SUMMERTIME HEAT ACROSS THE UNITED STATES by

SUMMERTIME HEAT ACROSS THE UNITED STATES

by

Tiffany T. Smith

A dissertation submitted to Johns Hopkins University in conformity with the requirements

for the degree of Doctor of Philosophy

Baltimore, Maryland

August, 2016

© Tiffany T. Smith

All Rights Reserved

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ABSTRACT

Extreme summertime heat has been the most deadly natural hazard in the United States

over the past 30 years and is projected to become more intense, more frequent and longer

lasting in the second half of the century. We take this as motivation to improve our

understanding of the drivers in summertime heat across the Continental United States

(CONUS), and provide a framework to discussing results from studies with diverse

motivations. This dissertation attempts to (1) create a baseline in understanding in the way

heat waves are defined and how this impacts conclusions of the patterns and trends of heat

waves, (2) investigate large scale drivers of summertime temperature on seasonal

timescales across variable-informed regions of CONUS, and (3) identify the impact of North

Atlantic Oscillation (NAO) definition on local heat waves as defined by two relevant

definitions. We find that (1) positive trends in heat waves are seen across most of the

United States where spatial patterns differ between definitions, (2) temperature variability

is sensitive to climate processes across CONUS regions, notably though that nonlinear

models produce improvement in explaining these relationships, and (3) that by defining

NAO by its centers of action, rather than phase, we increase our ability to model heat waves

in Baltimore, MD. This work will provide an outline for discussing results from heat wave

studies with diverse motivations, as well as deepen our understanding of the large-scale

drivers of summertime heat with the intention of informing and improving seasonal

forecasting and ultimately mitigate negative impacts heat has on the human population.

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Advisor:

Dr. Benjamin F. Zaitchik, Department of Earth and Planetary Sciences

Thesis Reader:

Dr. Darryn W. Waugh, Department of Earth and Planetary Sciences

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ACKNOWLEDGMENTS

As the saying goes, it takes a village. So I will attempt to thank my village, without whom I

would not be here today.

I would first like to thank my advisor, Ben Zaitchik, for being the academic role model I

needed for this journey. Ben took a chance on me when he decided that I would be the first

student he brought into Hopkins to begin building his lab group. Since then, Ben’s lab group

has grown and flourished and I am glad to have been part of that. Without the support,

patience and encouragement from Ben throughout this process, I would not be here today,

submitting this dissertation.

I would also like to thank the other members of my advisory committee, Darryn Waugh and

Carlos del Castillo. I would like to thank Darryn for his integral role in advocating for EPS to

be more involved in interdisciplinary research, without which I would have had no place

here. I would like to thank Carlos for having me as one of his “grasshoppers” and for always

reminding me that I do, in fact, know the answer.

In addition, I would like to thank the many colleagues I had the pleasure to collaborate with

throughout my dissertation work. In particular, Seth Guikema and Julia Gohlke, though

there are many more. Seth and Julia were integral to the science done for this dissertation,

and are the reason I was able to investigate heat waves in such an interdisciplinary matter.

Julia opened her world of public health research to me, which went on to be the driving

motivation throughout my dissertation. Seth gave me the most important, tangible skill set

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I acquired in grad school, which is first and foremost his love of statistics, but also his

ability to think outside of the box and always ask questions in new and interesting ways.

I would like to thank the EPS Front Office, Kim Trent, Jean Light, Teresa Healy, and

especially Kristen Heisey for making my grad student tenure as headache-free as possible.

In addition, I would like to thank Anand Gnanadesikan for always being willing to discuss

ideas no matter how periphery to his research they may have been.

This work would not have been possible without the financial support of the Department of

Earth and Planetary Sciences, The National Institute of Environmental Health Sciences

Grant R21 ES020205 and the National Science Foundation Hazard SEES Type 2 Grant #

1331399.

To Sara Rivero, Alex Fuller, Scott Pitz, Greg Henkes, Erin Urquhart, and all of the other EPS

students who I have built friendships and navigated grad school with, I am thankful. I am

particularly grateful to Saleh Satti, Asha Jordan, and Sophie Lehmann without whom I

would not have survived the many “off-hours” time spent in Olin over the past 13 months.

To my coworkers at Constellation, most importantly to the Fundamentals team, thank you

for your support and understanding. To my boss, Ed Fortunato, thank you for taking a leap

of faith in hiring me and for advocating and supporting the completion of my Ph.D. despite

the limited impact this milestone will have on our work.

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I would like to thank my family and friends for their support and understanding over the

last six years. I would first like to thank my family, my parents Bill & Carolyn Townsend, my

brother Jason Townsend and his partner Kevin Dang – thank you for your encouragement

and support as I navigated my doctoral education. To my parents, who have encouraged me

in whatever I chose to do over the past 29 years, while never once questioning if I could do

what I’d set my mind to (looking back on the stubbornness they endured through my

childhood, I’m sure they’re glad to see me put that quality to good use). And to my dad

especially, had I not been handed down your tenacity, inquisitiveness and penchant for

precision, I would not be the scientist I am today – I am proud that I’ll always be Little Bill

Fred. To my in-laws, Dixon, Kiki, Zach and Cragan Smith, thank you for always being a

breath of fresh air, especially when that air was from San Diego. To my friends, Sarah Isbell,

Jess & Eddie Nie, Anna Holland, Lauren & Rudi Greenberg, Katie Weber, Marcelle Empey,

Amy Bond, Molly Finch, Charlotte Smith, Alec Cronin, Teddy Davidson, Sean McCullagh,

Sara Atwater, Jason Vodzak, Kendie Bauer, Andrew & Kay Vassallo, Jimmy & Keisha Lewis,

Aaron Larrimore, Jen Gilbert, Lucy Rose Davidoff and Tori & Chris Hidalgo, thank you for

my sanity. I am so thankful my friends have been there, ready to drink a beer, hit the

weights, run the miles, go to the dog park, listen to me vent my academic stress and

everything in between. Over the past 13 months, my family and friends have received an

endless string of, “no’s” from me, but in reply I have heard only, “we’ll miss you, but we

understand”, “you got this” or “I’m so proud of you” – and for this, I am forever grateful and

indebted to you all.

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Last but not least, I would like to thank my husband and my best friend, Tucker Smith.

There are no words to accurately express the love and support Tucker has given me over

the past 12+ years, but especially over these last six. I arrived at Hopkins for new student

orientation five days after our wedding – our honeymoon was the first in a string of

sacrifices Tucker has so graciously made for me as I pursued my doctoral education. None

of these sacrifices has been so big as the decision to live here, in Baltimore, some 40 miles

from his place of work (~120,000 commuting miles over my grad school tenure…but,

who’s counting). He has propped me up when I needed it – the impossible problem sets, the

“conditional” passes that felt like failures, the moments of self-doubt and the tears of

frustration – and he has cheered for me when I deserved it – the acceptance letter, the

conference presentations, the first first-author publication, the Masters degree, the

interview offers and finally this dissertation. It is no secret how challenging it is to work full

time while completing your dissertation, but I simply would not have survived these past

13 months had Tucker not been there keeping me afloat. Tucker – thank you for riding this

roller coaster with me, and I cannot wait to see what post-Ph.D. life has in store for us.

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TABLE OF CONTENTS

ABSTRACT …………………………………………………………………………………………………………………… ii

ACKNOWLEDGMENTS ……………………...……………………………………………………………………….…. iv

LIST OF TABLES …………………………………………………………………………………………………………... xi

LIST OF FIGURES ………………………………………………………………………………………………………... xii

1. CHAPTER 1: INTRODUCTION ………………………………………………………………………………...… 1

1.1. Heat wave definitions ……………………………………………………………………………………..… 1

1.2. Drivers of summertime temperature across CONUS regions ……………………………….. 2

1.3. The impact of NAO on heat waves in Baltimore ………………………………………..……...… 3

1.4. Dissertation outline ……………………………………………………………………………………...…… 4

2. CHAPTER 2: HEAT WAVES IN THE UNITED STATES: DEFINITIONS, PATTERNS AND

TRENDS ………………………………………………………………………………………………………………...... 7

2.1. Introduction …………………………………………………………………………………………….............. 8

2.2. Materials and Methods ……………………………………………………………………………............ 11

2.2.1. Data ……………………………………………………………………………………………………… 11

2.2.2. Heat wave indices ………………………………………………………………………………….. 14

2.2.2.1. Relative thresholds ……………………………………………………………………... 14

2.2.2.2. Absolute thresholds ……………………………………………………………………. 16

2.2.3. Statistical analysis …………………………………………………………………………………. 17

2.3. Results ……………………………………………………………………………….…...……………………… 20

2.3.1. Average annual heat wave days ……………………………………………………………… 20

2.3.2. Temporal trends ……………………………………………………………………………………. 22

2.4. Discussion ………………………………………………………………………………………………………. 24

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2.5. Conclusions …………………………………………………………………………………………………….. 28

3. CHAPTER 3: LARGE-SCALE DRIVERS OF INTERANNUAL SUMMERTIME TEMPERATURE

VARIABILITY ACROSS THE CONTINENTAL UNITED STATES ……………………………….….. 33

3.1. Introduction …………………………………………………………………………………………………… 34

3.2. Methods …………………………………………………………………………………………………………. 37

3.2.1. Datasets ………………………………………………………………………………………………... 37

3.2.2. Regionalization ……………………………………………………………………………………... 41

3.2.3. Prediction ……………………………………………………………………………………………... 42

3.2.4. Leading Indicators ………………………………………………………………………………… 44

3.3. Results …………………………………………………………………………………………………………… 45


3.3.2. Prediction ……………………………………………………………………………………………... 46

3.3.2.1. Linear Trend Present (LTP) analysis ……………………………………………. 46

3.3.2.2. Linear Trend Removed (LTR) analysis ………………………………………… 51

3.4. Discussion ………………………………………………………………………………………………………. 57


3.4.2. Model Structure …………………………………………………………………………………….. 58

3.4.3. Predictors & Mechanism ………………………………………………………………………... 60

3.5. Conclusions …………………………………………………………………………………………………….. 64

4. CHAPTER 4: THE IMPACT OF THE NORTH ATLANTIC OSCILLATION ON HEAT WAVES

IN BALTIMORE ……………………………………………………………………………………………………… 71

4.1. Introduction …………………………………………………………………………………………………… 72

4.2. Methods …………………………………………………………………………………………………………. 75

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4.2.1. Data ……………………………………………………………………………………………………… 75

4.2.2. Heat wave indices ………………………………………………………………………………….. 77

4.2.3. Data evaluation and model fit ………………………………………………………………… 78

4.2.4. Prediction ……………………………………………………………………………………………... 79

4.3. Results …………………………………………………………………………………………………………… 80

4.3.1. Model fit ……………………………………………………………………………………………….. 80

4.3.2. Prediction ……………………………………………………………………………………………... 84

4.4. Discussions and conclusions ………………………………………………………………………..….. 87

5. CHAPTER 5: CONCLUSIONS ………………………………………………………………………………….... 98

5.1. Future work ………………………………………………………………………………………………….. 100

REFERENCES ……………………………………………………………………………………………………………. 101

AUTHOR’S CURRICULUM VITAE ………………………………………………………………………………... 110

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LIST OF TABLES

Table 2.1 Definitions of heat wave indices. *HI16 did not have enough data to include in this analysis.

Table 2.2 Average number of annual heat wave days, divided by region. Bold indicates region with highest

frequency of heat waves days for each HI. Regions are: Northwest (NW), Southwest (SW), Great Plains (GP),

Midwest (MW), Southeast (SE) and Northeast (NE).

Table 3.1 Bold indicates intraregional correlations Italics indicates interregional correlations

Table 3.2 Average (standard error) MSE, for holdout with LTP data; bold indicates top-performing model.

Table 3.3 Swings from BEST model using the LTP data, with relative rank in parenthesis, where (1) is most

important and (8) is least important, top three in bold.

Table 3.4 Average (standard error) MSE, for holdout with LTR data; bold indicates top-performing model.

Table 3.5 Swings from BEST model using the LTR data, with relative rank in parenthesis, where (1) is most


Table 4.1 Root mean square error (RMSE) for four GLM. Table 4.2 Mean square error (MSE) values from holdout analysis for HI02; * indicates top performing model.

Table 4.3 Mean square error (MSE) values from holdout analysis for HI11; * indicates top performing model.

Table 4.4 % impact on MSE each variable has for RF models for HI02. Higher values indicate variables of

higher importance.


higher importance.

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LIST OF FIGURES

Figure 2.1 Regional division of the Continental United States (CONUS).

Figure 2.2 (a) Average daily Tmax (ºC) over the time period 1979-2011 (b) Standard deviation of Tmax over

the time period 1979-2011 (c) 95th percentile of Tmax(ºC).

Figure 2.3 1979-2011, annual average number of heat wave days. Note the varying scales.

Figure 2.4 Trends in the number of annual heat wave days, over the period 1979-2011. White areas indicate

results below 95% significance. Units are days/year.

Figure 2.5 Average 95% significant trends in the number of annual heat wave days, over the period 1979-

2011, divided by region. The value printed in each cell is the trend value (in days/year). The color of the cell

represents positive (red) and negative (blue) trends. The shades of red and blue represent the landmass

percentage covered by this significant trend given by the scale bar. Regions are: Northwest (NW), Southwest

(SW), Great Plains (GP), Midwest (MW), Southeast (SE) and Northeast (NE).

Figure 3.1 (a) Map of regions and (b) the corresponding dendrogram. Y-axis in (b) is the sum of squared

distances within all regions, and is a measure of intra-regional variance.

Figure 3.2 Timeseries of Tmin, LTP (dashed red line) and Tmin, LTR (solid black line) for regions (a) NW, (b)

SW, (c) NGP, (d) South, and (e) NE.

Figure 3.3 Timeseries of LTP (dashed, red line) and LTR (black line) for all covariates: (a) ENSO, (b) NAO, (c)

PDO, (d) PNA, (e) GMSST, (f) AMO, and (g) AO.

Figure 3.4 Partial dependence plots for the three leading indicators in each region for models built with LTP

data: NW – (a) GMSST, (b) PNA, (c) NAO; SW – (d) GMSST, (e) PDO, (f) AO; NGP – (g) GMSST, (h) AO, (i) SM;

South – (j) GMSST, (k) AO, (l) NAO; NE – (m) GMSST, (n) ENSO, (o) SM.

Figure 3.5 Scatterplots of actual versus predicted Tmin for the best LTR models in (a) SW, (b) NGP, (c) South,

and (d) NE regions.

Figure 3.6 Temperature anomaly plots for (a) ENSO+, (b) ENSO-, (c) PDO+, (d) PDO-, (e) AO+, (f) AO-.

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Figure 3.7 Partial dependence plots for the three leading indicators in each region for models built with LTR

data: SW – (a) GMSST, (b) PDO, (c) AMO; NGP – (d) GMSST, (e) AO, (f) PNA; South – (g) GMSST, (h) AMO, (i)

NAO; NE – (j) ENSO, (k) GMSST, (l) SM.

Figure 3.8 Composite plots showing 300 hPa anomalies for the top five warmest years for (a) SW, (b) NGP,

(c) South, and (d) NE.

Figure 4.1. Timeseries of annual (July-August) heat wave (HW) day counts for (A) HI02 and (B) HI11.

Figure 4.2. Correlations between all variables included in models. Top right corner shows correlations,

where boxes are shaded according to the scale bar. Bottom left corner prints correlation values, also shaded

according to the scale bar, where values not printed were insignificant.

Figure 4.3 Actual versus fitted data for (A) HI02 and (B) HI11 where blue dots indicate Ind7 model results

and red dots indicate COA model results. A 1:1 line is provided for reference of a “perfect” fit.

