University of Southern California Dissertations and Theses

Investigating the global ocean biogeochemical cycling of alkalinity, barium, and copper using data-constrained inverse models

(USC Thesis Other)

Investigating the global ocean biogeochemical cycling of alkalinity, barium, and copper using data-constrained inverse models

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INVESTIGATING THE GLOBAL OCEAN BIOGEOCHEMICAL CYCLING OF ALKALINITY,
BARIUM, AND COPPER USING DATA-CONSTRAINED INVERSE MODELS
by
Hengdi Liang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(OCEAN SCIENCES)
August 2023
Copyright 2023 Hengdi Liang
Acknowledgements
I would like to express my deepest gratitude to my Ph.D. advisor, Seth John, for his invaluable guidance,
support, and encouragement throughout my doctoral studies. His knowledge and passion for research
have been a constant source of inspiration to me. Seth provided numerous opportunities for me to present
my research at various conferences and workshops, which helped me to refine my ideas, broaden my per-
spectives, and connect with other researchers in my field. I am immensely grateful for the opportunity to
work under Seth’s mentorship and for his endless patience and encouragement, which have been instru-
mental in my academic and personal growth. I could not have completed this work without his unwavering
dedication to my success.
I am also thankful for the members of my dissertation committee, William M. Berelson, James W.
Moffett, and Emily H. G. Cooperdock, for their invaluable insights, constructive criticism, and support
throughout my doctoral studies. Their expertise and guidance were invaluable in shaping my research
and guiding me through the writing process.
In addition, I would like to thank the professors who taught me in my classes throughout my Ph.D. pro-
gram. Their lectures, discussions, and feedback have been instrumental in shaping my academic journey
and research interests. I am deeply grateful for their passion for teaching and their dedication to inspiring
the next generation of scholars.
I am grateful to all my collaborators for their invaluable contributions to my research. Their expertise,
support, and willingness to share their knowledge have been instrumental in advancing my research and in
ii
shaping my perspectives on science and collaboration. I am also grateful to all people in the Marine Trace
Element Laboratory at USC for their support, friendship, and for making my time in the lab enjoyable and
fulfilling. I have learned a great deal from them and am grateful for the friendships that we have formed.
Lastly, I would like to express my sincere gratitude to my parents and Shangqin for their love, support,
and encouragement throughout my academic journey and life path. Their sacrifices, guidance, and belief
in me have been the foundation of my success, and I am forever grateful for their unwavering support.
Thank you all for your support and encouragement, and for being an integral part of my journey
towards achieving my Ph.D. degree.
iii
TableofContents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Scientific objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background and rational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Ocean biogeochemical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Ocean tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Ocean models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 2: Constraining CaCO
3
export and dissolution with an ocean alkalinity inverse model . . 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1.1 Model overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1.2 Sources and sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1.3 CaCO
3
export from the euphotic zone . . . . . . . . . . . . . . . . . . . . 19
2.2.2 CaCO
3
dissolution scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2.1 Model 1 (M1): Benthic only . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2.2 Model 2 (M2):Ω -dependent dissolution . . . . . . . . . . . . . . . . . . . 20
2.2.2.3 Model 3 (M3):Ω + respiration based dissolution . . . . . . . . . . . . . . 22
2.2.2.4 Model 4 (M4): Constant dissolution . . . . . . . . . . . . . . . . . . . . . 23
2.2.3 Sensitivity experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Model optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.4.1 Alkalinity data and metric definitions . . . . . . . . . . . . . . . . . . . . 25
2.2.4.2 Optimization criteria and genetic algorithm . . . . . . . . . . . . . . . . 28
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 Modeled vs. observed TA0 and TA* . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.2 CaCO
3
export . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.3 CaCO
3
dissolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.4 Sensitivity experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
iv
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Mixing alone cannot replicate TA* observations . . . . . . . . . . . . . . . . . . . . 37
2.4.2 Calcite and aragonite dissolution at bulk seawaterΩ cannot explain observed TA*
profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.3 CaCO
3
dissolution linked to aerobic OM respiration recycles alkalinity in the
upper ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.4 Constant dissolution model similar toΩ + respiration model at depth . . . . . . . . 41
2.4.5 Potential mechanisms driving dissolution above the saturation horizons . . . . . . 41
2.4.6 The importance of calcite vs. aragonite . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter 3: Precipitation and dissolution of pelagic barite: Insights from a global ocean dissolved
Ba model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.1 Observational datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.2 Multiple linear regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2.3 Barite saturation state (Ω barite
) calculations . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.4 Mechanistic model of the marine barium cycle . . . . . . . . . . . . . . . . . . . . 63
3.2.5 Optimization of the mechanistic model . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.6 Sensitivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.6.1 Bootstrap sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.6.2 Dissolved Ba sources for barite precipitation . . . . . . . . . . . . . . . . 70
3.2.6.3 Barite dissolution and the saturation index . . . . . . . . . . . . . . . . . 71
3.2.6.4 The impact of barite sinking velocity on the predicted marine Ba cycle . 72
3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.1 Global climatology of dissolved Ba predicted by the multiple linear regression model 73
3.3.2 Barite saturation state in global oceans . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.3 Mechanistic model prediction of dissolved Ba vs. GEOTRACES Ba observations . . 76
3.3.4 The origins of dissolved Ba for barite precipitation . . . . . . . . . . . . . . . . . . 78
3.3.5 The dependence of barite dissolution onΩ barite
. . . . . . . . . . . . . . . . . . . . 81
3.3.6 The global pelagic barite cycle calculated from the dissolved Ba model . . . . . . . 85
3.3.7 A comparison between the marine dissolved Ba and Si cycles . . . . . . . . . . . . 87
3.3.8 Implications of the water column Ba chemistry for utilizing Ba as a paleoproduc-
tivity proxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 4: Toward a Better Understanding of the Global Ocean Copper Distribution and Speciation
through a Data-constrained Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.1 Observational datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.2 Model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.4 Sensitivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2.4.1 Open- and closed-system models . . . . . . . . . . . . . . . . . . . . . . 109
4.2.4.2 Input fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.4.3 The importance of sedimentary Cu flux to generating linear profiles . . . 110
v
4.2.4.4 The importance of reversible scavenging to generating linear profiles . . 112
4.2.4.5 River input and scavenging in the Arctic Ocean . . . . . . . . . . . . . . 113
4.2.4.6 Chemical speciation of dissolved Cu in the ocean . . . . . . . . . . . . . 114
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.1 Comparison between model and observation . . . . . . . . . . . . . . . . . . . . . 114
4.3.1.1 Global overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.1.2 Surface ocean Cu concentrations . . . . . . . . . . . . . . . . . . . . . . 116
4.3.1.3 Cu concentrations below the surface . . . . . . . . . . . . . . . . . . . . 118
4.3.2 Labile Cu and inert Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.3 Cu fluxes and oceanic residence time . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4.1 Closed-system models and the importance of high Atlantic Cu fluxes in setting
global Cu distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4.2 Evaluation of the relative importance of the three possible external sources . . . . 126
4.4.3 The linear shape of Cu vertical profiles . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.4.3.1 Role of benthic Cu fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.4.3.2 Role of reversible scavenging . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.4.3.3 A complex mixture of processes leads to seemingly simple Cu profiles . 133
4.4.4 Specific details of Cu scavenging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.5 Cu in the Arctic Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.4.6 Labile and inert Cu speciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.1 Thesis summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
vi
ListofTables
2.1 Table2.1 Kinetic dissolution parameters for calcite and aragonite. . . . . . . . . . . . . . . 21
2.2 Table2.2 Optimized parameters, performance, and CaCO
3
export and dissolution for the
four base models. All fluxes are in units of Gt PIC y
-1
. . . . . . . . . . . . . . . . . . . . . . 30
2.3 SupplementaryTable2.1 Optimized parameter values for the four base models. . . . . . 47
3.1 Table3.1 The biogeochemical processes, parameters, and optimization of the mechanistic
dissolved Ba model. The optimized parameter values are based on the model control run. . 69
3.2 Table 3.2 Barite precipitation and dissolution fluxes (in Gmol y
-1
). Three tests focusing
on the Ba
2+
source origins for barite precipitation are listed, including a direct seawater
source, an intermediate source from organic matter, and a combination of both seawater
and organic sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.1 Table4.1 Estimates of global Cu inventory, input or output fluxes, and residence time of
marine Cu from previous literature and the base model of this study.The global Cu input
or output flux data used in previous literature are either based on measurements or from
data compilation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2 Table4.2 Base model parameter definitions, initial guesses, and final values after model
optimization. Model processes and optimization are described in Section 4.2.2 and 4.2.3. . . 115
vii
ListofFigures
1.1 Figure1.1 Inverse model flowchart. The inverse model involves several steps. (1) Specify
the initial conditions and constraints, and assign the initial values to the parameters
of the biogeochemical mechanisms and source/sink terms. (2) Send the model setup to
the AWESOME OCIM solver. (3) Simulate a model prediction of tracer concentrations.
(4) Calculate the root-mean-square deviation (RMSD) between predicted and observed
tracer concentrations. (5) Select a MATLAB optimization algorithm to determine if the
RMSD is minimized. If yes, the final model output is generated; if no, (6) calibrate the
model parameters, and repeat from Step 2. The inverse model aims to estimate the
unknown model parameters that best fit the observed data, allowing for the simulation of
unobserved scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Figure 2.1 Schematic diagram of the alkalinity model. Constraints based on external
datasets (fixed values) and variable parameters (optimized in each model run; marked in
blue) are fed into the Awesome OCIM framework. For each model iteration, the resulting
TA0 and TA* are compared to observed values based on GLODAP data. The optimized
parameters are adjusted, and the model rerun until a minimum cost is found. The four
different models of water column CaCO
3
dissolution used different parameters, as noted
by the superscripts (M2, M3, and M4) (see Section 2.2.2). . . . . . . . . . . . . . . . . . . . 17
2.2 Figure 2.2 Differences resulting from various approaches to estimating preformed
alkalinity, compared to TA0
AO
. Negative values represent deficits in preformed alkalinity,
which would be interpreted as excess CaCO
3
dissolution in TA analysis. The Alk*
approach yields relatively low preformed alkalinity, especially in the Southern Ocean,
resulting from assumptions about both preformed nutrients and alkalinity (combined
in a, and only alkalinity component in b). For approaches using circulation matrices to
reconstruct TA0, results are sensitive to the method used to define alkalinity at the base
of the mixed layer depth, for example either by locally-interpolated regression (c) or by
interpolation (d). In (c) and (d), TA0
Carter
refers to preformed alkalinity data from Carter
et al. (2021). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Figure 2.3 Example of two modeled transects (Pacific at 161 °W and Atlantic at 29°W)
compared to observations for M3 (Ω + respiration model). Observed TA0 and TA* based
on the GLODAP dataset (a and b); Modeled TA0 and TA* (c and d); and the difference
between model and observation (model - observation) (e and f). . . . . . . . . . . . . . . . 31
viii
2.4 Figure2.4 Difference between modeled and observed TA0 and TA* (TA0: a, e, i, m; TA*: c,
g, k, o) in representative transects (Pacific at 161 °W and Atlantic at 29°W). Joint probability
density function plots of modeled vs observed data in each grid cell show the relative
performance of each model (TA0: b, f, j, n; TA*: d, h, l, p). . . . . . . . . . . . . . . . . . . . 32
2.5 Figure 2.5 (a, c, e, g) CaCO
3
dissolution (µmol kg
-1
y
-1
) in all four base models for
representative transects (Pacific at 161 °W and Atlantic at 29°W). Black lines represent the
aragonite (dashed) and calcite (solid) saturation horizons. (b, d, f, h) Globally-integrated
vertical profiles of total water column and benthic dissolution for each model (Gmol
m
-1
y
-1
). Black lines indicate water column dissolution, and red lines indicate benthic
dissolution. M1 and M2 (benthic-only andΩ -dependent models) are dominated by benthic
dissolution at depth (b, d). M3 (Ω + respiration model) has an extreme dissolution peak in
the upper ocean (f inset), below which total dissolution is minor in comparison (f), and
below about 500 m, relatively similar to M4 (constant dissolution model) (h). . . . . . . . . 35
2.6 Figure2.6 Global average profiles of calcite and aragonite dissolution for the two models
that consider mineral kinetics (M2 and M3). The Ω -dependent model (M2) results in
disproportionate calcite dissolution at depth due to faster dissolution kinetics (a), while
theΩ + respiration model (M3) results in disproportionate calcite dissolution in the upper
ocean (b inset). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7 Figure 2.7 CaCO
3
export profiles for the three best-performing models in the export
sensitivity tests. “M3 (mid)”: Ω + respiration model with 1.1 Gt PIC y
-1
export. “M3
(high)”:Ω + respiration model with 1.8 Gt PIC y
-1
export. “M4 (mid)”: constant dissolution
model with 1.1 Gt PIC y
-1
export. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.8 Supplementary Figure 2.1 (a-d) Data inputs for deriving CaCO
3
export: P uptake (a)
× C:P ratio (b) × PIC:POC ratio (c) = CaCO
3
export (d). In addition, a scaling factor was
optimized for each model to adjust total CaCO
3
export. (e) Riverine alkalinity inputs
to the oceans, which are plotted as point sources at each river mouth. Data are before
adjustment by the scaling factor of 1.5 to balance burial fluxes (details in Section 2.1.2).
(f-h) Alkalinity burial fluxes of pelagic ocean (f), coastal ocean (g), and total burial (h).
Pelagic ocean burial data are derived from Dunne, Hales, and Toggweiler (2012) and
re-gridded to fit the model grids in this study. Coastal ocean burial data are derived from
O’Mara and Dunne (2019) and re-gridded to fit the model grids in this study. The total
burial is the sum of pelagic and coastal burial (details in Section 2.1.2). . . . . . . . . . . . . 48
2.9 Supplementary Figure 2.2 Observed and modeled TA0 and TA* for representative
transects (Pacific at 161 °W and Atlantic at 29°W). White lines represent the aragonite
(dashed) and calcite (solid) saturation horizons. Observed, calculated based on the
GLODAP alkalinity dataset and OCIM circulation (a, b); M1, benthic only model (c, d);
M2,Ω -dependent model (e, f); M3,Ω + respiration model (g, h); M4, constant dissolution
model (i, j). The transects for M3 (g, h) are shown in the main text in Fig. 2.3. . . . . . . . . 49
ix
2.10 SupplementaryFigure2.3 Observed and modeled TA0 and TA*, and model-observation
mismatch for the export sensitivity tests for M1 (benthic only model). Tests were run
for low (0.5 Gt C y
-1
), mid (1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export
from 73 m). (a, b) Observed TA0 and TA*, respectively. (c, g, k) Modeled TA0. (d, h, l)
TA0 model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation
mismatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.11 SupplementaryFigure2.4 Observed and modeled TA0 and TA*, and model-observation
mismatch for the export sensitivity tests for M2 (Ω -dependent model). Tests were run for
low (0.5 Gt C y
-1
), mid (1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export from 73
m). (a, b) Observed TA0 and TA*, respectively, calculated based on the GLODAP alkalinity
dataset and OCIM circulation. (c, g, k) Modeled TA0. (d, h, l) TA0 model-observation
mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation mismatch. . . . . . . . . . 51
2.12 SupplementaryFigure2.5 Observed and modeled TA0 and TA*, and model-observation
mismatch for the export sensitivity tests for M3 (Ω + respiration model). Tests were
run for low (0.5 Gt C y
-1
), mid (1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios
(export from 73 m). (a, b) Observed TA0 and TA*, respectively, calculated based on the
GLODAP alkalinity dataset and OCIM circulation. (c, g, k) Modeled TA0. (d, h, l) TA0
model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation
mismatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.13 SupplementaryFigure2.6 Observed and modeled TA0 and TA*, and model-observation
mismatch for the export sensitivity tests for M4 (constant dissolution model). Tests were
run for low (0.5 Gt C y
-1
), mid (1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios
(export from 73 m). (a, b) Observed TA0 and TA*, respectively, calculated based on the
GLODAP alkalinity dataset and OCIM circulation. (c, g, k) Modeled TA0. (d, h, l) TA0
model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation
mismatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.14 SupplementaryFigure2.7 Model-observation mismatch for the sinking speed sensitivity
tests for M2 (Ω -dependent model). Differences between modeled and observed (model
– observed) are shown for both TA0 (left column) and TA* (right column), at a range of
sinking speeds: 1 m d
-1
(a, b); 10 m d
-1
(c, d); 100 m d
-1
, the default sinking speed in the
base models (e, f); and 1,000 m d
-1
(g, h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.15 SupplementaryFigure2.8 Model-observation mismatch for the sinking speed sensitivity
tests for M3 (Ω + respiration model). Differences between modeled and observed (model
– observed) are shown for both TA0 (left column) and TA* (right column), at a range of
sinking speeds: 1 m d
-1
(a, b); 10 m d
-1
(c, d); 100 m d
-1
, the default sinking speed in the
base models (e, f); and 1,000 m d
-1
(g, h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.16 SupplementaryFigure2.9 Model-observation mismatch for the combined sinking speed
and calcite:aragonite ratio sensitivity tests for M2 (Ω -dependent model). Differences
between modeled and observed (model – observed) TA* are shown, at a range of sinking
speeds: 1 m d
-1
(a, b, c); 10 m d
-1
(d, e, f); 100 m d
-1
, the default sinking speed in the
base models (g, h, i); and 150 m d
-1
(j, k, l). The center column uses the spatially variable
calcite:aragonite ratio from the GFDL dataset, as used in all base models. . . . . . . . . . . 56
x
3.1 Figure 3.1 The marine Ba cycle, including the dissolved (black circle), organic (green
circle), and particulate (purple circle) Ba phases. Our mechanistic model represents the
dissolved pool explicitly, while the organic and particulate pools are included implicitly
through the exchanges with the dissolved pool. The biogeochemical processes that regulate
the conversions between these phases include: 1) the biological uptake of dissolved Ba
into marine organisms (red arrow), followed by organic matter remineralization at depths
(orange arrow), and 2) the precipitation (blue arrows) and dissolution (green arrow) of
barite. The arrow directions indicate the transfer of Ba from one phase to the other, while
the thickness of the arrows reflect the relative magnitudes of the fluxes, as predicted by
our mechanistic model. This figure is adapted from Horner et al. (2015). . . . . . . . . . . . 64
3.2 Figure 3.2 The multiple linear regression (MLR) model of dissolved Ba. The first row
shows scatter plots of observed and predicted Ba concentrations. (a) Train the MLR
algorithm with Atlantic Ba data (blue), and validate with the Pacific Ba data (red). (b) Train
the MLR algorithm with Pacific Ba data (red), and validate with the Atlantic Ba data (blue).
(c) Train the MLR algorithm with all data from GEOTRACES IDP2021, then predict the
global climatology of Ba and validate the model performance with the data predicted at
the same locations of observations. The second row shows global maps of MLR-predicted
(color field) and observed (filled circles) Ba concentrations at (d) surface ocean, (e) 1000 m,
and (f) 3000 m. The third row shows global maps of standard deviation (STD) resulting
from 1000 iterations of bootstrap sampling of the MLR model at (g) surface ocean, (h) 1000
m, and (i) 3000 m. The STD maps highlight regions with higher variability with darker
red color, providing insights into the robustness of the MLR model and potential sources
of uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3 Figure3.3 Global maps displaying the spatial distributions of the saturation state of barite
(Ω barite
) at various depths. CalculatedΩ barite
for pure barite at (a) surface ocean, (b) 2000
m, and (c) 3750 m. CalculatedΩ barite
for Sr barite at (d) surface ocean, (e) 2000 m, and (f)
3750 m. The solubility product constant is calculated following Rushdi et al. (2000). . . . . 77
3.4 Figure 3.4 The dissolved Ba concentrations predicted by the mechanistic model
compared to GEOTRACES IDP2021 observations. (a) Average vertical profiles of dissolved
Ba concentrations in the Atlantic (yellow) and Pacific (purple) Oceans. The data
points indicate observed average Ba concentrations in that ocean basin, with error bars
representing 1 standard deviation. The lines represent modeled average Ba concentrations,
with shaded areas representing 1 standard deviation. (b) Scatter plot comparing global
observed and modeled Ba concentrations, color-coded by sampling depth. Global maps of
dissolved Ba concentrations at (c) surface and (d) 2500 m, with model predicted dissolved
Ba concentrations represented by the color field and observations overlaid as filled circles. 79
3.5 Figure 3.5 Vertical profiles of global average dissolved Ba concentrations, from
observations (data points with error bars representing 1 standard deviation), the model
simulation which assumes the Ba source for barite precipitation is from seawater (red
line), the model simulation which assumes the Ba source for barite precipitation is from
organic matter (blue line), and the model simulation which assumes the Ba source for
barite precipitation is from both seawater and organic matter (grey areas presenting the
average± 1 standard deviation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
xi
3.6 Figure3.6 Sensitivity tests comparing the effects of different barite dissolution scenarios
on dissolved Ba (dBa) distributions. The data presented here are from the North Pacific
Ocean, where barite saturation states might influence dBa most significantly. (a-c) The
constant dissolution scenario, where the control run dissolution rate constant is optimized
to k
d
, and three sensitivity tests are plotted against the control run which set dissolution
rate constant to 0 (blue), k
d
/5 (purple), and k
d
×5 (red). (d-f) Barite dissolution rate is
formulated as a function of pure barite saturation state, with the reaction order (n) set to
1 (orange) or allowed to optimize (green). (g-i) Barite dissolution rate is formulated as a
function of Sr barite saturation state, with the reaction order (n) set to 1 (orange) or allowed
to optimize (green). (a, d, g) Vertical profiles of average dissolved Ba concentrations in
the North Pacific Ocean. (b, e, h) Total water column barite dissolution (in Gmol y
-1
) in
the North Pacific Ocean. (c, f, i) Total sedimentary barite dissolution (in Gmol y
-1
) in the
North Pacific Ocean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.7 Figure 3.7 Global pelagic barite precipitation and dissolution calculated from the
mechanistic model control run results. (a) Vertical profile of total pelagic barite
precipitation rate variations with depth (Gmol y
-1
). (b) The fraction of barite precipitation
accumulated with depth. The model results show that 90% of barite precipitation occurs in
the upper 900 m. (c) Vertical profile of total pelagic barite dissolution rate variations with
depth (Gmol y
-1
), with water column dissolution (yellow) and sedimentary dissolution
(green) displayed separately. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.8 Figure3.8 Comparison of three models investigating the influence of barite sinking rate
(v) on the marine Ba model, including the constant sinking rate scenario (left column), a
linear increase in sinking rates with depth (middle column), and assuming the particles
are composed of 50% small particles and 50% large particles which sink 100 times faster
than the small particles (right column). (a-c) The average dissolved Ba concentrations
as predicted by the three models, compared with GEOTRACES dBa observations. (d-f)
Vertical profiles of global total barite dissolution rates, estimated from the three models
with different barite sinking velocities. (g-i) The calculated global average pelagic barite
fluxes at various depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.9 Figure3.9 Comparison between marine dissolved Ba and Si. The dBa data are from our
control run, while the dSi data are sourced from World Ocean Atlas 2009. (a-c) Joint
probability density function plots of (a) total dBa and dSi, (b) preformed dBa and dSi, and
(c) regenerated dBa and dSi. A linear regression analysis is applied to show the linear
relationship of the two datasets (dashed line), withR
2
and root-mean-square-error (RMSE)
calculated for each pair of datasets. (d-f) Average vertical profiles of dBa (red) and dSi
(blue) concentrations, along with the tracer Ba* (green) in the (d) Atlantic, (e) Pacific, and
(f) Southern Oceans. Dashed black lines indicate concentrations equal to zero, providing
clarity on whether Ba* is negative or positive at each depth. . . . . . . . . . . . . . . . . . 89
xii
3.10 Supplementary Figure 3.1 Global pelagic barite precipitation, dissolution, and fluxes
calculated from the mechanistic model control run results. (a) Vertical profile of total
pelagic barite precipitation rate variations with depth (Gmol y
-1
). (b) The fraction
of barite precipitation accumulated with depth. The model results show that 90% of
barite precipitation occurs in the upper 900 m. (c) Vertical profile of total pelagic barite
dissolution rate variations with depth (Gmol y
-1
), with water column dissolution (yellow)
and sedimentary dissolution (green) displayed separately. (d) The pelagic barite flux
calculated at each depth (mol m
-2
y
-1
). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.11 SupplementaryFigure3.2 Predictions of Ba concentrations using five machine learning
algorithms. (a,f) Multiple linear regression (MLR). (b,g) Gaussian process regression
(GPR). (c,h) Decision tree. (d,i) Support vector machine (SVM). (e,j) Artificial neural
network (ANN). Ba data from the Atlantic and Pacific Oceans are plotted in blue and red,
respectively. (a-e) Train the algorithm using Atlantic data, then validate the model with
Pacific data. (f-j) Train the algorithm using Pacific data, then validate the model with
Atlantic data. The dashed lines indicate the 1:1 line, and the deviations of data points from
this line suggest inaccurate predictions of the data. The R-squared (R
2
) values for each
group of data are listed in each subplot. Note that the MATLAB artificial neural network
algorithm can produce different results every time due to the random initialization of the
weights and biases in the neural network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.12 Supplementary Figure 3.3 Average vertical composite profiles of dissolved Ba
concentrations in different ocean basins. The black data points with error bars are average
dissolved Ba concentrations from GEOTRACES IDP2021 with 1 standard deviation, while
the purple lines are the average modeled Ba at the same sampling locations. (a) North
Atlantic Ocean. (b) South Atlantic Ocean. (c) North Pacific Ocean. (d) South Pacific Ocean.
(e) Arctic Ocean. (f) Southern Ocean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.13 Supplementary Figure 3.4 Observed vs. modeled dissolved Ba concentrations along
four GEOTRACES cruises. (a-b) GA03 cruise (west leg). (c-d) GA02 cruise. (e-f) GP16
cruise. (g-h) GP15 cruise. The left column shows the dissolved Ba concentrations ([dBa]),
with color field indicating model predictions and filled circles indicating observations.
The right column shows the differences between model and observations at the sampling
locations, with color bars representing the predicted Ba minus observed Ba. . . . . . . . . 97
4.1 Figure4.1 Key processes in the marine biogeochemical cycling of Cu. The dashed black
line indicates the base of the euphotic zone. Total dissolved Cu is comprised of kinetically
labile Cu and inert Cu pools. The labile Cu is actively involved in biogeochemical
processes, including biological uptake by phytoplankton followed by remineralization
(green arrows), and reversible scavenging onto particles (red arrows). Upon reaching
the seafloor, a fraction of the biogenic and scavenged labile Cu remineralizes, while the
remaining fraction is buried in the sediments. Labile Cu is converted to inert Cu by strong
organic ligand binding throughout the water column, while inert Cu is converted back to
labile Cu in the euphotic zone through photodecomposition. External sources of Cu to the
ocean include rivers (which are assumed to be composed of 90% inert Cu and 10% labile
Cu), dust (entirely labile Cu), and a dissolved flux coming from nepheloid layer particles
(entirely labile Cu). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
xiii
4.2 Figure 4.2 Comparison between observed dCu from the GEOTRACES IDP2021 dataset
and dCu predicted by the base model. (a) Vertical profiles of average dissolved Cu in the
Atlantic (red) and Pacific (blue) Oceans. Observations are represented as dots with error
bars, while model predictions are shown as lines with shaded areas indicating 1 standard
deviation. (b-d) Global distributions of observed (filled circles) and model-predicted (color
field) dissolved Cu at (b) the surface ocean, (c) 1500 m depth, and (d) 3000 m depth. . . . . 115
4.3 Figure 4.3 Comparison of dissolved Cu concentrations from the GEOTRACES IDP2021
observations and model predictions from the base model. (a-d) Scatter plots showing the
relationship between modeled and observed total dCu concentrations in the (a) Atlantic,
(b) Pacific, (c) Indian, and (d) Arctic Oceans. The dashed black line represents the 1:1
line, and the solid black line is the linear regression line. Correlation coefficients ( R)
are provided for each sub dataset. (e-f) Cumulative joint probability density function of
modeled and observed dCu for (e) the global dataset and (f) the global dataset excluding
Arctic Ocean Cu data. The dashed black line represents the 1:1 line. . . . . . . . . . . . . . 117
4.4 Figure 4.4 Comparison of modeled and observed dissolved Cu concentrations along
several GEOTRACES transects. (a) Global surface map of dissolved Cu concentrations
from the base model prediction (color field). Selected GEOTRACES cruises are plotted
as observed Cu concentrations (filled circles) with cruise names near the observation
data points. (b-g) Modeled (color field) and observed (filled circles) Cu along different
GEOTRACES cruises, including three Pacific cruises (b) GP02, (c) GP13, (d) GP16, two
Atlantic cruises (e) GA03 (west leg), (f) GA10, and one Indian cruise (g) GI04. . . . . . . . . 119
4.5 Figure 4.5 Comparison of modeled and observed distributions of labile and inert Cu.
(a) Labile Cu concentrations and (b) the percentage of inert Cu along the GEOTRACES
GP15 cruise. (c) Labile Cu concentrations and (d) the percentage of inert Cu along the
GEOTRACES GA03 cruise. The modeled values are shown as the background color field,
while the observed values are overlaid as filled circles. (e-f) Vertical profiles of the modeled
average labile Cu (light blue) and inert Cu (dark blue) concentrations in the (e) Atlantic
and (f) Pacific Oceans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.6 Figure 4.6 Flux estimates for internal cycling of Cu within the oceans, and external
sources of Cu to the oceans. (a) The Cu fluxes associated with each biogeochemical
process, calculated from the base model optimized results. (b) Estimates of external
sources of Cu from our base model compared with estimates from previous literature,
where different colors represent different source types (river, margin, dust, sediment, or
nepheloid layer particles). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Figure4.7 Basin-average vertical profiles of dissolved Cu concentrations in the Atlantic
(red) and Pacific (blue) Oceans, as estimated by the closed-system model. GEOTRACES
observations are represented as dots with error bars, while the closed-system model
predictions are shown as lines with shaded areas indicating 1 standard deviation. . . . . . 125
xiv
4.8 Figure 4.8 Sensitivity tests illustrating model response to changes in source flux
magnitudes. The base model optimized value of one of the three sources (river, dust,
and nepheloid layer particles in Row 1, 2, and 3, respectively) is multiplied by a scaling
factor (SF) of 0.1, 0.2, 0.5, 1 (same as base model), 2 , 5, or 10. Average vertical profiles
of dissolved Cu in the Atlantic (red) and Pacific (blue) Oceans are shown. GEOTRACES
observations are plotted as dots with error bars, and the model predictions are plotted as
lines with shaded areas representing 1 standard deviation. The flux estimates are listed
as numbers below each profile plot, with river (green), dust (yellow), nepheloid layer
particles (purple), and total fluxes (grey) calculated in the unit of Gmol y
-1
. The underlined
number indicates the fixed flux in that sensitivity test, and the model is then re-optimized
to allow for changes in the magnitudes of the other two sources. . . . . . . . . . . . . . . . 128
4.9 Figure 4.9 The impact of sedimentary input and reversible scavenging on global Cu
distribution. Average vertical profiles of dissolved Cu are plotted for the Atlantic (red)
and Pacific (blue) Oceans to investigate the processes that contribute to the nearly-linear
vertical Cu profiles. GEOTRACES observations are shown as dots with error bars, and the
optimized model results are represented by lines with shaded areas indicating 1 standard
deviation. (a) Model without an external sedimentary Cu source from the nepheloid layer.
(b) Model without sedimentary regeneration of biogenic and scavenged Cu. (c) Model
without any sedimentary input of Cu. (d) Model without reversible scavenging of Cu onto
particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.10 Figure 4.10 Impact of various parameterizations of scavenging on global distributions
of total Cu and labile Cu. (a, c, e, g, I, k, m) Average vertical profiles of dissolved Cu in
the Atlantic (red) and Pacific (blue) Oceans. GEOTRACES observations are represented
as dots with error bars, and the model predictions are plotted as lines with shaded
areas indicating 1 standard deviation. (b, d, f, h, j, l, n) Labile Cu concentrations at
Station 29 (0°, 152°W) from the GEOTRACES GP15 transect, with black dots representing
observations and red lines representing model predictions. (a-b) Model prediction with
uniform reversible scavenging (base model). (c-d) Model prediction without scavenging.
(e-f) Model prediction with uniform irreversible scavenging. (g-h) Model prediction with
irreversible scavenging onto POC. (i-j) Model prediction with reversible scavenging onto
POC. (k-l) Model prediction with reversible scavenging following the
230
Th scavenging
pattern. (m-n) Model prediction with reversible scavenging following the
231
Pa scavenging
pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.11 Figure4.11 Modeled and observed Cu distributions in the Arctic Ocean for four different
models. Observed Arctic Cu concentrations from the GEOTRACE IDP2021 dataset are
represented by black dots with error bars. Model predictions of average Cu concentrations
in the Arctic Ocean are shown as lines for four different model configurations: the base
model (dark blue), the model with Arctic rivers optimized separately at a higher level than
the base model (green), the model without scavenging in the Arctic Ocean (yellow), and
the model with a separately optimized value for Arctic riverine Cu concentrations and
without scavenging in the Arctic Ocean (red). . . . . . . . . . . . . . . . . . . . . . . . . . 140
xv
4.12 Figure 4.12 The impact of speciation on total Cu, labile Cu, and inert Cu distributions
in the global ocean. (a) Model assuming all dissolved Cu has the same biogeochemical
behavior in the ocean, with black data points representing observed global average Cu
concentrations and light blue areas representing modeled total dissolved Cu. (b) Model
assuming separate pools of labile and inert Cu in the ocean, as defined as the base model
in this study, with black data points representing observed average Cu concentrations,
light blue areas representing modeled average labile Cu concentrations, and dark blue
areas representing modeled average inert Cu concentrations. . . . . . . . . . . . . . . . . . 142
4.13 SupplementaryFigure4.1 Dissolved Cu concentrations compared to salinity (S) in the
Arctic Ocean. Both Cu and salinity data are from GEOTRACES IDP2021 Arctic cruises.
(a) Scatter plot of seawater Cu concentrations versus salinity from all depths in the Arctic
Ocean. The negative slope of the linear regression (black line) and high correlation
coefficient ( R) suggest a potential source of Arctic Cu from freshwater. (b) Scatter plot of
Cu concentrations versus salinity in the surface Arctic Ocean seawater samples (0 - 73 m),
which is a subset of dataset from (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.14 Supplementary Figure 4.2 The impact of different scavenging scenarios on Cu
concentrations in the Arctic Ocean. The black dots with error bars represent observed
average Cu concentrations from GEOTRACE IDP2021 Arctic cruises. The red lines with
shaded areas indicating 1 standard deviation represent model predictions of average Cu
concentrations under six different scavenging scenarios discussed in Section 4.4.4. (a)
No scavenging. (b) Uniform irreversible scavenging. (c) Irreversible scavenging onto
POC. (d) Reversible scavenging onto POC. (e) Reversible scavenging following the
230
Th
scavenging pattern. (f) Reversible scavenging following the
231
Pa scavenging pattern. The
models have the best performance in the Arctic Ocean when global Cu scavenging follows
the
230
Th or
231
Pa patterns (e-f). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
xvi
Abstract
The ocean plays a vital role in the regulation of the global climate system, and understanding the mech-
anisms that control the distribution and cycling of key elements in the ocean is essential for predicting
and mitigating the impacts of climate change. In this thesis, I investigate ocean biogeochemical processes
through three chemical tracers, including alkalinity, barium, and copper, using both observations and an
ocean circulation inverse model.
Alkalinity is a key parameter in the ocean carbon cycle. A global alkalinity model is developed to
constrain the cycling of calcium carbonate (CaCO
3
) in the ocean. The results reveal that CaCO
3
dissolution
must occur throughout the water column to match observed alkalinity distributions, suggesting potential
microbial processes that drive dissolution in supersaturated waters. CaCO
3
export is constrained within a
wide range, and the observed alkalinity features can be reproduced by the model as long as the magnitudes
of CaCO
3
export and upper ocean dissolution are coupled.
The dissolved and particulate phases of barium (Ba) can be used as proxies for organic carbon res-
piration and export productivity. I combine Ba observations, a multiple linear regression model, and a
global dissolved Ba model to investigate the marine Ba cycle, with a focus on the distribution of dissolved
Ba in the ocean and how the dissolved phase relates to the organic and particulate phases. Results show
that the precipitation and dissolution of barite (BaSO
4
) play a major role in regulating the distribution of
dissolved Ba. The model suggests that the dissolved Ba for barite precipitation originates mainly from
ambient seawater, and that barite dissolution rate is relatively independent of barite saturation states.
xvii
Copper (Cu) is a trace metal that is involved in many biogeochemical processes in the ocean, including
biological uptake, reversible scavenging, and organic complexation. I use observations and a global model
to investigate the distribution of Cu in the ocean and how Cu interacts with marine organisms, organic
matter, and particles. The model explicitly represents Cu partitioning between labile and inert phases
through the slow conversion of labile Cu to inert in the whole water column, and the photochemical
degradation of inert Cu to labile in the euphotic zone. The model results suggest that linear increases in
Cu concentrations with depth require both a sedimentary source and reversible scavenging onto particles.
Cu cycling in the Arctic Ocean appears to be different from other oceans, requiring relatively high Cu
concentrations in Arctic rivers and reduced scavenging in the Arctic.
Overall, this thesis highlights the potential of ocean tracers as a powerful tool for investigating ocean
biogeochemical processes, and the role of ocean inverse models in simulating and analyzing the complex
processes that occur within the marine environment. The findings presented in this thesis advance our
understanding of the biological and chemical processes that regulate the ocean system, while emphasizing
the importance of the interconnections between different biogeochemical cycles in the ocean.
xviii
Chapter1
Introduction
1.1 Scientificobjectives
The ocean plays a crucial role in the global carbon cycle, regulating the Earth’s climate by absorbing and
storing a significant proportion of atmospheric carbon dioxide (CO
2
). It is also an essential habitat for
numerous marine organisms and supports global fisheries. However, the vastness and complexity of the
ocean system make it challenging to study. Ocean biogeochemistry is an important area of ocean research
that requires interdisciplinary approaches, including biology, chemistry, physics, and geology. Under-
standing the biogeochemical processes in the ocean is critical to understanding the marine ecosystems, as
well as their interactions with the Earth’s climate system.
Ocean tracers are important tools for studying ocean biogeochemistry because they can be used to
trace the movement of water masses and the exchange of material between different parts of the ocean.
Some examples of ocean tracers include oxygen, nitrogen, phosphorus, trace metals, and isotopes of these
elements. By measuring the concentrations and isotopic compositions of these tracers in the ocean, marine
scientists can infer the processes that control their distribution, such as the rates of nutrient uptake and
recycling by phytoplankton and zooplankton, and the rates of ocean mixing and ventilation.
This thesis aims to study the global cycling of three ocean tracers, alkalinity, barium, and copper, while
quantifying the biogeochemical processes that regulate these tracers. To achieve this objective, I employ a
1
combination of observational data and biogeochemical models. A comprehensive database of ocean tracer
concentrations is compiled from a variety of sources, which will be used to develop and constrain biogeo-
chemical models that simulate the global distribution of tracers based on pre-computed ocean circulation
and biological and chemical mechanisms. Then, inverse modeling techniques are used to quantify the
biogeochemical processes that control the distribution of these tracers, including the interactions of these
tracers with marine organisms, particles, and organic matter. The modeling results can provide insights
into how the ocean functions as a complex system, and how these processes may be affected by climate
change and other environmental stressors.
1.2 Backgroundandrational
1.2.1 Oceanbiogeochemicalprocesses
Ocean biogeochemical processes drive the cycling of elements and nutrients in the ocean. In the surface
ocean, marine organisms, such as phytoplankton, can take up nutrients including nitrogen, phosphorus,
and iron, which are essential for the growth and survival of marine life, and their availability can limit
primary productivity in the ocean. In the deep ocean, the nutrient regeneration process releases nutrients
from sinking organic matter back to seawater. These nutrients can then be upwelled to the surface layer
and utilized by phytoplankton to sustain primary productivity in the ocean. Particles such as particulate
organic matter and minerals can sink to the seafloor, where they can be buried and stored for long periods
of time. This sedimentation process plays an important role in the global carbon and nutrient cycles.
Understanding these biogeochemical processes and their interactions is essential for comprehending the
functioning of the ocean ecosystem.
2
The study of ocean biogeochemical processes is important due to its role in regulating the Earth’s
ecosystem and climate. The ocean acts as a significant carbon sink, absorbing atmospheric CO
2
and se-
questering carbon in the ocean interior (Friedlingstein et al., 2022). This uptake of CO
2
leads to the acidifi-
cation of the ocean, which can have profound impacts on marine organisms and ecosystems. A thorough
understanding of the biogeochemical processes that regulate carbon uptake and storage in the ocean is nec-
essary to predict how the ocean will respond to future changes in the climate system. A variety of tools and
techniques can be used to study ocean biogeochemical processes, including observational data, laboratory
experiments, and numerical models. Observational data, such as satellite measurements, oceanographic
cruises, and buoy data, provide important information on the physical and chemical properties of the
ocean. Laboratory experiments help determine tracer concentrations and understand the biological and
chemical processes that occur in the ocean under controlled conditions. Numerical models are used to
simulate ocean processes under different scenarios, allowing scientists to mathematically understand the
past and modern oceans and make predictions about the future marine environment.
Over the past few decades, the field of ocean biogeochemistry has made significant strides in advanc-
ing our understanding of the complex biogeochemical processes that regulate the ocean ecosystem. One
major achievement has been the development of a comprehensive understanding of the global carbon
cycle, including the ocean’s critical role in sequestering atmospheric CO
2
. This understanding has been
facilitated by the use of sophisticated modeling techniques and innovative observational methods such as
autonomous floats, which have enabled the collection of detailed data on the distribution of carbon and
other key tracers in the ocean. There is also significant progress in identifying key biogeochemical pro-
cesses and the role of trace elements in regulating these processes. For example, we now know that iron is
a critical cofactor for photosynthesis and that its availability can limit primary productivity in many ocean
regions (Martin & Fitzwater, 1988). In addition, advances in observational techniques and technology have
enabled scientists to explore previously inaccessible regions of the ocean, such as deep-sea hydrothermal
3
vents (e.g. German et al., 2016). These explorations have yielded new insights into the diversity of ma-
rine life and the complex biogeochemical processes that sustain it, which have significantly advanced our
understanding of global biogeochemical cycles and the impacts of natural and anthropogenic activities on
the marine environment.
While much progress has been made in understanding ocean biogeochemical processes, there are still
several significant knowledge gaps in this field. One major gap is our understanding of the role of trace
elements in regulating these processes. While we know that trace elements such as iron, zinc, and copper
are essential for many biogeochemical reactions in the ocean, we do not fully understand the mechanisms
by which these elements are cycled through the ocean or the extent to which they limit or regulate bi-
ological productivity. Another significant knowledge gap is our understanding of the impacts of global
environmental changes on ocean biogeochemistry. While changes such as ocean warming, acidification,
and deoxygenation are known to have significant effects on the ocean ecosystem, we do not fully under-
stand how these changes will impact biogeochemical processes at regional or global scales. In addition,
there are still significant gaps in our understanding of the links between different biogeochemical cycles
and the ways in which they interact to regulate the ocean ecosystem. For example, while we know that
the ocean carbon cycle is closely linked to the nitrogen cycle and the cycling of other elements, it remains
unclear about the nature of these links or the ways in which they may be affected by changing environ-
mental conditions. More research on ocean biogeochemical processes is essential for understanding the
dynamics of the ocean ecosystem and predicting how it will respond to future changes.
1.2.2 Oceantracers
Ocean tracers refer to elements or chemical compounds that can be used to track the movement of water
masses, identify the sources and sinks of different compounds, and understand how these compounds are
4
transformed over time. These tracers are an important tool for understanding the physical and biogeo-
chemical processes that occur in the ocean. There are many different types of ocean tracers, including
dissolved gases, stable isotopes, radioisotopes, and trace metals. Each of these tracers has unique prop-
erties that make it well-suited for studying different aspects of the ocean system. For example, dissolved
gases such as oxygen and carbon dioxide can be used to track the exchange of gases between the ocean
and atmosphere, while some stable isotopes can be used to track ocean circulation and identify the rate of
nutrient uptake.
One important group of tracers used in oceanography are trace metals, which exist in seawater at very
low concentrations. Trace metals play a critical role in the functioning of the ocean ecosystem, as they are
involved in a variety of biogeochemical processes and are closely linked to the ocean carbon cycle. Some
trace metals (e.g. iron, zinc) are essential micronutrients for phytoplankton growth, and their availability
can limit primary productivity in the ocean. Understanding the distribution and cycling of trace metals in
the ocean is essential for predicting how marine ecosystems will respond to climate change and human
activities. Recent research has shown that changes in the availability of trace metals can have significant
impacts on primary productivity and carbon sequestration in the ocean (e.g. Boyd and Ellwood, 2010), and
that these impacts may be exacerbated by human activities such as pollution and nutrient runoff (Yeats &
Bewers, 1983).
Overall, ocean tracers, including trace metals, are useful tools for studying physical, chemical, and
biological oceanography. Marine biogeochemists have made significant progress in recent years in elu-
cidating the complex processes that control the biogeochemical cycles of these tracers. Further research
is needed to better understand the rates and mechanisms of trace metal uptake and cycling in the ocean,
and to determine how these processes are influenced by changing oceanic conditions such as eutrophica-
tion and deoxygenation. This field of research will be crucial for predicting how the ocean will respond
5
to climate change and other anthropogenic activities, and for informing policy decisions related to ocean
conservation and management.
1.2.3 Oceanmodels
Ocean models are used to simulate the physical, chemical, and biological processes through computers,
which help scientists understand and predict the behavior of the ocean. These models use mathematical
equations to describe how water moves and mixes in the ocean, as well as how nutrients are cycled through
the ecosystem. They also incorporate data from observations of the ocean, such as measurements of tem-
perature, salinity, and nutrient concentrations. Ocean biogeochemical models can simulate the cycling of
nutrients in the ocean, as well as the growth and decomposition of marine organisms. Some models can
also be used to predict how the ocean will respond to changing environmental conditions, such as how
increasing atmospheric CO
2
concentrations or changes in nutrient inputs from rivers will affect ocean
chemistry, and how this, in turn, will affect the growth and survival of marine organisms. By running
model simulations with different scenarios, scientists can estimate how these changes will affect future
ocean biogeochemistry and the marine ecosystem.
Global ocean models are usually complex and computationally intensive, and are often used to study
large-scale dynamics of the ocean, including ocean circulation, heat transport, and the carbon cycle. The
most commonly used global ocean models include the Community Earth System Model (CESM), the Geo-
physical Fluid Dynamics Laboratory (GFDL) models, and the MIT General Circulation Model (MITgcm).
Regional ocean models, on the other hand, simulate the ocean processes in a specific region or area of
interest, often with higher resolution than global models. These models are particularly useful for study-
ing smaller-scale ocean phenomena, such as coastal upwelling, estuarine dynamics, and marine ecosystem
dynamics. A popular regional ocean modeling tool is the Regional Ocean Modeling System (ROMS), which
is powerful for simulating regional ocean circulation and biogeochemistry.
6
Forward and inverse models are two widely used methods for studying the ocean’s biogeochemical
processes. Forward models use equations and physical parameters to simulate the behavior of the ocean
system over time. These models can be used to make predictions about how ocean conditions may change
in response to different scenarios, such as increased CO
2
emissions or changes in ocean circulation pat-
terns. In contrast, inverse models are used to estimate unknown parameters in a system by comparing
observations to model output, which can provide valuable insights into the complex interactions between
ocean tracers and biogeochemical processes. In this thesis, I will apply the inverse modeling method to
the three global ocean tracer models, using the water transport from the Ocean Circulation Inverse Model
(OCIM) (DeVries, 2014; DeVries & Primeau, 2011), and developing the models within the framework of
AWESOME OCIM (John et al., 2020). The procedures of the inverse models developed in this thesis are
shown in Fig. 1.1.
Despite many advantages and extensive use, ocean models also have several limitations. One signifi-
cant challenge is the complexity of the ocean system, which can make it difficult to develop accurate and
reliable models. Another limitation of ocean models is that they require extensive data to develop and
validate. This can be particularly challenging in remote areas of the ocean where data is scarce, such as
