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Spatial and temporal patterns of long-term temperature change in Southern California from 1935 to 2014

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Spatial and temporal patterns of long-term temperature change in Southern California from 1935 to 2014

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Spatial and temporal patterns of long-term temperature change in
Southern California from 1935 to 2014

by

M. Faith Webster

A Thesis Presented to the
Faculty of the USC Graduate School
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
Master of Science
(Geographic Information Science and Technology)

May 2016

Copyright © 2015 by M. Faith Webster
All Rights Reserved

To my family, both by blood and choice, but especially my son,
Stephen Harold.
I hope to make you all proud.
Thank you for your love and support
iv
Table of Contents
List of Figures .............................................................................................................................. vii
List of Tables .............................................................................................................................. viii
Acknowledgements ...................................................................................................................... ix
List of Abbreviations .................................................................................................................... x
Abstract ......................................................................................................................................... xi
Chapter 1 Introduction................................................................................................................. 1
Study Area ...........................................................................................................................3
Project Overview .................................................................................................................6
1.2.1. Homogenization .........................................................................................................7
1.2.2. The Hurst Exponent ...................................................................................................8
1.2.3. Spatial Properties .......................................................................................................9
Outline of this document ....................................................................................................10
Chapter 2 Background Literature ............................................................................................ 12
Global Temperature Change ..............................................................................................12
2.1.1. Anthropogenic Climate Change ...............................................................................13
Regional Climate Change Analysis ...................................................................................15
2.2.1. Impacts of Climate Change in California ................................................................17
Homogenization of Climate Data ......................................................................................19
The Hurst Exponent in Climate Change Studies ...............................................................20
The Environmental Variables Affecting the Rate of Climate Change...............................22
2.5.1. The Effect of Aspect ................................................................................................22
2.5.2. The Effect of Elevation ............................................................................................22
v
2.5.3. Land cover and Climate Change ..............................................................................23
Methodological Inspiration ................................................................................................24
Chapter 3 Methods ..................................................................................................................... 28
Data ....................................................................................................................................28
3.1.1. Station Elevation ......................................................................................................32
3.1.2. Station Aspect ..........................................................................................................33
3.1.3. Land cover Data .......................................................................................................35
3.1.4. Population Density ...................................................................................................37
Calculation of the Hurst Exponent .....................................................................................37
Hot Spot Analysis ..............................................................................................................39
Analysis of the Spatial Components ..................................................................................40
Chapter 4 Results ........................................................................................................................ 41
Southern California Temperature Trends ..........................................................................41
Analysis of the Hurst Exponent Results ............................................................................42
Relationship between Elevation and Temperature Trends ................................................46
Relationship between Aspect and Temperature Trends .....................................................47
Land Use, Population Density and Temperature Trends ...................................................49
Hot Spot Analysis ..............................................................................................................51
Chapter 4 Summary ...........................................................................................................54
Chapter 5 Discussion .................................................................................................................. 55
Evaluation of the Research Questions ...............................................................................55
5.1.1. What is the spatial pattern of H-values by season as determined by optimized hot
spot analysis? ..............................................................................................................55
vi
5.1.2. What is the correlation between H-values and elevation? .......................................56
5.1.3. What is the correlation between H-values and aspect? ............................................56
5.1.4. What is the correlation between H-values and the land covers “Urban” and
“Rural”? ......................................................................................................................57
5.1.5. Can census data be used to track changes in population density to evaluate changes
in urbanization? ..........................................................................................................57
Issues Addressed in the Study ............................................................................................58
5.2.1. Issues from Data Quantity and Quality ....................................................................58
5.2.2. Using H-values in spatial analysis ...........................................................................58
5.2.3. Exploration of the QD series....................................................................................59
Conclusion .........................................................................................................................59
REFERENCES ............................................................................................................................ 60
Appendix A: Population Density ............................................................................................... 64
Appendix B: Station Cumulative Deviation Series .................................................................. 66
Appendix C: H-Values by Station ............................................................................................. 75
Appendix D: Population Density for Census Tract by Station ............................................... 78
vii
List of Figures
Figure 1: Surface temperature anomalies relative to 1951-1980 (A) Global annual mean
anomalies. (B) Temperature anomaly for the first half decade of the 21
st
century. ........... 2
Figure 2: Temperature change in California from 1900 to 2000 .................................................... 4
Figure 3: Study Area: 10 counties of Southern California ............................................................. 5
Figure 4: The original 13 homogenized stations ........................................................................... 29
Figure 5: Active and historic temperature stations ....................................................................... 30
Figure 6: Homogenized stations by location ................................................................................ 32
Figure 7: Histogram of distribution of stations at elevations. ...................................................... 33
Figure 8: 1 arc-second DEM for Southern California .................................................................. 34
Figure 9: Aspect derived from the DEM for Southern California ................................................ 34
Figure 10: Land cover data with station land-use classification ................................................... 36
Figure 11: 80 years of temperature data by month shown in *C x100 ......................................... 38
Figure 12: QD series graph for station 40439: Bakersfield .......................................................... 41
Figure 13: Distribution of H-value data as a histogram ................................................................ 43
Figure 14: Persistence of Temperature change in H-values ......................................................... 45
Figure 15 Hurst exponent values against the elevation of the station........................................... 47
Figure 16: Seasonal H-values plotted against numerical aspect .................................................. 48
Figure 17: Proportional symbol population and population density change in Southern California
from 1910 to 2010 ............................................................................................................. 50
Figure 18: Optimized hot spot analysis of seasonal H-values by station. ................................... 53

viii
List of Tables
Table 1: Homogenized station list with associated coop number ................................................ 31
Table 2: Approximate QD inflection points of representative stations ........................................ 42
Table 3: Stations by mean H-value, highlighting the persistence categories ............................... 44
Table 4: Mean H-value of stations based on cardinality ............................................................... 49
Table 5: Mean H-values for urban and rural stations ................................................................... 49
Table 6: Selection of population density data ............................................................................... 51

ix
Acknowledgements
I am grateful to my advisor and mentor, Professor Karen Kemp. You provided me with direction
and guidance I needed to complete this project in a timely manner. I thank my committee
members, Su Jin Lee and Laura Loyola. Su Jin, thank you for encouraging me to evaluate
climate change, and starting me on this winding wonderful path. I am especially grateful to
Mathew Mene, a Physical Scientist with NOAA's National Centers for Environmental
Information (NCEI). The homogenized temperature data that was provided was an essential
component of this entire project. This project would not have been possible without your
contribution; thank you.

x
List of Abbreviations
ACC Anthropogenic climate change
CDIAC Carbon Dioxide Information analysis center
DEM Digital Elevation Model
GCM Global Climate Model
GIS Geographic information system
masl meters above sea level
NCDC National Climate Data Center
NCEI National Centers for Environmental Information
NCEP National Centers for Environmental Protection
NED National Elevation Dataset
NHGIS National Historic Geographic Information System
NLCD National Land Cover Dataset
NOAA National Oceanic and Atmospheric Administration
OEHHA Office of Environmental Health Hazard Assessment
QA Quality assurance
QD Cumulative deviation
SST Sea and surface temperatures
UHI Urban heat island
WRCC Western Regional Climate Center

xi
Abstract
Climate change is a pressing issue, and regional studies play an important part in understanding
the impact of global climate change. This project explored the spatial and temporal patterns
apparent in temperature records from 1935 to 2014 using homogenized station data from 66
stations in Southern California. Using Hurst Exponent, an index used to explore the persistence
of trends in longitudinal data, the strength of the increasing temperature trend observed at every
station was evaluated. Hurst Exponent values were calculated for the high, mean, and low
temperature series for both the summer and winter 3-month period. The spatial distribution of
each of the six Hurst values was examined with respect to location, elevation, aspect, land use,
and population density of each station using Microsoft Excel and ArcGIS. Results show that
there is persistence in the increase of temperature at all stations beginning around 1980, though
the strength of this persistence varies. Winter High temperature persistence is strongest in
coastal areas and weaker in the inland mountains as shown by the hot spot analysis.

1

Chapter 1 Introduction
Climate change is already affecting many places and people in the world. In order to understand
where the climate is going, and attempt to mitigate the consequences, it is important to
understand how climate has changed thus far. Evaluating climate long term and short term, on
both global and regional scales are all crucial. There are many measures of climate change, and
temperature change is a significant indicator (Karl et al 1997). This study evaluates spatio-
temporal temperature trends for 66 weather stations using homogenized data in the ten counties
of Southern California. Using the Hurst exponent, the degree of persistence of change at different
elevations, slopes, and aspects was evaluated to determine if there is an association between the
direction, magnitude, and speed of trends and these three variables in regards to station location.
This study helps understand the direction and degree of climate change in Southern California.
The term “climate” is a broad term that incorporates many facets of the environment. In
order to gauge climate change, quantifiable measures must be defined. Climate change can be
measured by changes in trends and extremes of temperature and precipitation, by the changing
patterns of flora and fauna, and variations in wildfire patterns (Karl et al. 1997). One of the most
frequently evaluated measures in climate change is temperature change, and that was the
indicator selected in this study to be analyzed. Global temperature increases have been observed
by many agencies and researchers, with an overwhelming majority of climate scientists believing
that the human activity is the cause of the observed temperature increases (Oreskes 2004, Doran
and Zimmerman 2009, and Anderegg et al. 2010).
Figure 1 illustrates the changing temperatures recorded on land and sea. Figure 1A shows
the global annual mean temperature change from the 1951-1980 base period. Figure 1B shows
the distribution of change of temperature averaged over 2001 to 2005 compared to the base
2

period. As can be seen in the first graph, in 1890 the mean global temperature was two degrees
below the base period and in 2010, the temperature was about 6 degrees above the base mean
(Hansen et al. 2006). This helps to demonstrate the pace at which temperatures are increasing
across the globe. The figure also shows that until about 1980, there were fluctuations in
temperatures above and below the mean; however, since about 1980 temperatures have only
ranged above the mean.

Figure 1: Surface temperature anomalies relative to 1951-1980 (A) Global annual mean
anomalies. (B) Temperature anomaly for the first half decade of the 21
st
century.
Source: Hansen et al. 2006
Climate change is important because of how the changing climate impacts agriculture,
economy, and environment on local and global scales. Where the effects of climate change can
be observed globally, they are and will be felt locally. As evidenced by Figure 1B, the way the
climate is changing can vary greatly by region. In order to understand what the impacts are going
to be, it is important to understand how each region has been affected by climate change.
Regional climate studies fill in this gap. Regional studies provide answers to the questions of
how the climate has changed and indicate the direction of change for that region.
3

Study Area
California is an ecologically diverse state. According to the Western Regional Climate
Center (WRCC 2015), biomes range from sub-tropic to sub-arctic depending on latitude,
elevation and proximity to the coast, with nearly all biomes represented. This is because of the
confluence of maritime air masses joining with continental currents, and the diverse topography.
There are several mountain ranges in California, with the highest peaks reaching over 14
thousand feet. California also has many low elevation areas with Death Valley being the lowest
point in the country with an elevation of 276 feet below sea level. Also, Southern California is
home to two of the largest counties in the United States. San Bernardino County is the largest
county by size, and Los Angeles County is the largest by population.
California has mostly dry summers and a comparatively wet winter. Northern California
typically has more year round rain, and can provide the state with over 70 percent of the its water
needs, when not experiencing severe drought as is the case as of 2015 (WRCC 2015). With
irrigation, California’s generally warm temperatures facilitate a lengthy growing season. The
coldest temperature on record of -45 degrees Fahrenheit was reported in 1937 from a location at
an elevation of 5,532 feet. To contrast the hottest temperature on record, as of December 2015
was 134 degrees Fahrenheit at -168 feet elevation (WRCC 2015). Figure 2 shows the 5-year
average temperatures of California over a 100-year period. Consistent with other temperature
data, temperatures have been entirely above the mean since 1980.
4

Figure 2: Temperature change in California from 1901 to 2000
Source: National Oceanic and Atmospheric Administration (NOAA)
http://ncdc.noaa.gov
Southern California has many definitions. Some definitions of Southern California are
based on membership in the Southern California Association of Governments, an association of
six counties: Imperial, Los Angeles, Orange, Riverside, San Bernardino, and Ventura. Where this
is convenient because it has an official sound to it, it excludes counties that are conceptually
ingrained in the concept of Southern California like San Diego. Other definitions based in
economics include only eight counties: Santa Barbara, Ventura, Los Angeles, San Bernardino,
Riverside, Orange, San Diego, and Imperial (US Census Bureau 1970). Because this project is so
heavily spatial in nature, Southern California is defined by the Southern versus Northern division
at 35° 47′ 28″ north latitude, as seen in Figure 3. This adds San Luis Obispo and Kern Counties
5

to the list to make a total of ten counties that have a balanced shape to serve as the study area of
this project.