Figure 4.4 P-values of covariates included (A) GLM-Ind7 and (B) GLM-COA. Stars indicate results for HI02,

and triangles indicate results for HI11. The horizontal dashed line represents 95% significance level; any

symbol below the dashed line is significant.

Figure 4.5. Partial dependence plots for the top two most important variables for HI02 for (A-B) RF-Ind7,

and (C-D) RF-COA.

Figure 4.6. Partial dependence plots for the top two most important variables for HI11 for (A-B) RF-Ind7,

and (C-D) RF-COA.

Figure 4.7 Composite anomaly plots for the top five hottest years according to (A) HI02 and (B) HI11 where

colors represent surface pressure and arrows represent vector winds. A box is located over the Azores for

reference.

Figure 4.8 Composite anomaly plots of 300 hPa geopotential heights for the top five hottest years according

to (A) HI02 and (B) HI11.

Figure 4.9 Composite anomaly plots of surface pressure (colors) and vector winds (arrows) for study time

period, 1950-2014.

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1. CHARPTER 1: INTRODUCTION

Extreme summertime heat has been the most deadly natural hazard in the United States

over the past 30 years (NOAA, 2015). As mean global temperatures rise (IPCC, 2007), there

has been increased attention to the frequency of extreme heat and the resulting impacts on

society. Between 1951-2003, statistically significant increases in minimum and maximum

temperature were seen over 40-75% of global land area (Alexander et al., 2006; Trenberth

et al., 2007). Over the Continental United States (CONUS), it has been projected that by mid-

Centry, 50% of all summers will be as hot at the top 5% of summers in the historic baseline

(Duffy and Tebaldi, 2012). In addition to increased frequency, it has been shown that

super-extreme (>3σ over mean) events have shifted from covering 1% of global landmass

to >10% of landmass by 2011 (Hansen et al., 2012).

1.1. Heat wave definitions

When discussing changes and trends of extreme summertime temperatures, it is

important to note that these discussions are related to studies of heat waves, but not

synonymous. This is partly due to the inherent differences between temperature,

typically evaluated as a continuous variable, and a heat wave event, understood as the

exceedance of a defined threshold. More importantly, there is no consensus definition of

heat wave throughout the literature due to the correspondingly diverse set of reasons

researchers study heat waves. Climate scientists, who are primarily interested in the

evolving statistics of weather and climate change, tend towards definitions that include

a probability of exceedance in some relatively straightforward metric, usually defined

relative to a long-term mean (e.g. Shar et al., 2004; Hansen et al., 2012). In contrast,

2

public health researchers are interested in the aspects of a heat wave that are most

relevant to human health and well being. These definitions are more likely to be

regionally specific than climate-focused definitions because people living in different

climates are known to experience heat waves differently, where mortality in the mild

climate of the Northeast increases 6.76% on heat wave days versus and increase of

1.84% in the warm, humid climate of the South (Anderson & Bell, 2011). These health

definitions are therefore more often informed by recognized links between heat and

morbidity/mortality, where it has been shown that relative threshold definitions

represent increased effects of temperature better than absolute threshold definitions

(Kent et al., 2014). As such, quantitative definitions of heat waves differ in (1) the

metric of heat used, (2) the manner in which thresholds of exceedance are defined,

and/or (3) the role of duration in a heat wave event. This diversity of definitions can

lead to some confusion in the broader discussion of climate trends and impacts of

climate change. So while there is value in monitoring and projecting each of these kinds

of heat extremes, there is also a need to be clear about definitions such that reported

patterns and trends can be understood in the context of other studies.

1.2. Drivers of summertime temperature across CONUS regions

Increased summertime temperatures have been associated with a wide range of

negative consequences including increased morbidity and mortality (Curriero et al.,

2002; Peng et al., 2011), increased wildfire activity (Westerling et al., 2006) and

decreased agricultural yields (Lobell et al., 2013). Because of the diversity of impacts, it

is important to clarify our understanding of the drivers of temperature trends and

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variability. These drivers can include remote large-scale modes (LSM) of climate

variability (Barnston 1996; Drosdowsky and Chambers, 2001; Kenyon and Hegerl,

2008) and local feedback mechanisms (Fischer et al., 2007; Portmann et al., 2009).

Historically, the most well studied LSM is the El Nino Southern Oscillation (ENSO).

However, more recently studies of CONUS temperatures have begun to include a wider

variety of large-scale modes of variability, including the Pacific-North American mode

(PNA), the Northern Annular mode (NAM), the Pacific Decadal Oscillation (PDO), the

North Atlantic Oscillation (NAO), and the Atlantic Multidecadal Oscillation (AMO)

(Loikith and Broccoli, 2014; Kenyon and Hegerl, 2008; Zhang et al., 2007; Sutton and

Hodson, 2005). Many studies highlight relationships between these LSM and

wintertime temperatures due to the inherent nature of the LSM being more active

during winter months (Visbeck et al., 2001) and the relationship between the LSM and

temperature being more robust (Becker et al., 2013). Studies of the relationship

between LSM and summertime climate have become increasingly common (Wang et al.,

2007; Krishnamurthy et al., 2015) in response to the plethora of evidence showing the

negative impacts of summertime climate (USGCRP, 2016).

1.3. Impact of North Atlantic Oscillation on heat waves in Baltimore

As noted above, people living in the mild climate of the Northeast experience a stronger

negative impact during a heat wave than those living in the warm, humid climate of the

South (Anderson & Bell, 2011). On the East coast, the intersection of the cool, dry

climate of the Northeast and the warm, humid climate of the South are found in the Mid-

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Atlantic region, centered near Baltimore, MD. Because of the multitude of negative

impacts summertime heat has in Baltimore, it is important we hone our understanding

of the drivers of the trends and variability in these heat waves.

As discussed in Section 1.2, a variety of work exists surrounding the impacts of LSM on

summertime heat. As explained in Section 1.1, summertime heat and heat wave events

are related but not always synonymous. As such, the current literature investigating the

impacts of LSM on heat wave events is thin.

Event-based research surrounding the definition of the LSM has become increasingly

prevalent, where event-to-event differences in ENSO spatial patterns and evolution has

lead to ENSO definitions on a continuum versus two distinct modes of variability

(Ashok et al., 2007; Singh et al., 2011; Capotondi et al., 2015). Similarly, temperatures

have been shown to be sensitive to not only the phase of the NAO, but also to the

location of the NAO’s centers of action (COA) (Castro-Diez et al., 2002). Asymmetry has

also been found between the NAO COA over the Azores High and the Icelandic Low,

where movements centered on the Icelandic Low are highly correlated to NAO phase

while the relationship with the Azores High was insignificant (Hameed and Pinotkovski,

2004). Recently, summertime temperatures were found to be more sensitive than

wintertime temperatures to the definitions of NAO (Pokorna and Huth, 2015).

1.4. Dissertation outline

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This dissertation is comprised of five chapters. Chapter 1 is an introduction to extreme

summertime temperatures and the motivation for this work.

Chapter 2 represents published work (Smith et al., 2013) on the definition of heat

waves. In this work, we analyze geographic patterns and trends over CONUS for fifteen

different, previously published heat wave indices. The objective of this study is to

describe and explain how the choice of definition influences conclusions regarding the

observed frequency of extreme heat events in different regions of CONUS in order to

provide a baseline for interpreting studies that project future trends in extreme heat

events.

Chapter 3 represents submitted work (Smith et al., 2016 under review) where a novel

regionalization of CONUS is presented followed by an investigation of LSM drivers to

summertime temperatures over these regions. Here we focus on a metric of seasonal

average temperatures in order to achieve stronger statistical relationships (Pepler et

al., 2015) and explain large-scale drivers of variability on seasonal timescales. Because

these LSM are known to persist, this work will inform future studies of seasonal

forecasting and climate change impacts specifically relevant across heat-vulnerable

regions of CONUS.

Chapter 4 presents a deep dive into the large-scale drivers of heat waves in Baltimore,

MD. Specifically, this work compares the effect of two NAO definitions, classically

defined NAO and COA-defined NAO, to heat waves in Baltimore, where a heat wave is

6

defined by both a relative and an absolute definition from Chapter 2. We also build a

framework for a predictive model of heat waves in Baltimore, and with this in mind,

include a variety of LSM as this will likely increase the predictive skill of these models.

Finally, Chapter 5 concludes the dissertation work.

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2. CHAPTER 2: HEAT WAVES IN THE UNITED STATES: DEFINITIONS, PATTERNS AND

TRENDS1

ABSTRACT

High temperatures and heat waves are related but not synonymous concepts. Heat waves,

generally understood to be acute periods of extreme warmth, are relevant to a wide range

of stakeholders because of the impacts that these events have on human health and

activities and on natural environments. Perhaps because of the diversity of communities

engaged in heat wave monitoring and research, there is no single, standard definition of a

heat wave. Experts differ in which threshold values (absolute versus relative), duration and

ancillary variables to incorporate into heat wave definitions. While there is value in this

diversity of perspectives, the lack of a unified index can cause confusion when discussing

patterns, trends, and impacts. Here, we use data from the North American Land Data

Assimilation System to examine patterns and trends in 15 previously published heat wave

indices for the period 1979-2011 across the Continental United States. Over this period the

Southeast region saw the highest number of heat wave days for the majority of indices

considered. Positive trends (increases in number of heat wave days per year) were greatest

in the Southeast and Great Plains regions, where more than 12% of the land area

experienced significant increases in the number of heat wave days per year for the majority

of heat wave indices. Significant negative trends were relatively rare, but were found in

portions of the Southwest, Northwest, and Great Plains.

1 Smith, T. T., B. F. Zaitchik and J. M. Gohlke. (2013) Heat waves in the United States: definitions, patterns and trends. Climatic Change, 118:811-825.

8

2.1. Introduction

As mean global temperatures rise (IPCC, 2007), there has been increased attention to

the frequency of heat extremes and their social and environmental impacts. In 2012

alone, the Intergovernmental Panel on Climate Change (IPCC) issued the full text of

their Special Report on Managing the Risks of Extreme Events and Disasters to Advance

Climate Change Adaptation (SREX), the Natural Resources Defense Council (NRDC)

released the report “Killer Summer Heat: Projected Death Toll from Rising

Temperatures in America Due to Climate Change”, and Climate Communications

released the report, “Heat Waves and Climate Change.” These studies provide

assessments of recent patterns and trends in heat extremes. They also address the

complexities involved in evaluating and projecting the frequency and intensity of heat

extremes in a changing climate. The occurrence of multiple high profile extreme heat

waves in recent years (e.g., Chicago, 1995; Europe, 2003; Russia, 2010) has highlighted

the importance of understanding and projecting patterns in extreme heat anomalies.

With respect to recent trends, the IPCC SREX cites the work of Trenberth et al. (2007)

and Alexander et al. (2006), who found that 70-75% of global land area with data

coverage saw a statistically significant increase in minimum temperatures (Tmin),

while 40-50% of global land area experienced an increase in maximum temperatures

(Tmax) over the period 1951-2003. However, Alexander et al. (2006) shows that some

regions departed from these trends, two of which were the eastern United States and

central North America. In these regions, negative trends in Tmin and Tmax were

observed, supporting Pan et al. (2004) who termed the phrase “warming hole” over this

9

region. In parallel, a number of studies have looked specifically at trends in heat wave

events rather than in temperature means (e.g., Meehl & Tibaldi 2004; Hansen et al.,

2012). The recent work in Hansen et al. (2012) describes that future (warmer) climates

will experience the emergence of a new category of extreme outliers (>3σ over the

mean). During the baseline period of 1951-1980, heat wave events classified as >3σ

over the mean, covered only 1% of landmass. However, in recent years (2006-2011) the

average landmass coverage of these extreme outliers has been 10%. Model results from

Meehl and Tebaldi (2004) show that heat waves will become more intense, more

frequent and longer lasting in the second half of the 21st century.

Trends in Tmin and Tmax are related, but not necessarily synonymous with trends in

heat wave events. In part this is due to the inherent difference between temperature,

typically evaluated as a continuous variable, and a heat wave event, understood as an

exceedance of some defined threshold. However, it is also a product of the fact that

there is no consensus on the definition of a heat wave. While a heat wave is generally

understood to be a period of extreme and unusual warmth, quantitative definitions of

heat waves differ in (1) the metric of heat used—e.g., daily mean temperature (Tmean)

(Anderson & Bell, 2011), daily Tmax (Peng et al, 2011; Meehl & Tebaldi, 2004),

temperature and humidity (Grundstein et al, 2012; Rothfusz, 1990) and apparent

temperature (Steadman, 1984)—(2) the manner in which thresholds of exceedence are

defined—as an absolute threshold (e.g., Tmax greater than 40.6°C (Robinson, 2001)), or

as a relative threshold, (e.g., the 95th percentile (Anderson & Bell, 2011))—and/or (3)

10

the role of duration in a heat wave definition (e.g., one day (Tan et al., 2007), or multiple

length criteria (Meehl & Tibaldi, 2004)).

The diversity of definitions reflects the diversity of reasons that heat waves are studied.

Climate scientists, who are primarily interested in the evolving statistics of weather in

climate change, tend towards definitions that include a probability of exceedance in

some relatively straightforward metric, usually defined relative to a long term mean

(e.g., Hansen et al., 2012; Schar et al., 2004). Health researchers, in contrast, are

interested in the aspects of a heat wave that are most relevant to human well-being.

These heat wave definitions are also more likely to be regionally specific than climate-

focused definitions, and may also target vulnerable subsets of the population. These

health definitions are often informed by recognized links between heat and morbidity

or mortality (Semenza et al., 1999; Hajat et al., 2006; Medina-Ramon and Schwartz,

2007, Anderson and Bell, 2009), which makes it possible to select or customize heat

wave indices for the purpose of predicting health impacts in specific geographic settings

or in particular populations (Barnett et al., 2010; Metzger et al., 2010; Williams et al.,

2012). Such studies can inform the use of heat wave indices in operational warning

systems.

Because of the diversity of stakeholders involved in the study of heatwaves, researchers

and health experts are able to collaborate to evaluate local health risks posed by climate

variability and change. However, the diversity of definitions can also lead to some

confusion in the broader discussion of climate trends and the impacts of climate change.

11

Indices that give a high weight to daily Tmax may be higher in hot, dry regions while

those focused on daily Tmin or apparent temperature would tend to be higher in humid

zones. There is value in monitoring and projecting each of these kinds of heat extremes,

but there is also a need to be clear about definitions such that reported patterns and

trends can be understood in the context of other studies.

In this paper we analyze geographic patterns and trends for the Continental United

States (CONUS) in fifteen different previously published heat wave indices (HI). The

objective is to describe and explain how the choice of definition influences conclusions

regarding the observed frequency of extreme heat events in different regions of the

CONUS over the past thirty-three years, in order to provide a baseline for interpreting

studies that project future trends in extreme heat events.

2.2. Materials and Methods

2.2.1. Data

The meteorological data used in this study are from Phase 2 of the North American

Land Data Assimilation System (NLDAS-2). The NLDAS-2 data have a spatial

resolution of 1/8 degree (~12.5km) and an hourly temporal resolution (Xia et al,

2012; Mitchell et al, 2004). As heat waves are the focus of this study, only data from

the warm season, May 1 – Sept 30, were considered. The analysis period is 1979-

2011.

12

NLDAS-2 was used for this study because it provides the most reliable, spatially

complete dataset of its kind. The six NLDAS-2 forcing fields used were temperature,

surface pressure, specific humidity, downward shortwave radiation, U-wind and V-

wind. From these fields, wind speed, net extra radiation per unit area of body

surface, relative humidity and vapor pressure were derived.

