Estimating Spatial Characteristics of Precipitation Associated with Tropical Cyclones Originating Over the North Atlantic Ocean

ESTIMATING SPATIAL CHARACTERISTICS OF PRECIPITATION ASSOCIATED WITH TROPICAL CYCLONES ORIGINATING OVER THE NORTH ATLANTIC OCEAN

YAO ZHOU

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2018

To my family

ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Corene Matyas, for her encouragement and commitment to help me to reach my goal. I would also like to thank my other committee members, Drs. Joann Mossa, Peter Waylen, and Stefan Gerber, for their invaluable insight and expertise. Thanks to all faculty members, staff, Hurricane research group, and graduate students of the Department of Geography at the University of Florida who were always willing to help me. This dissertation research was funded by National

Science Foundation (NSF) CAREER Award BCS-1053864. I would also like to extend my sincere appreciation to all my family members, for their unending love, support, and reliance.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 7

LIST OF FIGURES ...... 9

LIST OF ABBREVIATIONS ...... 11

ABSTRACT ...... 13

CHAPTER

1 INTRODUCTION ...... 15

Research Background ...... 15 Spatial Characteristics of TC Precipitation and Contributing Factors ...... 17 Research Objectives ...... 20

2 SPATIAL CHARACTERISTICS OF STORM-TOTAL RAINFALL SWATHS ASSOCIATED WITH TROPICAL CYCLONES OVER THE EASTERN UNITED STATES ...... 25

Background ...... 25 Data and Methodology ...... 29 Data ...... 29 Methodology ...... 30 Spatial Characteristics of TCP Regions over Land ...... 33 Change of Left Width of TCP Swath along Tracks ...... 36 Return Intervals of TC Rainfall and Wind Events ...... 40 Concluding Remarks...... 43

3 CONDITIONS ASSOCIATED WITH RAIN FIELD SIZE FOR TROPICAL CYCLONES LANDFALLING EASTERN U.S...... 53

Background ...... 53 Data and Methodology ...... 56 Data ...... 56 Methodology ...... 59 Area and Extent of TC Rain Field ...... 62 Statistical Modeling of TC Rainfall Size ...... 66 General Connections between TCP Size and Environmental Conditions ...... 67 Results of Generalized Regression Models...... 69 Conclusions and Discussions ...... 75

4 SPATIAL CHARACTERISTICS OF RAIN FIELDS ASSOCIATED WITH TROPICAL CYCLONES LANDFALLING OVER THE WESTERN GULF OF MEXICO AND CARIBBEAN SEA ...... 84

Background ...... 84 Data and Methodology ...... 87 Overview of Rain Field Metrics and Environmental Conditions ...... 94 Regional Variations of Rain Rates and Corresponding Environmental Conditions ...... 99 Overall Variations of Rain Rates and Corresponding Environmental Conditions .. 102 Rainfall Start Time and Average Duration ...... 106 Conclusions and Future Research ...... 108

5 CONCLUSIONS ...... 119

Summary ...... 119 Future Directions ...... 124

LIST OF REFERENCES ...... 127

BIOGRAPHICAL SKETCH ...... 140

LIST OF TABLES

Table page

2-1 Averages of the wind radii for 17-m/s wind (unit: km) ...... 47

2-2 Spatial characteristics of TCP swaths in Gulf Coast group (area unit:105 sq. km, width unit: km)...... 49

2-3 Spatial characteristics of TCP swaths in Florida group (area unit:105 sq. km, width unit: km)...... 49

2-4 Spatial characteristics of TCP swaths in East Coast group (area unit:105 sq. km, width unit: km)...... 50

2-5 Change in distance of left width in each group (unit: km)...... 51

2-6 Chi-square test results...... 51

3-1 Variables’ descriptions...... 79

3-2 Area and extent of rainfall fields of TCs (area unit:104 sq. km, width unit: km). .. 80

3-3 The correlation coefficients between area and extent of TC rain fields and predictors (Correlation coefficients greater than 0.30 and significant at 0.01). ... 82

3-4 Coefficients and model estimation of regression model to predict rainfall area over land and ocean (Variables significant at 0.1)...... 82

3-5 Coefficients and model estimation of extent regression models over land (Variables significant at 0.1)...... 83

3-6 Coefficients and model estimation of extent regression models over ocean (Variables significant at 0.1)...... 83

4-1 Abbreviations, units, source, and spatial range of TC attributes and environmental conditions...... 112

4-2 Number of features and statistics of metrics for all observations, hot spots, and cold spots of light rainfall (area unit:104 sq km, width unit: km) ...... 113

4-3 Name, unit and statistics of variables over entire region. Different number of observations is due to the missing data in SHIPS...... 113

4-4 Mann-Whitney U Tests results of conditions related to hot and cold spots of area, dispersion and displacement of light rainfall...... 116

4-5 Spearman’s rank correlation coefficients, time lags and spatial range between area, shape metrics and environmental conditions (Correlation coefficients greater than 0.3 and significant at 0.01)...... 116

LIST OF FIGURES

Figure page

1-1 Tracks of all tropical cyclones making landfall over U.S. coast in 1948-2015 and making landfall in 1998–2015 over the western Caribbean and/or Gulf coasts that examined in this dissertation. Elevation data were obtained from USGS...... 24

2-1 Extracting TCP from daily precipitation data...... 47

2-2 Example of data from Hurricane Frances (2004)...... 48

2-3 Shaded areas depicting total rainfall extent for all TCs in each group and tracks of TCs making landfall in three regions...... 48

2-4 TC tracks and change points in 4 groups...... 50

2-5 Return interval of TC rainfall and wind events per county...... 52

2-6 Frequency and return interval TCP event...... 52

3-1 Interpolated 3-hourly positions of tropical cyclones included in the study...... 79

3-2 Measuring the extent of rainfall field of Hurricane Floyd (1999)...... 80

3-3 Spatial distribution of TC rain field area averaged in 250 km cells (Area is classified by natural break classification method)...... 81

3-4 Spatial distribution extent of TC rain fields in 250-km cells...... 81

4-1 Tracks of 35 tropical cyclones that made landfall in 1998–2015 over the western Caribbean and/or Gulf coasts. Elevation data were obtained from United States Geological Survey...... 111

4-2 A comparison of rain fields from Tropical Storm Arlene (2011) and Hurricane Dean (2007)...... 111

4-3 A comparison of displacement of rain fields and wind shear from Hurricane Mitch (1998) and Hurricane Ernesto (2012) ...... 112

4-4 Distribution of storm intensity, average TPW over 0-400 km, SHRW, and SHRS...... 114

4-5 Hotspots maps of area, dispersion, and displacement of light rainfall...... 115

4-6 Hotspots maps of change of area, dispersion, and displacement of light rainfall...... 115

4-7 Start time of light and moderate rainfall relative to landfall...... 117

4-8 Average duration of light and moderate rainfall associated with TCs...... 118

4-9 Maximum duration of light and moderate rainfall associated with TCs...... 118

LIST OF ABBREVIATIONS

CAG Central American gyres

CHIRPS Climate Hazards Group InfraRed Precipitation with Stations data

CMORPH CPC morphing technique

CONUS the contiguous U.S.

CPC Climate Prediction Center

EBT Extended Best Track

ESRI Environmental Systems Research Institute

ET Extratropical transition

FEMA Federal Emergency Management Agency.

GFS Global Forecast System

GIS Geographic Information System

GPM Global Precipitation Measurement

GSMaP Global Satellite Mapping of Precipitation

IBTrACS International Best Track Archive for Climate Stewardship

IMERG Integrated Multisatellite Retrievals for GPM

MJO Madden-Julian oscillation

NCEP National Centers for Environmental Prediction

NHC National Hurricane Center

NOAA National Oceanic and Atmospheric Administration

PHRaM Parametric Hurricane Rainfall Model

PRISM Parameter-elevation Regressions on Independent Slopes Model

PT Post-tropical cyclone

ROCI Radius of Outermost Closed Isobar

SHIPS Statistical Hurricane Intensity Scheme

TC Tropical cyclone

TCP Tropical cyclone precipitation

TMPA Multi-satellite Precipitation Analysis

TRMM Tropical Rainfall Measuring Mission

TS Tropical storm

UPD U.S. Unified Precipitation Data

UTC Coordinated Universal Time

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

ESTIMATING SPATIAL CHARACTERISTICS OF PRECIPITATION ASSOCIATED WITH TROPICAL CYCLONES ORIGINATING OVER THE NORTH ATLANTIC OCEAN

Yao Zhou

May 2018

Chair: Corene J. Matyas Major: Geography

A thorough understanding of the spatial patterns of tropical cyclone precipitation

(TCP) and the factors that contribute to high rain rates and large raining areas are essential for both improvement of rainfall forecasts and regional hazard preparation and mitigation. In this dissertation, three related studies investigate the spatial patterns of rain fields associated with tropical cyclones (TCs) that originate over the North Atlantic basin. The first study develops a Geographic Information System method to delineate rainfall swaths for U.S. landfalling TCs and measures the rainfall swath areas and average widths over land. The TCs exhibiting the expansion of left width had attributes of being hurricanes at landfall, re-intensifying over land, undergoing extra-tropical transition, and/or moving near the coastline. This study also discovers that more locations were affected by rainfall than by tropical storm-force wind from these systems.

The second study measures the area and average extent of rain fields associated with U.S. landfalling TCs as detected by satellites at a three-hour resolution.

Statistical models are developed to predict the area and extent of rainfall before and after landfall. As TCs move inland, although the area and extent in rear quadrants decays, the rainfall in front quadrants can still extend farther than 300 km from the storm

center. The statistical models reveal that moisture and upper-level divergence are associated with both area and extent in all quadrants. The storm intensity and distance to coastline have different influence on rainfall when over ocean and over land. The third study examines area, dispersion, and displacement of light and moderate rain fields of TCs making landfall over the western Caribbean and Gulf coasts. The rainfall coverage is largest as TCs approach the Caribbean coast, while rain fields enlarge as

TCs move back over the Gulf of Mexico. The rain fields have more displacement to east and north over western and central Caribbean Sea and central Gulf of Mexico, and to west and south over the southern Gulf of Mexico. About half of storms produce rain over land about 48 hours before landfall.

CHAPTER 1 INTRODUCTION

Research Background

Tropical cyclones (TCs) are warm-cored, intense cyclonic, atmospheric vortices that develop over the warm tropical oceans and have a horizontal scale that extends hundreds to 1000 km and extend vertically throughout the depth of the troposphere.

TCs are one of the most devastating natural hazards as they cause numerous fatalities and huge economic losses (Rappaport 2000, 2014; Pielke et al. 2003; Czajkowski,

Simmons, and Sutter 2011). Atlantic basin TCs caused more than 2500 deaths in the

United States (U.S.) and its coastal waters during 1963 to 2012, which means on average, one out of five or six Atlantic TCs causes fatalities in the U.S. (Rappaport

2014). The economic loss caused by TCs is around 417.9 $ billion, which accounts highest absolute number and percentage of hazard damage in U.S. during 1980-2011, and exhibits an upward trend from 1900-2015 (Smith and Katz 2013; Estrada, Botzen, and Tol 2015; Zhang and Weng 2015). Although only a small portion of Atlantic TCs make landfall over Mexico and Central American countries, hurricanes like Mitch (1998) and Stan (2005) have also caused thousands of deaths and significant economic losses

(Pielke et al. 2003). Many studies have shown that in the North Atlantic, the frequency, intensity and tropical cyclone precipitation (TCP) rates have changed in the last several decades or will change in a greenhouse warming climate, with a change ranging from 3 to 37 % (Santer et al. 2006; Knutson et al. 2006; Holland and Webster 2007; Knutson et al. 2010; Romero-Lankao et al. 2014;). Future TC damage will increase significantly in

North America due to dense population and economics (Pielke 2007; Mendelsohn et al.

