoptic to multi-millennial and longer scales, using instrumental
and ice cor e data, and e xplaine d the obser v e d scaling e xp onents with a v ertical turbulent transp ort mo del
Pelletier ( 1998 ). In a landmark pap er , Huyb ers and Curr y ( 2006 , her eafter HC06) adde d many mor e data
sour ces, e xtende d the analysis to much longer timescales, and pr op ose d that “annual, orbital and con-
tinuum temp eratur e variability jointly r epr esent the r esp onse to deterministic insolation for cing” . The y
identifie d tw o distinct scaling r egimes, with a br eak at centennial scales, but did not pr o vide an e xplanation
for this br eak
Re cent s tudies hav e lo oke d for similar b ehavior in temp eratur e fields simulate d by climate mo dels, and
sho w that the scaling e xp onents that describ e the simulate d temp eratur e variability ar e to o small compar e d
to those fr om instrumental ( Go vindan et al., 2002 ; Laepple and Huyb ers, 2014a ) and pale o climate ob er va-
tions (Laepple and Huyb ers, 2014b ; A ult et al., 2014 ; Parsons et al., 2017 ). Ther e ar e at least four r easons to
r eser v e caution in this comparison. First, climate pr o xies ar e kno wn to filter climate inputs (Evans et al.,
2013 ; De e et al., 2015 ), so simulate d temp eratur es and pr o xy measur ements ar e not dir e ctly comparable
(Laepple and Huyb ers, 2013 ; De e et al., 2017 ). Se cond, the comparisons done to date hav e include d a l im-
ite d numb er of pr o xies with sub-centennial r esolution ( <20); it is ther efor e critical to up date this pictur e
with mor e complete data syntheses, including annually-r esolv e d obser vations. Thir d, the mo del e valua-
tions mentione d ab o v e hav e fo cuse d on simulations of the past millennium (850-1850 CE); no systematic
comparison has b e en carrie d out with longer transient simulations. Lastly , a lack of global co v erage b e-
y ond the past millennium had r estricte d pr e vious studies to fo cus on r egional temp eratur e variability , y et
global temp eratur e is mor e informativ e of changes in Earth’s energy budget. Thus, w e fo cus her e on the
global signal.
Her e w e addr ess these challenges and find a variety of climate mo dels to b e consistent with scaling
b e havior obser v e d acr oss a range of pale o climate ar chiv es. The r obustness of this r esult has imp ortant
implications for climate pr e dictability . W e also pr o vide a ne w e xplanation for the transition b etw e en
scaling r egimes.
2.2 Completing the Continuum
W e first estimate the sp e ctrum of global-av erage temp eratur e variability , le v eraging ne w measur ements
and data syntheses ( Jouzel et al., 2007 ; Morice et al., 2012 ; Sny der , 2016 ; P A GES 2k Consortium, 2017 ; Ahn
et al., 2017 ) (T able 2.1 ) as w ell as impr o v e d sp e ctral metho ds (Kir chner and Neal, 2013 ) ( Metho ds ). Notably ,
the latest P A GES2k compilation (P A GES 2k Consortium, 2017 ), which gathers obser vations fr om coral,
glacial ice cor e , marine and lake se dimentar y , sp ele othem, tr e e-ring, and do cumentar y ar chiv es, allo ws
us to fill the afor ementione d sp e ctral gap in the centennial to millennial band. Individual sp e ctra e xhibit
scaling b ehavior ( lack of obvious scaling br eaks, Figur e S2.7 ) for all ar chiv e typ es e xcept for glacier ice ,
11
0.5 1 2 5 10 20 100 1 k 10 k 100 k 1 m
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
HadCRUT4 ( = 0.80±0.15)
S16 GAST ( = 2.63±0.05)
ProbStack ( = 2.36±0.11)
EDC ( = 2.36±0.12)
PAGES2k/LMR GAST
( = 0.94±0.04)
Figur e 2.1: A sp e ctral estimate of the global-av erage surface temp eratur e variability using instru-
mental and pale o climate datasets ( scale d degr e es K elvin), as w ell as pr o xy-base d r e constructions
of surface temp eratur e variability . (HadCRU T4) The Met Office Hadle y Centr e gridde d dataset of
global historical surface temp eratur e anomalies (Morice et al., 2012 ). (P A GERS2k/LMR GAST) The Last
Millennium Reanalysis frame w ork (Hakim et al., 2016 ; T ar dif et al., 2019 ) applie d to the P A GES2k dataset
(P A GES 2k Consortium, 2017 ). The t hick r e d cur v e denotes the me dian p o w er sp e ctral density (PSD ), the
dark r e d shade d ar ea denotes the inter quartile range , and the light r e d ar ea denotes the central 95% range ,
fr om 2.5% to 97.5%. (S16 GAST) The r e construction of global av erage surface temp eratur e (Sny der , 2016 ).
(Pr obStack) A pr obabilistic P lio cene-P leisto cene stack of b enthic δ
18
O ( Ahn et al., 2017 ). β ’s denote the es-
timate d scaling e xp onents o v er each appr opriate fr e quency band. Details of their estimation ar e pr esente d
in the Metho d s se ction and SI T e xt 2.7.3 . The r egional dataset (EDC) EPICA Dome C Ice Cor e 800K Y r Deu-
terium Data and T emp eratur e Estimates ( Jouzel et al., 2007 ) is include d as a p oint of comparison.
wher e high-fr e quency signals ar e kno wn to b e damp e d by a range of pr o cesses , including diffusion and
compaction ( Cuffe y and Steig, 1998 ; De e et al., 2015 ). The me dian scaling e xp onents ar e close to 0.45,
with no clear spatial tr end (Figur e S2.8 ). Our analysis confirms the e xistence of scaling b ehavior in the
de cadal to centennial range , r obustly acr oss ar chiv e typ es. Each ar chiv e is affe cte d by differ ent pr o cesses
and timescales (Evans et al., 2013 ; De e et al., 2015 ), distorting sp e ctra in various ways. Ho w e v er , none
of these pr o cesses can cr eate scaling on their o wn (De e et al., 2017 ), suggesting that the obser v e d scaling
b e havior is a pr op erty of the climate , and not the pr o xy ar chiv es. This pictur e may change when mor e
complete pr o xy system mo dels ar e consider e d.
Ne xt, w e use this dataset to estimate global mean surface temp eratur e with a state-of-the-art pale o cli-
mate state estimation metho dology , the Last Millennium Reanalysis (LMR, Hakim et al., 2016 ; T ar dif et al.,
2019 ). LMR uses an ensemble K alman filter to optimally combine information fr om transient climate mo del
simulations and annually-r esolv e d pale o climate obser vations (P A GES 2k Consortium, 2017 ) (SI T e xt 2.7.2 ).
12
T able 2.1: The o v er vie w information of the instrumental obser vations, r eanalysis, r e constructions base d
on pr o xy r e cor ds, and mo del simulations that b eing use d in this pap er .
Dataset T yp e Time Span Exp onent Estimation Scales ( yrs)
Obs./r e cons.
HadCRU T4 (Morice et al., 2012 ) instrumental 1850-2017 AD 1/6-50
P A GES2k/LMR GAST (Hakim et al., 2016 ) r eanalysis 1-2000 AD 2-1000
M13 (Mar cott et al., 2013 ) r e construction 11.3 kyr BP-1940 AD 50-500
S16 GAST (Sny der , 2016 ) r e construction 2 Myr BP-950 AD 2,000-100,000
Pr obStack ( Ahn et al., 2017 ) pr o xy 5 Myr BP-1950 AD 10,000-100,000
EDC ( Jouzel et al., 2007 ) r e construction 800 Myr BP-1911 AD 1,500-50,000
Mo del simulations
T raCE-21ka (Liu et al., 2009 ) deglaciation 22 kyr BP-1979 AD 400-2000, 20-400
DG
ns
(Menviel et al., 2011 ) deglaciation 18 kyr BP-3 kyr BP 400-2000, 20-400
SIM2bl (Timm and Timmermann, 2007 ) deglaciation 21 kyr BP-1949 AD 400-2000, 20-400
PMIP3 (Braconnot et al., 2012 ) last millennium 850-1850 AD , 850-2011 AD 2-500
Imp ortantly , this appr oach only uses climate mo dels to pr o vide physically plausible co variances within
and among climate fields; all of the temp oral variability , and thus the sp e ctral b ehavior , originate in the
pale o climate obser vations. Figur e 2.1 sho ws scaling b ehavior in the P A GES2k-base d LMR estimate , with
de cadal-to-centennial scaling e xp onents ar ound unity , in go o d agr e ement with global instrumental tem-
p eratur e (HadCRU T4, Morice et al., 2012 ).
Pr ogr essing to war ds lo w er fr e quencies, w e consider the ice-cor e-base d r e construction fr om EPICA
Dome C ( Jouzel et al., 2007 ), which nearly doubles the co v erage of the V ostok data use d by HC06 (800
v ersus 420 kyr ), as w ell as tw o r e cent estimates base d on marine se diments: the Globally A v erage Surface
T emp eratur e r e construction of r ef (Sny der , 2016 ) ( her eafter S16), base d primarily on sea-surface temp era-
tur e pr o xies ( alkenones, Mg/Ca, and faunal assemblages) and the latest b enthic stack base d on foraminiferal
δ
18
O (Pr obStack Ahn et al., 2017 )). All thr e e of these datasets sho w consistently ste ep centennial-to-orbital
scaling e xp onents ar ound 2.5 (Figur e 2.1 ). A s b efor e , the r obustness acr oss differ ent pale o climate ar chiv e ,
sensor , and obser vation typ es is a cogent indication that the y ar e featur es of the climate , not pr o xy-r elate d
artifacts. The EDC sp e ctrum flattens considerably at scales shorter than millennial, which can b e trace d to
its lo cal natur e (Figur e S2.6 ) and p ossi ble aliasing of the annual cy cle (Laepple et al., 2018 ).
O v erall, Figur e 2.1 highlights a scaling br eak b etw e en the de cadal-to-centennial band ( β ≈ 1 ) and
the centennial-to-Milanko vitch band ( β ≈ 2.5 ). This confirms the e xistence of the tw o scaling r egimes
p o inte d out by HC06, who place d this transition at centennial scales. In contrast, our analysis shifts this
scaling br eak to the vicinity of the millennial scale . A s sho wn in SI T e xt 2.7.4 , the lo cation of the br eak
in fr e quency space is quite variable fr om one r e cor d to the ne xt, and only with global syntheses do es it
emerge at millennial scales. One p ossibility is that the fr e quency of the scaling br eak dep ends on w eighting
pr o xies that r e cor d mor e of the global-mean, rather than a lo cal, signal ( e .g., Figur e 7 in Ryp dal, Ryp dal,
and Fr e driksen ( 2015 )). Another p ossibility is that the sp e ctral br eak is p e culiar to the time of analysis; i.e .,
not a pr op erty of the stationar y statistics of the climate system. In any case , do climate mo del simulations
e v en contain a sp e ctral transition?
13
2.3 Simulating the continuum
W e no w consider long transient integrations of general cir culation mo dels, including the PMIP3 last mil-
lennium (past1000) simulations (Braconnot et al., 2012 ) app ende d with “historical” CMIP5 simulations, and
the T raCE-21ka suite of e xp eriments (Liu et al., 2009 ). W e also include simulations fr om tw o Earth System
Mo dels of Interme diate Comple xity (EMICs) co v ering the last deglaciation, DG
ns
(Menviel et al., 2011 ) and
SIM2bl (Timm and Timmerma nn, 2007 ) (SI T e xt 2.7.2 ). O v er the de cadal-to-centennial band, Figur e 2.2
(top) indicates that the PMIP3 simulations shar e similar scaling e xp onents ar ound unity , consistent with
obser v e d sp e ctra (Figur e 2.1 ). Sp e cifically , the inset plot sho ws the distribution of the scaling e xp onents
of the PMIP3 simulations against those obtaine d fr om the P A GES2k-base d LMR, in which w e find go o d
agr e ement for the central quantiles, and large inter-mo del spr ead. This agr e ement stands in contrast to
pr e vious w ork sho wing differ ences b etw e en sp e ctra in climate mo dels and data (Lo v ejo y , Schertzer , and
V ar on, 2013 ; Laepple and Huyb ers, 2014b ; A ult et al., 2014 ; Parsons et al., 2017 ; De e et al., 2017 ).
One imp ortant distinction b etw e en our study and pr e vious ones is that our comparisons fo cus on
global, rather than r egional, variability since the Last Glacial Maximum. Giv en a mo del’s finite r esolution,
accurately mo deling lo cal and r egional variability is mor e difficult than mo deling global variability (SI T e xt
2.7.4 ). Mo del biases diminish fr om lo cal to continental scales, and lo cal variability at small spatial scales,
r efle cting short temp oral scales, is smo othe d. A s sho wn by Fr e driksen and Ryp dal ( 2015 ) and Ryp dal,
Ryp dal, and Fr e driksen ( 2015 ), this smo othing ste ep ens global sp e ctra r elativ e to lo cal sp e ctra.
Figur e 2.2 ( b ottom) sho ws a sp e ctral analysis of the T raCE-21ka, DG
ns
, and SIM2bl transient simula-
tions, which co v er the last 10 to 20 kyr (SI T e xt 2.7.2 ). All thr e e simulations sho w a similar scaling br eak
ar ound timescales of 300-1000 yr . Henceforth, w e defineβ
CM
as the centennial-to-millennial scaling e x-
p onent ( estimate d o v er 400-2000 yr ) andβ
DC
as the de cadal-to-centennial scaling e xp onent ( estimate d
o v er 20-400 yr ). All thr e e simulations display β
CM
≈ 2.5 andβ
DC
≈ 1 consistent with the obser v e d
sp e ctra (Figur e 2.1 ). These r esults ar e r obust to definitions of the scaling ranges (SI T e xt 2.7.9 ). Ho w e v er ,
these simulate d β
DC
’s arise for differ ent r easons than in the PMIP3 past1000 simulations: (1) none of these
deglacial simulations ar e subje ct to v olcanic aer osol for cing, the largest sour ce of lo w-fr e quency variance
for PMIP3 past1000 simulations (Schur er , T ett, and Hegerl, 2013 ); (2) DG
ns
do es not include the industrial
warming p erio d (T able 2.1 ), y et it sho ws similarβ
DC
compar e d with T raCE-21ka and SIM2bl, as w ell as
mo dern and pale o climate obser vations, implying that the industrial warming p erio d is not the only e xpla-
nation forβ
DC
≈ 1 ( se e “Climate Implications”); (3) The T raCE-21ka e xp eriment was designe d in part to
captur e climate variability inferr e d fr om Gr e enland ice cor e r e cor ds and for ce d, e .g., thr ough fr eshwater
fluxes, to captur e that variability . This pr esents the p ossibility of cir cular logic to conclusions base d on
T raCE-21ka sp e ctra, though the simulation do es r emarkably w ell in r epr o ducing the phase and magnitude
of millennial-scale variability in Southern Hemispher e r e cor ds, for which it was not tune d (Pe dr o et al.,
2016 ).
14
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
PMIP3 simulations
bcc_csm1_1 ( = 1.25±0.06)
CCSM4 ( = 1.05±0.07)
FGOALS_gl ( = 0.88±0.15)
FGOALS_s2 ( = 1.22±0.05)
IPSL_CM5A_LR ( = 1.14±0.05)
MPI_ESM_P ( = 1.05±0.09)
CSIRO ( = 1.22±0.10)
HadCM3 ( = 0.93±0.07)
CESM (n=10) ( = 1.10±0.08)
GISS (n=3) ( = 1.25±0.09)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
Deglaciation simulations
TraCE-21ka (
CM
= 2.28±0.32;
DC
= 0.78±0.02)
DG
ns
(
CM
= 3.16±0.38;
DC
= 1.08±0.05)
SIM2bl (
CM
= 2.61±0.38;
DC
= 0.73±0.03)
0.5
1.0
1.5
LMR PMIP3
2.0
2.5
3.0
3.5
observations models
Figur e 2.2: The p o w er sp e ctral density (PSD ) of transient mo del simulations. In the upp er panel,
β is estimate d o v er 2-500 yr . The inset plot compar es distributions of the scaling e xp onents ( estimate d
o v er 2-500 yr ) of GAST in P A GES2k-base d LMR vs the PMIP3 simulations. In the lo w er panel, β
CM
is the
centennial-to-millennial scale e xp onent estimate d o v er 400-2000 yr , while β
DC
is the de cadal-to-centennial
scale e xp onent estimate d o v er 20-400 yr . The inset plot compates theβ values of the mo del simulations
(r e d , gr e en, and blue dots) and that of the obser vations ( gray dots). The gray cur v es ar e identical as those
in Figur e 2.1 . Note that cur v es lab ele d ’CESM’ and ’GISS’ ar e the ensemble av erage of the PSDs of 10 and
3 memb ers for each mo del, r esp e ctiv ely .
2.4 A tale of tw o r egimes
What physical me chanisms underlie the scaling br eak? Nilsen, Ryp dal, and Fr e driksen ( 2016 ) suggest that
Holo cene temp eratur e r e constructions ar e consistent with a single scaling r egime , and that the scaling
15
br eak likely originates fr om the large-amplitude Dansgaar d-Oeschger (D-O ) e v ents of the past glacial p e-
rio d. A s long as the analyze d r e cor ds contain such abrupt e v ents, the y argue that one should e xp e ct a
scaling br eak in the fr e quency domain. This is supp orte d by our analysis of 253 Holo cene r e cor ds (Figur e
S2.12 ), sho wing a single scaling r egime thr oughout the inter val.
T o further test this idea, w e inv estigate the sp e ctral density of the output of the T raCE-21ka full sim-
ulation b efor e and after 8 kyr BP (Figur e S2.13 , SI T e xt 2.7.7 ). This choice av oids the 8.2 kyr e v ent, thus
delineating a p erio d of rapid transition b efor e this p oint (the deglaciation) and a stable climate after war ds.
The r esult indicates that the timeseries b efor e 8 kyr BP sho ws a PSD similar to that of the full se ries, while
the timeseries after 8 kyr BP lacks a scaling br eak. This suggests that the scaling br eak originates in the
early part of the timeseries. A scalogram of the T raCE-21ka full simulation (Figur e S2.14 ) r e v eals tw o
underlying factors for the scaling br eak: 1) abrupt, large-amplitude e v ents as suggeste d ab o v e; 2) the grad-
ual transition fr om glacial to interglacial states. The first factor is identifie d by the energetic ar ea in the
scalogram ar ound 12.5 ky BP b etw e en p erio ds of 500 and 2000 yr , coincident with the simulate d Bölling-
Allerö d/Y ounger Dr yas couplet. This me chanism is r epr o ducible using simple mo dels (SI T e xt 2.7.7 ). Such
impulses cr eate bumps in the PSD (Figur es S2.15 and S2.17 , right), which cascade do wn to smaller scales,
disapp earing at p erio ds near 300 yr , wher e the scaling br eak o ccurs. The se cond fac tor is visible ar ound
p erio ds of 5ky , b etw e en 7 to 20 ky BP , and r efle cts orbitally driv en changes in the Earth system (SI T e xt
2.7.8 ). The y mirr or the pattern se en in the CO
2
timeseries obtaine d fr om the EPICA Dome C I ce cor e
(Figur e S2.22 ) as w ell as the b est estimates of the ice-v olume e quivalent sea-le v el function (Figur e S2.23 ).
T o further disentangle the influence of the various for cings, w e le v erage the T raCE-21ka single-for cing
e xp eriments (Liu et al., 2009 ). Figur e 2.3 confirms that orbital for cing ( ORB) acts as the se cond factor ,
driving the slo w transition fr om glacial to interglacial states; this is sufficient to generate a scaling br eak at
millennial scales ( orange cur v e). For cing fr om gr e enhouse gases ( GHG) and transient ice she ets (ICE) act to
amplify this transition. On the other hand, transient Northern Hemispher e meltwater fluxes (MWF) act as
the first factor: the y generate a bump in the PSD that shifts the scaling br eak to p erio ds near 300y . Be cause
these signals do not pr opagate instantly ar ound the glob e , the br eak w ould b e e xpr esse d in differ ent r e cor ds
at differ ent scales, ranging fr om centennial to millennial.
16
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
TraCE-21ka
full (
CM
= 2.28±0.32;
DC
= 0.78±0.02)
MWF (
CM
= 2.40±0.31;
DC
= 0.65±0.04)
ORB (
CM
= 1.49±0.25;
DC
= 0.34±0.02)
ICE (
CM
= 2.29±0.33;
DC
= 0.09±0.03)
GHG (
CM
= 2.29±0.27;
DC
= 0.58±0.02)
Figur e 2.3: Effe ct of for cings on scaling b ehavior in the T raCE-21ka simulations The full simula-
tion is for ce d by transient Northern Hemispher e meltwater fluxes (MWF), orbital for cing ( ORB), changing
continental ice she ets (ICE), and transient gr e enhouse gas for cing ( GHG). Conv entions identical to Figur e
2.2 .
2.5 Climate Implications
By incorp orating a wide range of pr o xy data, mo dels, and data assimilation appr oaches to climate vari-
ability , w e find tw o scaling r egimes linking orbital to annual scales, as HC06 found fr om r egional r e cor ds.
These r egimes ar e r obust acr oss multiple obser vation typ es. Incr easing the density of r e cor ds in the cen-
tennial band by 2 or ders of magnitude , w e find that the r egime transition for global-av erage temp eratur e
variability o ccurs at millennial scales.
At scales shorter than millennial, w e find go o d agr e ement b etw e en mo dele d and obser vationally de-
riv e d scaling e xp onents. Y et the sp e ctra ar e qualitativ ely differ ent: the same CMIP5 mo dels hav e b e en
sho wn to o v ersimulate interannual variance and undersimulate de cadal variance ( A ult et al., 2013 ; Laep-
ple and Huyb ers, 2014a ; Parsons et al., 2017 ). This r esults in ste ep er scaling at high fr e quencies, and flatter
scaling at de cadal and longer timescales, in the past1000 simulations.
At scales up to10
4
yr , w e find that mo dels of var ying comple xity closely r epr o duce the obser v e d scaling
laws o v er the past deglaciation, including the scaling br eak ar ound 10
3
yr . In the T raCE-21k simulations,
this transition is primarily driv en by orbital for cing, and mo dulate d by fr eshwater fluxes. This raises the
question of what le v el of comple xity is r e quir e d for mo dels to co rr e ctly r epr o duce the obser v e d continuum.
All mo dels consider e d her e lack interactiv e ice she ets, and most lack an interactiv e carb on cy cle . Such
mo dels ther efor e r e quir e information ab out these systems to b e supplie d via b oundar y conditions in or der
17
to r epr o duce obser v e d climate traje ctories ( and ther efor e , sp e ctra). In r eality , of course , insolation is the
only true for cing on these timescales; ice she et top ography , gr e enhouse gas le v els, and fr eshwater fluxes
all ar e Earth system r esp onses to this for cing. The r esp onse of the climate system to insolation for cing is
state-dep endent, which intr o duces a sto chastic (unpr e dictable) comp onent to the r esp onse . A surprising
finding is that e v en simplifie d mo dels like ECBilt-CLIO (use d in SIM2bl) can pr o duce a r ealistic global-
av erage temp eratur e continuum at sub-millennial scales when supplie d with information ab out gradual
climate for cings o v er the past deglaciation (Figur e 2.2 b ottom).
In contrast, most of the de cadal to centennial variability in PMIP3 past1000 simulations originates fr om
v olcanic for cing (Schur er , T ett, and Hegerl, 2013 ). This dominance is partly the r esult of such simulations
b e ing o v erly sensitiv e to stratospheric aer osol loading (Stoffel et al., 2015b ), due to incomplete r epr esen-
tations of stratospheric aer osol chemistr y (LeGrande , T sigaridis, and Bauer , 2016 ). Ho w e v er , our analysis
suggests that de cadal to centennial climate continuum could b e inherite d fr om b oundar y conditions that
far pr e-date the last millennium. This is supp orte d by the linear analysis of Fr e driksen and Ryp dal ( 2017 ),
which e xpr esse d temp eratur e at timet as a conv olution b etw e en the transient for cing and the impulse
r esp onse function to that for cing at all past instants. Comparing simulate d and obser v e d temp eratur e ,
one e valuates not only the mo del ( which appr o ximates the impulse r esp onse), but also the for cing. It is a
distinct p ossibility that such e valuations impr op erly place the blame on the mo dels, while it should lie in
the for cing.
Put another way , a plausible e xplanation for our r esults is tha t, on a global scale , the past millennium
still contains e cho es of the deglaciation. The systems’ adjustment to smo othly-var ying insolation generates
substantial de cadal to centennial variability at the surface , despite the for cings containing little energy at
these scales (Figur e S2.21 - S2.23 ). Thus, our r esults affirm and e xtend HC06’s conclusion that continuum
temp eratur e variability is an integral part of the r esp onse to insolation for cing; de cadal to centennial
variability in global-av erage temp eratur e is partly a conse quence of changes in Earth’s orbital parameters.
This is also consistent with the the or etical r esults of Ryp dal and Ryp dal ( 2014 ).
W e surmise that the lack of lo w-fr e quency variability in PMIP3 past1000 simulations prior to 1850 AD
is r elate d to these simulations b eing initialize d fr om a quasi steady state in e quilibrium with b oundar y
conditions characteristic of 850 AD . W er e the same PMIP3 mo dels to b e initialize d fr om an o cean state
that b or e the imprint of the last deglaciation, w e pr e dict that the y w ould e xhibit mor e vigor ous internal
variability at de cadal to centennial scales, and that the fraction of surface temp eratur e variance imputable
to v olcanic for cing w ould b e r elativ ely lo w er . This “ e cho es” hyp othesis may b e teste d in de dicate d e xp er-
iments with a hierar chy of climate mo dels.
That the o cean state should integrate for cings o v er a long p erio d of time is not a no v el idea (Hasselman,
1976 ; Frae drich, Luksch, and Blender , 2004 ; Ryp dal and Ryp dal, 2014 ); the surprising implication is that
this pr op erty could dir e ctly b ear on the amplitude of climate variability at scales far shorter than orbital,
and ther efor e on the p er ceiv e d r eliability of mo del-base d pr e dictions on so cietally-r ele vant horizons. W er e
the e cho es hyp othesis to b e confirme d by subse quent studies, it w ould b ear fav orably on the pr osp e cts for
pr e diction, at least for the global mean. This suggests tw o pathways to sensibly e valuate mo del b ehav-
ior . The first is to use compr ehensiv e Earth system mo dels (including dynamic ice she ets) to simulate the
climate continuum with sole kno wle dge of orbital for cing. This w ould r e quir e integrating such mo dels
18
o v er a full glacial cy cle (ideally , multiple ones), which is only pr esently in r each of the largest available
sup er computers ( Ab e-Ouchi et al., 2013 ). The se cond way w ould b e to initialize shorter simulations ( e .g.
past1000) fr om a state informe d by pale o-obser vations of the de ep o cean state , and diagnose their tem-
p eratur e continuum as done her e . A dvances in pale o climate state estimation Emile-Geay et al., 2017 may
so on make this p ossible .
Scaling b ehavior is nearly univ ersal, app earing in conte xts as div erse as fluid dynamics (Lo v ejo y et
al., 2008 ), hy dr o chemistr y (Kir chner and Neal, 2013 ), metab olism (W est and Br o wn, 2005 ; Mar quet et al.,
2014 ), e conomic gr o wth (Stanle y and Mantegna, 1995 ), and city size (Lob o et al., 2013 ). The e xistence of
scaling b ehavior in climate timeseries is ther efor e unsurprising, though ther e is curr ently no consensus on
its cause (Frae drich, Luksch, and Blender , 2004 ; Lo v ejo y and Schertzer , 2013 ; Fr e driksen and Ryp dal, 2017 ).
For this r eason, it is not obvious whether the climate mo dels inv estigate d her e r epr o duce this b ehavior
for the right r easons. Inde e d, the notable consistency b etw e en scaling b ehavior in such a wide range of
mo dels and obser vations suggests that it is a r elativ ely crude constraint. A stricter metric w ould b e to
aim for consistency at lo cal or r egional scales, which ar e of gr eatest inter est for adaptation and planning,
and wher e discr epancies b etw e en mo dels and obser vations r emain (Laepple and Huyb ers, 2013 ; Laepple
and Huyb ers, 2014a ). Enhance d data availability may also enable the e valuation of higher-or der sp e ctral
moments, which could help r e v eal other differ ences. Base d on pr esent e vidence , ho w e v er , w e conclude
that it w ould b e pr ematur e to dismiss the capabilities of Earth system mo dels to pr e dict global tr ends on
so cietally-r ele vant timescales (10-100y ). W e suggest that the ke y to simulating the climate continuum o v er
such scales lies in pr op erly initializing the lo w-fr e quency couple d state of the climate system, esp e cially
the o cean; ho w to do so r emains an op en pr oblem.
2.6 Metho ds
2.6.1 Sp e ctral estimation
Be cause pale o climate data ar e often une v enly sample d in the time domain, a common strategy for their
analysis is to first p erform interp olation so that traditional sp e ctral analysis metho ds, such as the p eri-
o dogram (Schuster Arthur , 1898 ) or multi-tap er metho d (MTM, Thomson, 1982 ), can b e applie d. Ho w e v er ,
interp olation can bias sp e ctral estimation as w ell. T o sidestep interp olation, the Lomb-Scargle Fourier
transform (Lomb , 1976 ; Scargle , 1982 ) is often use d, y et is is kno wn to o v er estimate the amplitudes at
the high-fr e quency end (Schulz and Mudelse e , 2002 ). Mor e o v er , Fourier transform-base d metho ds assume
stationar y pr o cesses, an oft-violate d assumption in ge ophysical timeseries. The r esulting e dge effe cts ar e
typically mitigate d by detr ending (W u et al., 2007 ), an imp erfe ct fix b e cause of the intrinsic d ifficulty of
identifying the tr end without compr omising the signal.
W e addr ess these challenges via the W eighte d W av elet Z-transform (W WZ, Foster , 1996 ), which sup-
pr esses the energy leakage cause d by the data gaps. It is wav elet-base d, and ther efor e do es not r ely on
interp olation or detr ending. In particular , w e use its variant (Kir chner and Neal, 2013 ), in which basis
r otations mitigate the numerical instability that o ccurs in pathological cases with the original algorithm.
19
The W WZ metho d has one adjustable parameter , a de cay constant that balances the time r esolution
and fr e quency r esolution of the wav elet analysis. The smaller this constant, the sharp er the p eaks. W e
cho ose the value 0.001 to obtain smo oth sp e ctra that lend themselv es to b etter scaling e xp onent estimation,
while still capturing the main p erio dicities. For the purp ose of sho wing the scalogram, w e use the larger
value(8π
2
)
−1
, justifie d else wher e (Foster , 1996 ; Witt and Schumann, 2005 ). The metho d is implemente d
via the Pyleoclim Python pa ckage (Khider et al., 2018 ). Details ar e pr o vide d in SI T e xt 2.7.3 .
2.6.2 Estimation of scaling e xp onents
T aking the log on b oth sides of Eq. ( 2.1 ) yields: log S ∝ (−β) logf . Ther efor e , β is estimate d via linear
r egr ession in log space . T o mitigate biases arising fr om non-uniform spacing in log co or dinates (mor e
p oints ar e lo cate d in the high-fr e quency side than in the lo w-fr e quency side), w e apply HC06’s fr e quency
binning pr o ce dur e . When estimating the scaling e xp onents of the HadCRU T4 dataset, the annual cy cle
is r emo v e d to av oid biasing the estimate . W e also estimate the scaling e xp onents o v er fr e quency ranges
wher e the p o w er law is w ell follo w e d, which leads to differ ent fr e quency inter vals for differ ent series.
Conclusions do not dep end sensitiv ely on these definitions, as similar r esults ar e obtaine d with o v erlapping
inter vals.
2.7 Supplementar y Information
2.7.1 Data Sour ces
Datasets information
T able 2.1 pr o vides an o v er vie w of the instrumental obser vations, r eanalysis, r e constructions base d on
pr o xy r e cor ds, and mo del simulations use d in this pap er . The details ar e as follo ws:
P A GES2k and LMR The P A GES 2k phase 2 compilation is a community-sour ce d database of temp eratur e-
sensitiv e pr o xy r e cor ds spanning all or part of the Common Era (P A GES 2k Consortium, 2017 ). It gath-
ers 692 series fr om 648 lo cales, with obser vations made on coral, glacial ice , marine and lake se diments,
sp ele othem, tr e e-ring, and do cumentar y ar chiv es.
T o obtain temp eratur e estimates, w e applie d the last millennium r eanalysis (LMR) frame w ork (Hakim
et al., 2016 ; T ar dif et al., 2019 ) on the P A GES 2 k dataset, with the follo wing sp e cifications:
• statistical for war d op erators r elating temp eratur e and pr e cipitation anomalies fr om a climate sim-
ulation to annually r esolv e d pr o xy values using or dinar y least squar es r egr ession. Pr e dictors use
annual mean temp eratur e ( GISTEMP , Hansen et al., 2010 ) and pr e cipitation ( GPCC, Schneider et al.,
2017 ) for all pr o xies e xcept tr e e-ring width and w o o d density , for which seasons ar e obje ctiv ely de-
termine d. Seasons for temp eratur e and pr e cipitation calibration ar e chosen obje ctiv ely and indep en-
dently by cy cling o v er a set of seasonal options and sele cting the season with the b est fit as define d
by the mean squar e of the r esiduals. Seasonal options include: De cemb er-Februar y , De cemb er-May ,
June- A ugust, and June-No v emb er .
20
• 51 r e construction e xp eriments, wher e each e xp eriment draws a random sample of 100 ensemble
memb ers fr om the climate simulation and a random sample of 75% of the pr o xies, yielding 5100
r e constructions in total.
• a co variance lo calization ra dius of 25,000 km.
• ensembles ar e drawn randomly fr om the last millennium simulation of the CCSM4 mo del (Landrum
et al., 2012a )
Be cause these for war d mo dels r e quir e an instrumental calibration, only a subset of r e cor ds with long
enough (≥ 30 y ) instrumental o v erlap ar e r etaine d for these e xp eriments.
HadCRU T4 T o characterize instrumental temp eratur e variability w e use the Met Office Hadle y Cen-
tr e gridde d dataset of global historical surface temp eratur e anomalies (HadCRU T4, Morice et al., 2012 ),
which co v ers 1850 to pr esent at monthly r esolution. It is a combination of anomalies ( departur es fr om
monthly-mean seasonal cy cle) in surface air temp eratur e o v er land ( CRU TEM4) and sea-surface temp era-
tur e (HadSST3). The globally av erage d climatology for the base p erio d 1961-90 ( h t t p s : / / c r u d a t a . u e a . a c
.uk/cru/data/temperature/ ) is adde d back to the dataset to include the annual cy cle .
S16 GAST Sny der (S16, Sny der , 2016 ) pr op ose d a r e construction of globally av erage d surface tem-
p eratur e ( GAST) o v er the past 2 million y ears bas e d on a multi-pr o xy database that consists of Mg/Ca,
alkenones, and faunal assemblages obtaine d fr om marine se diments. These ar e sea-surface temp eratur e
pr o xies, and the r e construction allo ws to inv estigate global surface temp eratur e variability o v er scales of
10
3
to10
6
y ears.
Pr obStack Pr obStack is a P lio cene-P leisto cene stack of the globally distribute d b enthic δ
18
O r e cor ds
obtaine d fr om marine se diments ( Ahn et al., 2017 ). It is constructe d base d on a hidden Marko v mo del,
and is pr obabilistic in the sense that it incorp orates the variability of multiple r e cor ds b eing use d and the
uncertainty in the alignments of r e cor ds. Pr obStack depicts climate variability o v er an inter val that is
comparable to that of S16, ser ving as a cr oss-che ck. Like HC06 (their supplementar y T able 1), w e use a
factor of 4K/‰ to conv ert fr om b enthic δ
18
O to temp eratur e units.
EDC EPICA Dome C Ice Cor e (EDC) is a high-r esolution Antar ctic deuterium pr ofile co v ering the past
800 kyr ( Jouzel et al., 2007 ). It has b e en interpr ete d as a global temp eratur e r e cor d, using a conv ersion
fr om p olar to global temp eratur es on millennial scales.
T raCE-21ka T raCE-21ka ar e a set of transient simulations of the last 21 kyrs using a couple d atmospher e-
o cean general cir culation mo del ( Community Climate System Mo del v ersion 3, CCSM3, Liu et al. ( 2009 )).
The full simulation contains transient Northern Hemispher e meltwater fluxes (MWF), orbital for cing ( ORB),
changing continental ice she ets (ICE), and transient gr e enhouse gas for cing ( GHG). Se v eral sub-simulations
w er e conducte d with individual for cings, allo wing to disentangle their influence . The y w er e sho wn to con-
tribute appr o ximately linearly to the whole (Liu et al., 2009 ).
21
SIM2bl and DG
ns
W e also consider tw o Earth system mo dels of interme diate comple xity . The SIM2bl
simulation (Timm and Timmermann, 2007 ) is a deglaciation simulation conducte d with the ECBILT -CLIO
couple d mo del, wher e ECBILT ( Opste egh et al., 1998 ) is the atmospher e comp onent and CLIO ( Go osse
and Fichefet, 1999 ) is the o cean comp onent. Compar e d with CCSM3, b oth of the atmospher e and o cean
comp onents ar e much simplifie d. ECBilt is a sp e ctral T21 global 3-le v el quasi-ge ostr ophic mo del with
simplifie d parameterizations for diabatic heating, while CLIO is a global, fr e e surface o cean general cir cu-
lation mo del couple d with a sea ice mo del (Fichefet and Morales Maque d, 1997 ). Similar time-dep endent
b o undar y conditions to those of T raCE-21ka ar e applie d, but without meltwater fluxes.
The DG
ns
simulation (Menviel et al., 2011 ) is a similar run with the couple d atmospher e-o cean-sea
ice-carb on cy cle mo del LO VECLIM ( Go osse et al., 2010 ). This mo del consists of the atmospheric com-
p onent ECBilt, the o cean comp onent CLIO , the v egetation comp onent VECODE Br o vkin, Ganop olski,
and Svir ezhe v , 1997 , the ice she et comp onent A GISM (Huybr e chts, 2002 ), and the o cean carb on and the
bioge o chemical comp onent LOCH (Mouchet and François, 1996 ). In this sp e cific simulation, only the
atmospher e and o cean comp onents ar e interactiv e , while other comp onents ar e pr escrib e d with similar
time-dep endent b oundar y conditions as in T raCE-21ka, e xcept that the CH
4
and N
2
O ar e fixe d. In this
configuration, LO VECLIM’s comple xity is identical to ECBilt-CLIO’s.
Comparing CCSM3 to the latter tw o , the main differ ence is a drastically simplifie d atmospher e in
ECBilt, particularly in the tr opics, wher e the quasi-ge ostr ophic appr o ximation br eaks do wn ( Charne y ,
1963 ). For this r eason and b e cause of the coarse r esolution of CLIO’s o cean, neither of these mo dels
simulates interannual variability comparable to the El Niño-Southern Oscillation (ENSO , Sarachik and
Cane , 2010 ), unlike CCSM3. Ho w e v er , b e cause the T raCE-21ka output is only available at 20y r esolution,
these differ ences ar e not appar ent in the sp e ctra. The b oundar y conditions use d in each simulation ar e
summarize d in T able S2.1 .
PMIP3 PMIP3, as a mo del inter comparison pr oje ct, is a colle ction of mo del simulations with similar
b o undar y conditions (Schmidt et al., 2012 ; Braconnot et al., 2012 ). W e collate global mean temp eratur e
simulate d by 10 GCMs (BCC CSM1.1 (W u et al., 2014 ), CCSM4 (Landrum et al., 2012a ), FGO ALS-gl (Zhou
et al., 2008 ), FGO ALS-s2 (Bao et al., 2013 ), IPSL-CM5A -LR (Dufr esne et al., 2013 ), MPI-ESM-P (Raddatz
et al., 2007 ), CSIRO Mk3L-1-2 (Rotstayn et al., 2012 ), HadCM3 ( Gor don et al., 2000 ), CESM ( Otto-Bliesner
et al., 2015 ), and GISS-E2_R (Schmidt et al., 2006 )).
The past1000 e xp eriments co v er the p erio d 850-1849 AD . The industrial era (1850-2005) is also in-
clude d her e; it was either generate d as part of continuous simulations (HadCM3, CESM), or came fr om
“historical” CMIP5 simulations app ende d to the past1000 simulations ( all others).
2.7.2 Timeseries P lots
T o get a sense of the data sour ces use d in this study , w e also sho w the publishe d timeseries in their original
units.
Figur e S2.1 sho ws the timeseries of the pr o xy-base d r e constructions, r eanalysis, and instrumental ob-
ser vations. It can b e se en that Pr obStack, S16 GAST , and EDC sho w v er y similar oscillations during their
common time span.
22
The timeseries of the PMIP3 simulations ar e sho wn in Figur e S2.2 , in which w e se e consistent rapid
temp eratur e de cr easing and r e co v ering e v ents due to v olcanic for cing, as w ell as the industrial warming
tr end.
Figur e S2.3 sho ws the timeseries of the deglaciation simulations. All thr e e simulations shar e similar
onset of the warming at 17.5 kyr BP and the subse quent o v erall tr end after that. SIM2bl and DG
ns
sho w
comparable temp eratur e le v els as the y ar e b oth base d on ECBilt-CLIO , while T raCE-21ka is ab out 4 K
colder on av erage . DG
ns
and T raCE-21ka sho w consistent oscillations b etw e en 13 kyr to 11 kyr AD due to
the fact the y hav e similar meltwater flux for cing.
2.7.3 Sp e ctral Analysis
Pale o-obser vations ar e usually non-uniformly sample d in time domain, y et classical Fo urier-base d sp e ctral
analysis metho ds ar e constructe d base d on the orthogonality of the basis functions, which do es not hold
for non-uniformly sample d data. The usual w orkar ound is to apply an interp olation pr o ce dur e on the
data b efor e sp e ctral analysis, but it will ine vitably intr o duce some bias. In this se ction, w e first pr esent an
interp olation-fr e e metho d, the W eighte d W av elet Z-transform (W WZ), b efor e demonstrating its advantage
comparing to one of the standar d sp e ctral analysis metho ds designe d for uniformly sample d data – the
multi-tap er metho d (MTM).
The W eighte d W av elet Z-transform
W e consider the w eighte d wav elet Z-transform (Foster , 1996 ), in the bias-corr e cte d v ersion of Kir chner
and Neal ( 2013 ). The general frame w ork of the W WZ metho d is a b est fit of the time series to a set of thr e e
basis functions:
x =
∑
ω
a
0
Ψ
0
+
∑
ω
a
1
Ψ
1
+
∑
ω
a
2
Ψ
2
, (S2.1)
wher ex is the timeseries,ω the angular fr e quency , a
i
’s the co efficients at each ω , andΨ
i
’s the basis func-
tions at eachω . Note that her e w e hav e omitte d the subscriptω of thosea
i
’s andΨ
i
’s for simplicity . With
differ ent basis functions, w e will hav e differ ent analysis metho ds. For e xample , with the basis functions
b e lo w w e will get a Fourier transform
Ψ
0
=1(t), Ψ
1
= cos(ωt), Ψ
2
= sin(ωt), (S2.2)
wher e1(t) is a constant v e ctor with values 1 and the length of the time v e ctor t . For a wav elet analysis,
w e hav e
Ψ
0
=1(t), Ψ
1
= cos(ω(t−t
∗
)),
Ψ
2
= sin(ω(t−t
∗
)), (S2.3)
wher et
∗
is t he center time of the wav elet.
23
T o handle the irr egularly sample d data, a w eighte d inner-pr o duct of tw o arbitrar y timeseries f andg
is define d as
⟨f |g⟩ =
∑
N
i=1
w
i
f(t
i
)g(t
i
)
∑
N
i=1
w
i
,
wher et
i
is each time p oint,N the numb er of total time p oints, and
w
i
=e
−cω
2
(t
i
−t
∗
)
2
the w eight of ea ch time p oint, which is determine d by its squar e d distance to the center time of the wav elet
(t
i
−t
∗
)
2
and a de cay constantc that usually takes a small value such as 1/(8π
2
) , 0.0125, or 0.001. Note
that this inner-pr o duct is symmetric, i.e ., ⟨f |g⟩ =⟨g|f⟩ . It can b e also r egar de d as a pr oje ction.
W e then define a sup er-matrix
S =