NLDAS-2 forcing fields are derived from the National Centers for Environmental

Prediction (NCEP) North American Regional Reanalysis (NARR) data. NARR fields

have a 32km spatial resolution and 3-hourly temporal resolution. The NARR fields

are derived from the 3-hourly NCEP Eta Data Assimilation System (EDAS) when

available (~92% of the time), otherwise the 3-hourly and 6-hourly Eta mesoscale

model forecast fields are used (Cosgrove et al., 2003). The NARR assimilation

system is fully cycled including prognostic land states with a 3-hourly forecast from

the previous cycle serving as a first guess for the next cycle (Mesinger et al., 2006).

Additional information about the NARR field processing can be found in Mesinger et

al. (2006).

The NLDAS processing system performs a spatial interpolation to downscale NARR

fields to the NLDAS 0.125° grid. For all fields used in this study, a bilinear

interpolation procedure is used. This interpolation method conserves the area-

averaged values, while simultaneously allowing for interpretation to a higher

resolution grid (Cosgrove et al., 2003). Following this, a temporal interpolation is

performed to adjust to the NLDAS hourly resolution. Once the other interpolations

13

are completed, Geostationary Operational Environmental Satellite (GOES) based

shortwave radiation data are used to produce that NLDAS forcing fields (Cosgrove et

al., 2003).

The topography of the NLDAS 12.5km grids is different from the NARR 32km grids,

and therefore temperature, pressure, humidity and longwave radiation fields must

be adjusted. First, a lapse rate of -6.5 K km-1 is applied to adjust temperature over

the change in elevation. Using the adjusted temperature, the 2m pressure fields are

adjusted using the Hydrostatic Approximation and Ideal Gas Law. Specific humidity

fields are adjusted by assuming constant relative humidity across the change in

elevation, as well as the equations of state for water vapor and dry air, the definition

of specific humidity and Wexler’s saturated water vapor pressure equation.

Downward longwave radiation is adjusted using the Stefan Boltzman law.

Further details and equations for the interpolations and elevation adjustments can

be found in Cosgrove et al., 2003. The implication of the interpolation method for

this study is that heat indices defined by absolute thresholds will be responsive to

lapse rate corrections, while indices defined using local statistical distributions will

be insensitive to the static in time local corrections. We note that for all indices the

resolution of NLDAS-2 is appropriate for regional studies but is inadequate to

address questions related to urban heat islands, within-municipality variability in

extreme heat exposure, or localized effects of contrasts in topography and land

cover.

14

Quality control of the NLDAS-2 forcing fields is based on the Assistance for Land

surface modeling Activities (ALMA) forcing data conventions. In addition, validation

studies have shown NLDAS forcing fields to be extremely realistic (Cosgrove et al.,

2003). One such study focuses on the NLDAS forcing fields validated against in-situ

measurements from the Oklahoma Mesonet monitoring network (Luo et al., 2003).

The fields of air temperature, surface pressure, specific humidity, downward

shortwave and longwave radiation all had an R ≥ 0.92, while wind speed has an

R=0.75. Similar validation studies are being completed on NLDAS-2 forcing fields

(http://ldas.gsfc.nasa.gov/nldas/NLDAS2valid.php).

2.2.2. Heat wave indices

Table 2.1 shows the sixteen, previously published HI used in this study. The indices

are divided into two main groups according to the type of threshold used in defining

heat wave days: relative thresholds and absolute thresholds. Data from the warm

season (1 May – 30 September) was used for the years 1979-2011.

2.2.2.1. Relative thresholds

All relative threshold heat indices use the climatological mean over the 1979-

2011 time period to calculate the percentiles.

Indices HI01 through HI06 are drawn from Anderson and Bell (2011). For each,

a threshold defined on the basis of the long-term local temperature record must

15

be met for at least two consecutive days. HI01 uses daily Tmean and the 95th

percentile as the threshold. HI02, HI03 and HI04 apply the same rule to the 90th,

98th, and 99th percentiles of daily Tmean, respectively. HI05 uses the 95th

percentile of Tmin and HI06 uses the 95th percentile of Tmax.

HI07 (Peng et al, 2011; Meehl and Tebaldi, 2004) applies a three-step process to

define heat wave days. First, for every day in a heat wave the Tmax must be over

the 81st percentile. Second, the Tmax must exceed the 97.5th percentile for at

least three consecutive days within the heat wave, but also allowing for days

with Tmax < 97.5th percentile. Lastly, the whole time period classified as a heat

wave must have an average Tmax greater than the 81st percentile.

HI08, HI09 and HI10 are based on thresholds of Apparent Temperature (AT).

Following Steadman (1984), AT is calculated as:

𝐴𝑇 = −1.8 + 1.07𝑇 + 2.4𝑉𝑃 − 0.92𝑣 + 0.044𝑄𝑔 (2.1)

where AT is measured in ºC, T is temperature in ºC, VP is vapor pressure in kPa,

v is wind speed in m s-1, and Qg is net extra radiation per unit area of body

surface in W m-2. AT is calculated every hour throughout the day, and then daily

ATmax is classified into one of three categories: hot (> 85th percentile), very hot

(> 90th percentile) and extremely hot (>95th percentile).

16

2.2.2.2. Absolute thresholds

HI11 uses a straightforward approach: everyday that Tmax is over 35ºC is

classified as a heat wave day (Tan et al, 2007).

HI12 (Robinson, 2001) uses both Tmin and Tmax to define heat wave days: the

threshold value for Tmax is 40.6°C and for Tmin is 26.7°C. At least one of these

thresholds must be met on at least two consecutive days to classify each of those

days as a heat wave day.

HI13 through HI16 use the National Weather Service’s (NWS) heat index

(INWS). INWS is calculated using temperature and relative humidity, however

other factors such as vapor pressure, wind speed, characteristics of human

activity levels, sweating rate etc. were used to parameterize the equation

(Rothfusz, 1990). The heat index is calculated using Equation 2.2:

𝐼𝑁𝑊𝑆 = −42.379 + 2.04901523𝑇 + 10.14333127𝑅 − 0.22475541𝑇𝑅 − 0.00683783𝑇2 −

0.05481717𝑅2 + 0.00122874𝑇2𝑅 + 0.00085282𝑇2𝑅2 − 0.00000199𝑇2𝑅2 (2.2)

where INWS is the heat index in ºF, T is the temperature in ºF and R is relative

humidity measured as a percentage (Rothfusz, 1990; Steadman, 1979). INWS is

calculated at each hour throughout the day, and then the daily maximum INWS is

classified into one of four categories: 1) Caution: >80ºF [HI13], 2) Extreme

17

Caution: >90ºF [HI14], 3) Danger: >105ºF [HI15] and 4) Extreme Danger:

>130ºF [HI16].

There are two instances where an adjustment is made to the calculation of INWS

(http://www.hpc.ncep.noaa.gov/heat_index/hi_equation.html). First, if R is less

than 13% and T is between 80°F and 112°F, then the following adjustment value

is subtracted:

13−𝑅

4∗ √

17−|𝑇−95|

17 (2.3)

Second, if R is greater than 85% and T is greater than 80°F but less than 87°F,

then the following adjustment value is added:

𝑅−85

10∗87−𝑇

5 (2.4)

The highest threshold value, HI16, was too rare to inform statistical analyses of

frequency or trends. Because of this, HI16 results will not be shown.

2.2.3. Statistical analysis

For each HI, the number of heat wave days was summed annually (warm season) at

the NLDAS grid cell scale. To gain insight into regionalized patterns of the HI, CONUS

was divided into six regions: Northwest (Washington, Oregon, Idaho), Southwest

(California, Nevada, Utah, Arizona, New Mexico and Colorado), Great Plains (North

Dakota, South Dakota, Montana, Wyoming, Nebraska, Kansas, Oklahoma, Texas),

Midwest (Minnesota, Iowa, Missouri, Wisconsin, Illinois, Indiana, Ohio, Michigan),

18

Southeast (Arkansas, Louisiana, Mississippi, Alabama, Tennessee, Kentucky,

Georgia, Florida, South Carolina, North Carolina, Virginia) and Northeast

(Pennsylvania, New Jersey, New York, Rhode Island, Connecticut, Massachusetts,

Vermont, New Hampshire, Maine, Maryland, West Virginia, Delaware). These

regions are depicted in Figure 2.1 and approximately match the six geographical

regions used for regional climate change analysis in the United States Global Change

Research Program (USGCRP) report Global Climate Change Impacts in the United

States (2009).

Figure 2.1 Regional division of the Continental United States (CONUS).

For each of the fifteen HI, the total number of annual heat wave days was averaged

over the 33-year timespan at the NLDAS grid cell scale. These results were then

19

averaged over the six CONUS regions to arrive at the average number of heat wave

days unique for each heat wave index and region.

These heat wave day averages were then assessed for their trends over the 1979-

2011 time period using ordinary least squares (OLS) regression. As the OLS

residuals exhibited non-normality for several indices (as shown by Shapiro-Wilks

normality testing), significance tests were performed using the Mann-Kendall tau

test. The Mann-Kendall tau test is a nonparametric test that does not assume an

underlying probability distribution of the data, and is also robust to outliers

(Moberg et al., 2006). Because of this, it is valuable when assessing trends in climate

data and therefore has been used in previous studies of trends in extreme

temperature indices (El Kenawy et al, 2011; Efthymiadis et al, 2011; Kuglitsch et al,

2010). A trend was considered statistically significant if the p-value was smaller

than the significance level α of 0.05. Based on the results of the Mann-Kendall

testing, all insignificant trends were masked out. The average of the resulting

significant trends was computed for each of the six CONUS regions for all fifteen HI.

Results are reported for trends calculated over the entire 1979-2011 period of

record available at the time the study was performed. The sensitivity of trends to

choice of time period was assessed by repeating the trend analysis with the

beginning date shifted between 1979 and 1981 and the end date shifted between

2007 and 2012 (provisional data used for 2012). It was found that results were very

similar for all analyses that included data through at least 2009. For periods that

20

excluded recent years the geographic pattern and direction of trends was similar,

but statistical significance of trends tended to be reduced.

To compliment these trend values, landmass coverage was calculated. These

landmass coverage percentages represent the number of cells covered by significant

trends (which were averaged) divided by the total number of cells in that region.

2.3. Results

To provide an example of the prevailing climate characteristics used to define the

relative HI, Figure 2.2 shows the average daily Tmax, standard deviation of the daily

Tmax, and the 95th percentile threshold for Tmax for May-September 1979-2011. That

is to say, for HI06 the temperature field mapped in Figure 2.2c must be met for at least

two consecutive days for those days to count as a heat wave day.

Figure 2.2 (a) Average daily Tmax (ºC) over the time period 1979-2011 (b) Standard deviation of Tmax

over the time period 1979-2011 (c) 95th percentile of Tmax(ºC).

2.3.1. Average annual heat wave days

21

Figure 2.3 shows the results of the analysis of the average number of annual heat

wave days; note that scale bars differ depending on the definition so as to

accentuate the spatial patterns. To get a quantitative look at these differences, Table

2.2 shows the results of this analysis for each of the six CONUS regions.

Figure 2.3 1979-2011, annual average number of heat wave days. Note the varying scales.

22

The Northwest region experienced the highest frequency of heat wave occurrence

for HI01-HI05, HI08 and HI09, the Southeast experienced the highest frequency for

HI06, HI07, HI10, HI11, and HI13-HI15 and the Southwest experienced the highest

frequency for HI12. The Great Plains, Midwest and Northeast regions did not see the

highest frequency of heat wave occurrence for any HI. The range of averages

between the six regions was much smaller for relative threshold definitions than the

range seen between absolute threshold definitions.

2.3.2. Temporal trends

Figure 2.4 shows the results of temporal trend analysis. Only the trends with

significance over 95%, based on the Mann-Kendall test, are shown in color. The

majority of the trends are positive, indicating that from 1979 to 2011 the average

number of annual heat wave days has increased. Figure 2.5 summarizes this trend

information for defined CONUS regions in terms of magnitude and extent of

significant trends. The value printed in each cell is the trend value (in days/year).

The color of the cell represents the direction of the trend, where red represents

positive trends and blue represents negative trends. The shades of red and blue

represent the landmass percentage covered by this significant trend, increasing in

percentage from the lightest shades to the darkest shades.

23

Figure 2.4 Trends in the number of annual heat wave days, over the period 1979-2011. White areas

indicate results below 95% significance. Units are days/year.

The majority of the trends observed across CONUS regions are positive, with the

largest positive trends found in the Southeast and Great Plains regions. For the

positive trends, the percentage of landmass covered ranges from 0-38%. Positive

24

trends were found across more than 12% of the landmass area for the majority of HI

for the Southeast and Great Plains regions; coverage over 12% was found for twelve

HI in the Southeast and eight indices in the Great Plains. The largest magnitude

negative trend was found in the Southwest region, with other negative trends seen

in the Northwest and Great Plains regions. Landmass coverage of these negative

trends ranged from 0 -12%.

Figure 2.5 Average 95% significant trends in the number of annual heat wave days, over the period

1979-2011, divided by region. The value printed in each cell is the trend value (in days/year). The color

of the cell represents positive (red) and negative (blue) trends. The shades of red and blue represent the

landmass percentage covered by this significant trend given by the scale bar. Regions are: Northwest

(NW), Southwest (SW), Great Plains (GP), Midwest (MW), Southeast (SE) and Northeast (NE).

2.4. Discussion

25

The results of the index intercomparison presented in this study are generally

consistent with warming trends observed in previous studies (Meehl and Tebaldi, 2004;

Schar et al., 2004; Hansen et al., 2012). Our study shows that in the past 33 years the

frequency of heat waves days has increased across most CONUS regions, according to

the majority of HI. Some of our results show regional exceptions to these overall trends:

negative trends were found for HI01 and HI02 in the Northwest, HI13 in the Southwest

and Great Plains and HI14 and HI15 in the Southwest.

In looking at the frequency of heat wave days over the past 33 years, the geographical

patterns are varied between HI. Most of the patterns shown in Figure 2.3 have a

sensible explanation based on what information was included in the definition of a heat

wave day. For example, the geographical patterns of high heat wave day frequency in

HI13 and HI14 correspond to the areas of CONUS with high humidity; this is consistent

with the fact that these definitions include both temperature and relative humidity data.

Our results do differ from some previous studies of heat wave trends in the United

States. These apparent inconsistencies can be attributed to differences in time period of

analysis, data source, spatial resolution of analysis, and heat wave definitions. For

example, Alexander et al. (2006) found that the Southeast region has experienced a

decrease in heat waves, but their study used an earlier time period, 1951-2003, and

defined a heat wave on the basis of single day Tmax. Robinson (2001) also found

decreases in heat waves throughout the US South. That study uses the HI12 definition of

a heat wave day, but is based on an earlier time period, 1951-1990, and uses station

26

data that resulted in a coarser temporal resolution. Such discrepancies make it difficult

to compare results across studies and can lead to some confusion in assessments of the

magnitude and geography of heat wave trends.

The diversity of HI found in the literature is understandable, considering the range of

reasons that heat waves are studied. While climate scientists are often concerned with

trends in the statistics of high temperature, health experts focus on indices that capture

impacts on human well-being, which are frequently influenced by social factors such as

acclimation and exposure. Collaboration between climate and health communities is

particularly valuable in this context. For example, a number of health-oriented studies

have demonstrated that the largest mortality effects due to increased heat occur in

northern cities in the United States, or areas with milder summers (Anderson and Bell,

2011; Medina-Ramon and Schwartz, 2007; Curriero et al., 2002). Here, we find that in

the NLDAS record, ten of the fifteen indices show that the percent area experiencing

significant increases in heat waves is larger in the Southeast than in the Northeast, and

that for nine of these ten indices the magnitude of trend has been greater in the

Southeast than the Northeast. Therefore, according to the majority of indices

considered in this study the Southeast has seen larger and more spatially extensive

trends than the Northeast. Future studies can pair this information with the relative

health effects of heat waves in differing regions to grasp a complete understanding for

planning health interventions and climate change adaptation strategies. The Northwest

region is another example of the potential value in communication across fields: while

several of the objective indices in this study had their highest frequency in the

27

Northwest, health experts recognize that heat waves have not been a major health

concern in that region relative to other parts of the country.