Figure 3: Study Area: 10 counties of Southern California
Temperature change in Southern California was evaluated by the Office of
Environmental Health Hazard Assessment (OEHHA). They found that the annual mean
temperatures have increased 1.5 degrees Fahrenheit per century since 1895, while average
minimum (low) temperatures are up 1.99 degrees (OEHHA 2013). According to the report,
average maximum (high) temperatures were up only 1.01 degrees. These numbers serve as a
6

foundation for understanding that temperatures are increasing in Southern California. The goal of
this project is to contribute to the understanding of how persistent that change is.
Project Overview
This study evaluates persistence of temperature change using homogenized seasonal
high, mean and low monthly temperature data from 66 stations across Southern California from
December 1934 to August 2014. Persistence is measured using the Hurst Exponent. This study
tests H-values in correlation to elevation, aspect, and land cover to provide insight to the spatial
trend in temperature change. These are the Research Questions that were addressed:
1. Is there a spatial pattern of H-values by season as determined by optimized hot spot
analysis; if present, how is the correlation best described?
2. Is there a correlation between H-values and elevation; if present, how is the
correlation best described?
3. Is there a correlation between H-values and aspect; if present, how is the correlation
best described?
4. Is there a correlation between H-values and the land covers “Urban” and “Rural”; if
present, how is the correlation best described?
There are several different types of sciences involved in climate change research. In this
case, the focus is on geographic information science (GISci). Mapping and spatial analysis,
major components of GISci, have been important to understanding and displaying climate data
(Thornthwaithe 1948, Daly et al. 2002). One of the best ways to interpret climate data is by
understanding the space in which it occurs. As a result, much of the analysis in this project is
illustrated with maps.
7

1.2.1. Homogenization
Homogenization is a process of treating climate data to remove the impact of urban heat
islands (UHI), ensure that that recorded data is reliable, and maintain the consistency of the time
series (Longobardi, and Mautone 2015). This editing, filtering and filling in of data creates a
stronger, more consistently reliable set of data from which further analysis is strengthened. The
NOAA Carbon Dioxide Information Analysis Center (CDIAC) published a report of
homogenized stations (Menne et al. 2015) that produced a long-term series for the conterminous
United States. The report details the homogenization and quality assurance processes that
produce the end data. The quality assurance (QA) of the data is an integral step in data
homogenization and includes (Durre et al 2010):
1. Basic Integrity Check - looks for data duplication;
2. Outlier tests (19 checks) - looks for values that are outside of the presumed value
range.
3. Internal and temporal consistency - evaluates ranges in the data;
4. Spatial consistency - makes sure the values are consistent with surrounding sites;
5. Meta-consistency – observations not flagged by other checks are verified for
integrity.
The specific methodology of homogenization is discussed in Chapter 2. In brief, Menne
and Williams (2007) use a pairwise comparison algorithm to analyze consistency of the
observations of adjacent stations, checking for outliers, missing data and possible errors. This is
an important contribution to preparing data for climate change analysis because the alternative is
to rely on station metadata that is not always consistent in availability and/or quality.
8

1.2.2. The Hurst Exponent
Harold Edwin Hurst created a method of rescaling time series data in 1951. The goal was
to evaluate the discharge of the Nile before it was to be dammed. The resulting analysis process
is seen as pioneering work in fractal geometry (Mandelbrot 1982, Outcalt 1997). The Hurst
Formula, shown in (1), from Outcalt (1997), measures how the trends in a time series move
towards or away from the mean of the entire series.
[
𝑅 (𝑛 )
𝑆 (𝑛 )
] ∞ 𝑛 𝐻 (1)
Here, n is the number of data points in the time series, R(n) is the range of the n values,
and S(n) is the standard deviation of the values. H is the slope of the line from log [R(n)/S(n)]. H
is the vital portion of the equation, and is known as the Hurst Exponent. While Hurst used the
method first, the equation was developed by Mandelbrot (1967) who named it after Hurst.
The power of the Hurst Exponent is its ability to qualify the time series. H-values range
between 0 and 1. A value greater than 0 but less than 0.5, indicates that change within the series
is cyclical. The further away from 0.5 the more pronounced the cyclic pattern. 0.5 indicates an
entirely random series, so as values approach 0.5, the more random the series variation is. Values
greater than 0.5 indicate persistence of change. As the value approaches 1, the stronger is the
persistence of the apparent trend, and likewise the closer to 0.5 the value is, the weaker and more
random the series variation is. The H-value does not report the direction of the persistence, only
its strength. The direction of the persistence must be independently determined by reviewing the
trends in the data itself. The Hurst Exponent is the theoretical construct where H-value is what
can be calculated.
9

1.2.3. Spatial Properties
The H-value was used as a tool to evaluate the relationship between long-term
temperature changes and various spatial variables associated with each station’s location. The
variables evaluated in this study were aspect, elevation and urbanization. The H-value of each
station’s series provided a means to evaluate the strength or persistence of the temperature
increases at that station. To formally frame the analysis described here, a hypothesis for each
spatial property is presented below.
1.2.3.1. Aspect
Aspect in this case is the cardinal direction of the slope of the plane valuing from 0 to 360
with 0/360 representing due north and 180 representing due south. The earth is far from a flat
surface, and southern facing planes receive more sun in the northern hemisphere than northern
facing planes. The hypothesis is that stations on a southern facing plane will have higher
H-values reflective of more persistent temperature changes over stations located on a northern
facing plane.
1.2.3.2. Elevation
There are myriad regional climate studies, and many of those studies are showing that
high elevations are more sensitive to changing climate conditions and may act as early indicators
of impending change at lower elevations (Giorgi, Hurrell and Marlnucci 1996; Diaz and Bradley
1997; Hansen et al. 1999; Van Beusekom, Gonzalez, and Rivera 2015). Because higher
elevations are often more sensitive they can help show the direction that the regional climate
trend is headed. Therefore, the hypothesis is that stations located at higher elevations will
produce higher H-values reflecting increased persistence of temperature change at higher
elevations over stations at lower elevations
10

1.2.3.3. Urbanization
The urban heat island (UHI) effect has been well studied (Easterling, Peterson, and Karl
1997; Tett et al. 1999; Kalnay and Cai 2003; Hayhoe et al. 2004, Ruddell 2013) and urbanization
has been shown to have a significant impact on temperatures causing more pronounced
temperature increases. Even though the data used in this study has been homogenized to
minimize the UHI effect spatially, the expectation is that over the time series, stronger
persistence of temperature increases should be observed at stations with an urban land cover.
Because urbanization changes over time but land use data is difficult to find for the full range of
dates included in this study, census population density was used as a proxy for urbanization. The
hypothesis is that there will be higher H-values showing higher degrees of persistence of
temperature change at stations with higher population densities (i.e. more urbanized) than
stations with lower population densities (i.e. more rural).
Outline of this document
Chapter 2 discusses some of the myriad studies in climate change focusing on studies that
are relevant to the study area or the study methodology. Works analyzing global temperature
climate change show that around the world temperatures have been increasing over the last
century with the most significant increases from 1980. Not only are temperatures increasing, but
the driving forces linked to temperature increases are attributed to human activity. This is called
anthropogenic climate change (ACC) (IPCC 2007), and is addressed in Section 2.1. Regional
studies help scientists to understand which areas are being most affected by climate change.
Section 2.2 discusses some of the methodology for regional analysis of temperature changes, and
the results of regional studies for California and Southern California. Homogenization is
discussed in Section 2.3. Section 2.4 talks about the Hurst-Exponent, and how it is used in a
11

research setting. The rest of Chapter 2 discusses how the spatial variables used in the study are
reflected in the research.
Chapter 3 addresses the methodology employed. The data that was used, how it was
obtained and the important metadata are addressed in Section 3.1. The rest of the chapter is
dedicated to explicating how the Hurst data was generated and employed in analysis. Section 3.2
focuses on the Hurst Exponent, and Section 3.3 looks at the Hot Spot Analysis. The spatial
dimensions of the study are addressed in Section 3.4
All of the results of the study are displayed in Chapter 4. Section 4.1 reviews the
temperature trends where Section 4.2 shows the results of the Hurst analyses.
The final chapter addresses the problems that arose during the study. Chapter 5 also
covers a few afterthoughts and suggestions for future research based both on the methodology
and the data set created. Lastly, the significance of this study is relayed. This very last section of
Chapter 5 is arguably the most important because it not only covers what the study
accomplished, but how it might help other studies in the future.
12

Chapter 2 Background Literature
Climate change is an incredibly widely studied field. There are journals, such as Climate
Change, Climate, and Climate Dynamics, among others, exclusively dedicated to climate change.
With an average of about 1,400 articles on climate published each year (Powell 2012), there is no
shortage of studies to report. This chapter focuses on some major keystone articles, articles
specifically about the study area, and some recent works relative to each section.
Climate is defined as the weather conditions prevailing in an area in general or over a
long period. Weather conditions are generally thought of as temperature and precipitation, and
maybe wind, but ways of measuring climate change extend far beyond that. Karl et al (1996)
outline in detail many of the ways that climate change can be measured through its impacts on
flora and fauna, oceanography, wildfire patterns, and of course atmospheric conditions like
precipitation and temperature, the latter the focus of this research.
Global Temperature Change
Tracking temperature change is one of the primary means of evaluating climate change.
As early climatic sensor technology proliferated, the ability to quantify climate became a reality
(Thornthwaite 1948). The next challenge was to disambiguate climate study from meteorology,
statistical rational analysis was one means of accomplishing this (Thornthwaite 1948). Chapter 1
already discussed how temperatures are rising around the globe, but many research studies cover
the myriad aspects of the globally increasing temperatures. In 2006, Hansen et al. compared
predictive temperature models from the 1980’s and compared their predictions to real instrument
readings during the prediction years. This served to evaluate the accuracy of predictive models,
and assess the current rate of temperature increase. Not only does their paper show the
magnitude of global temperature increases, but it also looks at three scenarios for continuing
13

trends based on carbon dioxide emissions estimates. Their conclusion is that the earth is as warm
as the Holocene maximum. As temperatures approach the warmest in a million years, the effects
of the temperature increases constitute significant levels of change.
Most scientists attribute the rise in temperatures to increases in greenhouse gasses such as
carbon dioxide. Greenhouse gasses not only increase temperatures but also increase solar
radiation levels as discussed by Schlesinger (2011). He reports that global air temperatures are
expected to increase from 2 degrees to 4.5 degrees Celsius because of increased concentrations
of greenhouse gasses.
These are just a couple articles that show that global surface temperatures are on the rise.
Even though we know that temperatures are on the rise, regional studies help scientists
understand how the global increases are impacting people, plants, and animals on a local level.
This is part of the reason that there are so many regional studies on climate change, and
temperature increases in particular. Temperature increases are happening globally, but change is
observed on the regional scale.
2.1.1. Anthropogenic Climate Change
Anderegg et al. (2010) did a meta-study looking not at climate change or its causes, but
instead looked at a database of 1,372 leading scientists and their research to address the apparent
disagreement about anthropogenic climate change (ACC) perceived by the American public.
According to that study, about 98 percent of researchers publishing in the field of ACC agree
with the results of the Intergovernmental Panel on Climate Change. Not only this, but the
roughly 2 percent of researchers who do not hold this belief are much less prominent
professionally. This really translates to the vast majority of the scientific community as a whole
agree that the patterns being observed as climate change have been caused by human action.
14