⟨Ψ
0
|Ψ
0
⟩ ⟨Ψ
0
|Ψ
1
⟩ ⟨Ψ
0
|Ψ
2
⟩
⟨Ψ
1
|Ψ
0
⟩ ⟨Ψ
1
|Ψ
1
⟩ ⟨Ψ
1
|Ψ
2
⟩
⟨Ψ
2
|Ψ
0
⟩ ⟨Ψ
2
|Ψ
1
⟩ ⟨Ψ
2
|Ψ
2
⟩



and form a linear e quation b elo w to solv e Eq. ( S2.1 )
S



a
0
a
1
a
2


 =



⟨x|Ψ
0
⟩
⟨x|Ψ
1
⟩
⟨x|Ψ
2
⟩


. (S2.4)
The original metho d in the study Foster ( 1996 ) solv es the linear e quation Eq. ( S2.4 ) with matrix inv er-
sion that
a
i
=
∑
j
S
−1
i,j
⟨x|Ψ
j
⟩.
wher eS
i,j
is the element of the inv erse d matrix of S . Ho w e v er , matrix inv ersion could cause some nu-
merical instability when the matrix is singular or near so .
T o alle viate this issue , the study Kir chner and Neal ( 2013 ) first r eplaces the center timet
∗
in Eq. ( S2.3 )
with a time-shift factor
τ =
1
2ω
tan
−1
[F],
wher e
F =
2(⟨Ψ
1
|Ψ
2
⟩−⟨Ψ
1
|Ψ
0
⟩⟨Ψ
2
|Ψ
0
⟩)
(⟨Ψ
1
|Ψ
1
⟩−⟨Ψ
1
|Ψ
0
⟩
2
)−(⟨Ψ
2
|Ψ
2
⟩−⟨Ψ
2
|Ψ
0
⟩
2
)
24
and form a ne w set of basis functions
Ψ
0
=1(t), Ψ
1
= cos(ω(t−τ)),
Ψ
2
= sin(ω(t−τ)), (S2.5)
so that the orthogonality b etw e en Ψ
1
andΨ
2
can b e guarante e d for b oth time-e v enly and time-une v enly
sample d data.
Then w e hav e the solutions for a
1
anda
2
as
a
1
=A cos(ωτ)−B sin(ωτ)
a
2
=A sin(ωτ)−B cos(ωτ),
wher e
A = 2(⟨x|Ψ
1
⟩−⟨x|Ψ
0
⟩⟨Ψ
1
|Ψ
0
⟩), (S2.6)
B = 2(⟨x|Ψ
2
⟩−⟨x|Ψ
0
⟩⟨Ψ
2
|Ψ
0
⟩), (S2.7)
ar e the co efficients for the basis functions in Eq. ( S2.5 ), thusa
1
anda
2
ar e the co efficients for the basis
functions in Eq. ( S2.2 ). One can v erify the “r otation” of basis functions using the triangle e xpansion
formulas. T o get the wav elet co efficients , w e should r otate the basis functions fr om Eq. ( S2.5 ) to Eq. ( S2.3 ).
Then w e get
a
1
=A cos(ω(τ−t
∗
))−B sin(ω(τ−t
∗
)),
a
2
=A sin(ω(τ−t
∗
))−B cos(ω(τ−t
∗
)).
Comparison with the multi-tap er metho d (MTM)
W e use synthetic data to compar e the W WZ metho d and the oft-use d MTM (Thomson, 1982 ; Huyb ers
and Curr y , 2006 ). First, w e generate a color e d noise pr o cess with scaling e xp onent β = 1 and length
n = 2001 (Figur e S2.4 top). Then, w e randomly delete 900 p oints fr om the original timeseries to simulate
une v en sampling, and then p erform linear and cubic spline interp olation on this series. W e then apply the
W WZ metho d on the une v enly-sample d data and MTM on the cubic-interp olate d and linear-interp olate d
timeseries (Figur e S2.4 b ottom).
W e se e that since MTM r e quir es interp olation on the une v enly-sample d data, the high fr e quency en-
ergy is lo w er than the analytical value due to the smo othing effe ct intr o duce d by the interp olation. In
contrast, W WZ sidesteps interp olation, with a much mor e faithful scaling e xp onent. The estimate d high
fr e quency energy is a bit higher than the analytical value due to aliasing cause d by nonuniform sampling,
which affe cts all sp e ctra metho ds unless e xplicitly corr e cte d (Kir chner , 2005 ).
25
Be cause of interp olation, the sp e ctrum estimate d by MTM de viates fr om a p o w er law at the high fr e-
quencies, generating a spurious tw o-r egime pattern, while the sp e ctrum estimate d by W WZ corr e ctly es-
timates the scaling b ehavior of the r eal signal in spite of 45% of the data b eing missing. At lo w-fr e quencies,
b o th metho ds p erform similarly .
2.7.4 Distinguishing lo cal, r egional, and global variability
It is kno wn that lo cal, r egional, and global temp eratur e variability e xhibit differ ent scaling laws Fr e driksen
and Ryp dal, 2015 , ther efor e it is imp ortant to take these spatial scales into account in sp e ctral compar-
isons b etw e en mo dels and obser vations. Her e w e e xplor e these differ ences using a p erfe ct mo del scenario
(T raCE-21ka simulation). A s an e xample , w e define tw o sets of co or dinates base d on the lo cations of the
pr o xy data use d in Laepple and Huyb ers ( 2013 ) ( her eafter LH14), wher e the pr o xy data b eing analyze d has
tw o distinct spans: a span shorter than 800 yrs, which consists of coral r e cor ds; another is a long span
ar ound 6000 yrs, which consists of marine se dimentar y r e cor ds. Then w e subsample the mo del’s surface
temp eratur e at these co or dinates, and e valuate the sp e ctral characteristics of the av erage temp eratur e o v er
this set of lo cations.
The blue cur v es on Figur e S2.5 sho w that the sp e ctra at tw o individual lo cations ar e quite differ ent,
while the r e d and gr e en solid cur v es sho w that r egional av erages shar e much mor e similar sp e ctra. Ne xt,
w e estimate global variability thr ough the sp e ctrum of the globally av erage d temp eratur e field. The gray
cur v e sho ws that the global variability is differ ent fr om the r egional variability sample d at the tw o lo cation
gr oups, esp e cially at high fr e quencies.
Be cause pr o cesses that hav e large spatial scales typically inv olv e long timescales as w ell, it is natu-
ral to ask o v er which sp e ctral range these spatial differ ences matter . In particular , w e ask whether the
“global r e cor ds” b eing analyze d in our study (Pr obStack and S16 GAST) ar e truly r epr esentativ e of global
variability . Figur e S2.6 sho ws the sp e ctra of the global mean surface temp eratur e in the T raCE-21ka full
simulation, DG
ns
, and SIM2bl simulations, and the sp e ctra of the av erage temp eratur e at the grid p oints
picke d near est to the lo cations of the r e cor ds going into the Pr obStack and S16 GAST timeseries. A similar
e xer cise is carrie d out for the EDC dataset.
It can b e se en that the sp e ctra of the r egional av erage temp eratur es o v er lo cations of Pr obStack and
S16 GAST ar e close to each other , and to the sp e ctrum of the globally av erage temp eratur e . Thus, the
Pr obStack and S16 GAST datasets ar e go o d pr o xies of global variability at the scales inv estigate d her e . In
contrast, the lo cal r e cor d of EPICA Dome C (EDC) de viates significantly fr om the global av erage: it sho ws
higher o v erall variability , and a flat tail at scales shorter than millennial. This shap e is highly r eminiscent
of the actual EDC dataset (Figur e 2.1 ), and suggests that the flat high-fr e quency tail could b e a featur e of
Antar ctic temp eratur e , not an obser vational artifact of the ice cor e .
The differ ence b etw e en lo cal variability and r egional variability can also b e se en in P A GES 2k r e cor ds
(Figur e S2.7 and Figur e S2.10 ). These sho w that the lo cal featur es of differ ent ar chiv es tend to cancel out
in comp osites, and the scaling e xp onents conv erge to a similar value when going fr om lo cal to r egional
scales.
Thus, w e conclude that:
26
• T o suppr ess the distortion of climate signal in pr o xy data, one can fo cus on r egional variability o v er
a large ar ea, ideally the entir e glob e .
• The datasets b eing analyze d in our study (Pr obStack and S16 GAST), although not spanning the
entir e glob e , ar e r epr esentativ e of glo bal variability .
2.7.5 Analysis of P A GES 2k r e cor ds
Since P A GES 2k r e cor ds ar e the ke y data sour ce in the LMR GAST , it is imp ortant to assess their sp e ctral
content. Her e w e first analyze the dataset at lo cal scales, and then mo v e on to r egional av erages.
Analysis of unpr o cesse d r e cor ds
A s suggeste d by a r e cent study (De e et al., 2017 ), pr o xy data may sho w differ ent scaling e xp onents b etw e en
the interannual scale and de cadal to centennial scales, esp e cially for ice cor e data, and w e inv estigate this
b e havior in the P A GES 2k database .
Follo wing the same definition of the tw o scales (interannual vs de cadal to centennial) as De e et al.
( 2017 ), Figur e S2.7 sho ws the sp e ctral estimates of P A GES 2k r e cor ds stratifie d by ar chiv e typ e , and the dis-
tribution of the estimate d interannual scaling e xp onent β
I
( estimate d o v er p erio ds of 2-8 yrs) and de cadal
to centennial scaling e xp onent β
D
( estimate d o v er p erio ds of 20-2 00 yrs).
In the figur e , w e do not obser v e a scaling br eak for most of the typ es, e xcept for ice cor e r e cor ds, which
sho w much largerβ
I
thanβ
D
due to the diffusion and compaction effe cts that pr efer entially damp high-
fr e quencies ( Cuffe y and Steig, 1998 ; De e et al., 2015 ). Ther efor e , w e conclude that the scaling b ehavior
(β
I
≈β
D
) is w ell follo w e d in most of t he P A GES 2k r e cor ds.
A spatial analysis (Figur e S2.8 ) r e v eals no clear r elation b etw e en lo c ation and scaling e xp onent.
Analysis of comp osites
Another appr oach is to deriv e simple comp osites of the pr o xy r e cor ds fr om differ ent ar chiv e typ es and
estimate their scaling e xp onents. The pr o ce dur e follo ws P A GES 2k Consortium ( 2017 ). That is:
• Sign adjustment. Since not all of the r e cor ds ar e p ositiv ely corr elate d to temp eratur e , the sign of
the r e cor d is flipp e d if the raw d ata is negativ ely corr elate d to temp eratur e .
• Normalization. Map each r e cor d to a standar d normal distribution via inv erse transform sampling
(Emile-Geay and Tingle y , 2016 ), which yields series with zer o-mean and unit-variance .
• Binning. Each r e cor d is time-av erage d with 10-yr bins. After binning, all the une v enly space d data
ar e aligne d to a common time a xis.
• Bo otstrap . Perform b o otstrap r esampling (Efr on and Tibshirani, 1994 ) among the r e cor ds for each
time bin, obtaining statistics s uch as mean and variance .
27
• Scaling. After p erforming the binning and computing the av erage d series for the target r efer ence ,
w e p erform linear r egr ession b etw e en the pr o xy comp osites and target r efer ence , and scale the pr o xy
comp osites to temp eratur e .
The target r efer ence is HadCRU T4 (Morice et al., 2012 ) and the r esults ar e sho wn in Figur e S2.9 . It can
b e se en that the comp osites hav e a high linear corr elation with HadCRU T4 instrumental r e cor ds, and it is
thus acceptable to r egar d the comp osites as linearly r elate d to temp eratur e , hence justifying the conv ersion
to the unit of temp eratur e by linear r egr ession.
W e then p erfor m sp e ctral analysis on each comp osite as w ell as the LMR GAST , sho wn in Figur e S2.10
(top). W e se e the scaling e xp onents of the pr o xy comp osites ar e o v erall close to what w e get fr om LMR
GAST , although the values ar e mor e variable than the global comp osite o wing to the smaller sample sizes
( esp e cially for marine se diments). This discr epancy b etw e en r egional and global scales is w ell r epr o duce d
in Figur e S2.10 ( b ottom), in which surface air temp eratur e in one memb er of CESM last millennium ensem-
ble ( Otto-Bliesner et al., 2015 ) is analyze d at P A GES 2k lo cations stratifie d by ar chiv e typ e . It is obser v e d
that the r egionally av erage d surface temp eratur e at lo cations of differ ent ar chiv es display scaling e xp o-
nents b etw e en 0.6-0.8, while the global av erage surface temp eratur e displays a scaling e xp onent ar ound
1. Ther efor e , much of the discr epancy sho wn in Figur e S2.10 (top) b etw e en pr o xy comp osites and LMR
GAST could plausibly b e e xplaine d by pur ely ge ographic differ ences b etw e en r egional and global comp os-
ites, and do not giv e cause for concern with the r eal P A GES 2k comp osites ( their inher ent uncertainties
notwithstanding).
Also , tr e e-ring comp osites in Figur e S2.10 (top) app ear to sho w a ste ep slop e , although it is still an
op en question whether the detr ending metho ds use d in the P A GES 2k phase 2 dataset can captur e most
of the lo w-fr e quency climate variability . Despite these cav eats, the P A GES 2k dataset is curr ently the
most compr ehensiv e , community-curate d pr o xy dataset co v ering the Common Era, and thus pr o vides a
r easonable b ottom line for our analysis.
2.7.6 Analysis of PMIP3 simulations of the last millennium
When e valuating PMIP3 simulations, a choice has to b e made: should w e use the last millennium time span
850-1850 only or should w e also include the industrial warming p erio d a fter 1850? In other w or ds, do es
the industrial warming p erio d contain significant amount of climate variability that w e should not ignor e
when w e compar e mo del simulations to coral r e cor ds or instrumental obser vations that hav e include d the
p erio d after 1850?
T o inv estigate the influence of the industrial warming p erio d, w e compar e P A GES 2k/LMR GAST and
the PMIP3 simulations o v er time spans that either include or e xclude the industrial warming p erio d (Figur e
S2.11 ).
When the industrial warming p erio d is include d, b oth P A GES 2k/LMR GAST and the simulations sho w
a go o d fit to the instrumental r e cor d (HadCRU T4). The inset plot on the left panel indicates that the dis-
tributions of the scaling e xp onents ( estimate d o v er 2-500 yrs) of P A GES 2k/LMR GAST and those of the
PMIP3 simulations ar e o v erall comparable , although the spr ead of the simulations is br oader . Mor e sp e cif-
ically , the simulations and the P A GES 2k/LMR GAST ar e mor e comparable at de cadal than interannual
28
scales (2-8 y ears), which might b e due to the fact that these mo dels tend to simulate an o v erly vigor ous
ENSO ( A ult et al., 2013 ).
When the industrial warming p erio d is e xclude d, w e obser v e a consistent de cr ease of the scaling e xp o-
nents for b oth the P A GES 2k/LMR GAST and the simulations, and their distributions ar e still comparable .
Either way , PMIP3 simulations display comparable scaling e xp onents to P A GES 2k/LMR GAST when b oth
ar e tr eate d consistently .
Note that since the PSD is estimate d by integrating the scalogram o v er time axis, the industrial warm-
ing p erio d is mor e than 10% of the whole length (150 yrs to 1150 yrs) in past1000 simulations, which has
a non-negligible effe ct on the PSD . In contrast, the industrial p erio d bar ely co v ers 1% of the length of
deglaciation simulations (150 yrs to 21 kyrs), which is to o short to contribute . Thus, industrial warming is
not what driv esβ
DC
≈ 1 in deglaciation simulations.
2.7.7 An ideal test of the scaling br eak hyp othesis
In the main te xt, the Se ction title d “ A tale of tw o r egimes” mentions tw o fundamental me chanisms: 1)
abrupt climate change e v ents, and 2) a gradual, large-amplitude transition. The first me chanism was first
pr op ose d in Nilsen, Ryp dal, and Fr e driksen ( 2016 ), along with the suggestion that Holo cene climate is
to o stable to sho w a scaling br eak. This is consistent with the p o w er sp e ctra of 253 Holo cene r e cor ds
interpr ete d as temp eratur e pr o xies
∗
, as sho wn in Figur e S2.12 : the top panel displays individual sp e ctra
stratifie d by latitude , and the b ottom panel sho ws that the distributions of the scaling e xp onents o v er dif-
fer ent timescales o v erlap substantially , with similar me dian values, indicating a single r egime thr oughout
this range of scales.
T o se e if this featur e is captur e d by mo del simulations, Figur e S2.13 compar es the p o w er sp e ctral den-
sity (PSD ) cur v es of the T raCE-21ka full simulation timeseries b efor e and after 8.2 ka. The timeseries b efor e
8.2 ka contains b oth abrupt climate change e v ents and the gradual transition fr om glacial to interglacial
states, while the timeseries after 8.2 ka contains neither . The latter PSD cur v e confirms that no scaling
br eak o ccurs in the absence of one or b oth me chanisms. Performing wav elet analysis on the full T raCE-
21ka simulation (Figur e S2.14 ), one can identify b oth me chanisms, y et whether abrupt climate change is
ne cessar y and sufficient to cause a scaling br eak r emains an op en question.
T o test this hyp othesis under an ideal setting, w e sup erp ose a Fano r esonance
†
(Fano , 1961 ) as an
impulse onto a white noise backgr ound to emulate the bump se en in the T raCE-21ka full simulation (upp er
panel of Figur e S2.14 ). That bump is b elie v e d to b e a temp eratur e r esp onse to the meltwater flux for cing
( Osip o v and Khlysto v , 2010 ), which is similar to a r esonance pr o cess (Timmermann et al., 2003 ). The Fano
r esonance is just one way to emulate such a bump; others pr o duce similar r esults as sho wn later in Figur e
S2.19 and Figur e S2.20 .
Figur e S2.15 sho ws that the Fano r esonance impulse sup erp ose d onto a white noise backgr ound do es
pr o duce a scaling br eak. Its wav elet analysis is pr esente d in Figur e S2.16 , which sho ws an energetic ar ea
ar ound the lo cation of that impulse , cascading to higher fr e quencies. The energy dissipates during the
∗
Data citations liste d in https://github.com/fzhu2e/continuum_redux/blob/master/Holocene_records.csv
†
https://terpconnect.umd.edu/~toh/spectrum/BWF.m
29
cascading pr o cess and depletes ar ound the p erio d of 10 y ears, wher e w e se e the scaling br eak. Ther efor e ,
the sp e cific lo cation of the scaling br eak is dep endent on the p erio dicity and amplitude of the impulse –
the dominant lo w fr e quency for cing in this case .
The ideal test can also b e conducte d with a pink noise (V oss and Clarke , 1978 ) backgr ound, which yields
similar r esults, though with a w eaker contrast b etw e en e xp onents, as e xp e cte d (Figur es S2.17 and S2.18 ).
These r esults suggests that, as long as the lo w fr e quency for cing is dominant ( significantly higher
energy compar e d to the high fr e quency band), one should obser v e a similar scaling br eak.
2.7.8 W av elet analysis of time-dep endent b oundar y conditions
One main conclusion of this study is that the ke y to simulating the continuum of the temp eratur e variability
as w ell as the scaling br eak lies in the b oundar y conditions. Ther efor e , w e no w inv estigate their sp e ctral
content.
Figur e S2.21 sho ws the wav elet analysis of the summer solstice insolation at 65
◦
N. The Matlab script
(Huyb ers and Eisenman, 2006 ) use d for the calculation is base d on the classic w ork of Berger ( 1978 ). A c-
cor ding to the scalogram, w e se e stationar y Milanko vitch cy cles along the whole time span.
Similarly , Figur e S2.22 sho ws the analysis of the atmospheric CO
2
for cing use d in DG
ns
simulation
obtaine d fr om the EPICA Dome C ice cor e (Lüthi et al., 2008 ), in which w e se e a scaling br eak ar ound 1000
y ears and a scaling b ehavior with a scaling e xp onent ar ound 2 o v er timescales longer than 1000 y ears.
Finally , Figur e S2.23 sho ws the wav elet analysis of the b est estimates of the ice-v olume e quivalent
sea-le v el function ( esl, Lamb e ck et al., 2014 ) displaying scaling b ehavior with an e xp onent near 4 o v er
timescales longer than 500 y ears. Since sea-le v el variations at those scales ar e linearly corr e late d to the
global ice-v olume , the esl value is r epr esentativ e of ice she et for cing.
Base d on our analysis, insolation for cing pr o vides the main sour ce of lo w-fr e quency energy , while
the transient CO
2
for cing and ice-she et for cing b o ost the total energy of the climate variability o v er long
timescales, all together driving the scaling b ehavior in temp eratur e in CCSM3 (Fig 3). Whether curr ent
Earth system mo dels can generate similar variability with sole kno wle dge of orbital for cing r emains an
op en question.
2.7.9 Comparing mo del simulations and obser vational r e cor ds o v er similar time spans
When comparing the sp e ctral content of tw o timeseries, it is b est to do so o v er o v erlapping time spans.
Ho w e v er , this is not always feasible b e cause of disparate data availability . Her e w e test whether the com-
parisons carrie d out in Figur e 2.2 and Figur e 2.3 ar e r obust to this consideration.
Figur e S2.24 sho ws the comparisons b etw e en mo del simulations and each obser vational r e cor d in the
fr e quency domain o v er similar time spans. It can b e se en that, when compar e d o v er o v erlapping time
spans, the conclusions fr om Figur e 2.2 and Figur e 2.3 still hold: the mo del simulations and differ ent obser-
vational datasets sho w comparable p o w er sp e ctra.
30
5.0
4.5
4.0
3.5
3.0
2.5
18
O ( )
ProbStack
8
4
0
4
T anom. (K)
S16 GAST
5000 4000 3000 2000 1000 0
Time (kyr AD)
12
8
4
0
4
T anom. (K)
EDC
0 250 500 750 1000 1250 1500 1750 2000
Time (yr AD)
0.8
0.4
0.0
0.4
0.8
T anom. (K)
PAGES2k/LMR GAST
1850 1875 1900 1925 1950 1975 2000 2025
Time (yr AD)
1
0
1
T anom. (K)
HadCRUT4
Figur e S2.1: The timeseries of the pr o xy-base d r e constructions, r eanalysis, and instrumental ob-
ser vations. With r esp e ct to P A GES 2k/LMR GAST , the dark r e d shade d ar ea denotes the inter quartile
range , and the light r e d shade d ar ea denotes the central 95% range , fr om 2.5% to 97.5%.
31
800 1000 1200 1400 1600 1800 2000
Time (yr AD)
4
3
2
1
0
1
2
T anom. (K)
bcc_csm1_1
CCSM4
FGOALS_gl
FGOALS_s2
IPSL_CM5A_LR
MPI_ESM_P
CSIRO
HadCM3
CESM (n=10)
GISS (n=3)
Figur e S2.2: The timeseries of the PMIP3 simulations. Note that the cur v es for CESM and GISS ar e 10
and 3 memb ers r esp e ctiv ely .
20000 15000 10000 5000 0
Time (yr)
282
284
286
288
Temperature (K)
17.5 kyr BP
TraCE-21ka (CCSM3)
DG
ns
(LOVECLIM)
SIM2bl (ECBilt-CLIO)
Figur e S2.3: The timeseries of the deglaciation simulations.
32
0 500 1000 1500 2000
Time
200
0
200
Value
timeseries deleted points
2 5 10 20 50 100 200 500 1000 2000
Period (years)
10
2
10
3
10
4
10
5
10
6
Spectral Density
analytical
MTM on cubically-interpolated data
MTM on linearly-interpolated data
WWZ on unevenly-sampled data
Figur e S2.4: (top) The timeseries with length of 2001 along with the delete d 900 p oints, and ( b ottom) the
analytical PSD cur v e along with the PSD estimate fr om W WZ applying on the une v enly-sample d data and
that fr om MTM applying on the cubic-interp olate d and linear-interp olate d data.
33
T able S2.1: The b oundar y conditions b eing use d in T raCE-21ka, SIM2bl, and DG
ns
.
Boundar y conditions T raCE-21ka (Liu et al., 2009 ) SIM2bl (Timm and Timmermann, 2007 ) DG
ns
(Menviel et al., 2011 )
ORB transient transient transient
ICE transient transient transient
CO
2
transient transient transient
CH
4
transient transient fixe d
N
2
O transient transient fixe d
MWF transient none transient
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
Spectra of TraCE21ka simulation
global average
regional average (locs of short duration proxies)
regional average (locs long duration proxies)
local (lat:57.52, lon:7.50)
local (lat:1.86, lon:11.25)
Figur e S2.5: The sp e ctra of the global mean surface temp eratur e in the T raCE-21ka full simulation and
the asso ciate d sp e ctra of the av erage temp eratur e of the grid p oints picke d near est to the corr esp onding
obser vation lo cations of the pr o xies use d in LH14 and other tw o arbitrarily sele cte d lo cations. The short
duration pr o xies hav e duration less than 1000 y ears, while the long duration pr o xies hav e duration longer
than 1000 y ears.
34
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
Spectra of TraCE-21ka full simulation
global average
regional average (ProbStack locs)
regional average (GAST locs)
regional average (EDC loc)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
Spectra of DG
ns
simulation
global average
regional average (ProbStack locs)
regional average (GAST locs)
regional average (EDC loc)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
Spectra of SIM2bl simulation
global average
regional average (ProbStack locs)
regional average (GAST locs)
regional average (EDC loc)
Figur e S2.6: The sp e ctra of the global mean surface temp eratur e in the (top) T raCE-21ka full simulation,
(middle) DG
ns
, and ( b ottom) SIM2bl simulations, and their asso ciate d sp e ctra of the av erage temp eratur e
of the grid p oints picke d near est to the corr esp onding obser vation lo cations of the Pr obStack, GAST , and
EDC datasets.
35
2 5 10 20 50 100 200 500
Period (years)
10
4
10
2
10
0
10
2
10
4
Spectral Density
coral, 96 records
2 0 2 4
0.0
0.2
0.4
D
= 1.18 (17 records)
I
= 0.88 (90 records)
2 5 10 20 50 100 200 500
Period (years)
10
4
10
2
10
0
10
2
10
4
Spectral Density
lake sediment, 42 records
2 0 2 4
0.00
0.25
0.50
0.75
D
= 0.52 (22 records)
I
= 0.55 (16 records)
2 5 10 20 50 100 200 500
Period (years)
10
4
10
2
10
0
10
2
10
4
Spectral Density
marine sediment, 58 records
2 0 2 4
0.0
0.2
0.4
0.6
D
= 0.33 (9 records)
2 5 10 20 50 100 200 500
Period (years)
10
4
10
2
10
0
10
2
10
4
Spectral Density
glacier ice, 49 records
2 0 2 4
0.0
0.5
1.0
D
= 0.12 (41 records)
I
= 1.07 (37 records)
2 5 10 20 50 100 200 500
Period (years)
10
4
10
2
10
0
10
2
10
4
Spectral Density
tree, 415 records
2 0 2 4
0.00
0.25
0.50
0.75
D
= 0.50 (343 records)
I
= 0.34 (415 records)
Figur e S2.7: The p o w er sp e ctral density of P A GES 2k dataset stratifie d by ar chiv e typ e along with
the distribution of the corr esp onding β
I
and β
D
. The interannual scaling e xp onent β
I
is estimate d
o v er p erio d of 2-8 y ears, while the de cadal to centennial scaling e xp onent β
D
is estimate d o v er p erio d of
20-200 y ears. In the right panel, only the β values with standar d err or less than or e qual to 0.5 is taken
into account. The solid notch indicates the me dian ofβ
D
, and the dashe d notch indicates that of β
I
. Note
thatβ
I
for mari ne se dimentar y r e cor ds is not calculable due to their limite d temp oral r esolution.
36
Interannual Scaling Exponent
bivalve
borehole
coral
documents
glacier ice
hybrid
lake sediment
marine sediment
sclerosponge
speleothem
tree
2.0
1.6
1.2
0.8
0.4
0.0
0.4
0.8
1.2
1.6
2.0
I
2 0 2
0.0
0.2
0.4
0.6
0.8
Distribution
median: 0.435
Decadal to Centennial Scaling Exponent
2.0
1.6
1.2
0.8
0.4
0.0
0.4
0.8
1.2
1.6
2.0
D
2 0 2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distribution
median: 0.457
Figur e S2.8: Maps of scaling e xp onents estimate d fr om the P A GES 2k phase 2 datasets. The inter-
annual scaling e xp onent β
I
is estimate d o v er p erio d of 2-8 y ears, while the de cadal to centennial scaling
e xp onentβ
D
is estimate d o v er p erio d of 20-200 y ears. The sites in gray ar e not calculable due to limite d
temp oral r esolution and/or length, or the standar d err or is gr eater than 0.5.
37
0
100
200
300
400
500
600
700
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
PAGES2k, 692 records
proxy, conversion factor = 1.371, r = 0.920
instrumental
0
20
40
60
80
100
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
coral, 96 records, bin_width = 10
proxy, conversion factor = 0.439, r = 0.622
instrumental
0
10
20
30
40
50
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
glacier_ice, 49 records, bin_width = 10
proxy, conversion factor = 1.205, r = 0.586
instrumental
0
10
20
30
40
50
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
lake_sediment, 42 records, bin_width = 10
proxy, conversion factor = 1.271, r = 0.919
instrumental
0
10
20
30
40
50
60
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
marine_sediment, 58 records, bin_width = 10
proxy, conversion factor = 0.807, r = 0.634
instrumental
0
100
200
300
400
# records
0 500 1000 1500 2000
year (AD)
2
1
0
1
2
proxy
tree, 415 records, bin_width = 10
proxy, conversion factor = 1.096, r = 0.859
instrumental
Figur e S2.9: Ar chiv e-sp e cific comp osites of the P A GES 2k phase 2 dataset, scale d to HadCRU T4
temp eratur e . The upp er left sho ws all ar chiv es together , while the others stratify the comp osites by
ar chiv e typ e . The time series ar e 10-y ear binne d for the calculation of the linear corr elation b etw e en the
instrumental temp eratur e r e cor ds and the comp osites. The shade d bars sho w 95% confidence inter vals
calculate d by a b o otstrap pr o ce dur e .
38
2 5 10 20 50 100 200 500 1000
Period (years)
10
3
10
2
10
1
10
0
10
1
10
2
10
3
Spectral Density
LMR (
DC
= 1.00±0.09)
PAGES2k
mix (692 records,
DC
= 0.73±0.22)
coral (96 records,
DC
= 0.53±0.20)
lake sediment (42 records,
DC
= 0.70±0.14)
marine sediment (58 records,
DC
= 0.17±0.09)
glacier ice (49 records,
DC
= 0.59±0.12)
tree (415 records,
DC
= 0.91±0.14)
2 5 10 20 50 100 200 500 1000
Period (years)
10
3
10
2
10
1
10
0
10
1
10
2
10
3
Spectral Density
global (
DC
= 1.00±0.21)
CESM-LME at PAGES2k locations
mix (692 records,
DC
= 0.79±0.27)
coral (96 records,
DC
= 0.74±0.28)
lake sediment (42 records,
DC
= 0.83±0.21)
marine sediment (58 records,
DC
= 0.65±0.28)
glacier ice (49 records,
DC
= 0.66±0.13)
tree (415 records,
DC
= 0.66±0.27)
Figur e S2.10: Sp e ctral estimates of (top) the comp osites of P A GES 2k r e cor ds stratifie d by ar chiv e
typ e and that of the LMR r eanalysis ensemble (50 memb ers); ( b ottom) one of the CESM last
millennium ensemble memb er’s global mean surface temp eratur e ( o v er time span 850-2005) and
r egional mean surface temp eratur e at P A GES 2k lo cations stratifie d by ar chiv e typ e . The solid
dark cur v e is the ensemble me dian PSD of LMR. The de cadal and centennial scaling e xp onent β
DC
is
estimate d o v er p erio d 20-300 y ears.
39
2 5 10 20 50 100 200 500 1000 2000
Period (years)
10
3
10
2
10
1
10
0
10
1
10
2
10
3
10
4
Spectral Density
LMR
PMIP3 past1000
HadCRUT4
0.0
0.5
1.0
1.5
LMR PMIP3
Industrial warming period included
2 5 10 20 50 100 200 500 1000 2000
Period (years)
10
3
10
2
10
1
10
0
10
1
10
2
10
3
10
4
Spectral Density
LMR
PMIP3 past1000
0.0
0.5
1.0
1.5
LMR PMIP3
Industrial warming period excluded
Figur e S2.11: The comparison b etw e en the scaling e xp onents of P A GES 2k/LMR GAST and that
of the PMIP3 simulations o v er time span with or without industrial warming p erio d. ( left) Com-
parison o v er time span with industrial warming p erio d include d. (right) Comparison o v er time span with
industrial warming p erio d e xclude d. The dark r e d shade d ar ea denotes the inter quartile range of LMR, and
the light r e d shade d ar ea denotes the central 95% range , fr om 2.5% to 97.5%. β s ar e estimate d o v er 2-500
yrs.
40
2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
0
10
20
30
40
50
60
70
80
90
Latitude ( N/ S)
5.0 2.5 0.0 2.5 5.0 7.5 10.0
0.0
0.1
0.2
0.3
0.4
0.5
S
= 1.17 (10-100 yrs, 9 records)
M
= 0.97 (100-1000 yrs, 55 records)
L
= 1.06 (1-10 kyrs, 121 records)
Figur e S2.12: (top) The sp e ctra of the Holo cene temp eratur e pr o xies (253 r e cor ds). The c olors denote
differ ent latitudes. Data citations se e the fo otnote in the te xt. ( b ottom) The distribution of the scaling
e xp onentβ ’s o v er differ ent p erio ds. The solid notch indicates the me dian of eachβ .
41
20000 10000 0
Year
280
281
282
283
284
285
286
Temperature (K)
whole length
before 8kyr BP
after 8 kyr BP
20 50 100 200 500 1 k 2 k 5 k 10 k 20 k
Period (years)
10
2
10
0
10
2
10
4
10
6
Spectral Density
whole length (
L
=2.28;
S
=0.78)
before 8 kyr BP (
L
=2.80;
S
=0.72)
after 8 kyr BP ( =1.05)
Figur e S2.13: The p o w er sp e ctral density estimations of the timeseries b efor e and after 8 kyr BP
in the T raCE-21ka full simulation. β
S
is estimate d o v er the p erio d of 20-400 yrs, and β
L
is estimate d
o v er the p erio d of 400-2000 yrs. Note that for the timeseries after 8 kyr BP , w e do not se e a scaling br eak,
andβ is e stimate d o v er p erio ds of 20-2000 yrs.
282
284
286
20000 17500 15000 12500 10000 7500 5000 2500 0
Year (AD)
50
100
200
500
1000
2000
5000
10000
Period (years)
0.00 0.04 0.08 0.12 0.16 0.20
10
0
10
3
Spectral Density
Estimated spectrum
AR(1) 95%
S = 0.74, L = 2.51
Figur e S2.14: W av elet analysis of the T raCE-21ka full simulation. The upp er panel is the timeseries
of the simulation, the main panel is the wav elet analysis plot, and the right panel is the corr esp onding
p o w er sp e ctral density .β
S
is estimate d o v er the p erio d of 50-300 yrs, and β
L
is estimate d o v er 300-5000
yrs.
42
0
5
10
Value
impulse (I)
0 1000 2000
Year
5
0
5
10
Value
white noise (W)
W+I
2 5 10 20 50 100 200 500 1000
Period (years)
10
1
10
0
10
1
10
2
Spectral Density
W (
L
=-0.05;
S
=-0.06)
W+I (
L
=0.95;
S
=0.08)
Figur e S2.15: (upp er left) The Fano r esonance impulse (I); ( lo w er left) The white noise (W) and that with
the impulse sup erp ose d (W +I); (right) The PSDs of those tw o signals.
0
5
10
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
2
5
10
20
50
100
200
500
1000
Period (years)
0.00 0.36 0.72 1.08 1.44 1.80
10
0
10
1
10
2
Spectral Density
Estimated spectrum
AR(1) 95%
S = 0.08, L = 0.95
Figur e S2.16: W av elet analysis of the mixe d signal with a Fano r esonance impulse sup erp ose d
onto a white noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yr , and β
L
is estimate d o v er
20-200 yrs.
43
0
5
10
Value
impulse (I)
0 1000 2000
Year
5
0
5
10
Value
pink noise (P)
P+I
2 5 10 20 50 100 200 500 1000
Period (years)
10
1
10
0
10
1
10
2
10
3
Spectral Density
P (
L
=1.12;
S
=1.07)
P+I (
L
=1.94;
S
=1.07)
Figur e S2.17: (upp er left) The Fano r esonance impulse (I); ( lo w er left) The pink noise (I) and that with the
impulse sup erp ose d (P+I); (right) The PSDs of those tw o signals.
0
5
10
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
2
5
10
20
50
100
200
500
1000
Period (years)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
10
1
10
0
10
1
10
2
10
3
Spectral Density
Estimated spectrum
AR(1) 95%
S = 1.07, L = 1.94
Figur e S2.18: W av elet analysis of the mixe d signal with a Fano r esonance impulse sup erp ose d
onto a pink noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yrs, and β
L
is estimate d o v er
20-200 yrs.
44
0
5
10
Value
impulse (I)
0 1000 2000
Year
5
0
5
10
Value
pink noise (P)
P+I
2 5 10 20 50 100 200 500 1000
Period (years)
10
1
10
0
10
1
10
2
10
3
Spectral Density
P (
L
=1.12;
S
=1.07)
P+I (
L
=2.08;
S
=1.07)
Figur e S2.19: (upp er left) The Gaussian impulse (I); ( lo w er left) The pink noise (I) and that with the impulse
sup erp ose d (P+I); (right) The PSDs of those tw o signals.
0
5
10
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
2
5
10
20
50
100
200
500
1000
Period (years)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
10
1
10
0
10
1
10
2
10
3
Spectral Density
Estimated spectrum
AR(1) 95%
S = 1.07±0.02, L = 2.08±0.14
Figur e S2.20: W av elet analysis of the mixe d signal with a Gaussian impulse sup erp ose d onto a
pink noise backgr ound. β
S
is estimate d o v er the p erio d of 2-20 yrs, and β
L
is estimate d o v er 20-200 yrs.
45
450
500
550
Insolation (W/m
2
)
1750000 1500000 1250000 1000000 750000 500000 250000 0
Year (AD)
10
20
50
100
Period (kyrs)
0.0 0.4 0.8 1.2 1.6 2.0
10
3
10
5
10
7
Spectral Density
Estimated spectrum
AR(1) 95%
480
500
520
Insolation (W/m
2
)
17500 15000 12500 10000 7500 5000 2500 0
Year (AD)
0.05
0.1
1.0
5.0
10.0
Period (kyrs)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
10
1
10
5
Spectral Density
Estimated spectrum
AR(1) 95%
= 4.23
Figur e S2.21: W av elet analysis of the calculate d summer solstice insolation at 65
◦
N. The pr e cession
and obliquity harmonics ar e e vident, with a much lesser amplitude for the 100 kyr cy cle , as note d in
Huyb ers ( 2006 ). The upp er panel sho ws the r esult o v er the past 2 my , while the lo w er panel sho ws that
o v er the past 20 kyr , in whichβ is estimate d o v er 100-1000 yrs.
46
200
250
CO
2
(ppm)
16000 14000 12000 10000 8000 6000 4000 2000
Year (AD)
200
500
1000
2000
5000
10000
Period (years)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
10
1
10
3
Spectral Density
Estimated spectrum
AR(1) 95%
S = -0.44, L = 1.93
Figur e S2.22: W av elet analysis of the atmospheric CO
2
for cing use d in DG
ns
simulation obtaine d
fr om the EPICA Dome C ice cor e . β
S
is estimate d o v er the p erio d of 200-1000 yrs, and β
L
is estimate d
o v er 1000-5000 yrs.
.
47
100
50
0
esl (m)
16000 14000 12000 10000 8000 6000 4000 2000
Year (AD)
200
500
1000
2000
5000
10000
Period (years)
0.0 0.1 0.2 0.3 0.4 0.5
10
0
10
2
10
4
Spectral Density
Estimated spectrum
AR(1) 95%
= 4.00
Figur e S2.23: W av elet analysis of the b est estimates of the ice-v olume e quivalent sea-le v el func-
tion ( esl). β is estimate d o v er 400-5000 yrs.
48
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
TraCE-21ka (-20050 ~ 950 AD)
GAST (-20050 ~ 950 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
SIM2bl (-19050 ~ 950 AD)
GAST (-19050 ~ 950 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
TraCE-21ka (-20050 ~ 1950 AD)
ProbStack (-20050 ~ 1950 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
SIM2bl (-19050 ~ 1949 AD)
ProbStack (-19050 ~ 1950 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
TraCE-21ka (10 ~ 1980 AD)
LMR (1 ~ 2000 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
SIM2bl (1 ~ 1949 AD)
LMR (1 ~ 2000 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
TraCE-21ka (1860 ~ 1980 AD)
HadCRUT4 (1850 ~ 1979 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
SIM2bl (1850 ~ 1949 AD)
HadCRUT4 (1850 ~ 1949 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
DGns (-16050 ~ -1050 AD)
GAST (-16050 ~ -1050 AD)
0.5 1 2 5 10 20 100 1 k 10 k 100 k
Period (years)
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
1 yr 23 kyr 41 kyr 100 kyr
DGns (-16050 ~ -1050 AD)
ProbStack (-16050 ~ -1050 AD)
Figur e S2.24: The comparison b etw e en mo del simulations and obser vations in the fr e quency do-
main o v er similar time spans. Note that the DG
ns
simulation has no o v erlapp e d t ime span with LMR
and HadCRU T4, and the HadCRU T4 analyze d her e is the annualize d v ersion so that its magnitude or der
w ould b e similar to that of the mo del simulations.
49
Chapter 3
Evaluating the temp eratur e r esp onse to v olcanic for cing
Abstract
Explosiv e v olcanism imp oses impulse-like radiativ e for cing on the climate system, pr o viding a natural e x-
p eriment to study the climate r esp onse to p erturbation. Pr e vious studies hav e identifie d disagr e ements
b e tw e en pale o climate r e constructions and climate mo del simulations ( GCMs) with r esp e ct to the mag-
nitude and r e co v er y fr om v olcanic co oling, questioning the fidelity of GCMs, r e constructions, or b oth.
Using the pale o envir onmental data assimilation frame w ork of the Last Millennium Reanalysis, this study
inv estigates the causes of the disagr e ements, using b oth r eal and simulate d data. W e demonstrate that
discr epancies since 1600 CE can b e largely r esolv e d by assimilating tr e e-ring density r e cor ds only , target-
ing gr o wing-season temp eratur e instead of annual temp eratur e , and p erforming the comparison at pr o xy
lo cales. Simulations of eruptions earlier in the last millennium may also r efle ct uncertainties in for cing
and mo dele d aer osol micr ophysics.
3.1 Intr o duction
V olcanic eruptions influence the climate system thr ough their dir e ct effe ct on shortwav e radiation entering
the earth system and the subse quent r esp onse of major mo des of o cean-atmospher e variability (Handler ,