2012; Romero-Lankao et al. 2014; Visser, Petersen, and Ligtvoet 2014). Thus, there is

a need to fully document and understand all hazardous aspects of TCs to enhance public awareness and hazard mitigation, and in turn save lives and avoid economic loss.

TCs pose significant threats to society and environment through storm surge, heavy rainfall, intense wind and tornadoes (Kovach and Konrad 2014). Among all hazards related to TCs, precipitation associated with TCs, and induced inland flooding, can cause significant economic loss and fatalities over broad areas adjacent to and away from the storm track (Czajkowski, Simmons, and Sutter 2011). About one-third of the deaths in the U.S. that are related to TCs are a result of rainfall-induced flooding, which is the most frequent hazard associated with TCs (Rappaport 2000, 2014;

Czajkowski, Simmons, and Sutter 2011). During 2006-2016, the U.S. did not experience the landfall of a major hurricane (Hart, Chavas, and Guishard 2016). However, less intense hurricanes like Irene (2011), Sandy (2012), and Matthew (2016), still cause fatalities and billions of economic loss through precipitation and induced flooding. TCP is the primary cause of flooding risk in the eastern U.S. and Puerto Rico, Mexico and other Central American countries (e.g. Belize), with flood peak properties that are closely linked to the spatial and temporal distribution of tropical cyclone rainfall (Villarini and Smith 2010; Kunkel et al. 2013; Villarini et al. 2014; Brena-Naranjo et al. 2015;

Wright, Knutson, and Smith 2015; Hernández Ayala et al. 2017). Despite these negative socio-economic impacts, landfalling TCs have also been found to have a significant role that relives drought conditions and hydrological resource by recharging reservoirs and elevating soil moisture (Maxwell et al. 2013; Xu, Osborn, and Matthews 2017).

When concerning the potential for a TC to produce rainfall capable of causing flooding, three important factors must be considered: rainfall intensity, spatial distribution, and duration (Rezapour and Baldock 2014; Lin, Zhao, and Zhang 2015).

The distribution is defined as an area of rainfall over a given rain rate threshold

(Rezapour and Baldock 2014). While the winds in most TCs decay rapidly during and after landfall (Yaukey 2011) so that the wind damage is normally limited once inland, rain rates can intensify and rain fields can expand in coverage under certain environmental conditions (Atallah, Bosart, and Aiyyer 2007) . The larger coverage of

TCP implies that a longer duration of rainfall will occur over a given location. In other cases, TC rain rates decrease after landfall, rain fields decay in size or become fragmented in spatial coverage, and they do not pose a flood threat. Therefore, a thorough understating of spatial patterns of TCP and the factors that contribute to large raining extent are essential for both improvement of rainfall forecasts and regional hazard preparation and mitigation.

Spatial Characteristics of TC Precipitation and Contributing Factors

Previous studies have determined that TCs are comprised of clouds that produce convective and stratiform rainfall. Then they classified rainfall features into different parts, including eyewall and inner core rainbands (e.g. principle rainbands and secondary rainbands), inner rainbands, and outer rainbands (Corbosiero and Molinari

2002; Houze 2010; Jiang, Ramirez, and Cecil 2013). The eyewall and inner core rainbands contain convective rainfall where rainfall rates could reach above 23-48 mm/h. These regions are usually within 30-50 km of the storm center. The inner rainbands region includes spiral rainbands with a mixture of convective and stratiform rainfall immediately outside of the inner core boundary, and usually extends from the

inner core boundary outward about 100 km. The outer rainband region includes outward spiral rainbands and any rainfall features associated with the storms located beyond about 150–200 km from the storm center, with a mean extent of 502 km (Jiang,

Ramirez, and Cecil 2013). These outer rain band areas can also contain elongated clusters of convective rainfall (Matyas 2009). The entire rainfall size might extend to

800-1000 km, varying greatly between individual TCs.

Previous numerical and observational research examined a variety of TC attributes and environmental conditions that contribute to rainfall structures of TCs, including storm intensity, motion speed and direction, environmental moisture, wind shear, and upper-level outflow. Stronger storm intensity and higher environmental moisture contributes to higher convective rainfall magnitude and larger rainfall coverage with more cohesive pattern (Cerveny and Newman 2000; Lonfat et al. 2007; Jiang,

Halverson, and Zipser 2008; Kimball 2008; Konrad and Perry 2010; Hill and Lackmann

2009; Zick and Matyas 2016; Hernández Ayala and Matyas 2016). Moreover, the stronger upper-level troposphere divergence is also related to larger TC size and rainfall potential (Jiang et al. 2008; Konrad and Perry 2010).

TC precipitation asymmetries are related to the vertical wind shear, storm motion, interactions with topography, moisture source, and even locations of upper-level divergence. Specific to storm motion, several studies have documented that azimuthal asymmetries of rainfall have maximum in the front side or right-front quadrant due to surface friction(Shapiro 1983; Rodgers and Pierce 1995; Corbosiero and Molinari 2002), while Frank (1977) found a nearly symmetric distribution of precipitation with a slight preference for the right side or right-rear quadrant. More recent studies indicated that

TC precipitation asymmetries are more related to the vertical wind shear (Corbosiero and Molinari 2002; Chen, Knaff, and Marks 2006; Ueno 2007; Cecil 2007). Strong vertical wind shear causes rainfall to occur in the downshear direction, especially to the downshear left side in the inner portion of the storm (< 100 km) (Chen, Knaff, and Marks

2006; Cecil 2007; Wingo and Cecil 2010) and downshear or downshear right in the outer rainbands (100-300 km) (Corbosiero and Molinari 2002; Matyas 2010a). As shown in these studies, the wind shear effect overwhelms the storm motion effect on TC rainfall asymmetry, e.g., rainfall maxima are still located downshear or left-of-shear even when storm motion should induce a different pattern. Moreover, moisture distribution also influences the symmetry of TC rainfall. When relatively dry air is drawn into a TC’s circulation from one side, it reduces rainfall on that side (Kimball 2006, 2008; Matyas and Cartaya 2009).

As TCs move to the midlatitudes, they may experience changes in environmental conditions including increased baroclinicity, enhanced horizontal moisture gradients, strong vertical wind shear, interaction with frontal systems or troughs, and they may undergo an extra-tropical transition (ET) (Atallah and Bosart 2003; Jones et al. 2003).

Trough interaction leads to faster forward speed of TCs and strong vertical wind shear

(Atallah and Bosart 2003; Jones et al. 2003). Konrad and Perry (2010) found that heavier precipitation events were associated with a front in the vicinity. The ET is especially common for North Atlantic TCs as nearly half undergo this process that involves significant changes in the strength and spatial pattern of precipitation(Hart and

Evans 2001). During ET process, the structure of the TCs changes dramatically as it loses symmetric structure and gradually takes on the appearance of an extratropical

cyclone. At the beginning of ET process, the rainfall area ahead of the storm center begins to expand due to warm and moist tropical air being lifted over poleward region

(north or northwest) since TC intersect with an upstream trough and/or with a low-level baroclinic zone, while the rain fields decrease (“dry slot”) behind storm center because of advection of relatively drier and cooler air to the rear of the storm center (south or southwest) (Jones et al. 2003). As ET proceeds, a right-to-left cross-track shift in the rainfall distribution might be observed and high rain rate regions can extend a few hundred kilometers from the storm center (Atallah, Bosart, and Aiyyer 2007; Evans et al.

2017).

Although many studies have investigated TCP over land or ocean and multiple contributing factors by both using dynamical modeling and empirical methods, the examination of comprehensive spatial pattern of TCP from these storms during the entire storm period from a geographical perspective has received less attention, despite the freshwater floods that can result from these storms. Moreover, since spatial patterns of TCP are extremely complex and undergo rapid changes, traditional methods that analyze rainfall within a set distance of TC center limit the ability to fully understand

TCP spatial pattern. Therefore, correctly predicting the specific areas that will experience TCP is extremely important in disaster mitigation. A need exists to quantify the spatial distribution of TCP and find the factors that contribute to these patterns through the analysis of a large sample of TCs utilizing various statistical modeling techniques.

Research Objectives

This dissertation presents a spatial analysis of precipitation associated with associated with Atlantic TCs making landfalls over U.S. coastline, Gulf coast and

western Caribbean coast during the last 67 years (1948-2015) (Figure 1-1), with the specific aim of understanding several aspects of storm rainfall including area, extent, dispersion and displacement and then relating them to TC attributes and environmental conditions. This dissertation develops geospatial techniques for representing the spatial and temporal evolution of rainfall, and the regional extent of flooding associated with landfalling tropical cyclones. These analyses, based on a large sample of observational data, will provide improved accuracy in defining where rainfall occurs or higher rain rates within storms, which is valuable to hydroclimatology modeling and hazard mitigation, while knowing the factors that correspond to the patterns is important for rainfall forecasting. This dissertation is divided in three main chapters in which each of those research questions is addressed and organized as follows. The last chapter presents an overview of this dissertation’s conclusions and future directions of research.

Chapter 2 presents a detailed climatology of spatial characteristics of inland storm-total TCP extent for eastern U.S. In this study, we develop a Geographic

Information System (GIS)-based method to delineate rainfall swaths for 257 U.S. landfalling TCs during 1948 to 2014 using a daily gridded dataset. We then describe spatial patterns of TCP using three methods. First, we measure the rainfall swath areas and average widths over land, and examine them by grouping their landfall locations and inland durations. Second, trends in the change of left extent of TCP swaths are analyzed and TC attributes related to these trends are explored. Last, we construct a series of maps with return intervals and frequency distributions for inland TCP and tropical storm-force winds. The identification of the edges of TC rainfall and

identification of conditions associated with expanding rainfall areas should benefit forecasting, hydroclimatologic analyses, and risk analysis for TC hazards.

Different from establishing a long-term climatology of storm-total rainfall., the aims of Chapter 3 are to measure the size of TC rain fields and identify the factors contributing to the organization of rainfall while these systems are over the ocean prior to making landfall, and after they make landfall over the U.S. The research questions are: first, what is the spatial variation in the size of TC rain fields before and after landfall? Second, how does rainfall size of landfalling TCs respond to a combination of storm attributes and environmental conditions, such as TC motion and intensity, environmental moisture, upper troposphere divergence and vertical wind shear? To answer these questions, this study examines the size of rain fields associated with TCs making landfall over the U.S. from 1998- 2015 through a GIS-based analysis of satellite- estimated rain rates. Regions of moderate rainfall (rain rate > 2.5 mm/h) belonging to each TC are converted into polygons and measurements are made of their area and average extent in each of four quadrants placed according to storm motion (right front, left front, left rear and right rear). A grid with a cell size of 250 km is constructed to calculate the average area and extent of rain field in each cell and illustrate the spatial patterns of TC rain fields. We then relate the size of the rainfall field to TC attributes and environmental conditions by using Spearman’s rank Correlation tests and generalized regression models.