Studies regarding the changes seen in the climate and possible causes began decades ago.
There was an IPCC on climate change in 1990 that attributed the increases in global temperature
to human activities (Santer et al 1996). By 1999, scientist attributed increases in temperature to
the increased levels of carbon dioxide in the atmosphere, and the increase use of sulphate
aerosols (Tett et al 1999). In 2013, Ryerson et al. directly addressed atmospheric pollution and
climate change. The goal was to record how much of what is going into the air, and how that
might potentially be affecting the climate. The correlation here between population growth and
urbanization with climate change is obvious. They were even able to record leaks in the natural
gas infrastructure, which might have been overlooked as a contributing factor had it not been
included in their research. They also looked at how air pollution in Los Angeles might be
moving across the valleys and affecting air quality elsewhere.
One of the earliest papers identified that correlates climate change with population
growth showed that even in the small towns of less than 10,000 people there was on average a
0.1 degree Celsius increase in temperature from nearby stations with more than 2,000 people
(Karl et al. 1988). That study evaluated 1219 weather stations from 1901 to 1984.
One human activity other than carbon emissions that is known to increase temperatures is
the amount of ground covered by pavement and buildings. Since soil is not very reflective, as the
sun hits the soil it will absorb heat. Concrete on the other hand reflects the heat back to be
bounced off nearby buildings. The reflectivity and absorption of heat by a surface is called
albedo. Concrete and other man made structure have a high albedo and are very reflective, where
trees, grass, and soil absorb heat more than reflect it, and have a low albedo (Taha 1997). As
solar radiation as heat hits the earth, the radiation and heat are either absorbed by surface or
reflected back functionally increasing temperatures (Raupach and Finnigan 1997). The effect is
15

similar to the impact a mirror has on light. A single candle only produces so much light on its
own, but if the candle is placed in front of a mirror the light of the candle is almost doubled.
Regional Climate Change Analysis
Regional climate studies are important in understanding how the changing climate has
impacted and will impact specific areas on a smaller scale. Kuepper et al. (2005) discuss the
significance and importance of regional studies in understanding global climate change. As of
2015, Global Climate Models (GCM) must be used and parred down to facilitate projections for
a region (Pierce 2004, Cayan 2008). Quality data and analysis for a region helps to fill in the
data gaps of the GCM to make the regional model more comprehensive, highlighting the
importance of quality regional climate change studies.
Studies of historical climate and temperature change at the local level are dependent upon
the availability of data. Ideally, the best data that has been collected or is available for that region
will be used. The data must have been consistently and reliably collected to be utilized as an
indicator in a study to evaluate temperature change, or any other aspect of climate change for
that matter. Each collected temperature set is a separate indicator. Daily high data is one example
of an indicator, and daily low temperatures is another. Indicators can also be the result of data set
analysis. This study used seasonal measures derived from the monthly high, mean and low
temperature reports.
Different climate stations report data differently; some stations report on daily
temperature high, and low, sometimes including a daily mean, while some stations in Europe,
report data according to Manheim hours (Rebetez and Reinhard 2007). Manheim hours take the
temperature measurements at specific times of day (morning, afternoon and evening) to calculate
monthly means instead of using the simply daily high and low temperatures. Other stations do
16

not report the daily mean at all, only the high and low. If the data for a specific measure is
sporadic or inconsistently collected, or has been shown to be in any other way unreliable, that
indicator is likely to be eliminated entirely from the analysis.
Data quality is an issue addressed in many ways. Most projects are usually only able to
use between three to five indicators to determine rate of change because of issues in data quality
for the other indicators. Garzena’s (2015) study of temperature change in the Italian Alps uses 6
indicators: Cold spell duration, Warm nights, Warm days, Cool nights, cool days, and Warm
spell duration. They used some satellite data to fill in some blanks offered from intermittent
ground station data. Some studies, such as Liu at al. (2004), have used interpolation to fill in
short periods of missing data. They evaluated 305 stations high, mean and low readings. They
likely interpolated missing values in order to maintain an even statistical weight between the
figures.
Booth, Byrne and Johnson (2012) evaluated climate change in western North America
using data from 485 stations. They were able to utilize consistent daily data from 1950 to 2005.
Six stations had long-term records that were analyzed for a hundred year interval starting in
1906. There were able to analyze 4 temperature indicators and 4 precipitation indicators from the
27 core climate change indicators developed by the World Meteorological Organization (WMO).
They evaluated the 22 westernmost states of the contiguous United States and 4 provinces from
Canada. Results showed that because of the diversity within the region, result of increases
varied, though warming trends were ubiquitous, and precipitation trends fluctuate between
increasing and decreasing trends. In California and southern California specifically, they found a
general warming trend with some coastal cooling.
17

An important paper that influenced this research is Rebetez and Reinhard (2007). Their
study also sought to analyze long-term temperature trends using spatial attributes like aspect, and
elevation. Using homogenized data, they evaluated temperature change in Switzerland at 13
stations. They compared temperatures to the global mean to assess degree of change. Using the
Ward Method for hierarchical clustering based on a Euclidean distance matrix they analyzed the
relationship between stations. They found that temperatures had increased 0.135 degrees Celsius
per decade in the last century, but 0.57 degree increase can be attributed to the last 30 years
alone. Seasonal warming trends fell into the 95 percent significance range. This key research is
reviewed in detail later in this chapter as a means of setting the framework for the research
reported in this document.
2.2.1. Impacts of Climate Change in California
Climate change is more than just temperature and precipitation changes. The impact that
these changing patterns have affects multiple systems. In this section, some of the other ways
that climate change has impacted California and Southern California are explored.
As temperatures increase and, especially in California, as precipitation decreases, some
species of plants thrive, while others wither or migrate to more suitable areas. Evaluating where
and how plant distribution is changing is one of the indicators of climate change (Karl et al.
1996). Kelly and Goulden (2008) cover over 30 years of floral distribution in Southern
California. They found that as temperatures increased and precipitation decreased, the elevation
of dominant species increased by approximately 65 m. Even some climate modeling scenarios
include projections regarding flora. Projections predict an increase in deciduous forest cover as
coniferous forests decline (Lenihan et al 2003, 2008). The viability and accuracy of modeled
18

plant ranges with projected climate change suggest that predictions may not have the desired
accuracy and how to possibly adjust the projections (Dobrowski et al. 2011).
Plant life migration patterns are only one of the impacts of climate change. Rising sea
level is one of the primary concerns in a global climate change scenario. The Pacific Ocean is a
significant contributor to the overall climate patterns in California. Cayan et al. (2008) examine
what effects climate change will have on sea levels along California’s coast. Because California
has such a long coast line, this global trend is regionally relevant. Ocean currents affect El Nino
patterns that contribute to precipitation patterns across the globe. Cayan et al. suggest that even
with the changes in precipitation in California, the increased temperatures will continue to reduce
snow pack. Further analysis of ocean cycles is seen in other articles.
Even though the primary focus of Hayward (1997) is on the Pacific Ocean as a whole, the
paper looks at changing plant life within the Pacific. The expectation is that there will be a
proliferation and abundance of some sea life, where other sea life will wither. The long ranging
effects of these changes was not evaluated in the paper, but because California has such a long
coast line, it may be assumed that climate changes affecting the abundance of ocean flora and
fauna will significantly influence California’s economy.
As temperatures increase and precipitation in California decreases, fire patterns are one
of the big climate change indicators. Fried, Tom, and Mills (2004) show that changes in the fire
patterns can demonstrate climate change in California. Their paper focuses on Northern
California specifically, and they found that as CO2 increases, fires are projected to burn more
intensely and spread faster. Westerling and Bryant (2008) discuss the importance of climate
change on fire seasons, and what possible impacts the regional climate change may have upon
19

California’s fire season. The study reported that the reduction in air and land moisture with
increased temperatures indicate there will be more large fires more often.
Homogenization of Climate Data
Ideally, data collected for any research objective is perfect with no instrument error or
gaps in data recording, and no external factors influencing readings. With most data sets this is
not the case, and climate data is no exemption. Changes in instruments, how data is recorded,
station location, and increases in urbanization all have impacts on climate data that make solid
meaningful statistical analysis difficult (Aguilar et al. 2003). This is where homogenization of
weather data for climate change research steps in.
Different studies use various methodologies for selecting data collection sites to use for
their studies, but many studies value homogeneity because it ensures consistency within the data.
(Vincent and Guillett 1999; Rebetez and Reinhard 2007; Garzena, Fratianni and Acquaotta 2015;
Longobardi and Mautone 2015). When sites have been moved, or have only sporadically
collected data, it can significantly affect analysis of temporal trends (Christensen et al. 2008;
Dibike et al. 2008). The results from statistical analysis can also be altered by sporadic and
erratic data. Using homogenized data ensures that these errors and gaps are eliminated from the
data as much as possible.
Much research has been dedicated to how to identify non-climatic contributions to
climate data, so there are many techniques and means by which homogenization can be done.
While some methods focus on analysis of the metadata to give clues to how data should be
adjusted, others use analytic methods directly on the data itself (Easterling, Peterson, and Karl
1995). For the research reported here, homogenization was performed using Mene and Williams
(2007) guidelines. They created an automated algorithm that performs pairwise comparisons of
20

data from a network of stations. The process looks at each of the readings from a diverse set of
stations to establish the most likely range of temperatures that exclude artificial discontinuities,
or “inhomogeneities” (Menne and Willaims 2007). The goal is to be able to detect disparities in
temperature that do not reflect the true variability. This is why the metadata is not as significant.
Regardless of the completeness of the metadata, or any previous knowledge regarding the
circumstances around the data collection, inhomogeneities should be snuffed out.
The pairwise comparison is combined with another algorithm that uses recursive testing
to correct multiple inhomogeneities simultaneously. Recursion relies on testing and analyzing
smaller versions of the same type of data. The series of data are also examined for improbable
shifts in temperatures from one day or one station to another. This method has a lower rate of
false alarm readings than the other methods for homogenization (Mene and Williams 2007). The
result produces homogenized monthly data from which further analysis can be performed.
The Hurst Exponent in Climate Change Studies
The Hurst exponent has seen most use in the financial sector to calculate predictability of
various markets. Carbone, Castelli, and Stanley (2004) calculated the H value for the minute to
minute ticks of the German market to determine the predictability. They estimated H using the
Detrending Moving Average technique. H-values calculated were all close to .5 in value, and it
was determined that the market has a low predictability.
Cajueiro and Tabak (2004) provides another example of the Hurst Exponent being
employed in finance. They sought to determine if emerging markets gain efficiency over time.
They evaluated 4 years of global market trends of young markets, such as Brazil, Latin America,
and Thailand. They found that higher H values reflected increasing efficiency expressed by most
young markets but not all.
21