1984 ; Hir ono , 1988 ; Rob o ck, 2000 ; A dams, Mann, and Ammann, 2003 ; Mann et al., 2005 ; Emile-Geay et al.,
2008 ; Schneider et al., 2009 ; Li et al., 2013 ; Ste v enson et al., 2016 ). Eruptions ther efor e offer unique natural
e xp eriments with which to pr ob e the fidelity of climate mo del simulations, understand the r esp onse of
the o cean and atmospher e cir culation to changes in radiativ e for cing, assess climate system fe e dbacks,
and e valuate solar radiation management pr op osals (So den et al., 2002 ; Timmr e ck, 2012 ). The sp oradic
o ccurr ence of large v olcanic eruptions means that de v eloping a de ep er understanding of their effe ct on
climate ne cessarily inv olv es analyzing the r esp onse to e v ents prior to the instrumental era.
Significant disagr e ements hav e b e en identifie d b etw e en pale o climate r e constructions of the large-scale
temp eratur e r esp onse to v olcanic eruptions and climate mo del simulations (D’ Arrigo , Wilson, and An-
chukaitis, 2013 ; Schur er et al., 2013 ; Stoffel et al., 2015b ). The IPCC AR5 (Masson-Delmotte et al., 2013 ),
which summarize d the state of kno wle dge at the time of publication, highlighte d a discr epancy in the
Zhu, F ., Emile‐Geay , J., Hakim, G. J., King, J., & Anchukaitis, K. J. (2020). Resolving the Differ ences in the Simulate d and
Re constructe d T emp eratur e Resp onse to V olcanism. Ge ophysical Resear ch Letters, 47(8), e2019GL086908. h t t p s : / / d o i . o r g /
10.1029/2019GL086908
50
intensity and duration of the simulate d v ersus pr o xy-base d r e constructe d temp eratur e r esp onse to e xplo-
siv e v olcanism (Figur e 3.1 b). Couple d Mo del Inter comparison Pr oje ct 5 ( CMIP5)/Pale o climate Mo deling
Inter comparison Pr oje ct 3 (PMIP3) mo del simulations for the last millennium e xp eriment (Schmidt et al.,
2012 ) sho w mor e co oling, and for a shorter duration, than pale o climate r e constructions (Briffa et al., 2001 ;
D’ Arrigo , Wilson, and Jacoby , 2006 ; Frank, Esp er , and Co ok, 2007 ; Mob erg et al., 2005 ). Comp ounding
this uncertainty , the pr e cise timing and lo cation of some v olcanic eruptions o v er the last millennium r e-
main unkno wn (Sigl et al., 2015 ; Ste v enson et al., 2017b ) as do es the magnitude of the radiativ e for cing
(Timmr e ck et al., 2009 ). A critical question is whether this mismatch is an artifact of uncertainties in (1)
the pale o climate pr o xy obser vations, (2) the r e construction pr o cess, (3) the for cing estimates, (4) climate
mo del physics, or (5) a combination ther e of ( Anchukaitis et al., 2012 ; Timmr e ck, 2012 ; D’ Arrigo , Wilson,
and Anchukaitis, 2013 ; LeGrande and Anchukaitis, 2015 ; Stoffe l et al., 2015b ; Ste v enson et al., 2016 ).
Her e w e e xplor e four major sour ces of uncertainty in r e constructions of surface air temp eratur e o v er
the past millennium: spatial co v erage , seasonality , biological memor y , and pr o xy noise . W e do so in
the conte xt of a pale o envir onmental data assimilation (PD A ) frame w ork, the Last Millennium Reanalysis
(LMR, Hakim et al., 2016 ; T ar dif et al., 2019 ), which pr o vides an obje ctiv e basis for combining information
fr om pr o xies and mo dels. W e sho w her e that the discr epancy in Figur e 3.1 b is pr esent in our r e construc-
tion (Figur e 3.1 c), but that it can b e largely r e concile d by accounting for the afor ementione d sour ces of
uncertainty .
3.2 Data and Metho ds
3.2.1 Pale o climate data assimilation
W e apply the pale o envir onmental data assimilation frame w ork of the Last Millennium Reanalysis (LMR,
Hakim et al., 2016 ; T ar dif et al., 2019 ) to b oth pseudopr o xy and r eal pr o xy data netw orks. LMR uses
an offline ensemble data assimilation pr o ce dur e for multivariate climate field r e construction (Steiger et
al., 2014 ), wher e information fr om a prior e xp e ctation of the climate , deriv e d fr om a climate mo del, is
optimally combine d with information fr om pr o xy r e cor ds. The r elativ e w eights ar e determine d fr om the
err or ratio in these tw o estimates of the climate , as define d by the up date e quation in the K alman filter ,
which is optimal if the err ors ar e unbiase d and normally distribute d.
The essential comp onents of the pr o ce dur e ar e (1) e xisting climate mo del data for the prior e xp e cta-
tion, which w e take fr om a last millennium simulation fr om the isotop e-enable d Community Earth System
Mo del (iCESM, Ste v enson et al., 2019 ; Brady et al., 2019 ); (2) pr o xy data netw orks, which w e take fr om the
P A GES 2k phase 2 compilation (P A GES 2k Consortium, 2017 , Figur e S3.1 ) and the Northern Hemispher e
T r e e-Ring Netw ork De v elopment (N TREND ) compilation (Wilson e t al., 2016 ; Anchukaitis et al., 2017 ,
Figur e S3.7 ); and (3) a “for war d op erator” or pr o xy system mo del (PSM), which pr e dicts the pr o xies giv en
the climate state . Her e the for war d op erator is a linear r egr ession pr o ce dur e , univariate on annual temp er-
atur e for corals and ice cor es, univariate on seasonal temp eratur e for maximum late w o o d density r e cor ds,
and bivariate on seasonal temp eratur e and seasonal pr e cipitation for tr e e-ring width r e cor ds, as in T ar dif
51
1400 1500 1600 1700 1800 1900
Year (AD)
0
20
40
60
80
100
120
140
160
Global total stratospheric
sulfate aerosol injection [Tg]
iCESM forcing (Gao et al., 2008)
selected events for iCESM
1600
1641
1673
1693
1815
1835
0
5
10
15
20
25
30
35
40
Volcanic stratospheric sulfur
injection of eruption [Tg S]
eVolv2k_v3 (Toohey and Sigl, 2017)
selected events for LMR (a)
1600
1640
1673
1695
1815
1835
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
NH temp. anom. (K)
GCMs
Reconstructions
(b)
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
NH temp. anom. (K)
GCMs
LMR (all)
LMR (TRW+MXD)
LMR (TRW)
LMR (MXD)
(c)
Figur e 3.1: ( a) Comparison b etw e en the v olcanic for cing ( Gao , Rob o ck, and Ammann, 2008 ) use d in the
isotop e-enable d Community Earth System Mo del (iCESM) simulation (Ste v enson et al., 2019 ; Brady et al.,
2019 ) and the e V olv2k v ersion 3 V olcanic Stratospheric Sulfur Inje ction (VSSI) compilation (T o ohe y and
Sigl, 2017 ). The triangles denote the sele cte d 6 large e v ents b etw e en 1400 and 1850 CE. ( b) Sup erp ose d
ep o ch analysis (SEA ) on simulate d and r e constructe d temp eratur e r esp onse to the 12 str ongest v olcanic
eruptions since 1400 AD , r epr o duce d fr om IPCC AR5 (Masson-Delmotte et al., 2013 ) Figur e 5.8b . ( c) Sup er-
p ose d ep o ch analysis on annual Northern hemispheric mean temp eratur e (NHMT) simulate d by 9 GCMs
(Se ction 3.2.2 , T able S1) and LMR r e constructions assimilating the whole netw ork ( solid black cur v e with
shading), the tr e e-ring netw ork ( dashe d br o wn cur v e), the tr e e-ring width (TRW) netw ork ( solid gr e en
cur v e), and the maximum late w o o d density (MXD ) netw ork ( solid blue cur v e), r esp e ctiv ely . The shading
encompasses the 5% and 95% quantiles of the ensemble , while the cur v es indicate the ensemble me dian
( s e e SI T e xt 3.5.1 for details ab out ensemble scheme).
52
et al. ( 2019 ). Further details of the LMR data assimilation pr o ce dur e for pale o climate r e construction may
b e found in Hakim et al. ( 2016 ).
This study utilizes a fast implementation of the LMR frame w ork, LMRt (Zhu et al., 2019a ) for com-
putational conv enience . A s a b enchmark, a r e construction of the spatiotemp oral variations of surface
temp eratur e o v er the Common Era is conducte d, using iCESM as the mo del prior and the P A GES 2k net-
w ork as obser vations. A s e xp e cte d, the D A pr o ce dur e yields a substantially b etter estimate of the temp oral
variability in the temp eratur e field than the prior , as quantifie d by the p ointwise corr elation with an inde-
p endent instrumental temp eratur e field ( se e Se ction 3.2.2 ) (Figur e S3.2 c, S3.2 d). This r e construction skill
le v el is comparable to a pr e vious implementation of LMR (T ar dif et al., 2019 ), and supp orte d by the similar-
ity b etw e en the r e constructe d NHMT using b oth v ersions of the co de (Figur e S3.2 a). For a mor e in-depth
e valuation of the LMR frame w ork, se e T ar dif et al. ( 2019 ).
T o assess the impact of the choice of prior and enable comparison with the LMR v ersion of r e cor d
(T ar dif et al., 2019 ), w e also teste d assimilation using the CCSM4 simulation of Landrum et al. ( 2012a ) as the
mo del prior . W e find virtually identical r esults, with no significant differ ence dete cte d in the temp eratur e
r esp onse to v olcanic eruptions after 1400 AD ( compar e Figur e S3.2 a to Figur e S3.2 b , Figur e 3.1 c to Figur e
S3.14 a, and Figur e 3.4 a to Figur e S3.14 b).
3.2.2 Simulate d and Instrumental T emp eratur e Obser vations
In or der to compar e pale o climate r e constructions to climate mo dels, w e consider simulations of past mil-
lennium climate fr om the follo wing mo dels: iCESM and CESM1 ( Otto-Bliesner et al., 2015 ), as w ell as
the PMIP3 mo dels (Schmidt et al., 2012 ; Braconnot et al., 2012 ), including BCC CSM1.1 (W u et al., 2014 ),
GISS-E2-R (Schmidt et al., 2006 ), HadCM3 ( Gor don et al., 2000 ), IPSL-CM5A -LR (Dufr esne et al., 2013 ),
MIROC-ESM (W atanab e et al., 2011 ), MPI-ESM-P ( Giorgetta et al., 2013 ), CSIRO (Rotstayn et al., 2012 ), and
CCSM4, as liste d in T able S3.1 .
W e also use tw o sets of instrumental temp eratur e obser vations, including the Berkele y Earth instru-
mental temp eratur e analysis (Rohde et al., 2013 ) and the Go ddar d Institute for Space Studies ( GISS) Surface
T emp eratur e Analysis ( GISTEMP , Hansen et al., 2010 ). GISTEMP and the gridde d pr e cipitation dataset (V6)
fr om the Global Pr e cipitation Climatology Centr e ( GPCC, Schneider et al., 2014 ) ar e also use d for PSM cal-
ibration in the bivariate frame w ork of T ar dif et al. ( 2019 ).
3.2.3 Sup erp ose d ep o ch analysis
Sup erp ose d ep o ch analysis (SEA, Haur witz and Brier , 1981 ) is a fr e quently use d te chnique to assess the
temp eratur e r esp onse to v olcanic eruptions ( A dams, Mann, and Ammann, 2003 ; Masson-Delmotte et al.,
2013 ; Rao et al., 2019a ). It consists of aligning temp eratur e anomaly series to the timing of v olcanic erup-
tions within a fixe d time windo w prior t o and follo wing the e v ent, and av eraging these r esp onses to esti-
mate the typical r esp onse to eruptions. The IPCC AR5 (Figur e 3.1 b) consider e d the r e constructe d temp er-
atur e r esp onse to the 12 str ongest eruptions since 1400 AD . Base d on the temp oral co v erage of available
pr o xies and mo del simulations, as w ell as the scientific kno wle dge of the eruptions, w e sele cte d a smaller
set of 6 large and w ell-date d eruption e v ents o v er the y ears 1600-1850 CE that ar e consistent in timing in
53
b o th the v olcanic for cing use d in iCESM ( Gao , Rob o ck, and Ammann, 2008 ) and the most r e cent compi-
lation of V olcanic Stratospheric Sulfur Inje ction (VSSI, T o ohe y and Sigl, 2017 ) (Figur e 3.1 a). For further
details ab out the sele ction, se e T e xt 3.5.3 . The LMR r esp onse to individual e v ents of the entir e millennium
is sho wn in Figur e S3.10 - S3.12 .
3.3 The Discr epancy and Its Causes
Figur e 3.1 b highlights discr epancies b etw e en mo del simulations and r e constructions in thr e e asp e cts: (1)
the magnitude of the p eak co oling (2) the timing of the p eak co oling (3) the length of the r e co v er y . Sp e cif-
ically , mo del simulations sho w a str onger p eak co oling amplitude , a slightly earlier p eak co oling, and
a shorter r e co v er y inter val than the r e constructions. A similar discr epancy pattern can b e se en when
comparing the LMR r e construction assimilating the P A GES 2k netw ork to the mo del simulations (Figur e
3.1 c). Comparing r esults for solutions assimilating the entir e P A GES 2k netw ork [LMR ( all), solid dark
gray cur v e] to those assimilating only its tr e e-ring r e cor ds [LMR (TRW +MXD ), dashe d br o wn cur v e],
w e se e that most of the r e constructe d v olcanic co oling originates fr om the information captur e d by the
tr e e-ring netw ork. The latter consists of tw o main obser vation typ es: (1) tr e e-ring width (TRW) and (2)
maximum late w o o d density (MXD ). A ssimilating these tw o pr o xy typ es separately , ho w e v er , sho ws dif-
fer ent r esp onses to v olcanism: TRW yields a lagge d p eak co oling y ear and a mor e pr olonge d r e co v er y
than MXD . This suggests that the differ ence b etw e en these tw o pr o xy typ es is ke y to understanding the
differ ent v olcanic co oling patterns in r e constructions.
Pr e vious studies (Timmr e ck et al., 2009 ; Timmr e ck, 2012 ; LeGrande and Anchukaitis, 2015 ; Stoffel et
al., 2015b ; LeGrande , T sigaridis, and Bauer , 2016 ) hav e inv estigate d the comp onents of the PMIP3 mo d-
els that could p otentially r esult in o v er estimate d co oling in simulations. Her e , with a fo cus on pr o xies
and r e constructions, w e inv estigate four factors that w e hyp othesize may account for these differ ences,
motivate d by prior studies and e xisting kno wle dge of the tr e e-ring pr o xy netw ork: (1) spatial co v erage
( Anchukaitis et al., 2012 ; D’ Arrigo , Wilson, and Anchukaitis, 2013 ) (2) seasonality (D’ Arrigo , Wilson, and
Jacoby , 2006 ; Stoffel et al., 2015b ; Anchukaitis et al., 2017 ) (3) biological memor y (Fritts, 1966 ; Krakauer
and Randerson, 2003 ; Frank et al., 2007 ; Esp er et al., 2015 ; Stoffel et al., 2015b ; Zhang et al., 2015 ; Lücke
et al., 2019 ), and (4) non-temp eratur e ‘noise ’ ( v on Stor ch et al., 2004 ; Rie dw yl et al., 2009 ; Neukom et al.,
2018 ).
3.3.1 Spatial co v erage
The P A GES 2k netw ork is comprise d of 336 TRW r e cor ds and 59 MXD r e cor ds o v er the Northern Hemi-
spher e (NH). MXD r e cor ds in P A GES2k ar e mainly limite d to North America and Scandinavia, while the
TRW r e cor ds co v er b oth North America and A sia. Evaluating the corr elation b etw e en the LMR r e construc-
tion and the Berkele y Earth instrumental temp eratur e analysis (Rohde et al., 2013 ) o v er the instrumental
era o v er 1880–2000, w e se e that assimilating the TRW netw ork yields a gr eater impr o v ement o v er the
mo del prior than assimilating the MXD netw ork (Figur es 3.2 a, 3.2 b). Is this differ ence due to the lo cation
54
corr(LMR, BerkeleyEarth), mean=0.36
(a)
corr(LMR, BerkeleyEarth), mean=0.21
(b)
1.0
0.5
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(f)
Figur e 3.2: Differ ences b etw e en P A GES 2k TRW and MXD r e cor ds r egar ding ( a, b) spatial co v erage , ( c,
d) seasonality dete cte d by the algorithm use d in T ar dif et al. ( 2019 ), and ( e , f) biological memor y quantifie d
by the partial auto corr elation function (P A CF). ( a) The spatial co v erage of TRW netw ork. ( c) The optimal
seasonality of the TRW netw ork. ( e) The P A CF of the TRW netw ork. ( b), ( d), and (f) ar e ar e as ( a), ( b), and
( e), r esp e ctiv ely , but for the MXD netw ork. The color contours in ( a, b) indicate the corr elation b etw e en
the LMR r e constructions and the Berkele y Earth instrumental temp eratur e analysis (Rohde et al., 2013 ).
55
or the quantity of each typ e of pr o xy r e cor d? T o inv estigate this question, w e use a pseudopr o xy e xp er-
iment (PPE) (Smer don, 2011 ). W e set the annual iCESM simulate d temp eratur e as our truth, and use it
as mo del prior in the D A frame w ork ( a “p erfe ct mo del” scenario). Pseudopr o xies ar e define d as p erfe ct
temp eratur e r e cor ders at thr e e sets of lo cations: (1) the lo cales of all the 336 NH P A GES 2k TRW r e cor ds
(2) the lo cales of randomly picke d 50 P A GES 2k TRW r e cor ds o v er North America and (3) the lo cales of
randomly picke d 50 P A GES 2k TRW r e cor ds o v er the NH.
The r esult of assimilating these thr e e pseudopr o xy netw orks is sho wn in Figur e S3.3 ( a, b , and c),
sho wing that b etter spatial co v erage yields a mor e accurate r e construction in the PD A frame w ork, with
all ot her things b eing e qual. This is r efle cte d in SEA as w ell: Figur e 3.3 a s ho ws that assimila ting 50 r e cor d s
spr ead thr oughout the NH yields a str onger and mor e accurate p eak co oling amplitude than assimilating
50 r e cor ds concentrate d o v er North America, suggesting that br oad spatial co v erage is mor e imp ortant
than the she er numb er of r e cor ds for r esolving p eak co oling amplitude . Lo cation do es matter to some
degr e e with r egar d to the large-scale tele conne ction patterns, and optimal placement could b e determine d
with the appr oach of Comb oul et al. ( 2015 ), y et this is b e y ond the scop e of this inv estigation.
3.3.2 Seasonality
An implicit assumption in r e constructing annual temp eratur e with tr e e-ring pr o xies is that gr o wing sea-
son temp eratur e is r epr esentativ e of annual temp eratur e (P A GES 2k Consortium, 2017 ). Ho w e v er , the
corr elation b etw e en summer and annual temp eratur es in the Northern Hemispher e is high for the o ceans
but r elativ ely lo w o v er continents (Figur e S3.3 f), wher e the tr e e-ring r e cor ds ar e lo cate d. T r e es r egister
climate primarily during their gr o wing season, which varies as a function of ge ography , sp e cies, and cli-
mate (Fritts, 1966 ; St. Ge orge , 2014 ; St Ge orge and A ult, 2014 ; Wilson et al., 2016 ; Stoffel et al., 2015b ).
Though the P A GES 2k metadat a contain some information ab out the seasonal sensitivity of all pr o xies, w e
follo w T ar dif et al. ( 2019 ) and identify optimal seasonal windo ws of temp eratur e and pr e cipitation for each
pr o xy r e cor d fr om a p o ol of pr e-define d seasonal windo ws. The windo ws ar e optimal in a least squar e
sense , using calibration o v er the historical p erio d. The start and end month of the gr o wing season ( base d
on temp eratur e) thus identifie d ar e sho wn in Figur es 3.2 c, 3.2 d. While in the Northern Hemispher e b oth
TRW and MXD pr o xies r e cor d largely b or eal summer conditions, the opt imal seasonality for TRW is often
br oader but typically less consistent than that for MXD .
A s b efor e , w e use a PPE to inv estigate the impact of gr o wth seasonality on the temp eratur e r e con-
struction. W e generate pseudo-P A GES2k TRW r e cor ds at their r eal lo cations as p erfe ct r e cor ders of lo cal
summer ( JJA ) temp eratur e and p erform e xp eriments targeting b oth JJA temp eratur e and annual temp era-
tur e . A s e xp e cte d, a much b etter r e construction is obtaine d for the b or eal summer temp eratur e field than
annual temp eratur e (Figur es S3.3 d, S3.3 e). This is also e vident in r e constructions using r eal pr o xies and
instrumental temp eratur e (Figur e S3.4 ). Ther efor e , summer-sensitiv e tr e es can only r e construct annual
temp eratur e to the e xtent that the summer and ann ual mean ar e corr elate d. While such seasonal effe cts
r esult in quite differ ent assessments of r e construction fidelity , this differ ence is har dly noticeable in SEA
(Figur e 3.3 b).
56
3.3.3 Biological memor y
Another imp ortant differ ence b etw e en TRW and MXD is biological memor y , wher eby tr e e gr o wth r efle cts
the influence of climate in pr e vious y ears (Fritts, 1966 ; Krakauer and Randerson, 2003 ; Frank et al., 2007 ;
Esp er et al., 2015 ; Zhang et al., 2015 ; Stoffel et al., 2015b ). W e quantify the p ersistence in TRW and MXD
in the P A GES2k using the partial auto corr elation function (P A CF) (Figur e 3.2 e , 3.2 f). A s e xp e cte d (Br eit-
enmoser et al., 2012 ; Esp er et al., 2015 ; Lücke et al., 2019 ), w e find that biological memor y in TRW acr oss
the P A GES2k netw ork is large and significant for lag-1 and lag-2, while for MXD it is limite d. Comparing
the pr o xy comp osites and the corr esp onding av erage instrumental temp eratur e at pr o xy lo c ales, w e se e
that the MXD comp osite captur es contemp orane ous temp eratur e variations, including the accurate tim-
ing of co oling e v ents, while the TRW comp osite app ears to smo oth interannual variability and integrate
temp eratur es o v er 2 to 5 y ears (Figur e S3.5 a, S3.5 b), leading to lagge d and p ersistent co oling e v ents (Frank
et al., 2007 ).
T o inv estigate the impact of such biological memor y on the magnitude of r e constructe d v olcanic co ol-
ing, w e again turn to PPEs. W e simulate a short-term memor y effe ct in TRW by designing pseudopr o xies
as a 5-yr mo ving av erage of the annual temp eratur e simulate d by iCESM, as sho wn in Figur e S3.5 c. A s-
similating these smo othe d pseudopr o xies yields a pr olonge d temp eratur e r e co v er y and a p eak co oling that
is b oth damp e d and lagge d (Figur e 3.3 c, the solid light gr e en cur v e). W e find that this o v erall r esult is not
sensitiv e to the pr e cise design of the filter use d to construct the smo othe d pseudopr o xies, so long as it
captur es this multiple y ear climate integration in some way . The p otential additional influence of soil
moistur e is not dir e ctly mo dele d her e , as these lagge d r elationship ar e obser v e d in temp eratur e-sensitiv e
TRW chr onologies irr esp e ctiv e of the p otential additional influence of soil moistur e (Franke et al., 2013 ;
Consortium, 2017 ), which w e confirm in sen sitivity e xp eriments (Figur e S3.15 ).
3.3.4 Pr o xy system noise
So far , our PPEs hav e emplo y e d noiseless temp eratur e r e cor ders for simplicity ( a signal-to-noise ratio
(SNR) of infinity , wher ein SNR is define d as the ratio of the standar d de viation of signal and that of noise ,
follo wing e xisting practice Smer don ( 2011 )). In r eality , of course , pr o xies ar e imp erfe ct r e cor ders of cli-
mate conditions. T o make the PPEs mor e r ealistic, w e no w add uncorr elate d Gaussian white noise to the
pr e viously describ e d pseudo-P A GES2k TRW r e cor ds. Using a l inear r egr ession pr o ce dur e , w e estimate a
SNR ar ound 0.3 (Figur e S3.6 ), which is comparable to the estimate of W ang et al. ( 2014 ). Since w e hav e al-
r eady emulate d the biological memor y utilizing the mo ving av erage filter , w e consider white noise instead
of r e d noise to av oid adding mor e memor y into the pseudopr o xies. The addition of noise to the pr e vious
case yields a mor e similar SEA pattern (Figur e 3.3 c, solid dark gr e en cur v e) to the r eal-w orld case (Figur e
3.1 c, solid gr e en cur v e): a mor e damp e d and pr olonge d r e co v er y compar e d to the noiseless case .
Considering the four factors ab o v e , w e ar e thus able to simulate the obser v e d discr epancy b etw e en
mo dele d and r e constructe d NH temp eratur e r esp onse to v olcanic eruptions. Can this kno wle dge b e use d
to minimize this discr epancy?
57
5 0 5 10
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LMR (perfect)
LMR (smoother)
LMR (.. + noise)
(c)
Figur e 3.3: SEA in pseudopr o xy e xp eriments, e valuating the impact of ( a) spatial co v erage , ( b)
seasonality , and ( c) biological memor y and noise . ( a) the r e d cur v e denotes the target, and the dashe d
light gr e en cur v e , the solid dark gr e en cur v e , and the solid light gr e en cur v e indicate the LMR r e construc-
tion assimilating 336 pseudo-P A GES2k TRW r e cor ds o v er the NH, 50 r e cor ds o v er North America, and 50
r e c or ds o v er the NH, r esp e ctiv ely . ( b) The solid r e d cur v e denotes the annual target, the dashe d r e d cur v e
denotes the b or eal summer target, and the gr e en cur v es indicate the LMR annual and summer r e construc-
tions assimilating the pseudo-P A GES2k TRW netw ork, r esp e ctiv ely . ( c) The solid r e d cur v e denotes the
annual target, and the gr e en cur v es denote the LMR r e construction assimilating pseudo-P A GES2k TRW
as p erfe ct temp eratur e r e cor ders ( dashe d), and temp eratur e smo others ( solid). The case of smo othe d tem-
p eratur e with adde d Gaussian noise (SNR=0.3) is in dark gr e en. All the r e construction cur v es r efer to the
ensemble me dian ( se e SI T e xt 3.5.1 for details ab out the ensemble design).
3.3.5 Re conciling the discr epancy
In the pr esent conte xt, noise r efle cts any non-temp eratur e influence on the pr o xy systems, including other
climate influences like soil moistur e , or biophysical pr o cesses that cannot b e ade quately mo dele d due
due to insufficient scientific kno wle dge , limite d input data, or b oth. The first thr e e factors can, ho w e v er ,
b e corr e cte d: to account for the limite d spatial co v erage , w e p erform SEA at pr o xy lo cations instead of
the whole NH; to minimize the seasonal bias, w e target b or eal summer temp eratur e instead of annual
temp eratur e; and to mitigate memor y effe cts, w e assimilate MXD r e cor ds only , leaving out TRW and
mixe d chr onologies. A s a r esult, w e ar e able to almost entir ely account for the pr o xy–mo del discr epancy
in Figur e 3.1 with the P A GES 2k netw ork (Figur e 3.4 a, Figur e S3.11 ). The same strategy can b e use d for other
pr o xy netw orks. For comparison, applying it to the N TREND netw ork (Wilson et al., 2016 ; Anchukaitis et
al., 2017 ) (Figur e S3.7 ) yields similar agr e ement b etw e en simulate d and r e constructe d temp eratur e (Figur e
3.4 b , Figur e S3.12 ). These r esults stand in sharp contrast to r esults wher e spatial co v erage , seasonality , and
biological memor y ar e not taken into account (Figur e S3.8 ).
That the discr epancy in Figur e 3.1 b can b e largely r e concile d by accounting for kno wn characteristics
of the pr o xy data is r eassuring, and b o des w ell for using v olcanic eruptions of the past millennium as a
test b e d for climate mo dels. W e no w discuss the br oader implications of this r esult.
58
5 0 5 10
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Figur e 3.4: ( a) Same as Figur e 3.1 c, after r esolving differ ences in the mo del and pr o xy domains asso ciate d
with seasonality , spatial distribution, and biological memor y . ( b) Same as ( a) but using the N TREND MXD
netw ork. A v ersion of this figur e sho wing each mo del simulation is available in Figur e S3.9 , and one u sing
mor e eruption e v ents is available in Figur e S3.13
3.4 Discussion
Using r e cent pr o xy compilations and climate field r e construction te chniques, w e hav e demonstrate d that
it is p ossible to largely r esolv e the discr epancy b etw e en the simulate d and r e constructe d temp eratur e
r esp onse to e xplosiv e v olcanism since 1600 CE. W e find that this gap was the r esult of four main factors:
spatial co v erage , pr o xy seasonality , biological memor y , and pr o xy noise . While pr o xy noise is difficult
to account for in mo del-data inter comparisons, the first thr e e factors can b e , if car e is taken in e valuating
comparable quantities. In particular , since our r e constructions ar e mor e r eliable at lo cations wher e pr o xies
ar e available than at distal lo cations ( Anchukaitis et al., 2017 ), carr ying out the comparison at pr o xy sites is
a simple and effe ctiv e way to r e duce the mismatch. That this is also true in the data assimilation frame w ork
(Steiger et al., 2014 ) suggests that e xpanding the spatial e xtent of pr o xy netw ork is ne cessar y to r esolv e
global-scale patterns. For v er y large eruptions such as the 1257 Samalas eruption, the 1450s eruptions,
and the 1815 T amb ora eruption, ho w e v er , significant mismatches r emain b etw e en mo del simulations and
r e c onstructions e v en when these factors ar e accounte d for (Figur e S3.11 , S3.12 ). While this has little impact
in a comp osite o v er all e v ents (Figur e S3.13 ), it warrants discussion.
Pr e vious w ork and our o wn analysis suggests thr e e major causes: (1) pr o xy attrition, (2) aer osol mi-
cr ophysics in mo dels, and (3) uncertainties in v olcanic for cing.
(1) In the absence of r eliable pr o xy data, offline data assimilation r e v erts to the mo del prior for its esti-
mate of climate . This r esults in generally damp e d variations in p erio ds of r e duce d and/or noisy co v erage ,
as se en by comparing the first to se cond millennium CE in Figur es S3.2 a and S3.2 b . Her e w e hav e mitigate d
this pr oblem by fo cusing on the r e cent p erio d with r elativ ely high pr o xy co v erage , but it is undoubte dly
59
an ingr e dient in the mismatch obser v e d for earlier eruptions like Samalas, when r elativ e fe w pr o xies ar e
available , esp e cially MXD r e cor ds (Figur es S3.1 b and S3.16 a).
(2) Some CMIP5-era GCMs pr o duce o v erly str ong r esp onses to v olcanic for cing due to unr ealistic r ep-
r esentation of aer osol micr ophysics (Timmr e ck et al., 2009 ; Timmr e ck, 2012 ; Stoffel et al., 2015b ; LeGrande ,
T sigaridis, and Bauer , 2016 ). Both Timmr e ck et al. ( 2009 ) and Stoffel et al. ( 2015b ) suggest that the discr ep-
ancy is cause d by the simplistic assumption use d in PMIP3 mo dels that aer osol optical depth is linearly
scale d to ice-cor e sulfate concentration. This assumption uses the 1991 Pinatub o eruption as the r efer ence ,
and is is unlikely to b e valid for many significantly larger eruptions. A s sho wn by Stoffel et al. ( 2015b ),
accounting e xplicitly for self-limiting aer osol micr ophysical pr o cesses can r e concile this discr epancy , an
idea later confirme d by Guillet et al. ( 2017 ) with b oth do cumentar y and tr e e-ring data.
(3) Many PMIP3 mo dels use d the Gao , Rob o ck, and Ammann ( 2008 ) for cing dataset, wher e the r e con-
structe d Samalas ae or osol loading was e xce e dingly large , and has since b e en r e vise d do wnwar d ( Jungclaus
et al., 2017 ). Ther e is also lingering uncertainty as to the magnitude , timing, and lo cation of tw o major
e v ents during the 1450s (Sigl et al., 2015 ; T o ohe y and Sigl, 2017 ; Hartman et al., 2019 ). Besides, appar ent
co oling fr om a 1761 eruption in some mo del simulations is actually the r esult of the misalignment of the
1783 for cing in the uncorr e cte d v ersion of the Gao , Rob o ck, and Ammann ( 2008 ) for cing (Ste v enson et al.,
2017b ). Regar dless of changes in physics, the r e vision in v olcanic for cing alone w ould help to r e duce the
discr epancy .
Pr ogr ess in r epr esenting v olcanic for cing (T o ohe y and Sigl, 2017 ; A ubr y et al., 2019 ), as w ell as im-
pr o v ements in mo del r esolution and pr o cesses ( e .g. activ e stratospheric chemistr y ) in PMIP4 (K age yama
et al., 2018 ) may lead to closer mo del-data matches in futur e w ork. Regar dless of these factors, our analysis
suggests that a critical ingr e dient of minimizing the mo del-r e construction mismatch is to e valuate simu-
late d temp eratur e at the times and places wher e it is r e cor de d by the pr o xy sensors ( Anchukaitis et al.,
2012 ). Naturally , past temp eratur e estimates may b e impr o v e d as w ell. While this study has fo cuse d on
the uncertainties in pr o xy measur ements in the conte xt of pale o envir onmental data assimilation, mor e
w ork should b e done to r e duce sour ces of uncertainty within the data assimilation metho d itself, such
as the for war d op erator err or , the mo del prior , and the lo calization scheme , as the coupling of all these
uncertainty sour ces can p otentially affe ct the SEA comparison. In particular , for war d op erators that allo w
for non-contemp orane ous influences of the state on the pr o xies [ e .g. time-integration, as is b elie v e d to
b e the case for TRW (Fritts et al., 1991 ; V agano v , Hughes, and Shashkin, 2006 )] w ould enable us to make
b e tter use of the information containe d in TRW r e cor ds. While such pr o cess-oriente d mo dels hav e b e en
de v elop e d (T olwinski- W ar d et al., 2011a ; Evans et al., 2013 ), their application to the D A conte xt is contin-
gent up on accurate sp e cification of obser vation err or variance and corr e cting for biases in the mo del prior .
Both tasks r emain activ e r esear ch ar eas (De e et al., 2016a ).
With r egar d to pr o xies, w e hav e confirme d that the lagge d co oling e xhibite d in pr e vious r e construc-
tions can b e e xplaine d as the conse quence of their using TRW r e cor ds. Other pr o xies that integrate climate
information o v er multiple y ears ( e .g. bioturbate d se diments) likely hav e a similar impact in multipr o xy
r e c onstructions. Since MXD r e cor ds ar e mor e faithful pale o-temp eratur e sensors than TRW r e cor ds (Es-
p er et al., 2015 ; Esp er et al., 2018 ), w e join others in calling for incr ease d colle ction and de v elopment of
MXD r e cor ds ( Anchukaitis et al., 2017 ; St. Ge orge and Esp er , 2019 ), particularly at lo cations wher e the y
60
ar e pr esently absent or co v er only part of the last millennium, e .g. the North American tr e eline and at
high ele vations in A sia ( Anchukaitis et al., 2017 ; Esp er et al., 2018 ).
While our appr oach r e conciles the discr epancy b etw e en mo del and pr o xy estimates of the surface
temp eratur e to mo derate eruptions of the last 400 y ears, imp ortant differ ences r emain for large e v ents
like T amb ora or Samalas. For such eruptions, impr o v e d estimates of the for cing, a mor e r ealistic mo del
r epr esentation of aer osol micr ophysics, and – for e v ents sparsely sample d by e xisting pr o xy netw ork – an
e xpande d pr o xy co v erage may b e ne cessar y r esolv e e xtant differ ences. Futur e w ork will help elucidate the
r elativ e r ole of these thr e e factors on this particular comparison.
3.5 Supplementar y Information
3.5.1 Settings of the LMR frame w ork
The r e construction e xp eriments in this study follo w the general settings:
• Mo del prior: the isotop e-enable d Community Earth System Mo del (iCESM) simulation (Ste v enson
et al., 2019 ; Brady et al., 2019 ) is use d as the mo del prior . W e hav e also teste d using the CCSM4 last
millennium simulation (Landrum et al., 2012a ) as mo del prior (Figur e S3.2 a, S3.14 ) and no significant
differ ence is dete cte d in the temp eratur e r esp onse to v olcanic eruptions after 1400 AD .
• Ensemble design: 50 Monte Carlo iterations, each using a differ ent randomly chosen 100-memb er
ensemble states fr om the mo del prior , and 75% of randomly chosen available pr o xy r e cor ds for as-
similation (25% for indep endent v erification). This scheme was chosen and e xplaine d in Hakim et al.
( 2016 ) to balance the ne e ds of accuracy and uncert ainty quantification.
• Lo calization scheme: the Gaspari-Cohn lo calization function ( Gaspari and Cohn, 1999 ) is use d with
a radius of 25,000 km (T ar dif e t al., 2019 ).
• For war d op erator: A s in T ar dif et al. ( 2019 ), w e use seasonal bivariate (temp eratur e and moistur e)
linear r egr ession for tr e e-ring width (TRW) r e cor ds, seasonal univariate (temp eratur e) linear r e-
gr ession for maximum late w o o d density (MXD ) r e cor ds, and annual univariate (temp eratur e) linear
r egr ession for all other pr o xy typ es as the for war d op erator in r eal pr o xy e xp eriments. The for war d
op erator is calibrate d against the Go ddar d Institute for Space Studies ( GISS) Surface T emp eratur e
Analysis ( GISTEMP) (Hansen et al., 2010 ) instrumental obser vation and the gridde d pr e cipitation
dataset fr om the Global Pr e cipitation Climatology Centr e ( GPCC, Schneider et al., 2014 ) o v er the
timespan 1850-2015. In pseudopr o xy e xp eriments (PPE) the for war d op erator changes accor ding to
the e xp eriment ( se e main te xt), and is calibrate d against the mo del’s true state o v er the same inter val.
3.5.2 Re constructions using the Northern Hemispher e T r e e-Ring Netw ork De v elopment
(N TREND ) netw ork
The Northern Hemispher e T r e e-Ring Netw ork De v elopment (N TREND ) (Wilson et al., 2016 ; Anchukaitis
et al., 2017 ) consists of 54 tr e e-ring chr onologies spanning parts of North America and Eurasia. Of those
61
54 chr onologies, 1 8 ar e pur e maximum late w o o d density (MXD ), 13 ar e pur e tr e e-ring width (TRW), and
23 ar e mixe d comp osites of MXD and TRW . The spatiotemp oral sampling is sho wn in Figur e S3.7 a, S3.7 b .
A s a b enchmark, w e first assimilate the whole N TREND netw ork using the e xp ert-curate d seasonality ,
and the sup erp ose d ep o ch analysis (SEA ) sho ws a similar discr epancy pattern as in IPCC AR5 Figur e 5.8b
(Masson-Delmotte et al., 2013 , Figur e S3.8 ).
Applying our strategy for gap-bridging describ e d in the main te xt, w e assimilate only the 18 pur e MXD
r e c or ds, and r e construct the b or eal summer temp eratur e field, and then p erform SEA at pr o xy lo cales. The
r esult is sho wn in Figur e 3.4 b , which sho ws a b etter agr e ement b etw e en mo del simulations and the LMR
r e c onstruction. Note that since 18 r e cor ds ar e v er y fe w , w e assimilate all the r e cor ds in each ensemble
memb er of assimilation, yield quite narr o w uncertainty bands.
3.5.3 Choice of eruption ke y dates
Be cause sup erp ose d ep o ch analysis is an av eraging op eration, it inv olv es a trade off b etw e en, on the one
hand, maximizing the numb er of eruption ke y dates to r e duce uncertainties, and on the other hand con-
siderations particular to each eruption.
W e chose to e xclude eruptions after 1850 b e cause the PMIP3 past1000 pr oto col co v ers only the p erio d
(850-1850), and w e wante d to b e able to compar e the gr eatest numb er of simulations to r e constructions.
When a cluster of eruptions ar e close to each other within 10 yrs, w e sele ct only the last one to av oid
conflating the r esp onse of one eruption within the r e co v er y for a pr e ce ding e v ent. Note that not all PMIP3
simulations use the same v olcanic for cing dataset (Schmidt et al., 2012 ), and that all differ fr om the mor e
r e c ent estimates of T o ohe y and Sigl ( 2017 ), which is a sour ce of differ ences b etw e en simulations, and
b e tw e en simulations and r e constructions. Also note that neither 1452 nor 1459 (formerly attribute d to
the Kuwae caldera) is sele cte d. A ccor ding to T o ohe y and Sigl ( 2017 ), the 1452 e v ent in Gao , Rob o ck, and
Ammann ( 2008 ) was misaligne d and is actually the 1459 e v ent, so one should sele ct the 1452 e v ent instead of
the 1459 e v ent for GCM simulations. Ho w e v er , considering that the 1452 e v ent is close to the 1459 e v ent,
w e chose to skip b oth to av oid intr o ducing an obvious discr epancy sour ce for the comparison b etw e en