There are also discrepancies between the research literature and operational health

warnings. Davis et al. (2006) found that relative threshold HI are better predictors of

health impacts than those that use absolute thresholds. However, HI13-HI16, which use

absolute thresholds, are of particular importance to the general public because they

align with the heat alerts that are issued by the National Weather Service and broadcast

by organizations such as The Weather Channel. In a recent study of US football player

deaths, Grundstein et al. (2012) found that 45% of these deaths occurred in conditions

that did not trigger an NWS alert (meaning conditions less than the HI13 threshold).

The spatial patterns and trends observed in HI13-HI15 do not align particularly closely

with any other HI, which raises the question of whether the public is receiving the most

meaningful information regarding heat wave events.

The specific results of our study are limited by the dataset used in the analysis: NLDAS-

2 is the preeminent gridded land surface reanalysis for the United States, but it relies on

relatively coarse NARR fields as the foundation for meteorological estimates and its

downscaling routines do not account for localized differences in lapse rate or surface

properties or for nonstationarities such as land-use change. For this reason the patterns

and trends identified in this study must be understood as mesoscale results that do not

account for phenomena such as urban heat islands that are relevant to local health

impacts. In addition, only monotonic trends in heat wave days were considered; higher

28

order trend analysis could provide further insight on recent climate changes.

Nevertheless, it is shown that choice of index is critically important to the resulting

analysis of patterns and trends. In addition, these index comparisons could be

translated easily to different datasets for more focused local analyses.

2.5. Conclusions

This study demonstrates that estimates of the frequency, trends, and geographical

patterns of heat waves in the CONUS strongly depend on how heat waves are defined.

This fact, combined with discrepancies between studies in the time period considered,

meteorological datasets used, and spatial resolution of analysis, has led to a wide range

of conclusions regarding frequency and trends of extreme heat events in the United

States.

This study shows that across CONUS regions the range in average number of heat wave

days is greater for absolute HI than for relative HI. For both the relative and absolute HI,

the Southeast saw the highest values of average heat wave days, indicating that the

Southeast has experienced more heat wave days from 1979-2011 than any other

CONUS region. From the trend analysis, this study has shown that the Southeast and

Great Plains regions have experienced both the largest magnitude and most widespread

increases in heat wave days per year according to most indices.

Characterization and regionalization of heat waves across the United States is essential

to expanding our knowledge of climate change processes and impacts. Understanding

29

the role that definitions play in such studies is important for interpreting seemingly

contradictory results and for enhancing the quality of communication between climate

scientists, health researchers, and the general public. In this study, we have applied one

consistent dataset to compare patterns and trends across fifteen previously published

HI. Similar comparisons can be performed for other meteorological datasets and for

future climate projections in order to explore the full range of heat wave impacts

associated with climate variability and change.

30

Table 2.1 Definitions of heat wave indices. *HI16 did not have enough data to include in this analysis.

Heat Wave

Indices (HI) Temperature Metric Threshold Duration HI Type Reference(s)

HI01 Mean daily temperature > 95th

percentile 2+ consecutive days Relative Anderson and Bell (2011)







HI05 Minimum daily temperature > 95th


HI06 Maximum daily temperature > 95th


HI07 Maximum daily temperature

T1: > 81st

percentile Everyday, >T1; 3+

consecutive days, >T2;

Avg Tmax >T1 for whole

time period

Relative Peng et al (2011); Meehl and Tebaldi

(2004) T2: > 97.5th

percentile

HI08 Maximum daily apparent

temperature >85

th percentile 1 day Relative Steadman (1984)

HI09 Maximum daily apparent

temperature >90

th percentile 1 day Relative Steadman (1984)

HI10 Maximum daily apparent > 95th

percentile 1 day Relative Steadman (1984)

31

temperature HI11 Maximum daily temperature > 35°C 1 day Absolute Tan et al (2007)

HI12 Minimum & maximum daily

temperature

Tmin > 26.7°C ≥ 1 threshold for 2+

consecutive days Absolute Robinson (2001)

Tmax > 40.6°C

HI13 Maximum daily heat index >80°F 1 day Absolute National Weather Service, Rothfusz

(1990); Steadman (1979)


(1990); Steadman (1979)


(1990); Steadman (1979)

HI16* Maximum daily heat index > 130°F 1 day Absolute National Weather Service, Rothfusz

(1990); Steadman (1979)

32

Table 2.2 Average number of annual heat wave days, divided by region. Bold indicates region with highest

frequency of heat waves days for each HI. Regions are: Northwest (NW), Southwest (SW), Great Plains (GP),

Midwest (MW), Southeast (SE) and Northeast (NE).

NW SW GP MW SE NE

HI01 3.92 1.54 2.23 2.73 1.76 2.56

HI02 11.95 7.77 8.82 9.39 7.00 9.79

HI03 0.77 0.16 0.30 0.54 0.26 0.30

HI04 0.24 0.05 0.07 0.15 0.06 0.05

HI05 3.92 1.45 1.44 1.97 0.21 2.02

HI06 3.42 1.96 3.12 3.73 4.59 2.71

HI07 0.50 0.27 0.78 1.42 2.26 0.49

HI08 22.53 20.01 20.98 21.54 21.08 21.72

HI09 12.47 9.90 11.01 12.09 12.13 11.96

HI10 3.60 2.23 2.89 3.76 3.94 3.53

HI11 2.25 21.76 23.06 3.80 6.76 0.16

HI12 0.10 5.94 4.48 0.46 4.49 0.01

HI13 4.00 15.92 52.93 58.75 113.63 28.54

HI14 0.23 2.04 23.58 26.48 72.10 7.61

HI15 0.00 0.16 1.29 2.35 4.66 0.17

33

3. CHAPTER 3: LARGE-SCALE DRIVERS OF INTERANNUAL SUMMERTIME

TEMPERATURE VARIABILITY ACROSS THE CONTINENTAL UNITED STATES2

ABSTRACT

High summertime temperatures are associated with myriad impacts on humans and the

natural environment across the Continental United States (CONUS). As such, it is important

to improve understanding of the drivers of temperature variability in the summertime

season. Here, an objective regionalization of CONUS based on summertime temperature

variability is performed, yielding five regions that exhibit distinctly different behavior.

These regions are used to develop statistical models of July-August average daily minimum

temperatures (Tmin) in each region, from 1950-2012, as a function of large-scale climate

modes. Recognizing that summertime climate variability can be difficult to predict using

standard linear statistical techniques, multiple parametric and non-parametric statistical

modeling approaches are applied to capture non-linear responses and interactions

between climate modes. Results indicate that detrended summertime Tmin variability is

sensitive to different climate processes in different regions, including the Pacific Decadal

Oscillation variability in the Southwest, Arctic Oscillation in the Northern Great Planes,

Atlantic Multidecadal Oscillation in the South, and late spring soil moisture anomalies in

the Northeast. Notably, nonlinear models yielded the best results in all regions: a random

forest model is found to be most robust in the SW and South, while a generalized additive

model is most robust for the NGP and Northeast. These results are valuable for informing

2 Smith T.T., B. F. Zaitchik and S. D. Guikema, (2016) Large-scale drivers of interannual summertime temperature variability across the Continental United States. Journal of Applied Meteorology and Climatology. (Under review)

34

future improvements in seasonal forecasting of summertime temperatures and are

relevant for projections of summertime climate change across climatically distinct regions

of CONUS.

3.1. Introduction

It is well documented that mean global temperatures are on the rise (IPCC, 2007). Over the

time period 1951-2003, statistically significant increases in minimum and maximum

temperatures were seen over 40-75% of global land area (Alexander et al., 2006; Trenberth

et al., 2007). Over the Continental United Sates (CONUS), it has been projected that by the

mid-21st Century 50% of summers will be as hot as the top 5% of summers in the historic

baseline (Duffy and Tebaldi, 2012). Increased summertime temperatures have been

associated with consequences ranging from human morbidity and mortality (Peng et al.,

2011; Curriero et al., 2002) to increased wildfire activity (Westerling et al., 2006) and

decreased agricultural yields (Lobell et al., 2013).

Because of the diverse impacts that high summertime temperatures have in CONUS, it is

important to clarify our understanding of the drivers of temperature trends and variability.

These drivers can include remote large-scale modes (LSM) of climate variability (e.g.,

Barnston 1996; Drosdowsky and Chambers, 2001; Kenyon and Hegerl 2008) and local

feedback mechanisms (e.g., Fischer et al., 2007; Portmann et al., 2009).

Historically, the most well studied LSM is the El Nino Southern Oscillation (ENSO). For

several decades now, ENSO has been associated with changes in extreme temperature

35

frequencies across CONUS (Gershunov and Barnett, 1998). In addition, ENSO has been

shown to increase the predictability of climate variables, with the general consensus that

higher predictability is found in years when ENSO is strongest (Barnett et al., 1997;

Brankovic and Palmer, 2000; Visbeck et al., 2001; Becker et al., 2013). This result has been

broken down further to highlight the asymmetry between El Nino and La Nina events. For

instance, the low-level jet over the Great Plains was found to have a stronger relationship

with ENSO during El Nino events (Krishnamurthy et al., 2015), while hot and dry summers

in the central US have been attributed to La Nina events (Wang et al., 2007).

More recently, studies of CONUS temperatures have begun to include a wider variety of

large-scale modes of variability, including the Pacific-North American mode (PNA), the

Northern Annular mode (NAM), the Pacific Decadal Oscillation (PDO), the North Atlantic

Oscillation (NAO), and the Atlantic Multidecadal Oscillation (AMO) (Loikith and Broccoli,

2014; Kenyon and Hegerl, 2008; Zhang et al., 2007; Sutton and Hodson, 2005). Because of

the wealth of research surrounding ENSO, some studies focus on how a particular index

interacts with ENSO. Again, asymmetry has been found in these relationships, such as

differing correlation between precipitation and ENSO during the warm and cool phases of

the AMO (Hu and Feng, 2012).

Importantly, wintertime climate characteristics are known to have a more robust

relationship with LSM (Becker et al., 2013) due to the higher activity of most LSM during

the winter months (Visbeck et al., 2001). However, studies of LSM relationships to

summertime climate have become increasingly common (Wang et al., 2007; Krishnamurthy

36

et al, 2015) in response to the plethora of evidence showing negative impacts of

summertime climate on human health (USGCRP, 2016), and the increasingly extreme

patterns of summertime climate (Meehl & Tebaldi, 2004).

Here, we characterize and attempt to explain temperature variability in the two hottest

months of the year (July-August). We focus on variability in minimum daily temperature

(Tmin) for two reasons. First, though there is no consensus on what characteristics of heat

exposure are most harmful to human health (e.g., Anderson and Bell, 2011; Kent et al.,

2014), a number of studies suggest that elevated Tmin during a heat wave has specific

physiological impacts because the human body is given no relief at night (Schwartz, 2005;

Medina-Ramon et al., 2007). Second, it has been shown that Tmin is strongly influenced by

large-scale patterns whereas local effects have a major influence on maximum temperature

(Tmax) (Alfero et al., 2006), suggesting that there is greater potential to predict Tmin. In

addition, we chose to focus on the July-August average, as opposed to each month

individually, as multi-month means have been found to have higher predictive ability than

one-month means, in part on account of higher signal-to-noise ratio (Barnston, 1994;

Kumar et al., 2000; Becker et al., 2013).

In order to contend with the difficulty of predicting local climate variability as a function of

LSM in summer months we employ two statistical approaches to improve predictive power

of our models. First, we apply objective climate regionalization (Manning et al., 2008;

Dezfuli 2011; Badr et al., 2015) to divide CONUS into regions that are coherent with respect

to summertime temperature variability. This allows us to train and apply statistical models

37

using response regions that are optimally selected for homogenous temperature

variability. The use of standard climate regions (e.g., Melillo et al., 2014) or political

boundaries to define regions is not necessarily optimal for this problem. Second, we

employ a suite of parametric and non-parametric regression techniques to capture

nonlinear responses and interactions between predictors. Nonlinear statistical techniques

and machine learning algorithms have become increasingly common in climate analysis

and forecast application (Lobell et al., 2010; Rasouli et al., 2012; Nicholson, 2014; Badr et

al., 2014). To our knowledge, however, this is the first study that compares multiple

parametric and non-parametric techniques to study summertime temperature variability

in CONUS.

We note that this work is complementary to and distinct from extreme value analysis

applied to heat wave analysis and prediction (Tarleton and Katz, 1995; Cheng et al., 2014;

Hansen, 2012). Here we focus on a metric of seasonal average temperatures in order to

achieve stronger statistical relationships (Pepler et al., 2015) and explain large-scale

drivers of variability on seasonal timescales. Because these LSM are known to persist, this

work will inform future studies of seasonal forecasting and climate change impacts

specifically relevant across heat-vulnerable regions of CONUS.

3.2. Methods

3.2.1. Datasets

Temperature data for the study is from the Climate Research Unit (CRU) monthly

dataset (CRU TS3.21). This global dataset has a 0.5-degree spatial resolution and spans

38

the period 1901-2012. We choose CRU because of its long record, widespread use, and

global coverage, which makes it applicable for future studies outside of CONUS. This

study focuses on minimum temperature (Tmin) during the height of boreal summer,

July-August, for the years 1950-2012.

Large-scale mode (LSM) data for the study were gathered from the National Oceanic

and Atmospheric Administration (NOAA) Earth System Research Laboratory (ESRL);

additional information can be found at

http://www.esrl.noaa.gov/psd/data/climateindices/list. This study uses seven LSM

that have plausible associations with CONUS temperature variability: the El Nino

Southern Oscillation (ENSO), North Atlantic Osciallation (NAO), Pacific Decadal

Oscillation (PDO), Pacific-North American Mode (PNA), Atlantic Multidecadal

Oscillation (AMO), Arctic Oscillation (AO), and Global Mean Land/Ocean Temperature

Index (GMSST).

Pressure-based indices used in this study are NAO, PNA and AO. The NAO is an index of

sea level pressure (SLP) between centers of action over Iceland and the subtropical

Atlantic, near the Azores. The index if in its positive phase when SLP is below normal

near Iceland and above normal near the Azores; the negative phase is defined by the

opposite pattern (Barnston and Livezey, 1987). NAO varies on sub-seasonal timescales.

Here we use the July-August average as an indicator of the preferred orientation of NAO

in each year. The PNA is a pattern of anomalies in the 500 hPa geopotential height field

with centers of action over the Aleutian Islands and Southeast CONUS (Barnston and

http://www.esrl.noaa.gov/psd/data/climateindices/list

39

Livezey, 1987). Positive phase PNA brings above normal geopotential heights over

western CONUS and below normal geopotential heights over eastern CONUS. This

pattern in the geopotential height fields leads to cold, Canadian air spilling south into

eastern CONUS while western CONUS experiences above normal temperature; the

opposite is true during negative phase PNA. The AO, also known as the Northern

Annular Mode (NAM), is defined as the 1st empirical orthogonal function of the 100 hPa

height field poleward of 20N, and is normalized by the standard deviation of the

monthly 1979-2000 baseline monthly values (Higgins et al., 2000).