Despite its popularity in financial studies, the Hurst exponent was created for evaluating
geophysical time series data (Hurst 1951, Mandelbrot 1968), but it has many applications.
Outcalt (1997) outlines a number of other uses and applications. He suggests using H-values to
assess distribution of trees and sunspot pattern analysis, and, with respect to climate studies, for
temperature, precipitation and drought analysis.
A very interesting study was done in 2003 by Koutsoyiannis. He took 1000 years of
temperature data inferred from various sources such as isotope readings, tree ring analysis, and
ice core samples. Because of the nature of the inferred data, the study covered the northern
hemisphere. The researcher’s interest was to determine hydrological cycles based on temperature
persistence. He found that climate fluctuates at all time scales, and calculated an H value of 0.88
for the long-term memory of the proxy annual temperatures.
Another long range temperature study that used inferred data covered 125 years of ocean
compared to land temperatures of the Northern Hemisphere (Alvarez-Ramirez et al. 2008). They
found that temperatures, while rising, are also cyclical annually and inter-annually determined by
12 month and 2 month running means.
Rangarajan and Sant (2004) used meaned monthly data to calculate seasonal H-values of
monsoon seasons in India to see if there was a correlation between temperatures and
precipitation. Their study used GHCN data of 31 stations .H-values greater that 0.5 can also
show predictability. Some stations high H-values reflected high predictability, but not all.
Ruddell et al. (2013) used the Hurst exponent to evaluate long-term temperature changes
to quantify the UHI. Temperature data from urban Phoenix, AZ was compared to temperature
data from the nearby Gila Bend, AZ, a much less urbanized community. They examined the
extremes in temperatures: frost days, and misery days from 1900 to 2007 and calculated H-
22

values for the time series data. The results showed fewer frost days and increases in misery days
in Phoenix, while the conditions were relatively stable with only moderate increases in Gila
Bend.
The Environmental Variables Affecting the Rate of Climate Change
2.5.1. The Effect of Aspect
Around the northern world, as in California, on north-facing slopes snow tends to last
longer and temperatures tend to be cooler (WRCC 2015). This is due to differences in solar
radiation and suggests that south-facing slopes (in the northern hemisphere) may feel the effect
of climate change more strongly. Rebetez and Reinhard (2007) found that to be the case in their
study of the Alps. They found that stations on the south-facing sides warmed an average of 0.13
degrees, and temperatures on the north-facing sides increased only 0.10 degrees. No other studies
that included aspect as part of a temperature change study were found, even though slope and
aspect are key to understanding species distribution and ecosystem processes (Bennie et al.
2008). Environmental Variables Affecting the Rate of Climate Change
2.5.2. The Effect of Elevation
It is common knowledge that the high elevations have different climatic attributes from
the low lands of Southern California (WRCC 2015). Many “flatlanders” escape the summer heat
by retreating to the cooler mountain temperatures, and visits to the snow in winter, when there is
snow, is not uncommon either. The question is how the effect of difference in elevation has been
expressed in the climate change research.
There are studies dedicated exclusively to climate change at high elevations. In many
measures of climate change, higher elevations are more sensitive to the impacts of higher
temperatures. Beniston, Diaz and Bradley (1997) looked at a centuries worth of data and the
23

impacts for climate change in high elevations exclusively. They note the difficulty in performing
a thorough analysis because of the lack of high elevation stations. Even still they were able to
find that the magnitude of change in high elevations exceeds the global rate of change.
Mote (2006) looked at snow pack levels in western North America. Though Southern
California was left out of the study, the results for the mountains of Northern California and the
Cascades show that Pacific climate variability accounts for 10 to 60 percent of April snow water
equivalent levels. In other words, the snow pack is melting. Pacific climate variability is the
interannual and decal oscillating patterns and fluctuations of currents within the oceans and
atmosphere that have effects upon the weather in the northern hemisphere. (Di Lorenzo et al.
2010)
The Tibetan plateau has been the focus of many of the high elevation research studies
(Liu et al 2008, You el al. 2010). You et al. (2010) tested correlations in the temperature trend
for annual mean temperature and seasonal temperatures with elevation using National Center for
Environmental Protection (NCEP) data. 11 indicators at 71 stations all above 2000 m found no
correlation between elevation and the magnitude of the rising temperature trend. Liu et al (2008)
found elevation dependency in the Tibetan Plateau similar to the types of dependency found in
the Alps, and the Rockies. They found increasing temperature trends from 116 stations using
monthly low temperature data.
2.5.3. Land Use and Climate Change
Evaluating land use change in association with temperature change is one component of
understanding anthropogenic climate change. Changes in albedo is one of the most direct effects
of population growth upon the local ecology and thus suggests impacts on temperature change.
24

Early studies such as Taynac and Toros (1997) focused on individual cities and climate change.
They looked at four developing cities in Turkey from 1951-1990, and found urban heat islands
with marked increases in annual temperature during this time period, but there were no perceived
changes in precipitation. A 2003 study by Kalnay and Cai attributed a 0.25 degree temperature
increase over the past fifty years to surface temperature changes. In 2008, Grimm et al.
performed a continental research program to evaluate small and large cities and the effects of
land cover change. Satterthwaite (2009) looked at carbon emissions as a driving force for climate
change and argued that it is not so much population increase, but the carbon footprint of the
populations that are driving climate change. Thus, the role of urbanization on climate change is a
diversely studied and intensely interesting research topic.
Methodological Inspiration
After reading many academic articles on regional climate change, Rebetez and
Reinhard’s (2007) study of temperature changes in the Swiss Alps was selected as a preliminary
study template. Station elevation ranged from 316 m to 2490 m in their report, which is similar
enough to the range of values of Southern California stations (- 36.9 m to 2091.7 m) to serve as a
viable model. Also, the time frame is similar; Rebetez and Reinhard were able to obtain
homogenized data from 1901-2000. This study ranged from 1935 to 2014, providing an 80 year
analysis in place of the 100 year study. At the initial inception of the project there were data for
only 13 homogenized stations in Southern California, and the Rebetez and Reinhard study used
12 stations. The objective, data and ranges were thus similar enough to justify considering
employing their research methodology as a model.
The data set used by Rebetez and Reinhard had 12 homogenized stations with monthly
Manheim temperatures. Manheim temperatures report three values each day: an early morning, a
25

peak afternoon, and an evening temperature instead of the high, low, and mean temperatures
seen in the majority of U.S. temperature station data. It was from the daily Manheim values that
their study calculated a mean temperature for each month. The monthly data available from
NOAA that reports temperatures in North America, including Southern California, employs the
more typical daily high and low and mean temperatures. This use of a different type of
temperature series was the first major divergence from the original template methodology. The
second was a fortuitous acquisition of more homogenized Southern California temperature data
that permitted this study to expand to a consideration of 66 stations.
Rebetez and Reinhard used the Ward method to perform a cluster analyses to analyze the
relationships between the stations. The Ward method is an agglomerative hierarchical clustering
using a Euclidean distance matrix to explore similarities and differences in stations and months.
Unfortunately, most programs which perform this type of analysis, such as SPSS, are not
spatially oriented. They use latitude and longitude values, which are degree measurements that
change in distance measure as the distance from the poles changes, as Cartesian x,y values. As a
result, Euclidean distances from such coordinates are not accurate measures of true distance.
The Ward method puts greater importance on closer stations with results similar to a
nearest neighbor distance weighting. This is done by sequentially incorporating clusters by
proximity starting with each point as its own “cluster” and building from there. ArcGIS has the
ability the run a distance analysis from a projected coordinate system where distance measured is
relatively accurate to reality, and is therefore inherently a better means to perform the same type
of analysis. In this study, an optimized hotspot analysis was used in place of the Ward clustering.
This became another point in which the methodology of this study deviated from the original
template study.
26

Rebetez and Reinhard employed a Fisher test to determine the exact p-value of trends for
individual stations. P-value is the likelihood that a randomization of the variable will match what
is actually observed. It is used to determine how likely the reality is to be random or correlated.
The Fisher test runs every iteration of the possible paired values for all variables to produce a p-
value that reports the strength of the correlation in the data.
The Hurst Exponent also measures the strength of temporal autocorrelation of a time
series. In this study it was chosen over the Fisher test because the Hurst Exponent was developed
to analyze time series specifically, where the Fisher test is employed in all forms of statistics for
all forms of data types. Also the Hurst Exponent not only measures autocorrelation and
randomness, but also identifies cyclical patterns and is therefore offers a stronger analysis of the
time series.
Rebetez and Reinhard compared their results to global data from the Climatic Research
Unit as a baseline for comparison of changes. However, the Hurst Exponent offers a cumulative
deviation time series that can be used to understand the trends for each station. A more regional
comparison was deemed a more appropriate means to evaluate change in this study.
The template study compared the north- and south-facing aspects of the slopes in the
Alps by comparing the mean temperature increase at stations on the northern versus southern
side of the Swiss mountain ranges. That inspired the aspect analysis performed by this project,
but again GIS facilitates a more concise evaluation of slope and aspect derived from a DEM.
Webster used the derived aspect to assign numerical aspect values (0-360) for each station. The
H-values for each station were then compared to the aspect values using scatter plots as a
correlation analysis.
27

Finally, in a complete deviation from the template study, this study also evaluated land
use and population change to see if there was a connection between stations demonstrating
higher persistence of increasing temperature change and higher urbanization levels.
This chapter could have continued to discuss climate change in depth for many more
pages. This background chapter served to provide a foundation and justification for the research
and methodology presented.
28

Chapter 3 Methods
This project sought to understand the spatial and temporal trends in temperature change in
Southern California that are evident in homogenized monthly temperature data from 1935 to
2014. The Hurst Exponent was used as the key metric in assessing the strength of trends. By
comparing elevation, aspect, land cover, and historic population density with the H-values at
each station, relationships between long-term temperature changes and these environmental
variables were explored.
The hypothesis for elevation was that temperature increases would be more pronounced
and accelerated as indicated by higher H-values at stations at elevations greater than 1,000
meters above sea level. The hypothesis for aspect was that south-facing stations would have
experienced higher temperatures overall, and more pronounced and intense temperature
increases indicated by higher H-values. The hypothesis for land cover was that there would be
more persistence in increasing temperature trends, or higher H-values, at stations in urban areas
than stations in rural areas. Lastly, the hypothesis for population would mirror that for land cover
as higher density was used as a proxy for urbanization.
Data Sets Employed
This project was data intensive. Weather data for 66 stations giving monthly high, mean,
and low temperatures were required. Stations location and temperature data came from NOAA’s
climate data website, the National Climatic Data Center. Homogenized station data was obtained
from Mathew Mene at NOAA's National Centers for Environmental Information (NCEI).
NOAA has a great climate data download site at the National Climatic Data Center. The
site provides access to stations and the associated data in .csv format. That document can then be
imported to Excel, and from Excel a feature class can be created using the latitude and longitude
29

coordinates provided. The coordinates are provided in the ten-thousandths, which for Southern
California equals about 11 meter accuracy. The coordinates provided were in WGS 84. All data
imported was projected into California State Plane V for spatial analysis. This projection was
selected because it was designed specifically for Southern California to balance area and shape.
Because Rebetez and Reinhard (2007) used homogenized stations, homogenized station
data was sought out on the NOAA site. A preliminary search yielded the 13 homogenized
stations for Southern California shown in Error! Reference source not found.A couple
problems were immediately evident: not all counties were represented with at least 1 station, and
there is not a good distribution of stations in general across the landscape. That indicated that in
order to perform the desired spatial analysis, more stations would need to be homogenized.

Figure 4: The Original 13 Homogenized Stations
Given that homogenized data for a larger set of stations was not immediately available,
all of the stations in Southern California were evaluated for longevity and completeness of the
time series. A map of all the stations evaluated is shown in Error! Reference source not
found.This included 70 stations including the original 13 with available data dating from at least
30

1950 to the end of 2014 and with at least 70 percent complete data completeness. It was from
these stations that the homogenized station data would be created.