Chapter 4 examines spatial patterns of rain fields associated with TCs making landfall over western Gulf Coast and Caribbean Sea Coast during 1998-2015. These

TCs should exhibit rainfall patterns different to those making landfall over the U.S. as

they are not undergoing an extratropical transition. The widespread rainfall associated with TCs making landfall over western Gulf Coast and Caribbean Sea Coast caused numerous fatalities and divesting damage. However, few studies have been examined these regions in detail. There are three main research objectives here. First, after measuring area, dispersion, and displacement of light and moderate rain fields, spatial and temporal patterns of rainfall metrics are examined. The second goal is to determine which TC attributes and environmental conditions are associated with the spatial configuration of light and moderate rain rates for TCs. This is accomplished by comparing sub-areas with distinct rain rate spatial patterns through Mann-Whitney U

Tests for spatially-clustered regions of rain rate patterns and calculating Spearman’s rank correlation coefficients for the entire study region to relate the four metrics and atmospheric moisture, vertical wind shear, storm motion, and storm intensity. Finally, light and moderate rainfall polygons were used to determine the time that rainfall reaches land relative to the time that the storm’s center makes landfall, and calculate the average and maximum duration of rainfall from TCs. Identifying regions where rainfall areas are increasing in area, spreading out, and affecting land days before the

TC center makes landfall is an important step towards improving lead times for the evacuation of flood-prone areas.

Figure 1-1. Tracks of all tropical cyclones making landfall over U.S. coast in 1948-2015 and making landfall in 1998–2015 over the western Caribbean and/or Gulf coasts that examined in this dissertation. Elevation data are obtained from United States Geological Survey (https://lpdaac.usgs.gov).

CHAPTER 2 SPATIAL CHARACTERISTICS OF STORM-TOTAL RAINFALL SWATHS ASSOCIATED WITH TROPICAL CYCLONES OVER THE EASTERN UNITED STATES

Background

In the United States, precipitation associated with tropical cyclones (TCs) forming in the North Atlantic basin has caused significant impacts both along the coast and inland. Flooding associated with landfalling TCs is one of the most devastating natural hazards to society with numerous fatalities and huge economic losses (Rappaport 2000,

2014; Czajkowski, Simmons, and Sutter 2011). Since the 1960s, freshwater flood deaths related to tropical cyclone precipitation (TCP) are more frequent than other TC- induced hazards (Rappaport 2014). On the other hand, precipitation associated with landfalling TCs can have a positive hydro-climatic influence on the ecological system, particularly when relieving drought conditions (Sugg 1967; Maxwell et al. 2013; Brun and Barros 2014). To fully understand the inland impact of TCP, it is important to know the extent of TCP produced during each event where the extent is defined as the area receiving rainfall greater than a certain threshold (Rezapour and Baldock 2014).

Producing a spatial climatology from these rainfall swaths not only provides a measure of how far from the storm track TCP can extend on average, but also facilitates the identification of locations frequently receiving TCP.

Many studies separate TCP from rainfall generated by other weather systems by searching a uniform radius outward from the storm track and considering all rainfall within this radius to have been generated by the TC. Typically, a 500- to 600-km radius has been used (Lonfat, Marks, and Chen 2004; Larson, Zhou, and Higgins 2005; Lonfat et al. 2007; Kunkel et al. 2010; Nogueira and Keim 2010, 2011; Prat and Nelson 2013;

Villarini et al. 2014; Hernández Ayala and Matyas 2016). This is because the radius of

outer closed isobar (ROCI), which is defined as the average of distance from the TC center to the closed isobar of surface pressure located farthest from the center, typically encompasses the entire TC rain field, and the average extent of ROCI for about 90% of

TCs in the North Atlantic is less than 555 km (Merrill 1984; Kimball and Mulekar 2004;

Matyas 2013, 2010b). Yet studies have shown that rainfall patterns in landfalling TCs are complex and vary greatly among individual storms (Konrad, Meaux, and Meaux

2002; Chen, Li, and Cheng 2010; Matyas 2010b). Thus, applying a uniform and symmetric search radius may underestimate or overestimate TCP area. To account for variations in TC size, Zhu and Quiring (2013) used moving ROCI buffers to approximate the zone of TCP, but we are not aware of a study that extracts TC precipitation features utilizing a method that defines the outermost boundary of TCP, or rainfall swath, over land. Developing such a technique should improve accuracy when measuring TCP extent and approximating the temporal duration of TCP events.

Most previous studies involving the inland impact of TCP have focused on spatial-temporal variations of TCP characteristics, including rainfall accumulations, areas, volumes, and contribution of TCP to total/extreme precipitation. Knight and Davis

(2007) investigated TCP variation during 1980-2004 over the southeastern U. S. and found that the distribution of annual average total TCP shows a clear decline from the

Atlantic and Gulf coastlines to northern and inland areas, with highest annual average amounts of TCP over Florida and the Carolinas. Regional studies of TCP over the

Carolinas (Konrad and Perry 2010) and Texas (Zhu and Quiring 2013; Zhu, Quiring, and Emanuel 2013) support portions of findings of Knight and Davis (2007), and offer more details from an increased number of local observations and longer period within

their study area. Nogueira and Keim (2010) assessed temporal trends in TCP area, depth and volume since 1960 in the eastern U.S. They found that annual TCP volumes and areas show multi-decadal variations over the entire period which greatly increase after the 1990s. In all of these studies, a TCP region was defined as a fixed distance from the storm center (e.g. 500 km) or as approximate estimation (Zhu and Quiring

2013), independent of the shape of the actual rain shield. Although the amount and contribution of TCP have been documented over regional scales, there is a need to construct a spatial climatology based on actual TCP swaths in the eastern U.S. using long-term surface-based observations.

After landfall, the rainfall associated with TCs may decrease both in magnitude and total area due to a decrease in latent heat flux and increase in surface roughness

(Kimball 2008), while previous studies have also shown that TCP can be enhanced and/or be redistributed asymmetrically about the storm track under certain conditions.

TCs with greater intensity are correlated with higher rainfall accumulations and more intense rain rates, as well as a more symmetric rainfall pattern over a larger spatial scale (Konrad, Meaux, and Meaux 2002; Lonfat et al. 2007; Konrad and Perry 2010).

When TCs move into the middle latitudes, they can be restructured into extratropical cyclones as increases occur in baroclinicity, vertical wind shear, horizontal moisture gradients, and the Coriolis parameter (Atallah and Bosart 2003; Jones et al. 2003). As the extratropical transition (ET) proceeds, the area covered by winds expands, while rainfall regions become more dispersed, extending a few hundred kilometers from the storm center with a shift of heavy rainfall to the left (north or northwest) of track (Jones et al. 2003; Atallah, Bosart, and Aiyyer 2007; Zick and Matyas 2016). Although some

studies have explored the impacts of environmental conditions on storm structure and the resulting rain rate, magnitude, and areal coverage (Lonfat et al. 2007; Konrad and

Perry 2010; Matyas 2013), there is still a need to analyze TCP events from a longer record to determine which aspects of a TC are associated with rainfall swaths that expand, contract, or do a combination of both as they pass over the U.S.

TCs pose significant impacts on the environment and society from several factors: storm surge, strong wind, heavy rainfall, and tornadoes (Kovach and Konrad

2014). Among these factors, wind and rain hazards can occur far inland and cover large areas (Kaplan and Demaria 1995; Lonfat et al. 2007; Villarini et al. 2014). Two previous studies estimated the cumulative frequency or return interval of wind events associated with TCs as they pass over the U.S. Zandbergen (2009) examined the inland exposure of U.S. counties to tropical storm- and hurricane- force winds by using symmetric, uniform distance buffers along the track. Kruk et al. (2010) improved this method by using asymmetric wind swaths according to the average size of TC wind fields from

1988-2008 to calculate distributions of return intervals for inland TC wind events over the eastern U.S. Yet we are not aware of a study employing similar methods to measure

TCP return intervals. Using a more accurate technique to outline TC rainfall swaths would then enable the calculation of TCP event frequency comparable with that of TC winds to offer an improved understanding of climatologically- favored regions for TC conditions.

The goal of this study is to construct a spatial climatology of inland TCP extent during 1948-2014. We first describe a new Geographic Information System (GIS)-based method utilizing regions of daily rainfall from a gridded dataset of surface observations

and their location relative to storm track to delineate the outermost extent of TC rainfall.

Second, we measure the spatial characteristics of rainfall swaths for 257 TCs, including area and extent on each side of the storm track. Next, we examine the trend of rainfall extent to the left of track as the right widths frequently intersect the coastline so that their true extent cannot be accurately measured. TC attributes related to these trends are explored. After we describe the return interval and cumulative frequency for receipt of TCP, we finally compare the rainfall swaths developed in this study to wind swaths constructed as reported in previous studies to determine the frequency with which locations receive either condition produced by TCs. This analysis allows for an improved picture of inland hazards posed by TCs from a climatological perspective.

Data and Methodology

Data

Daily precipitation totals were obtained from the U.S. Unified Precipitation Data

(UPD) from NOAA Climate Prediction Center (CPC). This dataset contains daily rainfall measurements accumulated at 1200 UTC from rain gauges throughout the contiguous

U.S. (CONUS) since 1948 (Higgins et al. 2007). The gridded precipitation values are obtained from over 8,000 daily station reports from the CPC’s unified rain gauge dataset, and interpolated onto a 0.25° latitude by 0.25° longitude grid using an Optimal

Interpolation scheme (Higgins et al. 2007; Higgins and Kousky 2013). Previous studies using the UPD dataset to examine rainfall from Eastern North Pacific and Atlantic TCs noted that this dataset is ideal for climatological studies since it offers complete spatial and temporal coverage of observational data over U.S. land areas by applying a uniform interpolation method and error corrections (Atallah, Bosart, and Aiyyer 2007;

Corbosiero, Dickinson, and Bosart 2009; Higgins and Kousky 2013). Atallah et al.

(2007) reported that the spatial distribution of the storm-total precipitation approximating

25.4 mm is well replicated for most TCs. The limitations are the daily rather than six- hourly or hourly temporal increments and the fact that the interpolation hinders the ability to identify extreme precipitation values. The precipitation data are also only available over land. Previous studies have shown that UPD produces nearly the same annual totals as the rain gauge data, while it overestimates frequency of light rainfall (<

10 mm per day) and underestimates frequency and maximum values of heavy rainfall

(Atallah, Bosart, and Aiyyer 2007; Ensor and Robeson 2008).

The TC tracks were obtained from International Best Track Archive for Climate

Stewardship (IBTrACS/NOAA), which provides TC center locations and storm intensity every 6 hours at the standard synoptic times each day beginning at 0000 UTC for

Atlantic basin TCs since 1851 (Knapp et al. 2010). To explore TCP patterns over land, we included all 257 TCs making landfall over the U.S. Gulf and East Coasts during

1948-2014. Previous research (Jones et al. 2003; Nogueira and Keim 2010; Matyas

2014) determined that land areas can receive heavy rainfall from TCs prior to the circulation center’s landfall, continue to receive it for days after the storm has tracked inland, and can even receive it after the TC’s wind circulation has dissipated over land.

As our goal was to include all rainfall from the 257 landfalling TCs, the analysis began on the day when the TC first passed within 550 km of the U.S. coastline and ended on the day it moved beyond 550 km of the U.S. or dissipated over the U.S.