the Southern Ocean and the Arctic Ocean. Finally, ocean models are limited by their spatial and temporal
resolution. Global models are useful for understanding the large-scale dynamics of the ocean, but they may
not be able to capture small-scale processes that occur in coastal regions and nearshore areas. In contrast,
regional ocean models focus on specific regions or coastal areas and have a higher horizontal resolution,
but can lead to uncertainties in boundary conditions and forcing from larger scales.
Ocean models are a valuable tool for understanding ocean biogeochemistry. By simulating the phys-
ical, chemical, and biological processes that occur in the ocean, scientists can better understand how the
ocean functions and how it responds to changing environmental conditions. This information is critical
7
Mechanisms
Sources/sinks
AWESOME OCIM
Model prediction
of tracer
concentrations
Root-mean-square
deviation minimized?
Observations
of tracer
concentrations
Final model
output
yes
no
Update model
parameters
Send to
solver
biogeochemistry +
ocean circulation
Calculate model-data misfit
Initial conditions
Figure1.1 Inverse model flowchart. The inverse model involves several steps. (1) Specify the initial con-
ditions and constraints, and assign the initial values to the parameters of the biogeochemical mechanisms
and source/sink terms. (2) Send the model setup to the AWESOME OCIM solver. (3) Simulate a model
prediction of tracer concentrations. (4) Calculate the root-mean-square deviation (RMSD) between pre-
dicted and observed tracer concentrations. (5) Select a MATLAB optimization algorithm to determine if
the RMSD is minimized. If yes, the final model output is generated; if no, (6) calibrate the model parame-
ters, and repeat from Step 2. The inverse model aims to estimate the unknown model parameters that best
fit the observed data, allowing for the simulation of unobserved scenarios.
8
for developing strategies to mitigate climate change. As our understanding of ocean biogeochemistry con-
tinues to grow, ocean models will continue to play an essential role in advancing our knowledge of the
complex ocean ecosystem.
1.3 Outlineofthethesis
This thesis aims to use inverse modeling approaches to study the global cycling of ocean tracers while
quantifying the biogeochemical processes that regulate these tracers. The thesis will be structured as
follows:
Chapter 1 provides a background on the field of ocean biogeochemistry, highlighting the importance
of understanding the global cycling of ocean tracers. This chapter also outlines the research questions and
knowledge gaps that the thesis aims to address. These questions provide a roadmap for the rest of the
thesis, guiding readers through the research objectives, methods, and findings that will be presented in
subsequent chapters.
Chapter 2 investigates the processes that control the distribution of alkalinity in the ocean through
a global inverse model. Using alkalinity as a metric, the model tries to constrain the global export of
calcium carbonate out of the surface ocean, and investigate the possible dissolution mechanisms of calcium
carbonate in the ocean interior.
Chapter 3 focuses on developing a mechanistic model to study the marine barium cycle, as well as
assessing the roles of barite and organic matter in regulating dissolved barium distributions. This study
utilizes data from ocean observations, a multiple linear regression model, and a global mechanistic model
to quantify the biogeochemical mechanisms that control the global cycling of barium in the ocean. The
model also examines the origins of barium to precipitate pelagic barite and the dissolution patterns of
barite in the water column.
9
Chapter 4 develops an inverse model to study the global distribution and cycling of copper in the
ocean. The model incorporates observations and biogeochemical models to quantify the biogeochemical
processes that control the distribution of copper, including its uptake and release by marine organisms,
reversible scavenging onto sinking particles, and complexation by organic ligands. The model investigates
several copper questions in the ocean, including the magnitudes of external sources that deliver copper
to the ocean, the reasons for the nearly-linear increases in copper concentrations with depth, the unique
copper distributions in the Arctic Ocean, and the partition between labile and inert phases.
Chapter 5 summarizes the main findings of the thesis and discusses their implications for our under-
standing of ocean biogeochemistry and the global cycling of ocean tracers. It also outlines future research
directions and potential applications of the modeling approaches developed in this thesis.
10
Chapter2
ConstrainingCaCO
3
exportanddissolutionwithanoceanalkalinity
inversemodel
Abstract
Ocean alkalinity plays a fundamental role in the apportionment of CO
2
between the atmosphere and
the ocean. The primary driver of the ocean’s vertical alkalinity distribution is the formation of calcium
carbonate (CaCO
3
) by organisms at the ocean’s surface, and its dissolution at depth. This so-called “CaCO
3
counterpump” is poorly constrained, however, both in terms of how much CaCO
3
is exported from the
surface ocean, and at what depth it dissolves. Here, we created a steady-state model of global ocean
alkalinity using Ocean Circulation Inverse Model (OCIM) transport, biogeochemical cycling, and field-
tested calcite and aragonite dissolution kinetics. We find that limiting CaCO
3
dissolution to below the
aragonite and calcite saturation horizons cannot explain excess alkalinity in the upper ocean, and that
models allowing dissolution above the saturation horizons best match observations. Linking dissolution
to organic matter respiration, or imposing a constant dissolution rate both produce good model fits. Our
best performing models require export between 1.1 and 1.8 Gt PIC y
-1
(from 73 m), but all converge to 1.0
Gt PIC y
-1
export at 279 m, indicating that both high- and low-export scenarios can match observations, as
long as high export is coupled to high upper ocean dissolution. These results demonstrate that dissolution
is not a simple function of seawater CaCO
3
saturation (Ω ) and calcite or aragonite solubility, and that
11
other mechanisms, likely related to the biology and ecology of calcifiers, must drive significant dissolution
throughout the entire water column.
2.1 Introduction
The global ocean is the largest reservoir of carbon (C) on Earth’s surface, storing nearly 50 times more C
than the atmosphere, and acting as a significant sink of anthropogenic CO
2
emissions (Friedlingstein et al.,
2022). The magnitude of ocean C storage is largely controlled by the distribution of alkalinity, which is
mediated by the so-called “CaCO
3
counterpump” or “hard tissue pump”. The CaCO
3
counterpump is driven
by calcifying planktonic organisms such as coccolithophores, foraminifera, and pteropods that remove
alkalinity in the form of CaCO
3
from the surface ocean, and transport it to depth upon sinking. The process
is termed a counterpump—in contrast to the organic C pump—because it increases CO
2
and decreases
alkalinity at the ocean surface, and conversely decreases CO
2
at depth when alkalinity is regenerated upon
CaCO
3
dissolution. This reduction of alkalinity at the ocean surface reduces the ocean’s buffering capacity
with respect to the atmosphere. Thus, the amount of CaCO
3
formed and exported from the surface, and
the depth at which alkalinity is regenerated by dissolution, is an important control on atmospheric CO
2
.
The CaCO
3
counterpump remains poorly constrained, especially with respect to a) how much and what
form of CaCO
3
is exported from the surface; b) where in the water column or sediment it dissolves; and c)
what mechanisms drive dissolution. Estimates of global CaCO
3
export range between 0.4 to 1.8 Gt PIC y-1
(W. Berelson et al., 2007; Sulpis et al., 2021), supported by studies using a range of techniques, including
satellite data combined with sinking estimates (Dunne et al., 2007; Sarmiento, 2006); seasonal variation in
surface alkalinity (Lee, 2001); water column alkalinity analysis (Sulpis et al., 2021); and global circulation
and earth system models (Battaglia et al., 2015; Gangstø et al., 2008; Jin et al., 2006; Ridgwell et al., 2007).
Canonical understanding posits that approximately three quarters of this export dissolves and the remain-
der is buried in sediments, however the uncertainty in export mass translates directly into uncertainty in
12
the amount dissolved. Historically, export was thought to be dominated by the more thermodynamically
stable form of CaCO
3
, calcite, produced by coccolithophores and foraminifera. Recent studies, however,
have considered the importance of more soluble morphotypes, including aragonite (produced primarily
by pteropods) and amorphous and high-Mg calcite (produced by teleosts (finned fish)) that may dissolve
higher in the water column (Bednaršek et al., 2012; Buitenhuis et al., 2019; Gangstø et al., 2008; Wilson et
al., 2009; Woosley et al., 2012). A growing database of planktonic calcifier observations is helping quantify
the spatial distribution of calcite and aragonite production, but it remains spatially and temporally limited,
and there is not yet any direct evidence to quantify fish CaCO
3
production (Buitenhuis et al., 2013; Daniels
et al., 2018).
Because alkalinity in the surface ocean is so important in mediating atmospheric CO
2
concentrations,
the second point outlined above—where CaCO
3
dissolves—is often the primary focus of CaCO
3
counter-
pump studies. Dissolution deep in the water column effectively sequesters alkalinity on the >1,000-year
timescale of ocean overturning, whereas shallower dissolution may return alkalinity to the surface by
isopycnal or diapycnal mixing. CaCO
3
dissolution is relatively slow, so in situ measurements are challeng-
ing and sparse, leaving mostly models and analyses of water column chemistry to quantify dissolution
rates. Historically, dissolution was thought to occur only below the lysocline, for example at the sediment-
water interface, where CaCO
3
is exposed to seawater with a low mineral saturation index (Ω ), and can sit
for thousands of years (Sverdrup et al., 1942). More modern studies, however, have considered dissolu-
tion higher in the water column once particles fall below the calcite and aragonite saturation horizons
where increased pressure and decreased carbonate ion concentration (resulting from organic matter (OM)
remineralization) decrease mineral stability. Some studies have also indicated the possibility of dissolu-
tion even higher in the water column, above the saturation horizons, based on observed excess alkalinity
13
(Chung et al., 2003; Feely et al., 2002; Sabine et al., 2002), in situ dissolution rates and C isotopic measure-
ments (Subhas et al., 2022), and decreased sinking fluxes of CaCO
3
particles in the upper water column
(W. Berelson et al., 2007; Dong et al., 2019; Milliman & Droxler, 1996).
There are currently three primary mechanisms to explain alkalinity accumulation high in the water
column, above thermodynamic saturation horizons. The most simple explanation is that previous analyses
do not fully consider accurate ocean mixing, and that isopycnal mixing (and to a lesser extent diapycnal
mixing) between low-alkalinity, shallow waters and higher-alkalinity deeper waters can explain much of
the observed pattern (Friis et al., 2006). However, this explanation ignores the observed decrease in sinking
CaCO
3
particles above the saturation horizons. Another potential mechanism is that CaCO
3
particles in
microenvironments with aerobic OM respiration (e.g., in organic particles, fecal pellets, and/or zooplank-
ton guts) experience localized undersaturation (Alldredge & Cohen, 1987; Freiwald, 1995). Alternatively, if
export of more soluble CaCO
3
morphotypes (e.g., aragonite or amorphous CaCO
3
from teleosts) is indeed
significant, they may contribute to upper ocean dissolution (Wilson et al., 2009).
These different hypotheses illustrate the difficulty of using models to constrain the CaCO
3
cycle, as
the amount and type of mineral exported, mechanisms driving dissolution (including uncertainty in ki-
netic rate parameters), and ocean circulation and mixing must all be accounted for accurately. Previous
modeling efforts have taken various approaches to this challenge, ranging from simple 1D approaches
with no circulation (Jansen et al., 2002) to more complex models using 3D global circulation (Battaglia
et al., 2015; Friis et al., 2006; Gangstø et al., 2008; Gehlen et al., 2007; Koeve et al., 2014). We describe a
few here to illustrate the range of approaches. Using the MIT global circulation model, Friis et al. (2006)
considered dissolution driven by thermodynamic undersaturation of calcite alone (i.e., no aragonite and
no respiration-driven dissolution), with a reaction rate order of 4.5. Taking a similar approach, Gehlen
et al. (2007) used the PISCES biogeochemical model with reaction order of 1; Gangstø et al. (2008) subse-
quently added aragonite dissolution to the model, but–given the information available at that time–used
14
the same reaction rate for both minerals. Koeve et al. (2014) used a transport matrix model extracted from
the MIT general circulation model and applied a mechanistically-agnostic exponential decay function to
represent CaCO
3
dissolution. Finally, Battaglia et al. (2015) used a Monte Carlo approach with the Bern3D
Earth System Model, varying CaCO
3
export, calcite:aragonite ratios, and dissolution dependence onΩ for
both mineral types. While all of these studies have provided valuable insight into the ocean CaCO
3
cycle,
Battaglia et al. (2015) found that different model parameterizations can perform well, highlighting the fact
that our understanding of dissolution mechanisms remains poorly constrained.
Here, we use Ocean Circulation Inverse Model (OCIM) transport coupled with biogeochemistry im-
plemented in the AWESOME OCIM (AO; A Working Environment for Simulating Ocean Movement and
Elemental cycling within an Ocean Circulation Inverse Model; John et al., 2020) to test several hypothe-
ses of CaCO
3
export and dissolution. We also use the most recent formulations of calcite and aragonite
dissolution kinetics available, derived from in situ experiments (Dong et al., 2019; Naviaux, Subhas, Dong,
et al., 2019; Subhas et al., 2022). Because OCIM-based models are less computationally intensive than other
earth system or global circulation models, we are able to test several hypotheses, in each case optimizing
model parameters over thousands of individual simulations in order to match observations. Specifically,
we test the following four hypotheses: 1) CaCO
3
dissolution occurs only at the seafloor; 2) dissolution in
the water column is driven only by water columnΩ , at rates defined by calcite and aragonite dissolution
kinetics; 3) water column dissolution also depends on OM respiration; and 4) water column dissolution is
constant and uncorrelated withΩ .
15
2.2 Methods
2.2.1 Modelframework
2.2.1.1 Modeloverview
The AWESOME OCIM (AO) is a MATLAB-based modeling tool to simulate ocean tracer distributions
through biogeochemical processes with the application of a transport matrix model (TMM). Global ocean
circulation is represented by a water transport matrix generated by the Ocean Circulation Inverse Model
(OCIM 1.0; DeVries, 2014; DeVries and Primeau, 2011), which is constrained by global observational data,
including temperature, salinity, CFCs, and radiocarbon. An advantage of AO is its computational efficiency,
with each solution of a 3-D tracer distribution taking approximately 8 seconds on a laptop under the con-
ditions used in this study, allowing multiple parameters to be optimized for each model configuration of
hypothetical biogeochemical processes.
To constrain the global ocean alkalinity cycle, we incorporated into the AO several spatially-explicit
observational and modeled datasets as well as biogeochemical process rates (Fig. 2.1). These inputs are
described in more detail in the following sections. The spatial distribution of CaCO
3
export from the ocean
surface, and dissolution within the ocean interior by several different hypothetical mechanisms was then
modeled, with specific parameter values optimized to best match the observed ocean alkalinity distribution
from the GLODAP version 2 mapped data product (Lauvset et al., 2016).
2.2.1.2 Sourcesandsinks
Alkalinity supply to the ocean is calculated by multiplying river alkalinity concentrations with river dis-
charge, reaching a total riverine alkalinity flux to the ocean of 27.8 Tmol yr
-1
. Our model includes the
world’s 34 major rivers with the largest discharge and/or those which have reliable measurements from
previous reports (Amiotte Suchet et al., 2003) (Fig. S2.1e). This approach ignores smaller rivers, and thus
16
Model processes:
River alkalinity input
CaCO
3
export
POP production
C:P ratio
PIC:POC ratio
mineralogy (calcite, aragonite)
export scaling factor
Water column CaCO
3
dissolution
Kinetic parameters
M2,M3
OM respiration dependence
M3
Constant dissolution rate
M4
Sedimentary burial
AWESOME
OCIM
Reset
parameters
GLODAP
TA
0
and TA
*
Cost minimized?
Final model result
yes
no
Modeled
TA
0
and TA
*
misfit
Figure2.1 Schematic diagram of the alkalinity model. Constraints based on external datasets (fixed values)
and variable parameters (optimized in each model run; marked in blue) are fed into the Awesome OCIM
framework. For each model iteration, the resulting TA0 and TA* are compared to observed values based
on GLODAP data. The optimized parameters are adjusted, and the model rerun until a minimum cost is
found. The four different models of water column CaCO
3
dissolution used different parameters, as noted
by the superscripts (M2, M3, and M4) (see Section 2.2.2).
underestimates global fluvial alkalinity discharge. Therefore rivers entering each ocean basin (Pacific, At-
lantic, Indian, Arctic, Mediterranean) are multiplied by a separate scaling factor so that the alkalinity influx
to each basin matches reported estimates according to the procedure of (Amiotte Suchet et al., 2003).
Modern ocean alkalinity is assumed to be in steady state, with alkalinity supply exactly balancing alka-
linity burial in sediments (described in the next paragraph). Published riverine alkalinity fluxes, however,
are deficient compared to estimated CaCO
3
burial, potentially due to the contribution of non-riverine al-
kalinity input (e.g., anaerobic respiration on continental shelves) and/or alkalinity in riverine particulate
matter, which has traditionally not been considered in riverine alkalinity flux measurements (Middelburg
et al., 2020). Thus, assuming that riverine alkalinity sources may be underestimated, we applied an addi-
tional scaling factor, increasing each river’s alkalinity flux so that total river alkalinity flux equaled total
burial flux; this required a global scaling factor of 1.5.
17
Benthic alkalinity sinks via burial are based on previous model-based estimates of CaCO
3
burial in
both coastal and pelagic ocean sediments, where the total alkalinity burial flux to the sediments reaches
41.5 Tmol yr
-1
globally, contributed by pelagic burial of 22.2 Tmol yr
-1
and coastal burial of 19.3 Tmol yr
-1
,
repectively (Dunne, Hales, & Toggweiler, 2012; O’Mara & Dunne, 2019)(Fig. S2.1f-h), which is balanced by
the estimated riverine alkalinity flux multiplied by a scaling factor of 1.5, as described in the previous para-
graph. It is important to note that our model only simulates planktonic CaCO
3
production, and does not
explicitly model coral or other benthic CaCO
3
formation in coastal areas. For grid cells in which high rates
of coastal CaCO
3
burial exceed surface ocean CaCO
3
production, alkalinity is removed from the overlying
model grid cell, effectively simulating benthic CaCO
3
production. Because our model’s grid is coarser than
the original studies, some areas with high coral CaCO
3
production may be missed. However, CaCO
3
burial
attributed to coral formation does not significantly influence either the distribution of alkalinity within the
ocean or the global balance of sources and sinks. Other sources and sinks of alkalinity such as submarine
groundwater discharge, hydrothermal vents, anaerobic respiration, marine silicate weathering and reverse
weathering were not considered due to their small and/or uncertain magnitudes (Middelburg et al., 2020).
In addition to balancing external sources and sinks, our steady-state model also requires a constraint
on the total amount of alkalinity in the ocean system, because the external source and sink of alkalinity
incorporated into the model are relatively small to regulate the global alkalinity inventory. This is accom-
plished by imposing a very small flux of alkalinity into every ocean model grid cell, and this additional
input flux equals to the global average alkalinity concentration ( c) divided by one million years (c/10
6
yr
-1
).
The small source is then balanced by a slow, first-order loss of alkalinity from every grid cell, also occur-
ring on a timescale of 1 million years. The small source and sink both occur on a geological timescale of
1 million years, much longer than the ocean mixing time of 1,000 years, and are slow enough to have
negligible influence on alkalinity distributions while setting the mean global concentration of alkalinity.
18
2.2.1.3 CaCO
3
exportfromtheeuphoticzone
In the AO, the top two layers (sea surface to 73 m) are considered the euphotic zone, where calcifying
organisms precipitate CaCO
3
. CaCO
3
export is calculated based on net phosphorus uptake (P
uptake
) in the
euphotic zone, multiplied by the C:P ratio and the ratio of particulate inorganic carbon (PIC) to particulate
organic carbon (POC) (PIC:POC ratio, also known as the rain ratio):
CaCO
3
export=(POC)(PIC :POC)=(P
uptake
)(C :P)(PIC :POC) (2.1)
P
uptake
is an output from a previous phosphorus model under the OCIM framework (Weber et al., 2018).
Instead of using the canonical Redfield C:P ratio 106, we adopted the C:P ratios that vary geographically as
a function of NO3 concentrations, with the highest C:P ratios in the subtropical gyres (Martiny et al., 2013)
(Fig. S2.1a-d). We used spatially-varying PIC:POC ratios from GFDL-ESM2M modeling results. The GFDL-
ESM2M model has a full ecosystem of plankton community, and also splits PIC into calcite and aragonite
components, which we utilize in a subset of our models, as described below (Dunne, John, et al., 2012).
Using this approach, the total modeled CaCO
3
export is 2.3 Gt PIC y
-1
, exceeding most current estimates.
Therefore, we introduced an optimizable scaling factor into each model, constraining total export between
estimates of 0.3 to 1.8 Gt PIC y
-1
(W. Berelson et al., 2007). The uncertainties in CaCO
3
export estimates
largely lie in the PIC:POC ratio estimates, and the scaling factor serves as an adjustment to allow for
uncertainty in global CaCO
3
export (Balch et al., 2005; Sarmiento et al., 2002). Then for each mole of
CaCO
3
produced, two moles of alkalinity are consumed due to the loss of a CO
3
2-
(and Ca
2+
) ion. This
process is represented as alkalinity loss in each grid cell by multiplying each cell’s CaCO
3
net production
by two.
19
In addition to the optimized export for each model, we also performed sensitivity tests in which we
enforced low, medium or high export (0.5, 1.1, and 1.8 Gt PIC y
-1
, respectively), as described in Section
2.2.3.
2.2.2 CaCO
3
dissolutionscenarios
Exported CaCO
3
may dissolve either in the water column or upon reaching the sediments, returning alka-
linity to seawater. Here, we tested four scenarios of CaCO
3
dissolution: 1) dissolution only at the seafloor,
2) dissolution based on the saturation state (Ω ), 3) dissolution based uponΩ with an additional contribu-
tion to dissolution associated with OM remineralization, and 4) constant dissolution of CaCO
3
particles
throughout the water column, unrelated to any specific biogeochemical mechanism.
Each of the four models has different optimized adjustable parameters. In all four models, the CaCO
3
export scaling factor and global mean alkalinity concentration, as described above, were optimized. In
Models 1 and 2, dissolution is prescribed, whereas Models 3 and 4 have additional optimized parameters
related to dissolution mechanisms, as described below. The optimized parameters for each model are listed
in Table 2.2.
2.2.2.1 Model1(M1): Benthiconly
As particulate CaCO
3
reaches the seafloor in our model, all or a fraction of that CaCO
3
may be buried, as
set by the burial data described above. Any CaCO
3
reaching the seafloor in excess of burial is assumed to
dissolve, releasing alkalinity to seawater. Within M1, all CaCO
3
produced in the euphotic zone reaches the
sediments and is either buried or dissolves into the overlying ocean-bottom grid cell.
2.2.2.2 Model2(M2):Ω -dependentdissolution
Our second model considers benthic dissolution, as above, as well as dissolution within the water column as
driven by thermodynamic undersaturation of calcite and aragonite. We obtained the saturation states (Ω )
20
of calcite and aragonite from the GLODAP mapped product (Lauvset et al., 2016). The kinetic dissolution
of the two minerals is described as a function of the saturation states using an empirical formulation (Keir,
1980; Morse et al., 1979):
R
kinetic
=k(1− Ω)
n
(2.2)
where k (g g
-1
d
-1
) is the rate constant and n is the reaction order. The k and n values for both calcite and
aragonite species were based on dissolution studies in seawater across a wide range of saturation states,
which were adjusted to the temperature and pressure conditions where the majority of water column
dissolution occurs (5 °C and below 700 m) (Dong et al., 2018; Naviaux, Subhas, Rollins, et al., 2019; Subhas
et al., 2018) (Table 2.1). We note that this empirical function is not mechanistically accurate (Dong et
al., 2020; Naviaux, Subhas, Dong, et al., 2019), as dissolution rates transition occurs at Ω critical
values at
which the dominating dissolution mechanism changes above vs. below the values. However, the kinetic
formulation provides a simple approximation and is thus adopted here.
Table2.1 Kinetic dissolution parameters for calcite and aragonite.
21
Here we adopted the terminology of previous literature, but implemented Eq. 2.2 with R
kinetic
being a
dissolution rate constant, which controls the magnitude of particle flux attenuation through:
F
i
=F
i− 1
exp(− R
kinetic
h
i
v
) (2.3)
whereF
i
is the CaCO
3
particle flux entering the i
th
model layer from the top of the grid,h
i
is the height of
the i
th
model layer, andv is the particle sinking speed in m d
-1
. Since we assume net production of CaCO
3
in the top two layers, the particle flux entering the top of the 3
rd
layer is the CaCO
3
export from the top
73 m.
M2 uses Eq. 2.2 and 2.3, combined with a canonical CaCO
3
sinking rate (100 m d
-1
), to calculate CaCO
3
dissolution below the euphotic zone. This model thus allows for CaCO
3
dissolution in undersaturated
seawater, as well as in sediments. As we discuss later and explore in more detail in our sensitivity analyses
(Section 2.2.3), the sinking velocity of PIC is a poorly constrained yet important parameter in all model
formulations.
2.2.2.3 Model3(M3):Ω +respirationbaseddissolution
Our third model includes benthic andΩ -driven CaCO
3
dissolution as in M2, and adds an additional driver
of dissolution coupled to the remineralization of OM. Respiratory acids from aerobic OM respiration have
been hypothesized to stimulate CaCO
3
dissolution, either within sinking particles or in the guts or feces
of grazers, although a global-scale formulation of the dependence of dissolution on respiration remains
elusive (Milliman et al., 1999). In M3, we parameterize this process by including a CaCO
3
dissolution
component linked to OM respiration (R
respiration
) specified by:
R
respiration
=xP
m
rem
(2.4)
22
where P
rem
is the remineralization rate of particulate organic phosphorus within each grid cell, and x and
m are model-optimized scaling parameters. The vertical P
rem
profile built into the AO follows the classic
Martin curve, wherein the exponent b in the Martin curve has been optimized to 0.92 by Weber et al.
(2018) to fit observed phosphate data. Particulate organic phosphorus remineralization is used here, as it is
assumed to be proportional to organic carbon remineralization. Then we useR
kinetic
+R
respiration
, instead of
R
kinetic
alone, as the dissolution rate constant and implemented it into Eq. 2.3 to model the CaCO
3
particle
flux. In this model, x and m for calcite and aragonite are optimized separately to simulate the respiration
effect on the dissolution of each mineral.
2.2.2.4 Model4(M4): Constantdissolution
Our fourth model does not consider seawater Ω or OM respiration, and instead assumes a fixed length-
scale for remineralization below the euphotic zone. As our models assume a single fixed sinking rate
for carbonate (100 m d
-1
), this is equivalent to specifying a fixed dissolution rate constant R
const
, which
is optimized by the model, to substitute for R
kinetic
in Eq. 2.3. As with the other three models, CaCO
3
reaching the seafloor in excess of prescribed burial is returned to the water column as alkalinity by benthic
dissolution.
This mechanism is independent ofΩ , and has no specific biogeochemical interpretation, though it has
been previously employed in other models and produces a reasonable match to observations (Battaglia
et al., 2015; Ridgwell & Hargreaves, 2007).
2.2.3 Sensitivityexperiments
Three sets of sensitivity tests were conducted to evaluate the model sensitivity to key processes includ-
ing S1) the magnitude of surface CaCO
3
export, S2) the effect of particle sinking speed, and S3) the cal-
cite:aragonite ratio.
23
The total magnitude of CaCO
3
export from the surface ocean in the four base models is optimized.
To test whether our models are sensitive to surface export, however, a separate set of experiments was
performed for each model in which we specified ‘low’, ‘medium’ and ‘high’ export levels of 0.5, 1.1, 1.8
Gt PIC yr
-1
, respectively. In subsequent discussions, the four optimized export models are referred to as
“base” models, in contrast to the twelve “export sensitivity” models which have fixed CaCO
3
export fields.
Our base models assume a fixed particle sinking speed of 100 m d
-1
, based on previous observations
and modeling efforts (Battaglia et al., 2015). However, real-ocean particle sinking speeds are related to both
particle size and density, and a wide range of sinking speeds can be generally consistent with ocean obser-
vations (Cael et al., 2021). Thus, to examine the extent to which sinking speed impacts CaCO
3
dissolution
profiles, we varied sinking speeds between 1 - 1,000 m d
-1
for M2 and 50 - 200 m d
-1
for M3. Note that M1
is not affected by sinking speed, since no particles dissolve before settling at the seafloor. M4 is similarly
unaffected because the model-optimized rate constant Rconst is inversely related to sinking velocity, so an
increase in sinking rate has the same effect as a decrease in the optimized dissolution constant.
The two mineral forms of CaCO
3
considered in this study, calcite and aragonite, have distinct properties
in terms of morphology, solubility and dissolution rates. We rely on the global distributions of surface
calcite and aragonite from an ecosystem model that includes various plankton types (Dunne, John, et al.,
2012). However, the actual global distribution of calcite and aragonite export is poorly constrained. Thus,
to investigate how the relative export of calcite vs. aragonite influences model performance, end-member
scenarios were tested assuming that all CaCO
3
export is calcite, or that it is entirely aragonite. Again
this has no impact on the M1 and M4 models, but it affects both other models as the dissolution kinetics
and respiration sensitivity of aragonite and calcite dissolution differ (Eq. 2.2 and Eq. 2.4). We performed
this end-member test based on M2, since changing the calcite:aragonite ratio could significantly modify
the dissolution patterns of this model, where the kinetic dissolution of these two minerals is the only
mechanism that drives water column CaCO
3
dissolution.
24
2.2.4 Modeloptimization
2.2.4.1 Alkalinitydataandmetricdefinitions
While our model simulates the cycling of total alkalinity (TA) in the global oceans, the specific quantities
it seeks to match to observations is not TA, but rather two components of TA: preformed alkalinity (TA0)
and alkalinity from CaCO
3
dissolution (TA*), both of which are calculated as described below.
CaCO
3
dissolution cannot feasibly be measured directly, so researchers instead use metrics for cal-
culating accumulated alkalinity from dissolution since a water mass leaves the surface ocean. There are
two similar but distinct approaches commonly in use: 1) potential alkalinity (P
ALK
) (Brewer et al., 1975;
Carter et al., 2014; Sarmiento et al., 2002); and 2) TA* (Feely et al., 2002). Essential to both methods is
the understanding that TA can be deconstructed into three components: 1) preformed alkalinity, or the
alkalinity of a water mass at the time of last ventilation; 2) addition of alkalinity through CaCO
3
dissolu-
tion; and 3) consumption of alkalinity by the release of inorganic acids following OM respiration (Brewer
et al., 1975; Wolf-Gladrow et al., 2007). Other sources and sinks of TA are considered trivial. Preformed
alkalinity accounts for at least 95% of alkalinity in all water masses, followed by CaCO
3
dissolution, and to
a smaller degree consumption of alkalinity by respiratory acids. The small amount of alkalinity added by
CaCO
3
dissolution relative to the large background of preformed alkalinity necessitates that we quantify
both components accurately.
By this formulation, we define TA as:
TA=TA0+TA∗− TAr (2.5)
where TA0 is the preformed component, TA* is accumulated alkalinity from CaCO
3
dissolution, and TAr
is alkalinity consumed by respiration-derived acids. TA0 has typically been quantified by linear regression
using salinity (S), PO, NO (measured plus estimated consumed O
2
from aerobic respiration, as measured
25
by phosphate or nitrate concentrations, respectively), and/or potential temperature; and TAr has been
estimated with PO or apparent O
2
utilization (Feely et al., 2002; Koeve et al., 2014). Improved surface ob-
servations and circulation models have enabled better modeling of both TA0 and preformed nutrients, the
latter enabling calculation of TAr by subtracting preformed from measured nutrients, then multiplying by
an alkalinity scaling factor (Carter et al., 2021). Given the AO’s capability to calculate TA0 and preformed
nutrients using a circulation matrix, we use this latter approach.
It is worth briefly explaining another common alkalinity metric, P
ALK
, both for comparison and to jus-
tify our choice of using TA*. Whereas the TA* approach uses explicit values for each alkalinity component,
P
ALK
is a composite metric (combining TA and TAr = 1.26 [NO
3
-
]
0
) useful for analysis of water mass chem-
istry when preformed values are unknown (Brewer et al., 1975). P
ALK
can also be used to interpret global
alkalinity patterns caused by CaCO
3
cycling by subtracting a conservative potential alkalinity component
(Carter et al., 2014; Fry et al., 2015). For example, the Alk* metric used by Carter et al. (2014) is calcu-
lated as P
ALK
minus 66.4 S. This approach only accounts for variation in conservative alkalinity caused
by freshwater cycling, and does not consider variation in preformed alkalinity or nutrients; thus, it is not
intended to represent CaCO
3
dissolution within a given water mass. Misusing P
ALK
approaches in this
way may lead to erroneous conclusions about CaCO
3
dissolution. This is most obvious in the Southern
Ocean, where upwelling of high alkalinity and nutrient water leads to both higher than average preformed
alkalinity and non-negligible preformed nutrients in subsequently subducted water masses (Fig. 2.2a and
2.2b) (Carter et al., 2021; Duteil et al., 2012; Koeve et al., 2014). Given our model’s ability to incorporate
preformed values, we avoided this issue by using the TA* approach instead.
Using the TA* approach, there are still decisions to be made about how to calculate TA0 and preformed
nutrients. We adopted the method described in Carter et al. (2021) using concentrations at the deepest
monthly-mean mixed layer depths as boundary conditions in the OCIM circulation matrix. Concentrations
at the base of the mixed layer can be calculated either by regression against other variables (e.g., T and S)
26
(b) “PALK0” - TA0
AO
(66.4 S - TA0
AO
)
(a) “PALK0” - nutrients - TA0
AO
(66.4 S – 1.26[NO
3
]
0
- TA0
AO
)
(c) TA0
Carter (regression)
- TA0
AO
(d) TA0
Carter (interpolation)
- TA0
AO
Figure2.2 Differences resulting from various approaches to estimating preformed alkalinity, compared to
TA0
AO
. Negative values represent deficits in preformed alkalinity, which would be interpreted as excess
CaCO
3
dissolution in TA analysis. The Alk* approach yields relatively low preformed alkalinity, especially
in the Southern Ocean, resulting from assumptions about both preformed nutrients and alkalinity (com-
bined in a, and only alkalinity component in b). For approaches using circulation matrices to reconstruct
TA0, results are sensitive to the method used to define alkalinity at the base of the mixed layer depth, for
example either by locally-interpolated regression (c) or by interpolation (d). In (c) and (d), TA0
Carter
refers
to preformed alkalinity data from Carter et al. (2021).
27
or by linear interpolation of gridded alkalinity datasets Carter et al. (2021). We adopted the latter approach,
interpolating TA concentrations from the GLODAP mapped dataset (Lauvset et al., 2016). For comparison,
our calculated TA0 data show only minor deviations from previously published TA0 data in Carter et al.
(2021), e.g. in the deep Pacific Ocean compared to their regression-based TA0 (Fig. 2.2c) and little difference
compared to their interpolation-based TA0 (Fig. 2.2d). To calculate TAr, we multiplied excess PO
4
3-
(i.e.,
PO
4
3-
above the preformed value, where the preformed PO
4
3-
is calculated in a similar approach as TA0)
by an alkalinity:PO
4
3-
ratio of 21.8 (Wolf-Gladrow et al., 2007).
2.2.4.2 Optimizationcriteriaandgeneticalgorithm
Each model is optimized towards a fit with a global database of alkalinity observations, starting with TA
as taken from the GLODAP mapped product (Lauvset et al., 2016), re-gridded to fit the AO with a data
density of 2°x2° horizontally and 24 vertical depth levels. For each model run, the modeled TA0 and TA*
(TA0
model
and TA*
model
) in each grid cell were compared to their respective “observed” values (TA0
obs
and
TA*
obs
). TA0
obs
was calculated from GLODAP alkalinity observations at the base of the mixed layer as a
constraint within our circulation model (Section 2.2.4.1). For each grid cell, TA*
obs
was calculated using
Eq. 2.5, where TA is from the GLODAP dataset, and TA0
obs
and TAr
obs
are as described in Section 2.2.4.1.
Note that TA, TA0
obs
, and TAr
obs
, and hence TA*
obs
, are all derived entirely from the GLODAP dataset
and our OCIM circulation matrix, and do not depend on other model parameters. During the optimization
process, grid cells at high latitudes (north of 70°N and south of 70°S) are excluded, since sparse temporal
and spatial sampling introduces uncertainty in observational data. The data in the top two model layers
are also excluded from optimization, as a small change in the export scaling factor could lead to a large
change in surface alkalinity, resulting in the overweighting of the surface ocean at the expense of the ocean
interior where CaCO
3
dissolution occurs.
28
A genetic algorithm (GA) was applied to tune the free model parameters regulating CaCO
3
export and
dissolution rates (Table 2.2), and seek the best model fit to observational data. The natural selection process
of this algorithm helps the model start from random initial parameter guesses within the given ranges, and
is therefore less likely to be trapped in a local minimum. We utilized the MATLAB Global Optimization
Toolbox which offers the function ‘ ga’ to facilitate the use of this optimization solver. The GA tries to
find the minimum of a function, in this case the misfit between model simulation and observational data,
weighted by a volume factorw (w=volumeineachmodelgrid/globaloceanvolume), according to the cost
function:
cost=Σ N
obs
i=1
(TA0
model,i
− TA0
obs,i
)
2
w
i
+Σ N
obs
i=1
(TA∗ model,i
− TA∗ obs,i
)
2
w
i
(2.6)
We defined the cost with both TA0 and TA*, instead of just TA, as TA on its own conceals error in its
components (e.g., positive TA0 misfit and negative TA* misfit would cancel each other, resulting in a “good”
TA fit). It is important to note that the modeled TA0 and TA* are not completely independent, as surface
CaCO
3
export, which feeds TA* in the ocean interior, reduces surface alkalinity, thus impacting TA0. Thus,
a good match between modeled and observed TA0 alone is not sufficient to conclude that the model is
accurately describing alkalinity cycling, if the model fit to observed TA* is not good, and vice versa. Hence
our equal weighting of both quantities in the cost function puts equal emphasis on TA0 and TA* to constrain
each component of alkalinity separately.
2.3 Results
2.3.1 Modeledvs. observedTA0andTA*
The four dissolution mechanisms produce distinct results for both TA0 and TA*, although some similar
characteristics are observed across models. An example of optimized model results for M3 is shown in
29
Fig. 2.3. (All base models are shown in Fig. S2.2.) Modeled TA0 exhibits small error relative to TA0
obs
,
with a significant misfit concentrated in the low-latitude surface mixed layer and in the North Atlantic
Deep Water (NADW), reflecting ocean circulation patterns (Table 2.2; Fig. 2.3a, 2.3c, 2.3e). The error
in TA* is similar in magnitude to TA0, but with larger horizontal and vertical spatial variations due to
the uncertainties associated with CaCO
3
export and vertical dissolution profiles (Fig. 2.3b, 2.3d, 2.3f).
Specifically, this dissolution mechanism allows for high dissolution rates in the upper ocean driven by OM
respiration and lower rates of dissolution in the deeper waters driven by undersaturation.
Table2.2 Optimized parameters, performance, and CaCO
3
export and dissolution for the four base models.
All fluxes are in units of Gt PIC y
-1
.
30
TA
0
TA*
(a)
(b)
(c)
(d)
(e) (f)
Figure2.3 Example of two modeled transects (Pacific at 161 °W and Atlantic at 29°W) compared to obser-
vations for M3 (Ω + respiration model). Observed TA0 and TA* based on the GLODAP dataset (a and b);
Modeled TA0 and TA* (c and d); and the difference between model and observation (model - observation)
(e and f).
Considering TA0, the two simpler models, M1 and M2, match observations relatively well below the
euphotic zone (Fig. 2.4a-b and Fig. 2.4e-f), whereas the two models that allow dissolution in oversaturated
water in the upper water column (M3 and M4), have a worse model-data fit, especially in the North Atlantic
Ocean (Fig. 2.4i-j and Fig. 2.4m-n). The reduced performance in the two latter models is mostly a result
of higher optimized CaCO
3
export (details in Section 2.3.2) and thus reduced TA0 in surface water prior
to subduction. All models yield a deficit in TA0 compared to TA0obs at low- and mid-latitudes in the
upper ocean, potentially due to overproduction of CaCO
3
in the surface. However, since these areas are
not significant downwelling areas, this does not greatly affect TA0 in the abyssal ocean.
The four models also produce distinct patterns in TA*. M1 has the worst fit to TA*obs (Fig. 2.4c-d).
Because all CaCO
3
dissolves at the seafloor, modeled TA* exceeds observations near the sediment-water
interface and has a deficit in shallower water. M2 shows slightly better model performance, because it
allows for calcite and aragonite to dissolve in undersaturated waters (Fig. 2.4g-h). However, the dissolution
31
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m) (n) (o) (p)
Benthic only
(M1)
W-dependent
(M2)
W + respiration
(M3)
Constant
(M4)
Figure 2.4 Difference between modeled and observed TA0 and TA* (TA0: a, e, i, m; TA*: c, g, k, o) in
representative transects (Pacific at 161 °W and Atlantic at 29°W). Joint probability density function plots of
modeled vs observed data in each grid cell show the relative performance of each model (TA0: b, f, j, n;
TA*: d, h, l, p).
rate constants and sinking speed (100 m d
-1
) used in the base model do not facilitate significant water
column dissolution, thus the majority of particles (80%) still dissolve at the seafloor. M3 improves the
model-data fit by shifting dissolution upward in the water column (Fig. 2.4k-l). In this scenario, most of
the exported CaCO
3
(77%) dissolves in the upper 15 levels of the model, above 1,700 meters, primarily due
to respiration-driven dissolution. As a result of the upward shift in dissolution, the excess deep ocean TA*
observed in M1 and M2 is minimized, but not entirely resolved. M4 also reproduces TA* well, with errors
spread more evenly throughout the ocean, and a slightly better fit than M3 (Fig. 2.4o-p).
All four models do relatively well in reproducing TA* in the North Atlantic, where water mass age is
young and observed TA* is low. In contrast, because TA* is cumulative, model biases accumulate as a water
mass ages, so errors are largest in the oldest waters in the North Pacific Ocean, as seen most obviously in
M1 and M2. The model performance of TA* relative to water age is also apparent in the joint probability
32
density function plots for M1 and M2, where TA* is modeled well for low TA* waters, then becomes too
low at intermediate TA* concentrations (Southern Ocean, upper Pacific Ocean) and too high at the highest
TA* sites (deep North Pacific Ocean) (Fig. 2.4d and 2.4h). All four models consistently underestimate TA*
in the Southern Ocean.
2.3.2 CaCO
3
export
Optimized export fluxes differ across the four base models. M1 and M2 optimize at lower CaCO
3
export
since particles have no or little chance of dissolving in the water column, both with 0.7 Gt PIC y
-1
export out
of the top 73 meters (Table 2.2). In contrast, M3 has the highest optimized CaCO
3
export from the surface,
reaching the upper bound of the constrained range, 1.8 Gt PIC y
-1
. This high export is necessary to satisfy
high rates of dissolution linked to OM respiration below the mixed layer. We note that maximum export
was constrained to 1.8 Gt PIC y
-1
; given a higher constraint, it is possible that the model could optimize to
an even higher export value. M4 has an intermediate CaCO
3
export compared to the other three models,
resulting in 1.1 Gt PIC y
-1
export out of the top 73 m.
2.3.3 CaCO
3
dissolution
The four models also produce distinct CaCO
3
dissolution vs. depth patterns (Fig. 2.5). In M1, constraining
dissolution to the bottom grid cell naturally results in high rates of dissolution at depth and no water-
column dissolution (Fig. 2.5a-b). M2 introduces dissolution to the undersaturated waters, but the slow
rates result in small dissolution in the water column, which increases gradually with depth as the satu-
ration state decreases, with most dissolution again occurring at the seafloor (Fig. 2.5c-d). As a result, M2
yields significant benthic dissolution both in the abyssal ocean and in shallow waters on the continen-
tal shelves, where export is high and the water column is oversaturated with respect to both calcite and
33
aragonite. Linking CaCO
3
dissolution to OM respiration (M3) results in significant water column disso-
lution, characterized by two distinct dissolution peaks: one at shallow depths just below the surface and
another near the seafloor, with less dissolution occurring at intermediate depths (Fig. 2.5e-f). Extremely
high rates of water-column dissolution in the upper 500 m dominate the total dissolution pattern, while
water-column dissolution below 500 m decreases continuously with depth since the respiration driver of
dissolution outweighs any potential increase driven by undersaturation. Benthic dissolution is significant
at shallow shelves and below 2,500 m at seafloor. The constant dissolution model (M4) spreads dissolution
relatively evenly throughout the water column (Fig. 2.5g-h). M4 does not produce a peak in upper ocean
dissolution such as observed in M3, however below about 500 meters, it exhibits a relatively similar trend,
with a gradual decrease in water-column dissolution (Fig. 2.5f, 2.5h). Both M3 and M4 have high dissolu-
tion rates throughout the water column in the highly productive North Atlantic compared to the rest of
the oceans.
In the two models considering mineral dissolution kinetics (M2 and M3), the relative magnitudes and
profiles of calcite and aragonite dissolution differ. In M2, there is no or little dissolution of either mineral in
the upper ocean where most of the seawater is supersaturated, and aragonite and calcite dissolution rates
are approximately equal until about 2,500 m (Fig. 2.6a). Although much of the ocean volume above this
depth is undersaturated with respect to aragonite, but not calcite, the kinetics of aragonite dissolution are
relatively slow, resulting in similar dissolution for both minerals. Similarly, the slow aragonite dissolution
kinetics prevent any obvious peak in dissolution rates near the aragonite saturation horizon. Below 2,500
m, calcite dissolution dominates due to its higher export and higher kinetic rate parameters. In contrast,
M3 exhibits very different calcite vs. aragonite dissolution profiles in the upper ocean, with an extreme
surface peak dominated by calcite (Fig. 2.6b). The model optimizes such that calcite is preferentially
dissolved in the upper ocean by OM respiration, apparently in order to maximize the export and dissolution
of aragonite at intermediate depths, above the calcite saturation horizon. Below the surface peak, calcite
34
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure2.5 (a, c, e, g) CaCO
3
dissolution (µmol kg
-1
y
-1
) in all four base models for representative transects
(Pacific at 161 °W and Atlantic at 29°W). Black lines represent the aragonite (dashed) and calcite (solid)
saturation horizons. (b, d, f, h) Globally-integrated vertical profiles of total water column and benthic
dissolution for each model (Gmol m
-1
y
-1
). Black lines indicate water column dissolution, and red lines
indicate benthic dissolution. M1 and M2 (benthic-only andΩ -dependent models) are dominated by benthic
dissolution at depth (b, d). M3 (Ω + respiration model) has an extreme dissolution peak in the upper ocean
(f inset), below which total dissolution is minor in comparison (f), and below about 500 m, relatively similar
to M4 (constant dissolution model) (h).
35
(a) (b)
Figure 2.6 Global average profiles of calcite and aragonite dissolution for the two models that consider
mineral kinetics (M2 and M3). TheΩ -dependent model (M2) results in disproportionate calcite dissolution
at depth due to faster dissolution kinetics (a), while theΩ + respiration model (M3) results in dispropor-
tionate calcite dissolution in the upper ocean (b inset).
dissolution decreases rapidly, following the decrease in OM respiration according to the adjusted power-
law Martin curve, and only starts rising again below about 2,500 m due to the onset of undersaturation-
driven dissolution. Aragonite dissolution also decreases with depth, but less dramatically than calcite,
given its shallower saturation horizon.
2.3.4 Sensitivityexperiments
The low/medium/high export sensitivity tests revealed that M1 and M2 optimized best at low export (0.5
Gt C y
-1
); M3 optimized well for both medium and high export (1.1 and 1.8 Gt C y
-1
, respectively); and M4
optimized well only for medium export (Figs. S2.3-S2.6). Of all scenarios tested, the TA* fit was best for
M3 medium, M3 high export, and M4 medium export.
In the sinking speed sensitivity test for M2, scenarios with sinking speeds >=100 m d
-1
all yielded
excess TA* at depth, and the best TA* model fit was achieved for sinking speeds between 5 and 10 m d
-1
36
(Fig. S2.7). However, at slower sinking speeds, TA* accumulation at depth shifts away from the North
Pacific, and into the North and central Atlantic. Limited sensitivity tests for sinking speed in M3 revealed
a similar trend (Fig. S2.8).
Varying calcite and aragonite endmember fractions in M2 made little difference under the base sinking
speed of 100 m d
-1
. A combined sensitivity analysis with sinking speed showed that slower sinking speeds
again improved model performance slightly for both the calcite and aragonite scenario, but TA* nonetheless
accumulated in the Atlantic with either endmember (Fig. S2.9).
2.4 Discussion
2.4.1 MixingalonecannotreplicateTA*observations
The well-documented presence of positive TA* above the calcite and aragonite saturation horizons is typ-
ically interpreted as evidence that CaCO
3
must dissolve high in the upper water column, prior to thermo-
dynamic expectations based on seawaterΩ (Feely et al., 2002). Friis et al. (2006) suggested an alternative
explanation, that water mass mixing is sufficient to explain much of the observed TA*. The poor perfor-
mance of M1 and M2 however, shows that restricting CaCO
3
dissolution to depths below the calcite and
aragonite saturation horizons cannot adequately explain observed TA* distributions (Fig. 2.4c-d, 2.4g-h).
These models do show—similar to Friis et al. (2006)’s model—that non-negligible TA* indeed accumulates
above the saturation horizons as a result of mixing; however this mixing is insufficient to replicate the
overall TA* distribution. Instead, alkalinity deficiency persists in the upper ocean, and excess alkalinity
accumulates at depth. This is most prominent in the North Pacific, where water masses are oldest, and
thus error in modeled TA* accumulates. Excess TA* at depth in the North Pacific, relative to GLODAP ob-
servations, is also evident in Friis et al. (2006)’s model. The circulation component of our model includes
37
diapycnal and isopycnal mixing, and is one of the most accurate representations of ocean circulation avail-
able (DeVries, 2014; John et al., 2020), so we doubt that circulation deficiencies could be significant enough
to explain the error in TA* in M2. Rather, limiting dissolution to below the saturation horizon clearly
concentrates TA* at depth and suggests a missing source of alkalinity in the upper ocean.
2.4.2 CalciteandaragonitedissolutionatbulkseawaterΩ cannotexplainobservedTA*
profiles
The addition of water column dissolution in M2 shifted only a small amount of alkalinity regeneration
upwards compared to M1 (Fig. 2.4g-h). However, this model is highly sensitive to the relative dissolution
rate, which varies as a function of both sinking speed and kinetics (Fig. S2.7). At our default sinking speed
of 100 m d
-1
, the TA* distribution is similar to M1, suggesting that dissolution kinetics are too slow and/or
sinking speed too fast to support significant water column dissolution. The kinetic parameters for CaCO
3
dissolution have been debated at length (reviewed in Sarmiento (2006)), but those we used have been
extensively tested, including field-verified at depth in the North Pacific (Dong et al., 2019; Naviaux, Subhas,
Dong, et al., 2019; Subhas et al., 2022). That said, kinetic parameters are known to vary as a function of
calcifier morphology and mineralogy, seawater DOC content, and pressure, among other factors, and this
variability is not accounted for in our model (Dong et al., 2018; Naviaux, Subhas, Dong, et al., 2019). Sinking
speed also introduces significant uncertainty, as it may vary by many orders of magnitude depending on
particle size and morphology. Measured sinking speeds range from <1 m d
-1
for single coccoliths, to 5,000
m d
-1
for large foraminifera, with most observations for individual coccolithophores, foraminifera, and
pteropods falling between 100 to 1,000 m d
-1
(Bergan et al., 2017; Engel et al., 2009; Schiebel & Hemleben,
2017; Walker et al., 2021; Zhang et al., 2018). The actual sinking speed profile of CaCO
3
particles is most
certainly a distribution across these values. For modeling simplicity, we assumed a single sinking speed
of 100 m d
-1
in our base models, but also considered sinking speeds between 1 and 1,000 m d
-1
in our
38
sensitivity analysis. Because both sinking speed and dissolution rate affect dissolution linearly in our
model, this range captures three orders of magnitude of uncertainty in either sinking speed or dissolution
rate.
The optimized sinking speed for a kinetics-only scenario (a sensitivity test based on M2) was 5-10 m d
-1
(Fig. S2.9f), which is likely too slow for realistic CaCO
3
particles. Furthermore, as sinking speed decreased,
excess TA* at depth simply shifted away from the North Pacific, and into the North and central Atlantic.
This pattern arises because the relatively deep saturation horizons in the Atlantic (>2 km depth) allow
dissolution of slowly sinking particles, and accumulation of alkalinity in the NADW. In the North Pacific,
however, the shallow saturation horizons (<1 km depth) allow dissolution near the surface, where alkalinity
becomes entrained into the TA0 pool, leaving little CaCO
3
export to feed TA* at depth. Ultimately, both
fast and slow sinking speed scenarios (or equivalently, slow and fast dissolution kinetics) result in excess
TA* at depth: either concentrated in the Atlantic (slower sinking speeds), or in both oceans (faster sinking