GCM simulations and LMR r e constructions. A dditionally , the 1761 and 1783 e v ents ar e also skipp e d due
to issue of misalignment accor ding to Ste v enson et al. ( 2017b ) and Lücke et al. ( 2019 ).
3.5.4 Softwar e
All the analysis in this study was p erforme d in the op en-sour ce Python pr ogramming language (V an
Rossum and Drake Jr , 1995 ), v ersion 3.7, with the follo wing packages:
• numpy (W alt, Colb ert, and V ar o quaux, 2011 )
• scipy (Virtanen et al., 2019 )
• pandas (McKinne y , 2010 )
• statsmodels (Seab old and Perktold, 2010 )
• matplotlib (Hunter , 2007 )
62
• seaborn (W askom et al., 2018 )
All r e constructions w er e p erforme d with the Last Millennium Reanalysis fast implementation ( LMRt ),
of Zhu et al. ( 2019a ). This implementation yields nearly identical r esults compar e d to the official r e con-
struction (Figur e S3.2 a), but with additional featur es:
• Gr eater fle xibility
– Easy installation
– Easy imp orting and usage in Jup yter noteb o oks
– Easy setup for differ ent priors, pr o xies, and Pr o xy System Mo dels (PSMs)
• Faster sp e e d
– Much faster PSM calibration due to optimization of algorithm
– Easy parallel computing with multipr o c essing and other te chniques
• Mor e mo dular co de structur e
Bivalve_d18O (n=1)
Corals and Sclerosponges_Rates (n=8)
Corals and Sclerosponges_SrCa (n=25)
Corals and Sclerosponges_d18O (n=60)
Ice Cores_MeltFeature (n=1)
Ice Cores_d18O (n=31)
Ice Cores_dD (n=7)
Lake Cores_Misc (n=3)
Lake Cores_Varve (n=6)
Tree Rings_WidthPages2 (n=347)
Tree Rings_WoodDensity (n=59)
(a)
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
0
100
200
300
400
500
number of proxies
Tree Rings_WidthPages2
Corals and Sclerosponges_d18O
Tree Rings_WoodDensity
Ice Cores_d18O
Corals and Sclerosponges_SrCa
Corals and Sclerosponges_Rates
Ice Cores_dD
Lake Cores_Varve
Lake Cores_Misc
Ice Cores_MeltFeature
Bivalve_d18O
(b)
Figur e S3.1: Data fr om the P A GES 2k netw ork (P A GES 2k Consortium, 2017 ) assimilate d in LMR .
( a) Spatial co v erage by ar chiv e typ e . ( b) T emp oral availability by ar chiv e typ e .
63
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
1
0
1
NHMT anom. (K)
LMRt (iCESM prior)
iCESM
(b)
corr(iCESM, BerkeleyEarth), mean=0.14
(c)
corr(LMR, BerkeleyEarth), mean=0.53
(d)
1.0
0.5
0.0
0.5
1.0
r
0 250 500 750 1000 1250 1500 1750 2000
Year (AD)
1.0
0.5
0.0
0.5
1.0
NHMT anom. (K)
LMRv2.1 (CCSM4 prior) LMRt (CCSM4 prior)
(a)
Figur e S3.2: ( a) The r e constructe d northern hemispher e mean temp eratur e (NHMT) series using the official LMR
implementation (T ar dif et al., 2019 ) and the lightw eight implementation use d in our study LMRt (Zhu et al., 2019a ),
using the same CCSM4 mo del prior (Landrum et al., 2012a ) and the P A GES 2k phase 2 dataset (P A GES 2k Consortium,
2017 ). ( b) The LMR r e constructe d NHMT series assimilating the P A GES 2k netw ork, along with its mo del prior , the
simulate d NHMT series fr om the isotop e-enable d Community Earth System Mo del (iCESM, Ste v enson et al., 2019 ;
Brady et al., 2019 ). ( c) The corr elation b etw e en the surface temp eratur e simulate d by iCESM and the instrumental
obser vation Berkele y Earth instrumental temp eratur e analysis (Rohde et al., 2013 ) o v er 1880 to 2000. ( d) Same as ( b)
but for LMR r e construction assimilating the P A GES 2k netw ork. The symb ols follo w that in Figur e S3.1 .
64
corr(LMR, iCESM annual), mean=0.63
(a)
corr(LMR, iCESM annual), mean=0.43
(b)
corr(LMR, iCESM annual), mean=0.55
(c)
1.0
0.5
0.0
0.5
1.0
r
corr(LMR, iCESM JJA), mean=0.53
(d)
corr(LMR, iCESM annual), mean=0.41
(e)
corr(iCESM annual, iCESM JJA), mean=0.70
(f)
1.0
0.5
0.0
0.5
1.0
r
Figur e S3.3: The pseudopr o xy e xp eriments (PPEs) that indicate the impact of spatial co v erage and
seasonality on the corr elation b etw e en r e construction and the pseudo-truth. ( a) The pseudopr o x-
ies ar e generate d as p erfe ct temp eratur e r e cor ders of the annual temp eratur e simulate d by iCESM, and the
whole netw ork is assimilate d. ( b) Same as ( a), but only 50 r e cor ds o v er North America (NA ) r egion ar e
assimilate d. ( c) Same as ( a), but only 50 r e cor ds o v er Northern Hemispher e (NH) ar e assimilate d. ( d) Same
as ( a), but the pseudopr o xies ar e generate d as p erfe ct temp eratur e r e cor ders of the summer temp eratur e
simulate d by iCESM, and summer temp eratur e field is r e constructe d. ( e) Same as ( d), but annual tem-
p eratur e field is r e constructe d. (f) The corr elation b etw e en annual temp eratur e and summer temp eratur e
simulate d by iCESM.
T able S3.1: Last millennium mo del simulations consider e d in this study
Mo del Exp eriment ID
iCESM (Ste v enson et al. , 2019 ; Brady et al., 2019 ) -
CESM1 ( Otto-Bliesner et a l., 2015 ) b .e11.BLMTRC5CN.f19_g16.001
BCC CSM1.1 (W u et a l., 2014 ) past1000_r1i1p1
GISS-E2-R (Schmidt et al., 2006 ) past1000_r1i1p1
HadCM3 ( Gor don et al., 2000 ) past1000_r1i1p1
IPSL-CM5A -LR (Dufr esne et al., 2013 ) past1000_r1i1p1
MIROC-ESM (W atanab e e t al., 2011 ) past1000_r1i1p1
MPI-ESM-P ( Giorgetta et al. , 2013 ) past1000_r1i1p1
CSIRO (Rotstayn et a l., 2012 ) past1000_r1i1p1
CCSM4 (Landrum et al. , 2012a ) past1000_r1i1p1
65
corr(LMR, BerkeleyEarth), mean=0.21
(a)
corr(LMR, BerkeleyEarth), mean=0.22
(b)
1.0
0.5
0.0
0.5
1.0
r
Figur e S3.4: Impact of seasonality on the corr elation b etw e en the r e constructions assimilating the MXD
netw ork and the Berkele y Earth instrumental temp eratur e analysis (Rohde et al., 2013 ). ( a) Re constructing
annual temp eratur e ( b) Re constructing summer temp eratur e . Note that b oth e xp eriments use r eal, not
pseudo , pr o xies.
66
1900 1910 1920 1930 1940 1950 1960 1970 1980
Year (AD)
0.5
0.0
0.5
1.0
Value
Correlation between GISTEMP seasonal temp and NH TRW records (n=336)
temp @ TRW locs
TRW (r=0.13)
(a)
1900 1910 1920 1930 1940 1950 1960 1970 1980
Year (AD)
2
1
0
1
2
Value
Correlation between GISTEMP seasonal temp and NH MXD records (n=59)
temp @ MXD locs
MXD (r=0.74)
(b)
1900 1910 1920 1930 1940 1950 1960 1970 1980
Year (AD)
2
1
0
1
2
Value
Correlation between iCESM annual temp and pseudo-TRW records
temp @ pseudo-TRW locs
TRW (r=0.61)
(c)
Figur e S3.5: ( a) The NH TRW comp osites compar e d to the seasonal obser vational temp eratur e , the Go ddar d
Institute for Space Studies ( GISS) Surface T emp eratur e Analysis ( GISTEMP , Hansen et al., 2010 ), at pr o xy
lo cales. ( b) Same as ( a), but for MXD . ( c) The comp osite of the pseudopr o xy t hat is generate d as temp eratur e
smo other with a 5-yr mo ving av erage filter , compar e d to the iCESM simulate d temp eratur e at the pr o xy
lo cales.
67
0.00 0.25 0.50 0.75 1.00
SNR
0
25
50
75
100
number of records
SNR distribution
Tree Rings_WidthPages2 (median=0.27)
Tree Rings_WoodDensity (median=0.63)
Figur e S3.6: The signal-to-noise ratio (SNR) in TRW (T r e e Rings_WidthPages2) and MXD (T r e e Rings_-
W o o dDensity ) r e cor ds dete cte d by the for war d op erator calibration pr o ce dur e ( se e SI T e xt 3.5.1 for details)
that follo ws T ar dif et al. ( 2019 ) in LMR, with curate d pr e-define d seasonal windo ws. Higher SNR indicates
mor e fraction of signal can b e e xplaine d by seasonal temp eratur e and moistur e via bivariate and univariate
linear r egr ession.
68
TRW (n=13)
MXD (n=18)
MIX (n=23)
(a)
1000 1500 2000
Year (AD)
0
10
20
30
40
50
number of proxies
TRW
MXD
MIX
(b)
1 2 3 4 5 6 7 8 910
Lag
0
1
PACF
NTREND TRW (n=13)
(c)
1 2 3 4 5 6 7 8 910
Lag
0
1
NTREND MXD (n=18)
1 2 3 4 5 6 7 8 910
Lag
0
1
NTREND MIX (n=23)
Figur e S3.7: The Northern Hemispher e T r e e-Ring Netw ork De v elopment (N TREND , Wilson et al., 2016 ;
Anchukaitis et al., 2017 ). ( a) The spatial co v erage of each pr o xy typ e . ( b) The temp oral availability of each
pr o xy typ e . ( c) The partial auto corr elation function (P A CF) up to lag-10 for each pr o xy typ e .
69
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
NH temp. anom. (K)
GCMs
LMR (NTREND)
Figur e S3.8: The comparison b etw e en the mo del simulate d temp eratur e r esp onse and the LMR r e construc-
tion assimilating the whole N TREND netw ork. SEA applie d on the annual NHMT o v er the whole NH.
5 0 5 10
Years relative to event year
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
temp. anom. at proxy locales (K)
GCMs
LMR (PAGES2k)
(a)
5 0 5 10
Years relative to event year
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
GCMs
LMR (NTREND)
bcc
GISS
HadCM3
IPSL
MIROC
MPI-ESM-P
CSIRO
CCSM4
iCESM
CESM-LME
(b)
Figur e S3.9: Similar to Figur e 3.4 , but with the r esult of each mo del simulation plo tte d out.
70
Figur e S3.10: The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
whole P A GES 2k Netw ork and GCM simulations, targeting NHMT . The blue title denotes the 6 eruption
e v ents that ar e sele cte d for SEA in our study .
71
Figur e S3.11: The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
P A GES 2k MXD Netw ork and GCM simulations, targeting mean summer temp eratur e at pr o xy lo cales.
The blue title denotes the 6 eruption e v ents that ar e sele cte d for SEA in our study .
72
Figur e S3.12: The temp eratur e r esp onse to individual eruptions in LMR r e constructions assimilating the
N TREND MXD Netw ork and GCM simulations, targeting mean summer temp eratur e at pr o xy lo cales. The
blue title denotes the 6 eruption e v ents that ar e sele cte d for SEA in our study .
73
5 0 5 10
Years relative to event year
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
temp. anom. at proxy locales (K)
GCMs
LMR (PAGES2k)
(a)
5 0 5 10
Years relative to event year
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
GCMs
LMR (NTREND)
(b)
Figur e S3.13: Same as Figur e 3.4 , but SEA takes all eruption e v ents liste d in Figur e S3.10 .
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
T anom. (K)
GCMs
LMR (all)
LMR (TRW+MXD)
LMR (TRW)
LMR (MXD)
(a)
5 0 5 10
Years relative to event year
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
temp. anom. at proxy locales (K)
GCMs
LMR (PAGES2k)
(b)
Figur e S3.14: ( a) Same as Figur e 3.1 c, but using CCSM4 as prior . ( b) Same as Figur e 3.4 a, but using CCSM4
as prior .
74
5 0 5 10
Years relative to event year
0.6
0.4
0.2
0.0
0.2
T anom. (K)
GCMs
LMR (TRW, bivariate PSM)
LMR (TRW, univariate PSM)
Figur e S3.15: Same as Figur e 3.1 c, but using CCSM4 as prior and only sho wing the r e constructions assim-
ilating the P A GES2k TRW netw ork, with b oth bivariate and univariate for war d op erator calibration. The
comparison indicates that moistur e information do es not alle viate the issue of lagge d r esp onse to v olcan-
ism in TRW r e cor ds.
75
Proxies w/ start year <= 1257 AD (n=132)
Bivalve_d18O (n=1)
Ice Cores_MeltFeature (n=1)
Ice Cores_d18O (n=23)
Ice Cores_dD (n=4)
Lake Cores_Misc (n=3)
Lake Cores_Varve (n=5)
Tree Rings_WidthPages2 (n=86)
Tree Rings_WoodDensity (n=9)
(a)
Ages of PAGES2k records
(b)
0
200
400
600
800
1000
age [yrs]
Figur e S3.16: ( a) Same as Figur e S3.1 a, but for pr o xies with start y ear older than or e qual to 1257 AD . The
shap es and colors denote each pr o xy typ e . ( b) A ges of P A GES2k r e cor ds. The shap e is same as in ( a), while
the colors denote differ ent ranges of age .
76
Chapter 4
A r e-appraisal of the ENSO r esp onse to v olcanic for cing
Abstract
The p otential for e xplosiv e v olcanism to affe ct the state of the El Niño-Southern Oscillation (ENSO ) has
b e en debate d since the 1980s. Se v eral obser vational studies, largely base d on tr e e rings, hav e since found
supp ort for a p ositiv e ENSO phase in the y ear follo wing large eruptions. Mo dels of differ ent comple xities
also simulate such a r esp onse , dete ctable ab o v e the backdr op of internal variability – though the y disagr e e
on the underlying me chanisms. In contrast, r e cent coral data fr om the heart of the tr opical Pacific suggest
no uniform ENSO r esp onse to all eruptions o v er the last millennium. Her e w e le v erage pale o climate data
assimilation to integrate the latest pale o climate e vidence into a consistent dynamical frame w ork and r e-
appraise this r elationship . Our analysis finds only a w eak statistical asso ciation b etw e en v olcanism and
ENSO , suggestiv e of either no causal asso ciation, or of an insufficient numb er of large v olcanic e v ents o v er
the past millennium to obtain r eliable statistics. While curr ently available obser vations do not supp ort the
mo del-base d infer ence that tr opical eruption s pr omote an ENSO r esp onse , ther e ar e hints of a r esp onse
to hemispherically asymmetric for cing, consistent with the ”I T CZ shift” me chanism. W e discuss the dif-
ficulties of conclusiv ely establishing a v olcanic influence on ENSO giv en the many degr e es of fr e e dom
affe cting the r esp onse , including eruption season, spatial characteristics of the for cing, and ENSO phase
pr e conditioning.
4.1 Intr o duction
The El Niño-Southern Oscillation (ENSO ), the quasi-p erio dic alternation of warm and cold phases of the
tr opical Pacific o cean-atmospher e system, is the leading sour ce of global interannual climate variability
(Sarachik and Cane , 2010 ). ENSO influences w eather conditions not only in the tr opical Pacific (McP haden,
Le e , and McClurg, 2011 ), but also globally thr ough atmospheric tele conne ctions (Diaz, Ho erling, and E is-
cheid, 2001 ). Skillful pr e diction of the ENSO cy cle , including its phase and amplitude , is ther efor e ke y to
the successful for e casting of w orldwide mete or ological and o ceanographic conditions at sub-seasonal to
seasonal scales.
Zhu, F ., Emile‐Geay , J., Anchukaitis, K. J., Hakim, G., Wittenb erg, A. T ., Morales, M. S., & King, J. (2021). V olcano es and
ENSO: a r e-appraisal with the Last Millennium Reanalysis. Natur e Communications. In Re vie w . https://doi.org/10.21203
/rs.3.rs- 130239/v1
77
External for cing has the p otential to affe ct ENSO variability (Mann et al., 2005 ). In particular , e x-
plosiv e v olcanism may inje ct large amounts of sulfate aer osols into the atmospher e , abruptly r e ducing
incoming shortwav e radiation and affe cting the subse quent global o cean-atmospher e climate variability
for se v eral y ears (Rob o ck, 2000 ). A causal r elationship b etw e en large eruptions and ENSO w ould b e a
significant sour ce of climate pr e dictability on interannual scales, and w ould b e imp ortant for e valuating
climate mo dels’ sensitivity to v olcanic for cing, as w ell as assessing the risk of ge o engine ering solar radi-
ation management schemes that emulate the stratospheric sulfate aer osol loading characteristic of large
e xplosiv e eruptions (Rob o ck et al., 2009 ). The link b etw e en v olcanism and ENSO has b e en vigor ously de-
bate d since it was first pr op ose d(Handler , 1984 ). Since then, se v eral tr e e-ring base d obser vational studies
hav e found supp ort for an El Niño-like r esp onse in the y ear follo wing large eruptions ( A dams, Mann, and
Ammann, 2003 ; McGr egor , Timmermann, and Timm, 2010 ; Li et al., 2013 ; W ahl et al., 2014 ; McGr egor
et al., 2020 ) and at least fiv e me chanisms hav e b e en pr op ose d to account for this r elationship: (i) the o cean
dynamical thermostat ( OD T) ( Clement et al., 1996 ; Mann et al., 2005 ; Emile-Geay et al., 2008 ), which states
that the up w elle d water in the eastern Pacific (EP) makes the r egion less sensitiv e to radiativ e for cing than
the w estern Pacific, and leads to nonuniform Pacific SST r esp onse to uniform incoming solar radiation
r e d uctions after eruptions; (ii) the land-o cean temp eratur e gradient (LO T G) me chanism ( Ohba et al., 2013 ;
Pr e dybaylo et al., 2017 ; Kho dri et al., 2017 ), which states that the lo w thermal inertia of the land intr o duces
a LO T G after eruptions, which affe cts the Pacific zonal wind anomalies and hence the o cean temp era-
tur e; (iii) the subtr opical wind str ess curl me chanism (McGr egor and Timmermann, 2011 ; Ste v enson et al.,
2017a ), which states that the initial enhance d co oling in EP after eruptions leads to a negativ e ( anticy-
clonic) subtr opical wind str ess curl, which driv es e quator war d conv ergence of warmer subtr opical waters
and delays the OD T; (iv ) the e xtratr opical tele conne ction me chanism (Kho dri et al., 2017 ; Pausata et al.,
2020 ), which states that v olcanically induce d co oling of tr opical Africa w eakens the W est African monso on
and alters the W alker cir culation; and ( v ) the Inter T r opical Conv ergence Zone (I T CZ) shift me chanism
(Pausata et al., 2015 ; Ste v enson et al., 2016 ; Ste v enson et al., 2017a ; Pausata et al., 2020 ), which states that
the Northern Hemispher e (NH) co oling after NH eruptions shift the I T CZ southwar d, which w eakens the
Pacific trade winds and leads to an El Niño-like r esp onse . Se v eral studies hav e also suggeste d a La Niña-
like r esp onse 2 y ears after an eruption(Sun et al., 2019 ; McGr egor et al., 2020 ), which could b e due to the
oscillator y natur e of ENSO dynamics (McGr egor et al., 2020 ), or to the eastwar d p osition of the anomalous
w estern North Pacific anticy clone , e xciting up w elling K elvin wav es and enhancing thermo cline fe e dback
and zonal adv e ction, leading to a gr eater co oling rate in the eastern Pacific (Sun et al., 2019 ).
Ensemble simulations with a highly simplifie d ENSO mo del (Emile-Geay et al., 2008 ) suggeste d a
thr eshold effe ct that w ould make ENSO insensitiv e to all but the largest eruptions of the past millennium
( appr o ximately the magnitude of Krakatau and ab o v e). This has generally b e en confirme d by e xp eriments
with mor e r ealistic mo dels (Pausata et al., 2015 ; Ste v enson et al., 2016 ; Ste v enson et al., 2017a ; Pausata
et al., 2020 ; Pr e dybaylo et al., 2020 ). Ho w e v er , a r e cent analysis of a long, monthly coral r e cor d fr om the
heart of the tr opical Pacific ( Cobb , Charles, and Hunter , 2001 ; Cobb et al., 2003 ) suggests no uniform ENSO
r esp onse to all eruptions o v er the last millennium, e v en for the largest eruptions (De e et al., 2020 ). This
is in line with r esults fr om r e cent mo deling studies using large ensembles that allo w quantification of the
influence of sto chastic as w ell as deterministic elements(Pr e dybaylo et al., 2020 ). Inde e d, ENSO is thought
78
to b e affe cte d by multiple uncertain or p o orly constraine d factors, including the phase of the quasi-biennial
oscillation ( QBO ) (T aguchi, 2010 ), the for cing magnitude , lo cation, and season of the eruption (Ste v enson
et al., 2017a ; Pr e dybaylo et al., 2020 ), as w ell as pr e-conditioning of the ENSO state (neutral, Central Pa-
cific El Niño , Eastern Pacific El Niño , or La Niña) (Pr e dybaylo et al., 2017 ). Y et, obser vational studies on
this track ar e hinder e d by the limite d numb er of w ell kno wn eruption e v ents, the temp oral r esolution of
v olcanic for cing r e constructions, and the spatial and temp oral availability of pr o xy r e cor ds.
Pale o climate r e cor ds offer a longer p erio d of obser vation but conflicting accounts: r e constructions
base d mostly on tr e e-ring pr o xiesA dams, Mann, and Ammann, 2003 ; McGr egor , Timmermann, and Timm,
2010 ; Li et al., 2013 ; W ahl et al., 2014 ; McGr egor et al., 2020 , which e xp erience ENSO thr ough tele con-
ne ctions, hav e b e en use d to argue of an El Niño-like r esp onse within a y ear of the eruption; in contrast,
r e c onstructions using corals fr om the cor e ENSO r egion ( Cobb et al., 2003 ; Tierne y et al., 2015 ; De e et al.,
2020 ) – which pr o vide a firsthand, alb eit discontinuous, account of ENSO variations – do not supp ort this
conclusion.
In this study , w e r e-appraise the p otential links b etw e en v olcanism and ENSO , by integrating the latest
pale o climate e vidence fr om b oth tr e e rings and corals into a consistent dynamical frame w ork, the Last
Millennium Reanalysis (LMR) (Hakim et al., 2016 ; T ar dif et al., 2019 ), and interpr et the r esults in the conte xt
of r e cent mo deling w ork sho wing a large r ole for b oth initial and b oundar y conditions in shaping the
climate r esp onse to v olcanism (Pr e dybaylo et al., 2017 ; Pr e dybaylo et al., 2020 ).
4.2 Corals vs T r e e Rings
Coral ar chiv es ar e a natural choice for ENSO r e construction due to their ge ographical pr o ximity to ENSO
centers of action (Wilson et al., 2010 ) and the demonstrate d link b etw e en the ge o chemistr y of their skele-
tons and ENSO conditions (Lough, 2010 ; Emile-Geay et a l., 2020 ). Ho w e v er , their limite d time span pr o-
duces discontinuous r e cor ds, which can only b e pie ce d together by splicing ( Cobb et al., 2003 ). The longest
and most complete coral ENSO r e cor d publishe d to date ( Cobb et al., 2003 ; Cobb et al., 2013 ; De e et al.,
2020 ) is lo cate d at Palmyra atoll, at the e dge of the Niño 3.4 r egion. The r e cor d co v ers 535 of the past 1000
y ears, leaving many gaps, and with limite d r eplication o v er common inter vals. T r e e-ring base d pr o xies,
on the other hand, hav e b e en use d to build long, cr oss-date d, and heavily r eplicate d r e constructions that
continuously span the Common Era. Their distance to ENSO centers of action means that the y r ely on
tele conne ctions b etw e en the tr opical Pacific and their lo cal terr estrial rainfall and temp eratur e anomalies,
leaving them vulnerable to confounding factors. Combining data fr om b oth ar chiv es could ameliorate
their individual limitations. Befor e doing so , ho w e v er , w e compar e r e constructions assimilating the tw o
ar chiv es separately , as this pr o vide insights into the p ossible causes of the discr epancy b etw e en pr e vious
studies and on ho w to interpr et a combine d signal.
Our strategy le v erages the data assimilation algorithm of the Last Millennium Reanalysis (Metho ds).
W e first assimilate corals to r e construct tr opical Pacific surface temp eratur e during the b or eal winter (DJF).
Our coral colle ction includes the synthesis of Ocean2k (Tierne y et al., 2015 ; P A GES 2k Consortium,
2017 ), supplemente d by the latest Palmyra r e cor d (De e et al., 2020 ). The r esultant r e construction is denote d
as LMR ( Corals), and its spatial and temp oral skill is pr esente d in Figur e 4.1 ( a,d). The skill of the Niño 3.4
79
r e c onstruction is r emarkably high compar e d to many other e xisting r e constructions ( se e Figur e 4.5 ), with
a temp oral corr elation co efficient (R ) of 0.86 (that is, 74% of shar e d variance) and a co efficient of efficiency
(CE )(Nash and Sutcliffe , 1970 ) of 0.71 against ERSST v5 (Extende d Re constructe d Sea Surface T emp eratur e
v5) (Huang et al., 2017 ). Ho w e v er , due to the temp oral gaps in the Palmyra r e cor d, the r e construction
is incomplete o v er the last millennium (Figur e 4.2 b) and the ensemble-mean variability collapses when
Palmyra obser vations ar e unavailable .
The assimilation of tr e e rings for Niño 3.4 r e construction is challenging due to their distance to the
target r egion. T o o v er come this, w e gather the six b est tr e e-ring base d Niño 3.4 pr e dictors i dentifie d by
Li et al.(Li et al., 2013 ) ( denote d as Li13b6): the first tw o principal comp onents of the North American
Dr ought Atlas (NAD A ) (V ersion 2a)( Co ok et al., 2004 ) and Monso on A sia Dr ought Atlas (MAD A ) ( Co ok
et al., 2010 ), the K auri tr e e-ring comp osite (Fo wler et al., 2008 ), and the South America Altiplano tr e e-ring
comp osite (Morales et al., 2012 ) (Figur e 4.6 ), and assimilate them in LMR as pr o xies for Niño 3.4 SST ( se e
Metho ds). The r esultant r e construction, denote d as LMR (Li13b6) in Figur e 4.1 b ,e displays skill comparable
to LMR ( Corals), though slightly w eaker , with R = 0.75 andCE = 0.57 . Note that the scatter plots in
Figur e 4.6 (m-r ) indicate that Li13b6 pr e dictors tend to under estimate the Niño 3.4 anomaly in y ear 1 after
instrumental era eruptions ( as the color e d dots tend to ho v er ab o v e the linear mo del fit), y et this b ehavior is
not obvious in the r e construction LMR (Li13b6) (Figur e 4.1 h), suggesting an advantage for pr o c essing the
pr o xy obser vations within the LMR pale o-data assimilation frame w ork. The spatial v erification (Figur e
4.1 b) indicates that the r e construction skill p eaks ar ound the center of the Niño 3.4 r egion and de cays
quickly away fr om it. A major advantage of the tr e e-base d r e construction is its continuous natur e o v er
the past millennium (Figur e 4.2 c).
W e ne xt assess the ENSO r esp onse to v olcanism in b oth r e constructions. T o p erform an e quitable
comparison, w e sele ct large eruptions define d as v olcanic stratospheric sulfur inje ction (VSSI) gr eater
than 6 T g S accor ding to the e V olv2k v ersion 3 dataset(T o ohe y and Sigl, 2017 ), and fo cus on p erio ds when
the Palmyra coral r e cor d is available (Figur e 4.2 a). W e assess the for ce d ENSO r esp onses using b oth the
widely-use d sup erp ose d ep o ch analysis (SEA ) appr oach ( also kno wn as comp ositing), as w ell as a ranking
analysis ( se e Metho ds). The SEA (Figur e 4.3 a,b) applie d to the 12 large e v ents when Palmyra is available
(Figur e 4.2 a) suggests that ther e is no Niño 3.4 comp osite value that is significantly higher than that of
randomly drawn non-v olcanic y ears, e v en at the r elativ ely p ermissiv e 90% le v el.
Ho w e v er , SEA is sensitiv e to dating uncertainties, as the comp ositing pr o ce dur e r e quir es that the r e-
construction segments of individual e v ents align pr e cisely , without which other wise minor timing offsets
can comp ound and damp the comp osite signal. SEA may also b e affe cte d by the small sample size . This
may first come into play thr ough a typ e I err or , which is teste d in the SI T e xt 2. W e find that e v en small
ensembles ( n = 5 ) can mitigate this pr oblem, so it is not material for this particular issue . Ho w e v er ,
like all av eraging metho ds, an SEA carrie d o v er a small sample may b e dominate d by a small numb er of
e v ents with e xtr eme anomalies, with most e v ents sho wing a mo dest r esp onse(Rao et al., 2019b ). Thus, a
“significant” comp osite r esp onse is a ne cessar y but insufficient condition to establish a physical r esp onse .
Only when most of the e v ents sho w str ong r esp onses can w e b e confident ab out the r obustness of the
r elationship . Ther efor e , it is imp ortant to parse comp osites into the contributions fr om, and consistency
of, individual e v ents. This is achie v e d thr ough a ranking analysis (Figur e 4.3 c-f), which compar es the
80
Niño 3.4 r esp onse of each e v ent to the distribution of all non-v olcanic y ears. Ev ents with r esp onse values
larger than a certain quantile ( say , 80, 90, or 95%) of the distribution of non-v olcanic y ears ar e consider e d
“significant” .
Though the ranks of eruption-y ear e v ents in the tw o r e constructions do not agr e e with each other in
detail, b oth LMR ( Corals) and LMR (Li13b6) p oint to the same conclusion: that most eruption y ears ar e
not statistically differ ent fr om non-eruption y ears in b oth y ear 0 and y ear 1, at any significance le v el.
4.3 Combining Corals and T r e e Rings
Giv en this agr e ement, w e combine b oth ar chiv es to p erform a continuous r e construction, denote d as LMR
( Corals+Li13b6). V erification statistics (Figur e 4.1 c,f) sho w a slight skill impr o v ement compar e d to LMR
( Corals), withR = 0.86 andCE = 0.71 against ERSST v5. Mor e imp ortantly , the temp oral gaps in LMR
( Corals) o v er the past millennium ar e no w fille d with the information fr om Li13b6 (Figur e 4.2 ), which
allo ws a larger sample size of eruption e v ents, hence a mor e r obust e valuation of ENSO’s r esp onse to
v olcanism.
The SEA on LMR ( Corals+Li13b6) suggests once again t hat ther e is no significant p ost eruption Niño
3.4 comp osite r esp onse (Figur e 4.4 a,b) whether using the pr e viously sele cte d 12 e v ents, or all 22 large
eruptions of the last millennium (Figur e 4.2 a). Similarly , the ranking analysis (Figur e 4.4 c-f) indicates lo w
significance ratio in y ear 0 and y ear 1 for b oth cases of sele cte d e v ents.
O v erall, b oth SEA and ranking analysis supp ort the conclusion that the statistical link b etw e en ENSO
phases and last millennium v olcanism is w eak. It is w orth noting that, comparing rankings in the case of
12 (Figur e 4.4 c,e) vs. 22 e v ents (Figur e 4.4 d,f), e v ents after 1850 CE app ear to b e significant mor e likely ,
suggesting that the sensitivity is time-dep endent, a p ossibility that w e inv estigate b elo w .
4.4 A non-stationar y sensitivity?
While our r esults app ear to r e concile pr e vious r esults obtaine d fr om corals and tr e e rings, discr epancies
r emain in the publishe d literatur e ( e .g. De e et al. ( 2020 , her eafter D20), vs Li et al. ( 2013 , her eafter Li13)).
An imp ortant factor in such comparisons is the choice of e v ents use d to diagnose the v olcanic signal.
Due to the temp oral co v erage of the Palmyra coral r e cor d, D20 p erforme d SEA mainly on early eruptions
(1171, 1230, 1258, 1458, 1641, 1695 CE), while Li13 p erforme d SEA on a p o ol with mor e r e cent eruptions
(1350, 1360, 1450, 1580, 1586, 1593, 1600, 1641, 1660, 1673, 1680, 1815, 1822, 1831, 1835, 1883, 1902, 1913,
1951, 1963, 1982, 1991 CE). Figur e 4.7 a indicates that the Li13 r e construction is heavily heter oske dastic:
the variance is less than 1 o v er much of the pr e-instrumental p erio d ( b efor e 1850 CE), and larger after that
p oint. If p ost 1850 CE e v ents ar e e xclude d, the significance le v el of the y ear 1 r esp onse dr ops fr om >99%
to ar ound 90% (Figur e 4.7 b , dashe d dotte d cur v e). This alone suggests that instrumental-era e v ents ar e
dominating the SEA, leading to a biase d r esult.
T o assess individual e v ents, w e compar e rankings using all eruptions vs pr e-instrumental eruptions
only (Figur e 4.7 c,d). It can b e se en that the instrumental p erio d eruptions o v erall sho w a str onger Niño
3.4 anomaly than the pr e-instrumental p erio d eruptions (Figur e 4.7 c). Without instrumental-era eruptions,
81
only (3, 2, 1) out of 15 e v ents sho w a larger Niño 3.4 r esp onse than (80%, 90%, 95%) of the non-v olcanic y ears
(Figur e 4.7 d), indicating that most of the pr e-instrumental p erio d eruptions ar e not significantly differ ent
fr om non-v olcanic y ears.
The ab o v e analysis suggests that the r e constructe d ENSO r esp onse to v olcanism is non-stationar y , at
least b etw e en pr e-instrumental and instrumental p erio d eruptions.
This could b e cause d by data attrition, which r e duces variability of a r e construction going back in
time since the pr o xy obser vations pr o vide the only sour ce of variability in our r e constructions. Mor e o v er ,
MAD A is compile d using a corr elation-w eighte d, ensemble-base d mo dification of the “p oint-by-p oint r e-
gr ession”( Co ok et al., 2010 ), and the ensemble memb ers b e come less similar to each other during earlier
p erio ds, o v er which temp oral variability is damp e d compar e d to r e cent inter vals. In addition, dating ac-
curacy is a non-negligible pr oblem for fossil corals ( Comb oul et al., 2014 ), wher e err ors comp ound back in
time , p otentially r e ducing the variability of comp osite series deriv e d fr om them(Emile-Geay et al., 2020 ).
In addition, w e note that the instrumental p erio d is quite short and de v oid of the v er y large eruptions that
o ccur in the pr e-instrumental p erio d, so r esults obtaine d o v er this p erio d may not b e statistically r epr esen-
tativ e . Furthermor e , instrumental r e cor ds hav e sho wn e vidence of the p otential of coincidence b etw e en
ENSO activity and v olcanism, at least for the A gung (1963), El Chichon (1982), and Pinatub o (1991) erup-
tions, when str ong El Niño e v ents w er e alr eady under way b efor e the eruptions w ent off (Lehner et al.,
2016 ).
Rep eating the ab o v e analysis in Figur e 4.7 on LMR (Li13b6) and LMR ( Corals+Li13b6), w e se e similar
characteristics (Figur es S4.5 & S4.6 ) to that of Li13, suggest ing that the se emingly div ergent conclusions
b e tw e en Li13 and our study , r egar ding the statistical significance of ENSO r esp onse to v olcanism, ar e
mainly cause d by differ ent choices of eruption ke y dates ( se e SI T e xt 3 for details).
4.5 Effe cts of For cing A symmetr y
Pr e vious studies hav e suggeste d that the hemispheric asymmetr y of v olcanic for cing is another factor
that may differ entially affe ct ENSO activity ( Ohba et al., 2013 ; Pausata et al., 2015 ; Pausata et al., 2020 ;
Pr e dybaylo et al., 2020 ). Ther efor e , w e inv estigate the r elationship b etw e en for cing parameters and the
Niño 3.4 SST fr om LMR ( Corals+Li13b6). T r opical eruption e v ents ar e categorize d by differ ent hemispheric
asymmetr y le v els ( b elo w 0.8, b etw e en 0.8 and 1.5, and ab o v e 1.5) define d as aer osol spr ead base d on ratio of
Gr e e nland to Antar ctic sulfate flux (T o ohe y and Sigl, 2017 ). Extr eme e v ents ar e define d as having a VSSI>20
(1230, 1257, 1458, 1815). Figur e 4.8 indicates a consistently p ositiv e linear r elationship b etw e en VSSI and
y ear 0 Niño 3.4 r esp onses for e v ents with hemispheric asymmetr y larger than 1.5, and b etw e en 0.8 and
1.5, although the latter categor y is dominate d by the 1257 e xtr eme e v ent. The r elationship for y ear 1 Niño
3.4 r esp onses is w eak for b oth categories, and ther e ar e not enough e v ents to get a ny meaningful insights
for e v ents with asymmetr y smaller than 0.8, nor with e xtr eme e v ents. The p ositiv e linear r elationship
b e tw e en VSSI and y ear 0 Niño 3.4 r esp onse for str ongly asymmetric tr opical eruptions is in agr e ement
with the I T CZ shift me chanism (Pausata et al., 2015 ; Ste v enson et al., 2016 ; Ste v enson et al., 2017a ; Pausata
et al., 2020 ). Ho w e v er , the r elativ ely small sample size invites caution ab out the interpr etation. Potentially
confounding factors ar e discusse d b elo w .
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4.6 Discussion
Using state-of-the-art datasets and metho ds, combining the str engths of b oth coral and tr e e-ring r e cor ds,
the pr esent e vidence is as y et unable to dete ct an effe ct of e xplosiv e v olcanism on ENSO phase , consistent
with D20 (De e et al., 2020 ). This conclusion is supp orte d by corals and tr e es indep endently . Y et, corals
and tr e es disagr e e r egar ding the r elativ e rank b etw e en individual e v ents (Figur e 4.3 ). This issue might
b e cause d by attrition in b ot h netw orks, which r e duces r e construction variance back in time . Similarly ,
temp oral gaps in the Palmyra coral r e cor d limit the p o ol of eruption e v ents and non-v olcanic y ears to a
smaller size , making the comparison less stable .
Be y ond the issue of attrition, pr o xy ar chiv es harb or limitations of their o wn. The tr e e-ring r e cor ds
use d her e , for instance , ar e sensitiv e to the lo cal hy dr ological e xpr ession of v olcanic eruptions, which
may b e mistaken for the r emote effe cts of ENSO via tele conne ctions (Ste v enson et al., 2016 ). The ENSO
r e c onstruction base d on the South American Altiplano comp osite (Morales et al., 2012 ) also suggests that
the non-stationar y b ehavior of ENSO variance is maske d by intrinsic tr e e-ring width variability . Inde e d,
when ENSO variance is lo w , the tele conne ction is w eak, and tr e e ring variability is mor e r efle ctiv e of lo cal
temp eratur e and moistur e conditions than those fr om the r emote tr opical Pacific; such non-stationarity
may obscur e the v olcano es-ENSO link. The curr ent coral netw ork is mor e pr o ximal to ENSO centers of
action, y et is dominate d by r e cor ds fr om the w estern and central e quatorial Pacific (Figur e 4.1 a) which
captur e La Niña e v ents mor e faithfully than El Niño e v ents, and tend to under estimate the amplitude of
large eastern Pacific (EP) e v ents (Emile-Geay et al., 2013 ; Emile-Geay et al., 2020 ). The sparse ge ographical
co v erage is another issue , pr e v enting the estimation of tr opics-wide SST in a way that w ould allo w for
a r obust calculation of r elativ e sea surface temp eratur e (RSST)(Kho dri et al., 2017 ). Inde e d, it has b e en
suggeste d that El Niño phases could b e enhance d by v olcanism e v en when the absolute SST signal in the
central and eastern tr opical Pacific is w eak (Rob o ck, 2020 ).
RSST highlights the impact of v olcanism on ENSO r elativ e to the tr opical mean co oling, and is com-
putable in our r e constructe d SST fields. This is sho wn in Figur e 4.9 , which displays a temp orally-flat
tr opical av erage temp eratur e anomaly for most of the y ears b etw e en 1100-2000 CE, r esulting in RSST -
base d Niño 3.4 anomalies that ar e indistinguishable fr om the SST -base d ones. This is a dir e ct r esult of
the sparse coral netw ork b efor e the ninete enth centur y , and will not impr o v e until this netw ork is vastly
e xpande d o v er tr opical o ceans. Ho w e v er , e v en with the RSST conv ersion, w e still obser v e consistently
lo w significance ratio in the ranking analysis of the last millennium climate mo del simulations ( se e SI T e xt
S4 for details).
Another cav eat comes fr om limitations asso ciate d with the choice of the mo del prior in the LMR pale o-
D A frame w ork. The mo del prior her e r efers to the mo del simulation fr om which climate states ar e chosen at
random by the K alman filter algorithm. Its chief r ole is to pr o vide the spatial co variance information within
and b etw e en fields, and affe cts ho w the information fr om pr o xy obser vations pr opagates to lo cations wher e
those obser vations ar e not available . A ccor ding to a r e cent study Sanchez, Hakim, and Saenger ( 2020 ), the
kno wn biases in the lo cation of the South Pacific Conv ergence Zone (SPCZ) in most climate mo dels leads
to incorr e ct infer ences ab out Niño 3.4 SST fr om corals lo cate d in the SPCZ r egion, in such a pale o climate
data assimilation conte xt. Mor e o v er , Sanchez, Hakim, and Saenger ( 2020 ) sho ws that corals lo cate d in
83
b o th the SPCZ and Niño 3.4 r egions pr o duce lo cal co oling during the 1809 and 1815 eruptions, but all prior
ensembles consider e d (including those drawn fr om 20th centur y r eanalyses) hav e a co variance pattern that
yields r emote influence (that is, the influence of one r egion on another ) inconsistent with this pattern. In