Methodology

Separating rainfall into TC and non-TC components is an important and challenging task (Larson, Zhou, and Higgins 2005) as precipitation may arise from the influence of nearby weather systems such as fronts (Knight and Davis 2009) in addition

to rainfall directly produced by the TC. A GIS and a set of python scripts developed within the Environmental Systems Research Institute (ESRI) ArcGIS environment were employed for the analyses. Daily precipitation values from UPD are accumulated at

1200 UTC, and TC observations are available every 6 hours starting at 0000 UTC. To match 6-hourly TC positions with daily precipitation, TC observations from 1200 UTC -

1200 UTC were used to delineate daily storm motion. Then, a value of 12.5 -mm per day was employed as a threshold to define precipitation regions. This threshold was chosen because it falls within the most accurate range (10-30 mm per day) of UPD

(Ensor and Robeson 2008), and has been used to identify moderately heavy rainfall from TCs or other weather systems (Konrad, Meaux, and Meaux 2002; Groisman,

Knight, and Karl 2012). The first step was to generate all 12.5 -mm/day contours and convert them to polygons. The second step was to separate TC precipitation features from non-TC precipitation features. After locating the centroid of each polygon, its distance from the nearest point along the storm track was measured. TC precipitation features were identified if the distance between the centroids of rainfall polygons and

TC track on that day is less than 550 km (Figure 2-1A). This method, also utilized by

Jiang, Liu, and Zipser (2011) to identify precipitation features belonging to TCs as detected using satellite data, ensures that rainfall produced by a TC is included if it occurs more than 550 km from the storm track so long as the centroid of the rainfall region falls within 550 km of the storm track. On a day when precipitation produced by a

TC and a nearby front became merged, all of this rainfall was included in our study as there is not a way to distinguish the rainfall belonging to each system. It should be noted that storm-total rainfall in this study is not purely tropical in nature for all TCs as in

addition to situations where TCs merged with fronts, we also included precipitation during the conversion of a TC into an extratropical cyclone. Isolated small features were excluded if their areas are less than four UPD pixels in size (~> 3,360 sq. km). Finally, all daily TCP features identified for each storm (Figure 2-1B) were merged to generate storm-total rainfall regions, or rain swaths.

After generating storm-total TC precipitation features, the next step was to measure the area and width of the precipitation features. The area was calculated using the USA Contiguous Albers Equal Area Conic Projection. Note that we could only measure rainfall over U.S. land areas due to the limits of dataset. Then a GIS-based method was developed to measure the widths on both left and right sides of TC tracks.

Every 10 km along the track, a straight line was drawn perpendicular to the track segment until it intersected with the TCP polygon edge. If the points of intersection between the lines and the edges of swaths were located on the U.S. border or coastline, these lines were discarded as it is unknown how far the swath extends beyond the edge of the rainfall dataset (Figure 2-2A). The lengths of the remaining lines were calculated to get the width of rainfall extent. Finally, we calculated the average width and changes of width on the right and left sides of the track when 70% of measurements along the track were available on a side to examine the evolution of TCP extent as the storms moved over land.

To compare the extent of rainfall with TC wind, we also generated wind swaths for all TCs during the same period. The distances that we employed to construct our swaths were taken from the work of Kruk et al. (2010). They developed a method whereby multi-distance asymmetrical buffers were used to identify areas affected by

inland TC wind over threshold speeds of 17-, 26-, and 33-m/s. They divided TCs into six categories according to intensity based on the Saffir-Simpson Scale: post-tropical (PT) for storms completing an extratropical transition, tropical storm (TS), Category 1

Hurricane, Category 2 Hurricane, Category 3 Hurricane, and Category 4-5 Hurricane.

For each category, overland average distances in each of four quadrants (northeast, northwest, southeast, and southwest) for each wind intensity threshold were calculated using the extended best-track dataset available from 1988-2008. In the current study, we constructed the wind swaths for our 257 TCs using the distance parameters for 17- m/s wind offered by Kruk et al. (2010) (Table 2-1) (Figure 2-2B).

Last, we produced a series of maps with frequency distribution for overland locations impacted by wind and rainfall associated with TCs. The frequency was summarized in county units, since many tasks including hazard preparation and planning, loss estimation, risk analysis, mitigation, and response to TCs are handled at the county level (Keim and Muller 2007; Zandbergen 2009; Czajkowski, Simmons, and

Sutter 2011; Esnard, Sapat, and Mitsova 2011). To further estimate how frequently a particular location was impacted by TCP events, we calculated return intervals, which are defined as the ratio of study period (e.g. 67 years) over frequency count (Keim and

Muller 2007; Konrad and Perry 2010; Kruk et al. 2010). An event with return interval of

20-yr means the probability of occurrence in any given year is 1 in 20 years or 0.05.

Spatial Characteristics of TCP Regions over Land

In this section, the spatial characteristics of storm-total TCP regions of 257 TCs making landfalls over eastern U.S. during 1948-2014 are summarized. Previous studies suggested different TCs striking the same stretch of coastline tend to approach along a similar path, which indicates that they encounter similar synoptic-scale environments

while moving inland (Jagger and Elsner 2012). Thus, we categorized the TCs landfalls into three regions including the Gulf Coast from Texas to Alabama, Florida, and the

East Coast from Georgia to Maine (Jagger and Elsner 2006, 2012)(Figure 2-3). TCs in the Gulf Coast category are expected to move poleward and interact with the relatively dry environment of the mid-U.S. if they do not dissipate shortly after landfall (Kimball

2006; Andersen and Shepherd 2014), and it should be possible to measure rainfall extent on both sides of the track in most cases. Many TCs making landfall over Florida spend a short amount of time over land and cross back over the ocean without dissipating over land. For both Florida and East Coast tracks, only area and left side width are examined since most TCs track near to the coastline if they move poleward.

For TCs that make multiple landfalls within the study region, if the rainfall area is connected despite differing landfall locations, the TC is categorized according to its first landfall location. Otherwise, rainfall regions are split into different landfalling regions. For example, as Hurricane Katrina in 2005 made its first landfall over Florida on August 25,

2005 and a second landfall over the Gulf Coast four days later, its rainfall regions are separated into two groups, namely Florida and Gulf Coast.

A total of 104 TCs made landfall from Texas to Alabama during the study period.

TCs making landfall over this region have the longest period over land averaging 2.1 days. Precipitation associated with TCs in this group influences the largest geographic region, with a total area of 39.86× 105 sq. km, which covers almost the entire eastern two-thirds of the U.S. For individual storms, the Gulf Coast TCs impact the largest area on average, with a mean TCP area of 4.88 × 105 sq. km. The average left extent of TCP swaths is about 196 km among 76 TCs whose left extents could be measured, which is

the smallest width among the three groups. The right sides of these TCs are about 295 km on average. We further divided TCs according to the time spent over land (Table 2-

2). The results show that average TCP area and left extent increase with period length over land, while the right extent shows a decline for TCs spending longer than 3 days over land. This result generally agrees with the previous research that as TCs make landfall over Gulf Coast and move inland, the rainfall pattern becomes more asymmetric with expanding left/forward side of outer edge of rainfall and diminished rainfall on the right/ rear side due to the ET process and/or dry air intrusion in this region (Zick and

Matyas 2016).

Florida has the most frequent TC activity with 108 landfalls. For TCs making landfall over the Florida panhandle, most of them approach from the south or southwest, tracking towards the northeast as they move inland. TCs cross the peninsula from the west or east. The average period over land is about 1.5 days in this group, with rainfall covering 21.73 × 105 sq. km. Individual TCs have an average value of 3.31 × 105 sq. km for TCP area, and area in this region also shows large variability with a standard deviation of 3.20 × 105 sq. km due to the different track patterns. More than half of

Florida TCs spend less than one day over the peninsula and thus leave the smallest rainfall footprints (Table 2-3). The average and median values of left extent are 233 km and 209 km respectively, which is the largest left extent among the three groups. When comparing TCs with periods between 1- 3 days and greater than 3 days over land, the left extent also increased with the period over land, which agrees with what was found for Gulf region cases.

A total of 53 TCs made landfall over the East Coast region. The average period over land of 1.1 days is the shortest compared to the other two groups, and only one TC in this group spent more than three days over the U.S. As would be expected given that the right side of the storm may produce rainfall offshore as these storms track poleward, the average TCP area, 2.89 × 105 sq. km, is much smaller here. However, the average and median values of left extent of rainfall swaths are about 228 km and 223 km, respectively, which are comparable to those from the Florida region, and larger than those from the Gulf Coast region. The most interesting result from this region is that the rainfall areas of TCs spending less than one day over land (Table 2-4) are the largest among the three groups. This result occurs because many TCs produce precipitation over the coastal area before they make landfall in the East Coast region (Figure 2-3C).

For example, Hurricane Sandy (2012) produced rainfall over Florida and North Carolina before it made landfall over New Jersey. Also, many TCs in this region are undergoing

ET which is known to increase the areal coverage of rainfall ahead of the storm center

(Atallah, Bosart, and Aiyyer 2007; Matyas 2010b). This fact supports the need to include data from the period prior to landfall in construction of storm-total rainfall maps. The average left extent of TCP swath also increases for longer periods over land as in the other two regions.

Change of Left Width of TCP Swath along Tracks

The previous section showed that on average, the left sides of rainfall swaths increased in width for TCs spending more time over land. In this section, we tested for trends in the expansion or contraction of the left side of TCP swaths. Only TCs that spent at least 1.5 days over land with a swath length more than 500 km were included to allow for trends to be identified. A total of 88 TCs met these criteria, representing

about a third of the original dataset. The width data are smoothed with a moving average window of 100 km based on width measurements taken every 10 km. A set of simple trend analyses were utilized. First, a linear regression was used to test the overall trend for the entire swath, and then the slope and coefficient of determination

(R2) were examined. As values of R2 greater than 0.3 are significant at the 0.05 level,

TCs meeting this criterion were deemed to have a significant linear change in width while over land. If the value of R2 is smaller than 0.3, this implies that there were no overall trends in left rainfall width. For these cases, a joinpoint regression analysis was run to determine where a change of trend occurs and the slope of each segment. The results of these two tests allow us to place TCs into one of four classes for increasing

(Group I), decreasing (Group II), decreasing-increasing (Group III), and increasing- decreasing (Group IV) trends (Figure 2-4). There are three TCs which show a relatively constant left width, so they are not included in these four groups. We also applied the same thresholds to measure widths to the right of track, however, only 35 TCs fulfilled the criteria for analysis. These results are not presented given that not enough samples exist for statistical analysis after placing them into the same four groups.

Table 2-5 summarizes the changes in left extent for TCs in the four groups. The change magnitude was calculated by subtracting the first width measurement from the last width measurement of a segment with a significant trend. Group I includes 40 TCs which is nearly half of the total cases. The average and median magnitudes of increase in left width are about 210 km and 190 km, respectively, with a standard deviation of

121 km. Group II includes 18 TCs with decreasing trends of left side, with average

(median) decrease magnitude of left width approximating 98 (81) km, and a standard

deviation of 64 km. Cases in Groups III and IV have significant changes in the trend of left width. Group III includes 15 TCs with decreasing left width during the first segment and increasing left widths during the second segment. The total change in width of this group is positive for 13 out of 15 TCs, with an average (median) value of 63 (55) km, indicating that the overall trend of this group is increasing. Group IV includes 12 TCs with increasing left width first followed by decreasing left widths, which is the smallest group. The total change over land in width of this group is negative for 10 out of 12 TCs, with an average value of 37 km and a median value of 19 km, which means the overall trend of this group is decreasing. In summation, Groups I and III (II and IV) feature left widths that are increasing (decreasing) overall.