speeds). Thus, there must be a significant source of CaCO
3
dissolution above the calcite and aragonite
saturation horizons.
2.4.3 CaCO
3
dissolution linked to aerobic OM respiration recycles alkalinity in the
upperocean
The two models that allowed dissolution above the saturation horizons – M3 and M4 – both yielded TA*
distributions that better match observations, compared to the models restricting dissolution to depth (Fig.
2.4). Because the oxidation rate of sinking organic particles is highest near the surface ocean, linking dis-
solution directly to OM respiration (M3) resulted in an extreme dissolution peak in the upper ocean, and
consequently required more CaCO
3
export (1.8 Gt PIC y
-1
) to supply sufficient TA* at depth. The sensi-
tivity test imposing a lower export (1.1 Gt PIC y
-1
) also performed well, with a weaker model-optimized
dependence on OM respiration, and therefore less total CaCO
3
dissolution (Fig. S2.5). These observations
39
match the findings of Battaglia et al. (2015), that both high and low CaCO
3
export scenarios can produce
realistic alkalinity distributions, when balanced by higher or lower dissolution in the upper ocean, respec-
tively. Indeed, across the four base models, the model-optimized CaCO
3
export is correlated to the amount
of dissolution in the upper ocean (Table 2.2). Interestingly, high export from the surface ocean (73 m) in
M3 does not result in decreased TA0 relative to M4, which has lower optimized export (Fig. 2.4i and 2.4m).
This suggests that high export, coupled to high dissolution in the upper ocean, does not significantly al-
ter surface alkalinity, and that regenerated alkalinity is retained within the upper ocean. In other words,
surplus “export” in high-export scenarios can effectively be considered upper ocean recycling.
The optimized export for M3 (1.8 Gt PIC y
-1
) is on the high end of published values (W. Berelson et
al., 2007; Sulpis et al., 2021). A confounding issue with published export values, however, is that export is
defined at different depths. If dissolution is indeed concentrated in the upper water column, then the export
gradient will be steep across shallow depths, and the defined export will vary significantly depending on
the reference depth chosen, ranging from 73 m (our study, as well as Battaglia et al., 2015; Jin et al., 2006),
100 m (Gangstø et al., 2008; Sarmiento et al., 2002), 200 m (W. Berelson et al., 2007), or 300 m (Sulpis et al.,
2021). Because we defined a shallow export horizon, our export in M3 may therefore not be anomalously
high, but rather it may include a large amount of CaCO
3
that is dissolved between 73 and 300 m. For
example, our modeled export at 279 m is 1.0 Gt PIC y
-1
for the base model and 0.9 Gt PIC y
-1
for the lower-
export sensitivity test, strikingly close to each other, and to other recent estimates (0.9 Gt PIC y
-1
from
300 m; Sulpis et al., 2021) (1.1 Gt PIC y
-1
from the mixed layer; Jin et al., 2006; Lee, 2001). Considering
the geographically-variable, maximum monthly-mean mixed layer depth built into our model, instead of
a constant 279-m horizon, yields an intermediate M3 export value of 1.5 Gt PIC y
-1
.
While dissolution in M3 is concentrated in the upper water column, dissolution throughout the water
column is still higher than that driven by calcite and aragonite undersaturation alone (Fig. 2.5d, 2.5f), in-
dicating that OM respiration drives dissolution throughout the entire water column, not only in the upper
40
ocean where respiration rates are high. Below 2,500 m, dissolution at the sediment-water interface also
becomes significant (0.2 Gt PIC y
-1
). This general pattern of two prominent dissolution zones–one in the
upper ocean and one at the sediment-water interface–was recently suggested by Sulpis et al. (2021), using a
completely different approach, combining Alk* analysis for the water column and a coupled geochemical-
hydrodynamic sediment model. Our modeled results also show this pattern, however we see a more grad-
ual decrease in dissolution with depth, as opposed to a dissolution minima at 600 m in their study (Fig.
2.5f). Our model also predicts more total water column dissolution, and less benthic dissolution than their
analysis, which could be a result of their Alk* analysis, which cannot differentiate benthic and pelagic
sources of alkalinity.
2.4.4 ConstantdissolutionmodelsimilartoΩ +respirationmodelatdepth
Optimized CaCO
3
export in M4 is significantly less than in the optimized M3, however as noted above, both
models converge to 1.0 Gt PIC y
-1
at 279 m (Fig 2.7). Furthermore, they are surprisingly similar at depth (>
500 m), despite their different “mechanisms” (Fig. 2.5f, 2.5h). For example, total pelagic dissolution below
1,700 m is 0.3 and 0.2 Gt PIC y
-1
for M4 and M3, respectively. The lower dissolution in the latter model is
compensated for by higher benthic dissolution. The similarities in model performance at depth reinforce
the observation that alkalinity regenerated from upper ocean dissolution in M3 is largely retained and
recycled in the upper ocean, and does not impact the water column TA* inventory.
2.4.5 Potentialmechanismsdrivingdissolutionabovethesaturationhorizons
The potential for significant upper ocean dissolution has been discussed for decades, and is supported by
several lines of observational evidence, including excess alkalinity and decreased sinking fluxes of calcitic
particles (Feely et al., 2002; Milliman & Droxler, 1996; Sabine et al., 2002). More recent trap data has specif-
ically shown upper water column disappearance of aragonite (Dong et al., 2019) and specific calcifying
41
Figure2.7 CaCO
3
export profiles for the three best-performing models in the export sensitivity tests. “M3
(mid)”: Ω + respiration model with 1.1 Gt PIC y
-1
export. “M3 (high)”: Ω + respiration model with 1.8 Gt
PIC y
-1
export. “M4 (mid)”: constant dissolution model with 1.1 Gt PIC y
-1
export.
42
groups, including pteropods (R. L. Oakes & Sessa, 2020) and coccolithophores (Ziveri et al., 2022). The
mechanistic link between dissolution and OM respiration has been proposed as either CaCO
3
experienc-
ing low-Ω microniches caused by microbial respiration within sinking particles, or low-Ω environments
in the guts of grazers. Our models do not attempt to determine which mechanism is more important, as
concentrations of OM and grazers are closely linked. With either mechanism, however, bulk water col-
umnΩ may not accurately reflect the Ω experienced by CaCO
3
particles. Subhas et al. (2022) used water
column pH, nutrient, and C isotope measurements to show that respiration and CaCO
3
dissolution are in
fact tightly coupled in waters oversaturated for calcite in the North Pacific.
A constant dissolution scenario, in which dissolution is completely independent of seawater Ω and
OM respiration, has been previously proposed for modeling simplicity, sidestepping the question of mech-
anisms (Battaglia et al., 2015). In theory, such a dissolution profile could be produced by a combination
of respiration-driven dissolution and variable sinking speeds that effectively spread regenerated alkalinity
throughout the water column. For example, particles with very slow sinking speeds following seasonal
phytoplankton blooms could theoretically provide a nearly constant TA* source to the water column. Such
ephemeral dissolution sources may be missed in observations, yet may be important in defining vertical
alkalinity distribution (Schiebel, 2002). Similarly, rapidly sinking particles may also be missed in export
measurements (Schiebel, 2002; Smith et al., 1996).
Another potential explanation for significant dissolution in the upper ocean, not associated with OM
respiration, is the presence of more soluble forms of CaCO
3
, including those produced by teleosts. Using
liberal production and dissolution assumptions, teleost-produced crystallites may constitute as much as
45% of ocean CaCO
3
production (Wilson et al., 2009). However, we still know relatively little about teleost
spatial and depth distribution, and essentially nothing about depth of crystallite production and excre-
tion, crystallite production rates, and mineralogy/solubility in the open ocean (Irigoien et al., 2014; Lam
& Pauly, 2005; Perry et al., 2011; Salter et al., 2017, 2018, 2019). Teleosts typically migrate between 200
43
to 1,000 m depth during the day, and the surface where they feed at night. The uptake of alkalinity (via
CaCO
3
crystallite formation) and release of alkalinity (via crystallite excretion and subsequent dissolution)
may therefore occur at various depths within this range, depending on where the CaCO
3
is formed, where
it’s excreted, and how quickly it sinks and dissolves. For example, an upward alkalinity flux could theo-
retically occur if crystallites are formed at depth and excreted at the surface where they dissolve quickly.
Alternatively, crystallites which are produced, excreted, and dissolved at the same depth would have no
net effect on alkalinity. Given the right combination of formation vs excretion depth and mineral solubil-
ity, it is possible that teleost-produced CaCO
3
could contribute to a “constant” dissolution profile. More
research is needed to better constrain the magnitude of teleost CaCO
3
production, as well as where in the
water column it is produced, excreted, and dissolves.
Considering the similar dissolution profiles for the constant and respiration models below 500 m, one
can imagine a combination of processes contributing to either one, or a hybrid, of the two models. Pro-
cesses of potential importance include strong coupling of dissolution with OM respiration, variable particle
sinking rates, CaCO
3
consumption and excretion by grazers, and highly soluble “fish CaCO
3
”. Note that
these are all fundamentally connected to the biology and ecology of calcifiers, and cannot be constrained
by current modeling capabilities or chemical oceanographic analyses alone. Continued observations in
the geographic and seasonal distribution of planktonic calcifiers (Buitenhuis et al., 2013), as well as related
modeling efforts, will therefore be useful in constraining these factors (Bednaršek et al., 2012; Buitenhuis
et al., 2013; O’Brien et al., 2013; Schiebel & Movellan, 2012; Žarić et al., 2006).
2.4.6 Theimportanceofcalcitevs. aragonite
The relative contribution of calcite vs. aragonite to alkalinity regeneration is another important component
linking ecological structure and the CaCO
3
pump, especially in light of changing ocean conditions that
may alter planktonic ecosystem dynamics. The contribution of aragonite to total CaCO
3
export is still
44
poorly constrained, with observations ranging from 1 to 98% (Anglada-Ortiz et al., 2021; Berner & Honjo,
1981; Dong et al., 2019; Fabry & Deuser, 1991; Ziveri et al., 2022). However, a recent global compilation of
available data suggests that aragonite constitutes at least one third of CaCO
3
export (Buitenhuis et al., 2019).
The relative importance of aragonite vs. calcite dissolution depends greatly on the mechanisms driving
dissolution. If only considering seawaterΩ and dissolution kinetics, aragonite is indeed disproportionately
important to upper water column dissolution due to its shallow saturation horizon. For example, in M2,
aragonite accounted for only 28% of export, but 50% of pelagic dissolution above 1700 m. (Our sinking
speed sensitivity test showed this was true for all sinking speeds >5 m d
-1
). Gangstø et al. (2008) came to
similar results in their model, despite using different kinetic parameters. An important caveat, however,
is that M2 is dominated by dissolution deeper in the water column and at the sediments, so upper water
column dissolution is miniscule by comparison. At depth, calcite dissolution is much more significant than
aragonite due to its higher export and faster kinetics (Fig. 2.6a).
If dissolution is linked to OM respiration (as in M3), however, upper ocean alkalinity regeneration
can be driven by both calcite (78%) and aragonite (22%), in fractions similar to their export ratios (Fig.
2.6b). Although calcite is more thermodynamically stable in upper ocean conditions, observations support
our finding that both calcitic and aragonitic particles dissolve significantly in the upper ocean (Manno
et al., 2007; R. Oakes et al., 2019; R. L. Oakes & Sessa, 2020; Schiebel, 2002; Subhas et al., 2022; Ziveri
et al., 2022). Furthermore, experiments have shown that aragonite production and dissolution alone is
insufficient to explain upper ocean alkalinity (Fabry, 1990). These studies and our modeled results indicate
that bulk seawaterΩ and mineral solubility may be less important than factors related to respiration-driven
dissolution, such as the extent of mineral-associated labile OM, sinking speed, and grazing pressure. For
example, pteropods have been shown to dissolve from the inside-out due to respiration of internal OM,
irrespective of seawater Ω (R. Oakes et al., 2019). Foraminifera, on the other hand, often sink as empty
tests following reproduction (Schiebel & Hemleben, 2017). Finally, coccolithophores do not sink quickly
45
unless aggregated in organic particles, effectively “waiting” until they associate with organic matter and
the potential for OM respiration (Biermann & Engel, 2010; Engel et al., 2009). These examples illustrate
that the importance of aragonite vs calcite to upper ocean dissolution is ecosystem- and species-dependent,
and will also benefit from continued progress in plankton biogeographic surveys.
2.5 Conclusions
Testing four different models of CaCO
3
dissolution (benthic only,Ω -dependent,Ω + respiration, and con-
stant dissolution), we have shown that circulation alone cannot explain observed TA* distributions, and
that dissolution must occur above the calcite and aragonite saturation horizons. In our best-performing
models (Ω + respiration and constant dissolution), both of which allow significant dissolution above the
saturation horizons, we found a range of optimized CaCO
3
export values from 1.1 to 1.8 Gt PIC y
-1
just be-
low the model euphotic zone at 73 m. However, considering a deeper export depth (279 m), export for both
models converged at 1.0 Gt PIC y
-1
. The surplus dissolution in the higher export model was effectively re-
cycled within the upper ocean, suggesting that a range of “export” values can be accommodated in CaCO
3
cycling scenarios, as long as recycling is proportionately increased in the uppermost ocean. Below 500
m, both theΩ + respiration and constant dissolution models had similar dissolution profiles, supporting
higher dissolution rates than what would occur due to mineral undersaturation alone. While our models
cannot conclusively determine mechanisms driving CaCO
3
dissolution, we clearly show that dissolution
is not simply a function of seawater Ω and calcite and aragonite dissolution kinetics. Rather, potential
dissolution mechanisms are all intrinsically related to the biology and ecology of calcifiers inhabiting the
ocean’s surface.
46
SupplementaryTable2.1 Optimized parameter values for the four base models.
47
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Supplementary Figure 2.1 (a-d) Data inputs for deriving CaCO
3
export: P uptake (a) × C:P ratio (b) ×
PIC:POC ratio (c) = CaCO
3
export (d). In addition, a scaling factor was optimized for each model to adjust
total CaCO
3
export. (e) Riverine alkalinity inputs to the oceans, which are plotted as point sources at
each river mouth. Data are before adjustment by the scaling factor of 1.5 to balance burial fluxes (details
in Section 2.1.2). (f-h) Alkalinity burial fluxes of pelagic ocean (f), coastal ocean (g), and total burial (h).
Pelagic ocean burial data are derived from Dunne, Hales, and Toggweiler (2012) and re-gridded to fit the
model grids in this study. Coastal ocean burial data are derived from O’Mara and Dunne (2019) and re-
gridded to fit the model grids in this study. The total burial is the sum of pelagic and coastal burial (details
in Section 2.1.2).
48
TA0 TA*
obs
M1
M4
M3
M2
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
Supplementary Figure 2.2 Observed and modeled TA0 and TA* for representative transects (Pacific at
161°W and Atlantic at 29°W). White lines represent the aragonite (dashed) and calcite (solid) saturation
horizons. Observed, calculated based on the GLODAP alkalinity dataset and OCIM circulation (a, b); M1,
benthic only model (c, d); M2, Ω -dependent model (e, f); M3, Ω + respiration model (g, h); M4, constant
dissolution model (i, j). The transects for M3 (g, h) are shown in the main text in Fig. 2.3.
49
Observations
Low export
0.5 Gt PIC y
-1
Mid export
1.1 Gt PIC y
-1
High export
1.8 Gt PIC y
-1
(a) (b)
(c) (d) (e) (f)
(g) (h) (i) (j)
(k) (l) (m) (n)
TA0 TA0 model-obs misfit TA* TA* model-obs misfit
Supplementary Figure 2.3 Observed and modeled TA0 and TA*, and model-observation mismatch for
the export sensitivity tests for M1 (benthic only model). Tests were run for low (0.5 Gt C y
-1
), mid (1.1 Gt C
y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export from 73 m). (a, b) Observed TA0 and TA*, respectively.
(c, g, k) Modeled TA0. (d, h, l) TA0 model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-
observation mismatch.
50
Observations
Low export
0.5 Gt PIC y
-1
Mid export
1.1 Gt PIC y
-1
High export
1.8 Gt PIC y
-1
(a) (b)
(c) (d) (e) (f)
(g) (h) (i) (j)
(k) (l) (m) (n)
TA0 TA0 model-obs misfit TA* TA* model-obs misfit
Supplementary Figure 2.4 Observed and modeled TA0 and TA*, and model-observation mismatch for
the export sensitivity tests for M2 (Ω -dependent model). Tests were run for low (0.5 Gt C y
-1
), mid (1.1 Gt C
y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export from 73 m). (a, b) Observed TA0 and TA*, respectively,
calculated based on the GLODAP alkalinity dataset and OCIM circulation. (c, g, k) Modeled TA0. (d, h, l)
TA0 model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation mismatch.
51
Observations
Low export
0.5 Gt PIC y
-1
Mid export
1.1 Gt PIC y
-1
High export
1.8 Gt PIC y
-1
(a)
(b)
(c) (d) (e) (f)
(g) (h) (i) (j)
(k) (l) (m) (n)
TA0 TA0 model-obs misfit TA* TA* model-obs misfit
Supplementary Figure 2.5 Observed and modeled TA0 and TA*, and model-observation mismatch for
the export sensitivity tests for M3 (Ω + respiration model). Tests were run for low (0.5 Gt C y
-1
), mid
(1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export from 73 m). (a, b) Observed TA0 and TA*,
respectively, calculated based on the GLODAP alkalinity dataset and OCIM circulation. (c, g, k) Modeled
TA0. (d, h, l) TA0 model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation
mismatch.
52
Observations
Low export
0.5 Gt PIC y
-1
Mid export
1.1 Gt PIC y
-1
High export
1.8 Gt PIC y
-1
(a) (b)
(c) (d) (e) (f)
(g) (h) (i) (j)
(k) (l) (m) (n)
TA0 TA0 model-obs misfit TA* TA* model-obs misfit
Supplementary Figure 2.6 Observed and modeled TA0 and TA*, and model-observation mismatch for
the export sensitivity tests for M4 (constant dissolution model). Tests were run for low (0.5 Gt C y
-1
), mid
(1.1 Gt C y
-1
), and high (1.8 Gt C y
-1
) export scenarios (export from 73 m). (a, b) Observed TA0 and TA*,
respectively, calculated based on the GLODAP alkalinity dataset and OCIM circulation. (c, g, k) Modeled
TA0. (d, h, l) TA0 model-observation mismatch. (e, i, m) Modeled TA*. (f, j, n) TA* model-observation
mismatch.
53
(a) (b)
(c) (d)
(e) (f)
(g) (h)
TA0 TA*
Supplementary Figure 2.7 Model-observation mismatch for the sinking speed sensitivity tests for M2
(Ω -dependent model). Differences between modeled and observed (model – observed) are shown for both
TA0 (left column) and TA* (right column), at a range of sinking speeds: 1 m d
-1
(a, b); 10 m d
-1
(c, d); 100
m d
-1
, the default sinking speed in the base models (e, f); and 1,000 m d
-1
(g, h).
54
(a) (b)
(c) (d)
(e) (f)
TA0 TA*
SupplementaryFigure2.8 Model-observation mismatch for the sinking speed sensitivity tests for M3 (Ω + respiration model). Differences between modeled and observed (model – observed) are shown for both
TA0 (left column) and TA* (right column), at a range of sinking speeds: 1 m d
-1
(a, b); 10 m d
-1
(c, d); 100
m d
-1
, the default sinking speed in the base models (e, f); and 1,000 m d
-1
(g, h).
55
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
100% calcite GFDL calcite:aragonite 100% aragonite
Supplementary Figure 2.9 Model-observation mismatch for the combined sinking speed and cal-
cite:aragonite ratio sensitivity tests for M2 (Ω -dependent model). Differences between modeled and ob-
served (model – observed) TA* are shown, at a range of sinking speeds: 1 m d
-1
(a, b, c); 10 m d
-1
(d, e, f);
100 m d
-1
, the default sinking speed in the base models (g, h, i); and 150 m d
-1
(j, k, l). The center column
uses the spatially variable calcite:aragonite ratio from the GFDL dataset, as used in all base models.
56
Chapter3
Precipitationanddissolutionofpelagicbarite: Insightsfromaglobal
oceandissolvedBamodel
Abstract
The oceanic barium (Ba) cycle has been studied for years, and researchers have explored the potential
use of Ba as a proxy for paleoproductivity. This study aims to improve our understanding of the global Ba
cycle in the ocean, with a focus on the dissolved Ba distributions and the biogeochemical processes that
regulate it, particularly the impact of pelagic barite. We utilize a combination of observations and multiple
linear regression models to obtain global Ba climatology, enabling us to calculate the saturation states of
barite (Ω barite
) in global oceans. The results show that barite is only supersaturated in specific regions,
including the surface Southern Ocean, surface Arctic Ocean, intermediate North Pacific Ocean, and inter-
mediate Indian Ocean. To better understand how barite precipitation and dissolution impact the dissolved
Ba cycling, a data-constrained global mechanistic model is developed to simulate the biogeochemical pro-
cesses that might impact dissolved Ba distributions. Our investigation of the sources of Ba used to form
pelagic barite shows that ambient seawater Ba is the primary source, with the amount of Ba sourced from
organic matter being negligible. Lastly, we examine the dissolution patterns of barite particles as they sink
through the water column, finding that barite dissolution rates are relatively independent of the degree
57
of barite undersaturation. Overall, this study provides new insights into the global Ba cycle in the mod-
ern ocean, emphasizing the importance of pelagic barite in regulating dissolved Ba, and highlighting the
mechanisms that govern the formation and dissolution of barite in the ocean.
3.1 Introduction
The transport of organic carbon from the surface ocean to the deep ocean is an important mechanism to
mitigate atmospheric carbon dioxide (CO
2
) and sequester carbon in the ocean interior, which is crucial for
regulating the Earth’s climate. This process, known as the biological carbon pump, is driven by the sinking
of organic matter produced by marine phytoplankton. However, accurately quantifying export production,
particularly in the paleo-ocean, remains challenging. The mineral barite (BaSO
4
) is often used as a proxy
to reconstruct past ocean export productivity, since the sedimentation rates of barite are coupled to the
carbon burial rates (Paytan & Kastner, 1996).
Barite minerals are ubiquitous in seawater, despite the ocean being mostly undersaturated with re-
spect to barite (Monnin et al., 1999; Rushdi et al., 2000). Explanations of this paradox have suggested that
organic matter respiration creates a microenvironment that facilitates barite precipitation within organic
aggregates (Bishop, 1988; Chow & Goldberg, 1960; Dehairs et al., 1980), which is supported by the role of
marine bacteria in the bioaccumulation of Ba on biofilms (Martinez-Ruiz et al., 2018). The abundance of
pelagic barite and bacterial activity both peak in the 200-600 m depth zone, further supporting the link
between barite precipitation and organic matter remineralization (Dehairs et al., 1991; Stroobants et al.,
1991). As particles sink to the deeper ocean, barite dissolution occurs. While laboratory experiments have
formulated the dissolution rate as a function of barite undersaturation degree (Dove & Czank, 1995; Zhen-
Wu et al., 2016), it has been suggested that barite dissolution may occur in supersaturated waters, albeit
through an unclear mechanism (Rahman et al., 2022). A comprehensive understanding of the precipitation
58
and dissolution mechanisms of barite is required to evaluate its potential as a proxy to quantify export
production.
Barium (Ba) is a heavy trace metal that is ubiquitously present in seawater, primarily in the dissolved
phase (dBa) and the particulate phase (pBa), mainly as barite. Typically, dissolved Ba concentration in-
creases with depth, exhibiting a “nutrient-like” vertical profile. This vertical distribution of dissolved Ba
has been attributed to the barite cycle, whereby barite precipitates in the upper ocean, causing a decline
in dBa concentration, and dissolves at depth, leading to an increase in dBa concentration (Horner et al.,
2015).
The weathering of Ba-containing minerals on land can transport Ba to the ocean via rivers (Wolge-
muth & Broecker, 1970), which is further enhanced by estuarine processes that effectively release Ba from
suspended particles (Bridgestock et al., 2021). Other sources of oceanic Ba include submarine groundwater
discharge and hydrothermal fluids, with large uncertainties in the global flux estimates of these sources
(Hsieh et al., 2021; Mayfield et al., 2021). Based on prior estimates of global Ba input fluxes, the oceanic
residence time of dissolved Ba ranges from 3,500 to 21,000 years, which is longer than the ocean mixing
time of 1,000 years (Dickens et al., 2003; Horner & Crockford, 2021; Rahman et al., 2022). The long resi-
dence time of Ba suggests that these external sources might play an insignificant role in the pelagic ocean
Ba distributions.
To date, global oceanic Ba cycle modeling has been restricted to simple box models. The first two-box
model was constructed by Wolgemuth and Broecker (1970), which calculated the Ba exchange between the
surface and deep oceans. Assuming a single external Ba source from rivers and steady-state conditions,
they calculated that 86% of the pelagic barite would dissolve, while the remaining 14% gets buried. Paytan
and Kastner (1996) refined this two-box model by adjusting the flux rates and source terms, estimating a
burial rate of approximately 18%, while 82% would be regenerated mostly at sediments and, to a lesser
degree, in the water column. Building on these prior efforts, Dickens et al. (2003) quantified the barite
59
precipitation, dissolution, and burial fluxes to be 103.1, 85.0, and 18.1 Gmol y
-1
, respectively. These mod-
eling efforts quantitatively investigate the correlation between export production and sedimentary barite
preservation, while constraining the global input fluxes to the ocean and exchange rates between surface
and deep oceans. However, spatial variations in Ba distributions are not revealed due to the limitations of
box models. Furthermore, barite precipitation and dissolution mechanisms cannot be integrated with flux
estimates.
This study employs global observations, a multiple linear regression model, and a three-dimensional
global mechanistic model to investigate the cycling of marine dissolved Ba, including the biogeochemical
processes regulating it and the effects of pelagic barite, which can also provide insights into the utilization
of the Ba proxy in paleo studies. It is worth noting that this study focuses on the Ba cycling in the water
column rather than at the ocean boundaries. Global models have the advantage of capturing large-scale
patterns, but put poor constraints on the smaller contributors of the modeled tracer. As for oceanic dis-
solved Ba, the external sources and sedimentary burial are overshadowed by global ocean circulation and
barite cycling, and the global dissolved Ba model does not consider these smaller components because they
cannot be accurately represented or constrained.
3.2 Methods
3.2.1 Observationaldatasets
The dissolved Ba concentrations used as observational data in this study are from the GEOTRACES pro-
gram Intermediate Data Product 2021 (IDP2021), with sampling locations in the Atlantic, Pacific, and Arctic
Oceans (GEOTRACES, 2021). The observed Ba concentrations are used to train the multiple linear regres-
sion model (Section 3.2.2) and constrain the inverse model (Section 3.2.4).
60
Global ocean in situ temperature, salinity, oxygen, and silicate data used for training the multiple linear
regression model (Section 3.2.2) or calculating the barite saturation states (Section 3.2.3) are obtained from
the World Ocean Atlas 2009 (Levitus et al., 2010), regridded to fit the Ocean Circulation Inverse Model
(OCIM) with 2° horizontal resolution and 24 vertical layers (DeVries, 2014; DeVries & Primeau, 2011).
3.2.2 Multiplelinearregressionmodel
A multiple linear regression (MLR) model is adopted to predict the global climatology of marine dissolved
Ba, which is a prerequisite for calculating the global variations in barite saturation states (Section 3.2.3).
The dissolved Ba concentration (dependent variable) is predicted based on its relationships with other
independent variables. Six independent variables are chosen as the input for the regression algorithm,
including the cosine of latitude, depth, temperature, salinity, oxygen, and silicate concentrations. These
selected predictors either have a strong correlation with the dependent variable (Fig. S3.1), or contain
information about geographic location, hydrography, or nutrients, which might affect seawater Ba con-
centrations.
We utilize the MATLAB function fitlm to train the MLR model with six independent variables as inputs.
The function fits a linear model by minimizing the sum of the squares of the residuals between the predicted
and observed Ba concentrations. To test the robustness of the algorithm and evaluate the reliability of the
predicted Ba concentrations in unseen regions, we perform three tests: 1) train the MLR algorithm using
all data from the Atlantic Ocean, and validate the algorithm by comparing the predicted and observed Ba
in the Pacific Ocean, 2) train MLR based on Pacific Ocean data, and validate it with the Atlantic Ocean
data, and 3) train the MLR algorithm using all Ba data from the GEOTRACES IDP2021, and predict the
global climatology of Ba. The first two tests separate observations into a training dataset and a validation
dataset, where the regression model learns from the linear correlation in one ocean basin and predicts
Ba data in another ocean basin that the model has never seen before. The accuracy of the predicted Ba
61
in the validation dataset provides a rigorous test to demonstrate the model’s ability to extrapolate the
dataset with observations into larger regions where observations do not exist. After assessing the model
performance through cross-validation, we use all observational data in the IDP2021 to perform MLR again
and extrapolate the Ba concentrations into the global oceans.
In addition to the multiple linear regression model, we have explored various machine learning models
such as Gaussian process regression, decision tree, support vector machine, and artificial neural network, to
predict global Ba climatology. However, while these machine learning algorithms are able to reproduce the
training dataset well, they do not perform better than the MLR method in predicting the validation dataset
(Fig. S3.2). Therefore, we have chosen the MLR method as it is the simplest and most well-understood
algorithm for extrapolating datasets.
3.2.3 Baritesaturationstate(Ω barite
)calculations
The world ocean is mostly undersaturated with respect to barite (Monnin et al., 1999; Rushdi et al., 2000).
The saturation state of barite, denoted as Ω barite
, which might affect barite precipitation and dissolution
rates, is an essential index for investigating the marine Ba cycle. The saturation state is calculated as:
Ω barite
=
[Ba
2+
][SO]
2− 4
K
sp
(3.1)
where [Ba
2+
] is the concentration of the dissolved Ba in seawater that exists in the form of Ba2+, obtained
from the predicted 3-D Ba climatology (Section 3.2.2). The seawater sulfate ion ([SO
4
2-
]) is conservative,
with a constant concentration of 28 mM in the modern ocean. The solubility product constant K
sp
can be
calculated as a function of temperature, salinity, and pressure, following Rushdi et al. (2000).
The K
sp
value of barite is affected by the presence of other ions in the system. In seawater, barite
can contain various impurities, including strontium (Sr), which is relatively abundant in seawater and can
readily substitute for Ba in the barite crystal lattice (Dehairs et al., 1980). The presence of Sr in barite can
62
increase its solubility, making it more soluble than pure barite (Hanor, 1969). While Rushdi et al. (2000)
calculated a 30% increase in barite solubility due to the presence of Sr, Monnin and Cividini (2006) did
not find a significant difference in Ω barite
when accounting for Sr impurities. To evaluate the potential
influence of the compositions of pelagic barite on barite dissolution patterns, we calculate two sets of
K
sp
values, and thus two sets ofΩ barite
values, for both pure barite and Sr-containing barite based on the
parameters estimated by Rushdi et al. (2000). These two sets of solubility data are used for predicting barite
dissolution dependence on barite saturation states in Section 3.2.6.3. By comparing both cases, we aim to
obtain a more comprehensive understanding of the potential impact of Sr impurity and the accuracy of
Ω barite
calculations on barite dissolution behavior.
3.2.4 Mechanisticmodelofthemarinebariumcycle
The global mechanistic model of oceanic dissolved Ba is developed in the AWESOME OCIM framework
(John et al., 2020). The three-dimensional global ocean circulation is obtained from the Ocean Circulation
Inverse Model (OCIM) (DeVries, 2014; DeVries & Primeau, 2011). The biogeochemical processes controlling
marine Ba distributions are designed specifically for this study, as detailed below, and coupled to the OCIM
water transport matrix.
The marine Ba cycle is comprised of the dissolved, particulate, organic phases, and the fluxes between
these phases. Our model explicitly simulates the global dissolved Ba distributions that are influenced by
large-scale circulation and biogeochemical processes, while the particulate and organic Ba phases are im-
plicitly considered when their variations affect the dissolved Ba concentration. The major biogeochemical
processes that regulate marine dissolved Ba distributions include biological uptake in the surface ocean
followed by remineralization at depth, as well as precipitation and dissolution of pelagic barite, which
represent the conversion of dissolved Ba between the organic and particulate phases, respectively (Fig.
3.1).
63
seawater
dissolved Ba
uptake
remineralization
phytoplankton
pelagic barite
particles
dissolution
precipitation
sinking
Figure 3.1 The marine Ba cycle, including the dissolved (black circle), organic (green circle), and partic-
ulate (purple circle) Ba phases. Our mechanistic model represents the dissolved pool explicitly, while the
organic and particulate pools are included implicitly through the exchanges with the dissolved pool. The
biogeochemical processes that regulate the conversions between these phases include: 1) the biological
uptake of dissolved Ba into marine organisms (red arrow), followed by organic matter remineralization at
depths (orange arrow), and 2) the precipitation (blue arrows) and dissolution (green arrow) of barite. The
arrow directions indicate the transfer of Ba from one phase to the other, while the thickness of the arrows
reflect the relative magnitudes of the fluxes, as predicted by our mechanistic model. This figure is adapted
from Horner et al. (2015).
64
Marine phytoplankton take up dissolved Ba from surface seawater (Fisher et al., 1991; Lea & Spero,
1994; Sternberg et al., 2005). The uptake of Ba is assumed to be proportional to the uptake of phosphorous
(P), following the equation:
Ba
up
=R
Ba:P
P
up
(3.2)
where R
Ba:P
represents the cellular uptake ratio of Ba to P, and P
up
is the P uptake rate obtained from a
previous P model (Weber et al., 2018). The value of R
Ba:P
determined from previous experiments ranges
by orders of magnitude, e.g. 0.5 µ M:M (Sternberg et al., 2005) and 0.44 mM (Horner et al., 2017). Our
mechanistic model optimizes this ratio as a globally uniform value, within the range between 0.5 µ M:M
and 0.5 mM:M. The biological uptake process occurs in the surface euphotic zone, which is set as the top 73
m in the model. As biogenic particles settle down into the deeper ocean, the microbial oxidation of organic
matter gradually releases Ba back to seawater (Ganeshram et al., 2003). Part of the released organic matter-
mediated Ba serves as a source to precipitate barite, which will be discussed below, while the remaining
fraction is recycled following the classic Martin curve (Martin et al., 1987):
F
z
=F
z0
(
z
z0
)
− b
(3.3)
The particulate flux at depth z (in meters) is dependent on the flux out of the euphotic zone (z0 = 73 m)
and attenuates exponentially with exponent b = 0.92, which is an optimized result of a previous P model,
representing the best estimate for the magnitude of particulate P flux attenuation (Weber et al., 2018). The
organic particles that do not remineralize in the water column during gravitational sinking are assumed
to completely remineralize at the sediment-water interface.
Barite precipitation occurs when supersaturated conditions are created, which is possible in the marine
microenvironment facilitated by organic matter respiration. Thus, the barite precipitation rate is modeled
as a function of P remineralization rate (P
rem
) obtained from a previous P model (Weber et al., 2018), which
65
effectively represents the microbial oxidation rate. There are two potential sources of dissolved Ba to form
barite (Horner et al., 2015). First, the Ba may come directly from seawater. Second, Ba can be released from
organic aggregates during remineralization. The rate of barite precipitation (R
ppt
) is thus formulated as:
R
ppt
=(k
p
[Ba]+fR
Ba:P
)P
rem
(3.4)
Barite precipitation from the seawater source is assumed to be a first-order process, so that the pre-
cipitation rate is proportional to the ambient dissolved Ba concentration, scaled with an optimizable rate
constantk
p
. The other Ba source from organic matter is scaled with the stoichiometry of Ba:P, the same as
R
Ba:P
from Eq. 3.2, then multiplied by the parameterf which is the fraction of the organic matter-associated
Ba that is converted into barite. The fractionf is thus constrained between 0 and 1, which is optimized at a
value that is most consistent with observations. The remaining fraction of Ba taken up by phytoplankton,
which is not used to precipitate barite, is released back to seawater during organic matter remineralization
following Eq. 3.3. Because barite precipitation is proportional to P remineralization (P
rem
), which occurs
below the euphotic zone (from 73 m to seafloor) and attenuates following the Martin curve, the model as-
sumes that the highest precipitation rate occurs just below 73 m and gradually decreases with increasing
depth in the ocean.
After barite particles are formed, they sink to the deeper ocean where they undergo dissolution. The
model assumes a settling rate of 500 m y
-1
for the barite particles. The kinetic dissolution rate (R
diss
) of a
mineral is often related to the degree of undersaturation, fitted to an empirical rate law (Lasaga, 1998):
R
diss
=k
d
(1− Ω)
n
(3.5)
where k
d
denotes the dissolution rate constant and n refers to the reaction order, both of which can be
determined experimentally under specific temperature, pressure, pH, and ionic strength conditions. When
66
Ω <1, dissolution occurs; whenΩ ≥ 1, there is no dissolution due to supersaturation. This rate law has been
applied to the dissolution of several minerals, including calcium carbonate (Keir, 1980) and silica (Dove
et al., 2008). Previous laboratory studies on barite dissolution kinetics have used similar formulations of
Eq. 3.5, either with a reaction order n = 1 suggesting a linear correlation (Christy & Putnis, 1993; Dove &
Czank, 1995), or asR
diss
=k
d
(1-Ω n
) (Zhen-Wu et al., 2016). Such experiments provide valuable insights into
barite dissolution kinetics in aqueous systems, but their laboratory conditions are different from the pelagic
ocean conditions in terms of temperature, pH, and pressure, which can significantly affect dissolution rates.
Therefore, we cannot directly obtain the rate parameters ofk
d
and n from literature. Instead, we allow the
model to optimize these two parameters, in order to seek the best mathematical approximation of these
kinetic rate constants in the marine environment and determine the relationship between barite dissolution
rates and barite saturation index (Ω barite
) in the real ocean.
Alternatively, a recent study suggests that barite might dissolve in supersaturated waters, or that barite
dissolution rate is not directly related to Ω barite
in the pelagic ocean (Rahman et al., 2022). In order to
explore the possibility of the independence of barite dissolution rate on Ω barite
, another formulation of
barite dissolution rate is given as:
R
diss
=k
d
(3.6)
where barite dissolution rates are the same everywhere in the water column regardless of Ω barite
. Our
mechanistic model tests both dissolution formulations (Eq. 3.5 or Eq. 3.6) in order to explore how well
these different formulations can reproduce observed dissolved Ba distributions in the ocean.
The input fluxes of Ba from land are small compared to the ocean circulation and internal cycling of Ba.
The mechanistic model is therefore insensitive to the magnitudes of these external sources and unable to
accurately constrain these fluxes through optimization. Because introducing these fluxes to the model does
not improve the model performance, we choose to ignore these minor factors which do not significantly
contribute to the global Ba distributions, and focus on the internal cycling and biogeochemical processes.
67
The mechanistic model is thus set as a closed-system model, which does not take into account external
sources. For the marine Ba cycle, the major process that removes Ba from the ocean is barite preservation
in sediments. In a steady-state model, input and output fluxes should be balanced. Our model assumes that
all barite particles reaching the seafloor can be remineralized, thus ignoring sedimentary burial of barite.
However, without external sources or sinks, the total amount of dissolved Ba in the system cannot be
determined, and the model is unable to find a steady-state solution. In order to add additional constraints
on the amount of Ba in the ocean reservoir, we therefore impose flux terms with a very small source and
a very slow sink, following:
J
geo
=k
geo
([Ba]− [Ba]) (3.7)
wherek
geo
is a very small rate constant of 1/10
6
y
-1
, representing the geological timescale of 1 million years,
which is much longer than the ocean mixing timescale of 1,000 years. This function adds a very small
source of Ba to each grid cell at a rate ofk
geo
[Ba], where[Ba] is the average dissolved Ba concentration in
seawater. This extra source is balanced by a very small first-order sink of k
geo
[Ba]. These two terms play
the role of setting the mean concentration of Ba in the ocean by assigning the value of[Ba], while having
negligible influence on the distribution of dissolved Ba due to the small magnitudes of the fluxes.
3.2.5 Optimizationofthemechanisticmodel
The global dissolved Ba model is developed based on the biogeochemical mechanisms described in Section
3.2.4 and coupled with the pre-set ocean circulation matrix. Some model parameters are fixed values (e.g.
the value ofb in Eq. 3.3), while the other parameters are either previously undefined or poorly constrained
by prior experimental work. The optimization process aims to find the set of parameter values that can
68
Table 3.1 The biogeochemical processes, parameters, and optimization of the mechanistic dissolved Ba
model. The optimized parameter values are based on the model control run.
best reproduce the observed Ba distributions, by minimizing the root mean square error (RMSE) between
model-predicted Ba ([Ba]
model
) and observed Ba ([Ba]
obs
) concentrations:
RMSE =
v
u
u
t
m
X
i=1
w
i
([Ba]
model,i
− [Ba]
obs,i
)
2
(3.8)
The total number of observations re-gridded from the GEOTRACES IDP2021 is m, and the RMSE is
weighted with the ocean volume of each grid cell (w
i
). The optimization starts with initial guesses of pa-
rameter values, which are either obtained from previous literature or manually adjusted to simulate good
model predictions. Then we utilize the MATLAB optimization function fmincon to minimize the discrep-
ancy between modeled and observed Ba concentrations by adjusting the optimizable model parameters,
with each unknown parameter constrained within reasonable bounds (Table 3.1). The final model with
optimized parameters has the minimized model-data discrepancy, and is considered to represent the best
simulation of global ocean dissolved Ba distributions.
69
3.2.6 Sensitivitytests
3.2.6.1 Bootstrapsampling
The multiple linear regression (MLR) model, as described in Section 3.2.2, is based on the linear correla-
tion between the predictors and the Ba concentration variable. However, since the Ba observations are
sparsely distributed, representing only 1% of the global ocean model grids, it is important to evaluate the
reliability of the MLR algorithm in filling in data gaps without measurements. To achieve this goal, we
apply the bootstrap sampling approach to estimate the uncertainty of the MLR model prediction. We use
the bootstrap method to generate 1,000 random subsets of samples with replacement from the original Ba
observation dataset. Each bootstrap sample has the same size as the original dataset, but some observa-
tions may be randomly selected to be included in the new dataset more than once, while some may not
appear at all. For each bootstrap sample, we run the MLR model again, and record the fitted coefficients
and model prediction, which may differ from the original results. This process is repeated 1,000 times,
producing 1,000 estimates of global Ba climatology using the MLR method with different training datasets.
We then calculate the standard deviation of Ba concentrations in each model grid cell, providing a measure
of the variability and uncertainty associated with the predicted Ba concentration in each ocean grid cell.
This allows us to assess the reliability of the MLR model in different regions of the ocean.
3.2.6.2 DissolvedBasourcesforbariteprecipitation
Barite precipitation, which is facilitated by microbial oxidation, requires excess dissolved Ba to create the
supersaturated microenvironment. Dissolved Ba can originate from two sources: ambient seawater or
organic matter remineralization (Horner et al., 2015). However, the relative importance of each source is
poorly constrained by previous work. Our mechanistic model accounts for both sources and enables the
model optimizer to find the best mathematical solution. In addition, we conduct two endmember tests to
evaluate the relative contribution of each source to barite formation. We assign k
p
= 0 or f = 0 in Eq. 3.4
70
to simulate a scenario where the Ba source for barite precipitation is solely from organic matter or solely
from seawater, respectively. The magnitude of model degradation reflects the importance of each source
in the barite cycle.
3.2.6.3 Baritedissolutionandthesaturationindex
As particulate Ba sinks to the deep ocean with organic aggregates, the barite particles are gradually ex-
posed to undersaturated seawater, where dissolution occurs. However, the barite dissolution rates in global
oceans are highly uncertain due to a lack of direct measurements, leading to different hypotheses of the dis-
solution mechanisms. Although laboratory studies have investigated the correlation between dissolution
rates and barite undersaturation, parameters determined under lab conditions cannot be readily applied
to the marine environment (Christy & Putnis, 1993; Dove & Czank, 1995; Zhen-Wu et al., 2016). Addition-
ally, the calculation of barite saturation index (Ω barite
) relies on K
sp
, which varies with the composition
of pelagic barite. The potential inaccuracy inΩ barite
calculations can lead to uncertainties in dissolution
kinetics (Rushdi et al., 2000). There are also studies suggesting that barite dissolution can occur in su-
persaturated seawater, although the mechanisms behind this phenomenon remain unclear (Rahman et al.,
2022).
Due to these different possibilities of barite dissolution mechanisms, we perform the following disso-
lution sensitivity tests to better understand the general barite dissolution patterns in the global oceans,
and how these different scenarios affect dissolved Ba distributions.
1) Barite dissolution occurs at a constant rate, as given by Eq. 3.6. Because this is the simplest formu-
lation and has been implied by field measurements, we define this test as the “control run”, which is used
as the standard mechanistic model framework that will be discussed in the following sections, except for
dissolution sensitivity result discussions.
71
2) Assuming no barite dissolution occurs in the water column, all barite precipitated in the upper ocean
will sink and dissolve at the sediment-water interface, which recycles dissolved Ba to benthic seawater.
3) After the constant dissolution rate is optimized by the model, we increase or decrease the optimized
rate constant (k
d
) by 5-fold, and run the models with the other parameters optimized again, while fixing the
dissolution rate constant atk
d
×5 ork
d
/5. This experiment aims to examine how dissolved Ba distributions
will change if the barite dissolution rate is forced at a higher or lower level, which in turn validates the
sensitivity and accuracy of the optimized rate constant k
d
.
4) Assuming pelagic barite is pure barite without Sr, we simulate the barite dissolution rate as a function
of Ω barite
, following Eq. 3.5. Two experiments are performed with this kinetic equation, by fixing the
reaction order n = 1 or allowing the model to optimize n.
5) Assuming pelagic barite is Sr-barite, which increases barite solubility from pure barite, we perform
two tests similar to 4), adjusting the reaction order n = 1 or optimized.
These experiments assess the model sensitivity on the rate constant estimates, as well as looking into
other factors that could influence pelagic barite dissolution rates, including the barite saturation index and
the composition of pelagic barite.
3.2.6.4 TheimpactofbaritesinkingvelocityonthepredictedmarineBacycle
The control run model assumes a constant sinking velocity of 500 m y
-1
for barite particles. This value
does not necessarily need to be exact, because the model can optimize the dissolution rate constant k
d
to accommodate different sinking velocities, in which case the same model results can be achieved by
adjusting k
d
and sinking velocity proportionally. However, such a constant sinking speed represents a
simplified approximation that may not fully capture the complexity of particle sinking dynamics in the
ocean. To explore alternative formulations of particle sinking velocities that could better reflect realistic
72
sinking scenarios, two experiments are conducted based on the control run configuration, assuming a
constant dissolution rate.
The first experiment involves scaling the particle sinking velocity linearly with depth, which is sup-
ported by previous observations suggesting faster sinking rates in deeper oceans (W. M. Berelson, 2001).
The second model assumes a division of barite particles into two size fractions, 50% small particles and
50% large particles, where the large particles sink 100 times faster than the small particles. Subsequently,
two separate models are run based on these two hypotheses of barite settling rates, with the other model
parameters re-optimized to match the observed dBa concentrations. These experiments aim to investi-
gate whether these different representations of sinking velocities could influence the marine dissolved Ba
distributions, barite dissolution patterns, and the amount of barite particles settling on the seafloor.
3.3 Resultsanddiscussion
3.3.1 Global climatology of dissolved Ba predicted by the multiple linear regression
model
The MLR model, which extrapolates the global climatology of dissolved Ba based on the linear correlation
between Ba concentrations and six independent variables, exhibits a high correlation with observations
(Fig. 3.2). Cross-validation tests, which use Atlantic Ba data to predict the Pacific Ba concentrations (Fig.
3.2a) or use Pacific data to predict the Atlantic data (Fig. 3.2b), both achieve R
2
> 0.90 in the training dataset
and R
2
> 0.75 in the validation dataset, indicating that the MLR model effectively fits the observed data and
generalizes well to new, unseen data. However, one noteworthy deviation appears in the Pacific validation
dataset trained on Atlantic data, where the predicted Ba concentrations in the deep Pacific Ocean are lower
than observations (Fig. 3.2a). This is because the Atlantic Ocean has lower Ba concentrations than the
Pacific. The MLR model may not accurately predict high values when the training dataset predominantly
73
consists of low values. As a result, the model may not have learned the appropriate relationships between
the six predictors and Ba concentrations at higher values, leading to poor performance in this range. Hence,
it is important to ensure that the training dataset is representative of the entire range of seawater Ba
concentrations for the MLR model to learn the appropriate relationships across the entire range of values.
Therefore, our global Ba climatology utilizes the entire GEOTRACES IDP2021 dataset as the training
dataset, including lower values in the Atlantic Ocean and higher values in the Pacific Ocean, which achieves
a R
2
= 0.95 between the observed and predicted values (Fig. 3.2c). The model predicted Ba matches well
with observations across different ocean regions and at different depths (Fig. 3.2d-f), suggesting that the
MLR model is a reliable tool for predicting the global Ba distributions.
To assess the reliability of our global Ba climatology predicted by the MLR model, we utilize a bootstrap
sampling method, generating 1,000 samples with replacement from the original Ba observational dataset,
and performing MLR again to compare 1,000 results of predicted Ba climatology. We found that some ocean
regions exhibit higher standard deviations, indicating greater variability in the model predictions in those
regions (Fig. 3.2g-i). Generally, the Atlantic Ocean has the lowest standard deviation among all the ocean
regions, suggesting that the model performance in predicting Ba distributions is relatively consistent in
the Atlantic region. The surface Arctic Ocean, which has unique circulation and environment, exhibits the
highest standard deviation. In addition, the pelagic ocean is predicted with higher accuracy compared to
the coastal ocean. Nonetheless, the standard deviation of the 1,000 model predictions is small compared to
the seawater Ba concentrations, which demonstrates the reliability of the model predictions. The bootstrap
sampling results suggest that our MLR model provides accurate predictions in global Ba climatology, with
a high degree of certainty in some ocean regions compared to the other regions.
74
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure3.2 The multiple linear regression (MLR) model of dissolved Ba. The first row shows scatter plots
of observed and predicted Ba concentrations. (a) Train the MLR algorithm with Atlantic Ba data (blue), and
validate with the Pacific Ba data (red). (b) Train the MLR algorithm with Pacific Ba data (red), and validate
with the Atlantic Ba data (blue). (c) Train the MLR algorithm with all data from GEOTRACES IDP2021,
then predict the global climatology of Ba and validate the model performance with the data predicted at
the same locations of observations. The second row shows global maps of MLR-predicted (color field) and
observed (filled circles) Ba concentrations at (d) surface ocean, (e) 1000 m, and (f) 3000 m. The third row
shows global maps of standard deviation (STD) resulting from 1000 iterations of bootstrap sampling of the
MLR model at (g) surface ocean, (h) 1000 m, and (i) 3000 m. The STD maps highlight regions with higher
variability with darker red color, providing insights into the robustness of the MLR model and potential
sources of uncertainty.
75
3.3.2 Baritesaturationstateinglobaloceans
Based on the global 3-D Ba climatology presented in Section 3.3.1, the saturation state of barite can be
determined following Eq. 3.1. We calculateΩ barite
for both pure and impure (with Sr) barite based on the
constants from Rushdi et al. (2000), simulating two potential scenarios of pelagic barite saturation states
(Fig. 3.3). Generally, the incorporation of Sr in barite crystals increases solubility by 30%. We focus
our discussion on the Sr-barite saturation state, as it better reflects the realistic barite composition in the
marine environment.
The world oceans are mostly undersaturated for barite, except for certain regions such as the surface