Figure 5: Active and Historic Temperature stations
Mene and Williams’ homogenization methodology is provided in their 2007 report. This
project attempted to obtain the program used to homogenize data. When Mathew Mene was
contacted, he observed that it would be difficult to obtain the appropriate amount of data to
homogenize stations out of context, and added that he was in the process of homogenizing many
more stations nationwide. He offered to homogenize the Southern California stations that were
already under consideration for homogenization. This meant that the stations would be
homogenized using the same rigorous methodology employed by NOAA for all stations,
ensuring the highest quality of authoritative data possible.
Within a couple of weeks, 66 stations were returned with 100 percent completeness from
at least 1934 to 2014; a full list of station names and associated station number is shown in Table
31

1. A few stations of the 70 originally requested still had missing data and were eliminated from
the analysis. The final station selection is shown in Figure 6. The final selection represents all
counties more evenly. The only major area not well represented is the high desert of San
Bernardino County. Unfortunately, the region did not have a complete enough data set meet the
required completeness criteria.
Table 1: Homogenized station list with associated coop number

Station_ID Station_Name Station_ID Station_Name Station_ID Station_Name
COOP:040439 BAKERSFIELD COOP:044297 IRON MOUNTAIN COOP:046730 PASO ROBLES
COOP:040442 BKFLD MEADOWS FIELD AP COOP:044412 JULIAN CDF COOP:047253 RANDSBURG
COOP:040519 BARSTOW COOP:044647 LAGUNA BEACH COOP:047306 REDLANDS
COOP:040521 BARSTOW COOP:044735 LA MESA COOP:047740 SAN DIEGO WSO
COOP:040609 BEAUMONT NUMBER 2 COOP:044747 LANCASTER COOP:047785 SAN GABRIEL FIRE DPT
COOP:040741 BIG BEAR LAKE COOP:044749 LANCASTER ATC COOP:047810 SAN JACINTO
COOP:040742 BIG BEAR LAKE DAM COOP:045064 LOMPOC COOP:047888 SAN ANA FIRE STN
COOP:040924 BLYTHE COOP:045107 LOS ALAMOS COOP:047902 SANTA BARBARA
COOP:041048 BRAWLEY COOP:045115 LOS ANGELES DWTN USC COOP:047940 SANTA MARIA
COOP:041194 BURBANK VALLEY PUMP COOP:045502 MECCA FIRE STN COOP:047953 SANTA MONICA
COOP:041244 BUTTONWILLOW COOP:045756 MOJAVE COOP:047957 SANTA PAULA
COOP:041758 CHULA VISTA COOP:046118 NEEDLES COOP:048014 SAAUGUS PWR PLT
COOP:042214 CULVER CITY COOP:046154 NEW CUYAMA COOP:048826 TEHACHAPI
COOP:042239 CUYAMACA COOP:046175 NEWPORT HARBOR BEACH COOP:048829 TEHACHAPI 4 SE
COOP:042598 EAGLE MOUNTAIN COOP:046377 OCEANSIDE MARINA COOP:048839 TEJON RANCHO
COOP:042713 EL CENTRO 2 SSW COOP:046399 OJAI COOP:048973 TORRANCE AP
COOP:042805 ELSINORE COOP:046569 OXNARD COOP:049035 TRONA
COOP:042941 FAIRMONT COOP:046624 PALMDALE COOP:049099 TENTYNINE PALMS
COOP:043463 GLENNVILLE COOP:046635 PALM SPRINGS COOP:049152 UCLA
COOP:043468 GLENNVILLE MORROW RA COOP:046657 PALOMAR MT OBSTRY COOP:049325 VICTORVILLE PUMT PT
COOP:043855 HAYFIELD PUMP PLANT COOP:046699 PARKER RESRV COOP:049452 WASCO
COOP:044223 IMPERIAL COOP:046719 PASADENA COOP:049847 YORBA LINA
32

Figure 6: Homogenized stations by location
3.1.1. Station Elevation
The elevation for each station was provided by NCDC with the station data. Elevation is
reported in meters to the nearest tenth. Figure 7 displays a histogram of the distributions of
stations at given elevations. Ideally, a study of this kind would have an even distribution of
stations across elevations. Reality very rarely meets the ideal, and this is no exception. There are
a lot of stations at lower elevations and very few stations at the highest elevations. This uneven
distribution of data may make it harder to show a dependency of persistence at higher elevations.
33

Figure 7: Histogram of Distribution of stations at elevation in meters.
3.1.2. Station Aspect
The digital elevation model (DEM) obtained from the National Elevation Dataset (NED)
had 1 arc-second spacing, or 25.29 m at 35° latitude, and can be seen in Figure 8. The DEM
shows all of the ranges of elevations seen in Southern California, where the station elevation data
only addresses the elevations of climate stations. The most extreme elevations are not
represented by stations. The aspect surface that was created from that 1 arc-second DEM can be
seen in Figure 9.
34

Figure 8: 1 arc-second DEM for Southern California

Figure 9: Aspect derived from the DEM for Southern California
35

Because of the well-known problems with error in DEM data (Fisher and Tate 2014), the
aspect was smoothed by 3x3 pixel window. That smoothing created an overrepresentation of
southern facing planes. This is because if a pixel with the value of 12 (N) is averaged with a
pixel that has a value of 340 (also N), the new value will be 276 (S). If any interpolation or
further surface analysis were being performed this would have been a much more difficult issue
to tackle. However, because stations are points, it was possible to manually examine the
smoothed aspect values for all stations that returned a value of Southwest, South or Southeast
(112.5 to 247.5) in order to ensure that the station was truly in a predominately south-facing area.
Only about half of the stations needed to be manually evaluated. In this case the
smoothed aspect values at station locations were compared to the unsmoothed aspect values.
Stations that had a northern value (292.5 to 359.9 and 0 to 67.5) returned from the original
unsmoothed aspect surface required further evaluation. This was the case for 15 stations. For
those few stations, a new value was calculated manually. The values of the 9 pixels with the
station at the center were averaged by adding 360 to values below 67.5. This way if a cell with
the value of 12 is averaged with a cell of 340 ((12+360) +340)/2 is 356 which is a north-facing
aspect.
3.1.3. Land Cover Data
Land use/land cover data at 100 m resolution was downloaded from The National Land
Cover Database (NLCD). The 100 m dataset is a smoothed version of the original 30 m dataset,
developed to aid in the visualization of regional land use/land cover conditions. The 100 m
dataset was chosen for use in this project because it was determined that the 30 m resolution data
would have been too detailed to appropriately estimate urbanization levels of the area
36

surrounding the stations. This smoothed dataset was created in 2010 although it is based on 2001
Landsat satellite data. It is shown in Figure 10.

Figure 10: Land cover data with station urbanization
In order to extract land cover values for this analysis, the numeric class value was pulled
for each station. Then the classes were divided into “urban” and “rural” values to facilitate
comparison. “Urban” stations had a value of 22, 23 or 24. The value 21 (Developed open space)
was not included in the “Urban” classification because it was decided that even though there is
some development nearby, since weather stations should be at least 30 m from any large paved
area (Campbell Scientific 2015), it is likely that the area around the station was still open, thus
minimizing the impact from any Urban Heat Island effects. All other values were classed as
37

“Rural.” There were 25 stations located in rural classifications, and 41 stations located in urban
classifications.
3.1.4. Population Density
The extent of urbanization changes over time. The places that were urbanized in 2001
were likely either less urbanized or still rural in 1950. More often than not, high levels of
urbanization are associated with higher population densities. Since historic land use data could
not be obtained, population density was used as a proxy for urbanization because of the
relationship between density and urbanization levels.
Decadal population data from 1940 to 2010 were obtained from the National Historic
Geographic Information System (NHGIS). However this data contained population totals, not
densities directly, and until 1970 most population was reported at the county level only. As of
1980, all counties had been divided into smaller tracts. For each decade, the population and the
area of the coincident census zone were extracted for the location of each station using ArcGIS.
The density values were calculated by dividing population by the area of the census zone.
Densities for all decades were compiled into a single table, shown in Appendix A.
Calculation of the Hurst Exponent
The Hurst Exponent is a means to analyze a time series. A value of .01 to .049 indicates
that the series is cyclical; the closer to zero the more consistent the cycle. A value of 0.5
indicates a random series. The closer the H-value is to .5 the more random the series is. A value
greater than .5 and less than 1 indicates the persistence, or positive autocorrelation of the series
(Outcalt 1997). The Hurst Exponent is the crux of this research project.
Calculation of H is approached by first calculating the mean of the series, then creating a
mean-adjusted series, and then calculating the cumulative deviate (QD) series. Using the
38

minimum value and the maximum value of the QD, the range is calculated. The standard
deviation of the original series is then calculated. H is estimated by dividing the log of the range
over the standard deviation by the log of the number of values in series.
Because seasons are inherently cyclical, only the hottest and coldest months were
analyzed. The first step was to determine the pattern of temperatures for Southern California.
Temperature data for several stations was graphed so that the hottest and coldest months could
be determined. Figure 11 is one such graph. This is all 80 years of monthly data (x-axis) in
degrees Celsius times 100 (y-axis). June, July and August form the peak, and are the hottest
months; the coldest months were December, January and February.

Figure 11: 80 years of temperature data by month shown in *C x100
The mean for June, July, and August was calculated for each of the 80 years in the series
to get Summer Means. December from the previous year was averaged with January and
February to get the Winter Means. The analysis starts with December 1934, thus December
1934, January 1935, and February 1935 compose the 1935 winter season. Where this is more
MEAN 718 958 1252 1620 2082 2547 2895 2804 2431 1803 1132 694
39

complicated than using the last month from the same year, it makes more logical sense in terms
of seasons.
For each station’s three temperature measures (high, mean and low), an H-value was
calculated for each season (winter and summer). Each station had 6 H-values. To calculate the
H-values, Outcalt’s 1997 estimation of the Hurst Exponent was used (Error! Reference source
not found.):
𝐻 = 𝐿𝑜𝑔 (𝑅𝑎𝑛𝑔𝑒 / 𝑆𝐷 )/ 𝐿𝑜𝑔 (𝑛 ) (2)
Thus, for each station, first the mean of each seasonal series was found. Then, for each year the
distance from the mean of the series was determined. From that yearly difference, a running total
of distance from the mean, or Cumulate Deviation (QD) was calculated. The QD shows the trend
of the temperature change, and the winter and Summer High and Low QD graphed against the
decadal temperature averages for all stations can be seen in Appendix B.
To actually calculate the Hurst exponent, the max and the min of the QD was found, and
the Range (max- min) was established. The next step was to calculate the standard deviation
(SD) of the seasonal series. H is calculated by using Error! Reference source not found. where
n is the number of entries in the series. In the case n=80. All of the H-values for each station are
shown in Appendix C calculated to the nearest ten-thousandths.
Hot Spot Analysis
As explained in Chapter 2, once the H-values were calculated, an optimized hot spot
analysis was run using ArcGIS in place the Ward cluster analysis that Rebetez and Reinhard
(2007) employed. This method was selected because it allowed analysis of not only the location
40

of the stations, but also included the analysis of a single variable. In this instance, each H-series
was selected. This would serve to identify spatial patterns of each of the 6 series of data.
Analysis of the Spatial Components
The primary means of evaluating the spatial components relied on correlation analysis.
For the elevation analysis, each of the 6 H-value series were plotted against the elevation in a
scatter plot as a correlation analysis with the trend line displayed. If the hypothesis is correct and
there is more persistence in higher elevations, then the scatter plot would show an increasing
slope along the H-values as the elevation increases. H-value is plotted on the Y axis, where the X
axis is elevation in meters. R
2
shows how well the trend line fits the data, and was calculated
automatically by Microsoft Excel. An R
2
value of 1 is a perfect match.
Aspect was analyzed using a scatter plot for correlation as well. Instead of a linear trend,
a polynomial, or parabolic trend line was displayed. This is because both 0 and 360 represent a
northern facing slope and 180 refers to a southern facing slope. If the hypothesis is correct, and
there is a higher H value represented by southern facing stations, the trend line would be an
inverted “U”. Also, an H-value was established for each station by averaging the 6 H-values
from the indicators. Each station was assigned a cardinality based on the aspect value. A mean
was created from H-values with the same cardinality to compare H-values by cardinality.
Urbanization was evaluated with comparison of Urban versus Rural H-values. For each
indicator the mean rural value was compared to the mean urban value. The population density
data was prepared to compare the QD data to the density data. If the hypothesis was correct, the
QD would see an accent at significant rises in urbanization.