Temperature-based indices used in this study are PDO, AMO and GMSST. The PDO

consists of the first principal component (PC) of monthly sea surface temperature (SST)

anomalies in the Pacific Ocean poleward of 20N (Zhang et al., 1997). Positive phase

PDO, also referred to as the warm phase, is associated with a cold tongue of SST in the

interior North Pacific, with warm SSTs along the eastern edge of the Pacific basin. The

AMO is an index of North Atlantic (0-70N) SSTs, computed using Kaplan SST data

(Enfield et al., 2001); for this study, the unsmoothed version of the dataset was used.

The GMSST is an anomaly index produced by the Goddard Institute for Space Studies

(GISS) where positive (negative) values refer to a positive (negative) anomaly relative

to a 1951-1980 baseline (Hansen et al., 2010). Because values of these indices are

sometimes revised, it is important to note the dataset used herein was obtained on 11

April 2013.

40

In addition, this study uses the Multivariate ENSO Index (MEI) for the ENSO variable.

MEI uses the first, unrotated principal component of six observed fields over the central

Pacific Ocean: sea-level pressure, zonal surface winds, meridional surface winds, sea

surface temperature, and total cloudiness fraction of the sky (Wolter 1987). Positive

MEI values represent the well-known warm phase, El Nino, while negative MEI values

represent the cool phase, La Nina.

Lastly, this study includes local soil moisture as a proxy for local-scale feedback systems

that may be present in addition to large-scale forcings. The soil moisture (SM) data are

drawn from the NOAA Climate Prediction Center (CPC) Soil Moisture V2 dataset. CPC

Soil Moisture V2 is a global dataset with 0.5 degree spatial resolution that includes

monthly averaged soil moisture water height equivalents from 1948 to present (Fan

and van den Dool, 2004;

http://www.esrl.noaa.gov/psd/data/gridded/data.cpcsoil.html).

As the purpose of this study is explanatory modeling rather than forecasts, we apply all

predictors synchronously: July-August LSM are used to predict July-August Tmin. In

some cases lead-time predictors may actually have greater statistical power than

synchronous predictors, but exploratory analysis to support this study found that the

large majority of associations were strongest for synchronous analysis, so we do not

consider lead-time predictors in our models. The one exception to this is soil moisture.

Because local soil moisture anomalies are mechanistically linked to temperature

anomalies in many regions, July-August soil moisture is not an independent predictor of

http://www.esrl.noaa.gov/psd/data/gridded/data.cpcsoil.html

41

July-August Tmin. For this reason we use April-May soil moisture anomaly as a

predictor, with the understanding that late spring soil moisture has the potential to

impact late summer temperature through vegetation-mediated feedbacks (Fischer et

al., 2007).

3.2.2. Regionalization

For this study, regions were defined by the variable of interest, interannual variability

in July-August Tmin, using a hierarchical clustering analysis. Previous studies have

proposed objective regionalizations of CONUS based on mean climate conditions or

patterns of variability (Fovell and Fovell, 1993; Bukovsky et al., 2013), but for this study

it was important to utilize the variable of interest, specifically, to draw regional

boundaries so as to optimize the scope of this work. Regions for this study were defined

by Ward’s minimum variance clustering algorithm (Ward, 1963; Murtagh, 1983) as

implemented in the HiClimR package for R (Badr et al., 2015). Ward’s method aims to

find compact, n-spherical clusters by utilizing a minimum-variance method, and has

been used for similar climate regionalization applications in the past (Ward, 1963).

Regionalization was performed on detrended (linear trend removed) and standardized

Tmin data. Ward’s method was then applied, with the number of regions prescribed by

the user. Selection of the number of regions is a subjective process that depends on

application. Here we recognized that we needed a relatively small number of regions

(e.g., 4-7) in order to align our study with the scale of analysis used in the National

Climate Assessment (NCA) and other widely recognized CONUS climate analyses

42

(Melillo et al., 2014). This number of regions is also appropriate for associations with

LSM, which tend to have impacts across large areas within CONUS. Within these

subjective constraints, the final regions are selected based on objective metrics of

intraregional homogeneity versus inter-regional correlation that are produced by the

clustering algorithm.

Following initial regionalization, additional pre-processing was applied to the dataset to

remove cell values that were not well correlated with the region’s time series. The

motivation for this pre-processing was to remove noise and end with the most cohesive

regions to analyze. As such, the mean time series for each region was correlated to the

time series at each grid cell within the region using Pearson’s product moment to

calculate the correlation coefficient. All grid cells correlated less than 0.6 were then

removed from the dataset. Final regional time series were then re-calculated using only

the remaining grid cells.

3.2.3. Prediction

This study used a suite of statistical models to investigate the predictability of the

regionalized Tmin time series. The use of varied statistical techniques offers advantages

for capturing nonlinear effects, diagnosing variable importance, and accounting for

interacting relationships between predictors. The ability to capture these effects and

interactions is particularly important when studying diverse drivers of climate

variables, which often exhibit nonlinear and interacting effects.

43

This study includes three types of models--linear, additive, and tree-based--for a total of

five models. The first is a generalized linear regression model (GLM), which is an

ordinary least squares model with an added link function that allows for the model to

respond based on the distribution of the response variable. The response variable,

Tmin, displays a Gaussian (normal) distribution, and as such the identity link function is

used. The additive model used is a generalized additive model (GAM) that utilizes both

linear terms and terms with a cubic natural regression spline applied. The GAM is a

semi-parametric regression model that is based on a GLM, but adds the functionality of

a smoothing function (spline) to summarize the trends of the response variable against

the covariate(s) (Hastie and Tibshirani, 1986). When used, the smoothing functions are

fit using penalized likelihood maximization to prevent overfitting the model.

This study also used two tree-based models, a classification and regression tree (CART)

and a random forest (RF). Tree-based models use recursive binary partitioning of the

dataset to build either a single tree or an ensemble of trees. The CART model builds a

single tree by partitioning the dataset to reduce the sum of squared errors (SSE) and

then pruning this tree by removing nodes in an effort to reduce out of sample

prediction error. For this study, the RF model was built to an ensemble of 500 trees

using the mean square error (MSE) to determine the optimal partitioning of the dataset.

As a baseline comparison tool, a mean model (CLIM) was also calculated by taking the

average value of the response variable, Tmin.

44

To determine the model with the best predictive accuracy, a 100-fold holdout cross-

validation analysis was performed where a randomly selected 10% of the data (seven

years) were held out for each iteration. The models then predicted Tmin using the

remaining 90% of the data (56 years). Predictive accuracy was assessed using the

average and standard error of the mean squared error (MSE) of the 100-fold holdout

analysis.

To test for statistical significance, a student’s t-test was used to quantify p-values for

each model. These p-values where evaluated at the 95% confidence level for

independent tests, but also at two incrementally more stringent measures that adjust

for multiple comparisons. The first measure is false discovery rate (FDR), sometimes

referred to as Banjamini & Hochberg (BH), which controls for the expected proportion

of false discoveries amongst the rejected hypothesis (Benjamini and Hochberg, 1995).

The most stringent p-value adjustment method used was the Bonferroni correction

(BF), which submits strong control of the family-wise error rate by multiplying the p-

values by the number of comparisons. For the remainder of this study, significance is

defined by FDR unless otherwise noted.

3.2.4. Leading Indicators

Using the best model, as indicated by the holdout analysis, variable selection was

applied in each region to determine the leading indicators. To do so a method was

adapted from Shortridge et al. (2015), in which partial dependence plots were

developed by fitting the model using all covariates and then quantifying the marginal

45

influence that changing the covariate of interest while keeping all other covariates

equal has on model predictions. The influence of each covariate was then quantified as

the range of partial dependence value associated with that covariate, divided by the

total swing over all covariates in that model (Equation (3.1)).

influence𝑚𝑛 =max(𝑃𝐷𝑚𝑛)−min(𝑃𝐷𝑚𝑛)

∑ Swing𝑚𝑛𝑛 (3.1)

These swings were then used to rank variable importance level, where large (small)

swings indicate more (less) influence on model predictions.

3.3. Results


Figure 3.1a shows the final regions analyzed for this study, where associations were

determined using Ward’s method and cells correlated < 0.6 with the region’s time series

are masked out (no color). Figure 3.1b shows the corresponding dendrogram, where

the horizontal line indicates the cutoff used to differentiate between the number of

regions to include, where each stem the horizontal line touches represents one of the

five final regions. Table 3.1 shows the intraregional correlations and interregional

correlations for the final five regions. Intraregional correlations ranged from 0.60 to

0.81, while interregional correlations ranged from (absolute value) 0.12 to 0.56. NGP

had the highest intraregional correlation, while its highest interregional correlation was

with NE. Despite producing the lowest interregional correlation, the NW also had the

lowest intraregional correlation.

46

Figure 3.1 (a) Map of regions and (b) the corresponding dendrogram. Y-axis in (b) is the sum of squared

distances within all regions, and is a measure of intra-regional variance.

3.3.2. Prediction

3.3.2.1. Linear Trend Present (LTP) analysis

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47

First, the holdout analysis was completed using the time series with the linear trend

present, referred to hereafter as LTP. Figure 3.2 shows the time series of Tmin LTP

and Linear Trend Removed (LTR). Table 3.2 shows the average and standard error

of the MSE values resulting from the holdout analysis. Because the MSE is based on

the response variable (Tmin), which varies from region to region, it is only

appropriate to compare MSE values within regions and not across regions. Low

average and standard error MSE values indicate the model has high predictive

accuracy. GLM is the best performing model for the NW, SW and South regions,

while GAM has the lowest MSE for the NGP and NE regions; all of these models

significantly outperform the null model, CLIM (p < 0.05 with FDR adjustment).

48

Figure 3.2 Timeseries of Tmin, LTP (dashed red line) and Tmin, LTR (solid black line) for regions (a)

NW, (b) SW, (c) NGP, (d) South, and (e) NE.

1950 1960 1970 1980 1990 2000 2010

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in

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in

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LTP LTR

49

Figure 3.3 Timeseries of LTP (dashed, red line) and LTR (black line) for all covariates: (a) ENSO, (b)

NAO, (c) PDO, (d) PNA, (e) GMSST, (f) AMO, and (g) AO.

Table 3.3 shows the swing value of each covariate for the BEST LTP model for each

region. High value swings indicate that covariate had a large influence on model

predictions, while low value swings indicate the covariate had a small influence on

1950 1960 1970 1980 1990 2000 2010

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EN

SO

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O

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50

model predictions. Partial dependence plots for the three most influential covariates

(largest swings) for each region are shown in Figure 3.4.

Figure 3.4 Partial dependence plots for the three leading indicators in each region for models built

with LTP data: NW – (a) GMSST, (b) PNA, (c) NAO; SW – (d) GMSST, (e) PDO, (f) AO; NGP – (g)

GMSST, (h) AO, (i) SM; South – (j) GMSST, (k) AO, (l) NAO; NE – (m) GMSST, (n) ENSO, (o) SM.

a. c. b.

d. f. e.

g. i. h.

j. l. k.

m. o. n.

51

The leading indicator for all regions, regardless of model, was overwhelmingly

GMSST. For the NW region, PNA and NAO were the second and third most influential

variable. For the SW, PDO and AO were the second and third most influential

variable. For the NGP, AO and SM were the second and third most influential

variable. For the South, AO and NAO were the second and third most influential

variable. For the NE, ENSO and SM were the second and third most influential

variable.

3.3.2.2. Linear Trend Removed (LTR) analysis

Table 3.4 shows the average and standard error of MSE values resulting from the

holdout analysis for models trained to predict LTR temperature as a function of LTR

LSM. For all regions except the NW the best performing model—RF in NW and

South, GAM in NGP and NE—significantly outperforms CLIM. For simplicity, we will

sometimes refer to the top-performing model as the “BEST” model in the remainder

of the paper. Since we were not able to identify a model that significantly

outperforms CLIM in the NW we do not perform any additional analysis for LTR in

that region. Figure 3.5 shows actual Tmin versus modeled Tmin for the best LTR

models. In the SW and South (Fig 5(a,c)) models tend to under-predict extremely

warm and over-predict extremely cold summers. For the NGP and Northeast (Fig

5(b,d)) the dynamic range of models is a close match to observations.

52

Figure 3.5 Scatterplots of actual versus predicted Tmin for the best LTR models in (a) SW, (b) NGP,

(c) South, and (d) NE regions.

The notably stronger performance of nonlinear models for LTR is highlighted in

Figure 3.6, which maps July-Aug Tmin anomalies for the top (bottom) five years for

the positive (negative) phase of ENSO, PDO and AO, all of which are important

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53

predictors in some regions. For ENSO, a clear East-West pattern is seen for the

negative phase whereas the positive phase experiences a widespread negative

anomaly (Figure 3.6a,b). For PDO, a widespread positive anomaly is seen in the

negative phase while the positive phase experiences a cool anomaly throughout the

Rockies (Figure 3.6c,d). The AO shows a symmetric anomaly throughout the NGP,

but the area extending from Texas up the Eastern seaboard to the Mid-Atlantic

region experiences a warm anomaly in the negative phase, while the opposite is not

true of the positive phase (Figure 3.6e,f).

54

Figure 3.6 Temperature anomaly plots for (a) ENSO+, (b) ENSO-, (c) PDO+, (d) PDO-, (e) AO+, (f) AO-

.

Table 3.5 shows the swing of each covariate for the BEST LTR model for each region.

Partial dependence plots for the three most influential covariates (largest swings)

for each region are shown in Figure 3.7. For the SW region, the leading indicator of

Longitude

Latitu

de

30°N

35°N

40°N

45°N

a. b.

c. d.

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120°W 110°W 100°W 90°W 80°W 70°W

e. f.−2.0

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55

Tmin was GMSST, followed by PDO and AMO. For the NGP region, the leading

indicator of Tmin was GMSST, followed by AO and PNA. For the South region, the

leading indicator of Tmin was GMSST, followed by AMO and NAO. For the NE region,

the leading indicator was ENSO, followed by GMSST and SM.

a. c. b.

d. f. e.

g. i. h.

j. l. k.

56

Figure 3.7 Partial dependence plots for the three leading indicators in each region for models built

with LTR data: SW – (a) GMSST, (b) PDO, (c) AMO; NGP – (d) GMSST, (e) AO, (f) PNA; South – (g)

GMSST, (h) AMO, (i) NAO; NE – (j) ENSO, (k) GMSST, (l) SM.

Composite plots of detrended 300 hPa geopotential height anomaly for hot years in

each of the predictable LTR regions provide some indication of how LSMs influence

circulation patterns relevant to high temperatures (Figure 3.8). For each region

there is a clear high geopotential anomaly within or upstream of the region that

would be associated with a tendency to deflect the jet stream to the north.

57

Figure 3.8 Composite plots showing 300 hPa anomalies for the top five warmest years for (a) SW, (b)

NGP, (c) South, and (d) NE.

3.4. Discussion


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58

Numerous regionalizations of CONUS can be found in the literature, with the choice of

regions driven by the study’s motivation. For example, the National Climate Assessment

defines six regions that are drawn to be consistent with state borders, since the

Assessment was designed to be relevant to decision makers that include State officials

(Melillo et al., 2014). Bukovsky and Karoly (2011) divided North America into a smaller

set of regions in order to capture dominant eco-regions that might have differing

sensitivities to climate. Since the focus of this study was summertime temperature

variability, we performed our own objective regionalization based on interannual

variability in July-August Tmin. The exercise was found to be useful for developing

skillful and informative statistical models.