Arctic Ocean and surface Southern Ocean (Fig. 3.3d), and the intermediate Indian and Pacific waters (Fig.
3.3e), where barite supersaturation occurs. In contrast, the Atlantic Ocean is undersaturated with respect
to barite at all depths. Our calculations are consistent with theΩ barite
pattern determined from previous
measurements in different ocean basins (Monnin et al., 1999; Rushdi et al., 2000). Using the Ba climatology
produced by the MLR model, theΩ barite
distributions can be computed for the entire ocean in this study,
allowing for further parameterizations of barite dissolution in the mechanistic model (Section 3.3.5).
3.3.3 MechanisticmodelpredictionofdissolvedBavs. GEOTRACESBaobservations
The global dissolved Ba model is in good agreement with observational data (Fig. 3.4; Fig. S3.3). The model
accurately reproduces the observed vertical profiles of dissolved Ba in both Atlantic and Pacific Oceans
(Fig. 3.4a), achieving a high R2 value of 0.95 when comparing the model predictions and observed Ba
concentrations from the GEOTRACES IDP2021 dataset (Fig. 3.4b). The strong model performance suggests
that our dissolved Ba model is effectively representing the underlying biogeochemical mechanisms that
regulate the marine Ba cycle, including phytoplankton uptake followed by organic matter remineralization,
and the precipitation and dissolution of pelagic barite.
76
(a) (b) (c)
(d) (e) (f)
Figure 3.3 Global maps displaying the spatial distributions of the saturation state of barite (Ω barite
) at
various depths. CalculatedΩ barite
for pure barite at (a) surface ocean, (b) 2000 m, and (c) 3750 m. Calculated
Ω barite
for Sr barite at (d) surface ocean, (e) 2000 m, and (f) 3750 m. The solubility product constant is
calculated following Rushdi et al. (2000).
Despite its overall effectiveness, there are specific ocean regions where model predictions deviate from
observed Ba data, including overestimation of Ba concentrations in the surface Pacific Ocean and under-
estimation of Ba concentrations in the deep North Atlantic waters (Fig. 3.4; Fig. S3.4). These discrepancies
imply potential model limitations in the formulations of biogeochemical mechanisms or parameter values.
The model optimizes the surface Ba uptake to the lowest bound with a Ba:P uptake ratio of 0.5µ M:M (Ta-
ble 3.1), which is the best mathematical solution for minimizing the model-data discrepancy. However, the
R
Ba:P
value may vary for different types of phytoplankton, leading to differences in R
Ba:P
values in different
ocean regions. This variation could result in lower Ba concentrations in the surface Pacific Ocean if the
uptake rate of Ba by phytoplankton is higher than what the model predicts. As for the deep Atlantic wa-
ters where predicted Ba concentrations are lower than observations, the model might be underestimating
the rates of barite dissolution. This is because our standard model (defined as the control run) assumes
a constant dissolution rate throughout the ocean, independent of the barite saturation state. However, if
77
the dissolution rates are faster in more undersaturated waters in the real ocean, as suggested by mineral
dissolution kinetics, then barite dissolution in the Atlantic Ocean should be faster than the global average.
Even with previous evidence showing potential dissolution in supersaturated waters in the intermediate
North Pacific Ocean (Rahman et al., 2022), the specific mechanisms of barite dissolution in the real ocean
are not fully understood, which could lead to biased results if we assume a fixed barite dissolution rate
constant.
3.3.4 TheoriginsofdissolvedBaforbariteprecipitation
Barite precipitation occurs in organic aggregates when the microenvironment becomes supersaturated
with respect to barite, which requires an enrichment of dissolved Ba. The origins of the dissolved Ba
that forms barite have been proposed to be either a direct source from ambient seawater (Horner et al.,
2015) or an intermediate source from phytoplankton decomposition (Ganeshram et al., 2003), although the
relative contributions of each source remain unclear. Without experimental constraints on the proportions
of each contributor, our model incorporates both potential sources, allowing the optimizer to find the best
solution. The optimized fluxes suggest that over 99% of the BaSO
4
precipitated in the marine environment
is derived from dissolved Ba
2+
in seawater, while the organic matter-associated Ba2+ released through
remineralization is negligible (Table 3.2).
To assess the robustness of the estimated seawater and organic origins, and rule out any possibility
of optimization artifacts, two endmember tests were performed to retain only the seawater source or the
organic source for barite formation. The two new models exhibit distinct features in shaping dissolved Ba
vertical distributions (Fig. 3.5). When assuming that all Ba
2+
source for barite comes from seawater, the
model accurately matches observational data, and this optimized model is nearly identical to the original
model that allows two source origins. In contrast, when assuming that all Ba2+ source for barite comes
from phytoplankton decay, the model deviates from observations at all depths, with slight increases in
78
(a) (b)
(c) (d)
Figure3.4 The dissolved Ba concentrations predicted by the mechanistic model compared to GEOTRACES
IDP2021 observations. (a) Average vertical profiles of dissolved Ba concentrations in the Atlantic (yellow)
and Pacific (purple) Oceans. The data points indicate observed average Ba concentrations in that ocean
basin, with error bars representing 1 standard deviation. The lines represent modeled average Ba concen-
trations, with shaded areas representing 1 standard deviation. (b) Scatter plot comparing global observed
and modeled Ba concentrations, color-coded by sampling depth. Global maps of dissolved Ba concentra-
tions at (c) surface and (d) 2500 m, with model predicted dissolved Ba concentrations represented by the
color field and observations overlaid as filled circles.
79
Table3.2 Barite precipitation and dissolution fluxes (in Gmol y
-1
). Three tests focusing on the Ba
2+
source
origins for barite precipitation are listed, including a direct seawater source, an intermediate source from
organic matter, and a combination of both seawater and organic sources.
dissolved Ba concentrations with depth. This occurs even though the Ba uptake rate and the fraction of
organic Ba that goes into barite both reach the upper limit of the model setting (R
Ba:P
= 0.5 mM:M and
f = 1). This implies that the dissolved Ba sourced from organic matter remineralization is insufficient to
support pelagic barite precipitation and that the seawater source is likely the primary contributor.
To quantitatively demonstrate the insignificant role of organic matter as a Ba source, we calculate a
hypothetical scenario that compares the maximized organic Ba source with global estimates of pelagic
barite formation. Our model utilizes a previous P model to calculate Ba uptake based on P uptake (Weber
et al., 2018), which indicates that the global total P uptake rate in the surface ocean is 19.5 Tmol y
-1
.
Assuming that the cellular Ba:P ratio is 0.5 mM:M, which is the upper limit used in our model, the global
Ba uptake by phytoplankton is estimated to be 9.7 Gmol y
-1
. More than half of the particulate organic
phosphorus is released back to seawater through remineralization, so this remineralized fraction is scaled
the same for the organic Ba pool. Therefore, only 4.6 Gmol y
-1
of barite can precipitate globally if all
the remaining Ba is utilized in the barite-supersaturated microenvironment. This is much lower than the
global estimate of using seawater Ba as the Ba
2+
source for barite, which reaches 77.3 Gmol y
-1
barite
formation in our model, and even lower than a previous box model estimate of 103.1 Gmol y
-1
(Dickens
et al., 2003). Without sufficient barite formation in the upper ocean that can draw down dissolved Ba
80
Figure3.5 Vertical profiles of global average dissolved Ba concentrations, from observations (data points
with error bars representing 1 standard deviation), the model simulation which assumes the Ba source
for barite precipitation is from seawater (red line), the model simulation which assumes the Ba source
for barite precipitation is from organic matter (blue line), and the model simulation which assumes the Ba
source for barite precipitation is from both seawater and organic matter (grey areas presenting the average
± 1 standard deviation).
concentrations, and without sufficient subsequent barite dissolution at depths that can release dissolved
Ba back to seawater, the modeled dissolved Ba concentrations exhibit slight depth variations, which is
significantly different from observed Ba features that show apparent increases in concentrations with depth
(Fig. 3.5).
3.3.5 ThedependenceofbaritedissolutiononΩ barite
After barite is precipitated, mostly in the upper ocean below the euphotic zone, it undergoes dissolution
as it sinks to the deeper ocean. Our control run model optimizes the dissolution rate constant at 0.15 y
-1
,
balanced by a sinking velocity of 500 m y
-1
, resulting in an estimated dissolution rate of 0.03% per meter,
or 30%/1000 m. The modeled dissolved Ba profiles match well with observations in the ocean interior,
81
suggesting a good approximation of the dissolution rate. To evaluate the robustness of this estimate and
explore alternative formulations of barite dissolution mechanisms, we test other dissolution equations
and optimize the model under different scenarios, as outlined in Section 3.2.6.3. Comparisons between
different barite dissolution scenarios are shown in Fig. 3.6, focusing on the North Pacific Ocean where
seawater becomes supersaturated with respect to barite at intermediate depths, which might influence
barite dissolution rates and dissolved Ba distributions.
We first investigate the scenario with a constant dissolution rate. Our optimized rate constant results
in 0.03% dissolution per meter as barite sinks in the water column. When this rate constant is set to 0 or de-
creased 5-fold, barite dissolution becomes zero or lower in the water column and higher at sediments com-
pared to the control run, resulting in underestimated dissolved Ba concentrations at intermediate depths
and overestimated dissolved Ba concentrations near the seafloor (Fig. 3.6a-c). When the rate constant is
increased 5-fold, barite dissolution occurs more intensely below the euphotic zone, leading to an overaccu-
mulation of dissolved Ba in the upper ocean (Fig. 3.6a-c). These tests suggest that the optimized dissolution
rate constant provides a good constraint on this rate parameter, and that modifications could lead to larger
model deviations from observations.
The control run assumes that barite dissolves at a constant rate, but this seems counterintuitive since
mineral dissolution kinetics indicate that the dissolution rate is dependent on the saturation index of the
mineral. While the control run fits well with observed dissolved Ba data, it is worth exploring the potential
relationship between barite dissolution rate andΩ barite
. To investigate this, we simulate the model again
following Eq. 3.5, where dissolution rate is a function of the degree of undersaturation (1 -Ω barite
), based
on the two sets of calculatedΩ barite
(for pure barite and Sr-barite). Assuming pure barite, the seawater is
supersaturated at intermediate depths in the North Pacific Ocean, resulting in no water column dissolution
within this depth range (Fig. 3.6e). Consequently, the modeled dissolved Ba concentrations at this depth
are underestimated, indicating insufficient input flux to the dissolved Ba pool (Fig. 3.6d). Incorporating Sr
82
Constant dissolution
W: pure barite
W: Sr-barite
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure3.6 Sensitivity tests comparing the effects of different barite dissolution scenarios on dissolved Ba
(dBa) distributions. The data presented here are from the North Pacific Ocean, where barite saturation
states might influence dBa most significantly. (a-c) The constant dissolution scenario, where the control
run dissolution rate constant is optimized to k
d
, and three sensitivity tests are plotted against the control
run which set dissolution rate constant to 0 (blue),k
d
/5 (purple), andk
d
×5 (red). (d-f) Barite dissolution rate
is formulated as a function of pure barite saturation state, with the reaction order (n) set to 1 (orange) or
allowed to optimize (green). (g-i) Barite dissolution rate is formulated as a function of Sr barite saturation
state, with the reaction order (n) set to 1 (orange) or allowed to optimize (green). (a, d, g) Vertical profiles
of average dissolved Ba concentrations in the North Pacific Ocean. (b, e, h) Total water column barite
dissolution (in Gmol y
-1
) in the North Pacific Ocean. (c, f, i) Total sedimentary barite dissolution (in Gmol
y
-1
) in the North Pacific Ocean.
83
into the barite crystals increases barite solubility, which allows dissolution to occur in areas whereΩ barite
is greater than 1 assuming pure barite. In this case, barite dissolution can add to the dissolved Ba pool,
even though the low dissolution rate at intermediate depth is still observed (Fig. 3.6h). This suggests that
if barite dissolution is dependent onΩ barite
, the pelagic barite composition might be better represented by
incorporating Sr into pelagic barite. Another noteworthy point is that we tested two formulations of Eq.
3.5, fixing the reaction order n = 1 or allowing the model to optimize n. Whenn = 1, which indicates a linear
correlation between dissolution rate and undersaturation, the model performance is worse than the control
run. When the reaction order n is allowed to optimize, the model approaches the good performance of the
control run, but n is optimized to a very small number (10
-7
) so that Eq. 3.5 (R
diss
=k
d
(1-Ω )
n
) mathematically
approaches Eq. 3.6 (R
diss
=k
d
). This indicates that the model favors the constant dissolution scenario, which
results in better model fit to observed dissolved Ba distributions, especially in the intermediate and deep
oceans.
The predicted constant barite dissolution rates cannot be solely explained by seawater chemistry. A po-
tential explanation is the incorporation of barite particles into organic matter aggregates, which inhibits
the exposure of barite to undersaturated waters, resulting in barite dissolution rates not being directly
linked to ambient seawater undersaturation degree. An alternative explanation proposes the presence of
a diffusive boundary layer (DBL) enveloping the barite particles, creating a chemically uniform microen-
vironment. This microenvironment can act as a barrier, impeding direct interactions between the barite
particles and the surrounding bulk seawater. The existence of the DBL has been reported on the surface of
marine organisms and applied to particle microenvironment models (Bianchi et al., 2018; Cornwall et al.,
2013; Hendriks et al., 2017; Houlihan et al., 2020; Ploug et al., 1999, 2002). If barite dissolution indeed
occurs within this micro-layer, the dissolution rate would be dictated by the chemical conditions within
the DBL, rather than the saturation state of surrounding seawater.
84
3.3.6 TheglobalpelagicbaritecyclecalculatedfromthedissolvedBamodel
Our control run model shows a good agreement with the dissolved Ba data from GEOTRACES IDP2021,
which validates the accuracy of the modeled biogeochemical mechanisms. The dissolved Ba pool is mainly
regulated by the barite cycle, where the precipitation and dissolution of pelagic barite play crucial roles,
rather than the biological uptake and remineralization of dissolved Ba. The predicted global barite pre-
cipitation rate is 77 Gmol y
-1
, with 62% of barite dissolving in the water column as particulate Ba sinks
and the remaining 38% dissolving at the seafloor (Table 3.2). Because our closed-system model does not
consider barite burial in the sediment, the fraction of barite dissolving at different locations in the real
ocean could differ from our model results. Nonetheless, our model suggests that most barite dissolves in
the water column, as opposed to previous calculations which suggest a higher fraction of barite dissolving
at the sediment-water interface (Paytan & Kastner, 1996). Applying a slower water column dissolution
rate leads to poorer model performance, as evidenced by our dissolution sensitivity tests (Fig. 3.6a).
Generally, barite precipitation is most intense below the euphotic zone and decreases rapidly with
depth, facilitated by organic matter respiration and following the Martin curve in our model simulation.
This results in 90% of precipitation occurring in the upper 900 m of the ocean (Fig. 3.7a-b), which agrees
with previous observations that most barite precipitation occurs at shallow depths (Bates et al., 2017;
Horner et al., 2015). Barite dissolution occurs mostly in the water column, although sedimentary dissolu-
tion contributes more Ba to the benthic waters (Fig. 3.7c).
The control run model, which assumes constant barite dissolution rate and constant settling veloc-
ity, effectively reproduces observed dissolved Ba concentrations in global oceans. However, the simplified
representation of constant sinking speed prompts us to conduct sensitivity analyses exploring alternative
parameterizations of barite settling rates (Section 3.2.6.4). Incorporating a scenario where particle settling
rates increase linearly with depth, the simulated dBa concentrations show slightly less agreement with
observations compared to the control run, especially in the Pacific Ocean (Fig. 3.8b). The key difference
85
90% precipitation occurs
in the upper 900 m
(a) (b) (c)
Figure3.7 Global pelagic barite precipitation and dissolution calculated from the mechanistic model con-
trol run results. (a) Vertical profile of total pelagic barite precipitation rate variations with depth (Gmol
y
-1
). (b) The fraction of barite precipitation accumulated with depth. The model results show that 90%
of barite precipitation occurs in the upper 900 m. (c) Vertical profile of total pelagic barite dissolution
rate variations with depth (Gmol y
-1
), with water column dissolution (yellow) and sedimentary dissolution
(green) displayed separately.
lies in the predicted barite dissolution pattern, with pronounced water column dissolution occurring in
the upper ocean where barite sinks slowly (Fig. 3.8b). However, the overall water column dissolution ac-
counts for 68% of the total barite dissolution, similar to the predicted percentage of 62% from the control
run, suggesting less sedimentary dissolution compared to the water column dissolution. Another test in-
volving the separation of barite into small and large particles also exhibits a distinct dissolution pattern
compared to the control run, where water column dissolution is predominantly driven by small particles
that dissolve in the upper ocean. In contrast, sedimentary dissolution increases to contribute 55% of the
total barite dissolution, attributed to the rapid sinking of large particles that experience little water col-
umn dissolution before settling on the seafloor (Fig. 3.8f). Although these two sensitivity experiments on
particle sinking speed offer more realistic representations than assuming constant settling rates, they do
not achieve a better fit to observed dBa distributions (Fig. 3.8a-c), making it not convincing to suggest that
these sinking scenarios better represent the barite cycle in the ocean. However, the differing predictions of
barite dissolution patterns from these tests warrant careful examination (Fig. 3.8d-f), particularly in terms
86
of the percentage of barite that can survive water column dissolution. This aspect holds particular interest
when utilizing barite sedimentation rates to estimate paleoproductivity.
By integrating both precipitation and dissolution calculations, the simulated pelagic barite flux exhibits
a characteristic pattern of increasing from the base of the euphotic zone to the maximum level at about
250 m, followed by a subsequent decrease with depth. This observed trend holds true across all three
tests that consider different barite sinking velocities (Fig. 3.8g-i). Notably, this increasing-then-decreasing
barite flux pattern is consistent with measurements of particulate Ba concentrations (Light & Norris, 2021;
Martinez-Ruiz et al., 2019). However, this prediction of barite flux contradicts findings from a previous
sediment trap study that collected particulate Ba below 1000 m, which revealed an increase of particulate
Ba fluxes with depth (Dymond & Collier, 1996). The reason behind this discrepancy remains unknown,
and further investigation is required to understand the underlying factors contributing to this difference
between models and observations.
3.3.7 AcomparisonbetweenthemarinedissolvedBaandSicycles
Similarities between the marine Ba and Si distributions have been be observed across global oceans, as evi-
denced by a strong linear relationship between their concentrations (R
2
= 0.92) (Fig. 3.9a). This correlation
implies a potential connection between these two elements within the ocean. However, the underlying
biogeochemical mechanisms governing their cycles are distinct, leaving the reasons for their linear rela-
tionship largely unexplained.
A hypothesis proposes that the resemblance between the distributions of Si and Ba is primarily influ-
enced by large-scale ocean circulation patterns (Horner et al., 2015). To test this hypothesis, a comparative
analysis of preformed Ba and Si concentrations would be necessary. We have calculated the preformed
and regenerated Ba and Si concentrations using the method outlined in Carter et al. (2021), with the global
dBa distribution from our control run model results and the global dSi distribution from World Ocean
87
Constant sinking rate (v)
Sinking rate (v)
linearly related to depth
50% small particles
50% large particles
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure3.8 Comparison of three models investigating the influence of barite sinking rate (v) on the marine
Ba model, including the constant sinking rate scenario (left column), a linear increase in sinking rates
with depth (middle column), and assuming the particles are composed of 50% small particles and 50% large
particles which sink 100 times faster than the small particles (right column). (a-c) The average dissolved
Ba concentrations as predicted by the three models, compared with GEOTRACES dBa observations. (d-
f) Vertical profiles of global total barite dissolution rates, estimated from the three models with different
barite sinking velocities. (g-i) The calculated global average pelagic barite fluxes at various depths.
88
(a) (b) (c)
(d) (e) (f)
Figure3.9 Comparison between marine dissolved Ba and Si. The dBa data are from our control run, while
the dSi data are sourced from World Ocean Atlas 2009. (a-c) Joint probability density function plots of (a)
total dBa and dSi, (b) preformed dBa and dSi, and (c) regenerated dBa and dSi. A linear regression analysis
is applied to show the linear relationship of the two datasets (dashed line), withR
2
and root-mean-square-
error (RMSE) calculated for each pair of datasets. (d-f) Average vertical profiles of dBa (red) and dSi (blue)
concentrations, along with the tracer Ba* (green) in the (d) Atlantic, (e) Pacific, and (f) Southern Oceans.
Dashed black lines indicate concentrations equal to zero, providing clarity on whether Ba* is negative or
positive at each depth.
89
Atlas 2009 data. Remarkably, both the preformed and regenerated Ba concentrations exhibit a strong lin-
ear relationship with Si (R
2
= 0.89 and 0.87, respectively) (Fig. 3.9b-c). Notably, the preformed dBa and
dSi concentrations display a more pronounced linear shape, characterized by higher R
2
values and lower
root-mean-square-errors compared to the regenerated components, suggesting a larger contribution of
large-scale ocean circulation in driving the linear relationship between dBa and dSi. The regenerated Ba
and Si concentrations also demonstrate similarities, suggesting that the remineralization of barite and silica
occurs at comparable depths in the ocean.
Another hypothesis proposed to explain the resemblance between dBa and dSi distributions involves
the roles of diatoms. The cycling of Si is largely controlled by diatoms, which utilizes silicic acid to pro-
duce shells (Hamm et al., 2003). If diatoms also play a significant role in controlling the cycling of Ba in the
ocean, the observed similarity between these two elements is plausible. To investigate this hypothesis, a
closer examination of the Southern Ocean, where diatoms are prevalent, would be warranted. When com-
paring the vertical profiles of Southern Ocean [dBa] and [dSi], substantial variations are observed, with dSi
displaying greater depth variations compared to dBa (Fig. 3.9f). To further analyze the deviations between
Ba and Si, a tracer Ba*, adapted from Horner et al. (2015), is calculated based on the linear relationship
between the global average dBa and dSi concentrations as Ba* = [dBa] – 0.54[dSi] – 40.85. This tracer, Ba*,
reflects the deviations of Ba concentrations relative to Si. The surface Southern Ocean is characterized
by positive Ba*, indicating a preferential precipitation of silica. Conversely, the deep Southern Ocean is
characterized by generally negative Ba*, reflecting preferential silica dissolution. This vertical pattern sug-
gests that the Ba cycle is not as strongly influenced by diatoms as the Si cycle, pointing to a mechanistic
decoupling of the Ba and Si cycles. In contrast, positive Ba* values in the deep Atlantic and Pacific Oceans
suggest a greater prevalence of barite dissolution relative to SiO
2
dissolution at these depths (Fig. 3.9d-e).
Therefore, the observed similarities between the marine Ba and Si cycles cannot be primarily attributed
to the role of diatoms. Instead, we emphasize the significant influence of large-scale ocean circulation
90
and, to a lesser extent, the remineralization length scale of barite and silica minerals in driving the global
distributions of these two elements. By exploring these different angles, our understanding of the physical
and biogeochemical controls driving the distribution and cycling of dissolved Ba and Si in the global oceans
can be advanced.
3.3.8 ImplicationsofthewatercolumnBachemistryforutilizingBaasapaleoproductivity
proxy
Ocean dissolved and particulate Ba are often employed as tracers of ocean biogeochemical processes. Our
closed-system model ignores barite burial, which limits its ability to reconstruct export production through
sedimentary records. Nonetheless, other factors, including the uptake and release of Ba by marine organ-
isms, as well as the precipitation and dissolution of barite, can complicate the use of Ba as a proxy. Hence,
a better understanding of the Ba chemistry in the water column is necessary for the accurate utilization of
Ba as a paleoproductivity proxy and interpretation of past ocean conditions.
To investigate the relationship between surface export productivity and barite sedimentation rate, we
have performed two tests that adjust the export productivity to be either half or double of the control
run. Although burial is not considered in our closed-system model, we are able to estimate the amount
of barite particles falling on the seafloor which survive water column dissolution. When the export is
halved, the amount of barite particles reaching the seafloor is 39% lower than in the control run. When
the export is doubled, the amount of barite reaching the seafloor increases by 49% compared to the control
run. It is important to note that these results assume that barite dissolution rates remain consistent with
the control run. These results demonstrate a positive correlation between barite sedimentation rate and
export productivity; however, the relationship is not strictly proportional in this simplified experiment.
This points to the importance of comprehending the processes that influence barite behavior in the water
column, particularly when investigating paleo-oceans where seawater chemistry may significantly differ
91
from that of the modern ocean. Employing barite sedimentation rates as a proxy for paleoproductivity
necessitates a thorough understanding of barite dissolution in the water column.
We have examined various factors that affect the marine dissolved Ba cycle, with a focus on the effects
of pelagic barite. Our model supports the correlation between barite precipitation and organic matter res-
piration, which potentially links barite variations in sedimentary records to organic remineralization rates
in paleo oceans. Barite forms in the upper ocean and sinks, with only those particles that survive disso-
lution preserved in sedimentary records. The control run suggests a relatively constant dissolution rate
of barite in seawater, with most dissolution occurring in the water column and less at the seafloor. This
information can help us understand how barite may have dissolved in the past, and how these patterns
may have varied across different oceanic regions and geological time periods. Furthermore, by study-
ing the dissolution patterns of barite in the modern ocean, we can improve our ability to evaluate barite
as a paleoproxy for reconstructing past ocean export productivity and carbon cycling, and gain a more
comprehensive understanding of past environmental conditions in the ocean.
3.4 Conclusions
This study develops the first global three-dimensional ocean Ba model, providing a more comprehen-
sive understanding of the marine Ba cycle through modeling approaches, particularly the distribution of
dissolved Ba and the biogeochemical processes that regulate it. Our model results suggest that ambient
seawater Ba is the primary source of Ba to precipitate pelagic barite, whereas the amount of Ba sourced
from organic matter is negligible. Besides, by investigating the dissolution of barite particles as they sink
through the water column, we find that barite dissolution occurs more in the water column than at the
seafloor, and that water column barite dissolution rates are relatively independent of the degree of barite
undersaturation. These findings highlight the importance of pelagic barite in regulating dissolved Ba, and
92
shed light on the biogeochemical mechanisms that govern the formation and dissolution of barite parti-
cles in the ocean. Moving forward, the knowledge gained from this study on the modern ocean global Ba
cycle can inform future research on the changes in barite distribution and abundance over time, which can
provide valuable insights into past ocean chemistry and circulation. Besides, future studies may utilize Ba
isotopes to constrain the biogeochemical processes discussed in this study, including barite precipitation
and dissolution.
93
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
SupplementaryFigure3.1 Global pelagic barite precipitation, dissolution, and fluxes calculated from the
mechanistic model control run results. (a) Vertical profile of total pelagic barite precipitation rate variations
with depth (Gmol y
-1
). (b) The fraction of barite precipitation accumulated with depth. The model results
show that 90% of barite precipitation occurs in the upper 900 m. (c) Vertical profile of total pelagic barite
dissolution rate variations with depth (Gmol y
-1
), with water column dissolution (yellow) and sedimentary
dissolution (green) displayed separately. (d) The pelagic barite flux calculated at each depth (mol m
-2
y
-1
).
94
MLR GPR Decision Tree SVM ANN
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
Supplementary Figure 3.2 Predictions of Ba concentrations using five machine learning algorithms.
(a,f) Multiple linear regression (MLR). (b,g) Gaussian process regression (GPR). (c,h) Decision tree. (d,i)
Support vector machine (SVM). (e,j) Artificial neural network (ANN). Ba data from the Atlantic and Pacific
Oceans are plotted in blue and red, respectively. (a-e) Train the algorithm using Atlantic data, then validate
the model with Pacific data. (f-j) Train the algorithm using Pacific data, then validate the model with
Atlantic data. The dashed lines indicate the 1:1 line, and the deviations of data points from this line suggest
inaccurate predictions of the data. The R-squared (R
2
) values for each group of data are listed in each
subplot. Note that the MATLAB artificial neural network algorithm can produce different results every
time due to the random initialization of the weights and biases in the neural network.
95
(a) (b)
(c) (d)
(e) (f)
SupplementaryFigure3.3 Average vertical composite profiles of dissolved Ba concentrations in differ-
ent ocean basins. The black data points with error bars are average dissolved Ba concentrations from
GEOTRACES IDP2021 with 1 standard deviation, while the purple lines are the average modeled Ba at the
same sampling locations. (a) North Atlantic Ocean. (b) South Atlantic Ocean. (c) North Pacific Ocean. (d)
South Pacific Ocean. (e) Arctic Ocean. (f) Southern Ocean.
96
(a) (b)
(c) (d)
(e) (f)
(g) (h)
SupplementaryFigure3.4 Observed vs. modeled dissolved Ba concentrations along four GEOTRACES
cruises. (a-b) GA03 cruise (west leg). (c-d) GA02 cruise. (e-f) GP16 cruise. (g-h) GP15 cruise. The left col-
umn shows the dissolved Ba concentrations ([dBa]), with color field indicating model predictions and filled
circles indicating observations. The right column shows the differences between model and observations
at the sampling locations, with color bars representing the predicted Ba minus observed Ba.
97
Chapter4
TowardaBetterUnderstandingoftheGlobalOceanCopper
DistributionandSpeciationthroughaData-constrainedModel
Abstract
Copper (Cu) is an important micronutrient for marine organisms which can also be toxic at elevated
concentrations. Here we present a new model of global ocean Cu biogeochemical cycling, constrained by
GEOTRACES observations, with key processes including sources from rivers, dust, and sediments, biolog-
ical uptake and remineralization of Cu, reversible scavenging of Cu onto sinking particles, conversion of
Cu between labile and inert species, and ocean circulation. In order for the model to match observations, in
particular the relatively small increase in Cu concentrations between the deep Atlantic and Pacific basins
along the global ‘conveyor belt’, we find it is necessary to include significant external sources of Cu with
a magnitude of roughly 1.3 Gmol y
-1
, having a relatively stronger impact on the Atlantic, though the rela-
tive contributions of river, dust, and sediment sources are poorly constrained. The observed nearly linear
increase in Cu concentrations with depth requires a strong benthic source of Cu, which includes the sed-
imentary release of Cu that was reversibly scavenged from the water column. The processes controlling
Cu cycling in the Arctic Ocean appear to be unique, requiring both relatively high Cu concentrations in
Arctic rivers and reduced scavenging in the Arctic. Observed partitioning of Cu between labile and inert
phases is reproduced in the model by the slow conversion of labile Cu to inert in the whole water column
98
with a half-life of∼ 250 years, and the photochemical degradation of inert Cu to labile in the surface ocean
with a minimum half-life of∼ 2 years at the equator.
4.1 Introduction
Copper (Cu) is a bioessential trace metal required for phytoplankton growth, though it can also become
toxic at high concentrations (Brand et al., 1986; Moffett et al., 1997). The biological roles of Cu include
facilitating iron (Fe) uptake by diatoms (Maldonado et al., 2006), regulating denitrification in the nitrogen
cycle through a Cu-containing nitrous oxide reductase (Granger & Ward, 2003), and facilitating electron
transport during photosynthesis through Cu-containing plastocyanin (Peers & Price, 2006). In addition to
biological uptake and remineralization, the reversible scavenging of Cu onto sinking particles has been
proposed to strongly influence Cu distributions in the ocean (Boyle et al., 1977; Bruland & Lohan, 2006;
Craig, 1974). The global ocean inventory of Cu is regulated by the balance between external sources of Cu
from rivers, aerosols, and sediments, and removal by Cu burial in the sediments. However, uncertainties
in the estimates of both Cu input and output fluxes make it difficult to constrain the residence time ( τ res
)
of oceanic Cu, with estimates from previous studies varying by an order of magnitude, between 400 and
6,400 years (Boyle et al., 1977; Little et al., 2014, 2017; Richon & Tagliabue, 2019; Roshan et al., 2020; Takano
et al., 2014).
Despite prior efforts, several key features of the oceanic Cu cycle remain incompletely explained. A
unique feature of the marine Cu distribution is the shape of its vertical profiles. Unlike other trace metals
which have “nutrient-like” profiles (e.g. Fe, Zn, Cd), or elements with “scavenged-type” profiles (e.g. Al,
Co), Cu concentrations throughout the ocean increase in a nearly-linear fashion with depth. Some studies
have attributed this feature to reversible scavenging (Little et al., 2013; Richon & Tagliabue, 2019), while
other studies have emphasized the potential importance of a sedimentary source of Cu that sustains high
99
Cu concentrations at depth, based upon both models and analyses of near-sediment samples (Boyle et al.,
1977; Roshan et al., 2020; Takano et al., 2014).
The complexation of Cu by strong organic ligands is also a unique, and potentially important, feature
of marine Cu biogeochemistry (Ruacho et al., 2022). More than 99% of Cu in the surface ocean is bound
by organic ligands (Buckley & van den Berg, 1986; Coale & Bruland, 1988), while free Cu (Cu
2+
), which
is the most bioavailable and toxic species, only accounts for a small portion of the dissolved Cu pool.
Previous experimental studies have suggested that in addition to Cu
2+
, weakly complexed Cu can also
be utilized by phytoplankton (Semeniuk et al., 2015). Depending on whether Cu is complexed and the
binding strength of the ligands, dissolved Cu is often classified as Cu
2+
, weakly-complexed Cu ligands
(CuL2), and strongly-complexed Cu ligands (CuL1) (Moffett et al., 1990). One known organic chelator
source is biological production of strong extracellular Cu ligands by marine phytoplankton in response
to high Cu concentrations for detoxification (Croot et al., 2000; Moffett & Brand, 1996). In addition to
assessing ligand strength, previous studies have also attempted to determine whether Cu is kinetically
‘labile’ or ‘inert’ by performing competing ligand exchange experiments where the competitive ligand
is present at such high concentrations that it captures all of the Cu released from natural ligands. The
remaining non-exchangeable fraction can be considered inert (Kogut & Voelker, 2003). Recent analyses
on samples from the North Atlantic and North Pacific Oceans show that 60-90% of Cu exists in an inert
form, suggesting that most of the dissolved Cu in seawater is not bioavailable or actively exchanging with
binding sites on particles (Moriyasu & Moffett, 2022; Moriyasu et al., 2023).
Several modeling studies in recent years have explored the biogeochemical cycling of Cu on regional
and global scales. Using a one-dimensional model, Little et al. (2013) suggested that reversible scaveng-
ing is the major control of the linear vertical shape of Cu profiles, though this model ignored the effects
of ocean circulation and biological processes, which may limit its applicability to representing the real
ocean. Takano et al. (2014) determined Cu concentrations and isotopic compositions in several aquatic
100
reservoirs, and used this data to construct a four-box model of marine Cu. This simple box model provided
global-scale estimates of Cu fluxes based on mass balance calculations, but lacked detailed information for
regional studies. Richon and Tagliabue (2019) published the first three-dimensional Cu model using the
NEMO/PISCES global model, and again emphasized the importance of reversible scavenging on the verti-
cal profile of Cu, while also showing that organically-complexed Cu in addition to Cu2+ must be at least
partly bioavailable to support surface biological activity. Roshan et al. (2020) adopted an artificial neural
network approach to predicting global Cu concentrations, combined with an Ocean Circulation Inverse
Model (OCIM) to diagnose important global Cu fluxes. Without modeling specific biogeochemical mech-
anisms, their diagnostic modelling approach was used to predict the spatial locations where Cu is added
to and removed from the dissolved phase in the oceans. A key finding of this work was a large input of
Cu from the sediments, supporting the hypothesis that a benthic source of Cu contributes to the gradual
increase of Cu concentrations with depth. Recently, Cui and Gnanadesikan (2022) built a closed-system
model of global Cu cycling using the AWESOME OCIM framework (John et al., 2020) to simulate the global
distribution of Cu. Based on the strong correlation between Cu and Si in the oceans, as well as the higher
uptake stoichiometry of Cu:P in the Southern Ocean, they suggested that diatoms are the dominant species
that utilizes Cu in the oceans. However, the lack of external sources and sinks limits the applicability of
the model to exploring regional-scale patterns in Cu distribution.
Building on previous work, we present here a new three-dimensional model which aims to further con-
strain the sources, sinks, and internal cycling of Cu in the ocean, while exploring the specific mechanisms
which are most important to setting the global ocean distributions of Cu. Using tools from the AWESOME
OCIM (John et al., 2020), we have constructed a mechanistic model of global Cu cycling. We first describe
the modeling framework and observational datasets used in this study (Section 4.2), and present model-
data comparisons and flux estimates (Section 4.3). We then discuss the key findings of this modeling work,
as well as the uncertainties and limitations of this model (Section 4.4), including a comparison of closed-
101
and open-system Cu models, an evaluation of the importance of each external source, a summary of the
processes which contribute to the nearly-linear vertical Cu profiles, possible particle types onto which Cu
may be reversibly scavenged, unique features of Cu cycling in the Arctic Ocean, and the partitioning of
Cu into labile and inert phases.
4.2 Methods
4.2.1 Observationaldatasets
Seawater Cu concentrations were first measured in the 1970s (e.g. Bender and Gagner, 1976; Boyle et
al., 1977; Moore, 1978) and have grown more common in the following decades with the advances in
modern trace metal clean techniques for sampling and analysis. For this study, we utilize the most recent
dataset from the GEOTRACES program, Intermediate Data Product 2021 (IDP2021), which compiles high-
quality dissolved Cu concentration data from the Pacific, Atlantic, Indian, Arctic, and Southern Oceans
(GEOTRACES, 2021). This global coverage allows for a comprehensive study of Cu biogeochemistry in
different marine environments and serves as a powerful tool for constraining the marine Cu model.
Labile Cu concentrations were determined on seawater samples collected during the GP15 and GA03
cruises as part of the GEOTRACES program in the Pacific and Atlantic Oceans, respectively, and were
assessed for labile Cu concentrations using oxine as a strong competing ligand (Moriyasu & Moffett, 2022;
Moriyasu et al., 2023). Inert Cu concentrations are calculated by difference based on total dissolved Cu and
labile Cu concentrations. Total dissolved Cu concentration data from the GP15 cruise are obtained from
John (2022a, 2022b), which were not included in the GEOTRACES IDP2021. We use the labile Cu data from
GP15 samples as optimization datasets to train the model (see Section 4.2.3), and GA03 labile Cu data as
validation datasets to evaluate model performance.
102
4.2.2 Modelframework
The model was built using tools provided in the AWESOME OCIM (AO) (John et al., 2020), as well as
additional mechanisms and functions developed specifically for this model. The water transport matrix is
derived from the Ocean Circulation Inverse Model (OCIM 1.0), with a 2° × 2° horizontal resolution and 24
depth layers (DeVries, 2014; DeVries & Primeau, 2011). Labile and inert Cu are modeled as two separate
tracers, with conversions between the two forms of dissolved Cu. The general equations to solve global
steady-state labile Cu (Cu
L
) and inert Cu (Cu
I
) distributions are:
dCu
L
dt
=T[Cu
L
]− J
up
+J
rem
+J
scav
+J
hv
− J
bind
+J
riverL
+J
dust
+J
neph
(4.1)
dCu
I
dt
=T[Cu
I
]− J
hv
+J
bind
+J
riverI
(4.2)
Here, T is the OCIM water transport matrix, which is multiplied by the tracer concentration to rep-
resent the ocean circulation of the tracer, and J denotes biogeochemical processes that add or remove
the tracer from seawater. The ocean Cu cycle is illustrated in Fig. 4.1, with each biogeochemical process
described in more details below.
The term J
up
represents the biological uptake of labile Cu by marine phytoplankton in the euphotic
zone, governed by:
J
up
=βJ
up− P
[Cu
L
] (4.3)
where J
up-P
is the phosphorus (P) uptake rate in the surface ocean taken from a previous P model (Weber
et al., 2018), andβ is an optimizable rate constant to reflect the relative uptake rate of labile Cu compared to
P. Thus, Cu uptake rates are positively correlated with the total growth of phytoplankton (as reflected by
J
up-P
), and cellular Cu:P ratios increase linearly with ambient bioavailable Cu concentrations, as observed
103
Mineral dust
Nepheloid layer
Labile Cu Inert Cu
hv
Labile Cu Inert Cu
binding by
strong ligands
phytoplankton
uptake
remineralization
particles
reversible
scavenging
River
(90% inert + 10% labile)
circulation
circulation
Figure4.1 Key processes in the marine biogeochemical cycling of Cu. The dashed black line indicates the
base of the euphotic zone. Total dissolved Cu is comprised of kinetically labile Cu and inert Cu pools. The
labile Cu is actively involved in biogeochemical processes, including biological uptake by phytoplank-
ton followed by remineralization (green arrows), and reversible scavenging onto particles (red arrows).
Upon reaching the seafloor, a fraction of the biogenic and scavenged labile Cu remineralizes, while the
remaining fraction is buried in the sediments. Labile Cu is converted to inert Cu by strong organic ligand
binding throughout the water column, while inert Cu is converted back to labile Cu in the euphotic zone
through photodecomposition. External sources of Cu to the ocean include rivers (which are assumed to be
composed of 90% inert Cu and 10% labile Cu), dust (entirely labile Cu), and a dissolved flux coming from
nepheloid layer particles (entirely labile Cu).
104
in culture experiments (Sunda & Huntsman, 1995). The model assumes that net biological uptake only
occurs in the euphotic zone (sea surface to 73 m), followed by remineralization below 73 m described as:
J
rem
=− ∂
∂z
F
CuL
(4.4)
where J
rem
refers to the remineralization of Cu from organic materials during gravitational sinking and z
indicates depth (in meters). Remineralization is proportional to surface export and the fraction of export
that gets remineralized within each model layer. The vertical fluxes of particulate matter associated with
labile Cu (F
CuL
) attenuate with depth following the classic Martin curve with an exponent b value of 0.86
(Martin et al., 1987). As the biogenic particles reach the seafloor, the Cu contained in the particles may
either get buried, or be remineralized back into the overlying water column. The fraction of particles
that remineralize at the sediment-water interface is represented in the model as an optimizable parameter
f
sed
, which can be set between 0 and 1, indicating 100% burial and 100% sedimentary remineralization,
respectively.
The reversible scavenging flux of labile Cu is described as:
J
scav
=− ∂
∂z
(Kv[Cu
L
]) (4.5)
whereK is the equilibrium scavenging constant which represents the fraction of labile Cu that is adsorbed
onto particles, and v is the particle sinking speed which is set to 700 m y
-1
. As scavenged Cu reaches
the sediments, a fraction is remineralized and released back into the overlying water column, which is
determined by f
sed
, similar to the process described for biological uptake.
UV oxidation has been shown to damage strong Cu-complexing ligands, thus producing more free
cupric ions available for primary production (Laglera & van den Berg, 2006; Moffett & Zika, 1987; Moffett
et al., 1990; Shank et al., 2006). The photodecomposition of strong Cu ligands is described in the model
105
by converting inert Cu to labile Cu in the euphotic zone (top 73 m), at a rate which is dependent on the
amount of solar radiation and the inert Cu concentration. The inert Cu decomposition rate constant is
assumed to reach the maximum value at the equator with most sunlight (k
eq
), and decreases following the
cosine of latitude, so at poles where the cosine of 90° is zero, photodegradation is reduced to zero. This
process (J
hv
) is thus described as:
J
hv
=k
eq
cos(latitude)[Cu
I
] (4.6)
with k
eq
being an optimizable model parameter that scales the maximum inert Cu photodegradation rate.
Other factors, such as cloudiness and water clarity, could also affect the photodegradation rate of inert Cu
in surface seawater. However, due to their complex nature and the potential for unnecessary complications,
we have opted to maintain the simplicity of Eq. 4.6 by not incorporating them.
Labile Cu is converted to inert Cu by complexation with dissolved organic matter, which is assumed to
happen everywhere in the ocean as a first-order reaction. With an optimizable model parameter t
1/2
, which
denotes the half-life of labile Cu, the formation of Cu
I
(which is matched by a loss of Cu
L
) rate constantλ can be calculated. The complexation of labile Cu by strong ligands is given by:
J
bind
=λ [Cu
L
]=
ln2
t
1/2
[Cu
L
] (4.7)
which results in the conversion of Cu
L
to Cu
I
.
Cu is delivered to the ocean by several external sources, impacting both the total marine Cu inventory
and the distribution of Cu within the oceans. Previous studies have suggested three major Cu sources, from
rivers, atmospheric dust, and sediments, while other possible sources such as hydrothermal fluids seem to
have little influence on the global scale (Boyle et al., 1977; Gerringa et al., 2020; Little et al., 2013; Richon
& Tagliabue, 2019; Roshan et al., 2020; Ruacho et al., 2020; Takano et al., 2014). In this model, the riverine
106
Cu flux estimates are based on 23 major rivers around the world with large discharge to the oceans, and
the riverine Cu fluxes are calculated as the discharge of each river multiplied by the average riverine Cu
concentration. Riverine inert Cu has only been measured in the Columbia River, where it is greater than
90% of total dissolved Cu (Moriyasu et al., 2023). Based on this single (albeit large) river, we assume 90%
of the dissolved Cu entering the ocean from rivers is inert and the other 10% is labile. The riverine fluxes
of Cu to the ocean are thus:
J
riverL
=0.1[Cu]
river
Q
river
V
grid
(4.8)
J
riverI
=0.9[Cu]
river
Q
river
V
grid
(4.9)
where J
riverL
and J
riverI
are the riverine fluxes of labile and inert Cu, respectively. The optimizable term
[Cu]
river
represents the average dissolved Cu concentration in rivers. The termQ
river
denotes the discharge
of each river in m
3
y
-1
, whileV
grid
represents the volume of the ocean model grid cell (in m
3
). Mineral dust
deposition data (F
dust
) are originally from Brahney et al. (2015) and Chien et al. (2016), converted to the
unit of mg m
-3
y
-1
in AWESOME OCIM. Soluble aerosol Cu fluxes ( J
dust
) are calculated by multiplying
F
dust
by an optimizable soluble-Cu to dust flux ratio ( R
Cu:dust
). A similar method is applied to estimate the
input of Cu from benthic nepheloid layer particles (J
neph
), with an optimizable ratio of the Cu flux to the
mass of resuspended particles (R
Cu:particle
), while the particle concentration data (F
particle
) are obtained from
Gardner, Richardson, and Mishonov (2018) and Gardner, Richardson, Mishonov, and Biscaye (2018). The
dust and nepheloid layer input data have been re-gridded to fit the OCIM resolution (John et al., 2020), and
we assume these two sources deliver Cu to the ocean in the labile form following Eq. 4.10 and Eq. 4.11:
J
dust
=F
dust
R
Cu:dust
(4.10)
J
neph
=F
particle
R
Cu:particle
(4.11)
107
4.2.3 Optimization
The model optimization process searches for the set of model parameters which best simulate global Cu
distributions. The optimizable model parameters have been described in Section 4.2.2 and listed in Table
4.2. The best solution is found by minimizing a cost function, defined as the volume-weighted misfit
between model-predicted and observed Cu data:
cost=Σ n
i=1
w
i
([Cu]
model,i
− [Cu]
obs,i
)
2
+Σ m
i=1
w
i
([Cu
L
]
model,i
− [Cu
L
]
obs,i
)
2
(4.12)
where w
i
is the volume weight of the i
th
model grid cell. The observed total dissolved Cu concentration
data ([Cu]
obs
) are from GEOTRACES IDP2021, and the observed labile Cu concentration data ([Cu
L
]
obs
)
are based on GP15 labile Cu measurements from Moriyasu et al. (2023), as described in Section 4.2.1. The
parameters n and m are the numbers of grid cells with total dissolved Cu and labile Cu observations,
equaling to 4312 and 152, respectively.
Optimization is accomplished used the MATLAB function fminsearch. The model-optimizable param-
eters are described along with the corresponding biogeochemical processes in Section 4.2.2. The optimiza-
tion is begun with a set of initial guesses of parameter values, which are estimated based on the ranges
constrained by prior lab studies or modeling simulations, then manually adjusted to achieve a reasonably
low cost, and sent to the fminsearch solver for the final optimization.
In some cases, the model is optimized subject to constraints on the values of certain parameters, using
the MATLAB function fmincon. This is because in some sensitivity experiments (details in Section 4.2.4),
setting one parameter at a fixed value and optimizing other parameters can lead to a final solution with
some optimized parameters reaching values beyond reasonable ranges. If one or more parameters make no
sense in the real ocean (e.g. if the model predicts a negative aerosol Cu source when the riverine Cu source
is forced at a very high level) after the first optimization with fminsearch, we use fmincon to optimize the
108
same model for the second time in order to constrain the model parameters within reasonable bounds. For
example, the external Cu sources must be no less than 0, and the sedimentary remineralization fraction
f
sed
should be between 0 and 1.
4.2.4 Sensitivitytests
Six groups of sensitivity analyses were conducted to assess the sensitivity of predicted global Cu distri-
butions to specific choices of model configuration and parameter values, as described below. In each case
the “sensitivity-test model” output is compared to the output of the model that is optimized as described
in Section 4.2.2, which is referred to as the “base model” in the following discussions.
4.2.4.1 Open-andclosed-systemmodels
The base model is an open-system model, in which the ocean exchanges Cu with the land, atmosphere, and
sediment. To evaluate the importance of the external sources and sinks to the global Cu distribution in the
ocean interior and at land-sea boundaries, we perform a model experiment similar to the base model, but
without any exchange between ocean and other environments. In this closed-system model, the marine
Cu distribution is only modulated by ocean circulation and internal biogeochemical processes including
biological uptake by phytoplankton and remineralization, reversible scavenging onto particles, and con-
versions between the labile and inert Cu phases. All of the Cu which reaches the seafloor with particles is
entirely remineralized at the sediment-water interface and recycled back to the overlying water in the dis-
solved phase, so that there is no burial to remove Cu out of the ocean system. Two additional optimizable
model parameters are added to this closed-system model compared to the base model: the mean concen-
trations of labile Cu and inert Cu. These mean concentrations are set by adding a very small Cu source
to each grid cell while removing Cu from each cell by a first-order loss on timescales of a million years,
109
an approach which effectively sets the total inventory of a tracer within the model without impacting the
internal distribution to any practical extent (John et al., 2020).
4.2.4.2 Inputfluxes
The optimized base model includes rivers, dust, and nepheloid layer particles as the three external sources
of oceanic Cu. Previous estimates of these input fluxes can vary by an order of magnitude (Table 4.1),
and therefore we have sought to learn whether our model can constrain the magnitude of these fluxes
with greater certainty. This was accomplished by adjusting the flux magnitude of each source. In each
sensitivity experiment, one of the three source fluxes is set to a multiple of its flux in the base model, using
scaling factors of 0.1, 0.2, 0.5, 1, 2, 5, and 10. We then re-optimize the model, allowing all other optimizable
model parameters including the other two source fluxes to vary, in order to minimize the cost function (Eq.
4.12). The goal of this sensitivity analysis is to check whether model performance is significantly degraded
as individual fluxes are decreased or increased, with a large degradation in model performance helping us