Next, multiple Chi-square tests were conducted to determine which TC attributes are associated with expansion and contraction of rain fields. To fulfill the frequency requirements of the tests, we combined Group I and III together to represent TCs with increasing trends, and Group II and IV to represent TCs with decreasing trends. First,

TCs were divided into tropical depressions (TD), tropical storms (TS), and hurricanes

(HU) according to intensity at the best track position immediately prior to landfall, as

Konrad and Perry (2010) found a positive correlation between intensity and rainfall pattern over land. As TCs move inland, they might re-intensify due to the ET process, approaching coastline, or favorable surface conditions (Klein, Harr, and Elsberry 2000;

Andersen and Shepherd 2014). Those TCs which experienced reintensification over land were expected to have increasing left widths due to their structures becoming more symmetrical as moisture is advected to the left side. Furthermore, there are two main outcomes for TCs moving inland: they may cease to exist over land, or move back over

the ocean. In both cases, TCs may also undergo ET. We further examined these three situations’ impact on TCP size change individually. TCs that move back over the ocean may advect increasing amounts of low-level moisture into their circulation, leading to an increase in extent (Matyas 2007). As Matyas (2014) found that going through ET was associated with the largest rain field areas, we expect that TCs experiencing ET may expand their rainfall swaths left of the track. The TCs that cease to exist over land might encounter different situations: increasing left width for TCs that merged with or were absorbed by a front, or decreasing left width for TCs that dissipated/became a remnant low. The demise-type information was extracted from National Hurricane Center’s

(NHC) storm reports for TCs available beginning in 1995

(http://www.nhc.noaa.gov/data/tcr/), and preliminary TC reports and annual reports from

NHC for earlier TCs (Dunn, Davis, and Moore 1955). The demise of the TC is noted in the storm reports at the last synoptic time that the TC center position is available. Only

9% of TCs after 1995 were identified as being absorbed by or merging with fronts. For

TCs prior to 1995, we classified them as dissipating over land if they did not complete an ET and the report does not mention that synoptic-scale influences played a role in weakening the storm post-landfall.

All four Chi-square tests yielded statistically significant results with a 95% confidence level (Table 2-6). Two thirds of TCs in Groups I and III were hurricanes immediately prior to landfall, while 60% of TCs in Groups II and IV were tropical storms or tropical depressions. TCs that experienced re-intensification also showed higher probability to expand their left width. These results generally agree with Konrad and

Perry (2010), which found that TCs with lowest rainfall and smaller size over land were

tropical storms immediately prior to landfall, and rainfall of these events is mainly located on the right side of system. They explained these results by using conclusions from Matyas (2007) that weaker TC wind circulations advect less moisture towards the left or continental side of the cyclone.

Rainfall size tends to increase for TCs that move back over the ocean, as most

TCs in Groups I and III also re-intensify as they approach the coastline. TCs that dissipated over land show more probability to have a decreasing trend in rainfall size.

The results show that 17 out of 30 TCs in Group II and IV dissipated over land, and several TCs in this situation have very little rainfall during the end of the storm period.

We also found 11 TCs that dissipated over land yet had expanded their rainfall on the left side. Their expansion is most likely due to intersecting with fronts, approaching the coast, or reintensification over anomalously moist soil conditions (Arndt et al. 2009).

Last, TCs undergoing ET are also more likely to have an expanding rainfall swath on their left side. This result generally agrees with previous studies which suggested that these TCs will produce an asymmetric rainfall pattern as their rain fields expand on the left side of the storm and diminish on the right side (Jones et al. 2003; Atallah, Bosart, and Aiyyer 2007; Zick and Matyas 2016).

Return Intervals of TC Rainfall and Wind Events

By examining all rain and wind swaths associated with TCs during 1948 to 2014, we provide a climatological view of the areas of eastern U.S. that have been most affected by TCs. We found that 2435 counties in 25 states, covering 54 % of the

CONUS, have been affected by TCP at least once during the study period (Figure 2-

5A). Nearly every state east of the Rocky Mountains has experienced precipitation associated with an Atlantic Basin TC. The return interval of TCP events ranges from

one event every 0.61 to 67 years, the duration of the study period (Figure 2-5A). The distribution of TCP recurrence intervals shows a gradual decrease from southeastern coastal areas to inland areas. However, a prominent precipitation gradient becomes evident along the Appalachian Mountains, where strong orographic enhancement of precipitation often occurs on the windward southeastern slopes, while valleys to the northwest often experience sinking air not conducive to heavy rainfall (Knight and Davis

2007; Konrad and Perry 2010). The coastal states, including all of Florida, coastal counties in Louisiana, Mississippi, Alabama and Georgia, and eastern North and South

Carolina and Virginia average at least one TCP event each year. A vast and continuous region from coastal Texas extending northeastern to Vermont and Maine averages at least one TCP event every one to three years. Our results generally agree with spatial patterns of annual heavy TCP over the southeastern U.S. reported by previous studies

(Knight and Davis 2007; Konrad and Perry 2010; Nogueira and Keim 2011), and clearly show the regions at a higher risk of receiving TCP with recurrence of one year and one to three years over entire eastern U.S., especially over areas more than one hundred kilometers from the coastline and in the northeastern states.

When examining the wind swath data, 278 fewer counties receive one wind event per year as compared to those receiving one rainfall event per year (Figure 2-5B).

The regions with return intervals between 1 to 3 years also show a large difference in coverage. The wind events are mainly confined to the coastal states while rain events with similar return intervals extend west into Ohio and include all of Kentucky and

Tennessee. Only 147 counties have received more wind events than rain events (Figure

2-5C) and these are located in the western portion of the study region and in coastal

Texas. The likely reason for wind events to have occurred more frequently than rain events is that in these areas, rain field size tends to be smaller due to dry environmental conditions, especially on the left side of the storm. Also, the wind radii distances are calculated using historical averages rather than actual wind measurements, so that in reality, TC wind circulations could be smaller in these areas, but this size difference cannot be taken into account. For most regions, the rainfall occurrence is much more frequent than that for tropical storm-force winds. The largest differences occur in Florida and areas east of the Appalachian Mountains, which again suggests that increased moisture availability near the coast and orographic enhancement of precipitation are associated with larger rain field sizes.

To further explore inland TCP, Figure 2-6A represents the maximum annual frequency of TCP during the study period. The maximum annual frequency value per county ranges from 1 to 6, and the spatial patterns reveal that there is not a simple gradient from coastal to inland areas. There are several contiguous counties that have experienced 5 or 6 TCP events in one year. Among these clusters, counties in Florida,

Mississippi, Alabama and northern Georgia received maximum TCP hits in 2005, while clusters over northern Florida, North and South Carolina, Virginia, Pennsylvania, New

York, and Massachusetts received these events in 2004. Figure 2-6B summarizes the return interval of receiving multiple TCP events in one year. In all, 1953 counties experienced multi-TCP events at least once during the study period. The return period of multiple TCP ranges from 2.1 to 67 yrs., and the spatial pattern is a combination of the cumulative frequency and maximum annual frequency maps. All of Florida and coastal areas from Georgia to North Carolina experience multi-TCP events every 2.1 to

3 years. Finally, it should also be noted that numerous counties exhibiting no TCP or wind events in the current study are impacted by eastern Pacific tropical cyclones, as reported by Corbosiero, Dickinson, and Bosart (2009).

Concluding Remarks

This study addressed the need for a detailed climatology of the spatial characteristics of storm-total rainfall swaths from North Atlantic Basin TCs over the eastern U.S. In this study, a GIS-based method was developed to delineate rainfall swaths of 257 U.S. landfalling TCs during 1948 to 2014, and then calculate their area and width over land. This method improved upon previous research by extracting a more precise spatial pattern of TCP over land and measured the widths of rainfall on each side of the track. Statistical tests revealed differences in conditions associated with trends in the width of the swath on the left side of the track. Last, the return intervals and frequencies of rainfall and wind events associated with TCs were examined at the county level.

The average left width of TCP swaths ranges from 196 km in TCs making landfall along the Gulf Coast to 233 km for those making landfall over Florida. The average right width of rainfall swaths of TCs making landfalls over Gulf Coast is about 295 km. These statistics support the findings of Matyas (2010b) and should be useful for hydroclimatologists calculating the contribution of TCP to a regional water budget

(Knight and Davis 2007) and serve as a baseline for atmospheric scientists examining rainfall from TCs under future climate scenarios (Wright, Knutson, and Smith 2015).

Despite the tendency for TC wind fields to decrease in size after landfall, we found that

70 out of 85 TCs have rain swaths that expand in width on the left side at some point while over land. The TCs exhibiting this expansion had attributes of being hurricanes at

landfall, re-intensifying over land, undergoing ET, and/or maintaining a position near the coastline rather than tracking far inland. Thus, people located to the left of the projected storm track should monitor conditions closely as they may receive TCP even if located

100-200 km away from the storm center.

Last, we compared return intervals for rainfall and wind events from TCs at the county level. Most counties over the eastern U.S. are exposed more to rainfall than to wind from TCs, especially regions east of the Appalachian Mountains, where the rainfall frequency can be 1.6 to 2.9 times the wind frequency. The previous studies suggested that the wind intensity will decay and extent will decrease after landfall, especially on the left side of the track, while during ET process, the wind field will expand again on the right side (Kruk et al. 2010). The rainfall swaths are more likely expand on the left side in this region due to ET and high moisture availability from the ocean. While cumulative rainfall shows a gradual decrease from coastal counties in the southeast to inland areas, many inland regions have received 5-6 TCP events in a single season, which confirms that TCP should be a concern for people living inland as well as near the coast. It should be noted that the rainfall swaths were constructed based on a moderately heavy rainfall threshold (Groisman, Knight, and Karl 2012). The regions within these TCP swaths could be viewed as being at risk of flooding as a TC approaches, however the actual magnitude of the hazard will vary according to many conditions such as rainfall intensity, storm duration, surface slope, and whether soils are saturated (Villarini et al. 2011; Villarini et al. 2013; Rezapour and Baldock 2014; Villarini et al. 2014).

The TCP swaths data derived in this study are valuable to various aspects of society. The climatology of the frequency of storm-total rainfall from TCs may be useful to landuse planners when considering the potential flooding regions. From a hazard perspective, a combined dataset of TC rainfall and wind swaths could be input into models like FEMA's HAZUS, which will help government officials identify broad areas that are exposed to these conditions. A detailed analysis of the exposure of the population, urbanized areas, and the ecological system to TC conditions is necessary to evaluate the possible impact and risk of TCs. These swaths can also be useful in the analog approach to forecasting as TCs with similar trajectories might encounter similar synoptic environmental conditions and produce similar rainfall patterns. As such, we are making shapefiles of all 257 rainfall swaths available online

(https://hurricane.geog.ufl.edu/).