addition to mo del bias, this suggests that mo del priors conditional on eruption time w ould b e imp ortant
for pr op erly r epr esenting the information in pr o xy r e cor ds. W e note that, in the pr esent study , these biases
ar e mitigate d prior to 1800, when only pr o xies tie d to the Niño 3.4 inde x ar e use d.
Finally , a r e cent mo deling study (Pr e dybaylo et al., 2020 ) suggests that the ENSO r esp onse to v olcanism
is rather w eak during DJF b e cause it changes sign ar ound that season. Y et, the r esp onse could b e str ong b e-
for e the sign changes, which is usually during Januar y-Septemb er ( JAS) and/or Octob er-De cemb er ( OND ).
Rep eating our analysis using JAS and OND as target seasons, w e find our conclusions insensitiv e to this
choice (SI T e xt 5). This is in appar ent contradiction to that mo deling study (Pr e dybaylo et al., 2020 ), y et
may b e e xplaine d by the limitations of curr ently available pr o xy r e cor ds note d ab o v e . A ssigning eruption
e v ents to sp e cific y ears base d on v olcanic for cing r e constructions could also lead to time offsets in anal-
yses using differ ent target seasons ( Anchukaitis et al., 2010 ), which will p otentially obscur e the r elation
to eruption e v ents. This is a pr oblem that w e cannot r esolv e curr ently without a b etter kno wle dge of the
eruption season.
That w e do not find a consistent ENSO r esp onse in the r elativ ely small statistical sample of the last
millennium is not e vidence that ther e is zer o pr e dictability asso ciate d with v olcano es. A s suggeste d by
r e c ent mo deling studies (Pr e dybaylo et al., 2017 ; Pr e dybaylo et al., 2020 ), the for cing magnitude , lo cation,
and season of the eruption, as w ell as pr e-conditioning of the ENSO state can gr eatly affe ct the ENSO
r esp onse to v olcanic eruptions. These multiple factors must align to fav or the de v elopment of ENSO e v ents,
pr o viding a sour ce of pr e dictability only when these factors ar e kno wn with a sufficient degr e e of accuracy .
It is ther efor e r easonable to e xp e ct that the lack of an obser v e d, consistent r elationship b etw e en ENSO
phases and e xplosiv e v olcanism in our r e constructions may b e due , in part, to an imp erfe ct kno wle dge of
these factors. Ho w e v er , e v en when contr olling for eruption timing in PMIP3 and CESM-LME simulations,
a ranking analysis still demonstrates an inconsistent ENSO r esp onse to v olcanism when this major sour ce
of variability is held fixe d (SI T e xt 4), suggesting that all factors ne e d to b e jointly determine d, or that a
larger ensemble is ne e de d to discern common tr ends.
Giv en the large numb er of degr e es of fr e e dom, a large sample size is ne e de d to isolate a consistent signal
– larger p erhaps than offer e d by the past millennium. It is thus imp ortant to de v elop mor e high-r esolution
pr o xy r e cor ds spanning the tr opical o ceans o v er the last millennium, and p ossibly e xtend them thr ough the
longer Holo cene . The r e construction of v olcanic for cing also ne e ds to b e e xpande d with longer temp oral
co v erage for mor e r obust statistics. Until these goals hav e b e en achie v e d, it is unclear ho w much one can
conclude fr om the pale o climate r e cor d ab out the contribution of v olcanic eruptions to ENSO dynamics, or
to the assessment of the risks p ose d by solar radiation management strategies in r elation to ENSO .
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4.7 Metho ds
4.7.1 The Last Millennium Reanalysis data assimilation frame w ork
The v ersion of the Last Millennium Reanalysis (LMR) data assimilation (D A ) frame w ork use d her e (Hakim
et al., 2016 ; T ar dif et al., 2019 ) is an offline ensemble K alman filter (Ev ensen, 2009 ), optimize d for multivari-
ate climate field r e construction (Steiger et al., 2013 ). It consists of a colle ction of prior states generate d by
the CCSM4 climate mo del, a pr o xy database , a set of “for war d op erators” or pr o xy system mo dels (PSMs,
Evans et al., 2013 ) that translates the envir onmental variables to the pr o xy space , and an ensemble K alman
filter op erator . In our implementation, the temp oral variation of the p osterior stems entir ely fr om the
temp oral information fr om the pr o xies, while the co variance structur e of the mo del prior ser v es to spr ead
the temp oral information of each pr o xy to r emote r egions and other variables than those dir e ctly r elate d
to the pr o xy . For further details, se e studies Hakim et al. ( 2016 ) and T ar dif et al. ( 2019 ). For computational
conv enience , this study utilizes a fast implementation of the LMR frame w ork, LMRt (Zhu et al., 2019a ). In
each assimilation e xp eriment, w e p erform 50 Monte Carlo iterations, each using a differ ent randomly cho-
sen 100-memb er ensemble states fr om the CCSM4 last millennium simulation (Landrum et al., 2012b ) as
the mo del prior . No pr o xy randomization is p erforme d to guarante e the similarity b etw e en each ensemble
memb er so that the me dian cur v e of the r e constructe d Niño 3.4 inde x s eries is r epr esentativ e of the whole
r e c onstruction pr o duct. The default co variance lo calization ( Gaspari and Cohn, 1999 ) radius of 25,000 km
is applie d, and w e note that the r esults ar e insensitiv e to this e xact choice .
Note that the calibration p erio d for the PSMs is 1850-2000 CE so as to achie v e the b est r e construction
skill. T o guar d against p otential o v erfitting, as w ell as the p otential impact of climate change w e se e
in NAD A PC2 and the K auri comp osite (Figur e ⁇ d,e), a cr oss-validation of the r e constructe d Niño 3.4
is p erforme d with disjoint calibration and validation p erio ds ( se e SI T e xt 1); the r esult suggests that the
r e c onstruction skill is stable to this choice .
4.7.2 Data Sour ces
W e consider information fr om seasonally-sensitiv e or monthly-r esolv e d pr o xy r e cor ds. Coral r e cor ds ar e
fr om the Ocean2k compilation (Tierne y et al., 2015 ) up date d with the latest Palmyra data (De e et al., 2020 ).
Each coral r e cor d is tr eate d as a pr o xy for lo cal sea surface temp eratur e (SST), and is calibrate d o v er 1850-
2000 CE thr ough a univariate linear r egr ession pr o ce dur e against the lo cal, b or eal winter (DJF) SST , which
sho ws high r e construction skill as in pr e vious studies (Hakim et al., 2016 ; T ar dif et al., 2019 ). Exp eriments
with a mo del that takes the o xygen isotopic comp osition of seawater into account did not pr o duce no-
ticeable impr o v ements, which is in agr e ement with a r e cent study (Sanchez, Hakim, and Saenger , 2020 ).
T r e e-base d r e cor ds fr om b oth hemispher es ar e taken fr om a pr e vious r e construction (Li13, Li et al., 2013 ),
using se v en pr e dictor timeseries. The six b est pr e dictors ar e the first tw o principal comp onents (PCs) of
North American Dr ought Atlas (V ersion 2a) (NAD A, Co ok et al., 2004 ) and Monso on A sia Dr ought Atlas
(MAD A, Co ok et al., 2010 ), the K auri tr e e-ring comp osite Fo wler et al., 2008 , as w ell as the South Ameri-
can Altiplano comp osite(Morales et al., 2012 ), with the e xplaine d variance of Li13 b eing 11.2%, 8.4%, 40.5%,
24.2%, 38.1%, 56.5%, r esp e ctiv ely . The other pr e dictor is the w est-central Argentina comp osite (Villalba
85
et al., 1996 ), which contributes negligibly to r e construction skill ( with an e xplaine d variance of Li13 of
1.8%), and is ignor e d her e . W e r efer to these b est six r e cor ds as “Li13b6” .
W e r epr o duce d the principal comp onents of NAD A and MAD A via principal comp onent analysis (PCA,
Pearson, 1901 ), so that w e ar e able to e xtend the timespan of NAD A PCs to 1001-2000 CE, compar e d to the
original timespan (1300-2000 CE) in Li13. The timespan of the r epr o duce d MAD A PCs r emains 1300-2000
CE due to the temp oral co v erage of MAD A itself ( Co ok et al., 2010 ). The K auri tr e e-ring comp osite co v ers
the 1578-2003 p erio d, and the South American Altiplano tr e e-ring comp osite co v ers 1290-2010 CE. Data
b e y ond 2000 CE ar e not use d since our r e construction stops at 2000 CE. Note that the South American
Altiplano comp osite w e use is the r esidual chr onology instead of the standar d chr onology . A r esidual
chr onology is obtaine d by filtering (pr e whitening) the standar d chr onology via autor egr essiv e mo deling
( Co ok and K airiukstis, 1990 ). This pr o ce dur e r emo v es some lo w-fr e quency variability and ther efor e em-
phasizes the higher-fr e quency variability in tr e e-ring gr o wth and r emains appr opriate for the r e construc-
tion of interannual variability . All six pr e dictors ar e tr eate d as pr o xies for Niño3.4 SST and ar e calibrate d
o v er 1850-2000 CE thr ough a univariate linear r egr ession pr o ce dur e against the Niño3.4 inde x series de-
riv e d fr om a spatially complete d v ersion of HadCRU T4.6 (V accar o et al., 2021 ) le v eraging the GraphEM
( G uillot, Rajaratnam, and Emile-Geay , 2015 ) algorithm. Figur e 4.6 g-k sho w a temp oral v erification of each
pr e dictor against the Niño 3.4 series deriv e d fr om ERSST v5 as in Figur e 4.1 d-f.
4.7.3 Sup erp ose d ep o ch analysis
The sup erp ose d ep o ch analysis (SEA, Haur witz and Brier , 1981 ) is a widely-use d metho d for analyzing
the climate r esp onses to v olcanic eruptions (Li et al., 2013 ; De e et al., 2020 ; Zhu et al., 2020 ). In our case ,
w e e xtract the me dian Niño3.4 inde x series as the target for analysis for each LMR r e construction. Large
eruption e v ents ar e define d as a v olcanic stratospheric sulfur inje ction (VSSI) gr eater than 6 T g S accor ding
to the e V olv2k v ersion 3 dataset (T o ohe y and Sigl, 2017 ). SEA considers segments ar ound each e v ent, her e
e xtending fr om 3 y ears prior to the e v ent y ear and 6 y ears after the e v ent y ear . A s in pr e vious w ork (De e
et al., 2020 ), the mean of the 3 y ears prior to the e v ent y ear is r emo v e d so that each segment r epr esents
the anomaly r esp onse r elativ e to the mean state b efor e each e v ent. A comp osite is obtaine d by av eraging
these 10-y ear windo ws. A b o otstrap significance test is then p erforme d: the same numb er of y ears as
the eruption e v ents under consideration ar e randomly drawn fr om the p o ol of non-v olcanic y ears for
1000 times, and the comp osite is calculate d for each draw with an identical pr o cess that w e calculate the
comp osite for eruption y ears, base d on which w e calculate the 1%, 5%, 10%, 90%, 95%, and 99% quantiles
of the non-v olcanic y ears at each r elativ e y ear as the significance le v els. Her e the non-v olcanic y ears ar e
define d as the y ears e xcluding eruption e v ents define d as VSSI>1.
4.7.4 Ranking analysis
A ranking analysis ( Guillet et al., 2017 ) is designe d to assess whether the ENSO r esp onse to each individual
e v ent is significantly differ ent fr om non-v olcanic y ears. Similar to SEA, w e e xtract the me dian Niño 3.4
inde x series fr om each LMR r e construction as the target for analysis, and colle ct the segments ar ound each
eruption e v ent, with a windo w fr om 3 y ears prior to the e v ent y ear and 6 y ears after the e v ent y ear , and the
86
mean of the 3 y ears prior to each e v ent y ear is r emo v e d. Then w e de cide the r elativ e y ear w e w ould like
to e valuate ( y ear 0 and y ear 1 in this study ), and a list of Niño 3.4 anomaly values for each e v ent is forme d,
which w e sort in ascending or der . W e colle ct the Niño 3.4 anomaly values for all non-v olcanic y ears and
p erform a kernel density estimation with a Gaussian kernel with a bandwidth sele cte d by Scott’s Rule
(Scott, 1992 ), after which its 50%, 80%, 90%, and 95% quantiles ar e calculate d. Ev ents with r esp onse values
larger than the 80%, 90%, and 95% quantiles ar e consider e d “significant” at each le v el, and a significance
ratio is calculate d. For instance , a significance ratio (a,b,c)/n means that(a,b,c) out ofn e v ents hav e
r esp onse values higher than the (80%, 90%, 95%) quantiles of the distribution of non-v olcanic y ears.
T able 4.1: Metadata of the 22 large eruptions sho wn in Figur e 4.2 a accor ding to e V olv2k v ersion 3 (T o ohe y
and Sigl, 2017 ). Note that the value 0.0 in the column of Latitude denotes that the pr e cise eruption latitude is
unkno wn but the e v ent is define d as tr opical, and the value -1.0 in the column of A symmetr y ( hemispheric
asymmetr y for tr opical eruptions) denotes that the e v ent is define d as e xtratr opical.
Eruption y ear Latitude A symmetr y VSSI
1108 0.0 4.0 19.16
1171 0.0 1.8 18.05
1182 45.0 -1.0 10.05
1191 0.0 0.7 8.53
1230 0.0 2.1 23.78
1257 -8.4 1.4 59.42
1276 0.0 0.2 11.53
1286 0.0 1.2 15.06
1345 0.0 1.4 15.11
1453 0.0 4.9 9.97
1458 0.0 0.6 32.98
1585 19.5 10.6 8.51
1595 4.9 0.8 8.87
1600 -16.6 2.0 18.95
1640 6.1 2.8 18.68
1695 0.0 1.1 15.74
1783 64.4 -1.0 20.81
1809 0.0 1.3 19.26
1815 -8.0 0.8 28.08
1831 19.5 8.1 12.98
1835 13.0 2.0 9.48
1883 -6.0 1.7 9.34
VSSI=v olcanic stratospheric sulfur inje ction.
A symmetr y=hemispheric asymmetr y (NH/SH) of aer osol spr ead
for tr opical eruptions base d on ratio of Gr e enland to Antar ctic flux.
87
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.81, CE=0.63
d
LMR (Corals)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.75, CE=0.57
e
LMR (Li13b6)
1880 1900 1920 1940 1960 1980 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.86, CE=0.71
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
4 2 0 2 4
LMR (Corals)
4
2
0
2
4
ERSSTv5
R=0.81
g
4 2 0 2 4
LMR (Li13b6)
4
2
0
2
4
ERSSTv5
R=0.75
h
4 2 0 2 4
LMR (Corals+Li13b6)
4
2
0
2
4
ERSSTv5
R=0.86
i
Year 0 after eruptions
Year 1 after eruptions
Figur e 4.1: ( a-c) Spatial v erification of the me dian field of the LMR (Hakim et al., 2016 ; T ar dif et al., 2019 ) r e-
constructe d b or eal winter (De cemb er-Februar y , DJF) surface temp eratur e assimilating thr e e sour ces: ( a,d)
corals fr om the Ocean2k compilation (Tierne y et al., 2015 ) up date d with the latest Palmyra data (De e et
al., 2020 ); ( b ,e) the six b est pr e dictors fr om Li et al. ( 2013 ) ( denote d as Li13b6), and ( c,f) b oth data sour ces
combine d. V alidation is p erforme d against the Extende d Re constructe d Sea Surface T emp eratur e , V ersion
5 (ERSST v5) (Huang et al., 2017 ) o v er the instrumental p erio d (1881-2000 CE). The orange dots denote the
lo cation of the corals, the mint and blue squar es denote the lo cation of the North American Dr ought Atlas
(V ersion 2a) (NAD A, Co ok et al., 2004 ) and Monso on A sia Dr ought Atlas (MAD A, Co ok et al., 2010 ) sites,
the gr e en up war d triangle denotes the lo cation of the K auri tr e e-ring comp osite (W ahl et al., 2014 ), and
the gr e en do wnwar d triangle denotes the lo cation of the South America Altiplano (SA Altiplano) tr e e-ring
comp osite (Morales et al., 2012 ). ( d-f ) T emp oral v erification of the me dian of the LMR r e constructe d DJF
Niño 3.4 series ( color e d cur v es) against the ERSST v5 deriv e d Niño 3.4 ( black solid cur v e) o v er the instru-
mental p erio d (1873-2000 CE). For each r e construction, dark shading denotes the inter quartile range , and
light shading denotes the central 95% r egion, fr om 2.5% to 97.5%. R=corr elation co efficient, CE=co efficient
of efficiency (Nash and Sutcliffe , 1970 ). ( g-i) Scatter plot of the data p oints in ( d-f). The gr e y dashe d cur v e
r epr esents the linear r egr ession fitting cur v e . The black and color e d dots denote the data p oints at y ear 0
and y ear 1 r elativ e to large eruption y ears (1883, 1902, 1913, 1951, 1963, 1982, 1991) as in Li et al. ( 2013 ),
r esp e ctiv ely .
88
1100 1200 1300 1400 1500 1600 1700 1800 1900
0
10
20
30
40
50
60
70
VSSI [Tg S]
a Large eruptions (VSSI>6) in eVolv2k v3
events when Palmyra is unavailable
events when Palmyra is available
1108
1171
1182
1191
1230
1257
1276
1286 1345
1453
1458
1585 1595
1600 1640
1695
1783
1809
1815
1831
1835 1883
1100 1200 1300 1400 1500 1600 1700 1800 1900
4
2
0
2
4
Niño 3.4 [K]
b LMR (Corals)
median interquartile 2.5%-97.5%
1100 1200 1300 1400 1500 1600 1700 1800 1900
4
2
0
2
4
Niño 3.4 [K]
c LMR (Li13b6)
1100 1200 1300 1400 1500 1600 1700 1800 1900
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
d LMR (Corals+Li13b6)
Figur e 4.2: ( a) The 22 large eruption e v ents define d as the v olcanic stratospheric sulfur inje ction (VSSI)
gr eater than 6 accor ding to e V olv2k v ersion 3 (T o ohe y and Sigl, 2017 ). 12 e v ents o v er the y ears when the
Palmyra coral r e cor d ( Cobb et al., 2003 ; Cobb et al., 2013 ; De e et al., 2020 ) is available ar e color e d in black,
while other e v ents ar e color e d in gr e y . Se e T able 4.1 for the details of the metadata. ( b-d) Same as Figur e
4.1 d-f, but for the past millennium.
89
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
a
LMR (Corals)
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
99%
b
LMR (Li13b6)
Composite (n=12)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
KDE
1640
1276
1695
1453
1286
1257
1171
1182
1191
1345
1458
1230
Signif. ratio: (2,1,1)/12 Year 0
c
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1182
1453
1276
1230
1286
1345
1458
1640
1191
1695
1257
1171
Signif. ratio: (1,0,0)/12 Year 0
d
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
KDE
1640
1276
1171
1453
1182
1286
1695
1458
1345
1191
1257
1230
Signif. ratio: (4,1,1)/12 Year 1
e
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1453
1695
1257
1276
1458
1191
1182
1286
1640
1230
1171
1345
Signif. ratio: (1,0,0)/12 Year 1
f
80%
90%
95%
50%
Figur e 4.3: ( a-b) Sup erp ose d ep o ch analysis (SEA ) of the r e constructions LMR ( Corals) and LMR (Li13b6) r egar ding the 12
e v ents when Palmyra is available . Solid cur v es with dots denote the comp osite mean, and the light dots denote the Niño 3.4
anomaly at each y ear for each individual e v ent. The light gr e y dashe d cur v es denote the 1%, 5%, 10%, 90%, 95%, and 99% quantiles
of the comp osite means fr om 1000 b o otstrap draws fr om non-v olcanic y ears (Metho ds). ( c-d) Ranking analysis of the LMR
r e constructe d Y ear 0 Niño 3.4 values. The gr e y shade d ar ea denotes the distribution of the Niño 3.4 anomaly value o v er all non-
v olcanic y ears, whose 50%, 80%, 90%, and 95% quantiles ar e denote d by v ertical dot-dashe d cur v es, ser ving as significance le v els
(Metho ds). The v ertical solid lines mark individual v olcanic e v ents; for each, the horizontal axis p osition denotes the Niño 3.4
anomaly value , and the v ertical axis p osition denotes the r elativ e rank o f the Niño 3.4 anomaly value compar e d to all other e v ents.
The cir cle/do wnwar d triangle/up war d triangle/diamond marker r epr esents that a v olcanic e v ent has a Niño 3.4 anomaly value
that is b elo w 80%/b etw e en 80-90%/b etw e en 90-95%/ab o v e 95% of that o v er the non-v olcanic y ears. The significance ratio denotes
the numb er of e v ents that ar e ab o v e the 80%, 90%, and 95% significance le v els, r esp e ctiv ely , out of all v olcanic e v ents. ( e-f ) Same
as ( c-d), but for the y ear 1 Niño 3.4 values.
90
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
a
LMR (Corals+Li13b6), n=12
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
99%
b
LMR (Corals+Li13b6), n=22
Composite (n=22)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
KDE
1276
1453
1182
1640
1286
1695
1345
1191
1257
1458
1230
1171
Signif. ratio: (1,0,0)/12 Year 0
c
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1835
1276
1595
1453
1585
1600
1815
1182
1108
1831
1640
1286
1809
1695
1883
1345
1257
1191
1458
1230
1171
1783
Signif. ratio: (2,1,1)/22 Year 0
d
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
KDE
1453
1276
1695
1640
1182
1286
1458
1257
1171
1191
1345
1230
Signif. ratio: (2,1,1)/12 Year 1
e
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1835
1453
1276
1783
1600
1695
1595
1640
1182
1286
1458
1257
1809
1171
1191
1108
1585
1815
1831
1345
1230
1883
Signif. ratio: (4,2,1)/22 Year 1
f
80%
90%
95%
50%
Figur e 4.4: Same as Figur e 4.3 , but for LMR ( Corals+Li13b6) r egar ding the 12 e v ents when Palmyra is
available and all the 22 e v ents o v er the past millennium.
91
ERSSTv5
BC09
Li13
PHYDA
LMR (Corals)
LMR (Li13b6)
LMR (Corals+Li13b6)
ERSSTv5
BC09
Li13
PHYDA
LMR (Corals)
LMR (Li13b6)
LMR (Corals+Li13b6)
1
0.94 1
0.74 0.75 1
0.55 0.61 0.47 1
0.81 0.83 0.68 0.79 1
0.75 0.74 0.9 0.49 0.69 1
0.86 0.87 0.82 0.72 0.95 0.87 1
a
Correlation
ERSSTv5
BC09
Li13
PHYDA
LMR (Corals)
LMR (Li13b6)
LMR (Corals+Li13b6)
ERSSTv5
BC09
Li13
PHYDA
LMR (Corals)
LMR (Li13b6)
LMR (Corals+Li13b6)
1
0.85 1
0.41 0.45 1
0.23 0.26 0.081 1
0.63 0.65 0.39 0.41 1
0.57 0.53 0.74 0.055 0.47 1
0.71 0.71 0.65 0.2 0.9 0.5 1
b
Coefficient of Efficiency
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Figur e 4.5: ( a) Corr elation co efficient and ( b) co efficient of efficiency b etw e en instrumental obser vations
and r e constructions of De cemb er-Februar y (DJF) Niño 3.4 o v er timespan 1881-2000 CE. Data sour ces in-
clude: Extende d Re constructe d Sea Surface T emp eratur e , V ersion 5 (ERSST v5, Huang et al., 2017 ), Bunge
and Clarke ( 2009 ), Li et al. ( 2013 ), the Pale o Hy dr o dynamics Data A ssimilation pr o duct (PH YD A Steiger
et al., 2018 ), and the r e constructions of this study LMR ( Corals), LMR (Li13b6), and LMR ( Corals+Li13b6).
Note that Li13 is a No v emb er-Januray (NDJ) r e construction, and its corr elation to NDJ ERSST v5 and NDJ
BC09 is 0.76 and 0.75, r esp e ctiv ely , and the co efficient of efficient is 0.47 and 0.5, r esp e ctiv ely .
4.8 Supplementar y Information
4.8.1 Cr oss-validation of the last millennium r eanalysis r e constructions
The last millennium r eanalysis (LMR, Hakim et al., 2016 ; T ar dif et al., 2019 ) r e constructions in the main
te xt ar e p erforme d with a calibration p erio d o v er 1850-2000 CE, which o v erlaps with the validation p erio d
(1881-2000 CE) in Figur e 4.1 and leads to concerns of p otential o v erfitting.
T o e valuate whether o v erfitting actually o ccurs, w e r ep eat the LMR r e constructions describ e d in the
main te xt, LMR ( Corals), LMR (Li13b6), and LMR ( Corals+Li13b6), with calibration p erio d o v er 1881-1940
CE and 1941-2000 CE. For comparison, w e r ep eat the validation in Figur e 4.1 o v er 1881-1940 CE (Figur e
S4.1 ) and 1941-2000 CE (Figur e S4.2 ) as baselines (tagge d as T est I and II, r esp e ctiv ely ). The r e construction
with calibration p erio d o v er 1941-2000 CE is v erifie d o v er validation p erio d 1881-1940 CE (tagge d as T est
III) (Figur e S4.3 ), and the r e construction with calibration p erio d o v er 1981-1940 CE is v erifie d o v er valida-
tion p erio d 1941-2000 CE (tagge d as T est I V) (Figur e S4.4 ), so that the calibration and validation p erio ds
ar e disjoint.
The validation skill of the r e constructe d Niño 3.4 is summarize d in SI T able S4.1 . Comparing T est III
with T est I, the corr elation co efficient (R ) dr ops by 0.02, 0.06, and 0.04 for LMR ( Corals), LMR (Li13b6), and
LMR ( Corals+Li13b6), r esp e ctiv ely , while the co efficient of efficiency (CE ) (Nash and Sutcliffe , 1970 ) dr ops
by 0.03, 0.11, and 0.05, r esp e ctiv ely . Similarly , comparing T est I V with T est II, R dr ops by 0.05 for LMR
( Corals), LMR (Li13b6), and LMR ( Corals+Li13b6), while CE dr ops by 0.21, 0.11, and 0 .14, r esp e ctiv ely .
92
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC1)
a
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.39
g
4 2 0 2 4
NADA (PC1)
4
2
0
2
4
R=0.39
m
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC2)
b
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.27
h
4 2 0 2 4
NADA (PC2)
4
2
0
2
4
R=0.27
n
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC1)
c
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.46
i
4 2 0 2 4
MADA (PC1)
4
2
0
2
4
R=0.46
o
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC2)
d
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.33
j
4 2 0 2 4
MADA (PC2)
4
2
0
2
4
R=0.33
p
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
Kauri (TRW)
e
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.40
k
4 2 0 2 4
Kauri (TRW)
4
2
0
2
4
R=0.40
q
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
SA Altiplano (TRW)f
1880 1900 1920 1940 1960 1980 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
R=0.49
l
0 1 2
SA Altiplano (TRW)
4
2
0
2
4
R=0.49
r
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
Figur e 4.6: ( a-f ) Timeseries of the six b est pr e dictors fr om Li et al. ( 2013 ), including the first tw o principal
comp onents of NAD A and MAD A, the K auri tr e e-ring comp osite (Fo wler et al., 2008 ), as w ell as the South
American Altiplano tr e e-ring comp osite (Morales et al., 2012 ), o v er the past millennium (1100-2000 CE).
( g-l) Same as in ( a-f), but o v er the instrumental p erio d (1881-2000 CE). V alidation is p erforme d against
the De cemb er-Februar y (DJF) seasonally av erage d Niño 3.4 calculate d fr om Extende d Re constructe d Sea
Surface T emp eratur e , V ersion 5 (ERSST v5, Huang et al., 2017 ) o v er the instrumental p erio d (1881-2000
CE). (m-r ) Scatter plots of the data p oints in ( g-l). The black and color e d dots denote the data p oints at
y ear 0 and y ear 1 of large eruption y ears (188 3, 1902, 1913, 1951, 1963, 1982, 1991) as in Li et al. ( 2013 ),
r esp e ctiv ely . The dashe d gr e y lines denote the linear r egr ession fitting cur v es. R=corr elation.
93
1600 1700 1800 1900 2000
Year (CE)
4
3
2
1
0
1
2
3
4
Niño 3.4 [K]
a
Li13 reconstruction
50y rolling variance
2 0 2 4 6
Years relative to eruption
0.8
0.4
0.0
0.4
0.8
1.2
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
b
Large (VEI>4) eruptions (n=22)
excluding 1883, 1902, 1913, 1951, 1963, 1982, 1991 (n=15)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
KDE
Year 1
1835
1600
1673
1641
1586
1815
1350
1360
1680
1831
1450
1822
1593
1580
1660
Signif. ratio: (3,2,1)/15
d
excluding 1883, 1902, 1913, 1951,
1963, 1982, 1991 (n=15)
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
KDE
Year 1
1835
1600
1673
1641
1586
1815
1350
1360
1680
1831
1982
1450
1883
1822
1593
1902
1580
1951
1660
1913
1963
1991
Signif. ratio: (9,6,3)/22
c
Large (VEI>4) eruptions (n=22)
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
Figur e 4.7: ( a) The timeseries of t he Li et al. ( 2013 ) Niño 3.4 r e construction ( denote d as Li13). ( b) SEA of
Li13, comparing the p o ol of all 22 large eruptions define d as V olcanic Explosivity Inde x (VEI) larger than 4
and the p o ol e xcluding the e v ents o v er the instrumental p erio d after 1850 CE. ( c) Ranking analysis of Li13
with the p o ol of all 22 large eruptions. ( d) Ranking analysis of Li13 with the p o ol e xcluding the e v ents
o v er the instrumental p erio d after 1850 CE. The color denotes the eruption y ear .
94
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1257
1286
1345
1595
1695
1809
1815
R
2
=0.23
Year 0
a Asymmetry between [0.8, 1.5] (n=7)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1108
1171
1230
1453
1585 1600
1640 1831
1835
1883
R
2
=0.28
Year 0
b Asymmetry > 1.5 (n=10)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1191
1276
1458
Year 0
c Asymmetry < 0.8 (n=3)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1230
1257
1458
1815
Year 0
d Extreme events (n=4)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1257
1286
1345
1595
1695
1809
1815
R
2
=0.02
Year 1
e Asymmetry between [0.8, 1.5] (n=7)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1108
1171
1230
1453
1585
1600
1640
1831
1835
1883
R
2
=0.03
Year 1
f Asymmetry > 1.5 (n=10)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1191
1276
1458
Year 1
g Asymmetry < 0.8 (n=3)
0 20 40 60
VSSI
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1230
1257
1458
1815
Year 1
h Extreme events (n=4)
LMR (Corals+Li13b6)
Figur e 4.8: Scatter plots of the r e constructe d y ear 0 and y ear 1 Niño 3.4 anomaly in LMR ( Corals+Li13b6)
against VSSI fr om e V olv2k v ersion 3 (T o ohe y and Sigl, 2017 ) for tr opical eruption e v ents liste d in T able
4.1 , categorize d by ( a, e) A symmetr y b etw e en [0.8, 1.5], ( b , f ) A symmetr y > 1.5, ( c, g) A symmetr y < 0.8 ,
as w ell as ( d, h) e xtr eme e v ents with VSSI>20 (1230, 1257, 1458, 1815). The dashe d gr e y lines denote the
linear r egr ession fitting cur v es. R=corr elation co efficient. A symmetr y=hemispheric asymmetr y (NH/SH)
of aer osol spr ead for tr opical eruptions base d on ratio of Gr e enland to Antar ctic flux.
95
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Year (CE)
4
3
2
1
0
1
2
3
4
Temp. anom. [K]
LMR (Corals+Li13b6)
Tropical average (20S to 20N)
Niño 3.4 (SST)
Niño 3.4 (RSST)
Figur e 4.9: The timeseries of tr opical av erage (20S-20N) temp eratur e anomaly , sea surface temp eratur e
(SST) base d Niño 3.4, and r elativ e sea surface temp eratur e (RSST , Kho dri et al., 2017 ) base d Niño 3.4.
O v erall, the skill degradation is at an acceptable le v el, and w e conclude that o v erfitting is not a major
issue with the original r e constructions in the main te xt. It is also w orth noting that LMR ( Corals+Li13b6)
p erforms the b est in all of the tests compar e d to LMR ( Corals) and LMR (Li13b6), indicating that the strategy
of combining b oth tr e e-ring and coral ar chiv es is w orking as e xp e cte d.
T able S4.1: V alidation skill of the LMR-r e constructe d Niño 3.4.
T est Calibration p erio d V alidation p erio d LMR ( Corals) LMR (Li13b6) LMR ( Corals+Li13b6)
I 1850-2000 1881-1940 R = 0.75 ,CE = 0.52 R = 0.79 ,CE = 0.62 R = 0.83 ,CE = 0.66
II 1850-2000 1941-2000 R = 0.88 ,CE = 0.73 R = 0.72 ,CE = 0.51 R = 0.89 ,CE = 0.76
III 1941-2000 1881-1940 R = 0.73 ,CE = 0.49 R = 0.73 ,CE = 0.51 R = 0.79 ,CE = 0.61
I V 1881-1940 1941-2000 R = 0.83 ,CE = 0.52 R = 0.67 ,CE = 0.40 R = 0.84 ,CE = 0.62
R=corr elation co efficient, CE=co efficient of efficiency (Nash and Sutcl iffe , 1970 ).
4.8.2 T est on typ e I err or in sup erp ose d ep o ch analysis
Sup erp ose d ep o ch analysis (SEA ) is classic and widely use d for the analysis of ENSO r esp onse to v olcanism
(Haur witz and Brier , 1981 ; Li et al., 2013 ; De e et al., 2020 ), y et the sample size is usually small due to the
infr e quent natur e of e xplosiv e eruptions. Ther efor e , typ e I err or (false p ositiv e) is p otentially a risk of
the analysis, which means accidentally identifying significant ENSO r esp onse when the for cing is actually
none xistent.
W e p erform a typ e I err or test on SEA utilizing the GFDL CM2.1 simulation (Delw orth et al., 2006 ;
Wittenb erg et al., 2006 ), which is a 4000 y ear long simulation that is fr e e of v olcanic for cing. Follo wing the
pr o ce dur e of SEA describ e d in the Metho ds se ction of the main te xt, w e calculate the b or eal winter (DJF)
Niño 3.4 timeseries fr om the simulation, and conv ert it to y ear 1 Niño 3.4 anomaly , which is define d as the
original value at each y ear 1 with the mean of thr e e y ears prior to y ear 0 r emo v e d.
96
W e define a p ositiv e e v ent as the y ear when the comp osite of pr e-define d v olcanic y ears is larger than
a certain quantile (80%, 90%, or 95%) of the comp osites of randomly drawn non-v olcanic y ears, which
is appr o ximately the same quantile of all y ears, as w e test only with a small numb er of v olcanic y ears
compar e d to the whole 4000 y ears. Since the simulation is fr e e of v olcanic for cing, ther e could b e no
causal r elationship b etw e en v olcanism and ENSO e v ents, and any p ositiv e e v ent is hence false p ositiv e .
In practice , w e test the cases when the numb er of v olcanic y ears n = 3,5,10,15,20 . For instance ,
whenn = 20 , w e randomly draw 20 y ears as ” e v ent” y ears 10,000 times ( with r eplacement). Each time ,
w e calculate the comp osite of y ear 1 Niño 3.4 anomaly o v er v olcanic y ears, compar e it to the (80%, 90%,
or 95%) quantiles of the comp osites of all y ears, and flag the e v ent as p ositiv e when the comp osite value
of v olcanic y ears is larger than the (80%, 90%, or 95%) quantiles of all y ears. Then w e compute the false
p o sitiv e rate (FPR) as the numb er of p ositiv e e v ents divide d by 10,000.
T able S4.2: Pr obability of accidentally identifying significant ENSO r esp onse .
Sample size FPR (80%) FPR (90%) FPR (95%)
n=3 10.55% 1.6% 4×10
−4
n=5 5.49% 0.33% < 1×10
−4
n=10 1.21% 2×10
−4
< 1×10
−4
n=15 0.25% < 1×10
−4
< 1×10
−4
n=20 7×10
−4
< 1×10
−4
< 1×10
−4
FPR=false p ositiv e rate
T able S4.2 sho ws the pr obability of accidentally identifying significant ENSO r esp onse in such a SEA
setting. It can b e se en that for the 95% le v el, the FPR is close to 0 e v en for a tiny sample size n = 3 . For the
v er y r elaxe d 80% le v el, the FPR is non-ignorable when n≤ 5 , and gets b elo w 1.5% and b e come acceptable
whenn≥ 10 .
Base d on the r esults ab o v e , w e conclude that SEA is o v erall r obust r egar ding typ e I err or . It means
that, when the obje ct is the comp osite value , the small sample size is not likely to cause a false dete ction
of significant e v ent in practice . It is w orth noting, ho w e v er , that this do es not imply that SEA is r obust
r egar ding bias, as discusse d in the main te xt.
Non-stationar y sensitivity in the last millennium r eanalysis
Figur e 4.3 (main te xt) hav e sho wn a non-stationar y sensitivity of ENSO r esp onse to v olcanism in Li et al.
( 2013 ) r e construction ( her eafter Li13), b etw e en pr e-instrumental and instrumental p erio d eruptions. Her e
w e sho w that such n on-stationar y sensitivity also e xists in our LMR r e constructions, including b oth LMR
(Li13b6) (Figur e S4.5 ) and LMR ( Corals+Li13b6) (Figur e S4.6 ).
Similar to Li13, the LMR r e constructions also shar e the b ehavior of non-stationar y variance (Figur e
S4.5 a and Figur e S4.6 a), and the eruptions o v er instrumental p erio d ( after 1850 CE) ar e dominating the SEA
analysis in b oth LMR r e constructions that the significance le v el of the y ear 1 ENSO r esp onse dr ops fr om
>99% to b elo w 95% once the y hav e b e en e xclude d (Figur e S4.5 b and Figur e S4.6 b). The ranking analysis
sho ws that the eruptions o v er instrumental p erio d ar e o v erall follo w e d by str onger Niño 3.4 anomaly than
97
that of eruptions o v er the pr e-instrumental p erio d (Figur e S4.5 c and Figur e S4.6 c), and the significance ratio
in ranking analysis dr ops significantly once the eruptions o v er instrumental p erio d hav e b e en e xclude d
(Figur e S4.5 d and Figur e S4.6 d).
This comparison b etw e en Li13 and our LMR r e constructions indicates that all these r e constructions
shar e similar characteristics, and the se emingly incongruous conclusions b etw e en Li13 and our study ,
r egar ding the statistical significance of ENSO r esp onse to v olcanism, ar e mainly cause d by the differ ent
p o ols of eruption e v ents for analysis.
4.8.3 The ENSO r esp onse to v olcanism in PMIP3 and CESM-LME simulations
Pr e vious mo deling studies hav e suggeste d o v erall significant ENSO r esp onse to v olcanism (McGr egor ,
Timmermann, and Timm, 2010 ; Ste v enson et al., 2016 ). Her e w e inv estigate the ENSO r esp onse to v ol-
canism in Pale o climate Mo delling Inter comparison Pr oje ct P hase III (PMIP3, Braconnot et al., 2012 ) and
Community Earth System Mo del Last Millennium Ensemble simulations ( CESM-LME Otto-Bliesner et al.,
2015 ) with SEA and ranking analysis. Since tw o differ ent v olcanic for cing sour ces ( Gao , Rob o ck, and Am-
mann, 2008 ; Cr o wle y et al., 2008 ) ar e applie d in these simulations (T able S4.3 ), w e compar e these for cing
sour ces with e V olv2k v3 (T o ohe y and Sigl, 2017 ) that w e use d for the analysis for r e constructions, and
sele ct eruption e v ents that ar e in agr e ement but only with small temp oral offsets for our analysis (Figur e
S4.7 ). The r esults of SEA and ranking analysis applie d on SST base d Niño 3.4 anomaly values ar e sho wn in
Figur e S4.8 , S4.9 , and the same analyses applie d on r elativ e sea surface temp eratur e (RSST , Kho dri et al.,
2017 ) base d Niño 3.4 anomaly values ar e sho wn in Figur e S4.10 , S4.11 . The differ ence b etw e en SST and
RSST in individual simulations ar e sho wn in Figur e S4.12 .
Comparing the SST base d and RSST base d r esults, w e confirm t he impact of the RSST conv ersion on
the analyses as suggeste d in pr e vious studies (Kho dri et al., 2017 ; Rob o ck, 2020 ), which o v erall b o osts
the significance of ENSO r esp onse to v olcanism. Ho w e v er , w e note that, e v en with the RSST conv ersion,
insignificant r esp onses ar e still obser v e d in simulations such as BCC, FGO ALS, and MIROC in SEA. Mor e-
o v er , all simulations consistently sho w lo w significance ratio in ranking analysis for b oth y ear 0 and y ear
1 after eruptions.
A s mentione d in the main te xt, significance in SEA is ne cessar y but insufficient to confirm a r obust
r elationship b etw e en v olcanism and El Niño e v ents. When a r obust r elationship is assume d, any counter e x-
amples must b e coincident e v ents, and the significance ratio in ranking analysis should b e high enough,
say ab o v e 0.9. Y et, ranking a nalysis r esults in Figur e S4.10 , S4.11 indicate that the significance ratio is
consistently b elo w 0.5, e v en for the 80% significance le v el, among all the simulations, suggesting that the
r elationship b etw e en v olcanism and El Niño e v ents is not r eally r obust – the ENSO r esp onse after erup-
tions ar e not statistically differ ent fr om those in non-v olcanic y ears. This conclusion is in agr e ement with
our analysis on the LMR r e constructions.
98
T able S4.3: V olcanic for cing a pplie d in Pale o climate Mo delling Inter comparison Pr oje ct P hase III (PMIP3,
Braconnot et al., 2012 ) and Community Earth System Mo del Last Millennium Ensemble simulations
( CESM-LME Otto-Bliesner et al., 2015 ).
Mo del BCC CCSM4 MRI CESM FGO ALS IPSL GISS CISRO HadCM3 MIROC MPI
V olcanic for cing GRA GRA GRA GRA GRA GRA GRA CEA CEA CEA CEA
GRA = Gao , Rob o ck, and Ammann ( 2008 ); CEA = Cr o wle y et al. ( 2008 ).
4.8.4 Sensitivity to r e construction season in the last millennium r eanalysis
In main te xt, the r e construction season is De cemb er-Februar y (DJF), which is a typical season when the
ENSO signal is most pr ofound (Diaz, Ho erling, and Eischeid, 2001 ). Y et, a r e cent mo deling study (Pr e dy-
baylo et al., 2020 ) has suggeste d that the ENSO r esp onse to v olcanism is rather w eak during DJF , but