to constrain reasonable estimates of flux magnitudes.
4.2.4.3 TheimportanceofsedimentaryCufluxtogeneratinglinearprofiles
Previous work has focused on two different processes which may contribute to the linear increase in Cu
concentrations observed in the major ocean basins, a sedimentary input of Cu and reversible scavenging
of Cu onto sinking particles. We first look into the sedimentary Cu input, which consists of two compo-
nents, new Cu and regenerated Cu. New Cu is defined as the Cu released from the particles in the benthic
nepheloid layer which adds lithogenic Cu to the ocean system and serves as an external source. Regen-
erated Cu includes both the remineralization of biogenic Cu formed in the surface ocean which does not
remineralize in the water column but may remineralize within the sediments, and the release of scavenged
110
Table4.1 Estimates of global Cu inventory, input or output fluxes, and residence time of marine Cu from
previous literature and the base model of this study.The global Cu input or output flux data used in previous
literature are either based on measurements or from data compilation.
111
Cu which reaches the sediments with particles. We have therefore performed three separate tests to re-
move the benthic Cu source: 1) turning off the new Cu input by removing the nepheloid layer source, but
retaining a sedimentary source of Cu from regeneration of biogenic and scavenged Cu, 2) turning off the
regenerated Cu source by burying all particulate Cu reaching the seafloor, but retaining a new Cu source
from the nepheloid layer, and 3) turning off both new Cu and regenerated Cu sources so that there is no
benthic Cu input. If models without sedimentary inputs cannot reproduce the linear shape of Cu profiles
observed in the oceans, it suggests that the benthic source plays a key role in Cu vertical distributions.
4.2.4.4 Theimportanceofreversiblescavengingtogeneratinglinearprofiles
Scavenging is another process which has been suggested to greatly impact Cu vertical distribution in the
oceans. However, when including scavenging in a model, decisions must be made regarding the particle
types responsible for Cu scavenging. The base model assumes that Cu is reversibly scavenged onto a hy-
pothetical particle type that remains at a constant concentration throughout the water column, which is a
simplified yet unrealistic representation. Therefore, in addition to the base model assumption of globally
uniform reversible scavenging, we perform six sensitivity tests to evaluate the impact of various patterns
of scavenging: 1) no scavenging, 2) irreversible scavenging with a globally-uniform scavenging rate, 3)
irreversible scavenging onto particulate organic carbon (POC), 4) reversible scavenging onto POC, 5) re-
versible scavenging following the patterns of
230
Th scavenging, and 6) reversible scavenging following the
patterns of
231
Pa scavenging. Reversible scavenging onto POC assumes that POC attenuates with depth
following the Martin curve. The patterns of
230
Th and
231
Pa scavenging are based on the model simula-
tions of van Hulten et al. (2018) which takes into account two size classes and four particle types (POC,
biogenic silica, calcium carbonate, and lithogenic dust particles), and is implemented in the AWESOME
OCIM as described by John et al. (2022). For scavenging models 2-6, the scavenging process of Cu is opti-
mizable. The second and third scavenging sensitivity tests simply remove Cu either uniformly throughout
112
the ocean or in proportion to the abundance of POC, respectively. The fourth, fifth, and sixth scavenging
models allow for reversible scavenging of Cu, with the optimizable parameters reflecting Cu partitioning
between the dissolved phase and POC, a ratio of Cu to
230
Th scavenging sites on particles, and a ratio of
Cu to
231
Pa scavenging sites, respectively. The optimized Cu model outputs for all six scavenging types
are then compared with observed total dissolved Cu data as well as labile Cu concentration data, in order
to better understand which scenarios may represent Cu scavenging in the real ocean.
4.2.4.5 RiverinputandscavengingintheArcticOcean
A regional analysis is performed to explore the unique behavior of Cu in the Arctic Ocean. The distribution
of Cu in the Arctic is quite different from other ocean basins, being highest in the surface and decreasing
rapidly with depth in the shallow ocean, which has been previously attributed both to high riverine Cu
inputs to the surface Arctic and reduced scavenging (Charette et al., 2020; Jensen et al., 2022). We thus
perform three sensitivity tests to evaluate the importance of these two processes. The first test focuses
on Cu input from the four major rivers flowing into the Arctic Ocean (Ob, Yenisei, Lena, and Mackenzie
Rivers). While the base model optimizes the mean riverine Cu concentration for all of the world’s major
rivers, this sensitivity test allows for two separate parameters to be optimized, the mean concentration of
Cu in the four Arctic rivers, and the mean Cu concentration in the rest of the world’s rivers. Our second
test is to turn off reversible scavenging in the Arctic Ocean, while allowing the scavenging process to occur
in the rest of the oceans. The third test combines both adjustments, allowing the Arctic riverine Cu flux to
be optimized separately from other rivers, and turning off scavenging in the Arctic Ocean. Model outputs
from these three sensitivity tests are compared to GEOTRACES IDP2021 Cu data in the Arctic Ocean to
investigate whether these features could explain the unique Cu distribution observed in the Arctic Ocean.
113
4.2.4.6 ChemicalspeciationofdissolvedCuintheocean
The final sensitivity test was designed to investigate the effect of Cu kinetic lability on model performance.
In addition to the base model with dynamic conversions between the labile and inert phases, we perform
another sensitivity experiment assuming no chemical speciation of dissolved Cu, so that all dissolved
Cu plays the same role in biogeochemical processes. This sensitivity experiment, though not necessar-
ily characterizing realistic ocean Cu biogeochemistry, aims at exploring how other possibilities of model
representations of Cu chemical speciation might influence simulated Cu distributions in the ocean.
4.3 Results
4.3.1 Comparisonbetweenmodelandobservation
4.3.1.1 Globaloverview
Global dissolved Cu (dCu) concentrations simulated by the base model achieve a generally good fit com-
pared to the GEOTRACES IDP2021 dCu concentration data (Fig. 4.2) with the optimized model parameter
values listed in Table 4.2. The averaged vertical profiles of modeled dCu concentrations in the Atlantic
and Pacific Oceans match well with observations in both ocean basins, and the vertical profiles capture the
nearly-linear increase in dCu concentrations with depth (Fig. 4.2a). The horizontal spatial distributions of
dCu are reproduced at all depths from the surface to the abyssal ocean (Fig. 4.2b-d).
The correlation coefficients ( R) between model and observations are 0.72, 0.91, and 0.85 in the Atlantic,
Pacific, and Indian Oceans, respectively (Fig. 4.3a-c). The Arctic Ocean, however, is badly scaled with
R = -0.45 (Fig. 4.3d). While dCu concentrations increase linearly with depth in the rest of the oceans,
the Arctic ocean, which is unique in ocean circulation and trace metal supply, exhibits the highest dCu
concentrations at ocean surface which decreases rapidly within the top 500 meters and remains relatively
constant at deeper depths (Charette et al., 2020; Jensen et al., 2022). Therefore, in our base model where no
114
Table 4.2 Base model parameter definitions, initial guesses, and final values after model optimization.
Model processes and optimization are described in Section 4.2.2 and 4.2.3.
Atlantic
Pacific
(a) (b)
(c) (d)
Figure4.2 Comparison between observed dCu from the GEOTRACES IDP2021 dataset and dCu predicted
by the base model. (a) Vertical profiles of average dissolved Cu in the Atlantic (red) and Pacific (blue)
Oceans. Observations are represented as dots with error bars, while model predictions are shown as lines
with shaded areas indicating 1 standard deviation. (b-d) Global distributions of observed (filled circles) and
model-predicted (color field) dissolved Cu at (b) the surface ocean, (c) 1500 m depth, and (d) 3000 m depth.
115
special treatment is performed in the Arctic Ocean, the modeled dCu in the Arctic Ocean exhibits a gen-
erally increasing, rather than decreasing, trend with depth, resulting in a negative correlation coefficient.
Combining all data from the GEOTRACES IDP2021, our base model achieves a correlation coefficient of R
= 0.75 on a global scale (Fig. 4.3e), and R = 0.88 if the Arctic Cu data are excluded from the global dataset
(Fig. 4.3f).
4.3.1.2 SurfaceoceanCuconcentrations
In the surface ocean, dissolved Cu concentrations are lowest in the oligotrophic gyres (< 0.5 nM), with
slightly elevated concentrations near the equator, presumably due to enhanced equatorial upwelling, and
perhaps margin input (Fig. 4.2b). Dissolved Cu concentrations are lower at low latitudes than in the surface
Southern Ocean, where nutrient supply to the surface ocean from mixing and upwelling is high. However,
the model slightly overestimates surface dCu concentrations in the Southern Ocean, which could point to
a stronger biological demand for Cu by phytoplankton in the Southern Ocean compared to other regions,
as suggested by previous evidence that diatoms in Fe-limited waters have higher Cu requirement (Annett
et al., 2008; Biswas et al., 2013; Peers & Price, 2006; Peers et al., 2005). The higher Cu demand in the
Southern Ocean is not represented in our model, but has been parameterized or diagnosed by previous
modeling efforts (Cui & Gnanadesikan, 2022; Roshan et al., 2020).
Observed concentrations of dissolved Cu in the surface Arctic Ocean are much higher than in any
other ocean basin, with measurements reaching up to∼ 6 nM, which has been attributed to large riverine
fluxes of Cu to the Arctic (Charette et al., 2020; Jensen et al., 2022). While our base model includes riverine
Cu fluxes, the global model is optimized with river fluxes which might be too small, and perhaps with Cu
scavenging which is too intense, to account for observations in the Arctic Ocean. The particular behavior
of Cu in the Arctic is further investigated in sensitivity tests discussed in Section 4.4.5.
116
(a) (b)
(c) (d)
(e) (f)
Figure4.3 Comparison of dissolved Cu concentrations from the GEOTRACES IDP2021 observations and
model predictions from the base model. (a-d) Scatter plots showing the relationship between modeled and
observed total dCu concentrations in the (a) Atlantic, (b) Pacific, (c) Indian, and (d) Arctic Oceans. The
dashed black line represents the 1:1 line, and the solid black line is the linear regression line. Correlation
coefficients ( R) are provided for each sub dataset. (e-f) Cumulative joint probability density function of
modeled and observed dCu for (e) the global dataset and (f) the global dataset excluding Arctic Ocean Cu
data. The dashed black line represents the 1:1 line.
117
4.3.1.3 Cuconcentrationsbelowthesurface
From the surface to the deep ocean, dCu concentrations increase gradually with depth, except for the Arc-
tic Ocean (Fig. 4.2b-d). At depth, dCu concentrations are generally lowest in the North Atlantic Ocean,
increasing along the path of thermohaline circulation through the South Atlantic Ocean, Indian Ocean,
South Pacific Ocean, and eventually reaching their highest levels in the deep North Pacific Ocean, sug-
gesting that dCu concentrations build up in deep waters as the water masses age (Fig. 4.2c-d).
By comparing modeled and observed dCu concentrations along several GEOTRACES cruise transects,
some general features of Cu distributions can be summarized and compared between different ocean re-
gions. The zonal GP02 transect along 47°N in the North Pacific, is characterized by high dCu concentrations
which correlate with high phosphate concentrations in this region (Fig. 4.4b). In GP13, a zonal transect off
the coast of Australia, observations show enhanced dCu near 170°E at the bottom, which is underestimated
in the model, suggesting a source of Cu that exceeds the sedimentary input incorporated into our model
(Fig. 4.4c). The East Pacific Zonal Transect GP16 and the North Atlantic section GA03 (west leg) cross the
East Pacific Rise and Mid-Atlantic Ridge, respectively, but observed dCu concentrations do not increase
noticeably near the hydrothermal vents, indicating negligible Cu input with hydrothermal fluids, which
justifies our choice of not including a hydrothermal source of Cu in our model (Fig. 4.4d-e). A typical dCu
concentration distribution is observed along GA10 in the South Atlantic Ocean, where biological activity
and external sources are low, and the dissolved Cu exhibits a smooth increase with depth (Fig. 4.4f). The
meridional section GI04 in the Indian Ocean is characterized by high Cu concentrations in the surface off
the coast of the Arabian Sea, which is reproduced in our model due to high riverine and dust sources near
the continental margin (Fig. 4.4g).
118
GP16
GP13
GP02
GI04
GA03
w
GA10
(a)
(b) (c) (d)
(e) (f) (g)
Figure4.4 Comparison of modeled and observed dissolved Cu concentrations along several GEOTRACES
transects. (a) Global surface map of dissolved Cu concentrations from the base model prediction (color
field). Selected GEOTRACES cruises are plotted as observed Cu concentrations (filled circles) with cruise
names near the observation data points. (b-g) Modeled (color field) and observed (filled circles) Cu along
different GEOTRACES cruises, including three Pacific cruises (b) GP02, (c) GP13, (d) GP16, two Atlantic
cruises (e) GA03 (west leg), (f) GA10, and one Indian cruise (g) GI04.
119
4.3.2 LabileCuandinertCu
Our base model constrains labile and inert Cu concentrations based on samples from the GEOTRACES
GP15 cruise (152°W), including five full water column profiles (surface to ∼ 5,200 m) and five profiles be-
tween surface and 1000 m. A comparison between the simulated and observed labile Cu along this cruise
shows good model performance in reproducing the general features of labile Cu distribution, especially an
obvious benthic source (Fig. 4.5a-b). Inert Cu percentage, calculated as
InertCu
TotalDissolvedCu
× 100%, reaches a
maximum near 3000 m where inert Cu builds up and labile Cu concentrations are close to the upper ocean
levels, then decreases slightly near the seafloor where the model prescribes a labile Cu source (Fig. 4.5b).
The observed inert Cu percentage is at its lowest level near the surface, attributable to photodecomposition
(Moriyasu et al., 2023). The model underestimates the percentage of inert Cu in the surface ocean at low-
and mid-latitudes, which could be a result of the model overestimating photodegradation rates, producing
the excess labile Cu required to facilitate biological uptake. The Atlantic GA03 labile Cu measurements,
which are only used for validation instead of model optimization, show smaller concentration variations
with depth than the Pacific Ocean, with the only near-seafloor sample (collected near 30 °W) exhibiting a
slight increase in concentrations (Fig. 4.5c). The prescribed benthic source leads to an enrichment of mod-
eled labile Cu near 60°W, though observations are lacking at this station to support this feature. However,
the model slightly underestimates the inert Cu percentage along the GA03 cruise, especially in the surface
ocean (Fig. 4.5d). Despite the discrepancy, both the model and GA03 observations show inert Cu reaching
its highest percentage contribution to total dCu at intermediate depths, while surface and bottom waters
exhibit a lower proportion of inert Cu. Both observations and model simulations exhibit an increase of
inert Cu percentage from the Atlantic to Pacific Ocean (Fig. 4.5b, d).
Our model simulates labile Cu concentrations which are relatively constant from the surface ocean
through intermediate depths (Fig. 4.5e-f). In the surface ocean, labile Cu is removed by phytoplankton
uptake and intense scavenging onto particles, but also replenished through the photodegradation of inert
120
(a) Labile Cu concentration along GP15 cruise (b) Inert Cu percentage along GP15 cruise
(e) Atlantic
average profile
(f) Pacific
average profile
(c) Labile Cu concentration along GA03 cruise (d) Inert Cu percentage along GA03 cruise
Figure4.5 Comparison of modeled and observed distributions of labile and inert Cu. (a) Labile Cu concen-
trations and (b) the percentage of inert Cu along the GEOTRACES GP15 cruise. (c) Labile Cu concentrations
and (d) the percentage of inert Cu along the GEOTRACES GA03 cruise. The modeled values are shown as
the background color field, while the observed values are overlaid as filled circles. (e-f) Vertical profiles of
the modeled average labile Cu (light blue) and inert Cu (dark blue) concentrations in the (e) Atlantic and
(f) Pacific Oceans.
121
Cu. In the abyssal ocean, the increase in labile Cu concentration is attributable to labile Cu inputs from
sedimentary regeneration and nepheloid layer particles. In our model, inert Cu concentrations increase
with depth, due to the slow accumulation of inert Cu as water masses age away from exposure to sunlight,
as also evidenced by seawater sample measurements (Moriyasu et al., 2023; Ruacho et al., 2020). Inert Cu
concentrations are higher in the old deep Pacific waters compared to the relatively younger deep Atlantic,
in agreement with observations in Moriyasu et al. (2023).
The photodecomposition rate of inert Cu is optimized in the base model with a rate constant of 0.37 y
-1
in the euphotic zone (0-73 m) at the equator, equivalent to an inert Cu half-life of 1.9 years. As photode-
composition rates decrease towards high latitudes with less sunlight, the predicted half-life increases to
2.2 years at 30°N/S, and 3.8 years at 60°N/S. No direct measurements of inert Cu photodecomposition rates
with light intensity are available for comparison with these predictions, and in any case our predictions
do not directly account for the effects of seasonality and mixed layer depth. Labile Cu is converted to the
inert form throughout the water column with a globally uniform rate constant equivalent to a half-life of
250 years, representing the process of Cu incorporation into refractory organic matter.
4.3.3 Cufluxesandoceanicresidencetime
Internal cycling and external source fluxes of Cu, calculated from the base model simulation, are presented
in Fig. 4.6a. The two major internal processes are biological uptake of labile Cu in the surface ocean
followed by regeneration at depths, and reversible scavenging of labile Cu onto sinking particles. The
calculated Cu uptake by phytoplankton in the euphotic zone (0 - 73 m) is 1.92 Gmol y
-1
globally, similar to
the diagnosed net removal of dissolved Cu in the surface ocean at a rate of 1.7 Gmol y
-1
(Roshan et al., 2020).
Only 2% of the exported biogenic Cu is buried permanently in the sediments, while 98% is released back
to seawater either in the water column or at the seafloor. The model effectively simulates the adsorption
122
External fluxes
Internal cycling
Cu
I
↔Cu
L
(a) (b)
Figure4.6 Flux estimates for internal cycling of Cu within the oceans, and external sources of Cu to the
oceans. (a) The Cu fluxes associated with each biogeochemical process, calculated from the base model
optimized results. (b) Estimates of external sources of Cu from our base model compared with estimates
from previous literature, where different colors represent different source types (river, margin, dust, sedi-
ment, or nepheloid layer particles).
and desorption of Cu onto particles as a representation of the reversible scavenging process, resulting in
a total of 1.26 Gmol y
-1
of scavenged Cu buried in sediments with particles globally.
Fluxes of the interconversion between labile and inert Cu in the oceans are also calculated. Within the
optimized base model, we find that photodegradation converts inert Cu to labile Cu in the surface ocean
at a rate of 2.32 Gmol y
-1
globally, while labile Cu is bound by strong organic chelators and converted to
inert Cu at a rate of 1.82 Gmol y
-1
. The discrepancy between the creation and destruction of inert Cu is
due to the input of riverine Cu, which our model prescribes to be entering the ocean as 90% of inert Cu
and 10% of labile Cu.
The three external Cu sources deliver a combined flux of 1.30 Gmol Cu y
-1
to the ocean as estimated by
the base model, with rivers, mineral dust, and nepheloid layer particles supplying 0.55, 0.43, and 0.32 Gmol
Cu y
-1
, respectively. The three sources each are thus of similar magnitude (Fig. 4.6). The global ocean
inventory of Cu estimated from the base model is 2.9 Tmol, yielding a residence time of 2,200 years, an
intermediate value among prior estimates (Table 4.1). Since labile and inert Cu are brought to the ocean via
123
different external sources, their residence time estimates are calculated separately as 800 and 4,500 years,
which is consistent with the more active role of labile Cu in the dissolved Cu cycle.
4.4 Discussion
4.4.1 Closed-system models and the importance of high Atlantic Cu fluxes in setting
globalCudistribution
The ocean is an open system with exchanges of metals between the atmosphere and land. However, global
ocean models often treat trace metal cycling as a closed system, as has been done for Zn (Vance et al.,
2017; Weber et al., 2018), Ni (John et al., 2022), and Cu (Cui & Gnanadesikan, 2022). This is based upon
an assumption that the impact of external sources and sinks on the distribution of these metals is minor
compared with the influence of large-scale ocean circulation and internal cycling, and therefore that ne-
glecting sources and sinks of these metals does not significantly affect their distribution. Nonetheless,
including sources and sinks is important to constrain the ocean residence time of trace metals, and may
help to improve model performance in coastal oceans and at ocean boundaries. Also, if the residence time
of a tracer is not significantly longer than the ocean mixing timescale ( ∼ 1,000 years), including external
sources and sinks may be necessary to reproduce the global distribution of the tracer. In order to evaluate
the significance of input fluxes to the global Cu cycle, a sensitivity test is conducted with a closed-system
model without any external sources.
The closed-system Cu model, which has been re-optimized following the descriptions in Section 4.2.4.1,
exhibits significant discrepancies with observations (Fig. 4.7). Observed Cu concentrations in the surface
ocean are higher in the Atlantic Ocean than in the Pacific Ocean, pointing to the large surface inputs of Cu
from rivers including the Amazon River, and the importance of aerosol Cu sources including the Sahara
Desert. However, in our closed-system model with no riverine and aerosol sources, we find similar surface
124
Atlantic
Pacific
Figure4.7 Basin-average vertical profiles of dissolved Cu concentrations in the Atlantic (red) and Pacific
(blue) Oceans, as estimated by the closed-system model. GEOTRACES observations are represented as dots
with error bars, while the closed-system model predictions are shown as lines with shaded areas indicating
1 standard deviation.
Cu concentrations in the Atlantic and Pacific Oceans. Discrepancies between the closed-system model
and data are also observed in the deep ocean. Observations show that Cu concentrations are about 30%
higher in the deep Pacific compared to the deep Atlantic, while the closed-system model produces a nearly
100% increase between the deep Atlantic and deep Pacific. The large increase seen in the closed-system
model is reminiscent of other nutrient-type elements, for example roughly two-fold for Cd and P, and four-
fold for Zn and Si. A closed-system Cu model is unable to reproduce such a small concentration gradient
between the Atlantic and the Pacific, instead resulting in an optimized model where deep Atlantic dCu
concentrations (∼ 2 nM) are far below observations (∼ 3 nM).
125
The failure of the closed-system model to reproduce observations is attributed to the relatively larger
contribution of external Cu sources to the Atlantic compared to the Pacific. In the base model, external
sources contribute 10 times more Cu to the Atlantic Ocean compared to the Pacific Ocean per unit volume
of seawater. The net effect of these processes is that Cu builds up much less along the ‘conveyor belt’ than
other nutrient-type elements, and there is a relatively small increase in Cu concentrations from the deep
Atlantic to the deep Pacific.
Cui and Gnanadesikan (2022) also modeled global Cu distributions with a closed-system model, and
similar to our closed-system sensitivity test, their model underestimated deep Atlantic Cu concentrations
and overestimated the concentration difference between Atlantic and Pacific Oceans. Conversely, Richon
and Tagliabue (2019) implemented a large source through an open-system Cu model, where their estimated
total riverine Cu delivery to the global oceans is an order of magnitude higher than our model and other
previous studies, resulting in the calculated residence time of Cu an order of magnitude shorter than
previous estimates (Boyle et al., 1977; Little et al., 2014; Takano et al., 2014). Surprisingly, their model was
able to reproduce the general Cu distribution patterns, potentially because the large source is balanced
by a high burial flux as reflected by a concentration drawdown below 3,000 m, which is inconsistent with
observational data above the seafloor.
4.4.2 Evaluationoftherelativeimportanceofthethreepossibleexternalsources
The better performance of an open-system model compared to a closed-system model confirms the impor-
tance of external sources to global Cu distributions, motivating a sensitivity test to evaluate the relative
importance of riverine, aerosol dust, and sedimentary sources. A comparison of global Cu inventory and
flux estimates between this study and previous global Cu studies are presented in Table 4.1 and Fig. 4.6b.
Previous assumptions show large variations in the Cu fluxes estimated for rivers and aerosol dust, ranging
from comparable levels for the two sources (Boyle et al., 1977; Roshan et al., 2020; Takano et al., 2014) to
126
river fluxes which are more than 10 times greater than aerosol inputs (Little et al., 2014; Richon & Tagliabue,
2019). Due to the large uncertainties in the input flux estimates, and similar estimates of global oceanic
Cu inventory, Cu residence times estimated in the previous literature range between 400 and 6,400 years.
This residence time is short compared to some other trace metals (e.g. Cd, Zn), indicating a relatively
larger impact of external sources on oceanic Cu and a relatively smaller impact of ocean circulation on Cu
distributions.
Our sensitivity analyses are designed to evaluate how well the magnitudes of these various source
fluxes can be constrained. Each individual source flux was scaled by a factor of 0.1, 0.2, 0.5, 1, 2, 5, or 10,
then the model was re-optimized by tuning the other model parameters, including the other two source
fluxes. We find that decreasing one source leads to only slightly worse model performance, while increas-
ing any single one source by more than double the base model estimate leads to a much larger model-data
discrepancy (Fig. 4.8). This suggests that reducing one external source in the model can be largely compen-
sated for by increasing the other two sources, as long as the total input flux of Cu remains nearly constant.
When any single source is fixed at a high level that exceeds the total Cu input flux to the ocean from the
base model, the model can no longer accurately reproduce global Cu observations.
Thus, though we find that it is not possible to constrain the relative input magnitudes from these three
sources, our model appears to place a robust constraint on the total source flux of Cu to the oceans of
around 1.1-1.5 Gmol y
-1
. All three sources have a relatively larger impact (10-fold higher flux per vol-
ume) in the Atlantic compared to the Pacific. Thus, large increases in the magnitude of any single flux
in the model leads to an overaccumulation of Cu in the Atlantic and a decrease in predicted deep Pacific
Ocean Cu concentrations. That is, the model optimization tries to compensate for the increased source
flux with increased Cu burial, but in doing so too much Cu is removed from the deep Pacific. Conversely,
in the closed-system model without external Cu sources, the optimized model had too little Cu in the
deep Atlantic and too much in the deep Pacific (Section 4.4.1). This suggests that modeling studies are
127
River× SF
Dust× SF
Nepheloid× SF
Scaling factor (SF) = 0.1 0.2 0.5 1 2 5 10
Atlantic
Pacific
(a) (b) (c) (d) (e) (f)
(g) (h) (i) (j) (k) (l) (m)
(n) (o) (p) (q) (r) (s)
Fluxes (Gmol y
-1
):
River = 0.55
Dust = 0.43
Nepheloid = 0.32
Total = 1.30
0.055 0.81
0.51 1.37
0.11 0.76
0.49 1.36
0.28 0.63
0.43 1.33
1.10 0.15
0.04 1.29
2.76 0.00034
0.00037 2.76
5.51 0.00077
0.58 6.09
0.75 0.043
0.41 1.21
0.73 0.086
0.40 1.21
0.67 0.22
0.36 1.24
0.30 0.87
0.26 1.43
0.000049 2.16
0.00013 2.16
0.56 4.33
4.98 9.87
0.65 0.48
0.032 1.16
0.64 0.47
0.064 1.17
0.60 0.46
0.16 1.22
0.46 0.39
0.63 1.48
0.26 0.433
1.58 2.17
0.15 0.43
3.16 3.74
Figure 4.8 Sensitivity tests illustrating model response to changes in source flux magnitudes. The base
model optimized value of one of the three sources (river, dust, and nepheloid layer particles in Row 1, 2,
and 3, respectively) is multiplied by a scaling factor (SF) of 0.1, 0.2, 0.5, 1 (same as base model), 2 , 5, or
10. Average vertical profiles of dissolved Cu in the Atlantic (red) and Pacific (blue) Oceans are shown.
GEOTRACES observations are plotted as dots with error bars, and the model predictions are plotted as
lines with shaded areas representing 1 standard deviation. The flux estimates are listed as numbers below
each profile plot, with river (green), dust (yellow), nepheloid layer particles (purple), and total fluxes (grey)
calculated in the unit of Gmol y
-1
. The underlined number indicates the fixed flux in that sensitivity test,
and the model is then re-optimized to allow for changes in the magnitudes of the other two sources.
128
insufficient to constrain the relative magnitude of various Cu sources to the ocean, which motivates future
experimental and observational studies.
4.4.3 ThelinearshapeofCuverticalprofiles
One characteristic of ocean dissolved Cu is that concentrations increase in a nearly linear fashion with
depth in most of the ocean basins, instead of exhibiting a mid-depth maximum as observed for macronu-
trients and other trace metals. The two hypotheses which are generally invoked to explain the linear
profiles of Cu are a sedimentary source (Boyle et al., 1977; Roshan et al., 2020; Takano et al., 2014), and
reversible scavenging (Little et al., 2013; Richon & Tagliabue, 2019). We explore both hypotheses with
sensitivity tests.
4.4.3.1 RoleofbenthicCufluxes
A Cu source near the seafloor seems a straightforward explanation of deep Cu enrichment. There is evi-
dence showing the release of Cu from the benthic nepheloid layers (Gerringa et al., 2020), and experiments
have indicated a porewater source of Cu to benthic waters (Skrabal et al., 2000). The sedimentary Cu input
could be either new Cu or regenerated Cu, as defined in Section 4.2.4.3, though distinguishing the two
components through in situ measurements is challenging. The base model takes into account new Cu,
which is released from the nepheloid layer particles, and regenerated Cu, which is an optimized fraction
of particles that remineralize at the seafloor. In order to test whether each of the two components plays
an irreplaceable role in supplying Cu to the benthic waters, adjustments were made to the base model by
turning off 1) nepheloid layer source, 2) sedimentary regeneration, and 3) both nepheloid layer source and
sedimentary regeneration.
In the first sensitivity test targeting the importance of benthic input from nepheloid layer particles,
the flux of new Cu from the sediments is set to zero. This only has a slight impact on model performance,
129
noticeable mostly in the Atlantic where deep Cu concentrations are lower than in the base model (Fig. 4.9a),
which is attributable to the relatively high nepheloid layer particle concentrations in the deep Atlantic
(Gardner, Richardson, & Mishonov, 2018; Gardner, Richardson, Mishonov, & Biscaye, 2018). Still, the
linear increase in Cu concentrations with depth can be reproduced without a mid-depth maximum. This is
due to a compensation in the sensitivity-test model between the magnitude of the lithogenic sedimentary
source of new Cu and the effect of sedimentary regeneration from biogenic Cu and reversibly scavenged
Cu. In the base model, the sedimentary regeneration flux is optimized so that 69% of the particles reaching
the seafloor are regenerated to release dissolved Cu back to the water column, resulting in 2.93 Gmol y
-1
regenerated Cu while the lithogenic source is 0.32 Gmol y
-1
, adding up to a total of 3.25 Gmol y
-1
Cu input
to benthic waters, which is similar to the estimated benthic flux of 3.42 Gmol y
-1
by Roshan et al. (2020) and
3.7 Gmol y
-1
by Takano et al. (2014). When the lithogenic source of new Cu is removed, the model optimizes
with greater sedimentary Cu regeneration; 73% of particulate Cu is regenerated in the sediments, and the
benthic input reaches 3.05 Gmol y
-1
, accounted for entirely by sedimentary regeneration. When removing
the lithogenic source, the other two Cu sources at the surface, rivers and dust, also increase slightly to 0.66
and 0.48 Gmol y
-1
to compensate for the overall Cu influxes to the ocean, resulting in a slightly longer but
similar residence time estimate of 2,500 years. Therefore, a lithogenic sedimentary source of new Cu does
not seem to be a necessary component of our model when seeking to reproduce the global Cu distribution.
In the second sensitivity test, the regeneration of biogenic and reversibly scavenged Cu in the sediments
was set to zero, so that all particulate Cu reaching the seafloor is assumed to be buried. In this case, the
only benthic supply of Cu is new Cu from nepheloid layer particles that is optimized to 2.31 Gmol y
-1
,
which is 7 times the base model nepheloid layer source, but still does not fully compensate for the 3.25
Gmol y
-1
total benthic input. The model optimizer tries to enhance this benthic source to account for the
bottom Cu increase, but nepheloid layer particle concentrations are higher in the Atlantic compared to
the Pacific, such that when the dissolved Cu concentration is overestimated in the deep Atlantic Ocean, it
130
Reversible scavenging✕
External sedimentary source✕
Sedimentary remineralization✓
External sedimentary source✕
Sedimentary remineralization✕
Atlantic
Pacific
External sedimentary source✓
Sedimentary remineralization✕
(a) (b) (c) (d)
Figure4.9 The impact of sedimentary input and reversible scavenging on global Cu distribution. Average
vertical profiles of dissolved Cu are plotted for the Atlantic (red) and Pacific (blue) Oceans to investigate the
processes that contribute to the nearly-linear vertical Cu profiles. GEOTRACES observations are shown
as dots with error bars, and the optimized model results are represented by lines with shaded areas in-
dicating 1 standard deviation. (a) Model without an external sedimentary Cu source from the nepheloid
layer. (b) Model without sedimentary regeneration of biogenic and scavenged Cu. (c) Model without any
sedimentary input of Cu. (d) Model without reversible scavenging of Cu onto particles.
is still underestimated in the deep Pacific Ocean (Fig. 4.9b). Good model predictions of deep ocean Cu in
both ocean basins cannot be achieved with only a benthic input of new Cu from nepheloid layers.
While our work shows that a benthic source of new Cu from nepheloid layers cannot fully explain
the global Cu distributions, it is possible that a source of new Cu which is more intense in the Pacific
compared to the Atlantic could be consistent with the data. However, such a scenario would require a
very large benthic source of new Cu to the oceans. For example, the magnitude of benthic Cu sources
suggested by Roshan et al. (2020) and Takano et al. (2014)) are roughly an order of magnitude higher than
various estimates of the dust and riverine fluxes of Cu into the oceans (Table 4.1), and to our knowledge
there is no mechanism by which Cu, not quickly released from dust or riverine particles near the source,
would be released in the deep sediments. We also note that there is no evidence of an especially significant
new source of other trace metals, such as Zn and Ni, being released from the sediments (Little et al., 2014,
2020). And considering that aerosol and riverine particle fluxes are expected to be larger in the Atlantic, we
find it unlikely that a particularly strong source of new Cu exists in the Pacific compared to the Atlantic.
Thus, we conclude that the benthic Cu source is most likely to be dominated by regenerated Cu brought
131
to the sediments via reversible scavenging, rather than a new source of dissolved Cu through sediment
dissolution.
Finally, benthic Cu input was completely turned off by constraining the model with no input of new
Cu from nepheloid layers and complete burial of all particulate Cu reaching the sediments. In this case,
the simulated Cu profiles have a similar shape to those of other trace metals and macronutrients, reaching
a maximum concentration at about 2,000 m depth (Fig. 4.9c). This model optimizes surface sources high
enough to balance Cu burial and remain in steady state, reaching 2.48 and 0.16 Gmol y
-1
for riverine and
atmospheric delivery, respectively. This results in a residence time of 1,100 years, which is lower than the
base model estimate, but still within literature range. However, the overall vertical distribution of Cu is
very different from observations. Therefore, a benthic flux is presumed to be an important component of
global Cu biogeochemical cycling.
4.4.3.2 Roleofreversiblescavenging
Reversible scavenging has also been hypothesized to contribute to the observed linear increase in Cu con-
centrations with depth, suggested by previous studies using both 1-dimensional (Little et al., 2013) and 3-
dimensional models (Richon & Tagliabue, 2019). By removing reversible scavenging from a sensitivity-test
model, the resulting optimized Cu has a nutrient-like vertical distribution, with concentrations increasing
in the top 1 km and remaining roughly uniform below that depth (Fig. 4.9d). The failure of this model
to reproduce the characteristic vertical Cu distribution demonstrates that reversible scavenging plays a
crucial role in regulating ocean Cu cycling.
The role of reversible scavenging is also consistent with the significance of a sedimentary Cu source,
as highlighted in Section 4.4.3.1 and in diagnosed modeling approaches (Roshan et al., 2020). The release
of scavenged Cu into the ocean can serve as a benthic source when this process occurs at the sediment-
water interface. Existing measurements of benthic Cu fluxes have been unable to differentiate between a
132
new lithogenic Cu source and a recycled Cu source (Fischer et al., 1986; Heggie et al., 1987; Klinkhammer,
1980; Westerlund et al., 1986), which limits our ability to quantitatively determine the contributions of
each source to the linear vertical profile of dCu. Consequently, it is less reasonable to hypothesize that
the sedimentary Cu source is solely derived from lithogenic origins, while discounting the contribution of
scavenged Cu to the benthic flux.
4.4.3.3 AcomplexmixtureofprocessesleadstoseeminglysimpleCuprofiles
A nearly linear increase in Cu concentrations with depth, as occurs in both the Atlantic and Pacific Oceans,
might seem at first glance to imply simple biogeochemical processes. Indeed, similar linear increases in
230
Th are explained by the simple processes of uniform production throughout the water column from the
decay of
234
U, followed by reversible scavenging onto particles (Bacon & Anderson, 1982; Nozaki et al.,
1987). However, this provides a poor analogy for Cu because no similar source can supply Cu throughout
the water column. Moreover, the residence time of Cu in the oceans is much longer than
230
Th, so that Cu
distributions are greatly influenced by global ocean circulation. Consequently, a more complex mixture of
processes including significant benthic Cu inputs and reversible scavenging must combine to produce the
seemingly simple shape of observed Cu profiles.
4.4.4 SpecificdetailsofCuscavenging
The reversible scavenging parameterization used in the base model assumes a globally uniform Cu re-
versible scavenging rate. While this model provides crucial insight into the importance of reversible scav-
enging in the global Cu cycle, the specific formulation of scavenging is unrealistic. In fact, scavenging is
generally assumed to be more intense in the upper ocean where particle loads are high (Honeyman et al.,
1988; Lerner et al., 2018). The depth-dependence of scavenging rates can be related to the types of particles
present throughout the water column (Hayes et al., 2015; Lerner et al., 2018). Additionally, the intensity of
133
scavenging is expected to vary laterally depending on both the abundance and composition of particles in
the water column.
Previous studies of Cu have invoked different parameterizations of scavenging. The reversible scav-
enging process has been proposed to regulate Cu distributions in addition to conservative mixing, and clay
minerals were assumed to play a possible scavenging role (Craig, 1974). Little et al. (2013) incorporated
four particle types (POC, calcium carbonate, opal, dust) in a 1-D model to test Cu affinity to each particle
type, finding that different combinations of scavenging coefficients could achieve similarly good model
fits and highlighting the challenges of differentiating the specific particle types which may be responsible
for Cu scavenging. Richon and Tagliabue (2019) related reversible scavenging of Cu to organic particle
concentrations in a 3-D model, finding that the partition coefficient greatly influenced Cu distributions,
especially in the ocean interior. Experimental data are lacking which would provide solid evidence of the
particle types that play a role in Cu scavenging. We have therefore tested several different representations
of scavenging in our model to examine which are consistent with observed Cu distributions.
Sensitivity experiments explored six other possibilities, as outlined in Section 4.2.4.4, in addition to the
globally uniform reversible scavenging used in the base model. In the three cases where reversible scaveng-
ing is not applied, including no scavenging, uniform irreversible scavenging, and irreversible scavenging
onto POC, neither total dissolved Cu nor labile Cu shows a good fit between predictions and observa-
tions (Fig. 4.10c-h). We therefore conclude that reversible scavenging plays a crucial role in global Cu
biogeochemical cycling.
Three additional reversible scavenging parameterizations tested here, scavenging onto POC or follow-
ing the scavenging patterns of
230
Th and
231
Pa, all exhibit a good agreement with observed total dissolved
Cu concentrations (Fig. 4.10i, k, m). However, the distribution of labile Cu is more sensitive to the choice
of scavenging model, where differences are observed among the three reversible scavenging parameter-
izations. POC concentrations in our model follow the exponential attenuation of the Martin curve, such
134
that Cu scavenging onto POC is most intense in the upper ocean, leading the labile Cu concentrations to
be reduced to near zero in the surface ocean, which does not match well with the observations (Fig. 4.10j).
A more realistic pattern in labile Cu, with significant labile Cu present near the surface ocean, is observed
when reversible scavenging of Cu follows the
230
Th and
231
Pa patterns (Fig. 4.10l,n). These two scavenging
patterns take into account four particle types and two size classes, which are more representative of the
particle compositions in the real ocean.
The equilibrium scavenging constant K is optimized at 0.02 in the base model, meaning that 2% of
labile Cu is reversibly scavenged onto particles throughout the ocean. However, we note that K is not an
independent model parameter, being inversely related to the particle sinking rate v, which is set to 700
m y
-1
in the base model, as presented in Eq. 4.5. For example, if the sinking speed is halved (350 m y
-1
),
the equilibrium constant would optimize at double of the current value (0.04). Further complicating this
calculation, the particles responsible for scavenging Cu may span a range of sizes and densities, leading
to a spectrum of sinking speeds rather than a single number. We are therefore cautious about reporting
the equilibrium scavenging constant as an important finding, since this parameter is also impacted by the
choice of particle sinking velocity.
4.4.5 CuintheArcticOcean
Our base model has especially low skill in reproducing dissolved Cu concentrations in the Arctic Ocean.
Predictions of Cu concentrations increase with depth in the Arctic, similar to other ocean basins, while the
observed Cu peaks at the Arctic surface. This may be related to the unique circulation and biology of the
Arctic Ocean. The Arctic Ocean has the lowest salinity in surface waters due to large river discharges and
low evaporation, with rapidly increasing salinity below the mixed layer, opposite from the rest of the open
ocean where salinity is highest in the surface seawater. Additionally, biological productivity is low and
seasonally variable in the Arctic Ocean. Such unique characteristics of the Arctic Ocean could influence
135
Base model
(uniform reversible scavenging)
No scavenging
Uniform irreversible
scavenging
Irreversible scavenging
onto POC
Reversible scavenging
onto POC
Reversible scavenging
following
230
Th
Reversible scavenging
following
231
Pa
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(m) (n)
(k) (l)
Figure 4.10 Impact of various parameterizations of scavenging on global distributions of total Cu and
labile Cu. (a, c, e, g, I, k, m) Average vertical profiles of dissolved Cu in the Atlantic (red) and Pacific (blue)
Oceans. GEOTRACES observations are represented as dots with error bars, and the model predictions are
plotted as lines with shaded areas indicating 1 standard deviation. (b, d, f, h, j, l, n) Labile Cu concentrations
at Station 29 (0°, 152°W) from the GEOTRACES GP15 transect, with black dots representing observations
and red lines representing model predictions. (a-b) Model prediction with uniform reversible scavenging
(base model). (c-d) Model prediction without scavenging. (e-f) Model prediction with uniform irreversible
scavenging. (g-h) Model prediction with irreversible scavenging onto POC. (i-j) Model prediction with
reversible scavenging onto POC. (k-l) Model prediction with reversible scavenging following the
230
Th
scavenging pattern. (m-n) Model prediction with reversible scavenging following the
231
Pa scavenging
pattern.
136
Cu distributions and speciation in several ways: 1) low primary production leads to less Cu uptake by
phytoplankton, 2) low particle loads provide fewer scavenging sites, 3) large riverine input to the surface
brings more Cu into the ocean basin, 4) limited sunlight weakens the photodecomposition of inert Cu,
and 5) complex ocean circulation in this semi-enclosed basin makes it challenging to correctly simulate
the water transport. While low primary productivity and low photodegradation are embodied in the base
model, the other features in the Arctic Ocean are not well addressed, which is worth further exploration.
Circulation in the Arctic Ocean might not be as well simulated by the OCIM as in the other ocean
basins, due to sparse data coverage, seasonal variability, and complex density stratification due to ice
formation and melting near the surface (DeVries & Primeau, 2011). The potential circulation deficiencies
may impede our ability to correctly model Cu, but are beyond the scope of this paper. However, we do
note that the phosphorus model used in AO exhibits a commendable ability to reproduce the observed
Arctic phosphate patterns from the 2009 World Ocean Atlas dataset (Weber et al., 2018), which serves as
evidence supporting the overall reliability of Arctic Ocean circulation. Similarly, biogeochemical cycling
of elements in the Arctic is highly seasonal, yet Cu data used to constrain this model are only from the
Northern Hemisphere summer, and therefore may not be a good reflection of annual average patterns.
Thus conclusions about Cu cycling in the Arctic must be treated with some caution. None the less, we
focus here on the possible impacts of riverine Cu input and scavenging in the ocean interior in order to
ascertain whether such processes could account for the misfit between observations and our base model.
A large riverine source of Cu has been proposed to explain the high dissolved Cu concentrations mea-
sured in the surface Arctic Ocean samples (Charette et al., 2020; Jensen et al., 2022), supported by the
negative correlation between salinity and Cu concentrations in the Arctic Ocean (Fig. S4.1). Our base
model optimizes the average riverine Cu concentration to 42 nM, which is then multiplied by the dis-
charge of each river to calculate the riverine Cu input flux. Assuming rivers might bring more Cu to the
Arctic Ocean, we extracted the four major rivers flowing into the Arctic Ocean (Ob, Yenisei, Lena, and
137
Mackenzie Rivers) and optimized the average Cu concentration in these four rivers separately from the
other rivers, resulting in the optimized Cu concentration of 84 nM in these four rivers and 8 nM in the
other rivers. This implies that the model optimizer seeks to match the surface Cu enrichment in the Arctic
Ocean by choosing a higher riverine Cu input. This optimized average riverine Cu concentration, however,
is higher than the data compiled by Gaillardet et al. (2003), where the average Cu concentration of these
four rivers flowing into the Arctic Ocean is 24 nM. The model prediction might be overestimating riverine
Cu concentrations, potentially as a result of the model accounting for the missing smaller rivers in addi-
tion to the four major rivers. However, this adjusted model exhibits a surface average Cu concentration of
∼ 1.4 nM along GEOTRACES Arctic cruises, which is slightly higher than the 1 nM surface concentration
in the base model but still significantly lower than the observed average Cu concentration of ∼ 3.5 nM
along the same cruises (Fig. 4.11). Thus, additional Cu input from rivers does not fully resolve the Arctic
Cu model-data discrepancy in our model.
Reversible scavenging is another factor that influences Cu vertical distributions, which may be reduced
in the Arctic Ocean due to a lower particle load from low surface productivity. The base model assumes ho-
mogeneous scavenging intensity everywhere in the ocean, which might lead to overestimated scavenged
Cu in the Arctic Ocean and thus a gradual increase in concentrations with depth, similar to that observed
in other ocean basins. Therefore, we turned off the reversible scavenging process only in the Arctic Ocean,
and this sensitivity-test model simulation captures the correct vertical pattern, with highest Cu concentra-
tions in the surface, followed by attenuation in the subsurface and uniform concentration in deep ocean
(Fig. 4.11). The comparison between the base model and this sensitivity test implies that reversible scav-
enging is important for shaping the linear vertical shape of Cu, and that there is little scavenging of Cu
in the Arctic Ocean. Comparing among the six scavenging patterns discussed in Section 4.4.4, the model
predictions of dissolved Cu in the Arctic Ocean best match with observations when reversible scavenging
follows the
230
Th and
231
Pa patterns (Fig. S4.2). The low scavenging rate of Cu in the Arctic Ocean might
138
also reflect a high proportion of inert Cu, which does not scavenge. Additionally, our base model, even
with the latitude-dependence of photolysis, might be still producing too much labile Cu in the Arctic so
that scavenging is overestimated.
While the two sensitivity experiments targeting the Arctic Ocean improve the model performance
to some degree, they both have systematic deficiencies. When only increasing the riverine Cu input to
the Arctic Ocean, dissolved Cu still exhibits nearly-linear increase in concentrations with depth. By only
turning off reversible scavenging in the Arctic Ocean, the surface average Cu concentrations are still about
1.5 nM lower than observations. Combining both approaches results in a better fit to observations than
when the two adjustments are implemented individually (Fig. 4.11). In fact, the combination of elevated
riverine input and weak scavenging serves as a coherent explanation for the observed patterns of Cu
distribution in the Arctic region. When Cu is introduced into the ocean via rivers, it predominantly exists
in an inert form, hindered by strong organic complexation, thus impeding its adsorption onto particles.
To gain further insights into these influential factors contributing to the distinctive Cu distributions in the
Arctic Ocean, future experimental work could focus on determining the partitioning of labile and inert Cu
in Arctic rivers and surface seawater. Such studies hold the potential to elucidate the role of these factors
in shaping the unique Cu distribution patterns within the Arctic Ocean.
One noteworthy model deviation from observations is that the best-performing ]model still underes-
timates surface Cu concentrations, even when the riverine Cu flux is allowed to be optimized to higher
levels. One possible reason is that OCIM ocean circulation either does not transport tracers quickly enough
from the coastal river mouths to the mid-Arctic Ocean, or that the OCIM overestimates mixing in the up-
per ocean, where the real Arctic may be highly stratified due to the intense salinity gradient. Another
possibility is that, in addition to rivers, continental shelves release Cu to the Arctic Ocean from sediments,
submarine groundwater discharge, or ice melt. Shelf-derived materials have been found to deliver many
139
Figure 4.11 Modeled and observed Cu distributions in the Arctic Ocean for four different models. Ob-
served Arctic Cu concentrations from the GEOTRACE IDP2021 dataset are represented by black dots with
error bars. Model predictions of average Cu concentrations in the Arctic Ocean are shown as lines for
four different model configurations: the base model (dark blue), the model with Arctic rivers optimized
separately at a higher level than the base model (green), the model without scavenging in the Arctic Ocean
(yellow), and the model with a separately optimized value for Arctic riverine Cu concentrations and with-
out scavenging in the Arctic Ocean (red).
trace elements to the Arctic Ocean, including Co (Bundy et al., 2020),
228
Ra (Kipp et al., 2018), and Ba (Whit-
more et al., 2022). Such shelf sources, which are missing in the model configuration, might contribute a
significant amount of dissolved Cu to the Arctic Ocean. In this sensitivity experiment, the calculated resi-
dence time of Cu in the Arctic Ocean is 200 years, an order of magnitude shorter than the estimated global
residence time, highlighting the significance of external fluxes to this semi-enclosed basin.
140
4.4.6 LabileandinertCuspeciation
Marine Cu is mostly bound by ligands, yet the composition and structure of these chelators has not been
well understood. Possible ligands include thiol compounds (Laglera & van den Berg, 2003; Leal & Van
Den Berg, 1998; Whitby et al., 2018), humic and fulvic acids (Kogut & Voelker, 2001; Whitby & van den
Berg, 2015; Xue & Sigg, 1999), and sulfide complexes (Luther & Rickard, 2005; Rozan et al., 2000). The
complexation of Cu by these compounds effectively reduces the Cu
2+
concentrations and thus the toxicity
of Cu in aquatic systems. Cu bound by very strong ligands has been characterized with respect to ligand
concentration and binding strength using competitive ligand exchange techniques (Buckley & van den
Berg, 1986). Yet the majority of dissolved Cu in seawater is not exchangeable with this approach. One
hypothesis suggests that inert Cu is formed when labile Cu is incorporated and physically trapped in
colloidal materials (Kogut & Voelker, 2003). This has been described as an “onion” model where Cu can
“glue” together organic molecules through coordination bonds and build up layers of the “onion”, so that
the Cu sequestered in the inner sphere becomes kinetically inert; it does not exchange with seawater until
undergoing some sort of dissociation process to “peel the onion” (Mackey & Zirino, 1994). Such a process
would be consistent with our model, where labile Cu is slowly converted into inert Cu in the ocean, and
converted back to labile Cu through photolysis in the surface waters. However, previous data show that
only 25-45% of total dissolved Cu in the ocean is colloidal (Jensen et al., 2021; Roshan & Wu, 2018), whereas
approximately 75% of total dissolved Cu predicted by our model exists in the inert phase, which leads to
our hypothesis that inert Cu could be composed of different size fractions, as a combination of colloids
and smaller organic complexes.
Our base model simulates both labile and inert Cu with dynamic conversions between these phases, and