Some features of the regionalization are unsurprising: the mountain West is highly

heterogeneous, and this resulted in large parts of the NW and SW being masked out by

our minimum intraregional correlation requirement (Figure 3.1). It also might explain

why the NW proved to be a difficult region to predict. Other aspects of the

regionalization were unexpected. For example, instead of seeing distinct regions for the

Southern Great Plains, coastal Southeast, and Texas-Mexico (TexMex) areas, we found a

unified greater Gulf of Mexico region that extends from Texas to the East Coast (our

“South” region). It is also interesting that the NW and SW separate from each other

relatively cleanly, indicating that these two portions of the West have quite different

sensitivities for summertime temperature.

3.4.2. Model Structure

59

The clearest result drawn from the multiple model comparisons performed in this

study is that a linear regression model (GLM) is generally adequate for predicting

interannual variability in July-August Tmin when data are not detrended (the LTP

analyses). It is the top performing model in three regions and is close to the top

performing model in the other two (Table 3.2). This reflects the fact that GLM captures

the robust and, to first order, linear relationship between global SST and summertime

temperature in every region (see Figure 3.4), and is sufficient to provide good model fit

and strong out-of-sample predictive skill. This is a useful point of reference for certain

applications of statistical models. For example, climate change projections include

global climate model representations of both the global temperature trend and

changing patterns of large-scale climate modes. Statistical models are frequently used

to interpret these projections, and our results here suggest that linear statistical

formulations should be adequate in those applications.

For the second iteration of this study, using LTR data, GLM was no longer found to have

the most robust predictive accuracy for any region (Table 3.4). Instead, nonlinear or

nonparametric approaches—GAM in NGP and NE and RF in SW and South—showed

significant advantages in out-of-sample predictive skill. Notably, the GAM models in

NGP and NE captured the range of observed historical temperature variability, where

RF in the SW and South provided predictive skill but tended to underestimate extreme

years (Figure 3.5). The fact that nonlinear approaches are more valuable for analysis of

detrended temperature records is not surprising, since the presence of a strong linear

trend in the record favors linear models and its removal exposes nonlinear interactions

60

between LSMs in their influence on CONUS temperature variability; some of these

nonlinearities are evident in the composite plots shown in Figure 3.6. The finding is

useful, however, in that it demonstrates that linear approaches are suboptimal for

understanding drivers of interannual temperature variability or for predicting

variability on a year-to-year basis, when the long term trend is less relevant.

3.4.3. Predictors & Mechanism

As described in Section 3.3, the leading predictor of Tmin variability varied between

regions (Table 3.3). CONUS is known to be heterogeneous in climate variability, and the

time series plots in Figure 3.2 show that summertime Tmin variability is not consistent

across regions. The statistical models also indicate that the temperature response to

LSM variability is often nonlinear, such that GAM or RF were more skillful than GLM.

When predicting LTP data, these nonlinearities proved not to be a dominant issue. The

significant warming trend in all regions results in significant and reasonably linear

correlations with rising global GMSST over the period of analysis; this result is

consistent with previous studies (van Oldenborgh and van Ulden, 2003). There are

influential predictors beyond GMSST in these models, and they differ in interesting

ways between regions (Figure 3.4; Table 3.3). In the NW, both PNA and NAO have a

positive correlation to Tmin. In the SW, PDO has a negative correlation with Tmin while

AO has a positive correlation. In the NGP, both AO and SM have a positive correlation to

Tmin. In the South, AO is positively correlated to Tmin while NAO is negatively

61

correlated. In the NE, ENSO is negatively correlated with Tmin while SM is positively

correlated.

These results need to be interpreted in their proper context. If the objective is to

develop a model that predicts evolving Tmin over time, that can explain the recent

increase in CONUS Tmin, or that can be applied to project Tmin trends in coming years,

then it is useful to build a model that includes information on the GMSST trend.

However, the skill of these models overstates their ability to predict interannual

variability on shorter time scales, since much of the skill derives from the long term

trend. This is the reason that we pursued LTR models: the presence of the trend in LTP

models means that this approach is not optimized to explain shorter term variability or

to inform development of operational seasonal forecasts.

Shifting to the LTR results, we see that GLM is no longer the top performing result in

any region (Table 3.4). GMSST is still a highly influential variable—it has the largest

swing for three of the four regions in which skillful LTR prediction was possible—but

other predictors in the LTR iteration had a swing value magnitude closer to GMSST,

indicating that GMSST no longer dominates the models.

Using LTR data for the SW region, the top three leading indicators were GMSST, PDO,

and AMO. As shown by the partial dependence plots in Figure 3.7(a-c), Tmin is

positively associated with GMSST and AMO but negatively associated with PDO. The

advantage of the RF model is notable here as seen by the flattening of the relationship

62

between Tmin and the leading indicators for extreme values. This finding is supported

by Chylek et al. (2014), which suggests positive AMO leads to increased summertime

temperatures in the SW, and also Kurtz (2015), which found both AMO and PDO to be

influential over this same region. In addition, Figure 3.8(a) shows the composite plot of

the 300 hPa anomalies during the top five warmest years in the SW, where high

pressure is seen along the entire west coast, suggesting a tendency towards blocking

events that create clear-sky conditions and hence warmth over the West.

For the NGP region, the top three leading indicators were GMSST, AO, and PNA. As

shown by the partial dependence plots in Figure 3.7(d-f), Tmin is positively associated

with GMSST and AO, while the relationship with PNA is not monotonic. The positive

relationship exhibited between warmer Tmin and positive AO is consistent with the

accentuation of the jet stream during positive AO events, restricting colder arctic air

from flowing into the NGP. The positive relationship observed with both extremely

negative and positive PNA events is consistent with the understanding that the exact

location of the PNA’s ridge-trough delineation may vary such that neutral events see

little response in Tmin.

In Figure 3.8b 300 hPa anomalies of the top five warmest years are shown. The broad

high pressure feature seen over the northern area, covering NGP, is consistent with

positive AO and a deflection of the jet stream to the north of the NGP, allowing for

intrusion of warmer air from the south and for relatively stagnant conditions across the

region.

63

For the South region, the top three leading indicators were GMSST, AMO, and NAO. As

shown by the partial dependence plots in Figure 3.7(g-i), Tmin is positively associated

with GMSST and AMO, and negatively associated with NAO. These results suggest

positive phase AMO events lead to warmer Tmin, which is consistent with the well-

known relationship of positive AMO leading to warmth in the Gulf of Mexico region, and

extending to the land area north of the Gulf (Kurtz, 2015). Tmin association with

negative NAO is consistent with NAO-associated blocking and increased heat wave

activity (Wright et al., 2014). This blocking tendency is visible in the high pressure 300

hPa anomaly upstream of the South (Figure 7(c)).

For the NE region, the top three leading indicators were ENSO, GMSST, and April-May

SM. As shown by the partial dependence plots in Figure 3.7(j-l), Tmin is negatively

associated with ENSO, and positively, yet asymmetrically, associated with GMSST and

SM. This asymmetry again shows the importance of; non-linear techniques when

quantifying these relationships. In particular, the relationship between Tmin and SM is

flat when SM is negative and positive when SM is positive. Because this study uses

antecedent SM (April-May) and summertime Tmin (July-August), this relationship is

consistent with summertime warming due to early greening given a wet spring (Loikith

and Broccoli, 2014). The 300 hPa anomalies for warm years in the NE (Figure 3.8d)

show a high pressure blocking system over this region that is consistent with the jet

stream being deflected leading to stagnant, clear sky conditions that enhance warming.

64

3.5. Conclusions

This study began with an objective regionalization of CONUS on the basis of interannual

variability in summertime temperature. This allowed us to extract timeseries of the

variable of interest (Tmin) from regions that are coherent in Tmin variability, and these

timeseries were then used as the response variable for developing statistical models of the

large-scale drivers of summertime Tmin. Next, we compared multiple regression

approaches to determine the form of statistical model that best describes the relationship

between Tmin and the studied LSM. Using the best model, which was allowed to vary

between regions, the leading indicators of changes to Tmin were identified by calculating

the contribution of each LSM to the model’s predictive capacity.

Results show that detrended summertime Tmin is associated with different large-scale

climate modes in different regions of CONUS. In the SW, cooler summers are associated

with positive phase PDO. In the NGP, cooler summer Tmin is found when the jet stream is

accentuated during negative AO events. In the South, positive phase AMO is most closely

associated with warm summers. In the NE, wet spring conditions are associated with warm

summer Tmin. When the long-term trend is retained, Tmin in all regions is most closely

associated with global mean SST.

These results contribute to understanding and, potentially, prediction and projection of

summertime temperatures in three ways. First, the application of objective regionalization

65

using the specific climate variable of interest makes it possible to define spatial variability

in a way that is physically meaningful and relevant to predictive modeling.

Second, distinguishing between predictions with and without the long-term warming trend

included is important when developing and interpreting statistical models. Both types of

models have useful applications: when the trend is present, we see strong linear

relationships between GMSST and summertime temperature in all regions, which informs

climate projections. It also indicates that within the range of historically observed

variability a relatively simple linear regression is adequate to capture this relationship.

Removing the linear trend makes draws attention to the importance of large-scale climate

models that drive year-to-year variability and can add skill to seasonal forecasts.

Third, our comparison of multiple parametric and non-parametric regression techniques

shows that nonlinear techniques can be particularly useful for predicting variability in

detrended summertime temperatures. The prediction of summertime temperature is

known to be challenging, as LSM tend to be weak during this season and local climate

conditions are sensitive to geographic setting and land-atmosphere interactions. In this

context linear models fail to identify relationships between Tmin and LSM, but nonlinear

approaches can provide mechanistic insight and significant predictive skill.

66

Table 3.1 Bold indicates intraregional correlations Italics indicates interregional correlations

NW SW NGP South NE

NW 0.60 - - - -

SW 0.30 0.68 - - -

NGP -0.26 0.38 0.81 - -

South -0.41 0.44 0.53 0.71 -

NE -0.18 0.12 0.56 0.43 0.79

67

Table 3.2 Average (standard error) MSE, for holdout with LTP data; bold indicates top-performing model.

NW SW NGP South NE

GLM 0.461

(0.026)

0.489

(0.027)

0.572

(0.029)

0.456

(0.025)

0.530

(0.029)

GAM 0.520

(0.025)

0.550

(0.028)

0.505

(0.034)

0.486

(0.032)

0.477

(0.031)

CART 0.593

(0.032)

0.596

(0.032)

0.877

(0.045)

0.669

(0.043)

0.797

(0.038)

RF 0.515

(0.029)

0.505

(0.028)

0.615

(0.037)

0.581

(0.055)

0.651

(0.043)

CLIM 0.996

(0.047)

1.085

(0.056)

0.983

(0.050)

1.023

(0.085)

1.070

(0.055)

68

Table 3.3 Swings from BEST model using the LTP data, with relative rank in parenthesis, where (1) is most


NW SW NGP South NE

Model GLM GLM GAM GLM GAM

SM 0.204 (7) 0.013 (8) 1.335 (3) 0.060 (8) 1.133 (3)

ENSO 0.089 (8) 0.200 (5) 0.023 (8) 0.276 (6) 2.285 (2)

NAO 0.829 (3) 0.167 (6) 0.035 (7) 0.762 (3) 0.813 (4)

PDO 0.748 (4) 1.021 (2) 0.866 (6) 0.252 (7) 0.092 (6)

PNA 0.899 (2) 0.580 (4) 0.957 (5) 0.327 (5) 0.124 (5)

GMSST 2.686 (1) 2.552 (1) 2.746 (1) 2.411 (1) 2.997 (1)

AMO 0.259 (6) 0.102 (7) 1.088 (4) 0.476 (4) 0.000 (7)

AO 0.370 (5) 0.584 (3) 1.542 (2) 0.840 (2) 0.000(7)

69

Table 3.4 Average (standard error) MSE, for holdout with LTR data; bold indicates top-performing model.

NW SW NGP South NE

GLM 0.973

(0.064)

0.824

(0.045)

0.912

(0.058)

0.760

(0.036)

0.859

(0.043)

GAM 0.916

(0.051)

0.827

(0.046)

0.897

(0.060)

0.794

(0.042)

0.799

(0.048)

CART 1.463

(0.083)

1.287

(0.070)

1.326

(0.072)

1.243

(0.062)

1.175

(0.075)

RF 0.880

(0.052)

0.780

(0.045)

0.898

(0.054)

0.715

(0.036)

0.803

(0.045)

CLIM 0.990

(0.058)

1.002

(0.055)

1.131

(0.060)

0.994

(0.051)

1.105

(0.062)

70

Table 3.5 Swings from BEST model using the LTR data, with relative rank in parenthesis, where (1) is most


SW NGP South NE

Model RF GAM RF GAM

PNA 0.231 (7) 2.013 (3) 0.204 (8) 0.041 (8)

AO 0.356 (5) 2.209 (2) 0.347 (5) 0.985 (5)

GMSST 0.725 (1) 2.402 (1) 0.984 (1) 1.733 (2)

ENSO 0.375 (4) 0.432 (7) 0.214 (7) 2.197 (1)

NAO 0.108 (8) 0.083 (8) 0.570 (3) 0.984 (6)

PDO 0.588 (2) 1.096 (6) 0.428 (4) 0.272 (7)

AMO 0.575 (3) 1.164 (5) 0.726 (2) 1.001 (4)

SM 0.245 (6) 1.326 (4) 0.282 (6) 1.729 (3)

71

4. CHAPTER 4: THE IMPACT OF THE NORTH ATLANIC OSCIALLATION ON HEAT

WAVES IN BALTIMORE

ABSTRACT

Extreme summertime temperatures are the most deadly natural hazard in the United

States, and are known to negatively impact human health. Heat-related mortality increases

asymmetrically between warm and cool climates, and as such previous work shows that

heat waves defined with a relative (not absolute) threshold, represent increased effects of

heat. Here, we use summertime temperature data from the BWI airport to first, define heat

waves by two definitions, one absolute and one relative, over the period 1950-2014. Using

these two heat wave indices, we investigate the relationship they have with several large-

scale climate modes. We focus on the relationship heat waves in Baltimore have with the

North Atlantic Oscillation by replacing the classically defined NAO index with six derived

indices that shows variations in pressure, latitude and longitude of the Azores High and

Icelandic Low. This work shows that different heat wave indices are attributed to different

LSM, where the relative index used is attributed to the Azores High pressure and latitude,

while the absolute heat wave index used is attributed to the Pacific Decadal Oscillation. We

find that the centers of action approach to the NAO index produces better model fit for both

heat wave indices. Lastly, we built the groundwork for further investigation into creating a

model with the ability to use these large-scale climate modes to predict heat waves in

Baltimore. These results are valuable for informing future improvements to seasonal

forecasting of heat waves, which bring us closer to decreasing the negative effects heat

waves currently have on human health.

72

4.1. Introduction

Over the past 30 years, extreme summertime heat has been the most deadly natural

hazard in the United States (NOAA, 2015). This extreme heat is known as a heat wave,

but has myriad definitions throughout the scientific community, ranging from relative

to absolute thresholds, single-day to multi-day lengths and varying temperature-related

metrics (Smith et al., 2013). These definitions depend on what the focus of the study is,

climatological, public health, agriculture or otherwise. When studying human morbidity

and mortality, relative thresholds definitions are known to represent increased effects

of temperature better than absolute threshold definitions (Kent et al., 2014). In

addition, people living in different climates are known to experience heat waves

differently, where mortality in the mild climate of the Northeast increases 6.76% on

heat wave days versus an increase of 1.84% in the warm, humid climate of the South

(Anderson & Bell, 2011).