could b e str ong during Januar y-Septemb er ( JAS) and/or Octob er-De cemb er ( OND ). Ther efor e , w e r ep eat
our r e construction e xp eriments for these tw o seasons along with the SEA and ranking analysis to test the
sensitivity of our conclusion to the choice of the r e construction season.
First, w e e valuate the corr elation b etw e en the b est six pr e dictors in Li et al. ( 2013 ) (Li13b6) and the
Niño 3.4 signal in the Extende d Re constructe d Sea Surface T emp eratur e v5 (ERSST v5 Huang et al., 2017 )
during those tw o seasons (Figur e S4.13 and Figur e S4.14 ). It can b e se en that OND is o v erall a b etter target
season than JAS, although the corr elation skill with the JAS target is still acceptable . Ther efor e , w e may
tr eat Li13b6 as r eliable pr e dictors for b oth the JAS and OND ENSO signal. Besides, since the coral r e cor ds
w e use d for the r e construction ar e mainly monthly r esolv e d, the y can b e pr o cesse d to r e construct the JAS
and OND seasons without seasonal bias.
Figur e S4.15 and Figur e S4.16 indicate that the r e construction skill for the JAS and OND seasons is
comparable to that with a DJF r e construction season in main te xt. Sp e cifically , the skill for the JAS r e-
construction is slightly w eaker due to the w orse corr elation b etw e en Li13b6 and the JAS ENSO signal
(Figur e S4.13 ), while the skill for the OND r e construction is slightly b etter than that with a DJF target due
to the slightly b etter corr elation b etw e en Li13b6 and the OND ENSO signal (Figur e S4.14 ). Ther efor e , the
r e c onstructions for those tw o seasons ar e o v erall successful.
With the SEA and ranking analysis on the r e constructions of the JAS and OND seasons (Figur e S4.17
and Figur e S4.18 ), w e se e o v erall insignificant ENSO r esp onse to v olcanism, which is in agr e ement with
our D JF r e constructions. This test indicates that, our conclusion is insensitiv e to the choice of the r e con-
struction season, and our obser vational e vidence do es not supp ort the statement of the mo deling study
(Pr e dybaylo et al., 2020 ) that the ENSO r esp onse could b e str ong during JAS and/or OND seasons. W e note
that although this is in contradiction to the mo deling study (Pr e dybaylo et al., 2020 ), it may b e e xplaine d
by the limitations of curr ently available pr o xy r e cor ds and other cav eats that w e hav e discusse d in main
te xt.
4.8.5 A comparison b etw e en historical SST analyses pr o ducts
In our r e constructions, a spatially complete d v ersion of HadCRU T4.6 (V accar o et al., 2021 ) le v eraging
the GraphEM ( Guillot, Rajaratnam, and Emile-Geay , 2015 ) algorithm is use d as the target for calibration,
99
and the Extende d Re constructe d Sea Surface T emp eratur e v5 (ERSST v5, Huang et al., 2017 ) is use d for
validation. W e compar e them along with the NASA Go ddar d Institute for Space Studies ( GISS) Surface
T emp eratur e Analysis ( GISTEMP , Hansen et al., 2010 ), which is use d as the default calibration target in
the official LMR pr o ducts (Hakim et al., 2016 ; T ar dif et al., 2019 ). Figur e S4.19 sho ws that the long term
tr end of the DJF Niño 3.4 signal in the thr e e pr o d ucts ar e slightly differ ent, while the high-fr e quency
signal is o v erall consistent with slight differ ence . The fact that w e use differ ent targets for calibration and
validation and still get r e constructions with r emarkably high skill suggests an e vidence of r obustness of
our r e constructions.
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.88, CE=0.73
d
LMR (Corals)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.72, CE=0.51
e
LMR (Li13b6)
1940 1950 1960 1970 1980 1990 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.89, CE=0.76
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
Test I
Figur e S4.1: Same as Figur e 4.1 , but validation is p erforme d o v er 1881- 1940 CE.
100
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.88, CE=0.73
d
LMR (Corals)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.72, CE=0.51
e
LMR (Li13b6)
1940 1950 1960 1970 1980 1990 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.89, CE=0.76
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
Test II
Figur e S4.2: Same as Figur e 4.1 , but validation is p erforme d o v er 1941- 2000 CE.
101
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1880 1890 1900 1910 1920 1930 1940
4
2
0
2
4
Niño 3.4 [K]
R=0.73, CE=0.49
d
LMR (Corals)
1880 1890 1900 1910 1920 1930 1940
4
2
0
2
4
Niño 3.4 [K]
R=0.73, CE=0.51
e
LMR (Li13b6)
1880 1890 1900 1910 1920 1930 1940
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.79, CE=0.61
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
Test III
Figur e S4.3: Same as Figur e S4.1 , but the LMR r e constructions ar e p erforme d with calibration p erio d o v er
1941-2000 CE.
102
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.83, CE=0.52
d
LMR (Corals)
1940 1950 1960 1970 1980 1990 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.67, CE=0.40
e
LMR (Li13b6)
1940 1950 1960 1970 1980 1990 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.84, CE=0.62
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
Test IV
Figur e S4.4: Same as Figur e S4.2 , but the LMR r e constructions ar e p erforme d with calibration p erio d o v er
1881-1940 CE.
103
1600 1700 1800 1900 2000
Year (CE)
4
3
2
1
0
1
2
3
4
Niño 3.4 [K]
a
LMR (Li13b6)
50y rolling variance
2 0 2 4 6
Years relative to eruption
0.8
0.4
0.0
0.4
0.8
1.2
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
b
Large (VEI>4) eruptions (n=22)
excluding 1883, 1902, 1913, 1951, 1963, 1982, 1991 (n=15)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
Year 1
1835
1600
1680
1641
1360
1350
1822
1673
1815
1450
1831
1580
1593
1660
1586
Signif. ratio: (5,2,0)/15
d
excluding 1883, 1902, 1913, 1951,
1963, 1982, 1991 (n=15)
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
Year 1
1835
1600
1680
1641
1360
1350
1822
1673
1815
1450
1831
1580
1593
1660
1963
1586
1883
1951
1902
1982
1913
1991
Signif. ratio: (12,6,5)/22
c
Large (VEI>4) eruptions (n=22)
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
Figur e S4.5: Same as Figur e 4.3 , bu t for LMR (Li13b6).
104
1600 1700 1800 1900 2000
Year (CE)
4
3
2
1
0
1
2
3
4
Niño 3.4 [K]
a
LMR (Corals+Li13b6)
50y rolling variance
2 0 2 4 6
Years relative to eruption
0.8
0.4
0.0
0.4
0.8
1.2
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
b
Large (VEI>4) eruptions (n=22)
excluding 1883, 1902, 1913, 1951, 1963, 1982, 1991 (n=15)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
Year 1
1835
1600
1680
1641
1360
1350
1822
1673
1815
1450
1831
1580
1593
1660
1586
Signif. ratio: (5,2,0)/15
d
excluding 1883, 1902, 1913, 1951,
1963, 1982, 1991 (n=15)
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
Year 1
1835
1600
1680
1641
1360
1350
1822
1673
1815
1450
1831
1580
1593
1660
1963
1586
1883
1951
1902
1982
1913
1991
Signif. ratio: (12,6,5)/22
c
Large (VEI>4) eruptions (n=22)
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
1000
1200
1400
1600
1800
2000
Year (CE)
Figur e S4.6: Same as Figur e 4.3 , but for LMR ( Corals+Li13b6).
105
1100 1200 1300 1400 1500 1600 1700 1800
0
20
40
60
Toohey et al. (2017)
1230 1257 1286 1458 1585 1600 1640 1695 1783 1809 18151835
1100 1200 1300 1400 1500 1600 1700 1800
0
100
200
300
Gao et al. (2008)
1227 1258 1284 1459 1584 1600 1641 1693 1783 1809 18151835
1100 1200 1300 1400 1500 1600 1700 1800
Year (CE)
0
10
20
Crowley et al. (2008)
1228 1257 1285 1456 1585 1600 1641 1694 1784 1809 18151836
Figur e S4.7: The thr e e v olcanic for cing sour ces in timeseries: T o ohe y and Sigl ( 2017 ), Gao , Rob o ck, and
Ammann ( 2008 ), and Cr o wle y et al. ( 2008 ). V ertical gr e y cur v es denote the y ears with r elativ e large for c-
ing values ( > 6, > 20, > 2, r esp e ctiv ely ), among which the consistent e v ents ( with small temp oral offsets)
dete cte d in all of the thr e e sour ces ar e lab ele d with the y ear . The quantities of the thr e e sour ces ar e global
v olcanic stratospheric sulfur inje ction of eruption, global total stratospheric sulfate aer osol inje ction, and
av erage d e xtratr opical aer osol optical depth, r esp e ctiv ely .
106
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
b
BCC
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
c
CCSM4
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
d
MRI
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
e
CESM
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
f
FGOALS
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
g
IPSL
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
h
GISS
Composite (n=12)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1835
1815
1809
1783
1693
1284
1459
1600
1584
1227
1258
1641
Signif. ratio: (1,0,0)/12 Year 0
i
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1459
1641
1258
1600
1815
1835
1809
1783
1284
1227
1584
1693
Signif. ratio: (4,2,2)/12 Year 0
j
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1258
1809
1835
1641
1693
1783
1227
1584
1815
1600
1284
1459
Signif. ratio: (2,1,1)/12 Year 0
k
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1600
1641
1783
1835
1809
1258
1459
1815
1584
1693
1227
1284
Signif. ratio: (4,2,2)/12 Year 0
l
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1284
1641
1809
1584
1258
1600
1693
1783
1227
1459
1835
1815
Signif. ratio: (2,1,1)/12 Year 0
m
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1459
1258
1584
1284
1815
1783
1693
1600
1809
1227
1641
Signif. ratio: (2,1,0)/12 Year 0
n
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1815
1641
1227
1459
1600
1584
1809
1783
1693
1258
1835
1284
Signif. ratio: (1,1,0)/12 Year 0
o
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1258
1835
1783
1809
1693
1641
1459
1600
1584
1227
1815
1284
Signif. ratio: (2,0,0)/12 Year 1
p
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1258
1284
1459
1809
1815
1600
1693
1584
1641
1783
1835
1227
Signif. ratio: (4,1,1)/12 Year 1
q
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1783
1227
1258
1693
1459
1600
1835
1809
1815
1584
1284
1641
Signif. ratio: (3,0,0)/12 Year 1
r
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1693
1783
1641
1600
1284
1227
1835
1258
1809
1459
1815
1584
Signif. ratio: (4,2,1)/12 Year 1
s
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1835
1258
1693
1809
1815
1584
1600
1284
1227
1783
1641
1459
Signif. ratio: (2,0,0)/12 Year 1
t
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1258
1815
1600
1809
1641
1835
1693
1459
1783
1584
1284
1227
Signif. ratio: (1,1,0)/12 Year 1
u
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1815
1258
1835
1284
1600
1809
1584
1641
1227
1693
1459
1783
Signif. ratio: (2,2,2)/12 Year 1
v
80%
90%
95%
50%
Figur e S 4.8: Similar to Figur e 4.3 , but for mo del simulations with Gao , Rob o ck, and Ammann ( 2008 ) v ol-
canic for cing applie d.
107
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
b
CSIRO
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
c
HadCM3
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
d
MIROC
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
e
MPI
Composite (n=12)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1694
1836
1600
1228
1456
1784
1809
1257
1815
1641
1285
1585
Signif. ratio: (2,1,1)/12 Year 0
f
80%
90%
95%
50%
3 2 1 0 1 2 3
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1815
1694
1257
1285
1228
1784
1585
1456
1641
1809
1600
1836
Signif. ratio: (1,0,0)/12 Year 0
g
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1641
1784
1285
1456
1585
1815
1809
1257
1228
1836
1600
1694
Signif. ratio: (1,1,1)/12 Year 0
h
80%
90%
95%
50%
3 2 1 0 1 2 3
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1585
1809
1694
1836
1257
1815
1641
1456
1285
1784
1228
1600
Signif. ratio: (4,2,0)/12 Year 0
i
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1456
1257
1228
1600
1694
1641
1285
1836
1815
1809
1784
1585
Signif. ratio: (1,1,1)/12 Year 1
j
80%
90%
95%
50%
3 2 1 0 1 2 3
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1600
1456
1257
1815
1836
1285
1809
1228
1694
1641
1784
1585
Signif. ratio: (3,0,0)/12 Year 1
k
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1784
1228
1600
1585
1641
1456
1285
1809
1257
1815
1836
1694
Signif. ratio: (1,0,0)/12 Year 1
l
80%
90%
95%
50%
3 2 1 0 1 2 3
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1257
1456
1585
1694
1641
1815
1836
1809
1784
1228
1600
1285
Signif. ratio: (4,2,0)/12 Year 1
m
80%
90%
95%
50%
Figur e S4.9: Similar to Figur e S4.8 , but for mo del simulations with Cr o wle y et al. ( 2008 ) v olcanic for cing
applie d.
108
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
b
BCC
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
c
CCSM4
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
d
MRI
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
e
CESM
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
f
FGOALS
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
g
IPSL
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
h
GISS
Composite (n=12)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1815
1809
1783
1693
1459
1284
1584
1600
1227
1258
1641
Signif. ratio: (2,0,0)/12 Year 0
i
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1459
1258
1641
1815
1600
1809
1835
1783
1284
1227
1584
1693
Signif. ratio: (5,2,2)/12 Year 0
j
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1258
1809
1835
1783
1693
1641
1227
1815
1584
1600
1284
1459
Signif. ratio: (2,1,0)/12 Year 0
k
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1600
1641
1783
1835
1809
1258
1459
1815
1693
1584
1227
1284
Signif. ratio: (4,2,2)/12 Year 0
l
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1284
1641
1809
1584
1258
1600
1693
1783
1459
1227
1835
1815
Signif. ratio: (2,1,1)/12 Year 0
m
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1835
1459
1284
1815
1584
1600
1783
1693
1809
1258
1641
1227
Signif. ratio: (3,1,0)/12 Year 0
n
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1815
1459
1227
1641
1600
1584
1693
1809
1783
1835
1284
1258
Signif. ratio: (3,1,0)/12 Year 0
o
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1783
1258
1809
1693
1459
1641
1584
1600
1227
1284
1815
Signif. ratio: (2,2,0)/12 Year 1
p
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1284
1459
1809
1258
1693
1584
1600
1783
1815
1641
1835
1227
Signif. ratio: (5,3,1)/12 Year 1
q
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1783
1227
1459
1693
1600
1835
1584
1809
1284
1258
1641
1815
Signif. ratio: (6,4,2)/12 Year 1
r
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
1693
1783
1227
1641
1600
1284
1835
1459
1809
1258
1815
1584
Signif. ratio: (5,4,3)/12 Year 1
s
80%
90%
95%
50%
4 2 0 2 4
Niño 3.4 [K]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1835
1693
1809
1815
1258
1584
1227
1284
1600
1783
1459
1641
Signif. ratio: (2,0,0)/12 Year 1
t
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1815
1600
1809
1258
1641
1783
1459
1284
1693
1835
1584
1227
Signif. ratio: (1,1,1)/12 Year 1
u
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1815
1284
1835
1584
1600
1227
1809
1459
1641
1693
1258
1783
Signif. ratio: (4,2,2)/12 Year 1
v
80%
90%
95%
50%
Figur e S4.10: Similar to Figur e S4.8 , but the Niño 3.4 anomaly values ar e calculate d base d on r elativ e sea
surface temp eratur e (RSST , Kho dri et al., 2017 ).
109
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
b
CSIRO
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
c
HadCM3
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
d
MIROC
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
e
MPI
Composite (n=12)
individual events
1.0 0.5 0.0 0.5 1.0
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1694
1784
1836
1228
1600
1257
1456
1641
1815
1809
1285
1585
Signif. ratio: (6,2,1)/12 Year 0
f
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1815
1694
1257
1285
1784
1600
1228
1585
1641
1809
1456
1836
Signif. ratio: (3,1,1)/12 Year 0
g
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1641
1285
1784
1257
1815
1600
1585
1228
1809
1456
1836
1694
Signif. ratio: (2,1,1)/12 Year 0
h
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1694
1257
1585
1815
1809
1641
1836
1285
1228
1456
1784
1600
Signif. ratio: (5,2,0)/12 Year 0
i
80%
90%
95%
50%
1.0 0.5 0.0 0.5 1.0
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1784
1456
1641
1836
1285
1228
1694
1600
1809
1257
1585
1815
Signif. ratio: (4,3,2)/12 Year 1
j
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1600
1836
1257
1285
1456
1809
1815
1228
1784
1585
1694
1641
Signif. ratio: (3,3,0)/12 Year 1
k
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1784
1600
1585
1285
1228
1641
1257
1836
1456
1815
1809
1694
Signif. ratio: (1,0,0)/12 Year 1
l
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1257
1585
1456
1694
1641
1784
1836
1815
1285
1600
1228
1809
Signif. ratio: (5,4,2)/12 Year 1
m
80%
90%
95%
50%
Figur e S4.11: Similar to Figur e S4.9 , but the Niño 3.4 anomaly values ar e calculate d base d on r elativ e sea
surface temp eratur e (RSST , Kho dri et al., 2017 ).
110
850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850
Year (CE)
4
3
2
1
0
1
2
3
4
Temp. anom. [K]
Tropical average temperature in PMIP3 and CESM-LME simulations
BCC
CCSM4
CESM
CSIRO
FGOALS
GISS
HadCM3
IPSL
MIROC
MPI
MRI
Figur e S4.12: T r opical av erage temp eratur e (the differ ence b etw e en SST and RSST) in PMIP3 and CESM-
LME simulations.
111
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC1)
a
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.36
g
4 2 0 2 4
NADA (PC1)
4
2
0
2
4
R=0.36
m
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC2)
b
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.20
h
4 2 0 2 4
NADA (PC2)
4
2
0
2
4
R=0.20
n
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC1)
c
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.44
i
4 2 0 2 4
MADA (PC1)
4
2
0
2
4
R=0.44
o
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC2)
d
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.18
j
4 2 0 2 4
MADA (PC2)
4
2
0
2
4
R=0.18
p
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
Kauri (TRW)
e
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.39
k
4 2 0 2 4
Kauri (TRW)
4
2
0
2
4
R=0.39
q
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
SA Altiplano (TRW)f
1880 1900 1920 1940 1960 1980 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
R=0.43
l
0 1 2
SA Altiplano (TRW)
4
2
0
2
4
R=0.43
r
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
Figur e S4.13: Same as Figur e 4.2 , but with the July-Septemb er ( JAS) seasonally av erage d Extende d Re con-
structe d Sea Surface T emp eratur e v5 (ERSST v5, Huang et al., 2017 ).
112
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC1)
a
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.37
g
4 2 0 2 4
NADA (PC1)
4
2
0
2
4
R=0.37
m
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
NADA (PC2)
b
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.27
h
4 2 0 2 4
NADA (PC2)
4
2
0
2
4
R=0.27
n
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC1)
c
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.47
i
4 2 0 2 4
MADA (PC1)
4
2
0
2
4
R=0.47
o
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
MADA (PC2)
d
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.29
j
4 2 0 2 4
MADA (PC2)
4
2
0
2
4
R=0.29
p
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
4
2
0
2
4
Kauri (TRW)
e
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
R=0.41
k
4 2 0 2 4
Kauri (TRW)
4
2
0
2
4
R=0.41
q
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
SA Altiplano (TRW)f
1880 1900 1920 1940 1960 1980 2000
Year (CE)
0.0
0.5
1.0
1.5
2.0
R=0.52
l
0 1 2
SA Altiplano (TRW)
4
2
0
2
4
R=0.52
r
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
4
2
0
2
4
ERSSTv5
Figur e S4.14: Same as Figur e 4.2 , but with the Octob er-De cemb er ( OND ) seasonally av erage d Extende d
Re constructe d Sea Surface T emp eratur e v5 (ERSST v5, Huang et al., 2017 ).
113
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.80, CE=0.50
d
LMR (Corals)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.66, CE=0.40
e
LMR (Li13b6)
1880 1900 1920 1940 1960 1980 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.81, CE=0.50
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
4 2 0 2 4
LMR (Corals)
4
2
0
2
4
ERSSTv5
R=0.80
g
4 2 0 2 4
LMR (Li13b6)
4
2
0
2
4
ERSSTv5
R=0.66
h
4 2 0 2 4
LMR (Corals+Li13b6)
4
2
0
2
4
ERSSTv5
R=0.81
i
Year 0 after eruptions
Year 1 after eruptions
Figur e S4.15: Same as Figur e 4.1 , but for the July-Septemb er ( JAS) r e constructions.
114
a
LMR (Corals)
b
LMR (Li13b6)
c
LMR (Corals+Li13b6)
Corals NADA MADA Kauri SA Altiplano
0.0 0.2 0.4 0.6 0.8 1.0
R
2
(vs. ERSSTv5)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.83, CE=0.66
d
LMR (Corals)
1880 1900 1920 1940 1960 1980 2000
4
2
0
2
4
Niño 3.4 [K]
R=0.76, CE=0.57
e
LMR (Li13b6)
1880 1900 1920 1940 1960 1980 2000
Year (CE)
4
2
0
2
4
Niño 3.4 [K]
R=0.87, CE=0.74
f
LMR (Corals+Li13b6)
median
ERSSTv5
interquartile
2.5%-97.5%
4 2 0 2 4
LMR (Corals)
4
2
0
2
4
ERSSTv5
R=0.83
g
4 2 0 2 4
LMR (Li13b6)
4
2
0
2
4
ERSSTv5
R=0.76
h
4 2 0 2 4
LMR (Corals+Li13b6)
4
2
0
2
4
ERSSTv5
R=0.87
i
Year 0 after eruptions
Year 1 after eruptions
Figur e S4.16 : Same as Figur e 4.1 , bu t for the Octob er-De cemb er ( OND ) r e constructions.
115
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
a
LMR (Corals+Li13b6), n=12
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
99%
b
LMR (Corals+Li13b6), n=22
Composite (n=22)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
1276
1453
1182
1230
1286
1640
1257
1695
1191
1345
1171
1458
Signif. ratio: (2,0,0)/12 Year 0
c
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1595
1276
1600
1815
1453
1585
1831
1108
1182
1230
1286
1883
1809
1640
1257
1695
1191
1345
1171
1458
1783 Signif. ratio: (3,1,1)/22 Year 0
d
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
1453
1276
1695
1182
1257
1286
1640
1171
1458
1191
1230
1345
Signif. ratio: (2,0,0)/12 Year 1
e
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1453
1595
1276
1600
1695
1182
1257
1286
1783
1640
1171
1458
1809
1108
1815
1191
1230
1585
1831
1345
1883
Signif. ratio: (5,1,0)/22 Year 1
f
80%
90%
95%
50%
Figur e S4.17: Same as Figur e 4.4 , but for the July-Septemb er ( JAS) r e constructions.
116
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
Niño 3.4 [K]
1%
5%
10%
90%
95%
99%
a
LMR (Corals+Li13b6), n=12
Composite (n=12)
individual events
2 0 2 4 6
Years relative to eruption
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1%
5%
10%
90%
95%
99%
b
LMR (Corals+Li13b6), n=22
Composite (n=22)
individual events
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
1276
1453
1640
1182
1286
1695
1345
1257
1230
1171
1458
1191
Signif. ratio: (2,0,0)/12 Year 0
c
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1276
1595
1453
1815
1600
1585
1640
1182
1108
1286
1831
1883
1695
1809
1345
1257
1230
1171
1458
1191
1783
Signif. ratio: (2,1,0)/22 Year 0
d
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
KDE
1453
1276
1695
1640
1182
1286
1257
1171
1458
1191
1345
1230
Signif. ratio: (3,2,0)/12 Year 1
e
Volcanic events (< 80% non-volcanic years)
Volcanic events (between 80-90% non-volcanic years)
Volcanic events (between 90-95% non-volcanic years)
Volcanic events (>95% non-volcanic years)
Distribution of non-volcanic years
80%
90%
95%
50%
2 1 0 1 2
Niño 3.4 [K]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1835
1453
1783
1276
1595
1600
1695
1640
1182
1286
1257
1171
1809
1458
1108
1585
1815
1191
1345
1230
1831
1883
Signif. ratio: (5,3,0)/22 Year 1
f
80%
90%
95%
50%
Figur e S4.18 : Same as Figur e 4.4 , bu t for the Octob er-De cemb er ( OND ) r e constructions.
117
1860 1880 1900 1920 1940 1960 1980 2000 2020
4
3
2
1
0
1
2
3
4
DJF Niño 3.4 [K]
a DJF Niño 3.4 in historical SST analyses
1860 1880 1900 1920 1940 1960 1980 2000 2020
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
DJF Niño 3.4 [K]
b idem, 10-year lowpass filter, regression over the whole length
HadCRUT4.6 (GraphEM), 0.43 K/century
ERSSTv5, 0.37 K/century
GISTEMP, 0.30 K/century
1860 1880 1900 1920 1940 1960 1980 2000 2020
Year (CE)
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
DJF Niño 3.4 [K]
c idem, 10-year lowpass filter, regression over [1880, 2016]
HadCRUT4.6 (GraphEM), 0.35 K/century
ERSSTv5, 0.24 K/century
GISTEMP, 0.30 K/century
Figur e S4.19: Historical SST analyses pr o ducts of De cemb er-Februar y (DJF) Niño 3.4, including a spatially
complete d v ersion of HadCRU T4.6 (V accar o et al., 2021 ) le v eraging the GraphEM ( Guillot, Rajaratnam, and
Emile-Geay , 2015 ) algorithm, the Extende d Re constructe d Sea Surface T emp eratur e v5 (ERSST v5, Huang
et al., 2017 ), and the NASA Go ddar d Institute for Space Studies ( GISS) Surface T emp eratur e Analysis ( GIS-
TEMP , Hansen et al., 2010 ).
118
Chapter 5
Enhancing pale o climate data analysis and r epr o ducible
r esear ch
5.1 Intr o duction
Mo dern scientific r esear ch r elies heavily on pr ogramming to ols for data analysis and visualization. Ho w-
e v er , it r e quir es non-trivial data science skills, including pr ogramming, to handle w orkflo ws fluently . The
bar is often unne cessarily high if ther e is ne e d for r epr o ducibility or publication-quality figur es. Inde e d,
such aesthetic demands inv olv e the unique choices of fonts, colors, ratios, and other applicable elements
in a figur e , while r epr o ducibility r e quir es that the whole w orkflo w should b e clearly organize d and fully
automate d, i.e ., no manual p ost-pr o cessing is allo w e d, so that the same r esult can b e obtaine d e v er y time
with just “ one click of the start button” . It is thus not uncommon for a scientist to sp end a whole day only
to clean some raw data or to plot a figur e to r eady it for publication. Such tasks ar e essentially irr ele vant
to the cor e of science , but consume a significant amount of scientists’ energy .
Pale o climate data analysis is no e xception, with se v eral typical challenges: (i) Lack of standar dization.
Among scientific data typ es, pale o climate data ar e on the messy side due to the fact that pale o climatology is
highly inter disciplinar y; metadata entries ar e usually rich but non-standar dize d as scientists fr om differ ent
disciplines hav e differ ent practices and conv entions. Ther e ar e thr e e r e cent efforts tr ying to standar dize on
pale o climate data (Emile-Geay et al., 2018 ), including: (1) a standar d data format, namely the LiPD (Linke d
Pale oData) format (McK ay and Emile-Geay , 2016 ; Heiser et al., 2018 ), (2) a standar d terminology , namely
the Linke dEarth ontology
∗
, and (3) standar d practices, namely the Pale o climate Community r ep or Ting
Standar d (PaCTS, Khider et al., 2019 ). Ho w e v er , wide adoption of these standar ds is a slo w pr o cess.
(ii) T emp orally une v en sampling. The pale o climate signal is r e cor de d by differ ent ar chiv es (Figur e 1.2 )
with differ ent sampling rates. Some major ar chiv es, such as ice cor es, se dimentar y r e cor ds, and mollusk
shells, ar e temp orally une v enly-sample d, which means that classic analysis metho ds designe d for e v enly-
sample d data cannot dir e ctly apply unless interp olation is p erforme d ahead, y et interp olation itself is a
non-trivial pr o cessing step , and it may intr o duce une xp e cte d biases into the analysis.
W e designe d and de v elop e d a Python (V an Rossum and Drake Jr , 1995 ) package name d Pyleoclim to
impr o v e this situation, enhancing pale o climate data analysis and r epr o ducible r esear ch. It aims to pr o vide
∗
http://climdyn.usc.edu/publication/leo/
119
scientists with efficient to ols to fr e e their mind fr om te chnicalities, allo wing them to think at a higher le v el
of data analysis and paying mor e attention to scientific questions.
In the follo wing, w e first intr o duce the design of the co de structur e in Se ction 5.2 , and then in Se ction
5.3 w e sho w a list of usage e xamples r egar ding data cleaning and pr epr o cessing, data analysis, and data
visualization. Sp e cifically , w e will demonstrate ho w pale o climate data can b e handle d mor e easily with
Pyleoclim , le v eraging the LiPD format, and ho w scientific r esear ch can b e p erforme d in a mor e r epr o-
ducible fashion. In Se ction 5.4 , w e summarize the highlights of Pyleoclim , and discuss the cav eats and
the outlo ok.
5.2 Co de design
The Pyleoclim package consists of essentially tw o parts: (i) the utilities and (ii) the user interface ( UI) .
The utilities ar e essentially a colle ction of functions that implement detaile d pr o ce dur es, including fil-
tering, interp olation, binning, sp e ctral analysis, wav elet analysis, corr elation analysis, coher ence analysis,
causality analysis, principal comp onent analysis, etc. With the utilities, Pyleoclim can b e use d as a func-
tion librar y , i.e ., when p erforming an analysis task, users may call the available functions that the y ne e d
in Pyleoclim to build w orkflo ws for their o wn applications, which pr o vides sufficient fle xibility , but in
the meantime , the y ne e d to take car e of and pay attention to the details of the input and output of each
function calling.
The UI, on the other hand, allo ws users to interact and utilize those functions at a higher le v el, making
it easier to construct mor e complicate d w orkflo ws in a mor e concise and clear er style . If w e take an analogy
and r egar d the utilities as the engin e of a car , then the UI is the ste ering whe el and the p e dals that allo w
to contr ol the b ehavior of the car .
In this sense , the UI makes Pyleoclim a softwar e , or , in a mor e ne w-fashione d name , an application
( App). The UI follo ws the obje ct-oriente d pr ogramming ( OOP) paradigm (Pier ce , 2002 ), which is base d
on the concept of “ obje cts” and “metho ds” . For instance , in the conte xt of daily life , the command “take a
pictur e ” consists of “pictur e ” as the “ obje ct” , and “take ” as the “metho d”; in the conte xt of pale o climate data
analysis, once w e tr eat a time series as an “ obje ct” , w e may apply some “metho d” to it, such as standar d-
ization, detr ending, or p erforming an advance d analysis. These kind of op erations, in pseudo-co de , can
b e written as Object.method() with certain arguments for the metho d, so “take a pictur e ” can b e written
as Picture.take() , and “standar dize a time series” can b e written as Series.standardize() . This paradigm
pr o vides tw o major b enefits: (i) it brings r emarkable conciseness and r eadability to the co de , and (ii) the
functions in the librar y can b e linke d to sp e cific obje cts follo wing the natural r elationship b etw e en an
obje ct and a metho d, so that the functions ar e conceptually clearly organize d, and users will hav e lo w er
chance to get lost in the librar y of functions.
Figur e 5.1 sho w s the ar chite ctur e of the UI of the curr ent v ersion (0.6.2) of Pyleoclim . It ser v es as a
r oad map to the Pyleoclim univ erse , describing the r elationship b etw e en obje cts and metho ds, as w ell a s
the r elationship b etw e en obje cts. Due to the limitation of the figur e size , it only pr esents essential obje cts
such as Series , MultipleSeries , EnsembleSeries , PSD , Scalogram , MultiplePSD, Lipd , and LipdSeries , along
with their major corr esp onding metho ds. Her e , w e pr o vide a basic description of each obje ct as follo wing:
120
detrend() standardize() filter() spectral() wavelet() wavelet_ coherence() interp() bin() causality() convert_ time_unit() Preprocessing User Interface anomaly() ... MultipleSeries series_list EnsembleSeries (MultipleSeries) series_list Analysis correlation() stats() ... ssa() Visualization plot() distplot() summary_ plot() PSD frequency amplitude spec_method spec_arrgs period_unit ... Series time value time_name time_unit value_name value_unit ... signif_test() beta_est() plot() Scalogram frequency time amplitude wave_method wave_args period_unit ... signif_test() plot() Visualization plot() stackplot() Visualization plot_traces() stackplot() plot_ envelope() common_ time() interp() bin() ... Preprocessing convert_ time_unit() spectral() wavelet() pca() Analysis ... correlation() quantiles() correlation() Analysis ... MultiplePSD psd_list beta_est() plot() plot_ envelope() LipdSeries (Series) time value time_name time_unit value_name value_unit ... map() dashboard() Lipd usr_path lipd_dict mapAllArchive() to_ LipdSeries() to_ LipdSeriesList() to_tso() chronEnsemble ToPaleo() processing
methods Legends Objects pos. args keyw. args visualization
methods Figur e 5.1: The ar chite ctur e of the Pyleoclim user interface . Color e d squar es r epr esent obje cts along
with the p ositional arguments and ke y w or d arguments. Gr e y he xagons r epr esent pr o cessing metho ds of
the corr esp onding obje ct, while y ello w he xagons r epr esent visualization metho ds.
121
• Series : the most fundamental obje ct that r epr esents a time series. It can b e define d by the time
axis ( time ) and the value axis ( value ), along with optional names for t he tw o axes ( time_name and
value_name ), as w ell as the opti onal units for the tw o axes ( time_unit and value_unit ).
• MultipleSeries : a list of Series . It is useful to define such an obje ct when w e w ould like to p erform
a giv en metho d to a list of t ime series at once .
• EnsembleSeries : similar to MultipleSeries , but the list of Series come fr om an ensemble (that is, all
the series ther ein ar e vie w e d as r ealizations of the same dynam ical or statistical pr o cess, sampling a
range of p ossible b ehaviors).
• PSD : p o w er sp e ctral density , the r esult obje ct fr om the sp e ctral analysis metho d spectral() .
• Scalogram : wav elet scalogram, the r esult obje ct fr om the wav elet analysis metho d wavelet() .
• MultiplePSD : a list of PSD obje cts. It is useful to define such an obje ct when w e w ould like to p erform
a giv en metho d to a list of p o w er sp e ctra at once .
• Lipd : a handle for a LiPD file .
• LiPDSeries : a Series like obje ct loade d fr om a LiPD file .
Default parameters for the corr esp onding metho ds of these obje cts ar e e xp ert-curate d so that it r e quir es
only minimal input fr om users. For mor e details of all the available obje cts and the corr esp onding metho ds,
please r efer to the do cumentation on the UI
†
. In addition, Pyleoclim comes with customize d plotting
styles, which make it easy to pr o duce publication-r eady figur es.
In the ne xt se ction, w e pr esent a list of usage e xamples to sho w ho w pale o climate data analysis and
r epr o ducible r esear ch can b e enhance d with Pyleoclim .
5.3 Usage e xamples
5.3.1 Loading pale o climate data fr om a LiPD file
Ev er y LiPD file contains a dictionar y of data and metadata fr om a pale o climate study . Belo w , w e sho w a
basic w orkflo w of loading a LiPD file , taking t he study by Stott et al. ( 2004 ) as an e xample .
1 import pyleoclim as pyleo
2
3 url = ' http :// wiki . linked . earth / wiki / index . php / Special : WTLiPD ? op = export & lipdid = MD982176 . Stott
.2004 '
4 data = pyleo.Lipd(usr_path=url)
5 ts_list = data.to_tso()
6 ts_sst = pyleo.LipdSeries(ts_list)
7
8 # OUTPUT BELOW
†
https://pyleoclim- util.readthedocs.io/en/stable/core/ui.html
122
9 # extracting paleoData ...
10 # extracting : MD982176 . Stott .2004
11 # Created time series : 6 entries
12 # 0 : MD982176 . Stott .2004 : marine sediment : depth
13 # 1 : MD982176 . Stott .2004 : marine sediment : yrbp
14 # 2 : MD982176 . Stott .2004 : marine sediment : d18og . rub
15 # 3 : MD982176 . Stott .2004 : marine sediment : d18ow - s
16 # 4 : MD982176 . Stott .2004 : marine sediment : mg / ca - g . rub
17 # 5 : MD982176 . Stott .2004 : marine sediment : sst
18 #
19 # Enter the number of the variable you wish to use : 5
Her e , after imp orting the package , w e first define a Lipd file handle with a URL ( Uniform Resour ce
Lo cator , i.e ., a link) of the file , and then call the to_tso() metho d to conv ert it to a LiPD time series handle ,
and then define a LipdSeries obje ct with that handle . A pr ompt will app ear for users to cho ose which
time series the y w ould like to load, and w e se e ther e ar e 6 entries containe d in the file , including the sea
surface temp eratur e (SST) series that w e cho ose to load. No w w e ar e r eady to do a quick visualization of
the SST series, which is as simple as a one-liner with t he plot() metho d, and that is all it takes to generate
a publication-quality figur e:
1 ts_sst.plot()
0 2000 4000 6000 8000 10000 12000 14000
Age [yr BP]
26
27
28
29
30
31
sst [deg C]
MD982176.Stott.2004
Figur e 5.2: A quick visualization of the SST series using the plot() metho d.
Note that the names and units of the axes and the lab el of the series ar e automatically de duce d base d on
the mete data fr om the LiPD file , thanks to the underlying LiPD utilities and Pyleoclim UI. This featur e
is one p oint that makes sav es scientists some pr e cious time .
Her e , the app earance of the figur e w e se e is follo wing the default plotting style of Pyleoclim (name d
“journal”), which fits scenarios mainly for journal publications. W e may also switch to another , mor e
mo dern style for scenarios such as slide pr esentations or w eb articles:
123
1 pyleo.set_style( ' web ' )
2 ts_sst.plot()
0 2000 4000 6000 8000 10000 12000 14000
Age [yr BP]
26
27
28
29
30
31
sst [deg C]
MD982176.Stott.2004
Figur e 5.3: A quick visualization of the SST series with the “w eb ” style .
W e may also add a suffix to the name of the style to switch b etw e en mo des: curr ently , w e hav e the contr ol
of whether to turn on the grid and the spines by adding the suffixes _grid, _nogrid, _spines, _nospines .
For mor e details, please r efer to the Jup yter noteb o ok on plotting styles
‡
.
In addition to the basic series plotting, w e hav e a “killer” featur e to cr eate a dashb oar d fr om the
LipdSeries thr ough the dashboard() metho d, for a quick o v er vie w of the d ata:
1 ts_sst.dashboard()
‡
h t t p s : / / g i t h u b . c o m / L i n k e d E a r t h / P y l e o c l i m _ u t i l / b l o b / m a s t e r / e x a m p l e_ n o t e b o o k s / p l o t_ s t y l e s . i p y n
b
124
0 2000 4000 6000 8000 10000 12000 14000
Age [yr BP]
26
27
28
29
30
31
sst [deg C]
MD982176.Stott.2004
0 20 40
PDF
200 500 1000 2000 5000 10000 20000 50000 100000
Period [yrs]
10
1
10
2
10
3
PSD
MD982176.Stott.2004
AR(1), 95% threshold
archiveType: marine sediment
Authors: L.D. Stott;K.G. Cannariato;et al.
Year: 2004
DOI: 10.0138/nature02903
Variable: sst
units: deg C
Climate Interpretation:
Climate Variable: temperature
Detail: sea surface
Seasonality: NA
Direction: NA