the simulated labile and total Cu predictions match well with measurements (Fig. 4.5a-d), suggesting that
the predicted labile and inert Cu could be representative of the respective distributions of each species in
the real ocean. To determine if an inert fraction of Cu is essential to reproduce observations, a sensitivity
141
(a) (b)
Figure4.12 The impact of speciation on total Cu, labile Cu, and inert Cu distributions in the global ocean.
(a) Model assuming all dissolved Cu has the same biogeochemical behavior in the ocean, with black data
points representing observed global average Cu concentrations and light blue areas representing modeled
total dissolved Cu. (b) Model assuming separate pools of labile and inert Cu in the ocean, as defined as
the base model in this study, with black data points representing observed average Cu concentrations,
light blue areas representing modeled average labile Cu concentrations, and dark blue areas representing
modeled average inert Cu concentrations.
experiment is performed, which assumes that dissolved Cu is essentially homogenous with respect to
biological uptake or scavenging (i.e. no discrete labile and inert fractions). Though this assumption is
not consistent with the non-labile nature of the strongly complexed Cu ligands, this model is still able
to simulate the total dissolved Cu concentrations (Fig. 4.12a). This suggests that the exchange rate of
Cu between the inert and labile fractions, while undetectable experimentally, is fast enough given the
assumptions in our model to enable the inert fraction to exchange on the timescales of Cu residence time.
Incorporating both labile and inert species of dissolved Cu makes our model biogeochemically realistic.
It is important to note that the partitioning of labile and inert Cu is primarily determined based on
bioavailability. Bioavailable Cu, which is the labile fraction as represented in our model, is accessible
for uptake by marine organisms. Some phytoplankton species, such as diatoms, have been found to be
relatively more tolerantto Cu toxicity, while others, such as cyanobacteria, are more sensitive (Brand et
142
al., 1986; Mann et al., 2002). Therefore, understanding the partitioning between labile and inert Cu is
important for assessing the potential effects of Cu toxicity on marine ecosystems.
4.5 Conclusions
Cu is an essential trace metal for marine organisms, and its concentration increase with depth and strong
organic complexation features make oceanic Cu unique compared to other trace metals. Here we have
presented a three-dimensional global oceanic Cu model that investigates the distribution and speciation of
dissolved Cu in seawater while quantifying key biogeochemical processes that regulate marine Cu cycling.
This model successfully captures the features observed in GEOTRACES dissolved Cu measurements, in-
cluding the linear vertical profile and concentration gradients among ocean basins. The optimized external
sources and sinks of oceanic Cu in this open system model provide an estimate of the global Cu budget
and the oceanic residence time of 2,200 years. Sedimentary input combined with the reversible scavenging
process lead to the gradual increase of Cu concentrations with depth, and experiments excluding either
process result in no significant Cu increase in the deep ocean. Cu biogeochemical cycling in the Arctic
appears to be quite distinctive, with our model requiring both a relatively large Cu flux in Arctic rivers, and
a near absence of vertical scavenging in order to reproduce observed Cu concentrations. We also present
the first model of global Cu biogeochemical cycling which includes labile and inert Cu phases, and which
seeks to match observations of labile and inert Cu by proposing slow complexation of Cu into inert organic
ligands in the deep ocean, and photodegradation of these complexes in the surface ocean.
Uncertainties or limitations of this model can inspire future Cu studies. For example, the lithogenic
sedimentary source of Cu, which does not play a necessary role in our model, requires to be proved or
disproved by future experimental analyses. Other Cu-associated questions about a more realistic particle
scavenging scenario and size fractions of Cu ligands call for refined theoretical models and microstructure
143
(a)All depths (b) Surface to 73 m
Supplementary Figure 4.1 Dissolved Cu concentrations compared to salinity (S) in the Arctic Ocean.
Both Cu and salinity data are from GEOTRACES IDP2021 Arctic cruises. (a) Scatter plot of seawater Cu
concentrations versus salinity from all depths in the Arctic Ocean. The negative slope of the linear regres-
sion (black line) and high correlation coefficient ( R) suggest a potential source of Arctic Cu from freshwater.
(b) Scatter plot of Cu concentrations versus salinity in the surface Arctic Ocean seawater samples (0 - 73
m), which is a subset of dataset from (a).
studies. Besides, the Arctic Ocean, which exhibits unique trace metal distributions, is significantly influ-
enced by climate change, and understanding Arctic nutrient cycling can provide insights into future Arctic
ecosystem studies.
144
(a) (b) (c)
(d) (e) (f)
Supplementary Figure 4.2 The impact of different scavenging scenarios on Cu concentrations in the
Arctic Ocean. The black dots with error bars represent observed average Cu concentrations from GEO-
TRACE IDP2021 Arctic cruises. The red lines with shaded areas indicating 1 standard deviation represent
model predictions of average Cu concentrations under six different scavenging scenarios discussed in Sec-
tion 4.4.4. (a) No scavenging. (b) Uniform irreversible scavenging. (c) Irreversible scavenging onto POC.
(d) Reversible scavenging onto POC. (e) Reversible scavenging following the
230
Th scavenging pattern. (f)
Reversible scavenging following the
231
Pa scavenging pattern. The models have the best performance in
the Arctic Ocean when global Cu scavenging follows the
230
Th or
231
Pa patterns (e-f).
145
Chapter5
Conclusions
5.1 Thesissummary
George E. P. Box once said, "All models are wrong, but some are useful". The ocean is a complex system
with many interconnected processes, making it challenging to fully understand and predict how it will
respond to future changes. However, through the use of models, oceanographers can simplify and abstract
the ocean biogeochemical cycles, making it easier to identify important mechanisms and better understand
the ocean system. While these models may not perfectly represent the complexities of the ocean, they are
valuable tools for gaining insights into this important system and helping to inform decisions that will
impact both the ocean and the broader environment.
This thesis has provided a comprehensive investigation of three ocean tracers, alkalinity, barium, and
copper, through global inverse models. The results of these studies have provided significant insights
into the behavior of these tracers in the oceanic system, while shedding light on the complex interactions
between physical, chemical, and biological processes that control the distribution and cycling of these
tracers in the ocean.
In Chapter 2, a global ocean alkalinity model was developed focusing on its role in the global carbon
cycle. This model provided valuable insights into the factors that control alkalinity distributions in the
146
ocean and highlighted the use of alkalinity in quantifying calcium carbonate (CaCO
3
) export and disso-
lution in the ocean. CaCO
3
export out of the surface ocean is constrained within a relatively wide range
through current literature and modeling efforts. Good model performance of alkalinity distributions in the
upper ocean can be simulated under both low and high CaCO
3
export scenarios, which can be compen-
sated for by the upper ocean CaCO
3
dissolution at low or high magnitudes. The upper ocean is typically
supersaturated with respect to calcite and aragonite, but my model results suggest that dissolution must
occur in the supersaturated waters to reproduce the observed alkalinity distributions. Other biological
and ecological mechanisms, in addition to dissolution kinetics, should play a role in driving dissolution
throughout the water column. Overall, these findings have important implications for our understanding
of the ocean carbon cycle and the processes that regulate alkalinity distributions in the ocean.
In Chapter 3, I studied barium (Ba), a heavy trace metal that is involved in various biogeochemical
processes in the ocean. This model aims to provide a better understanding of the marine Ba cycle, with
a focus on the dissolved Ba distribution and how it is affected by pelagic barite precipitation and disso-
lution. Low dissolved Ba concentrations in the upper ocean are primarily attributed to the precipitation
of barite, which is facilitated by organic matter respiration below the euphotic zone, while phytoplankton
uptake and regeneration have little influence on dissolved Ba distributions. My model reveals that ambient
seawater is the primary source of Ba for barite precipitation, whereas Ba released from organic matter is
negligible. Barite dissolution releases dissolved Ba back to deep seawater, and the dissolution rate is not a
simple function of barite saturation states. Models with constant dissolution rates generate dissolved Ba
distributions that better match observations, though the mechanisms remain to be explored. My findings
also highlight the importance of barite dissolution in the water column, which is optimized higher than
sedimentary dissolution, in contrast to previous assumptions that barite mostly dissolves at the seafloor.
In Chapter 4, I looked into another trace metal, copper (Cu). This model investigates the biogeochem-
ical processes that control marine Cu distributions, which provides new insights into the global cycling of
147
Cu in the ocean. The model explicitly represents the chemical speciation of Cu based on kinetic lability,
while separately examining the processes that affect each species. One aspect of the study focuses on the
nearly-linear increases in Cu concentrations with depth, which have been proposed to be attributed to ei-
ther sedimentary input or reversible scavenging onto particles. My models test both hypotheses and show
that both processes are required to explain this seemingly simple vertical distribution. The model also
emphasizes Cu distributions in the Arctic Ocean, which exhibit distinct features compared to other ocean
basins. Instead of gradual increases in concentrations with depth, Arctic Cu has the highest concentrations
in the surface waters, likely due to the marginal sources from rivers. Cu concentrations in deep Arctic wa-
ters remain at a constant level, suggesting low particle concentrations that cannot effectively scavenge Cu.
Overall, this chapter investigates the integral role of oceanic Cu in biogeochemical processes, highlighting
the interactions between marine dissolved Cu and marine organisms, particles, and organic ligands.
Overall, the findings of this thesis have important implications for our understanding of the ocean bio-
geochemistry. The three global models presented in this thesis investigate the ocean carbon cycle through
alkalinity distributions, as well as the cycling of trace metals through barium and copper. These models
have helped to shed light on the complex interactions between physical, chemical, and biological processes
that regulate the cycling of these tracers in the ocean. Specifically, the alkalinity model developed in Chap-
ter 2 highlights the role of alkalinity in the quantification of CaCO
3
export and dissolution in the ocean,
while the Ba model presented in Chapter 3 emphasizes the importance of barite precipitation and disso-
lution in controlling dissolved Ba concentrations. The Cu model described in Chapter 4 investigates the
biogeochemical processes and chemical speciation of Cu. Together, these models provide a comprehensive
understanding of the biogeochemical processes that shape the distribution and cycling of ocean tracers,
which can inform future research efforts and improve our ability to predict the impacts of environmental
changes on ocean biogeochemistry.
148
5.2 Futuredirections
By compiling observational datasets and developing new models, this thesis has contributed to the devel-
opment of more accurate and comprehensive biogeochemical models of the ocean system. The findings
presented in this thesis pave the way for a number of future research directions in the field of ocean bio-
geochemistry.
First, future research could build on the models developed in this study to better understand the role
of other ocean tracers in biogeochemical processes. For example, research could focus on the role of other
trace metals, such as cadmium or chromium, in regulating phytoplankton growth, the ocean carbon cycle,
and other biogeochemical processes. Such investigations would contribute to our understanding of the
interconnections between different biogeochemical cycles and how they interact to regulate the ocean
ecosystem. In addition, isotope models can be developed to reveal biogeochemical processes and quantify
reaction rates. For example, the potential for Ba isotopes to serve as a powerful tracer of ocean circulation
and biogeochemical processes has been proposed experimentally, and it will be interesting to better utilize
this isotope tool from a modeling perspective.
Second, future research could use high-quality observational and experimental data to validate and
refine the models developed in this study, particularly in remote and under-sampled regions of the ocean.
Current datasets have relatively poor coverage in the Arctic Ocean and the Southern Ocean, which reduces
the reliability of inverse model performances in these regions. By comparing model predictions to real-
world observations, researchers can improve the accuracy and reliability of these models and identify areas
where further research is needed.
Third, future research could focus on developing new analytical techniques and technologies for mea-
suring ocean tracers and improving our ability to detect and track biogeochemical processes in the ocean.
For example, my Cu model partitions dissolved Cu into labile and inert species, which are challenging
149
to separate experimentally. Novel analytical techniques for speciation studies can improve our under-
standing of the inertness of trace metal and organic species. The Cu model also simplifies the particle
scavenging scenario due to the lack of measurements and observations, which could be better elucidated
by future studies on ocean particle types and compositions. Besides, my alkalinity model puts poor con-
straints on the global estimate of calcium carbonate export, which might be better constrained by future
satellite observations. The continued development of new technologies will be critical for advancing our
understanding of ocean biogeochemistry and its role in regulating the global ecosystem.
Fourth, future research should aim to refine the models by incorporating more realistic assumptions
and constraints that better reflect the true ocean environment. For example, my alkalinity and barium mod-
els have made simplified but unrealistic assumptions about the dissolution reaction mechanisms. Other
simplified assumptions include steady-state conditions and the absence of seasonal variations. Future
studies can focus on investigating the biogeochemical processes and mechanisms in the real ocean and
integrating them into the models to improve their accuracy and predictive capabilities.
Finally, as anthropogenic impacts continue to alter the ocean chemistry and ecosystem dynamics, fu-
ture research could investigate the response of ocean biogeochemical processes to global environmental
changes, such as eutrophication and deoxygenation due to enhanced nutrient runoff, and ocean warming
and acidification due to increasing atmospheric CO
2
. Future efforts can incorporate these impacts into
models to better understand the future trajectory of ocean biogeochemistry and its implications for the
global carbon and nutrient cycles.
In summary, the findings presented in this thesis provide a foundation for future research in the field
of ocean biogeochemistry, with numerous opportunities for further investigation and development of new
models, techniques, and technologies.
150
Bibliography
Alldredge, A. L., & Cohen, Y. (1987). Can microscale chemical patches persist in the sea? Microelectrode
study of marine snow, fecal pellets. Science, 235(4789), 689–691.
Amiotte Suchet, P., Probst, J.-L., & Ludwig, W. (2003). Worldwide distribution of continental rock
lithology: Implications for the atmospheric/soil CO2 uptake by continental weathering and
alkalinity river transport to the oceans. Global Biogeochemical Cycles, 17(2).
Anglada-Ortiz, G., Zamelczyk, K., Meilland, J., Ziveri, P., Chierici, M., Fransson, A., & Rasmussen, T. L.
(2021). Planktic foraminiferal and pteropod contributions to carbon dynamics in the Arctic Ocean
(North Svalbard Margin). Frontiers in Marine Science, 8, 661158.
Annett, A. L., Lapi, S., Ruth, T. J., & Maldonado, M. T. (2008). The effects of Cu and Fe availability on the
growth and Cu: C ratios of marine diatoms. Limnology and oceanography, 53(6), 2451–2461.
Bacon, M. P., & Anderson, R. F. (1982). Distribution of thorium isotopes between dissolved and
particulate forms in the deep sea. Journal of Geophysical Research: Oceans, 87(C3), 2045–2056.
Balch, W., Gordon, H. R., Bowler, B., Drapeau, D., & Booth, E. (2005). Calcium carbonate measurements in
the surface global ocean based on Moderate-Resolution Imaging Spectroradiometer data. Journal
of Geophysical Research: Oceans, 110(C7).
Bates, S. L., Hendry, K. R., Pryer, H. V., Kinsley, C. W., Pyle, K. M., Woodward, E. M. S., & Horner, T. J.
(2017). Barium isotopes reveal role of ocean circulation on barium cycling in the Atlantic.
Geochimica et Cosmochimica Acta, 204, 286–299.
Battaglia, G., Steinacher, M., & Joos, F. (2015). A probabilistic assessment of calcium carbonate export and
dissolution in the modern ocean. Biogeosciences Discussions, 12(24).
Bednaršek, N., Možina, J., Vogt, M., O’Brien, C., & Tarling, G. A. (2012). The global distribution of
pteropods and their contribution to carbonate and carbon biomass in the modern ocean. Earth
System Science Data, 4(1), 167–186.
Bender, M. L., & Gagner, C. (1976). Dissolved copper, nickel and cadmium in the Sargasso Sea. J. mar. Res,
34(3), 327–339.
151
Berelson, W. M. (2001). Particle settling rates increase with depth in the ocean. Deep Sea Research Part II:
Topical Studies in Oceanography, 49(1-3), 237–251.
Berelson, W., Balch, W., Najjar, R., Feely, R., Sabine, C., & Lee, K. (2007). Relating estimates of CaCO3
production, export, and dissolution in the water column to measurements of CaCO3 rain into
sediment traps and dissolution on the sea floor: A revised global carbonate budget. Global
Biogeochemical Cycles, 21(1).
Bergan, A. J., Lawson, G. L., Maas, A. E., & Wang, Z. A. (2017). The effect of elevated carbon dioxide on
the sinking and swimming of the shelled pteropod Limacina retroversa. ICES Journal of Marine
Science, 74(7), 1893–1905.
Berner, R. A., & Honjo, S. (1981). Pelagic sedimentation of aragonite: Its geochemical significance.
Science, 211(4485), 940–942.
Bianchi, D., Weber, T. S., Kiko, R., & Deutsch, C. (2018). Global niche of marine anaerobic metabolisms
expanded by particle microenvironments. Nature Geoscience, 11(4), 263–268.
Biermann, A., & Engel, A. (2010). Effect of CO 2 on the properties and sinking velocity of aggregates of
the coccolithophore Emiliania huxleyi. Biogeosciences, 7(3), 1017–1029.
Bishop, J. K. (1988). The barite-opal-organic carbon association in oceanic particulate matter. Nature,
332(6162), 341–343.
Biswas, H., Bandyopadhyay, D., & Waite, A. (2013). Copper addition helps alleviate iron stress in a coastal
diatom: Response of Chaetoceros gracilis from the Bay of Bengal to experimental Cu and Fe
addition. Marine Chemistry, 157, 224–232.
Boyd, P. W., & Ellwood, M. J. (2010). The biogeochemical cycle of iron in the ocean. Nature Geoscience,
3(10), 675–682.
Boyle, E., Sclater, F. R., & Edmond, J. (1977). The distribution of dissolved copper in the Pacific. Earth and
planetary science letters, 37(1), 38–54.
Brahney, J., Mahowald, N., Ward, D. S., Ballantyne, A. P., & Neff, J. C. (2015). Is atmospheric phosphorus
pollution altering global alpine Lake stoichiometry? Global Biogeochemical Cycles, 29(9),
1369–1383.
Brand, L. E., Sunda, W. G., & Guillard, R. R. (1986). Reduction of marine phytoplankton reproduction rates
by copper and cadmium. Journal of experimental marine biology and ecology, 96(3), 225–250.
Brewer, P. G., Wong, G. T., Bacon, M. P., & Spencer, D. W. (1975). An oceanic calcium problem? Earth and
Planetary Science Letters, 26(1), 81–87.
Bridgestock, L., Nathan, J., Paver, R., Hsieh, Y.-T., Porcelli, D., Tanzil, J., Holdship, P., Carrasco, G.,
Annammala, K. V., Swarzenski, P. W., et al. (2021). Estuarine processes modify the isotope
composition of dissolved riverine barium fluxes to the ocean. Chemical Geology, 579, 120340.
152
Bruland, K., & Lohan, M. (2006). Controls of trace metals in seawater. The oceans and marine
geochemistry, 6, 23–47.
Buckley, P. J., & van den Berg, C. M. (1986). Copper complexation profiles in the Atlantic Ocean: A
comparative study using electrochemical and ion exchange techniques. Marine Chemistry, 19(3),
281–296.
Buitenhuis, E. T., Le Quéré, C., Bednaršek, N., & Schiebel, R. (2019). Large contribution of pteropods to
shallow CaCO3 export. Global Biogeochemical Cycles, 33(3), 458–468.
Buitenhuis, E. T., Vogt, M., Moriarty, R., Bednaršek, N., Doney, S. C., Leblanc, K., Le Quéré, C., Luo, Y.-W.,
O’Brien, C., O’Brien, T., et al. (2013). MAREDAT: Towards a world atlas of MARine Ecosystem
DATa. Earth System Science Data, 5(2), 227–239.
Bundy, R. M., Tagliabue, A., Hawco, N. J., Morton, P. L., Twining, B. S., Hatta, M., Noble, A. E.,
Cape, M. R., John, S. G., Cullen, J. T., et al. (2020). Elevated sources of cobalt in the Arctic Ocean.
Biogeosciences, 17(19), 4745–4767.
Cael, B., Cavan, E. L., & Britten, G. L. (2021). Reconciling the size-dependence of marine particle sinking
speed. Geophysical Research Letters, 48(5), e2020GL091771.
Carter, B. R., Feely, R. A., Lauvset, S. K., Olsen, A., DeVries, T., & Sonnerup, R. (2021). Preformed
properties for marine organic matter and carbonate mineral cycling quantification. Global
Biogeochemical Cycles, 35(1), e2020GB006623.
Carter, B. R., Toggweiler, J., Key, R. M., & Sarmiento, J. L. (2014). Processes determining the marine
alkalinity and calcium carbonate saturation state distributions. Biogeosciences, 11(24), 7349–7362.
Charette, M. A., Kipp, L. E., Jensen, L. T., Dabrowski, J. S., Whitmore, L. M., Fitzsimmons, J. N.,
Williford, T., Ulfsbo, A., Jones, E., Bundy, R. M., et al. (2020). The Transpolar Drift as a source of
riverine and shelf-derived trace elements to the central Arctic Ocean. Journal of Geophysical
Research: Oceans, 125(5), e2019JC015920.
Chien, C.-T., Mackey, K. R., Dutkiewicz, S., Mahowald, N. M., Prospero, J. M., & Paytan, A. (2016). Effects
of African dust deposition on phytoplankton in the western tropical Atlantic Ocean off Barbados.
Global Biogeochemical Cycles, 30(5), 716–734.
Chow, T. J., & Goldberg, E. D. (1960). On the marine geochemistry of barium. Geochimica et
Cosmochimica Acta, 20(3-4), 192–198.
Christy, A. G., & Putnis, A. (1993). The kinetics of barite dissolution and precipitation in water and
sodium chloride brines at 44–85 C. Geochimica et Cosmochimica Acta, 57(10), 2161–2168.
Chung, S.-N., Lee, K., Feely, R., Sabine, C., Millero, F., Wanninkhof, R., Bullister, J., Key, R., & Peng, T.-H.
(2003). Calcium carbonate budget in the Atlantic Ocean based on water column inorganic carbon
chemistry. Global Biogeochemical Cycles, 17(4).
Coale, K. H., & Bruland, K. W. (1988). Copper complexation in the Northeast Pacific. Limnology and
Oceanography, 33(5), 1084–1101.
153
Cornwall, C. E., Hepburn, C. D., Pilditch, C. A., & Hurd, C. L. (2013). Concentration boundary layers
around complex assemblages of macroalgae: Implications for the effects of ocean acidification on
understory coralline algae. Limnology and Oceanography, 58(1), 121–130.
Craig, H. (1974). A scavenging model for trace elements in the deep sea. Earth and Planetary Science
Letters, 23(1), 149–159.
Croot, P. L., Moffett, J. W., & Brand, L. E. (2000). Production of extracellular Cu complexing ligands by
eucaryotic phytoplankton in response to Cu stress. Limnology and oceanography, 45(3), 619–627.
Cui, M., & Gnanadesikan, A. (2022). Characterizing the roles of biogeochemical cycling and ocean
circulation in regulating marine copper distributions. Journal of Geophysical Research: Oceans,
127(1), e2021JC017742.
Daniels, C., Poulton, A., Balch, W., Marañón, E., Adey, T., Bowler, B., Cermeño, P., Charalampopoulou, A.,
Crawford, D., Drapeau, D., et al. (2018). A global compilation of coccolithophore calcification
rates, earth syst. sci. data, 10, 1859–1876.
Dehairs, F., Stroobants, N., & Goeyens, L. (1991). Suspended barite as a tracer of biological activity in the
Southern Ocean. Marine Chemistry, 35(1-4), 399–410.
Dehairs, F., Chesselet, R., & Jedwab, J. (1980). Discrete suspended particles of barite and the barium cycle
in the open ocean. Earth and Planetary Science Letters, 49(2), 528–550.
DeVries, T. (2014). The oceanic anthropogenic CO2 sink: Storage, air-sea fluxes, and transports over the
industrial era. Global Biogeochemical Cycles, 28(7), 631–647.
DeVries, T., & Primeau, F. (2011). Dynamically and observationally constrained estimates of water-mass
distributions and ages in the global ocean. Journal of Physical Oceanography, 41(12), 2381–2401.
Dickens, G. R., Fewless, T., Thomas, E., & Bralower, T. J. (2003). Excess barite accumulation during the
Paleocene-Eocene Thermal Maximum: Massive input of dissolved barium from seafloor gas
hydrate reservoirs. Special Papers-Geological Society of America, 11–24.
Dong, S., Berelson, W. M., Adkins, J. F., Rollins, N. E., Naviaux, J. D., Pirbadian, S., El-Naggar, M. Y., &
Teng, H. H. (2020). An atomic force microscopy study of calcite dissolution in seawater.
Geochimica et Cosmochimica Acta, 283, 40–53.
Dong, S., Berelson, W. M., Rollins, N. E., Subhas, A. V., Naviaux, J. D., Celestian, A. J., Liu, X., Turaga, N.,
Kemnitz, N. J., Byrne, R. H., et al. (2019). Aragonite dissolution kinetics and calcite/aragonite
ratios in sinking and suspended particles in the North Pacific. Earth and Planetary Science Letters,
515, 1–12.
Dong, S., Subhas, A. V., Rollins, N. E., Naviaux, J. D., Adkins, J. F., & Berelson, W. M. (2018). A kinetic
pressure effect on calcite dissolution in seawater. GeochimicaetCosmochimicaActa,238, 411–423.
Dove, P. M., & Czank, C. A. (1995). Crystal chemical controls on the dissolution kinetics of the
isostructural sulfates: Celestite, anglesite, and barite. Geochimica et Cosmochimica Acta, 59(10),
1907–1915.
154
Dove, P. M., Han, N., Wallace, A. F., & De Yoreo, J. J. (2008). Kinetics of amorphous silica dissolution and
the paradox of the silica polymorphs. Proceedings of the National Academy of Sciences, 105(29),
9903–9908.
Dunne, J. P., Hales, B., & Toggweiler, J. (2012). Global calcite cycling constrained by sediment
preservation controls. Global Biogeochemical Cycles, 26(3).
Dunne, J. P., John, J. G., Adcroft, A. J., Griffies, S. M., Hallberg, R. W., Shevliakova, E., Stouffer, R. J.,
Cooke, W., Dunne, K. A., Harrison, M. J., et al. (2012). GFDL’s ESM2 global coupled
climate–carbon earth system models. Part I: Physical formulation and baseline simulation
characteristics. Journal of climate, 25(19), 6646–6665.
Dunne, J. P., Sarmiento, J. L., & Gnanadesikan, A. (2007). A synthesis of global particle export from the
surface ocean and cycling through the ocean interior and on the seafloor. Global Biogeochemical
Cycles, 21(4).
Duteil, O., Koeve, W., Oschlies, A., Aumont, O., Bianchi, D., Bopp, L., Galbraith, E., Matear, R., Moore, J.,
Sarmiento, J. L., et al. (2012). Preformed and regenerated phosphate in ocean general circulation
models: Can right total concentrations be wrong? biogeosciences, 9(5), 1797–1807.
Dymond, J., & Collier, R. (1996). Particulate barium fluxes and their relationships to biological
productivity. Deep Sea Research Part II: Topical Studies in Oceanography, 43(4-6), 1283–1308.
Engel, A., Szlosek, J., Abramson, L., Liu, Z., & Lee, C. (2009). Investigating the effect of ballasting by
CaCO3 in Emiliania huxleyi: I. Formation, settling velocities and physical properties of
aggregates. Deep Sea Research Part II: Topical Studies in Oceanography, 56(18), 1396–1407.
Fabry, V. J. (1990). Shell growth rates of pteropod and heteropod molluscs and aragonite production in
the open ocean: Implications for the marine carbonate system. Journal of Marine Research, 48(1),
209–222.
Fabry, V. J., & Deuser, W. G. (1991). Aragonite and magnesian calcite fluxes to the deep Sargasso Sea.
Deep Sea Research Part A. Oceanographic Research Papers, 38(6), 713–728.
Feely, R., Sabine, C., Lee, K., Millero, F., Lamb, M., Greeley, D., Bullister, J., Key, R., Peng, T.-H., Kozyr, A.,
et al. (2002). In situ calcium carbonate dissolution in the Pacific Ocean. Global Biogeochemical
Cycles, 16(4), 91–1.
Fischer, K., Dymond, J., Lyle, M., Soutar, A., & Rau, S. (1986). The benthic cycle of copper: Evidence from
sediment trap experiments in the eastern tropical north pacific ocean. Geochimica et
Cosmochimica Acta, 50(7), 1535–1543.
Fisher, N. S., Guillard, R. R., & Bankston, D. C. (1991). The accumulation of barium by marine
phytoplankton grown in culture. Journal of marine research, 49(2), 339–354.
Freiwald, A. (1995). Bacteria-induced carbonate degradation: A taphonomic case study of Cibicides
lobatulus from a high-boreal carbonate setting. Palaios, 337–346.
155
Friedlingstein, P., Jones, M. W., O’Sullivan, M., Andrew, R. M., Bakker, D. C., Hauck, J., Le Quéré, C.,
Peters, G. P., Peters, W., Pongratz, J., et al. (2022). Global carbon budget 2021.EarthSystemScience
Data, 14(4), 1917–2005.
Friis, K., Najjar, R., Follows, M., & Dutkiewicz, S. (2006). Possible overestimation of shallow-depth
calcium carbonate dissolution in the ocean. Global Biogeochemical Cycles, 20(4).
Fry, C. H., Tyrrell, T., Hain, M. P., Bates, N. R., & Achterberg, E. P. (2015). Analysis of global surface ocean
alkalinity to determine controlling processes. Marine Chemistry, 174, 46–57.
Gaillardet, J., Viers, J., & Dupré, B. (2003). Trace elements in river waters. Treatise on geochemistry, 5, 605.
Ganeshram, R. S., François, R., Commeau, J., & Brown-Leger, S. L. (2003). An experimental investigation
of barite formation in seawater. Geochimica et Cosmochimica Acta, 67(14), 2599–2605.
Gangstø, R., Gehlen, M., Schneider, B., Bopp, L., Aumont, O., & Joos, F. (2008). Modeling the marine
aragonite cycle: Changes under rising carbon dioxide and its role in shallow water CaCO 3
dissolution. Biogeosciences, 5(4), 1057–1072.
Gardner, W. D., Richardson, M. J., & Mishonov, A. V. (2018). Global assessment of benthic nepheloid
layers and linkage with upper ocean dynamics. Earth and Planetary Science Letters, 482, 126–134.
Gardner, W. D., Richardson, M. J., Mishonov, A. V., & Biscaye, P. E. (2018). Global comparison of benthic
nepheloid layers based on 52 years of nephelometer and transmissometer measurements.
Progress in Oceanography, 168, 100–111.
Gehlen, M., Gangstø, R., Schneider, B., Bopp, L., Aumont, O., & Éthé, C. (2007). The fate of pelagic CaCO 3
production in a high CO 2 ocean: A model study. Biogeosciences, 4(4), 505–519.
GEOTRACES, I. D. P. G. (2021). The GEOTRACES Intermediate Data Product 2021 (IDP2021) [Data set].
DOI:%2010.5285/cf2d9ba9-d51d-3b7c-e053-8486abc0f5fd
German, C. R., Casciotti, K., Dutay, J.-C., Heimbürger, L.-E., Jenkins, W. J., Measures, C., Mills, R.,
Obata, H., Schlitzer, R., Tagliabue, A., et al. (2016). Hydrothermal impacts on trace element and
isotope ocean biogeochemistry. Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences, 374(2081), 20160035.
Gerringa, L. J., Alderkamp, A.-C., Van Dijken, G., Laan, P., Middag, R., & Arrigo, K. R. (2020). Dissolved
trace metals in the Ross Sea. Frontiers in Marine Science, 7, 577098.
Granger, J., & Ward, B. B. (2003). Accumulation of nitrogen oxides in copper-limited cultures of
denitrifying bacteria. Limnology and Oceanography, 48(1), 313–318.
Hamm, C. E., Merkel, R., Springer, O., Jurkojc, P., Maier, C., Prechtel, K., & Smetacek, V. (2003).
Architecture and material properties of diatom shells provide effective mechanical protection.
Nature, 421(6925), 841–843.
Hanor, J. S. (1969). Barite saturation in sea water. Geochimica et cosmochimica Acta, 33(7), 894–898.
156
Hayes, C. T., Anderson, R. F., Fleisher, M. Q., Vivancos, S. M., Lam, P. J., Ohnemus, D. C., Huang, K.-F.,
Robinson, L. F., Lu, Y., Cheng, H., et al. (2015). Intensity of Th and Pa scavenging partitioned by
particle chemistry in the North Atlantic Ocean. Marine Chemistry, 170, 49–60.
Heggie, D., Klinkhammer, G., & Cullen, D. (1987). Manganese and copper fluxes from continental margin
sediments. Geochimica et Cosmochimica Acta, 51(5), 1059–1070.
Hendriks, I. E., Duarte, C. M., Marbà, N., & Krause-Jensen, D. (2017). Ph gradients in the diffusive
boundary layer of subarctic macrophytes. Polar Biology, 40, 2343–2348.
Honeyman, B. D., Balistrieri, L. S., & Murray, J. W. (1988). Oceanic trace metal scavenging: The
importance of particle concentration. Deep Sea Research Part A. Oceanographic Research Papers,
35(2), 227–246.
Horner, T. J., & Crockford, P. W. (2021). Barium isotopes: Drivers, dependencies, and distributions through
space and time. Cambridge University Press.
Horner, T. J., Kinsley, C. W., & Nielsen, S. G. (2015). Barium-isotopic fractionation in seawater mediated
by barite cycling and oceanic circulation. Earth and Planetary Science Letters, 430, 511–522.
Horner, T. J., Pryer, H. V., Nielsen, S. G., Crockford, P. W., Gauglitz, J. M., Wing, B. A., & Ricketts, R. D.
(2017). Pelagic barite precipitation at micromolar ambient sulfate. Nature Communications, 8(1),
1342.
Houlihan, E. P., Espinel-Velasco, N., Cornwall, C. E., Pilditch, C. A., & Lamare, M. D. (2020). Diffusive
boundary layers and ocean acidification: Implications for sea urchin settlement and growth.
Frontiers in Marine Science, 7, 577562.
Hsieh, Y.-T., Bridgestock, L., Scheuermann, P. P., Seyfried Jr, W. E., & Henderson, G. M. (2021). Barium
isotopes in mid-ocean ridge hydrothermal vent fluids: A source of isotopically heavy Ba to the
ocean. Geochimica et Cosmochimica Acta, 292, 348–363.
Irigoien, X., Klevjer, T. A., Røstad, A., Martinez, U., Boyra, G., Acuña, J. L., Bode, A., Echevarria, F.,
Gonzalez-Gordillo, J. I., Hernandez-Leon, S., et al. (2014). Large mesopelagic fishes biomass and
trophic efficiency in the open ocean. Nature communications, 5(1), 3271.
Jansen, H., Zeebe, R. E., & Wolf-Gladrow, D. A. (2002). Modeling the dissolution of settling CaCO3 in the
ocean. Global Biogeochemical Cycles, 16(2), 11–1.
Jensen, L. T., Cullen, J. T., Jackson, S. L., Gerringa, L. J., Bauch, D., Middag, R., Sherrell, R. M., &
Fitzsimmons, J. N. (2022). A Refinement of the Processes Controlling Dissolved Copper and
Nickel Biogeochemistry: Insights From the Pan-Arctic. Journal of Geophysical Research: Oceans,
127(5), e2021JC018087.
Jensen, L. T., Lanning, N. T., Marsay, C. M., Buck, C. S., Aguilar-Islas, A. M., Rember, R., Landing, W. M.,
Sherrell, R. M., & Fitzsimmons, J. N. (2021). Biogeochemical cycling of colloidal trace metals in
the Arctic cryosphere. Journal of Geophysical Research: Oceans, 126(8), e2021JC017394.
157
Jin, X., Gruber, N., Dunne, J., Sarmiento, J. L., & Armstrong, R. (2006). Diagnosing the contribution of
phytoplankton functional groups to the production and export of particulate organic carbon,
CaCO3, and opal from global nutrient and alkalinity distributions. Global Biogeochemical Cycles,
20(2).
John, S. G. (2022a). Dissolved concentrations of nickel and copper from bottle samples collected on Leg 1
(Seattle, WA to Hilo, HI) of the US GEOTRACES Pacific Meridional Transect (PMT) cruise (GP15,
RR1814) on R/V Roger Revelle from September to October 2018 [Data set].
http://lod.bco-dmo.org/id/dataset/885319
John, S. G. (2022b). Dissolved concentrations of nickel and copper from bottle samples collected on Leg 2
(Hilo, HI to Papeete, French Polynesia) of the US GEOTRACES Pacific Meridional Transect
(PMT) cruise (GP15, RR1815) on R/V Roger Revelle from October to November 2018 [Data set].
http://lod.bco-dmo.org/id/dataset/885335
John, S. G., Kelly, R. L., Bian, X., Fu, F., Smith, M. I., Lanning, N. T., Liang, H., Pasquier, B., Seelen, E. A.,
Holzer, M., et al. (2022). The biogeochemical balance of oceanic nickel cycling. Nature Geoscience,
15(11), 906–912.
John, S. G., Liang, H., Weber, T., DeVries, T., Primeau, F., Moore, K., Holzer, M., Mahowald, N.,
Gardner, W., Mishonov, A., et al. (2020). AWESOME OCIM: A simple, flexible, and powerful tool
for modeling elemental cycling in the oceans. Chemical Geology, 533, 119403.
Keir, R. S. (1980). The dissolution kinetics of biogenic calcium carbonates in seawater. Geochimica et
Cosmochimica Acta, 44(2), 241–252.
Kipp, L. E., Charette, M. A., Moore, W. S., Henderson, P. B., & Rigor, I. G. (2018). Increased fluxes of
shelf-derived materials to the central Arctic Ocean. Science Advances, 4(1), eaao1302.
Klinkhammer, G. P. (1980). Early diagenesis in sediments from the eastern equatorial pacific, ii. pore
water metal results. Earth and Planetary Science Letters, 49(1), 81–101.
Koeve, W., Duteil, O., Oschlies, A., Kähler, P., & Segschneider, J. (2014). Methods to evaluate CaCO 3 cycle
modules in coupled global biogeochemical ocean models. Geoscientific Model Development , 7(5),
2393–2408.
Kogut, M. B., & Voelker, B. M. (2001). Strong copper-binding behavior of terrestrial humic substances in
seawater. Environmental science & technology, 35(6), 1149–1156.
Kogut, M. B., & Voelker, B. M. (2003). Kinetically inert Cu in coastal waters. Environmental science &
technology, 37(3), 509–518.
Laglera, L. M., & van den Berg, C. M. (2003). Copper complexation by thiol compounds in estuarine
waters. Marine Chemistry, 82(1-2), 71–89.
Laglera, L. M., & van den Berg, C. M. (2006). Photochemical oxidation of thiols and copper complexing
ligands in estuarine waters. Marine Chemistry, 101(1-2), 130–140.
158
Lam, V., & Pauly, D. (2005). Mapping the global biomass of mesopelagic fishes. Sea Around Us Project
Newsletter, 30(4), 4.
Lasaga, A. C. (1998). Kinetic theory in the earth sciences. Princeton university press.
Lauvset, S. K., Key, R. M., Olsen, A., Van Heuven, S., Velo, A., Lin, X., Schirnick, C., Kozyr, A., Tanhua, T.,
Hoppema, M., et al. (2016). A new global interior ocean mapped climatology: The 1imes 1
GLODAP version 2. Earth System Science Data, 8(2), 325–340.
Lea, D. W., & Spero, H. J. (1994). Assessing the reliability of paleochemical tracers: Barium uptake in the
shells of planktonic foraminifera. Paleoceanography, 9(3), 445–452.
Leal, M. F. C., & Van Den Berg, C. M. (1998). Evidence for strong copper (I) complexation by organic
ligands in seawater. Aquatic geochemistry, 4, 49–75.
Lee, K. (2001). Global net community production estimated from the annual cycle of surface water total
dissolved inorganic carbon. Limnology and Oceanography, 46(6), 1287–1297.
Lerner, P., Marchal, O., Lam, P. J., & Solow, A. (2018). Effects of particle composition on thorium
scavenging in the North Atlantic. Geochimica et Cosmochimica Acta, 233, 115–134.
Levitus, S., Locarnini, R. A., Boyer, T. P., Mishonov, A. V., Antonov, J. I., Garcia, H. E., Baranova, O. K.,
Zweng, M. M., Johnson, D. R., & Seidov, D. (2010). World ocean atlas 2009.
Light, T., & Norris, R. (2021). Quantitative visual analysis of marine barite microcrystals: Insights into
precipitation and dissolution dynamics. Limnology and Oceanography, 66(10), 3619–3629.
Little, S. H., Archer, C., McManus, J., Najorka, J., Wegorzewski, A. V., & Vance, D. (2020). Towards
balancing the oceanic ni budget. Earth and Planetary Science Letters, 547, 116461.
Little, S. H., Vance, D., McManus, J., Severmann, S., & Lyons, T. W. (2017). Copper isotope signatures in
modern marine sediments. Geochimica et Cosmochimica Acta, 212, 253–273.
Little, S. H., Vance, D., Siddall, M., & Gasson, E. (2013). A modeling assessment of the role of reversible
scavenging in controlling oceanic dissolved Cu and Zn distributions. Global Biogeochemical
Cycles, 27(3), 780–791.
Little, S. H., Vance, D., Walker-Brown, C., & Landing, W. (2014). The oceanic mass balance of copper and
zinc isotopes, investigated by analysis of their inputs, and outputs to ferromanganese oxide
sediments. Geochimica et Cosmochimica Acta, 125, 673–693.
Luther, G. W., & Rickard, D. T. (2005). Metal sulfide cluster complexes and their biogeochemical
importance in the environment. Journal of Nanoparticle Research, 7, 389–407.
Mackey, D., & Zirino, A. (1994). Comments on trace metal speciation in seawater or do “onions” grow in
the sea? Analytica Chimica Acta, 284(3), 635–647.
159
Maldonado, M. T., Allen, A. E., Chong, J. S., Lin, K., Leus, D., Karpenko, N., & Harris, S. L. (2006).
Copper-dependent iron transport in coastal and oceanic diatoms. Limnology and oceanography,
51(4), 1729–1743.
Mann, E. L., Ahlgren, N., Moffett, J. W., & Chisholm, S. W. (2002). Copper toxicity and cyanobacteria
ecology in the sargasso sea. Limnology and Oceanography, 47(4), 976–988.
Manno, C., Sandrini, S., Tositti, L., & Accornero, A. (2007). First stages of degradation of Limacina
helicina shells observed above the aragonite chemical lysocline in Terra Nova Bay (Antarctica).
Journal of Marine Systems, 68(1-2), 91–102.
Martin, J. H., & Fitzwater, S. E. (1988). Iron deficiency limits phytoplankton growth in the north-east
Pacific subarctic. Nature, 331, 341–343.
Martin, J. H., Knauer, G. A., Karl, D. M., & Broenkow, W. W. (1987). VERTEX: Carbon cycling in the
northeast Pacific. Deep Sea Research Part A. Oceanographic Research Papers, 34(2), 267–285.
Martinez-Ruiz, F., Jroundi, F., Paytan, A., Guerra-Tschuschke, I., Abad, M. d. M., & González-Muñoz, M. T.
(2018). Barium bioaccumulation by bacterial biofilms and implications for Ba cycling and use of
Ba proxies. Nature communications, 9(1), 1619.
Martinez-Ruiz, F., Paytan, A., Gonzalez-Muñoz, M., Jroundi, F., Abad, M. d. M., Lam, P. J., Bishop, J.,
Horner, T., Morton, P. L., & Kastner, M. (2019). Barite formation in the ocean: Origin of
amorphous and crystalline precipitates. Chemical Geology, 511, 441–451.
Martiny, A. C., Pham, C. T., Primeau, F. W., Vrugt, J. A., Moore, J. K., Levin, S. A., & Lomas, M. W. (2013).
Strong latitudinal patterns in the elemental ratios of marine plankton and organic matter. Nature
Geoscience, 6(4), 279–283.
Mayfield, K. K., Eisenhauer, A., Santiago Ramos, D. P., Higgins, J. A., Horner, T. J., Auro, M., Magna, T.,
Moosdorf, N., Charette, M. A., Gonneea, M. E., et al. (2021). Groundwater discharge impacts
marine isotope budgets of Li, Mg, Ca, Sr, and Ba. Nature Communications, 12(1), 148.
Middelburg, J. J., Soetaert, K., & Hagens, M. (2020). Ocean alkalinity, buffering and biogeochemical
processes. Reviews of Geophysics, 58(3), e2019RG000681.
Milliman, J., & Droxler, A. (1996). Neritic and pelagic carbonate sedimentation in the marine
environment: Ignorance is not bliss. Geologische Rundschau, 85, 496–504.
Milliman, J., Troy, P., Balch, W., Adams, A., Li, Y.-H., & Mackenzie, F. (1999). Biologically mediated
dissolution of calcium carbonate above the chemical lysocline? Deep Sea Research Part I:
Oceanographic Research Papers, 46(10), 1653–1669.
Moffett, J. W., & Brand, L. E. (1996). Production of strong, extracellular Cu chelators by marine
cyanobacteria in response to Cu stress. Limnology and oceanography, 41(3), 388–395.
Moffett, J. W., Brand, L. E., Croot, P. L., & Barbeau, K. A. (1997). Cu speciation and cyanobacterial
distribution in harbors subject to anthropogenic Cu inputs. Limnology and Oceanography, 42(5),
789–799.
160
Moffett, J. W., Zika, R., & Brand, L. E. (1990). Distribution and potential sources and sinks of copper
chelators in the Sargasso Sea. Deep Sea Research Part A. Oceanographic Research Papers, 37(1),
27–36.
Moffett, J. W., & Zika, R. G. (1987). Solvent extraction of copper acetylacetonate in studies of copper (II)
speciation in seawater. Marine Chemistry, 21(4), 301–313.
Monnin, C., & Cividini, D. (2006). The saturation state of the world’s ocean with respect to (Ba, Sr) SO4
solid solutions. Geochimica et Cosmochimica Acta, 70(13), 3290–3298.
Monnin, C., Jeandel, C., Cattaldo, T., & Dehairs, F. (1999). The marine barite saturation state of the
world’s oceans. Marine Chemistry, 65(3-4), 253–261.
Moore, R. M. (1978). The distribution of dissolved copper in the eastern Atlantic Ocean. Earth and
planetary science letters, 41(4), 461–468.
Moriyasu, R., John, S. G., Bian, X., Yang, S.-C., & Moffett, J. W. (2023). Copper exists predominantly as
kinetically inert complexes throughout the interior of the Equatorial and North Pacific Ocean
[Unpublished manuscript].
Moriyasu, R., & Moffett, J. W. (2022). Determination of inert and labile copper on GEOTRACES samples
using a novel solvent extraction method. Marine Chemistry, 239, 104073.
Morse, J. W., de Kanel, J., & Harris, K. (1979). Dissolution kinetics of calcium carbonate in seawater; VII,
The dissolution kinetics of synthetic aragonite and pteropod tests. American Journal of Science,
279(5), 488–502.
Naviaux, J. D., Subhas, A. V., Dong, S., Rollins, N. E., Liu, X., Byrne, R. H., Berelson, W. M., & Adkins, J. F.
(2019). Calcite dissolution rates in seawater: Lab vs. in-situ measurements and inhibition by
organic matter. Marine Chemistry, 215, 103684.
Naviaux, J. D., Subhas, A. V., Rollins, N. E., Dong, S., Berelson, W. M., & Adkins, J. F. (2019). Temperature
dependence of calcite dissolution kinetics in seawater. Geochimica et Cosmochimica Acta, 246,
363–384.
Nozaki, Y., Yang, H.-S., & Yamada, M. (1987). Scavenging of thorium in the ocean. Journal of Geophysical
Research: Oceans, 92(C1), 772–778.
Oakes, R., Peck, V., Manno, C., & Bralower, T. (2019). Degradation of internal organic matter is the main
control on pteropod shell dissolution after death. Global Biogeochemical Cycles, 33(6), 749–760.
Oakes, R. L., & Sessa, J. A. (2020). Determining how biotic and abiotic variables affect the shell condition
and parameters of Heliconoides inflatus pteropods from a sediment trap in the Cariaco Basin.
Biogeosciences, 17(7), 1975–1990.
O’Brien, C., Peloquin, J. A., Vogt, M., Heinle, M., Gruber, N., Ajani, P., Andruleit, H., Arístegui, J.,
Beaufort, L., Estrada, M., et al. (2013). Global marine plankton functional type biomass
distributions: Coccolithophores. Earth System Science Data, 5(2), 259–276.
161
O’Mara, N. A., & Dunne, J. P. (2019). Hot spots of carbon and alkalinity cycling in the coastal oceans.
Scientific reports , 9(1), 4434.
Paytan, A., & Kastner, M. (1996). Benthic Ba fluxes in the central Equatorial Pacific, implications for the
oceanic Ba cycle. Earth and Planetary Science Letters, 142(3-4), 439–450.
Peers, G., & Price, N. M. (2006). Copper-containing plastocyanin used for electron transport by an
oceanic diatom. Nature, 441(7091), 341–344.
Peers, G., Quesnel, S.-A., & Price, N. M. (2005). Copper requirements for iron acquisition and growth of
coastal and oceanic diatoms. Limnology and oceanography, 50(4), 1149–1158.
Perry, C. T., Salter, M. A., Harborne, A. R., Crowley, S. F., Jelks, H. L., & Wilson, R. W. (2011). Fish as
major carbonate mud producers and missing components of the tropical carbonate factory.
Proceedings of the National Academy of Sciences, 108(10), 3865–3869.
Ploug, H., Hietanen, S., & Kuparinen, J. (2002). Diffusion and advection within and around sinking,
porous diatom aggregates. Limnology and oceanography, 47(4), 1129–1136.
Ploug, H., Stolte, W., Epping, E. H., & Jørgensen, B. B. (1999). Diffusive boundary layers, photosynthesis,
and respiration of the colony-forming plankton algae, phaeocystis sp. Limnology and
oceanography, 44(8), 1949–1958.
Rahman, S., Shiller, A. M., Anderson, R. F., Charette, M. A., Hayes, C. T., Gilbert, M., Grissom, K. R.,
Lam, P. J., Ohnemus, D. C., Pavia, F. J., et al. (2022). Dissolved and particulate barium
distributions along the US GEOTRACES North Atlantic and East Pacific Zonal Transects (GA03
and GP16): Global implications for the marine barium cycle. Global Biogeochemical Cycles, 36(6),
e2022GB007330.
Richon, C., & Tagliabue, A. (2019). Insights into the major processes driving the global distribution of
copper in the ocean from a global model. Global Biogeochemical Cycles, 33(12), 1594–1610.
Ridgwell, A., & Hargreaves, J. (2007). Regulation of atmospheric CO2 by deep-sea sediments in an Earth
system model. Global Biogeochemical Cycles, 21(2).
Ridgwell, A., Hargreaves, J., Edwards, N. R., Annan, J., Lenton, T. M., Marsh, R., Yool, A., & Watson, A.
(2007). Marine geochemical data assimilation in an efficient Earth System Model of global
biogeochemical cycling. Biogeosciences, 4(1), 87–104.
Roshan, S., DeVries, T., & Wu, J. (2020). Constraining the global ocean Cu cycle with a data-assimilated
diagnostic model. Global Biogeochemical Cycles, 34(11), e2020GB006741.
Roshan, S., & Wu, J. (2018). Dissolved and colloidal copper in the tropical South Pacific. Geochimica et
Cosmochimica Acta, 233, 81–94.
Rozan, T. F., Lassman, M. E., Ridge, D. P., & Luther III, G. W. (2000). Evidence for iron, copper and zinc
complexation as multinuclear sulphide clusters in oxic rivers. Nature, 406(6798), 879–882.
162
Ruacho, A., Bundy, R. M., Till, C. P., Roshan, S., Wu, J., & Barbeau, K. A. (2020). Organic dissolved copper
speciation across the US GEOTRACES equatorial Pacific zonal transect GP16. Marine Chemistry,
225, 103841.
Ruacho, A., Richon, C., Whitby, H., & Bundy, R. M. (2022). Sources, sinks, and cycling of dissolved
organic copper binding ligands in the ocean. Communications Earth & Environment, 3(1), 263.
Rushdi, A. I., McManus, J., & Collier, R. W. (2000). Marine barite and celestite saturation in seawater.
Marine Chemistry, 69(1-2), 19–31.
Sabine, C. L., Key, R. M., Feely, R. A., & Greeley, D. (2002). Inorganic carbon in the Indian Ocean:
Distribution and dissolution processes. Global Biogeochemical Cycles, 16(4), 15–1.
Salter, M. A., Harborne, A. R., Perry, C. T., & Wilson, R. W. (2017). Phase heterogeneity in carbonate
production by marine fish influences their roles in sediment generation and the inorganic carbon
cycle. Scientific Reports , 7(1), 765.
Salter, M. A., Perry, C. T., & Smith, A. M. (2019). Calcium carbonate production by fish in temperate
marine environments. Limnology and Oceanography, 64(6), 2755–2770.
Salter, M. A., Perry, C. T., Stuart-Smith, R. D., Edgar, G. J., Wilson, R. W., & Harborne, A. R. (2018). Reef
fish carbonate production assessments highlight regional variation in sedimentary significance.
Geology, 46(8), 699–702.
Sarmiento, J. L. (2006). Ocean biogeochemical dynamics. Princeton university press.
Sarmiento, J. L., Dunne, J., Gnanadesikan, A., Key, R., Matsumoto, K., & Slater, R. (2002). A new estimate
of the CaCO3 to organic carbon export ratio. Global Biogeochemical Cycles, 16(4), 54–1.
Schiebel, R. (2002). Planktic foraminiferal sedimentation and the marine calcite budget. Global
Biogeochemical Cycles, 16(4), 3–1.
Schiebel, R., & Hemleben, C. (2017). Planktic foraminifers in the modern ocean.
Schiebel, R., & Movellan, A. (2012). First-order estimate of the planktic foraminifer biomass in the
modern ocean. Earth System Science Data, 4(1), 75–89.
Semeniuk, D. M., Bundy, R. M., Payne, C. D., Barbeau, K. A., & Maldonado, M. T. (2015). Acquisition of
organically complexed copper by marine phytoplankton and bacteria in the northeast subarctic
Pacific Ocean. Marine Chemistry, 173, 222–233.
Shank, G. C., Whitehead, R. F., Smith, M. L., Skrabal, S. A., & Kieber, R. J. (2006). Photodegradation of
strong copper-complexing ligands in organic-rich estuarine waters. Limnology and
Oceanography, 51(2), 884–892.
Skrabal, S. A., Donat, J. R., & Burdige, D. J. (2000). Pore water distributions of dissolved copper and
copper-complexing ligands in estuarine and coastal marine sediments. Geochimica et
Cosmochimica Acta, 64(11), 1843–1857.
163
Smith, C. R., Hoover, D. J., Doan, S. E., Pope, R. H., Demaster, D. J., Dobbs, F. C., & Altabet, M. A. (1996).
Phytodetritus at the abyssal seafloor across 10 of latitude in the central equatorial Pacific. Deep
Sea Research Part II: Topical Studies in Oceanography, 43(4-6), 1309–1338.
Sternberg, E., Tang, D., Ho, T.-Y., Jeandel, C., & Morel, F. M. (2005). Barium uptake and adsorption in
diatoms. Geochimica et Cosmochimica Acta, 69(11), 2745–2752.
Stroobants, N., Dehairs, F., Goeyens, L., Vanderheijden, N., & Van Grieken, R. (1991). Barite formation in
the Southern Ocean water column. Marine Chemistry, 35(1-4), 411–421.
Subhas, A. V., Dong, S., Naviaux, J. D., Rollins, N. E., Ziveri, P., Gray, W., Rae, J. W., Liu, X., Byrne, R. H.,
Chen, S., et al. (2022). Shallow calcium carbonate cycling in the North Pacific Ocean. Global
Biogeochemical Cycles, 36(5), e2022GB007388.
Subhas, A. V., Rollins, N. E., Berelson, W. M., Erez, J., Ziveri, P., Langer, G., & Adkins, J. F. (2018). The
dissolution behavior of biogenic calcites in seawater and a possible role for magnesium and
organic carbon. Marine Chemistry, 205, 100–112.
Sulpis, O., Jeansson, E., Dinauer, A., Lauvset, S. K., & Middelburg, J. J. (2021). Calcium carbonate
dissolution patterns in the ocean. Nature Geoscience, 14(6), 423–428.
Sunda, W. G., & Huntsman, S. A. (1995). Regulation of copper concentration in the oceanic nutricline by
phytoplankton uptake and regeneration cycles. Limnology and oceanography, 40(1), 132–137.
Sverdrup, H. U., Johnson, M. W., Fleming, R. H., et al. (1942). The Oceans: Their physics, chemistry, and
general biology (Vol. 1087). Prentice-Hall New York.
Takano, S., Tanimizu, M., Hirata, T., & Sohrin, Y. (2014). Isotopic constraints on biogeochemical cycling of
copper in the ocean. Nature communications, 5(1), 5663.
Vance, D., Little, S. H., de Souza, G. F., Khatiwala, S., Lohan, M. C., & Middag, R. (2017). Silicon and zinc
biogeochemical cycles coupled through the Southern Ocean. Nature Geoscience, 10(3), 202–206.
van Hulten, M., Dutay, J.-C., & Roy-Barman, M. (2018). A global scavenging and circulation ocean model
of thorium-230 and protactinium-231 with improved particle dynamics (NEMO–ProThorP 0.1).
Geoscientific Model Development , 11(9), 3537–3556.
Walker, M., Hammel, J. U., Wilde, F., Hoehfurtner, T., Humphries, S., & Schuech, R. (2021). Estimation of
sinking velocity using free-falling dynamically scaled models: Foraminifera as a test case. Journal
of Experimental Biology, 224(2), jeb230961.
Weber, T., John, S., Tagliabue, A., & DeVries, T. (2018). Biological uptake and reversible scavenging of zinc
in the global ocean. Science, 361(6397), 72–76.
Westerlund, S. F., Anderson, L. G., Hall, P. O., Iverfeldt, Å., Van Der Loeff, M. M. R., & Sundby, B. (1986).
Benthic fluxes of cadmium, copper, nickel, zinc and lead in the coastal environment. Geochimica
et Cosmochimica Acta, 50(6), 1289–1296.
164
Whitby, H., Posacka, A. M., Maldonado, M. T., & van Den Berg, C. M. (2018). Copper-binding ligands in
the NE Pacific. Marine Chemistry, 204, 36–48.
Whitby, H., & van den Berg, C. M. (2015). Evidence for copper-binding humic substances in seawater.
Marine Chemistry, 173, 282–290.
Whitmore, L. M., Shiller, A. M., Horner, T. J., Xiang, Y., Auro, M. E., Bauch, D., Dehairs, F., Lam, P. J., Li, J.,
Maldonado, M. T., et al. (2022). Strong Margin Influence on the Arctic Ocean Barium Cycle
Revealed by Pan-Arctic Synthesis. Journal of Geophysical Research: Oceans, 127(4),
e2021JC017417.
Wilson, R., Millero, F., Taylor, J., Walsh, P., Christensen, V., Jennings, S., & Grosell, M. (2009).
Contribution of fish to the marine inorganic carbon cycle. Science, 323(5912), 359–362.
Wolf-Gladrow, D. A., Zeebe, R. E., Klaas, C., Körtzinger, A., & Dickson, A. G. (2007). Total alkalinity: The
explicit conservative expression and its application to biogeochemical processes. Marine
Chemistry, 106(1-2), 287–300.
Wolgemuth, K., & Broecker, W. (1970). Barium in sea water. Earth and Planetary Science Letters, 8(5),
372–378.
Woosley, R. J., Millero, F. J., & Grosell, M. (2012). The solubility of fish-produced high magnesium calcite
in seawater. Journal of Geophysical Research: Oceans, 117(C4).
Xue, H., & Sigg, L. (1999). Comparison of the complexation of Cu and Cd by humic or fulvic acids and by
ligands observed in lake waters. Aquatic Geochemistry, 5(4), 313–335.
Yeats, P., & Bewers, J. (1983). Potential anthropogenic influences on trace metal distributions in the North
Atlantic. Canadian Journal of Fisheries and Aquatic Sciences, 40(S2), s124–s131.
Žarić, S., Schulz, M., & Mulitza, S. (2006). Global prediction of planktic foraminiferal fluxes from
hydrographic and productivity data. Biogeosciences, 3(2), 187–207.
Zhang, H., Stoll, H., Bolton, C., Jin, X., & Liu, C. (2018). A refinement of coccolith separation methods:
Measuring the sinking characteristics of coccoliths. Biogeosciences, 15(15), 4759–4775.
Zhen-Wu, B., Dideriksen, K., Olsson, J., Raahauge, P., Stipp, S., & Oelkers, E. (2016). Experimental
determination of barite dissolution and precipitation rates as a function of temperature and
aqueous fluid composition. Geochimica et Cosmochimica Acta, 194, 193–210.
Ziveri, P., Gray, W., Ortiz, G., Manno, C., Grelaud, M., Incarbona, A., Rae, J., Subhas, A., Pallacks, S.,
White, A., et al. (2022). Pelagic carbonate production in the North Pacific Ocean. Revision at
Nature Communications.
165