41

Chapter 4 Results
The following presents the results from the various analyses using the Hurst Exponent on
historical homogenized monthly temperature station data from December 1934 to August 2014.
Southern California Temperature Trends
The QD trend lines for each station tell a unique story about the direction of temperature
change. Recall that QD shows the cumulative deviation from the mean of the entire series. Each
season, and each temperature measure has a unique pattern. Most lines have a decent, a plateau,
and an incline, though not all do. Figure 12 shows an example of a graph of QD lines for the
Summer and Winter High and Low temperatures at Bakersfield. A line showing the decadal
average temperature is also included (grey line). The end of the decent is marked with red, and
the start of the accent is marked in black. The individual stories for each station can be explored
in Appendix B which contains the graphs for all stations.

Figure 12: QD series graph for station 40439: Bakersfield
42

As Table 2 shows, the point of inflection upward, meaning the year at which the upward
trend becomes strongly persistent, is generally between 1975 and 1995, tending around 1980,
which is consistent with the global trend of temperature increases seen in Error! Reference
source not found.. This table cannot be reliably expanded because of the difficulty measuring
the inflection points precisely. The decadal temperature average lines plotted with the QD show
that temperatures are increasing all along Southern California. The H-value and associated QD
tell the story of the pattern of temperature changes, and the strength of the persistence of the
seasonal trend.
Table 2: Approximate QD inflection points of representative stations
WINTER HIGH SUMMER HIGH SUMMER LOW WINTER LOW
Station
ID
Decent
End
Accent
Begins
Decent
End
Accent
Begins
Decent
End
Accent
Begins
Decent
End
Accent
Begins
COOP:040439 1976 1996 1996 2001 1957 1983 1977 1977
COOP:040519 1951 1980 1983 1993 1957 1966 1977 1977
COOP:040521 1949 1975 1993 1993 1960 1983 1976 1976
COOP:040741 1984 1993 1983 1979
COOP:040742 1952 1979 1966 1993 1956 1969 1979
COOP:040924 1977 1955 1985 1957 1984
COOP:041048 2000 1976 1976
COOP:041194 1993 1976 1994
COOP:041244 1974 1990 2000 1980 1976
COOP:041758 1977 1980 1980 1976

Analysis of the Hurst Exponent Results
Each series of H-values has its own distribution patterns. Those patterns can be seen in
the histograms in Figure 13. Only 2 H-values were less than 0.5 for any indicator: Palm Springs
Summer High H= 0.47, and Big Bear Lake Winter High H=0.42. All other values are above .51
with the highest value being 0.795 at Newport for the Winter High. Summer Low H-values
show the highest level of persistence, meaning that there is stronger upward trend in the low
43

temperatures experienced during the summer months, while the Winter High H-values are on
average lower as indicated in the mean value.

Figure 13: Distribution of H-value data as a histogram
In order to classify the stations, the mean and range of H-values was calculated for each
station. The results of this are shown in Table 3 and the average H-value for stations ranged from
0.6 to 0.76, while the lowest value in the range was 0.60, and the highest range from 0.71 to
0.76. Given that 0.5 is random, and anything above that shows persistence. Therefore, the Hurst
values were classified as 0.4 to 0.5 showing no persistence; 0.51 to 0.6 as showing weak
persistence; 0.61 to 0.7 as persistence and 0.71 to 0.8 as strong persistence. This means in
general terms that most stations are showing persistence, 16 stations are showing strong
persistence and only 2 stations are showing weak persistence.
44

Table 3: Stations by mean H-value, highlighting the persistence categories

A complete visual representation of all the H-values by station is shown in Figure 14. The
H-values reflect degree of persistence quantified. Winter displays trends in the mean of
observations for the period December-February, and Summer displays trends in observations for
June-August. The H-values have also been qualified so there is a description of the strength of
the persistence attached. Anything below 0.5 is random and shows no persistence. Those stations
are represented in yellow, and there are very few stations in any season with that symbology.
Most stations show between weak to strong persistence.
Station_Name Range Mean Station_Name2 Range3 Mean4 Station_Name5 Range6 Mean7
TEHACHAPI 4 SE 0.144 0.6031 TRONA 0.073 0.6635 SAN JACINTO 0.111 0.6903
PALM SPRINGS 0.269 0.6051 OCEANSIDE MARINA 0.138 0.6644 SANTA BARBARA 0.103 0.6905
BEAUMONT NUMBER 2 0.144 0.6087 UCLA 0.052 0.6664 GLENNVILLE 0.144 0.6912
RANDSBURG 0.221 0.6093 LOS ANGELES DWTN USC 0.120 0.6676 SAN ANA FIRE STN 0.132 0.6942
FAIRMONT 0.115 0.6111 BAKERSFIELD 0.056 0.6688 LAGUNA BEACH 0.164 0.6962
TENTYNINE PALMS 0.208 0.6180 BARSTOW 0.204 0.6693 TEJON RANCHO 0.135 0.7001
PASO ROBLES 0.169 0.6220 PALOMAR MT OBSTRY 0.246 0.6703 LOS ALAMOS 0.069 0.7075
HAYFIELD PUMP PLANT 0.140 0.6234 BARSTOW 0.191 0.6711 YORBA LINA 0.045 0.7109
MOJAVE 0.182 0.6248 GLENNVILLE MORROW RA 0.055 0.6718 BAKERSFIELD MEADOWS 0.031 0.7110
PALMDALE 0.153 0.6321 TORRANCE AP 0.064 0.6736 SANTA MONICA 0.138 0.7118
VICTORVILLE PUMT PT 0.132 0.6430 PARKER RESRV 0.159 0.6779 SAN GABRIEL FIRE DPT 0.099 0.7144
NEW CUYAMA 0.141 0.6508 BUTTONWILLOW 0.114 0.6805 OJAI 0.063 0.7171
CUYAMACA 0.201 0.6514 WASCO 0.080 0.6807 SANTA MARIA 0.091 0.7183
JULIAN CDF 0.226 0.6514 BRAWLEY 0.142 0.6830 SANTA PAULA 0.130 0.7189
LANCASTER ATC 0.097 0.6520 IRON MOUNTAIN 0.137 0.6833 OXNARD 0.039 0.7192
BIG BEAR LAKE DAM 0.188 0.6561 TEHACHAPI 0.163 0.6841 ELSINORE 0.111 0.7193
EL CENTRO 2 SSW 0.209 0.6572 SAN DIEGO WSO 0.073 0.6856 MECCA FIRE STN 0.140 0.7241
EAGLE MOUNTAIN 0.118 0.6604 BURBANK VALLEY PUMP 0.143 0.6869 CULVER CITY 0.122 0.7313
LANCASTER 0.111 0.6618 IMPERIAL 0.049 0.6875 CHULA VISTA 0.058 0.7390
SAAUGUS PWR PLT 0.144 0.6622 LA MESA 0.123 0.6890 LOMPOC 0.112 0.7400
BIG BEAR LAKE 0.357 0.6627 BLYTHE 0.251 0.6891 PASADENA 0.093 0.7497
NEEDLES 0.096 0.6628 REDLANDS 0.059 0.6901 NEWPORT HARBOR BEACH 0.079 0.7579
45

Figure 14: Persistence of Temperature change in H-values
46

Relationship between Elevation and Temperature Trends
Figure 15 shows the scatter plot and trend line for the H-values for each indicator
measured against elevation. Winter High H-values offer a clear trend even if the R
2
of a fitted
trend line isn’t very strong. The slope is very small because the graph is in tenths. The most
interesting aspect of Winter High trend is that it shows a negative correlation between elevation
and the H-values. As the elevation increases, the H-values decrease. The expectation was to see
the inverse. The hypothesis was that there would be more persistent temperature increases at
higher elevations; that is not the pattern the data is demonstrating.
Summer High H-values show a very weak negative correlation. The slope is shallow, and
the R
2
is close to zero. The trend is so weak, it makes more sense to say there is no correlation
between persistence expressed as H-values and elevation. This supports the null hypothesis that
there is no difference in persistence of temperature increases at different elevations. Winter Mean
H-values also show a slight negative correlation. It is weak, with a low R
2
value, but is not so
weak as to claim it is nonexistent. The negative correlation works against the hypothesis.
Summer Mean H-values have no correlation to elevation. This supports the null
hypothesis. The Winter Low trend has a very weak R
2
combined with a very weak slope. This
shows support for the null hypothesis that there is no correlation between higher H-values and
higher elevations. Summer Low correlation also supports the null hypothesis that there is no
relationship between H-values and elevation. There is no visible slope and the R
2
is very low.
Both of those things suggest that the pattern of dispersion is random.
47

Figure 15 Hurst exponent values against the elevation of the station
Relationship between Aspect and Temperature Trends
Each of the 6 H-value series was plotted against the Aspect values using a scatter plot as
correlation analysis. If the hypothesis is correct there would be an inverted U shape in the graph
showing that as the H-values are increasing as to points approach a the southern values. In order
to accomplish that, a polynomial (parabolic) trend line was used. Where some of the trend lines
did display a weak arch, none of the R
2
values were high enough to really demonstrate any
correlation between persistence, expressed via the H-value, and station aspect. Figure 16 shows
48

the aspect correlation analysis charts by seasonal series. The highest R
2
value was for Winter
Mean values at 0.14; all other R
2
values were less than 0.1. They all support the null hypothesis
that there is no increase in persistence at temperature stations with a south-facing aspect.

Figure 16: Seasonal H-values plotted against numerical aspect
Because a weak relationship seemed to be evident, the station mean of the H-values was
used to average the H-values of stations with the same cardinality. A summary table, Table 4
shows the there is a slight difference in the mean H-values. The full data is included in
Appendix C. Stations with a northern cardinality have a mean H-value of .645, where stations
49

with a southern cardinality have a mean of .687. Where the difference is slight, it does show
what the slight parabolic inflections were indicating.
Table 4: Mean H-value of stations based on cardinality
Cardinality Mean H-value
North 0.6450
North East 0.6550
East 0.6849
South East 0.6642
South 0.6874
South West 0.6942
West 0.6837
North West 0.6540

Land Use, Population Density and Temperature Trends
Each of the 6 H-value series (winter and Summer High, mean and low) were averaged for
each set of stations (Urban and Rural) producing 2 mean values for each H-value series. These
are summarized in Table 5. The idea for this came from Rebetez and Reinhard. They averaged
the mean temperatures for north side and south side stations to compare change on one side
versus the other. Because the Urban and Rural classes provided a similar dichotomist
classification, that approach was applied to examining the Urbanization factor’s effect on
temperatures.
Table 5: Mean H-values for urban and rural stations

Winter
High
Summer
High
Winter
Mean
Summer
Mean
Winter
Low
Summer
Low
Land-Class
Mean
Mean Rural: 0.5919 0.6467 0.6239 0.6628 0.6408 0.6796 0.6410
Mean Urban: 0.6700 0.6909 0.6986 0.7146 0.6967 0.7238 0.6991
Indicator Mean 0.6380 0.6730 0.6685 0.6943 0.6742 0.7070

50

Consistently, the urban H-values are higher than the rural. Summer Mean and Summer
Low mean urban H-values range in the strong persistence category. Only Winter High rural
mean H-value is in the weak persistence range. The evidence fails to disprove that there is not
stronger persistence shown at stations with an urban land cover over stations with a rural land
cover; however, it also should be noted that the difference of 0.058 in the H-value puts both
classification in the “persistent” category. Urban stations’ H-values are only marginally higher.