Calibration:
Equation: NA
Notes: J. Bijma.1996
Figur e 5.4: A quick o v er vie w of the data using the dashboard() metho d.
The figur e w e obtaine d contains the original time series at the upp er left, the distribution of the data values
at the upp er right, the lo cation of the site at the lo w er left, the sp e ctrum with significance test at the lo w er
right, and the te xtual metadata in the side panel.
No w w e mo v e on to some fr e quently use d pr epr o cessing functionalities.
5.3.2 Data pr epr o cessing
5.3.2.1 Standar dization
Standar dization centers the series to hav e zer o-mean and scales the series to hav e unit variance and b e
unitless, and w e can standar dize a series in Pyleoclim by calling the .standardize() metho d:
1 ts_sst.standardize().plot()
125
0 2000 4000 6000 8000 10000 12000 14000
Age [yr BP]
3
2
1
0
1
2
3
sst [deg C]
MD982176.Stott.2004
Figur e 5.5: The standar dize d series obtaine d using the standardize() metho d.
Note her e w e ar e taking advantage of the metho d cascading featur e of Pyleoclim to combine tw o
steps
§
, standar dization and v isualization, into a one-liner . Other wise , one may get the same r esult via:
1 ts_std = ts_sst.standardize()
2 ts_std.plot()
5.3.2.2 Slicing
It is a common case that w e w ould like to slice a series o v er a sp e cific time span, and w e may call the
slice ([a, b]) metho d, wher e [a, b] sp e cifie s the starting and ending p oints of a time span. No w let us
slice the SST series and fo cus on the most r e cent 2000 y ears:
1 ts_sst. slice ([0, 2000]).plot()
§
In fact, such cascading can b e infinite as long as those metho ds apply . W e will se e e xamples of longer cascading in later
se ctions.
126
250 500 750 1000 1250 1500 1750 2000
Age [yr BP]
28.0
28.5
29.0
29.5
30.0
30.5
31.0
sst [deg C]
MD982176.Stott.2004
Figur e 5.6: The slice d series obtaine d using the slice () metho d.
Note that, o v er the Common Era, it may b e appr opriate to plot the time axis in the unit of calendar
y ears and in the pr ograde dir e ction (time incr easing to the right), and w e can easily achie v e that without
manual conv ersion of the time axis:
1 ts_slice = ts_sst. slice ([0, 2000]).convert_time_unit(time_unit= ' years ' )
2 ts_slice.time_name = ' Time ' # modify to an appropriate time name
3 ts_slice.plot()
0 250 500 750 1000 1250 1500 1750
Time [years]
28.0
28.5
29.0
29.5
30.0
30.5
31.0
sst [deg C]
MD982176.Stott.2004
Figur e 5.7 : The slice d series with the time axis conv erte d.
127
5.3.2.3 Anomalies
Anomalies ar e a common concept in climatology , r eferring to the departur e fr om a mean state o v er a
certain time span. W e may call the anomaly([a, b]) metho d to conv eniently calculate the anomaly of a
series against the time span [a, b] :
1 ts_anom = ts_slice.anomaly([1500, 1750])
2 ts_anom.value_name = ' sst anom . ' # modify to an appropriate value name
3 ts_anom.plot(marker= ' o ' )
0 250 500 750 1000 1250 1500 1750
Time [years]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
sst anom. [deg C]
MD982176.Stott.2004
Figur e 5.8: The anomaly series obtaine d using the anomaly() metho d.
Note that w e mo dify the argument marker in the plot() metho d to highlight that the data ar e une v enly-
space d, which pr e v ents the dir e ct application of many classic analysis metho ds such as the Fast Fourier
T r ansform (FFT) or Discr ete W av elet T ransform (D W T). In the ne xt tw o se ctions, w e sho w ho w to obtain
an e v enly-space d series fr om the original series via interp olation or binning metho ds.
5.3.2.4 Interp olation
Interp olation places the data on an e v enly-space d time axis and estimates the values at these ne w e v enly-
space d time p oints base d on the original values at the old une v enly-space d time p oints. Pyleoclim p er-
forms the interp olation via the interp() metho d. Note that ther e ar e se v eral interp olation metho ds avail-
able in Pyleoclim , thanks to the underlying Scipy package (McKinne y , 2010 ). Her e w e sho w only the
r esults fr om the linear , quadratic , and cubic metho ds as an e xample:
1 ts_interp_linear = ts_anom.interp(method= ' linear ' )
2 ts_interp_qudradic = ts_anom.interp(method= ' quadratic ' )
3 ts_interp_spline = ts_anom.interp(method= ' cubic ' )
4
5 # plot the results in one figure
128
6 fig, ax = ts_anom.plot(marker= ' o ' , mute=True, label= ' raw ' )
7 ts_interp_linear.plot(marker= ' v ' , ax=ax, label= ' linear ' )
8 ts_interp_quadradic.plot(marker= ' ^ ' , ax=ax, label= ' quadratic ' )
9 ts_interp_spline.plot(marker= ' s ' , ax=ax, label= ' cubic ' )
10 pyleo.showfig(fig)
0 250 500 750 1000 1250 1500 1750
Time [years]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
sst anom. [deg C]
raw
linear
cubic
quadratic
Figur e 5.9: The interp olate d series obtaine d using the interp() metho d.
Note her e w e hav e also demonstrate d ho w to plot multiple r esults in one figur e base d on the basic me ch-
anism of the Matplotlib package (Hunter , 2007 ). The major steps include using mute=True in the first
plot() call to hold on the display of the figur e , and using ax=ax in the later plot() calls so as to add ne w
mo difications to the e xisting figur e in the backgr ound, and then call pyleo.showfig(fig) to display the
final app earance of the figur e .
5.3.2.5 Binning
In some cases, w e w ould like to obtain an e v enly-space d series without interp olation to av oid intr o ducing
bias, but w e ar e w ell tolerant to lose some temp oral r esolution, then w e may cho ose to bin the data by
calling the bin () metho d:
1 ts_bin = ts_anom. bin ()
2 fig, ax = ts_anom.plot(marker= ' o ' , mute=True, label= ' raw ' )
3 ts_bin.plot(ax=ax, marker= ' s ' , label= ' binning ' )
4 pyleo.showfig(fig)
129
0 250 500 750 1000 1250 1500 1750
Time [years]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
sst anom. [deg C]
raw
binning
Figur e 5.10: The binne d series obtaine d using the bin () metho d.
5.3.2.6 Coarse-graining via a Gaussian kernel
In addition to interp olation and binning, w e may estimate a uniformly space d series base d on the original
une v enly-space d series via a Gaussian kernel (Rehfeld et al., 2011 ). By default, the maximum inter val in
the original une v enly-space d series will b e use d as the uniform spacing, and the uniformly space d values
will b e estimate d as the w eighte d av erage of the data p oints within each spacing with w eights follo wing
a Gaussian kernel. This metho d can b e applie d by calling the gkernel() metho d:
1 ts_gkernel = ts_anom.gkernel()
2 fig, ax = ts_anom.plot(marker= ' o ' , mute=True, label= ' raw ' )
3 ts_gkernel.plot(ax=ax, marker= ' s ' , label= ' gkernel ' )
4 pyleo.showfig(fig)
130
0 250 500 750 1000 1250 1500 1750
Time [years]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
sst anom. [deg C]
raw
gkernel
Figur e 5.11: The binne d series obtaine d using the gkernel() metho d.
5.3.2.7 Filtering
Filtering is another common use case in climatology . In many scenarios, w e w ould like to p erform either
a lo w-pass filtering in or der to e xtract the long-term variation of the climate , ignoring the high-fr e quency
signal, or a band-pass filtering in or der to e xtract the signal o v er a sp e cific fr e quency band ( e .g. the band of
2-7 yrs for the ENSO signal). In b elo w , w e sho w the e xample of a lo w-pass filtering at the scale of 300 yrs
to filter out higher fr e quency signal and a band-pass filtering b etw e en 100-250 yrs thr ough the filter ()
metho d:
1 ts_lp = ts_interp_quadradic. filter (cutoff_scale=300)
2 ts_bp = ts_interp_quadradic. filter (cutoff_scale=[100, 250])
3 fig, ax = ts_anom.plot(marker= ' o ' , mute=True, label= ' raw ' )
4 ts_lp.plot(ax=ax, marker= ' s ' , label= ' low - pass at 300 yrs ' )
5 ts_bp.plot(ax=ax, marker= ' s ' , label= ' band - pass between 100-250 yrs ' )
6 pyleo.showfig(fig)
131
0 250 500 750 1000 1250 1500 1750
Time [years]
0.5
0.0
0.5
1.0
1.5
2.0
2.5
sst anom. [deg C]
raw
low-pass at 300 yrs
band-pass between 100-250 yrs
Figur e 5.12: The filter e d series obtaine d using the filter () metho d.
5.3.2.8 Detr ending
Detr ending will r emo v e the dominant lo w er-fr e quency signal fr om the original series. This is usually
useful for sp e ctral analysis when the lo w er-fr e quency signal is dominant but is actually not our inter est.
T o demonstrate , w e p erform another slicing o v er 10k-14k yr BP , and p erform a detr ending step with the
detrend() metho d. Note that the default metho d is the Empirical Mo de De comp osition (EMD ) (Huang et al.,
1998 ), which de comp oses the signal into se v eral comp onents follo wing an empirical pr o ce dur e ( se e Huang
et al. ( 1998 )), and r emo v es the comp onent with the lo w est fr e quency . Ther e ar e other available metho ds
such as r emo ving the linear tr end or r emo ving a tr end estimate d with a Savitzky-Golay filter Savitzky and
Golay ( 1964 ) that fits successiv e adjacent data p oints with a lo w-degr e e p olynomial via linear least squar es,
and w e may inv oke it via the method argument:
1 ts_slice = ts_sst.standardize(). slice ([10000, 14000])
2 ts_detrend_emd = ts_slice.detrend(method= ' emd ' )
3 ts_detrend_sg = ts_slice.detrend(method= ' savitzky - golay ' )
4 ts_detrend_linear = ts_slice.detrend(method= ' linear ' )
5 fig, ax = ts_slice.plot(mute=True, label= ' raw ' )
6 ts_detrend_emd.plot(ax=ax, label= ' detrended w / EMD ' )
7 ts_detrend_sg.plot(ax=ax, label= ' detrended w / Savitzky - Golay ' )
8 ts_detrend_linear.plot(ax=ax, label= ' detrended w / linear ' )
9 pyleo.showfig(fig)
132
10000 10500 11000 11500 12000 12500 13000 13500 14000
Age [yr BP]
3
2
1
0
1
sst [deg C]
raw
detrended w/ EMD
detrended w/ Savitzky-Golay
detrended w/ linear
Figur e 5.13: The detr ende d series obtaine d using the detrend() metho d.
This concludes the most common usage cases of data pr epr o cessing with the Pyleoclim UI. No w w e
mo v e on to major data analysis tasks, such as corr elation analysis, sp e ctral analysis, wav elet analysis, and
wav elet coher ence analysis.
5.3.3 Data analysis
In this se ction, w e demonstrate data analysis w orkflo ws with the Pyleoclim UI. W e will intr o duce the
obje cts MultipleSeries and EnsembleSeries along with the corr esp onding metho ds in the conte xt of mo del-
data comparison, a main topic of this thesis.
W e first load the PMIP3 simulations of the global mean surface temp eratur e ( GMST) with the Pandas
package (The pandas de v elopment team, 2020 ) and p erform some basic cleaning:
1 import pandas as pd
2 url = ' https :// github . com / LinkedEarth / paleoHackathon / raw / main / data / PMIP3_GMST . txt '
3 df = pd.read_table(url)
4 # create a new pandas . DataFrame to store the processed data
5 df_new = df.copy()
6
7 # remove the data columns for CESM and GISS ensemble members
8 for i in range (10):
9 df_new = df_new.drop([f ' CESM_member_ { i +1} ' ], axis= 1)
10
11 df_new = df_new.drop([ ' GISS - E2 - R_r1i1p127 .1 ' ], a xis=1)
12 df_new = df_new.drop([ ' GISS - E2 - R_r1i1p127 ' ], axis=1)
13 df_new = df_new.drop([ ' GISS - E2 - R_r1i1p121 ' ], axis=1)
14
15 # calculate the ensemble mean for CESM and GISS , and add the results into the table
16 colname_list = [f ' CESM_member_ { i } ' for i in range (1, 11)]
133
17 df_new[ ' CESM ' ] = df[colname_list].mean(axis=1)
18
19 df_new[ ' GISS ' ] = df[[
20 ' GISS - E2 - R_r1i1p127 .1 ' ,
21 ' GISS - E2 - R_r1i1p127 ' ,
22 ' GISS - E2 - R_r1i1p121 ' ,
23 ]].mean(axis=1)
No w w e define Series with each simulation, after which w e form a MultipleSeries :
1 # store each Series object into a dictionary
2 ts_dict = {}
3 for name in df_new.columns[1:]:
4 ts_dict[name] = pyleo.Series(
5 time=df_new[ ' Year ' ].values, # the time axis
6 value=df_new[name].values, # the value axis
7 label=name, # optional metadata : the nickname of the series
8 time_name= ' Time ' , # optional metadata : the name of the time axis
9 time_unit= ' yrs ' , # optional metadata : the unit of the time axis
10 value_name= ' GMST anom . ' , # optional metadata : the name of the value axis
11 value_unit= ' K ' , # optional metadata : the unit of the value axis
12 )
13
14 ts_list = [v for k, v in ts_dict.items()] # a pythonic way to convert the pyleo . Series items in
the dictionary to a list
15 ms_pmip = pyleo.MultipleSeries(ts_list)
No w w e ar e r eady to visualize the simulations thr ough the plot() metho d:
1 ms_pmip.plot(lgd_kwargs={ ' bbox_to_anchor ' : (1.25, 1)})
800 1000 1200 1400 1600 1800 2000
Time [yrs]
3
2
1
0
1
GMST anom. [K]
bcc_csm1_1
CCSM4
FGOALS_gl
FGOALS_s2
IPSL_CM5A_LR
MPI_ESM_P
CSIRO
HadCM3
CESM
GISS
Figur e 5.14: A visualization of the PMIP3 simulations using the plot() metho d.
Or , w e may visualize thr ough the stackplot() metho d:
1 ms_pmip.stackplot(figsize=[5, 10])
134
-1.6
0.5
GMST anom. [K]
bcc_csm1_1
-1.9
0.7
GMST anom. [K]
CCSM4
-1.1
0.4
GMST anom. [K]
FGOALS_gl
-2.9
0.7
GMST anom. [K]
FGOALS_s2
-2.1
0.6
GMST anom. [K]
IPSL_CM5A_LR
-1.5
0.6
GMST anom. [K]
MPI_ESM_P
-1.3
0.4
GMST anom. [K]
CSIRO
-1.2
0.5
GMST anom. [K]
HadCM3
-0.7
0.4
GMST anom. [K]
CESM
-1.3
0.5
GMST anom. [K]
GISS
1000 1200 1400 1600 1800 2000
Time [yrs]
Figur e 5.15: A visualization of the PMIP3 simulations using the stackplot() metho d.
Similarly , w e form an EnsembleSeries obje ct with the ensemble memb ers of the LMR r e constructe d
GMST , and make a quick visualization thr ough its plot_envelope() metho d:
1 # load the LMR GMST ensemble data
2 url = ' https :// github . com / LinkedEarth / paleoHackathon / raw / main / data / lmr_gmst . pkl '
3 lmr_time, lmr_gmst = pd.read_pickle(url)
4 nt, nMC, nEns = np.shape(lmr_gmst)
5
6 # define Series and EnsembleSeries objects
7 ts_list = []
8 for i in range (nMC):
9 for j in range (nEns):
135
10 name = f ' LMR_member_ { i } '
11 ts_tmp = pyleo.Series(
12 time=lmr_time, # the time axis
13 value=lmr_gmt[:,i,j], # the value axis
14 label=name, # optional metadata : the nickname of the series
15 time_name= ' Time ' , # optional metadata : the name of the time axis
16 time_unit= ' yrs ' , # optional metadata : the unit of the time axis
17 value_name= ' GMST anom . ' , # optional metadata : the name of the value axis
18 value_unit= ' K ' , # optional metadata : the unit of the value axis
19 )
20 ts_list.append(ts_tmp)
21
22 es_lmr = pyleo.EnsembleSeries(ts_list)
23
24 # visualization
25 fig, ax = es_cesm.plot_envelope(lgd_kwargs={ ' ncol ' : 3, ' loc ' : ' upper left ' }, titl e= ' LMR v2 .1
GMST ' )
800 1000 1200 1400 1600 1800 2000
Time [yrs]
1.5
1.0
0.5
0.0
0.5
GMST anom. [K]
LMR v2.1 GMST
median 95% CI IQR
Figur e 5.16: A visualization of the ensemble series using the plot_envelope() metho d.
W e then load the obser vational datasets, the me dian of the LMR r e construction, and the deglaciation
simulations use d in Zhu et al. ( 2019b ) and define Series and MultipleSeries :
1 url = ' https :// github . com / LinkedEarth / paleoHackathon / raw / main / data / PNAS19_data. pkl '
2 time_dict, value_dict = pd.read_pickle(url)
3
4 for name in time_dict.keys():
5 # we may specify specific metadata for each dataset with the if - clauses
6 if name == ' LMR ' :
7 value_name = ' GSMT anom . '
8 value_unit = ' K '
136
9 elif name in [ ' trace21ka_full ' , ' DGns ' , ' SIM2bl ' ]:
10 value_name = ' GSMT '
11 value_unit = ' K '
12 else :
13 value_name = ' Proxy Value '
14 value_unit = None
15
16 if name == ' trace21ka_full ' :
17 label = ' TraCE -21 ka '
18 elif name in [ ' trace21ka_mwf ' , ' trace21ka_orb ' , ' trace21ka_ghg ' , ' trace21ka_ice ' ]:
19 continue
20 else :
21 label = name
22
23 ts_dict[name] = pyleo.Series(
24 time=time_dict[name],
25 value=value_dict[name],
26 label=label,
27 time_name= ' Time ' ,
28 time_unit= ' yrs ' ,
29 value_name=value_name,
30 value_unit=value_unit,
31 )
32
33 ms_obs = pyleo.MultipleSeries(
34 [ts_dict[name] for name in [ ' EDC ' , ' HadCRUT4 ' , ' GAST ' , ' ProbStack ' , ' LMR ' ]]
35 )
36 ms_deglacial = pyleo.MultipleSeries(
37 [ts_dict[name] for name in [ ' trace21ka_full ' , ' DGns ' , ' SIM2bl ' ]]
38 )
A g ain, w e may visualize them thr ough the stackplot() metho d, sp e cifying a color map via the cmap argu-
ment:
1 ms_obs.stackplot(figsize=[5, 3], cmap= ' Set1 ' )
137
-18.4
9.2
Proxy Value
EDC
8.2
19.6
Proxy Value
HadCRUT4
-10.4
5.4
Proxy Value
GAST
6.7
23.2
Proxy Value
ProbStack
-0.5
0.3
GSMT anom. [K]
LMR
4 3 2 1 0
Time [yrs]
1e6
Figur e 5.17: A visualization of the multiple obser vational series using the stackplot() metho d.
1 ms_deglacial.stackplot(figsize=[5, 3], cmap= ' Set1 ' )
276.3
290.2
GSMT [K]
TraCE-21ka
280.5
293.4
GSMT [K]
DGns
280.8
293.2
GSMT [K]
SIM2bl
20000 17500 15000 12500 10000 7500 5000 2500 0
Time [yrs]
Figur e 5.18: A visualization of the multiple simulation series using the stackplot() metho d.
No w w e ar e r eady to p erform the analysis tasks, and w e start with the most fr e quently use d corr elation
analysis.
5.3.3.1 Corr elation analysis
W e may calculate the corr elation b etw e en the LMR r e constructe d GMST ensemble and the ensemble mean
of the CESM simulations by calling the correlation() metho d, which will p erform the underlying corr_sig
function (Hu, Emile-Geay , and Partin, 2017 ), which by default tests the significance of the corr elation via
the “isosp e ctral” metho d (Ebisuzaki, 1997 ):
138
1 corr_res = es_lmr.correlation(ts_dict[ ' CESM ' ])
W e may print the details of the r esult, or visualize thr ough the plot() metho d:
1 print (corr_res)
2 # OUTPUT BELOW
3 # correlation p - value signif . w / o FDR ( alpha : 0.05) signif . w / FDR ( alpha : 0.05 )
4 # ------------- --------- ----------------------------- --------------------------
5 # 0.493998 < 1 e -4 True True
6 # 0.558781 < 1 e -4 True True
7 # 0.506874 < 1 e -4 True True
8 # 0.406745 < 1 e -4 True True
9 # 0.483987 < 1 e -4 True True
10 # 0.53441 < 1 e -4 True True
11 # 0.510878 < 1 e -4 True True
12 # 0.45701 < 1 e -4 True True
13 # 0.527196 < 1 e -4 True True
14 # 0.461815 < 1 e -4 True True
15 # 0.422063 < 1 e -4 True True
16 # 0.460294 < 1 e -4 True True
17 # 0.489373 < 1 e -4 True True
18 # 0.50508 < 1 e -4 True True
19 # 0.47805 < 1 e -4 True True
20 # 0.505907 < 1 e -4 True True
21 # 0.477982 < 1 e -4 True True
22 # 0.482629 < 1 e -4 True True
23 # 0.160105 0.46 False False
24 # ...
25 # 0.344552 < 1 e -4 True True
26 # 0.24371 0.08 False False
27 # 0.501487 < 1 e -4 True True
28 # 0.531941 < 1 e -4 True True
29 # 0.40935 < 1 e -4 True True
30 # 0.485541 < 1 e -4 True True
31 # Ensemble size : 2000
32
33 # visualization
34 fig, ax = corr_res.plot(xlim=[0, 0.6], figsize=[5, 3]) # xlim sets the limitation of the x - axis
139
0.0 0.1 0.2 0.3 0.4 0.5 0.6
r
0
200
400
600
800
1000
1200
1400
1600
Count
Fraction significant: 96.2%
Fraction significant: 96.2%
0.025 0.25 0.5 0.75 0.975
p 0.05
p < 0.05 (w/o FDR)
p < 0.05 (w/ FDR)
Figur e 5.19: A visualization of the ensemble of corr elation co efficients using the plot() metho d .
It indicates that the LMR r e constructe d GMST ensemble is significantly corr elate d with the ensemble mean
of the CESM simulate d GMST with a me dian corr elation co efficient ar ound 0.45. This r epr esents a mo del-
data comparison in the time domain. In the ne xt se ction, w e conduct a comparison in the fr e quency
domain.
5.3.3.2 Sp e ctral analysis
Since pale o climate r e cor ds ar e often une v enly-space d, w e p erform sp e ctral analysis thr ough the spectral
() metho d, utilizing the W eighte d W av elet Z-transform (W WZ, Foster , 1996 ; Kir chner and Neal, 2013 )
metho d, which can handle une v enly-space d data w ell without inv oking interp olation. Note each appli-
cation of the spectral() metho d r eturns a PSD obje ct, fr om which w e may form a MultiplePSD obje ct for
conv enience:
1 psd_wwz = {}
2 for name, ts in ts_dict.items():
3 psd_wwz[name] = ts.spectral(method= ' wwz ' )
4
5 mpsd_obs = pyleo.MultiplePSD(
6 [psd_wwz[name] for name in [ ' EDC ' , ' HadCRUT4 ' , ' GAST ' , ' LMR ' , ' ProbStack ' ]]
7 )
8 mpsd_deglacial = pyleo.MultiplePSD(
9 [psd_wwz[name] for name in [ ' trace21ka_full ' , ' DGns ' , ' SIM2bl ' ]]
10 )
11 pmip_names = [ ' bcc_csm1_1 ' , ' CCSM4 ' , ' FGOALS_gl ' , ' FGOALS_s2 ' , ' IPSL_CM5A_LR ' , ' MPI_ESM_P ' , '
CSIRO ' , ' HadCM3 ' , ' CESM ' , ' GISS ' ]
12 mpsd_pmip = pyleo.MultiplePSD(
13 [psd_wwz[name] for name in pmip_names]
14 )
No w w e visualize the p o w er sp e ctra of the obser vational datasets thr ough the plot() metho d:
1 period_ticks = [0.5, 1, 2, 5, 10, 20, 100, 1e3, 1e4, 1e5, 1e6]
2 period_ticklabels = [ ' 0.5 ' , ' 1 ' , ' 2 ' , ' 5 ' , ' 10 ' , ' 20 ' , ' 100 ' , ' 1 k ' , ' 10 k ' , ' 100 k ' , ' 1 m ' ]
140
3
4 fig, ax = mpsd_obs.plot(figsize=[8, 4], mute=True)
5 ax.set_xlim([1e7, 0.1])
6 ax.set_ylim([1e-4, 1e8])
7 ax.set_xticks(period_ticks)
8 ax.set_xticklabels(period_ticklabels)
9 ax.set_ylabel( ' Spectral Density ' )
10 pyleo.showfig(fig)
0.5 1 2 5 10 20 100 1 k 10 k 100 k 1 m
Period [yrs]
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
EDC
HadCRUT4
GAST
LMR
ProbStack
Figur e 5.20: The sp e ctral analysis of the obser vational datasets.
Then w e compar e the obser vational datasets with the the deglaciation simulations and the PMIP3 simula-
tions, r esp e ctiv ely , as in Zhu et al. ( 2019b ) ( Chapter 2 ):
1 fig, ax = mpsd_deglacial.plot(figsize=[8, 4], mute=True)
2 mpsd_obs.plot(ax=ax, legend=False, colors= ' grey ' , plot_kwargs={ ' alpha ' : 0.3})
3 ax.set_xlim([1e7, 0.1])
4 ax.set_ylim([1e-4, 1e8])
5 ax.set_xticks(period_ticks)
6 ax.set_xticklabels(period_ticklabels)
7 ax.set_ylabel( ' Spectral Density ' )
8 pyleo.showfig(fig)
141
0.5 1 2 5 10 20 100 1 k 10 k 100 k 1 m
Period [yrs]
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
TraCE-21ka
DGns
SIM2bl
Figur e 5.21: The sp e ctral analysis of the deglaciation simulations.
1 fig, ax = mpsd_pmip.plot(figsize=[8, 4], mute=True)
2 mpsd_obs.plot(ax=ax, legend=False, colors= ' grey ' , plot_kwargs={ ' alpha ' : 0.3})
3 ax.set_xlim([1e7, 0.1])
4 ax.set_ylim([1e-4, 1e8])
5 ax.set_xticks(period_ticks)
6 ax.set_xticklabels(period_ticklabels)
7 ax.set_ylabel( ' Spectral Density ' )
8 pyleo.showfig(fig)
142
0.5 1 2 5 10 20 100 1 k 10 k 100 k 1 m
Period [yrs]
10
4
10
2
10
0
10
2
10
4
10
6
10
8
Spectral Density
bcc_csm1_1
CCSM4
FGOALS_gl
FGOALS_s2
IPSL_CM5A_LR
MPI_ESM_P
CSIRO
HadCM3
CESM
GISS
Figur e 5.22: The sp e ctral analysis of the PMIP3 simulations.
5.3.3.3 W av elet analysis
W av elet analysis is useful to dete ct the the p erio dicity of a giv en series in a time-fr e quency domain and
che ck if such p erio dicity is stationar y . W e no w take the e xample sho wn in a w ebpage fr om the Matlab
w ebsite
¶
, and load the NINO3 SST series and the deasonalize d all Indian rainfall inde x to demonstrate the
usage of the wavelet() metho d of Series :
1 url = ' https :// github . com / LinkedEarth / paleoHackathon / raw / main / data / wtc_test_data_nino . csv '
2 df = pd.read_csv(url)
3
4 air = df[ ' air ' ]
5 nino = df[ ' nino ' ]
6 t = df[ ' t ' ]
7 ts_air = pyleo.Series(
8 time=t,
9 value=air,
10 value_name= ' Index ' ,
11 time_name= ' Time ' ,
12 time_unit= ' yr ' ,
13 label= ' Deasonalized All Indian Rainfall Index ' ,
14 )
15 ts_nino = pyleo.Series(
16 time=t,
17 value=nino,
18 value_name= ' SST anom . ' ,
¶
h t t p s : / / w w w . m a t h w o r k s . c o m / h e l p / w a v e l e t / u g / c o m p a r e - t i m e - f r e q u e n c y - c o n t e n t - i n - s i g n a l s - w i t h - w
avelet- coherence.html
143
19 value_unit= ' K ' ,
20 time_name= ' Time ' ,
21 time_unit= ' yr ' ,
22 label= ' NINO3 ' ,
23 )
24
25 ms_air_nino = pyleo.MultipleSeries([ts_air, ts_nino])
26 ms_air_nino.stackplot(figsize=[5, 2])
-993.4
993.4
Index
Deseasonalized All Indian Rainfall Index
-3.2
3.4
SST anom. [K]
NINO3
1880 1900 1920 1940 1960 1980 2000
Time [yr]
Figur e 5.23: A visualization of the indices using the stackplot() metho d.
No w w e p erform wav elet analysis with an AR(1) significance test, and visualize the r esult. Her e , w e
set the numb er of Monte-Carlo simulations to b e 1000 via the number argument:
1 ts_air.wavelet().signif_test(number=1000).plot()
2 ts_nino.wavelet().signif_test(number=1000).plot()
1880 1900 1920 1940 1960 1980 2000
Time [yr]
0.2
0.5
1
2
5
10
20
50
Period [yrs]
0
80
160
240
320
400
1880 1900 1920 1940 1960 1980 2000
Time [yr]
0.2
0.5
1
2
5
10
20
50
Period [yrs]
0.00
0.16
0.32
0.48
0.64
0.80
0.96
Figur e 5.24: The wav elet analysis of the tw o indices: ( left) the Deseasonalize d All Indian Rainfall Inde x
and (right) the NINO3 inde x.
144
W e se e a str ong p erio do city o v er the typical ENSO cy cles of 2-7 yrs in the NINO3 series ( as e xp e cte d), but
not much obvious signal in the Indian rainfall inde x.
5.3.3.4 W av elet coher ence analysis
W e no w p erform wav elet coher ence analysis b etw e en the NINO3 series and the Indian rainfall inde x with
AR(1) significance test:
1 ts_nino.wavelet_coherence(ts_air).signif_test(number=1000).plot()
1880 1900 1920 1940 1960 1980 2000
Time [yr]
0.2
0.5
1
2
5
10
20
50
Period [yrs]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figur e 5.25: The analysis of the wav elet coher ency b etw e en the tw o indices.
It indicates that the tw o series ar e significantly coher ent o v er the 2-7 yrs band with phase lags ar ound half
a cy cle (1-3.5 yrs). The r elativ e phase r elationship is sho wn as arr o ws with in-phase p ointing right and
anti-phase p ointing left, and NINO3 leading the Indian rainfall inde x by a quarter-cy cle p ointing up and a
half-cy cle p ointing left.
This concludes all the essential data analysis metho ds in the Pyleoclim UI. For mor e available meth-
o d s, please r efer to the do cumentation on the UI as mentione d earlier .
145
5.4 Summar y
In this chapter , w e hav e pr esente d the Python package Pyleoclim and demonstrate d ho w it can b e utilize d
to enhance pale o climate data analysis. W e hav e sho wn that, the Pyleoclim UI:
• takes advantage of the LiPD utilities to handle pale o climate data that ar e other wise challenging to
handle manually;
• follo ws an OOP paradigm that naturally links the functionalities to the obje cts that w e w ould like
to interact with in the conte xt of data analysis;
• takes curate d default arguments for most of the metho ds so that only minimal user input is ne e de d
in most the cases;
• enables the metho d cascading featur e that allo ws multiple steps in a w orkflo w ( e .g., all data pr o cess-
ing and visualization steps) to b e combine d into a one-liner if ne e de d, usually for a quick e valuation
of some idea;
With all these featur es, the data analysis w orkflo w is highly fle xible , and can b e organize d with r e-
markably concise and r eadable co de , which can further enhance r epr o ducible r esear ch. For instance , all
the figur es in this chapter ar e generate d by one single Jup yter noteb o ok, and one will get the same e xact
figur es no matter ho w many times the noteb o ok is run. In addition, since the L
A
T
E
X sour ce co de for this
chapter is using the generate d figur es dir e ctly fr om the noteb o ok, if any mo dificatio n is made to the note-
b o ok and the figur es ar e change d accor dingly , this chapter do cument will also b e up date d automatically
once r e-compile d. Follo wing the same idea and the same te chnical w orkflo w , one may write a whole jour-
nal pap er with a L
A
T
E
X do cument that loads fully r epr o ducible figur es fr om a set of Jup yter noteb o oks that
run Pyleoclim or any si milar practice , then the whole study is r epr o ducible , fr om start to finish.
Pyleoclim is, ho w e v er , still in its pr eliminar y stage (the curr ent v ersion is only 0.6.2). Mor e function-
alities ar e e xp e cte d, and s ome of the e xisting functionalities will b e further de v elop e d. Despite significant
time inv estments, ther e is still r o om for impr o v ement r egar ding the do cumentation to make it mor e user-
friendly and instructiv e .
With that said, the curr ent v ersion of Pyleoclim lays a solid foundation for the ne xt le v el, and w e
e xp e ct that pale o climate data analysis and r epr o ducible r esear ch can b e further enhance d in the futur e
once Pyleoclim 1.0 is r elease d. W e ar e planning to submit a pap er on this during Summer 2021, aiming
for Pale o ceanography and Pale o climatology .
146
Chapter 6
Conclusion
6.1 Summar y
This thesis aime d to validate climate mo dels o v er the Common Era and an e v en longer histor y since the
Last Glacial Maximum (LGM). W e tackle d this topic by comparing pale o climate simulations against ob-
ser vations, le v eraging the l ast millennium r eanalysis (LMR) pale o-data assimilation (PD A ) frame w ork and
the Pyle o clim package . This allo w e d us to optimally synthesize the latest obser vational e vidence and
r e c onstruct climate fields subje ct to dynamic constraints, and thus pr o vide a skillful estimate of the pa-
le o climate that can ser v e as an obser vational target for mo del e valuation. Sp e cifically , w e inv estigate d
thr e e sub-topics r egar ding the continuum of temp eratur e variability , the temp eratur e r esp onse to v olcanic
for cing, and the ENSO r esp onse to v olcanic for cing.
In Chapter 2 , w e e valuate d whether climate mo dels can r epr o duce the obser v e d continuum of the
temp eratur e variability . W e did so by first up dati ng estimates of the temp eratur e sp e ctrum acr oss scales
fr om annual to orbital scales with the latest obser vational e vidence , and then scrutinizing simulations
pr o duce d by mo dels with differ ent le v els of comple xities. The r esult indicate d that the curr ent hierar chy
of climate mo dels is capable of r epr o ducing the obser v e d sp e ctrum of the global-mean temp eratur e , but
with conditions.
By comparing the deglaciation simulations with differ ent for cings, w e found that it is of imp ortance
to for ce the mo dels with corr e ct and complete b oundar y conditions, and that the meltwater fluxes for cing
and the orbital for cing act as the first tw o most imp ortant for cings to form the pattern w e se e in the
temp eratur e sp e ctrum, while other for cings such as the gr e ehouse gases and the transient ice she ets act to
b o ost the sp e ctrum to a higher amplitude . Also , base d on the conceptual mo del of Ryp dal and Ryp dal ( 2014 )
and the idea that the curr ent climate state r efle cts the accumulate d histor y of past for cings, w e compar e d
the deglaciation simulations without v olcanic for cing and the last millennium simulations with v olcanic
for cing as the major b oundar y condition and surmise d that ther e e xist “ e cho es” of the de ep o cean state that
contribute to energetic surface temp eratur e variability at de cadal-to-centennial scales. W e thus conclude d
that successful climate pr e dictions at de cadal-to-centennial horizons hinge critically on the accuracy of
b o th the initial and b oundar y conditions, particularly for the de ep o cean state .
In Chapter 3 , w e inv estigate d the causes of the discr epancies b etw e en the simulate d and obser v e d
temp eratur e r esp onse to v olcanic for cing, as w ell as the corr esp onding strategies to account for these
factors. W e first utilize d the LMR frame w ork and r epr o duce d the comparison that w e se e in Figur e 5.8b of
147
IPCC AR5 as a setup of the pr oblem, after which w e p erforme d pseudopr o xy e xp eriments and confirme d
thr e e main factors r egar ding tr e e-ring r e cor ds that can e xplain the discr epancies (Fritts, 1966 ; St. Ge orge ,
2014 ; St Ge orge and A ult, 2014 ; Esp er et al., 2015 ; Frank et al., 2007 ; Krakauer and Randerson, 2003 ; Zhang
et al., 2015 ): (1) Limite d spatial co v erage . Both the tr e e-ring width and density netw orks ar e sparse; (2)
Seasonal bias. Since tr e es r egister climate only during their gr o wing season, the annual temp eratur e is
not their b est target for r e construction; and (3) Biological memor y issue . T r e e-ring width has significantly
larger lag-1 auto corr elation than w o o d density , which leads to a lag in r esp onse to v olcanic co oling.
T o account for these thr e e factors, w e: (1) assimilate d the density data without tr e e-ring width to al-
le viate the biological memor y issue; (2) r e constructe d the b or eal summer temp eratur e instead of annual
temp eratur e to suppr ess the seasonal bias, and (3) p erforme d the analysis at pr o xy lo cales only to account
for the limite d spatial co v erage . With these strategies, the discr epancies of Figur e 5.8b of IPCC AR5 ap-
p ear to b e largely r esolv e d, although w e note d that discr epancy r emains for e xtr emely large e v ents such
as the 1257 Samalas eruption, the 1450s eruptions, and the 1815 T amb ora eruption. This suggests that
the o v ersimplifie d aer osol micr ophysics schemes in CMIP5-era mo dels as p ointe d out by Timmr e ck et al.
( 2009 ), Timmr e ck ( 2012 ), Stoffel et al. ( 2015b ), and LeGrande , T sigaridis, and Bauer ( 2016 ) is inde e d a mo d-
eling issue that w e ne e d to solv e when the inje cte d sulfate aer osol amount is significantly higher than that
was inje cte d in the 1991 Pinatub o eruption. Base d on this, w e ne e d to b e mor e cautious ab out the o v er-
state d pr oje cte d outcome of ge o engine ering solar radiation management schemes pr o duce d by CMIP5-era
mo dels.
In Chapter 4 , w e r e-appraise d the hotly debate d r elationship b etw e en v olcanic for cing and ENSO r e-
sp onse . Since e xisting obser vational tr e e-ring base d studies ( e .g., A dams, Mann, and Ammann, 2003 ;
McGr egor , Timmermann, and Timm, 2010 ; Li et al., 2013 ; W ahl et al., 2014 ; McGr egor et al., 2020 ) and
coral-base d studies ( e .g. Cobb et al., 2003 ; Tierne y et al., 2015 ; De e et al., 2020 ) hav e se emingly div ergent
conclusions on whether ther e e xists a r obust linkage b etw e en v olcano es and ENSO , w e first e valuate d the
information obtaine d fr om the tw o data sour ces separately but within a unifie d frame w ork – LMR. The
analysis suggeste d that the se emingly div ergent conclusions obtaine d fr om e xisting tr e e-ring and coral-
base d studies is mainly due to the fact that the eruption e v ents b eing scrutinize d ar e differ ent, and w e ar e
able to get the same conclusion that most eruption y ears ar e not statistically differ ent fr om non-eruption
y ears when a consistent set of eruption e v ents ar e consider e d for the comparison.
W e then assimilate d b oth the tr e e-ring and coral r e cor ds in LMR, and pr o duce d a no v el, skillful r e con-
struction of the Niño 3.4 histor y o v er the last millennium in or der to combine the advantages of b oth data
sour ces. The analysis again demonstrate d a statistically w eak linkage b etw e en v olcano es and ENSO . W e
also found that the eruption e v ents app ear e d to b e follo wing a non-stationar y pattern that the p ost-1850
CE e v ents hav e a higher chance to b e r elate d to v olcanic for cings than the pr e-1850 CE e v ents, and that
the for cing asymmetr y might also b e at play , y et w e do not hav e enough eruption e v ents to meaningfully
e valuate this p ossibility . O v erall, w e suggeste d that the curr ent pr o xy e vidence do es not supp ort a r obust
r elationship b etw e en v olcano es and ENSO .
In addition to the scientific questions mentione d ab o v e , this thesis also co v ers the te chnical but imp or-
tant asp e ct of mo dern r esear ch – pr ogramming to ols for data analysis. Chapter 5 do cumente d a Python
package name d Pyleoclim that aims to enhance pale o climate data analysis and r epr o ducible r esear ch,
148
with a pr esentation of the motivation of the pr oje ct, the philosophy b ehind the co de design, and a colle c-
tion of usage e xamples on the essential functionalities and featur es of the package . Inde e d, Pyleoclim
was utilize d heavily for the sp e ctral and wav elet analyses, as w ell as the visualization, w e pr esente d in
Chapter 2 .
6.2 Cav eats and futur e w ork
T o tackle the scientific questions inv estigate d in Chapters 2 - 4 , this thesis r elie d heavily on the LMR PD A
frame w ork that le v erages the p o w er of fusing pale o climate obser vations and mo dels. It has pr o v e d to b e a
successful metho dology in the sense that is it able to assimilate temp eratur e-sensitiv e p r o xy obser vations
o v er the Common Era in a mathematically optimal way , and r e construct climate fields at annual r esolution
subje ct to dynamic constraints. Ho w e v er , cav eats e xist in se v eral asp e cts of the PD A frame w ork, including
the climate mo dels fr om which the prior states ar e e xtracte d, the pr o xy system mo dels that translate the
climate states to the pr o xy variables, and the r eal-w orld pr o xy obser vations (Figur e 1.3 ), which w e discuss
in details b elo w along with the futur e w ork. W e discuss each in turn.
6.2.1 Structural err ors in climate mo del simulations
The LMR frame w ork r elies on the co variance structur e e xtracte d fr om simulate d climate states (i.e ., the
prior ) to pr opagate the information fr om pr o xy lo cales to r emote ar ea wher e pr o xies ar e unavailable . Ho w-
e v er , such co variance structur e de duce d fr om climate mo dels has its limitations. A s discusse d in Chapter
4 , for instance , systematic biases e xists in the lo cation of the South Pacific Conv ergence Zone (SPCZ) in
most climate mo dels, which could lead to an incorr e ct infer ence of Niño 3.4 SST fr om corals lo cate d in that
r egion (Sanchez et al., 2020 ).
T o alle viate such biases, efforts fr om the climate mo deling community hav e b e en ongoing since the
1920s, as discusse d in Chapter 1 . CMIP6 mo del simulations (Eyring et al., 2016 ) hav e no w b e en incr easingly
accessible and e valuate d ( Jungclaus et al., 2017 ; K age yama et al., 2018 ; Parsons et al., 2020 ; Parsons, 2020 ).
The impr o v ement in mo del physics of these mo dels can r esult in a b etter co variance structur e in simulate d
climate states.
Mor e o v er , the concept of “sup erprior” was r e cently pr op ose d (Parsons et al., 2021 ). The idea is to
le v erage climate states fr om multiple mo dels to b etter constrain the structural uncertainties, and the y hav e
sho wn that a simple combination of multiple mo dels can de cr ease the r e construction err ors, comparing to
the single-mo del case . For futur e w ork, one may study in detail the structural err ors in each mo del and
tune the w eights of the multiple mo dels in combination to maximize the r e construction skill.
In addition, multivariate bias corr e ction appr oaches hav e b e en de v elop e d r e cently and can b e p ossibly
use d to impr o v e the co variance structur e in mo dels. Statistical metho ds such as dynamical Optimal T rans-
fer Corr e ction ( dO T C, Robin et al., 2019 ) and the Rank Resampling for Distributions and Dep endences
(R2D2 V rac, 2018 ) ar e capable of corr e cting the spatial pr op erties of a multivariate field, y et it b e comes
149
mor e challenging when the ge ographical ar ea is large . Machine learning base d metho ds such as Conv o-
lutional Neural Netw orks ( CNN, V alue va et al., 2020 ) and its variants ar e capable of learning the mapping
b e tw e en tw o images, and could b e p ossibly applie d for multivariate bias corr e ction.
PD A w ould b enefit fr om a mor e systematic application of these appr oaches on multivariate bias cor-
r e c tion.
6.2.2 Pr o xy system mo deling
The curr ent LMR frame w ork utilizes linear r egr ession-base d pr o xy system mo dels (PSMs) to translate the
envir onmental variables to the pr o xy space . The accuracy of such mo deling pr o cess will determine the
obser vation err or matrix in the formula of the K alman filter use d in the frame w ork, largely affe cting the
r e c onstruction skill. Ho w e v er , such a pr o cess could b e nonlinear for certain pr o xy typ es, and tr e e-ring
width (TRW) is arguably the most typical one , which has b e come one of the major typ es of pr o xy obser-
vations for climate field r e construction (Tingle y and Li, 2012 ), esp e cially the last m illennium r eanalysis.
A s discusse d in Chapter 3 , tr e es r egister thermal and hy dr ological conditions primarily during their
gr o wing season (Fritts, 1966 ; St. Ge orge , 2014 ; St Ge orge and A ult, 2014 ), leading to seasonal bias when the
annual temp eratur e is the r e construction target (Stoffel et al., 2015a ; Wilson et al., 2016 ; Zhu et al., 2020 ).
The y also ke ep a biological and physical memor y of the climate of pr e vious y ears (Fritts, 1966 ; Frank et al.,
2007 ; Esp er et al., 2015 ; Stoffel et al., 2015a ; Zhang et al., 2015 ), leading to a gr o wth r esp onse that lags b ehind
the r eal climatic variation, and causing challenges in faithfully capturing impacts fr om high-fr e quency
climate e v ents, such as v olcanic eruptions, in b oth time and magnitude . In addition, obser vational studies
(Rossi et al., 2007 ; D’ Arrigo et al., 2008 ) hav e suggeste d e vidence of a thr eshold effe ct of temp eratur e and
moistur e on tr e e gr o wth, .i.e , temp eratur e and moistur e ab o v e certain thr esholds will not make the gr o wth
r esp onse e v en str onger , and that b elo w certain thr esholds can pause the gr o wth. The memor y effe ct and
the thr eshold effe ct together indicate that tr e e-ring gr o wth is o v erall nonlinear to the climate .
Nonlinear TRW mo dels ar e ne cessar y to alle viate such bias. Biophysical base d appr oaches, such as
the V agano v-Shashkin (VS) mo del (V agano v , Hughes, and Shashkin, 2006 ; V agano v , Anchukaitis, and
Evans, 2011 ), its lite v ersion VS-Lite (T olwinski- W ar d et al., 2011b ; T olwinski- W ar d, Anchukaitis, and
Evans, 2013 ), the dendr o e cology mo del MAIDEN (Mo deling and Analysis In DENdr o e cology ) (Rezsöhazy
et al., 2020 ), and e v en the land surface mo del ORCHIDEE ( ORganizing Carb on and Hy dr ology In D ynamic
EcosystEms) (Druel et al., 2019 ) hav e b e en teste d for TRW mo deling, y et the y suffer fr om either the sins of
omission or the sins of commission: VS-Lite is to o simple to simulate the biological p ersistence of tr e e-ring
gr o wth, and VS, MAIDEN, and ORCHIDEE ar e to o complicate d to b e applie d due to lack of accessibiliy of
many parameters in practice . Re cently , I hav e pr op ose d a machine learning base d mo del name d deep-
Green to tackle the memor y and thr eshold effe cts in TRW mo deling with a balance b etw e en simplicity
and comple xity (in pr eparation), wher e the biggest challenge is the data availability , which applies to other
mo dels as w ell but could b e p ossibly r esolv e d by clustering metho ds.
In addition to the nonlinearity of pr o xy formation, mo del bias alone can cancel out the b enefits of pr o xy
system mo deling, and e v en degrade the r e construction skill (De e et al., 2016b ). Ther efor e , the efforts to
impr o v e the absolute values of the simulate d mo del states will also b enefit pr o xy system mo deling.
150
6.2.3 Pr o xy obser vation netw ork
In our PD A frame w ork, the r e constructe d temp oral variations ar e deriv e d solely fr om the pr o xy obser va-
tion netw ork. Chapters 3 - 4 hav e indicate d that the r e construction skill is largely affe cte d by the pr o xy data
availability and quality , and conclusions base d on such r e constructions cannot b e made with confidence
without a sufficient amount of pr o xy obser vations with pr op er spatiotemp oral co v erage .
Sp e cifically , corals ar e dir e ct obser vations of the tr opical o cean state , y et the curr ent netw ork in P A GES
2k v ersion 2 database is still r elativ ely sparse , with only 96 sites available (P A GES 2k Consortium, 2017 ),
and the curr ent obser vation of the Niño 3.4 r egion is mainly the Palmyra r e cor d ( Cobb et al., 2003 ; Cobb
et al., 2013 ; De e et al., 2020 ), which leav es many gaps o v er the last millennium. The CoralHy dr o2k w orking
gr oup
∗
is no w w orking activ ely to e xpand the coral database and has made some pr ogr ess (W alter et al.,
2020 ).
Similar efforts should b e continuously made to other pr o xy netw orks in r e ducing err or and e xpanding
availability . It will, ho w e v er , r e quir e significant amount of funding inv estment in e quipment/de vice/te ch-
nology de v elopment and pr o duction, as w ell as in situ field w ork and lab orator y w ork of scie ntists.
6.3 Outlo ok
In the pr e vious se ction, w e hav e discusse d the cav eats in the se v eral comp onents of the curr ent LMR PD A
frame w ork, along with the ongoing and other p ossible futur e w ork that could help the situation. With all
the mentione d efforts, w e should e xp e ct that the thr e e scientific questions pr op ose d in this thesis can b e
b e tter addr esse d.
Better corr e cte d structural err ors in climate mo del simulations will impr o v e the o v erall accuracy of
the r e construction wher e pr o xy obser vations ar e unavailable , and is a feasible and r elativ ely easy way to
impr o v e the r e construction skill when other comp onents of the frame w ork ar e fixe d or difficult to impr o v e
in the near futur e . This will bring us mor e confidence in the comparisons pr esente d in Chapters 2 - 4 .
The impr o v ement of the pr o xy system mo deling and the simulate d climate states will b enefit the ca-
pability of the frame w ork to b etter understand and e xtract the climatic information emb e dde d in the cur-
r ently available pr o xy obser vations, which will help to make the b est of the curr ent database and impr o v e
the situation e v en when no additional pr o xy obser vations ar e available in the near futur e . For instance ,
successful mo deling of the biological memor y in the TRW netw ork will make the TRW netw ork r e co v er
its usefulness r egar ding the temp eratur e r esp onse to v olcanic for cing, in which case w e do not hav e to
e xclude the TRW netw ork as in Chapter 3 , and w ould b e able to compar e simulations and r e constructions
o v er a larger r egion instead of only the lo cales of the density netw ork.
A multipr o xy obser vation netw ork with br oader and denser spatiotemp oral availability and higher
signal-noise-ratio (SNR) will fundamentally help the multivariate climate field r e constructions. W e w ould
b e able to hav e a finer and mor e complete comparison of the simulate d and obser v e d temp eratur e vari-
ability at r egional scales, instead of only the global scale as in Chapter 2 or only at limite d lo cations as in
Laepple and Huyb ers ( 2014a ). Also , w e may b e able to enlarge the r egion for the simulation-r e construction
∗
http://pastglobalchanges.org/science/wg/2k- network/projects/coral- hydro
151
comparison in Chapter 3 e v en further , and hav e a b etter e valuation of the mo dels’ sensitivity to v olcanic
for cing. Mor e o v er , w e may hav e a mor e r eliable e valuation of the v olcano-ENSO linkage than that dis-
cusse d in Chapter 4 , which suffers fr om data attrition and the limite d sample size of v olcanic eruptions
o v er the last millennium.
All this pr ogr ess will lay a solid foundation for the inv estigation of mor e scientific topics that ar e not
r estricte d to the last millennium temp eratur e . For instance ,
• Ho w w ould w e r eliably e xtend the LMR frame w ork to a time span b e y ond the Common Era, such
as the p erio d since the Last Glacial M aximum (LGM) or e v en de ep er times? This will help a b etter
understanding of the climate variability o v er the centennial-to-millennial scale or e v en the orbital
scale , and help r esolv e the “Holo cene conundrum” (Liu et al., 2014 ), which r efers to the misfit b e-
tw e en pale o climate simulations and obser vations r egar ding the e xistence of the Holo cene climatic
optimum.
• Ho w w ould w e r eliably r e construct the whole o cean state , and what is the r ole of the de ep o cean
state in climate variability? This will help v erify the “ e cho es” hyp othesis pr op ose d in Chapter 2 .
• Ar e the multivariate tele conne ction patterns w e obser v e in mo dern climate stable o v er the Common
Era or e v en since the LGM? This will help e valuate the climatic pr e dictability o v er a longer time scale .
• Ho w do es the climate sensitivity (Manab e and W etherald, 1967 ) e v olv e o v er the Common Era or
e v en since the LGM, and is it stationar y? This will help estimate climate risks o v er a longer time
scale .
In conclusion, the PD A frame w ork that fuses pale o climate obser vations and mo dels is a scalable ap-
pr oach that can continuously b enefit fr om the impr o v ement of its comp onents depicte d in Figur e 1.3 , with
which w e can b etter e valuate the climate mo dels and understand the climate system, se eing the futur e
thr ough the lens of the past.
152
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Abstract (if available)