Results in this study are subject to a few uncertainties. First, by examining rainfall regions greater than 12.5mm-day, we focused on the edge of the rainfall swath to determine which areas were impacted by TCP. To fully investigate rainfall impact, spatial analysis should be performed on precipitation datasets such as the Stage IV analysis that provides rain gauge-corrected radar estimates (Villarini et al. 2011) that do not smooth the extreme values that are needed to examine heavy rainfall impacts over land. Second, due to data limitations, we only measure the rainfall over land, which does not offer information about entire extent of the storm, especially to the right side of the TC center. Observations taken from satellites like Tropical Rainfall Measuring

Mission (TRMM) and Global Precipitation Measurement (GPM) (Hou et al. 2014), offer full spatial coverage in the tropics and subtropics to examine TC characteristics such as

rain field size, extent, and location relative to the track. Also, this study investigated the associations between several TC attributes and change in rainfall width. Although data span a shorter period and display some inconsistencies in representing TCs over the long-term (Zick and Matyas 2015), the North American Regional Reanalysis dataset has a similar spatial resolution to the GPM and TRMM datasets and could be employed to investigate synoptic-scale conditions (e.g. total precipitable water, vertical wind shear, temperature and moisture gradients associated with frontal boundaries) that may contribute to rain field expansion after landfall.

Figure 2-1. Extracting TCP from daily precipitation data. A) Daily rainfall on 8 September 2004 with solid line showing the storm track and dashed region encompassing daily rainfall equal to or greater than 12.5-mm produced by Hurricane Frances. B) Daily TCP regions of Hurricane Frances 5-10 September 2004.

Table 2-1. Averages of the wind radii for 17-m/s wind (unit: km) (Kruk et al., 2010). Category PT TS Category Category Category Category 1 2 3 4-5 Left radius 217 121 148 211 221 208 Right radius 357 186 240 300 328 268

Figure 2-2. Example of data from Hurricane Frances (2004). A) Measuring widths of TCP swaths (50 km interval shown here). B) Comparison of wind (dashed line) and rainfall (shaded area) swaths.

Figure 2-3. Shaded areas depicting total rainfall extent for all TCs in each group and tracks of TCs making landfall in A) Gulf Coast, B) Florida, and C) East Coast regions.

Table 2-2. Spatial characteristics of TCP swaths in Gulf Coast group (area unit:105 sq. km, width unit: km). Storm-total Variables Number Average Std. Percentile period of cases Deviation 25 50 75 < 1 day Area 32 2.05 2.33 0.50 1.24 2.71 Left width 12 144 130 33 95 274 Right width 9 269 165 70 329 377 1~3 days Area 46 5.84 3.96 2.17 4.83 9.64 Left width 41 189 120 98 165 263 Right width 42 316 186 197 306 398 > 3 days Area 26 6.52 3.16 4.20 6.77 8.14 Left width 23 236 173 120 204 298 Right width 21 264 115 154 272 376

Table 2-3. Spatial characteristics of TCP swaths in Florida group (area unit:105 sq. km, width unit: km). Storm-total Variables Number Average Std. Percentile period of cases Deviation 25 50 75 < 1 day Area 55 1.83 2.06 0.52 1.05 2.23 Left width 34 241 126 149 231 322 Right width 35 3.67 3.10 1.27 3.20 4.74 1~3 days Area 24 217 99 147 188 257 Left width 18 7.13 3.00 4.78 6.72 9.68 Right width 17 241 72 190 222 282 > 3 days Area 55 1.83 2.06 0.52 1.05 2.23 Left width 34 241 126 149 231 322 Right width 35 3.67 3.10 1.27 3.20 4.74

Table 2-4. Spatial characteristics of TCP swaths in East Coast group (area unit:105 sq. km, width unit: km). Storm-total Variables Number Average Std. Percentile period of cases Deviation 25 50 75 < 1 day Area 53 2.85 2.07 1.22 2.27 4.32 Left width 46 228 90 174 223 277 Right width 21 4.54 1.97 3.04 4.63 6.16 > 1 day Area 21 238 75 182 222 297 Left width 53 2.85 2.07 1.22 2.27 4.32 Right width 46 228 90 174 223 277

Figure 2-4. TC tracks and change points in 4 groups. A) Group I with increasing trends. B) Group II with decreasing trends. C) Group III with decreasing-increasing trends. D) Group IV with increasing-decreasing trends.

Table 2-5. Change in distance of left width in each group (unit: km). Group I Group II Group III Group IV Number of 40 18 15 12 TCs Mean Median Mean Median Mean Median Mean Median Total 212 190 -98 -81 63 55 -37 -19 change Increasing / / / / 134 106 96 97 segment Decreasing / / / / -73 -66 -133 -127 segment

Table 2-6. Chi-square test results. Attributes 휒2 p-value Sub-category Count Landfall intensity 5.914 0.015 I and III II and IV TD and TS 18 18 HU 37 12 Re-intensify over land 8.910 0.003 True 25 4 False 30 26 Moved back to ocean 5.559 0.018 True 23 5 False 32 25 Dissipated over U.S. 11.814 0.001 True 11 17 False 44 13 ET 5.686 0.017 True 35 11 False 20 19

Figure 2-5. Return interval of TC rainfall and wind events per county. A) Return interval of TCP events per county. B) Return interval of TC wind events per county. C) Difference in cumulative frequency of rainfall and wind events of TCs.

Figure 2-6. Frequency and return interval TCP event. A) Maximum annual frequency of TCP event. B) Return intervals for multi-TCP events per year.

CHAPTER 3 CONDITIONS ASSOCIATED WITH RAIN FIELD SIZE FOR TROPICAL CYCLONES LANDFALLING EASTERN U.S.

Background

When a tropical cyclone (TC) makes landfall and moves inland, storm surge, strong wind, intense rainfall, and tornadoes can cause tremendous damage and numerous fatalities in both coastal and inland regions. Among these TC-associated hazards, tropical cyclone precipitation (TCP) and induced inland freshwater flooding (or mudslides in mountains induced by flash flooding) are one of the most deadly and destructive hazards to society and the environment (Rappaport 2000, 2014). To correctly predict the specific areas that will experience moderate to high rain rates that can result in flooding is extremely important in disaster mitigation. When TCs approach the coastline and move over land, their rain fields exhibit high variability in sizes and distribution, which cause enormous operational challenges to the prediction of TCP

(Atallah, Bosart, and Aiyyer 2007; Lonfat et al. 2007; Zick and Matyas 2016). Knowing how far rain fields extend ahead of the storm center is key to forecasting when rainfall will begin ahead of landfall. Thus, presenting a climatology of the size of TC rain fields and identifying the factors contributing to the organization of rainfall while these systems are over the ocean prior to making landfall, and after they make landfall, are needed to improve the prediction of the spatial pattern of TCP (Lonfat, Marks, and Chen 2004;

2007; Matyas 2013; Rappaport 2014).

Traditionally, the sizes of TCs are measured as the radius of a particular wind speed (i.e., radius of gale-force winds) or the radius of the outermost closed isobar

(ROCI) (Kimball and Mulekar 2004; Knapp et al. 2010; Kruk et al. 2010). Besides these

intensively investigated TC attributes, size of TCP has drawn attention from scholars in recent years, due to its importance in hazard mitigation and the forecasting challenge it presents (Rezapour and Baldock 2014; Matyas 2010b; Lin, Zhao, and Zhang 2015).

Matyas (2010b) employed ground-based radar data and a Geographic Information

System (GIS) to measure the extent of rainfall in each quadrant as hurricanes crossed the U.S. coastline. Jiang, Liu, and Zipser et al. (2011) identified TCP features by using satellite data, which gives the area and volume information of heavy rainfall (rain rate >

5.0 mm/ h). Recently, more research employs gridded precipitation datasets with various spatial-temporal resolutions and different metrics to measure the size of TC

(Nogueira and Keim 2010; Zhu and Quiring 2013; Matyas 2014; Lin, Zhao, and Zhang

2015; Zhou and Matyas 2017). In these studies, the size of TCP is identified as the area or extent of TC rainfall area over a certain rain rate threshold. However, we are not aware of a study employing satellite-based estimations of precipitation to measure the size of TC rain fields prior to, during, and after landfall.

A number of factors are employed when forecasting the distribution of rainfall, including storm intensity, storm size, storm motion, vertical wind shear, and interaction with midlatitude systems (Lonfat et al. 2007). Previous numerical and observational research finds that increasing storm intensity and higher available environmental moisture contribute to higher convective rainfall magnitude and larger rainfall coverage

(Lonfat et al. 2007; Jiang, Halverson, and Zipser 2008; Kimball 2008; Hill and Lackmann

2009; Konrad and Perry 2010). The stronger upper-level troposphere divergence associated with middle tropospheric lifting of air containing copious amounts of water vapor is also related to larger TC size and rainfall potential (Jiang et al. 2008; Konrad

and Perry 2010). The asymmetry of a TC’s rain field is mostly influenced by the relative direction and magnitude of storm motion and vertical wind shear. When storm forward velocity increases, rainfall shifts to a location ahead of the storm due to the enhanced low-level convergence in the front quadrants (Shapiro 1983; Rodgers and Pierce 1995;

Corbosiero and Molinari 2002). As TCs move to the midlatitudes, they may experience changes in environmental conditions including increased baroclinicity, enhanced horizontal moisture gradients, strong vertical wind shear, interaction with frontal systems or troughs, and they may undergo an extra-tropical transition (ET) (Atallah and Bosart

2003; Jones et al. 2003). Strong vertical wind shear causes rainfall to occur in the downshear direction, especially to the downshear left side in the inner portion of the storm (< 100 km) (Chen, Knaff, and Marks 2006; Cecil 2007; Wingo and Cecil 2010) and downshear or downshear right in the outer rainbands (100-300 km) (Corbosiero and Molinari 2002; Matyas 2010a). Moreover, moisture distribution also influences the asymmetry of TC rainfall. When relatively dry air is drawn into a TC’s circulation from one side, it reduces rainfall on that side (Kimball 2006, 2008; Matyas and Cartaya

2009). Thus, to better predict which locations are at risk of receiving rainfall as a TC approaches, an analysis that examines the combination of these factors’ influence on

TC rain field area and extent is necessary. However, few studies have built statistical models that include a variety of the above-mentioned variables and determined which variables make the strongest contributions to the exact size of rainfall when TCs are located over land and water.

To explore the spatial extent of rainfall fields associated with landfalling TCs, a long-term climatology based on large samples of TCs is necessary. This study utilizes a

Geographic Information System (GIS) and a satellite-derived precipitation dataset to measure the area and extent of rain fields associated with TCs making landfall over the eastern U.S. from 1998 to 2015. The research questions are: first, what is the spatial variation in the size of TC rain fields in each quadrant of the storm before and after landfall? Second, which TC attributes and environmental conditions, such as TC intensity and motion, environmental moisture, upper troposphere divergence and vertical wind shear, have the highest correlations with size of TC rain fields and at which time lags over land and ocean? Last, what is the order of importance of storm attributes and environmental conditions for prediction of TC rain field size as revealed by using regression models? Identifying these conditions could help to improve the accuracy of the spatial distribution of TC precipitation in forecasts to so that people on either side of the forecasted TC track could better know the start time they will receive TCP, and whether or not they will receive TCP at all. Knowledge of the average extent of TC rainfall can also be utilized as guidance by for flooding hazard mitigation.