On the East coast, the intersection of the cool, dry climate of the Northeast and the

warm, humid climate of the South is found in the Mid-Atlantic region, centered in the

Baltimore-Washington corridor where 9.6 million people reside. As such, this work will

focus on the area of Baltimore, MD. Out of 11 cities throughout the Eastern Seaboard,

Baltimore has been shown to have the highest increase in mortality due to temperature,

where a large difference was seen even when compared to nearby city, Washington,

D.C. (Curriero et al., 2002). In addition to direct-effects of heat on humans, indirect

effects have also been found. In Baltimore, maximum temperature has the highest

correlation to increases in violent crime out of any meteorological variable, leading to

73

implications of hospital and police staffing (Michel et al., 2016). Globally, it is well

known that extreme temperatures are expected to increase in frequency, where Duffy

and Tebaldi (2012) expect by mid-century 50% of summers will be as hot as the

current top 5% of summers. Likewise, maximum temperatures that are currently a

once-per-season occurrence in Baltimore are expected to increase by 28% in frequency

by mid-century (Horton et al., 2015).

Because of the multitude of negative impacts summertime heat has in Baltimore, it is

important to clarify our understanding of the drivers of the trends and variability of

these heat waves. Previous work shows that drivers of summertime heat across the

United States can include large-scale modes (LSM) of climate variability (e.g. Barnston,

1996; Drosdowsky and Chambers, 2001; Kenyon and Hegerl, 2008) as well as local

feedback mechanisms (e.g. Fischer et al., 2007; Portmann et al., 2009). Throughout the

literature, several LSM are studied as potential drivers to climate variables, such as El

Nino Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Atlantic

Multidecadal Oscillation (AMO), Arctic Oscillation (AO) and Pacific Decadal Oscillation

(PDO) (Hurrell and van Loon, 1997; Gershuov and Barnett, 1998; Sutton and Hodson,

2005; Kenyon and Hegerl, 2008; Loikith and Broccoli, 2014). Historically, ENSO has

been the best studied LSM in the context of its impact on climate variables. ENSO has

been associated with extreme temperature frequencies across the United States

(Gershunov and Barnett, 1998), and has been shown to increase predictability of

climate variables (Barnett et al., 1997). More recently, research has highlighted a need

to better understand the event-to-event differences in ENSO spatial patterns and

74

evolution, as ENSO is increasingly defined as a continuum versus two distinct modes of

variability (Ashok et al., 2007; Singh et al., 2011; Capotondi et al., 2015).

Parallel to our increasing understanding of ENSO-driven climate variability, researchers

have begun to amass a knowledge base of NAO-driven climate impacts. The NAO is an

index of sea level pressure (SLP) between centers of action over Iceland and the

subtropical Atlantic, near the Azores. The index is in its positive phase when SLP is

below normal near Iceland and above normal near the Azores, where the negative

phase is defined when this pattern is relaxed (Barnston and Livezey, 1987). In the

landmark NAO paper from 1997, Hurrell and van Loon found that wintertime

circulation, and therefore temperature and precipitation, were impacted profoundly

due to variations in the NAO. Since then additional studies have worked to understand

these same phenomena during summertime as well as over other regions. Specifically,

NAO-related, upstream circulations were found to influence summertime temperatures

in the US Southwest (Myoung et al., 2015). In addition, cold Atlantic Ocean surface

temperatures (indicative of NAO patterns) are linked to stationary positions of the Jet

Stream that favors the development of high temperatures over Central Europe (Duchez

et al., 2016).

As our understanding of the NAO-driven impacts to climate variables increases, so does

our awareness of the limitations of the classical definition of NAO. Likewise to what has

emerged in the ENSO community, researchers of the NAO are turning their attention to

the way NAO is defined. In 2002, Castro-Diez et al. found that temperatures in southern

75

Europe are sensitive not only to the phase of the NAO, but also to the location of the

NAO’s centers of action (COA). Additional research indicates a non-symmetric response

between the COA over the Azores High and the Icelandic Low, where movements

centered on the Icelandic Low are highly correlated to NAO while the relationship with

the Azores High is insignificant (Hameed and Pinotkovski, 2004). More recently, it was

found that sensitivity to NAO definition was higher for summertime temperatures than

winter temperatures (Pokorna and Huth, 2015).

In this paper, we compare the effect of two NAO definitions, classically-defined NAO and

COA-defined NAO, to heat waves in Baltimore, where a heat wave is defined by both a

relative and an absolute definition. Other previously mentioned LSM are included in

this study as it is important to put these NAO results in the context of other

teleconnections. We also build the framework for a predictive model of heat waves in

Baltimore, and with this in mind, the inclusion of other LSM is likely to increase the

predictive skill.

4.2. Methods

4.2.1. Data

Temperature data for this study was acquired from the National Oceanic and

Atmospheric Administration (NOAA) Global Historical Climate Network (GHCN), a

dataset that spans back to 1880 and includes data from over 90,000 stations. The

GHCN dataset was developed for climate analysis and monitoring studies that

require sub-monthly time resolution, and as such was appropriate for this study

76

(Menne et al., 2012). For this study, we used the daily temperature (mean and

maximum) from the station located at Baltimore-Washington International airport

(BWI).

Seven of the large-scale climate mode (LSM) datasets were gathered from the NOAA

Earth System Research Laboratory (ESRL), these include the El Nino Southern

Oscillation (ENSO), North Atlantic Osciallation (NAO), Pacific Decadal Oscillation

(PDO), Pacific-North American Mode (PNA), Atlantic Multidecadal Oscillation

(AMO), Arctic Oscillation (AO), and Global Mean Land/Ocean Temperature Index

(GMSST). Additional information on these data can be found in Section 3.2.1 and at

http://www.esrl.noaa.gov/psd/data/climateindices/list.

The remaining six indices used in this study are NAO-based indices. These are

objective indices of pressure, latitude and longitude for the Azores High and

Icelandic Low. Additional information about the derivation of these indices can be

found in Hameed and Piontkovski (2004).

All data were analyzed for July-August months over the years 1950-2014. As

explained in Section 3.5, all predictors were detrended for this analysis. Because the

purpose of this study is to attribute LSM to heat waves, we apply all predictors

synchronously, where the July-August average of the LSM are used to predict counts

of heat wave days over July-August.

http://www.esrl.noaa.gov/psd/data/climateindices/list

77

4.2.2. Heat wave indices

Because there is no consensus definition of a heat wave event (Smith et al., 2013),

this study utilized two, exemplary and previously published indices for analysis. As

referenced in Chapter 3 and Smith et al. (2013), HI02 and HI11 are used herein.

HI02, initially from Anderson and Bell (2011), uses a relative threshold defined as

the 90th percentile of the long-term mean temperature, where the threshold must be

met for at least two consecutive days. For this study, the long-term average was

calculated on the 30-year baseline of 1980-2010. HI11, initially from Tan et al.,

2007, uses an absolute threshold defined as everyday that maximum temperatures

are greater than 35º C is classified as a heat wave day (Tan et al., 2007). Figure 4.1

shows the 1950-2014 timeseries of annual heat wave (HW) day counts for both

indices.

For this analysis the heat wave indices, HI02 and HI11, were defined as the number

of heat wave days, totaled over each summer (July-August) so that counts varied

annually between 0 and 62 days.

78

Figure 4.1. Timeseries of annual (July-August) heat wave (HW) day counts for (A) HI02 and

(B) HI11.

4.2.3. Data evaluation and model fit

First, we evaluated the correlations between HI02, HI11 and the thirteen covariates

through Pearson’s correlation method, where correlations were considered

# H

W d

ays

1950 1958 1966 1974 1982 1990 1998 2006 2014

010

20

30

A.# H

W d

ays

1950 1958 1966 1974 1982 1990 1998 2006 2014

010

20

30

B.

79

significant if p-values were less than 0.05 (95% level). Next, a generalized linear

model (GLM) was used to test the fit of the data. A GLM is an ordinary least squares

model with an added link function that allows for the model to respond based on the

distribution of the response variable. Because HI02 and HI11 exhibit a Poisson

distribution, a log link function was used for the GLM. Four GLM were built: HI02

with the original seven indices (Ind7), HI02 with the NAO centers of action indices

(COA), HI11-Ind7, and HI11-COA. These models are assessed for their fit of the data

through comparison of their root-mean square error (RMSE) values. From these

models, the p-value was used to indicate variable importance to each model, where

p-values less than 0.05 indicate statistical significance. We then use this variable

importance information to trim the number of variables included in the GLM, and

reevaluate the model fit.

4.2.4. Prediction

While the techniques discussed above are appropriate to understand and attribute

the LSM to heat waves, we also present a framework for predicting these heat

waves. To do so, the use of varied statistical techniques expands our ability to

capture nonlinear effects and account for interacting relationships between

predictors. As such, this work uses a similar suit of statistical models as explained in

Section 3.2.3 to investigate the predictability of HI02 and HI11. For this, we includ

the Poisson GLM explained in Section 4.2.3, but also a generalized additive model

(GAM), a classification and regression tree model (CART) and a random forest (RF).

To determine the model with the best predictive accuracy, a holdout cross-

80

validation analysis was performed. To test for statistical significance, a student’s t-

test was used to quantify p-values, which were evaluated at various confidence

levels. Additional details about these models and the holdout process can be found

in Section 3.2.3.

The model with the best predictive accuracy was determined by taking the average

mean square error (MSE) from the holdout analysis, where the model with the

lowest average MSE is best. Using this model, we determine the relative importance

of each variable by evaluating its impact on MSE by assigning the variable vales by

random permutation to evaluate the increase/decrease on MSE. Next, we

investigate partial dependence plots, as explained in Section 3.2.4, to visualize the

influence of important covariates over the response variables, HI02 and HI11.

4.3. Results

4.3.1. Model fit

Figure 4.2 shows the correlations between all variables and covariates in the dataset

used for this study. For HI02 we found that only AH.p and AH.lon were statistically

significant, with correlations of -0.34 and 0.25 respectively. For HI11 we found that

only PDO was statistically significant, with a correlation of 0.24.

81

Figure 4.2. Correlations between all variables included in models. Top right corner shows

correlations, where boxes are shaded according to the scale bar. Bottom left corner prints correlation

values, also shaded according to the scale bar, where values not printed were insignificant.

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

HI02

HI11

IL.p

IL.lon

IL.lat

AH.p

AH.lon

AH.lat

ENSO

AO

AMO

GMSST

NAO

PDO

PNA

0.9

−0.06

−0.24

0.03

−0.34

0.25

−0.02

0.05

0.04

0.18

0.24

−0.03

0.15

−0.01

−0.03

−0.19

−0.07

−0.21

0.22

−0.11

0.12

0.02

0.12

0.21

−0.07

0.24

−0.02

−0.02

−0.57

−0.15

−0.13

−0.32

0.15

−0.69

−0.02

−0.05

−0.63

−0.01

0.08

−0.17

0.12

−0.29

−0.12

−0.1

0.05

0.13

0.17

−0.3

0.01

0.22

0.37

0.39

0.63

−0.01

0.67

−0.21

−0.18

0.81

0.16

−0.31

0.05

0.19

0.26

0.27

−0.43

−0.18

0.43

0.26

0.01

0.65

0.11

0.22

−0.09

0

0.16

0.24

−0.24

−0.2

0.41

0.04

0.12

0.41

−0.13

−0.19

−0.23

−0.06

0.11

0.07

0.59

0.07

−0.04

−0.03

0.58

−0.03

−0.37

0.72

−0.26

−0.15

0.28

−0.21

−0.1

0.17

0.11

−0.220.21

82

To evaluate which models fit the data better, Table 4.1 shows the root mean square

error (RMSE) of the four variations of the GLM. For both HI02 and HI11, the RMSE

was improved (reduced) when the traditional NAO index was replaced with the COA

indices. To visualize this result, Figure 4.3 shows the relationship between actual

and fitted data from the four models.

Figure 4.3 Actual versus fitted data for (A) HI02 and (B) HI11 where blue dots indicate Ind7 model

results and red dots indicate COA model results. A 1:1 line is provided for reference of a “perfect” fit.

In evaluating the four iterations of the GLM, we gain insight into which variables are

driving these models. Figure 4.4 shows the p-value of each covariate included in the

GLMs. For the GLM-Ind7 (Figure 4.4a) we see that ENSO, PDO, PNA and GMSST are

all significantly at the 95% level for both HI02 and HI11. For GLM-COA (Figure

4.4b), we see that for HI02, AO, AMO, PNA, GMSST, IL.lon, AH.p, AH.lat and AH.lon

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83

are all significant at the 95% level. For the GLM-COA for HI11, we see that ENSO, AO,

AMO, PDO, GMSST, IL.lon, AH.lat and AH.lon are all significant at the 95% level.

Figure 4.4 P-values of covariates included (A) GLM-Ind7 and (B) GLM-COA. Stars indicate results for

HI02, and triangles indicate results for HI11. The horizontal dashed line represents 95% significance

level; any symbol below the dashed line is significant.

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valu

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84

Using the information from Figure 4.4, we trim the number of covariates in the

GLMs to include only those that are significant at the 95% level, but found the RMSE

were not improved in any of the GLMs for either heat wave index.

4.3.2. Prediction

Table 4.2 shows the average, mean square error (MSE) from the 100 holdouts for

each of the five models used for HI02. For both HI02-Ind7 and HI02-COA, the RF

performed the best as indicated by having the lowest MSE. Neither model run

produced a model that significantly outperformed CLIM at p <0.05. When comparing

the best performing model from each run for HI02, the COA-RF and the Ind7-RF, we

find them to be 99% similar.

Table 4.3 shows the average MSE from the 100 holdouts for each of the five models

used for HI11. For both HI11-Ind7 and HI11-COA, the RF performed the best as

indicated by having the lowest MSE. Neither model run produced a model that

significantly outperformed CLIM at p <0.05. When comparing the best performing

model from each run for HI11, the COA-RF and Ind7-RF, we find them to be 92%

similar.

Using the best performing model for each iteration (RF for all), we then determined

the most important variables in the model by evaluating the impact that variable has

on the model’s MSE. Table 4.4 shows the percent change in MSE for the models

evaluating HI02. Higher values indicate variables of higher importance. Figure 4.5

85

shows the partial dependence plots for the top two variables for the RF-Ind7 and

RF-COA models using HI02, where the leading indicators are GMSST and AMO for

RF-Ind7 and AH.p and AMO for RF-COA.

Figure 4.5. Partial dependence plots for the top two most important variables for HI02 for (A-B) RF-

Ind7, and (C-D) RF-COA.

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Table 4.6 shows the percent change in MSE for the models evaluating HI11. Figure

4.6 shows the partial dependence plots for the top two variables for the RF-Ind7 and

RF-COA for HI11, where the leading indicators are PDO and AMO for RF-Ind7, and

PDO and AH.p for RF-COA.

Figure 4.6. Partial dependence plots for the top two most important variables for HI11 for (A-B) RF-

Ind7, and (C-D) RF-COA.

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87

4.4. Discussions and conclusions

In this study, we examined the effect of two NAO definitions, classically-defined and

COA-defined, to heat waves in Baltimore, defined by both a relative and an absolute

definition. Results show that the inclusion of COA-defined NAO indices increases model

fit of the heat wave data, however results are not consistent across heat wave

definitions, where NAO is only important for the relative heat wave definition.

Our results show that only two indices were significantly correlated to HI02, AH.p and

AH.lon, where both are COA indices. In addition, when evaluating the GLM models,

RMSE values were improved (reduced) when the classically defined NAO index was

replaced with the COA indices. According to GLM-COA for HI02 (Figure 4.4b), we found

the following covariates were significant at the 95% level: AO, AMO, PNA, GMSST, IL.lon,

AH.p, AH.lat and AH.lon. This is supportive of the initial descriptive statistics that found

AH.p and AH.lon as significantly correlated to HI02. Through our attempt to gain

predictive skill, we found several non-linear relationships associated with the heat

wave indices. For HI02, AH.p was again confirmed as the most important variable in RF-

COA, and Figure 4.5c shows the non-linear dependence where low AH.p values are

associated with high counts of HI02. To visualize this, Figure 4.7 shows composite

anomaly plots of surface pressure (colors) and vector winds (arrows); for reference, a

box is located over the Azores.