Abstract (if available)

Abstract The ocean plays a vital role in the regulation of the global climate system, and understanding the mechanisms that control the distribution and cycling of key elements in the ocean is essential for predicting and mitigating the impacts of climate change. In this thesis, I investigate ocean biogeochemical processes through three chemical tracers, including alkalinity, barium, and copper, using both observations and an ocean circulation inverse model.
Alkalinity is a key parameter in the ocean carbon cycle. A global alkalinity model is developed to constrain the cycling of calcium carbonate (CaCO3) in the ocean. The results reveal that CaCO3 dissolution must occur throughout the water column to match observed alkalinity distributions, suggesting potential microbial processes that drive dissolution in supersaturated waters. CaCO3 export is constrained within a wide range, and the observed alkalinity features can be reproduced by the model as long as the magnitudes of CaCO3 export and upper ocean dissolution are coupled.
The dissolved and particulate phases of barium (Ba) can be used as proxies for organic carbon respiration and export productivity. I combine Ba observations, a multiple linear regression model, and a global dissolved Ba model to investigate the marine Ba cycle, with a focus on the distribution of dissolved Ba in the ocean and how the dissolved phase relates to the organic and particulate phases. Results show that the precipitation and dissolution of barite (BaSO4) play a major role in regulating the distribution of dissolved Ba. The model suggests that the dissolved Ba for barite precipitation originates mainly from ambient seawater, and that barite dissolution rate is relatively independent of barite saturation states.
Copper (Cu) is a trace metal that is involved in many biogeochemical processes in the ocean, including biological uptake, reversible scavenging, and organic complexation. I use observations and a global model to investigate the distribution of Cu in the ocean and how Cu interacts with marine organisms, organic matter, and particles. The model explicitly represents Cu partitioning between labile and inert phases through the slow conversion of labile Cu to inert in the whole water column, and the photochemical degradation of inert Cu to labile in the euphotic zone. The model results suggest that linear increases in Cu concentrations with depth require both a sedimentary source and reversible scavenging onto particles. Cu cycling in the Arctic Ocean appears to be different from other oceans, requiring relatively high Cu concentrations in Arctic rivers and reduced scavenging in the Arctic.
Overall, this thesis highlights the potential of ocean tracers as a powerful tool for investigating ocean biogeochemical processes, and the role of ocean inverse models in simulating and analyzing the complex processes that occur within the marine environment. The findings presented in this thesis advance our understanding of the biological and chemical processes that regulate the ocean system, while emphasizing the importance of the interconnections between different biogeochemical cycles in the ocean.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