Data and Methodology

Data

The precipitation data used in this study were taken from Tropical Rainfall

Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B42 precipitation product version 7 (Huffman et al. 2007). The TRMM 3B42 product contains rain rates derived from satellite-based passive microwave and infrared sensors and applies a correction using data from rain gauges. The TMPA 3B42 data are available every 3 hours during 1998 to 2015, with a spatial resolution of a 0.25° latitude-longitude grid over a global latitude belt from 50°S to 50°N (Huffman et al. 2007). The TMPA

3B42 dataset has been widely used to explore TCs rainfall regionally and globally

(Jiang, Liu, and Zipser 2011; Lau and Wu 2011; Lau and Zhou 2012; Prat and Nelson

2013; Matyas 2014; Xu, Jiang, and Kang 2014; Prat and Nelson 2016). Although the

TMPA dataset is subject to uncertainties over land, especially in regions of complex orography (Zhou, Lau, and Huffman 2015), TRMM 3B42 data still offer good quality when exploring TC rain fields over land and ocean due to their high spatial and temporal resolutions, semi-global coverage over land and ocean, and relative low bias compared to other satellites products, such as CPC morphing technique (CMORPH) and Global

Satellite Mapping of Precipitation (GSMaP) (Chen et al. 2013; Zagrodnik and Jiang

2013; Blacutt et al. 2015; Maggioni, Meyers, and Robinson 2016).

The TC position data were obtained from the IBTrACS database (Knapp et al.

2010), and plotted within a GIS to identify TCs making landfall over the Gulf and Atlantic coastlines of the U.S. during 1998-2015 (Figure 3-1). After excluding TCs that dissipated less than 12 hours after landfall and short-lived TCs that formed near the coastline, a total of 70 TCs were included in this study. The 6-hourly positions were interpolated to every 3 hours using a cubic spline method to match the timestamps of the TRMM observations (Jagger and Elsner 2006). The storm intensity, motion speed and direction were also calculated from interpolated tracks using ArcGIS. If the TCs get more intense, the circulation of the storms should get larger and stronger, which results in increasing rainfall size. Moreover, if TCs gain a faster speed to north or northeast direction, this implies that TCs are interacting with the westerlies which result in expansion in TC rainfall area, especially on the left side.

Several environmental conditions, including moisture, upper troposphere divergence, and wind shear, were employed to explore their associations with TC rain

field size. Variables that characterize the environmental conditions around the storms were obtained from the Statistical Hurricane Intensity Scheme (SHIPS) database

(DeMaria and Kaplan 1999; DeMaria et al. 2005). The SHIPS variables are derived from the National Centers for Environmental Prediction (NCEP) Global Forecast System

(GFS) model analyses and most variables are calculated over various annuli around the storm centers (DeMaria et al. 2005). The SHIPS data are available every 6 hours (00,

06, 12, and 18 UTC). In this study, these data were interpolated to 3-hourly data by a linear function as suggested by previous studies (Chen, Knaff, and Marks 2006; Matyas

2013). It should be noted that SHIPS data are only available for observations of tropical or subtropical storms.

Total precipitable water values from the SHIPS dataset were employed to characterize the moisture available for precipitation within and around the TC as suggested by previous studies (Jiang, Halverson, and Zipser 2008; Konrad and Perry

2010). The mean total precipitable water (TPW) values were calculated for the whole atmospheric column over different spatial ranges (e.g. 0-200 km, 0-400 km, 0-500 km,

0-600 km, 0-800 km, and 0-1000 km) in the SHIPS dataset, which allows us to examine the influence of moisture over different ranges from the storm center. In the current study, we aim to determine the regions over which moisture exhibits the strongest correlations with rain field extent. When more moisture is present, rain fields should occupy a larger area and extend farther outwards from the storm center in each quadrant.

The other variables used in this study from the SHIPS dataset included upper - level divergence, deep-layer vertical wind shear and distance to the coastline. The 200-

hPa divergence is derived for a radius of 0-1000 km about the circulation center. As suggested by previous research, we selected this variable to explore the relationship between upper-level outflow and TC rainfall size (Jiang et al. 2008; Konrad and Perry

2010; Kovach and Konrad 2014) as stronger divergence should allow for rain fields to extend farther from the storm center, particularly in the forward half of the storm as the source of divergence is likely a middle latitude trough or jet streak positioned north of the TC. The wind shear vectors were subdivided into south-to-north and west-to-east components, and then interpolated into 3-hourly values. Strong vertical wind shear should be associated with a larger extent of rainfall in the downshear quadrants and smaller extent of rainfall in the upshear quadrants. Thus, strong westerly shear should enhance rainfall on the east and north sides of the storm. After landfall, staying near the coastline may keep TCs located in a more moist environment, which should contribute to a larger rain field size (Zhou and Matyas 2017), particularly in the rear quadrants of the storm. Thus, the distance from the TC center to major landmass is also obtained from the SHIPS dataset. The distance values are positive over ocean and negative over land. All predictors are listed in Table 3-1.

Methodology

The first task was to extract the rainfall field associated with each TC from the

TRMM data. Each TC was examined at a 3-hour interval beginning from when it was first within 600 km of the U.S. coastline since previous research found that TC rainfall typically reaches land before landfall (Jones et al. 2003; Nogueira and Keim 2010). The analysis ended at the time when it dissipated over land or crossed back out over the ocean. To match the spatial coverage of TMPA data which extends to 50° N, and since the rain fields of TCs may extend outward to more than 500 km from storm center as

suggested by previous studies (Jiang, Liu, and Zipser 2011), we limited observations to those where the circulation center is located south of 45°N. This study employed a rain rate value of 2.5 mm/h when defining the edge of the rain field. This value was employed as previous studies found that the TMPA data underestimates heavy rainfall, especially over land (Chen et al. 2013) and our preliminary results showed that pixels with moderate to heavy rain rate (e.g. 5.0 or 7.5 mm/h) did not occur over land at many observation times. Moreover, the preliminary results in current study show that regions with light rainfall (e.g. rain rate < 1.5 mm/h) often become very large and connected with rainfall from other weather systems, which is possibly due to the spatial resolution of the data and slight overestimation of the spatial coverage of low rain rates (Jiang, Liu, and

Zipser 2011). Therefore, the 2.5 mm/h rain rates were contoured and converted into polygon features in ArcGIS. The polygons with centroids located within 500 km of the

TC center were deemed to comprise the TC rain fields, since precipitation features located outside of this distance could belong to other weather systems as suggested by previous research (Jiang, Liu, and Zipser 2011; Matyas 2014). This method includes precipitation areas beyond 500 km as long as the center of the rainfall polygons is within

500 km of the TC center. Isolated small features with areas less than 8 pixels were excluded.

Based on the extracted TC rain field polygons, the area and extent of TC rain fields were measured. The total area of rainfall greater than 2.5 mm/h was calculated.

The distance between the outmost edge of the rain field and the storm center was measured every 5 degrees (Figure 3-2). These distances were averaged within each quadrant, which was placed according to the direction of storm motion, namely left-front

(LF), left-rear (LR), right-rear (RR) and right-front (RF) quadrants. Then the quadrant- averaged extent was calculated for each observation time. Any quadrant lacking a measurable portion of the rain field was omitted.

The size metrics were summarized in two ways. First, we placed cases and all associated variables into an over-land or over-ocean group. For each TC observation, we made a 500-km buffer of the TC center, and if greater than 50% of the buffer area was located over the ocean (land), this observation was attributed to the over-ocean

(over-land) group. It is reasonable to divide observations in this way as there are differences in the underlying physics of the TMPA 3B42 algorithm and SHIPS environmental variables over ocean and land (DeMaria et al. 2005; Jiang, Halverson, and Zipser 2008). Second, to further explore the spatial distribution of TC rain fields, a grid was constructed to cover the entire eastern U.S. and adjacent ocean region within

600 km of the contiguous U.S. (CONUS). This grid was used to calculate the average values of the area and extent metrics and illustrate where these metrics are larger or smaller. Only cells that include more than two TCs and ten observations were included in analysis, with a total number of 68 cells. We performed a sensitivity analysis using grids with cell resolutions of 150×150 km, 200×200 km and 250×250 km. Yet, the area covered by cells with more than two TCs and ten observations decreased from 41×105 sq. km (at a resolution of 250×250 km) to 30 ×105 sq. km (at a resolution of 200×200 km) and 18×105 sq. km (at a resolution of 150×150 km), respectively. Thus, we only report results from the grid cells measuring 250 km on each side.

To reveal the factors most strongly contributing to the spatial patterns of TCP, statistical tests were employed for observations grouped according to their location over

land or ocean. We applied a set of correlation tests and regression methods to explore the relationships between the size of TCP fields and TC attributes and environmental conditions. First, Spearman’s rank correlation coefficients were calculated to identify the preliminary correlation between variables and the variables with the highest correlations to area and extent were selected to enter the regression models. Linear regression analysis has been applied in various TC research studies (Klotzbach and Gray 2003;

DeMaria et al. 2005; Mueller et al. 2006; Jiang, Halverson, and Zipser 2008; Matyas

2010b; Quiring et al. 2011). However, a linear regression model requires the response variables to be normally distributed, which is sometimes not the case for TC data sets.

Nonlinear models, such as Poisson series and regression trees, have also successfully been applied in several TC modeling studies (Jagger and Elsner 2009; Konrad and

Perry 2010; Villarini et al. 2011; Villarini et al. 2013), yet these models are complex and make it difficult to explain the relationship between the predictors and phenomena.

Thus, generalized linear regressions with standardized coefficients were utilized in this study to examine the relative contributions of each predictor to the area and extent of

TC rainfall in each quadrant over the ocean and over land.

Area and Extent of TC Rain Field

In this section, the spatial characteristics of the TC rain fields were analyzed, including the total area and average extent in four quadrants. Mann–Whitney U tests are conducted to determine if rain-field size differed between cases where the TCs are mainly over land and mainly over the ocean. The null hypothesis is that there is no difference in the areas or extents of the rainfall regions. The null hypothesis is rejected if the p-value of the test result was less than 0.05. The results show that as anticipated, area, RF extent, LR extent, and RR extent exhibit differences that are significant at a

level of 0.05 and that cases over the ocean are the largest (Table 3-2). The median value of rainfall area over the ocean is approximately twice that over land. For the extent values, the largest differences exist in the two rear quadrants, where the median value’s difference is around 100 km. Interestingly, the left-front extent has a similar median value between over land and over ocean stage. This suggests that rainfall does not diminish in this region as the storm approaches and moves over land, which should concern those located on the left side of the forecasted storm track.

The area distribution in Figure 3-3 further confirms that TC rainfall area is larger over the ocean than over land as expected. But a strong regional variability exists while

TCs are over the ocean. Predominantly, the region with larger TCP area is over southern and southeastern Gulf of Mexico. The larger rainfall area in this region might be partially related to intensification as TCs move over the deep layer of warm water associated with the Loop Current (Mainelli et al. 2008; Zick and Matyas 2016). We also observe a cell with larger rainfall area over the ocean near Delaware and Maryland, which is mostly due to Hurricane Isabel (2003) and Hurricane Sandy (2012) as they were undergoing the ET process in this region. Additionally, the rainfall area is smaller in the western Gulf of Mexico than the eastern Gulf of Mexico, which might be due to

TCs being encompassed by drier continental air masses over this region (Guo and

Matyas 2016). These results also support the findings of Zick and Matyas (2016), who found that TCs moving into this region are more fragmented and asymmetric than the east Gulf, meaning that their rain fields should cover a smaller area in the west Gulf.