88

Figure 4.7 Composite anomaly plots for the top five hottest years according to (A) HI02 and (B) HI11

where colors represent surface pressure and arrows represent vector winds. A box is located over the

Azores for reference.

The HI02 composite anomaly in Figure 4.7a shows where the area over the Azores

experiences lower pressure during hot years, as expected. This aligns with the

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89

mechanism we present through composite anomaly plots of 300 hPa geopotential

height anomalies in Figure 4.8.

Figure 4.8 Composite anomaly plots of 300 hPa geopotential heights for the top five hottest years

according to (A) HI02 and (B) HI11.

In these composite anomaly plots, we see the patter of a Rossby wave train, initiated in

the tropical Pacific. This feature persists during warm years, not in a typical “blocking”

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90

fashion, but in a way so as to organize the circulation regimes and allow heat to

stagnant over Baltimore. The wind vectors in Figure 4.7a support this mechanism

where anomaly winds are flowing against the typical southerly winds (shown in Figure

4.9) seen along the Eastern seaboard, indicating increased stagnation of this air

movement.

Figure 4.9 Composite anomaly plots of surface pressure (colors) and vector winds (arrows) for study

time period, 1950-2014.

Our results show that only PDO is statistically significantly correlated to HI11, but that

the replacement of NAO with the COA improved the fit of the GLM through a reduced

RMSE value. According to the GLM-COA for HI11 (Figure 4.4b), we found the following

covariates to be significant at the 95% level: ENSO, AO, PDO, GMSST, IL.lon, AH.lat,

AH.lon. This is supportive of the initial descriptive statistics that found PDO as

significantly correlated to HI11. We see in Figure 4.8b where 300 hPa anomalies for

HI11 hot years follow the same general pattern as for HI02, but shifted westward so

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91

that the anomaly ridge covers a greater area of the United States. On the surface

however, the HI11 anomalies look quite different than HI02, thus supporting our

findings of different important variables. Specifically, in the Pacific basin we see an

anomalous high pattern indicative of positive phase PDO, and in alignment with the

dependence plots results from our RF models (Figure 4.6 a,c).

As mentioned above, this study showed improvement in modeling the heat wave

indices by replacing NAO with the COA indices. As seen in Figure 4.3, the GLM using

COA was better able to fit summers with high counts of heat wave days. For HI02

(Figure 4.3a) we see where GLM-Ind7 never produces a value higher than 9 days, where

GLM-COA models counts up to 19 days. For HI11 (Figure 4.3b) we see where GLM-Ind7

produces values up to 16 days, where GLM-COA models counts up to 25 days. In

practice, the ability to model summers with higher

From the results discussed above, this study attempts to build on the ability to model

the summers by completing a comprehensive investigation into predicting HI02 and

HI11. The baseline metric for predictability is to outperform the climatologic average

(CLIM), which was not achieved for either HI02 or HI11. However, we found that again

COA improved models when replacing NAO as shown in Table 4.3 where the MSE value

is improved (lowered) for RF-COA over RF-Ind7. As such, it is recommended that

further research be done to improve predictability. The consistency of results across

techniques strengthens the results found in the first part of this study, but also support

the impetus behind building a predictive model. Recommendations for further work

92

include increasing the sample size through clustering station data from nearby cities

and evaluating the dataset in the same way, or to use the same BWI timeseries but the

employ more advanced statistical techniques, such as extreme value analysis, given the

inherent extreme nature of heat wave data.

In the end, this study was able to show that models of heat waves in Baltimore are more

robust when including COA indices over NAO in general, but also that the inclusion of

AH.p helps quantify blocking over the Atlantic, which leaves heat built up over the US.

We also showed that results differ between heat wave indices, indicating that results

across studies can only be compared when the heat wave index is defined consistently.

Lastly, we built the groundwork for further investigation into creating a model with the

ability to use these LSM to predict heat waves in Baltimore. These results are valuable

for informing future improvements to seasonal forecasting of heat waves, which bring

us closer to decreasing the negative effects heat waves currently have on human health.

93

TABLES Table 4.1 Root mean square error (RMSE) for four GLM.

HI02 HI11

Ind7 4.93 7.69

COA 3.95 7.03

94

Table 4.2 Mean square error (MSE) values from holdout analysis for HI02; * indicates top performing model. COA Ind7

GLM 35.42 31.61

CART 46.12 43.15

RF 26.39* 25.88*

CLIM 30.64 25.90

GAM 40.95 34.33

95

Table 4.3 Mean square error (MSE) values from holdout analysis for HI11; * indicates top performing model.

COA Ind7

GLM 119.71 81.63

CART 88.47 91.03

RF 61.63* 71.02*

CLIM 68.92 73.07

GAM 99.38 107.28

96


higher importance.

COA Ind7

AMO 1.69 2.82

AO 0.43 0.24

ENSO -0.06 0.39

GMSST 1.24 5.52

NAO - 0.42

PDO 0.80 1.18

PNA -0.34 0.41

AH.lat 0.35 -

AH.lon 0.76 -

AH.p 3.31 -

IL.lat 0.13 -

IL.lon 0.93 -

IL.p 0.76 -

97


higher importance.

COA Ind7

AMO 2.26 6.62

AO -0.24 -1.38

ENSO -1.01 -0.43

GMSST 2.00 1.96

NAO - -0.59

PDO 10.49 9.35

PNA 0.03 1.64

AH.lat 1.95 -

AH.lon 1.51 -

AH.p 4.52 -

IL.lat 0.38 -

IL.lon 1.09 -

IL.p 0.23 -

98

5. CHAPTER 5: CONCLUSIONS

Extreme summertime heat is the most deadly natural hazard in the United States (NOAA,

2015), where it has been projected that by mid-century, 50% of all summers will be as hot

as the top 5% of summers in the historic baseline (Duffy and Tebaldi, 2012). The preceding

chapters take this knowledge as motivation to improve our understanding of the drivers of

summertime heat across the United States. The intended outcome of this research is to

provide an outline for discussing results from studies with diverse motivations, as well as

creating a framework of understanding the large-scale drivers of summertime heat to

inform and improve seasonal forecasting.

Chapter 2 describes and explains how the choice of definition influences conclusions

regarding the observed frequency of extreme heat events in different CONUS regions in

order to provide a baseline for interpreting studies that project future trends in extreme

heat events. Over the 1979-2011 time period investigated, the Southeast region saw the

highest number of heat wave days for the majority of indices considered. Positive trends

(increases in number of heat wave days per year) were greatest in the Southeast and Great

Plains regions, where more than 12% of the land area experienced significant increases in

the number of heat wave days per year for the majority of heat wave indices. Significant

negative trends were relatively rare, but were found in portions of the Southwest,

Northwest, and Great Plains.

Chapter 3 first presents a novel regionalization of CONUS, where regions were selected by

temperature-informed hierarchical clustering analysis and yielded five regions that exhibit

99

distinctly different behavior. Seasonal average temperatures were then investigated to

explain large-scale driver of variability over these regions on seasonal timescales. Results

indicate that summertime temperature variability is sensitive to different climate

processes in different regions, including the Pacific Decadal Oscillation variability in the

Southwest, Arctic Oscillation in the Northern Great Planes, Atlantic Multidecadal Oscillation

in the South, and late spring soil moisture anomalies in the Northeast. Notably, nonlinear

models yielded the best results in all regions: a random forest model is found to be most

robust in the SW and South, while a generalized additive model is most robust for the NGP

and Northeast. These results are valuable for informing future improvements in seasonal

forecasting of summertime temperatures and are relevant for projections of summertime

climate change across climatically distinct regions of CONUS.

Chapter 4 presents a deep dive into the large-scale drivers of heat waves in Baltimore, MD.

Specifically, this work compares the effect of two NAO definitions, classically defined NAO

and COA-defined NAO, to heat waves in Baltimore, where a heat wave is defined by both a

relative and an absolute definition from Chapter 2. This work shows that replacement of

classically defined NAO definition with the COA-defined NAO indices increases model fit for

both heat wave definitions. This phenomenon is explained by the Azores High experiencing

lower pressure during hot years and the resulting Rossby wave train, which emulates an

atypical blocking pattern by organizing circulation regimes that allow heat to stagnate over

Baltimore. This work also built a framework for a predictive model of heat waves in

Baltimore, and despite not gaining predictive skill over climatology, we were able to

100

investigate non-linear variable responses to heat waves, which support our explanatory

mechanisms explained above.

5.1. Future work

The work presented in this thesis allows for multiple avenues of improvement by

extending these analyses. From Chapter 2, future studies can pair our findings with the

relative health effects of heat waves in differing regions to grasp a complete

understanding for planning health interventions and climate change adaptation

strategies. From the last two chapters, these works aimed to inform future studies of

seasonal forecasting and climate change impacts specifically relevant across heat-

vulnerable regions of CONUS. Thus, we suggest further work to incorporate these

findings into seasonal forecasting models to improve predictive skill in forecasting

summertime heat. One way to improve on the predictive skill of the models presented

in Chapter 4 is to automate a process to include a stepwise reduction in variables to find

the optimal conditions to predicting summertime heat waves. Extension of these

methods will significantly improve the prediction of summertime heat across the

United States and ultimately decrease the negative impacts heat has on the human

population.

101

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AUTHOR’S CURRICULUM VITAE

Tiffany T. Smith EDUCATION

2016 Ph.D. Earth Science

Department of Earth and Planetary Sciences, Johns Hopkins University

Advisor: Dr. Benjamin Zaitchik Dissertation: Summertime heat across the United States

2013 M.A. Earth Science


2009 B.S. Earth Science (Minor: Chemistry)

Department of Geosciences, Oregon State University

EXPERIENCE

2015 – present Market Analyst

Fundamentals and Analytics, Constellation Energy

2016 Lab Mentor

Department of Meteorology & Atmospheric Science, Penn State Univ Course: Weather Risk and Financial Markets (METEO 460)

2015 Instructor

Betamore Course: Introduction to Data Analysis Using R

2011, 2013 Teaching Assistant

Department of Earth and Planetary Science, Johns Hopkins University

Courses: Oceans and Atmospheres (AS.270.108); Introduction to Sustainability

(AS.270.107)

2010 – 2015 Graduate Research Assistant


Advisor: Dr. Benjamin Zaitchik Dissertation: Summertime heat across the United States

2009-2010 Research Intern

Hydrologic Sciences Branch, NASA Goddard Space Flight Center (GSFC)

Supervisor: Dr. Matthew Rodell Research: Variations in precipitation over India; compilation of groundwater

level data in Mississippi River Basin

Global Modeling and Assimilation Office, NASA GSFC

Supervisor: Dr. Randal Koster

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Research: Global analysis of water-limited versus energy-limited drought

environments

2009 GIS Assistant

Transboundary Freshwater Dispute Database, Oregon State University Research: Geographic and historic data conversion to online GIS system

2008 Instructor

Annapolis Sailing School Course: Adult learn-to-sail program, 5-day and 2-day sessions

2006-2009 Researcher’s Assistant

Center for Genome Research & Biocomputing, Oregon State University

James C. Carrington Lab Research: Investigation of RNA mutations in Arabidopsis thaliana

2006 Data Collector

Parks and Recreation Department, City of Boulder, CO Research: Data collection in the field to better understand the effects of the

bubonic plague on prairie dog populations

PUBLICATIONS

Smith TT, BF Zaitchik, and SD Guikema (2016) Large-scale drivers of interannual summertime

temperature variability across the Continental United States. Journal of Applied Meteorology and

Climatology. Under Review

Kent ST, LA McClure, BF Zaitchik, TT Smith, and JM Gohlke (2014) Heat Waves and Health

Outcomes in Alabama (USA): The Importance of Heat Wave Definition. Environmental Health

Persepctives. DOI:10.1289/ehp.1307262

Smith TT, BF Zaitchik, and JM Gohlke (2013) Heat waves in the United States: definitions,

patterns and trends. Climatic Change 118 (3-4):811-825. DOI: 10.1007/s10584-012-0659-2

Cuperus JT, TA Montgomery, N Fahlgren, RT Burke, T Townsend, CM Sullivan and JC

Carrington (2010) Identification of MIR390a Precursor Processing-Defective Mutants in

Arabidopsis by direct genome sequencing. Proc Natl Acad Sci. DOI: 10.1073/pnas.0913203107.

PRESENTATIONS

Smith TT (2015) Characterization, forcings, and feedbacks on summertime temperatures across

the United States. Invited George Mason University Climate Dynamics Seminar. March 25.

Fairfax, VA.

Smith TT, BF Zaitchik, and JA Santanello (2014) The role of land-atmosphere interactions

during the CONUS 2012 summertime heat wave. AGU Fall Meeting. December 15-19. San

Francisco, CA.

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Smith TT, BF Zaitchik, and SG Guikema (2014) Remote forcings on summertime heat waves

across the United States. AMS 26th

Conference on Climate Variability and Change. February 2-

6. Atlanta, GA

Gohlke JM, ST Kent, TT Smith, LA McClure, and BF Zaitchik (2013) Heat waves and health

outcomes: The importance of heat wave definition. ISPRS: Climate Variability and Health.

August 25-29. Arlington, VA.

Smith TT, BF Zaitchik, JM Gohlke, and SG Guikema (2013) Heat waves in the United States.

5th

Annual Atmosphere-Ocean Science Days. June 6-7. Baltimore, MD

Smith TT, BF Zaitchik, and JM Gohlke (2013) Heat waves in the United States: definitions,

patterns and trends. AMS Fourth Conference on Environment and Health. January 6-10. Austin,

TX.

Smith TT, BF Zaitchik, MC Anderson, MT Yilmaz, CA Alo, and M Rodell (2011) Remotely

Sensed Terrestrial Water Balance of the Nile Basin. AGU Fall Meeting. December 5-9. San

Francisco, CA.

PROFESSIONAL DEVELOPMENT

July 2013 WRF Users Tutorial

NCAR Foothills Laboratory

Boulder, CO

July 2013 Fifth Biannual Colloquium On Climate And Health

NCAR Foothills Laboratory/Center for Disease Control

Boulder, CO

January 2013 Extreme Weather, Climate and Health: Putting Science into Practice

National Institute of Health/Center for Disease Control

Washington, DC

November 2012 Climate Dynamics of Tropical Africa: Present Understanding and Future

Direction


Baltimore, MD

July 2011 Climate Resilience in the Blue Nile/Abay Highlands

Addis Ababa University/Johns Hopkins Univ. Global Water Program

Bahir Dar, Ethiopia

Apr 2011 Managing Climate Change Impacts on Water Resources

American Water Resources Association

Baltimore, MD

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Mar 2009 Current State of Palestinian Water Resources

Department of Earth and Environmental Sciences, Al-Quds University

Abu Dis, West Bank

HONORS AND AWARDS

2013 Graduate Student Summer Field Grant

Department of Earth & Planetary Sciences, Johns Hopkins University

PROFESSIONAL ACTIVITIES AND AFFILIATIONS

Journal Reviewer

Climatic Change

International Journal of Climatology

Journal of Health Geographics

Member

American Meteorological Society

American Geophysical Union

SKILLS

Mac, Windows & Unix environments

R

Python

MATLAB

NCAR Command Language (NCL)

Land Information System (LIS)

Weather Research and Forecasting Model (WRF)

NASA Unified WRF (NU-WRF)

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