Figure 17: Proportional Symbol Population and Population Density change in Southern
California from 1910 to 2010
51

The hope was that the census data would provide valuable information about the
changing population density of Southern California. Since all Southern California county
populations, and thus their densities, have increased significantly from 1910 to 2010, as shown in
Figure 17, there was an expectation to see increasing population densities that could then be
compared to the QD lines to determine if the inflection points coincided with significant
increases in population density. This trend is simply not reflected in the census tract data by
station location.
Unfortunately, since census tracts change each decade and in the early years population
was reported only at the county level for most of this region, the modifiable area unit problem
(MAUP) is exaggerated. As shown by the selection of data in Table 6, in the tracts that contain
stations, the population density does not appear to increase over time. In most cases the
population density remains fairly consistent, or fluctuates wildly. The density data is simply too
variable to provide any consistent information about the urbanization levels of the area around
each station. The full data set of population densities is shown in Appendix A. Maps of the
population density by station, included in Appendix D, do little to add further insight.
Table 6: Selection of population density data
Station 1940 1950 1960 1970 1980 1990 2000 2010
Bakersfield 16.6 28.0 2,695.9 1,420.0 1,471.0 1,506.5 1,136.4 999.5
Beaumont 2 14.4 23.3 1,230.5 1,647.1 1,708.1 2,098.4 2,171.4 2,303.0
Burbank 1,705.6 7,264.5 8,494.8 7,165.7 7,163.7 7,085.2 7,265.8 7,354.2
Eagle Mountain 14.4 23.3 0.7 1.1 1.2 1.2 2.9 0.5
Redlands 8.0 14.0 4,906.7 5,560.5 5,103.3 5,451.9 5,418.3 5,642.1
Hot Spot Analysis
In place of the Ward cluster analysis performed by Rebetez and Reinhard, an optimized
hot spot analysis was run to test the spatial relationship between the stations’ H-values to
52

visualize any spatial patterns present. Figure 18 shows the results for the 6 analyses run, one for
each H-series. The only series that has any real spatial pattern is the Winter High temperatures.
The pattern of hot spots and cold spots do not correlate very well with any of the other variables
explored. The hotspots seem to have a loose relationship with coastal regions which generally
have a low elevation, and the cold spots are generally in a mountain region, not all the hotspots
are coastal, and not all the cold spots are in higher elevations. This seems to be reflective of the
weak negative correlation between elevation and H-value seen in Figure 15 of the elevation
correlation results.
In the hotspot maps of H-values of monthly mean temperature, both summer and winter
show weak cold spots in the northern part of Los Angeles County but it is difficult to suggest a
cause for these within the context of this analysis. In summary, the hot spot analysis indicates
that the distribution of H-values is mostly random across the landscape. This supports all of the
null hypotheses that there are no increases in persistence corresponding to any spatially
dependent attribute evaluated by this study.
53

Figure 18: Optimized hot spot analysis of seasonal H-values by station.

54

Chapter 4 Summary
H-values of the summer and winter seasons were used to analyze spatial attributes of 66
temperature stations. H-value when analyzed against station elevation data displayed a negative
correlation supporting the elevation null hypothesis. Mean H-values of stations with a southwest
facing cardinality were the highest compared to all other cardinalities, though southern facing
stations did mean a higher H-value than northern facing stations. This provides weak support for
the aspect hypothesis. Urban stations have a mean H-value that is marginally higher than Rural
stations. This provides weak support for the land cover hypothesis. The hypothesis for
population density changes was not able to be tested.
55

Chapter 5 Discussion
This project sought to understand what trends in temperature change are evident based on
homogenized monthly data in Southern California from approximately 1935 to 2014 using the
Hurst Exponent evaluating seasonal data. The study examined elevation, aspect, and land cover
for each station using the H-values and optimized hotspot analysis to evaluate trends. This final
chapter reviews the results discussed in Chapter 4 and draws the final conclusions. The research
questions are re-examined to determine if they were addressed, and what conclusions can be
drawn. This chapter also discusses some areas of future research.
Evaluation of the Research Questions
The research questions are the backbone of a research project. This section looks at each
research question and addresses how well it was answered and the implications.
5.1.1. What is the spatial pattern of H-values by season as determined by optimized hot spot
analysis?
The only indicator that displayed a significant spatial trend was Winter High. All other
indicators displayed no significant trend. The expectation was that the hot spot analysis would
show trends that could be connected to the spatial variables. Without any trends, the analysis of
the trends to determine the nature of the spatial relationships could not be done. This is one of
the areas where much more is possible. There are a plethora of spatial analysis tools that could be
employed to evaluate if there are any spatial trends in the distribution of the H-values. Just
because the optimized hot spot analysis did not yield results does not necessitate that there is no
spatial trend in the spatial distribution of the H-values. Good avenues to explore are the other
hot spot analysis tools, as well as the regression analysis tools.
56

5.1.2. What is the correlation between H-values and elevation?
The null hypothesis was that there will be no persistence in temperature increases. The
hypothesis for elevation was persistence would be more pronounced expressed by higher H-
values as elevation increases. The results from the elevation analysis were surprising. The
correlation analysis showed that there is a negative correlation between elevation and
persistence, even though so many mountain ranges even those relatively local to Southern
California showed that the mountains were more sensitive to temperature increase exact
opposite. The hypothesis was rejected in favor of the null hypothesis.
5.1.3. What is the correlation between H-values and aspect?
The hypothesis for aspect was that stations on a southern face would have experienced
higher more persistent temperature increases than northern facing stations indicated by higher H-
values. Where the differences in H-values according to aspect were minor, they trends were
there. The mean H-value for stations on a north facing plane were the lowest, and southern
facing stations were markedly higher, with the highest being stations on a south-western face.
Averaging data does marginalize the figures, but also allowed the trend to present itself. The
correlation analysis alone yielded nothing but very weak results. The evidence marginally
supports the hypothesis. The null hypothesis can be rejected. There are more pronounced
increases in southern facing stations.
There is possibility for further study here also. One of the ways that aspect has been
evaluated by other climate studies has been to not necessarily look at the orientation of the exact
face that upon which that station rests, but rather to divide the mountain ranges into predominate
faces. There are norther, southern, eastern and western faces of the ranges that could be
57

evaluated for correlations in persistence. It could be that a stronger pattern would present itself if
the side of the mountain were evaluated over the face of the slope.
5.1.4. What is the correlation between H-values and the land covers “Urban” and “Rural”?
The hypothesis for land cover is that station located in more urban areas will experience
higher persistence expressed as higher H values than stations located in more rural areas. This
was another area where there was little to no precedent set on how to approach analyzing H-
values in correlation to urbanization levels. Because most comparisons were based on urban
versus rural readings, again averaging the stations with urban versus rural land covers seemed to
be the most quantifiable approach. The results were not as pronounced as expected. There is
speculations that this is due to the normalizing of the temperature data during homogenization.
One of the goals of homogenization is to mitigate the impact of urbanization on temperature
readings. However even using homogenized data, a marginal difference was detected between
persistence in urban stations versus rural stations supporting the hypothesis and rejecting the null
hypothesis that there is no relationship.
5.1.5. Can census data be used to track changes in population density to evaluate changes in
urbanization?
This area was an overall loss for the project. No analysis was possible because of the
inconsistency within census tracts. Where generally, urbanized areas are more densely populated,
census data is too malleable between census years to be able to provide viable comparisons. It
would have been exciting to evaluate the QD trends in association with periods of pounced
increases in population density. This is one area where future research is possible. The
relationship between urbanization and temperature increases are well documented. The issue
here is simply in the availability of the data. Perhaps individual counties have the data necessary
58

to perform this type of analysis. If viable data could be obtained, it would be interesting to see if
the QD lines reflected increases in population density.
Issues Addressed in the Study
Every project faces challenges. This section reviews the significant hiccups, how they
were addressed, and if there were any consequences upon the research.
5.2.1. Issues from Data Quantity and Quality
The final data set used for the analysis was both extensive and multi-dimensional. Three
temperature measurements for each of the 66 stations for 80 years created a large, bulky dataset
to manipulate in Excel. After analysis, the master table had station attribute data, H-values,
decadal temperature means, and decadal census tract densities. The master table was then
divided into more manageable tables for each of the station attributes evaluated. Database
management was essential to maintaining data integrity. The advantage of creating and
managing such a dataset in Excel, however, is the multiple ways the set can be manipulated and
analyzed using the available tools. Given the richness of the final data collection, many
additional questions arouse that remain to be addressed in future projects. Many of those
opportunities for further analysis are discussed below.
5.2.2. Using H-values in spatial analysis
Since there has been little previous research using H-values in spatial analysis, it was
difficult to determine the best means of employing the H-values to evaluate the persistence in
relation to the various spatial attributes of stations. Much additional research to mine the data
developed in this research remains to be done.
59

5.2.3. Exploration of the QD series
A lot of the research done with the Hurst Equation focuses on the trend of the series
viewed through the QD series (Oatcalt 1997, Ruddell 2013). That is not the direction this project
took. Where the QD is a significant part of the story that each station has to tell, it did not
become a major focus of this project. Evaluation of the spatial patterns was better served by the
Hurst Exponent. Also, when analyzing the trends in the QD series there was a degree of
subjectivity that made the researcher uncomfortable. The lowest point in the series was often
after a brief incline. It seemed arbitrary to place the end of decline inflection point at one place
versus the other. The graphs themselves are too individually unique to facilitate generalized
conclusions. Quantification of the data presented in the QD series is certainly one avenue for
future work on this data set.
Conclusion
The Hurst exponent is a powerful analysis tool. The persistence found in temperature
increases at Southern California stations were not surprising. Temperatures are increasing
worldwide, and regional studies show that temperatures are increasing in Southern California as
well. The interesting aspect of the work done lies in the ability to quantify the strength of the
trend using a different analysis than the Fisher test with p-value. While p-value is a useful
statistical tool, it overlooks the fractal nature of climatological processes. The H-value
recognizes that temporal patterns are assessed not only by the strength of their randomness, but
also their persistence or cyclical nature. This study makes a small step forward in showing how
the Hurst Exponent can be used to examine spatial attributes.

60

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64

Appendix A: Population Density
Population Density for stations by station and decade
Station ID 1940 1950 1960 1970 1980 1990 2000 2010
40439 16.6 28.0 2,695.9 1,420.0 1,471.0 1,506.5 1,136.4 999.5
40442 16.6 28.0 734.0 511.3 604.1 795.4 986.2 1,547.4
40519 8.0 14.0 1,988.6 1,547.5 1,213.8 908.2 698.4 813.8
40521 8.0 14.0 3,506.2 3,485.1 3,049.5 3,430.1 3,333.3 3,440.9
40609 14.4 23.3 1,230.5 1,647.1 1,708.1 2,098.4 2,171.4 2,303.0
40741 8.0 14.0 7.6 23.3 41.4 823.8 1,034.6 1,111.7
40742 8.0 14.0 7.6 23.3 41.4 5.2 6.4 7.3
40924 14.4 23.3 2,156.1 1,078.2 1,365.2 1,804.0 2,925.0 2,680.1
41048 13.3 14.0 16.1 16.1 1,263.8 1,286.1 1,840.5 2,093.5
41194 1,705.6 7,264.5 8,494.8 7,165.7 7,163.7 7,085.2 7,265.8 7,354.2
41244 16.6 28.0 17.2 12.5 13.3 15.1 16.3 21.2
41758 68.2 4,734.2 4,576.9 10,422.4 11,267.8 14,056.0 15,636.3 15,705.4
42214 2,611.3 7,072.3 9,995.4 14,821.0 9,264.6 10,350.3 10,214.6 9,779.5
42239 68.2 131.3 4.0 6.8 12.1 12.6 14.1 12.8
42598 14.4 23.3 0.7 1.1 1.2 1.2 2.9 0.5
42713 13.3 14.0 16.1 16.1 1,001.8 123.2 257.9 1,230.2
42805 14.4 23.3 516.0 98.9 182.9 507.8 1,431.3 1,665.9
42941 4.4 7.0 7.6 6.3 5.4 10.1 5.6 7.1
43463 16.6 28.0 1.2 0.7 1.3 5.9 5.9 5.6
43468 16.6 28.0 1.2 0.7 1.3 5.9 5.9 5.6
43855 14.4 23.3 0.7 1.1 1.2 1.2 2.9 0.5
44223 13.3 14.0 16.1 16.1 71.6 79.9 112.3 173.1
44297 8.0 14.0 4.6 5.7 7.1 2.0 2.1 2.2
44412 68.2 131.3 4.0 4.7 7.6 9.4 54.8 53.2
44647 163.8 270.8 152.1 265.0 439.3 686.0 720.0 721.4
44735 68.2 2,279.7 3,304.7 4,070.9 4,308.1 4,611.3 7,669.7 8,529.4
44747 23.7 56.6 323.2 351.1 578.9 1,591.3 5,169.8 5,620.2
44749 23.7 56.6 8.5 7.3 15.8 31.4 28.5 46.3
45064 25.7 35.7 8.7 992.0 1,113.0 2,870.6 3,349.1 3,203.1
45107 25.7 35.7 16.0 27.6 23.3 32.1 38.4 48.0
45115 4,561.1 5,078.8 2,194.1 5,448.5 9,038.0 3,659.8 2,771.0 1,618.3
45502 14.4 23.3 23.5 26.2 20.6 35.9 61.4 83.8
45756 16.6 28.0 190.8 201.1 212.9 204.0 171.9 189.2
46118 8.0 14.0 0.5 0.6 0.7 0.8 0.3 0.6
46154 37.5 61.7 1.2 1.0 1.0 1.0 1.2 1.1
46175 163.8 270.8 6,266.1 6,531.5 6,489.3 6,195.6 6,028.7 6,046.6
46377 68.2 131.3 123.6 5,127.1 6,721.5 6,942.6 6,362.7 4,579.1
46399 37.5 61.7 107.2 104.2 137.8 142.9 106.4 101.0
46569 37.5 61.7 107.2 333.9 766.1 12,621.2 8,248.1 3,656.2
46624 11.2 20.7 25.6 39.2 23.6 36.8 32.7 71.1
46635 14.4 23.3 817.8 852.2 1,535.7 1,896.5 144.4 438.7
46657 68.2 131.3 4.0 4.7 7.6 9.4 5.9 6.4
46699 8.0 14.0 0.5 0.6 0.7 0.8 0.3 0.6
65