Abstract The fate of humanity and countless other species depends sensitively on the behavior of the climate system. Our best guess as to this future behavior comes from climate model simulations, which span a broad range of scenarios. How well can we trust these models? ❧ Leveraging the last millennium reanalysis (LMR) paleoclimate data assimilation (PDA) framework, which enables the power of fusing paleoclimate observations and model simulations, this thesis tackles the question in three parts: The first part investigates the continuum of climate variability since the Last Glacial Maximum (about 21,000 years ago), and asks whether models can reproduce it. The second part hones in on the Common Era (past 2000 years), and explores the causes of disagreements between models and reconstructions of the global temperature response to the major forcingㅡmajor volcanic eruptions. The third part considers the El Niño-Southern Oscillation (ENSO) over the same interval, and explores endogenous and exogenous causes for its variations. The result of this study will advance not only science but also the well-being of society. ❧ The first part has been under investigation for almost 20 years, and most previous studies have claimed that climate models underestimate climate variability compared to proxy records. Such comparison is, however, overshadowed by the spatially and temporally limited number of available observations at their time. Our study, on the other hand, has utilized the most comprehensive proxy database, and has provided evidence that the current hierarchy of climate models is capable of reproducing the global-mean temperature variability that we see in observations. The robustness of our result has important implications for climate predictability over the coming century. ❧ The second part also tackles a long standing question: why do paleoclimate reconstructions and climate model simulations disagree so much about the climate response to volcanic eruptions? This question is important because volcanism is the main external forcing to climate system over the Common Era. Our work leveraged paleoclimate data assimilation, which is a recent endeavor that optimally combines both paleo-observations and model simulations and helps to constrain the uncertainties from both sides, and analyzed the leading causes of the discrepancy from the two sides, and updated the comparison by accounting for such causes. The result is a much closer agreement between model simulations and observation-based reconstructions. ❧ The third part studies a topic that is of particular importance to both climate science and the society, namely, El Niño-Southern Oscillation (ENSO). It is the leading pattern of year-to-year climate variability, influencing rainfall and temperature not only around the tropical Pacific, where it dwells, but also the North Atlantic sector and the Eurasian continent via teleconnections. Therefore, being able to predict the ENSO cycle, including its phase and amplitude, is a key to successful prediction of hydroclimate conditions of many regions with large consequences for the management of crops, wildfires, air quality, tourism, and operations for many industries. For instance, the 1997–98 El Niño event has caused $2.2 billion damage in California. Based on this, the understanding of the relationship between ENSO variability and external forcing (natural and anthropogenic) can help us better understand climate variability, improve the prediction, and thus lower the potential damage. We investigated the relationship between ENSO and volcanic eruptions leveraging paleoclimate data assimilation. A novel, skillful reconstruction of NINO3.4 sea surface temperature over the last millennium integrating the latest paleoclimate evidence is produced, and careful and original analyses of the volcano-ENSO link are performed. ❧ These three lines of inquiry shall provide key insights to the climate community and help better constrain near-term climate projections. In addition, these themes speak to the notion of climate risk, which the reinsurance industry now estimates as an existential threat to the world economy.

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Asset Metadata

Creator Zhu, Feng (author)

Core Title Seeing the future through the lens of the past: fusing paleoclimate observations and models

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Degree Conferral Date 2021-08

Publication Date 07/18/2021

Defense Date 05/21/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag climate response to volcanism,climate variability,model evaluation,OAI-PMH Harvest,paleoclimate data analysis,paleoclimate data assimilation,paleoclimate reconstruction

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Emile-Geay, Julien (committee chair), Corsetti, Frank (committee member), de Barros, Felipe (committee member)

Creator Email fengzhu@usc.edu,fzhu2e@outlook.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15602411

Unique identifier UC15602411

Legacy Identifier etd-ZhuFeng-9764

Document Type Dissertation

Format application/pdf (imt)

Rights Zhu, Feng

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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