The distributions and geochemistry of iodine and copper in the Pacific Ocean

PDF

The distribution and speciation of copper across different biogeochemical regimes

PDF

Environmental controls on alkalinity generation from mineral dissolution: from the mineral surface to the global ocean

PDF

Comparative behavior and distribution of biologically relevant trace metals - iron, manganese, and copper in four representative oxygen deficient regimes of the world's oceans

PDF

Concentration and size partitioning of trace metals in surface waters of the global ocean and storm runoff

PDF

Anaerobic iron cycling in an oxygen deficient zone

PDF

Carbonate dissolution at the seafloor: fluxes and drivers from a novel in situ porewater sampler

PDF

Going with the flow: constraining the lateral advection of redox-active metals from continental margins under differing oxygen regimes

PDF

Modeling deep ocean water and sediment dynamics in the eastern Pacific Ocean using actinium-227 and other naturally occurring radioisotopes

PDF

B-vitamins and trace metals in the Pacific Ocean: ambient distribution and biological impacts

PDF

The marine biogeochemistry of nickel isotopes

PDF

Calcite and aragonite dissolution in seawater: kinetics, mechanisms, and fluxes in the North Pacific

PDF

Investigations on marine metal cycling through a global expedition, a wildfire survey, and a viral infection

PDF

New insights into glacial-interglacial carbon cycle: multi-proxy and numerical modeling

PDF

Spatial and temporal investigations of protistan grazing impact on microbial communities in marine ecosystems

$Germanium-silicon fractionation in a continental shelf environment: insights from the northern Gulf of Mexico$

PDF

Germanium-silicon fractionation in a continental shelf environment: insights from the northern Gulf of Mexico

PDF

Discerning local and long-range causes of deoxygenation and their impact on the accumulation of trace, reduced compounds

PDF

The distribution of B-vitamins in two contrasting aquatic systems, and implications for their ecological and biogeochemical roles

PDF

Iron-dependent response mechanisms of the nitrogen-fixing cyanobacterium Crocosphaera to climate change

PDF

Diagenesis of C, N, and Si in marine sediments from the Western Tropical North Atlantic and Eastern Subtropical North Pacific: pore water models and sedimentary studies

Asset Metadata

Creator Liang, Hengdi (author)

Core Title Investigating the global ocean biogeochemical cycling of alkalinity, barium, and copper using data-constrained inverse models

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Ocean Sciences

Degree Conferral Date 2023-08

Publication Date 07/25/2023

Defense Date 07/24/2023

Publisher University of Southern California. Libraries (digital)

Tag GEOTRACES,inverse model,OAI-PMH Harvest,ocean biogeochemistry,trace metal

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor John, Seth (committee chair), Berelson, William (committee member), Cooperdock, Emily (committee member), Moffett, James (committee member)

Creator Email hengdili@usc.edu,lianghengdi@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113289543

Unique identifier UC113289543

Identifier etd-LiangHengd-12144.pdf (filename)

Legacy Identifier etd-LiangHengd-12144

Document Type Dissertation

Rights Liang, Hengdi

Internet Media Type application/pdf

Type texts

Source 20230726-usctheses-batch-1074 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA

Repository Email cisadmin@lib.usc.edu