Station ID 1940 1950 1960 1970 1980 1990 2000 2010
46719 8,780.4 10,641.3 10,390.7 8,937.5 7,939.3 9,045.4 9,981.3 5,130.3
46730 10.0 15.5 24.4 31.8 491.9 675.9 751.1 2,886.1
47253 16.6 28.0 2.9 5.2 7.3 5.5 4.3 6.6
47306 8.0 14.0 4,906.7 5,560.5 5,103.3 5,451.9 5,418.3 5,642.1
47740 68.2 661.4 99.6 33.0 183.9 179.8 207.8 113.7
47785 3,572.6 5,419.7 5,608.7 5,604.5 5,159.0 4,947.7 4,100.9 4,325.5
47810 14.4 23.3 2,581.2 4,354.1 4,613.2 6,150.7 6,544.2 5,367.5
47888 163.8 270.8 6,830.7 6,924.5 7,428.9 11,921.6 16,050.2 14,688.7
47902 25.7 35.7 5,086.0 5,027.5 5,643.8 5,577.9 6,198.5 6,417.9
47940 25.7 35.7 913.2 793.2 765.9 3,777.4 7,220.7 7,248.6
47953 7,507.8 9,123.8 6,452.6 4,489.9 3,971.7 3,745.9 3,892.9 5,807.7
47957 37.5 61.7 107.2 131.2 157.4 181.2 199.9 209.6
48014 10.7 19.6 8.6 9.5 37.8 52.9 14.3 23.4
48826 16.6 28.0 571.6 727.6 754.5 1,023.9 1,051.3 1,392.6
48829 16.6 28.0 2.5 1.9 5.5 10.8 14.4 8.0
48839 16.6 28.0 2.5 1.9 5.5 10.8 14.4 8.0
48973 172.6 686.5 1,070.5 3,983.1 2,590.3 2,334.5 2,373.0 2,369.8
49035 8.0 14.0 1.8 3.0 3.1 2.6 1.7 1.6
49099 8.0 14.0 4.6 5.7 7.1 53.4 404.1 1,161.3
49152 3,021.5 4,893.5 8,075.6 6,951.3 6,255.9 8,147.2 10,263.8 15,165.3
49325 8.0 14.0 3,045.8 3,298.9 3,296.5 3,825.5 3,448.9 3,877.6
49452 16.6 28.0 3,907.2 4,257.3 4,319.7 5,551.8 5,492.5 6,145.3
49847 163.8 270.8 89.3 2,516.8 3,793.8 3,967.6 4,000.6 4,264.5

66

Appendix B: Station Cumulative Deviation Series
The following are the high and low QD trend lines for both the summer and winter
seasons for each station as indicated. The four colored lines are the QD trend lines. The grey line
indicates the decal mean temperatures. Each chart has a unique temperature scale to reflect each
stations unique temperature ranges. The QD scales are not all exactly the same, but the range of
the scales are within proximity of each other. Some stations have inflection points indicated. Red
shows the end of the decent in the series, and black shows the incline of series.

67

68

69

70

71

72

73

74

75

Appendix C: H-Values by Station
Station_ID WinterH SummerH WinterM SummerM WinterL SummerL
40439 0.6742 0.6703 0.6847 0.6432 0.6421 0.6983
40442 0.7014 0.6954 0.7216 0.7142 0.7073 0.7260
40519 0.5482 0.6544 0.7006 0.7086 0.6754 0.7396
40521 0.5458 0.7496 0.5879 0.7331 0.6699 0.7292
40609 0.6614 0.6083 0.5926 0.6399 0.5172 0.6330
40741 0.4236 0.6935 0.6226 0.7396 0.7169 0.7802
40742 0.5395 0.7183 0.6194 0.7277 0.6223 0.7097
40924 0.5068 0.7583 0.6680 0.7465 0.7098 0.7453
41048 0.6025 0.6366 0.7126 0.7129 0.7450 0.6887
41194 0.6551 0.6161 0.6802 0.7339 0.6773 0.7590
41244 0.6813 0.6892 0.7275 0.6139 0.6935 0.6776
41758 0.7056 0.7153 0.7593 0.7343 0.7556 0.7638
42214 0.6679 0.7897 0.7136 0.7740 0.7276 0.7150
42239 0.5165 0.6749 0.6377 0.6561 0.7055 0.7177
42598 0.5805 0.6506 0.6628 0.6795 0.6982 0.6905
42713 0.5226 0.7313 0.6629 0.5876 0.7119 0.7268
42805 0.6605 0.7633 0.6870 0.7720 0.6910 0.7420
42941 0.5854 0.6677 0.5987 0.6514 0.6105 0.5531
43463 0.6256 0.6434 0.6919 0.7226 0.6940 0.7695
43468 0.6582 0.6686 0.6802 0.6501 0.6690 0.7049
43855 0.5855 0.7121 0.5720 0.6904 0.5933 0.5870
44223 0.6636 0.6870 0.6925 0.6861 0.7126 0.6833
44297 0.5916 0.6984 0.6772 0.6985 0.7282 0.7058
44412 0.5145 0.6807 0.5931 0.7066 0.6731 0.7404
44647 0.7208 0.7587 0.7188 0.7247 0.6600 0.5944
44735 0.6257 0.6597 0.6741 0.7347 0.6913 0.7485
44747 0.6017 0.6114 0.6875 0.6622 0.7122 0.6959
44749 0.5933 0.6636 0.6310 0.6750 0.6899 0.6592
45064 0.6720 0.7666 0.7201 0.7843 0.7299 0.7673
45107 0.6904 0.6800 0.7090 0.7310 0.6852 0.7494
45115 0.7061 0.6255 0.6387 0.6847 0.6152 0.7352
45502 0.6278 0.7662 0.7195 0.7678 0.7349 0.7283
45756 0.5225 0.6085 0.6356 0.6218 0.7045 0.6557
46118 0.6621 0.7006 0.6314 0.6886 0.6041 0.6898
46154 0.6573 0.5663 0.6946 0.6289 0.6498 0.7077
46175 0.7946 0.7520 0.7870 0.7405 0.7579 0.7153
46377 0.7365 0.5989 0.7073 0.6108 0.6358 0.6973
46399 0.7350 0.6799 0.7406 0.7369 0.6775 0.7328
46569 0.7267 0.7129 0.7222 0.7317 0.6929 0.7290
76

Station_ID WinterH SummerH WinterM SummerM WinterL SummerL
46624 0.6035 0.5834 0.5488 0.6698 0.6850 0.7022
46635 0.5821 0.4728 0.5322 0.6533 0.6480 0.7421
46657 0.5181 0.7184 0.5722 0.7638 0.6865 0.7628
46699 0.6341 0.5865 0.6701 0.7087 0.7232 0.7451
46719 0.6864 0.7732 0.7384 0.7798 0.7619 0.7588
46730 0.6436 0.6221 0.5460 0.6623 0.5447 0.7133
47253 0.5870 0.5060 0.5839 0.6110 0.6408 0.7272
47306 0.6752 0.6603 0.6882 0.7098 0.6882 0.7188
47740 0.7146 0.6999 0.6743 0.6938 0.6412 0.6896
47785 0.7183 0.6690 0.7223 0.7351 0.6735 0.7680
47810 0.6363 0.6497 0.6809 0.7192 0.7082 0.7473
47888 0.6813 0.6578 0.7427 0.6233 0.7553 0.7052
47902 0.7409 0.6868 0.7284 0.6382 0.6894 0.6592
47940 0.7155 0.7320 0.6826 0.7623 0.6717 0.7460
47953 0.7782 0.7499 0.7461 0.6751 0.6808 0.6406
47957 0.7506 0.7360 0.7131 0.7435 0.6204 0.7501
48014 0.5623 0.6782 0.6602 0.6972 0.6687 0.7064
48826 0.6526 0.5973 0.6711 0.7069 0.7168 0.7599
48829 0.5650 0.6597 0.6370 0.6711 0.5273 0.5587
48839 0.7403 0.6156 0.7046 0.7184 0.6705 0.7509
48973 0.6465 0.6469 0.6703 0.6712 0.7106 0.6962
49035 0.6533 0.6955 0.6559 0.6789 0.6224 0.6754
49099 0.6554 0.7181 0.5902 0.6635 0.5099 0.5708
49152 0.6851 0.6889 0.6664 0.6399 0.6364 0.6817
49325 0.5581 0.6570 0.6281 0.6560 0.6903 0.6687
49452 0.6881 0.6280 0.7030 0.6593 0.6972 0.7084
49847 0.7050 0.6813 0.7197 0.7109 0.7266 0.7221

77

H-values averaged by cardinality

78

Appendix D: Population Density for Census Tract by Station

79

80

81

Abstract (if available)

Abstract Climate change is a pressing issue, and regional studies play an important part in understanding the impact of global climate change. This project explored the spatial and temporal patterns apparent in temperature records from 1935 to 2014 using homogenized station data from 66 stations in Southern California. Using Hurst Exponent, an index used to explore the persistence of trends in longitudinal data, the strength of the increasing temperature trend observed at every station was evaluated. Hurst Exponent values were calculated for the high, mean, and low temperature series for both the summer and winter 3-month period. The spatial distribution of each of the six Hurst values was examined with respect to location, elevation, aspect, land use, and population density of each station using Microsoft Excel and ArcGIS. Results show that there is persistence in the increase of temperature at all stations beginning around 1980, though the strength of this persistence varies. Winter High temperature persistence is strongest in coastal areas and weaker in the inland mountains as shown by the hot spot analysis.

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Creator Webster, Melissa Faith (author)

Core Title Spatial and temporal patterns of long-term temperature change in Southern California from 1935 to 2014

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 02/24/2016

Defense Date 12/11/2015

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

Tag climate change,GIS,GIST,Hurst exponent,OAI-PMH Harvest,persistence,temperature change

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kemp, Karen (committee chair), Lee, Su Jin (committee member), Loyola, Laura (committee member)

Creator Email faithgreycloud@msn.com,mfwebste@usc.edu

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