The spatial pattern of quadrant-averaged extent exhibits large variability among the four quadrants, supporting the need to examine each quadrant separately (Figure 3-

4). Generally, the averaged extent of the right-front quadrant is the largest compared to the other three quadrants both over land and ocean (Figure 3-4B). This result agrees with previous research that the TCs have the ability to advect moisture into their circulations from the equatorward side and produce more rainfall on this side (Matyas

2010b). Also, as most TCs have a strong northward component to their motion and vertical wind shear tends to have a strong westerly component in the study area, the right-front overlaps with the downshear left quadrant where rainfall is also favored

(Corbosiero and Molinari 2002; Chen, Knaff, and Marks 2006; Wingo and Cecil 2010).

Most TCs with larger RF extent track over the south and east Gulf of Mexico and continue to have this large extent after landfall over the Florida panhandle and

Alabama. Matyas (2010) examined 31 hurricanes at the time of U.S. landfall and found that the northeast quadrant had the largest extent, which overlapped with the right front quadrant for most cases. Here, we find that this phenomenon continues for several days as the TCs move far inland.

The left front quadrant has the second largest extent over land and the third largest extent over the ocean (Table 3-2). There are only two grid cells with average LF extent greater than 300 km located over the ocean. The other four cells with average extents exceeding 300 km are located inland over northern Arkansas and Alabama, eastern Tennessee, and southeastern Virginia, which implies the LF extent can increase inland so that people on the left side of the forecasted storm track should be alerted to the possibility of heavy rain several hours before the TC approaches (Figure

3-4A). All of these grid cells contain at least two ET cases, and previous research confirms that during the transition process, rainfall may develop ahead and to the left of

the storm center (Atallah, Bosart, and Aiyyer 2007). In contrast to the other three quadrants, there is not a distinct region where TCs usually tend to have a larger LF extent. This likely occurs because all cells with larger LF extent are associated with TCs that are experiencing an ET and this process can occur anywhere within the study region. For example, the region over Alabama is associated with six TCs that underwent

ET, including Hurricane Isidore (2002), Hurricane Ivan (2004), Hurricane Cindy (2005),

Hurricane Katrina (2005), Tropical Storm Fay (2008), and Tropical Storm Lee (2011). As suggested by Klein, Harr, and Elsberry (2000), the average period of ET for North

Atlantic TCs is 74 hours, with a transformation period of 46 hours and re-intensification period of 28 hours. The time to ET completion ranges from 6 to 48 hours from when they first enter these cells that have a larger size, which suggests these TCs are in the late transformation or re-intensification period of ET.

Last, we discuss spatial distribution of the two rear quadrants. The right-rear quadrant has the second largest extent over the ocean, and its extent gets significantly smaller once storms move over land (Figure 3-4D). In general, the right-rear extent is much larger over the Gulf than Atlantic. This is possibly due to relatively high sea surface temperatures (SSTs) over Gulf of Mexico and Caribbean Sea that enhance evaporation (Wang and Lee 2007). TCs could advect higher humidity air from the deep tropics into their right-rear quadrants as suggested by Wu et al. (2012) which helps to create a larger region of rainfall. The left rear quadrant has the smallest extent both over land and ocean (Figure 3-4C). The spatial distribution shows that left rear extent gets smaller on average as storms approach the coastline. The left rear extent is smaller than 100 km for most inland areas, which means that rainfall will not last a long once the

storm center has passed, whereas rainfall may continue for a longer period on the right side of the storm. As described by previous researchers, the left rear quadrant typically contains the least convection at the time of landfall as offshore winds at the surface diverge and enhance downward motion that suppresses convection (Powell 1987;

Matyas 2010b; Braun, Sippel, and Nolan 2012; Wu et al. 2012). Moreover, smaller LR extents result from the advection of drier continental air into the circulation where increased stability helps to reduce rainfall on this side before the storm itself moves over land. Overall, our observations support the modeling work of Kimball (2008).

Statistical Modeling of TC Rainfall Size

In this section, we build statistical models to examine which TC attributes and environmental conditions are most strongly correlated with size of rain fields associated with TCs. Due to the availability of variables from the SHIPS dataset, we refined our observations to TCs with tropical storm and hurricane intensities. When the storms become waves, remnant lows, dissipating lows, or are within 18 hours of completing an

ET, the atmospheric conditions surrounding the storm are markedly different and thus would require the construction of a separate predictive model. After this selection, we applied Kolmogorov-Smirnov Tests to explore the normality of rainfall metrics and found that despite the large sample size (n = 1503), none of the extent metrics or rainfall area followed a normal distribution with a confidence level of 95 percent. Therefore, we first applied Spearman’s rank correlation tests to check the correlations between the size of

TC rain fields and TC attributes and environmental conditions at different time lags, and then applied generalized linear regression models to examine how the combination of

TC attributes and environmental conditions influences size of rain fields associated with

TCs. As discussed in the methodology section, we tested the TC observations in overland and over-ocean groups separately.

General Connections between TCP Size and Environmental Conditions

Before constructing the generalized linear regression models, we performed multiple Spearman’s rank correlation tests for three main purposes. First, we aimed to check whether collinearity exits between variables and to determine which individual variables might be strong predictors of TC rainfall area and extent. Second, previous research has found that time lags of 12-24 hours exist between the onset of environmental conditions and structural changes in the TCs (Frank and Ritchie 2001;

Jiang, Halverson, and Zipser 2008; Wingo and Cecil 2010; Matyas 2013). To encompass and expand the range of lags suggested by previous research, we examine correlations using time lags of 6, 12, 18, and 24 hours. Last, we explored which measure of TPW exhibited the strongest relationship with TC rainfall area and extent so that just one measure of moisture entered the regression analysis. We performed correlation tests with average TPW from 0-200 km to 0-1000 km at concurrent times and the four-time lags.

Table 3 lists the Spearman’s rank correlation coefficients between TC rainfall size and the potential predictor variables. We only list variables with coefficients greater than 0.3 and that are significant with a confidence level of 0.01. The results show that all variables have strong correlations with at least one size metric, which confirms our selection of variables to enter the regression analysis. Moreover, all correlations between variables have coefficient values lower than 0.75, which is the correlation level indicating no obvious collinearity between variables suggested by previous studies (Li,

Wei, and Korinek 2017).

Second, from a moisture perspective, we found that the strongest correlations occur between rainfall size and TPW averaged over 0-400 km from the storm center.

This result generally agrees with previous research which shows that the cyclonic convergent inflow is within a 4°-6°radius of the TC center (Frank 1977, Evans and Hart

2003). The overall cloud and precipitation amounts are determined by this vertical mass transport, which on average is upward over the region located within 400 km of the storm center (Houze 2010). Moreover, strong positive correlations (ρ > 0.3 at significance level of 0.05) exist between TCP coverage over land (ocean) for ranges from 200 km up to 800 km (1000 km) from storm center. This result supports the findings of Trenberth and Fasullo (2007), who suggest that moisture located approximately four times the radius of the TC’s circulation is still important to the storm’s water budget.

Last, we identify time lags between rainfall size and three environmental conditions, upper-level outflow, wind shear and total precipitable water for both over land and ocean periods. The TC rainfall size’s correlations with D200 and wind shear at a 12-hour lag have the highest coefficients comparing to other time lags. The correlations decline from the 12-hour lag to 24-hour lag. Although correlation coefficients of TPW slightly increase from 12-hour lag to 24-hour lag, we find that when performing the regression tests, TPW with a 12-hour lag has slightly higher R-squared values (0.703 over land and 0.635 over ocean) than regressions incorporating TPW with a 24-hour lag (0. 691 over land and 0.632 over ocean). As suggested by the correlation and regression results, a 12-hour time lag was included for all environmental conditions.

These results further confirm the findings from previous studies suggesting that there

are 12-24 hours between onset of environmental conditions and the TCP structure change.

Results of Generalized Regression Models

In this section, a total of 10 generalized linear regression models are applied to link the variables to storm rain field area and averaged extent in four quadrants both over ocean and over land. As a stepwise method is applied, the variables that are significant at a level of 0.1 are included in the models (Li, Wei, and Korinek 2017). All

VIF values are less than 5, which further confirms that collinearity is unlikely in these models. The variables’ coefficients and regression estimations of area and extent models over land and ocean are listed in Table 3-4, Table 3-5, and Table 3-6.

We first compared the R-squared values of the models to determine how well the observations are predicted. The model estimations show that the area models have a better performance than extent models both over land and ocean. A likely explanation for this result is that the moisture and divergence values in SHIPS are averaged within a radius around storm center. When considering the influence of moisture and upper-level divergence on extent of rainfall, their locations relative to storm are important. For example, Konrad and Perry (2010) stated that TC rainfall extends further to regions with higher moisture and divergence. Moreover, among the eight extent models, the left rear models have the lowest R-squared value over ocean and land. This is likely because rainfall remains closer to the storm center on average as compared to the other quadrants, thus there is a smaller variability among individual storms which cannot be predicted well.

Among all variables, the total precipitable water averaged over 0-400 km from the storm center exhibits the strongest influence in seven of the ten models, including

total area, extent of the right side over both land and ocean, and rear quadrants over land. Several observational studies have found that higher moisture environments favor more intense TCP with a larger coverage of the total raining area (Jiang et al. 2008;

2008; Matyas and Cartaya 2009; Konrad and Perry 2010; Matyas 2013; Hernández

Ayala and Matyas 2016) or expansion of rain field extent (Matyas 2010b). In current study, the median values are similar over land and ocean, which is about 58 mm, with standard deviation of 5.6 mm. However, for top 25 percent of observations with large rainfall area, the median value of TPW is about 62 mm. Based on water vapor budget theory, rainfall production is mainly controlled by moisture convergence and ocean surface moisture flux (Jiang, Halverson, and Zipser 2008). The results of this study add to previous research by examining moisture influence on different sides of the rain field both over land and ocean. Our results further show that the moisture coefficient is much higher over land than ocean, especially for the right-rear extent. The most likely explanation for this result is that while over land, the right rear quadrant typically remains on the southern or equatorward side of the storm. In cases where moisture is enhanced on the equatorward side of the storm, this moisture is being advected into the

TC’s circulation and contributing to a larger extent of rainfall as was recently discussed by Matyas (2017).

The divergence at 200 hPa is also a strong predictor of the area as well as the extent of the right front quadrant over ocean and land. The median value of D200 is 37×

107/s of all observations in the current study. This value is higher for the top 25 percent of observations with large rainfall area at 64×107/s. This finding is consistent with previous studies that showed the upper-level outflow is important for storm

intensification, storm size or rain potential (Croke 2005; Jones and Cecil 2007; Konrad and Perry 2010; Knaff, Sampson, and Chirokova 2017). Konrad and Perry (2010) analyzed precipitation associated with TCs over the Carolinas and found that TCs with precipitation displaced farther from the storm center had an overlapping region of high precipitable water and positive divergence at 200 hPa on the right side of the storm.

This suggests that strong upper-level divergence causes the tropical air mass with its high moisture content to be lifted through the middle levels of the troposphere to enhance rainfall production. Moreover, several studies revealed that the TC’s outflow is asymmetric, with a concentrated channel northeast of the storm center (Merrill 1988;

Barrett et al. 2016), which explains why divergence at 200 hPa has a stronger influence over the right side of the rain field. The physical mechanism by which the upper tropospheric forcing alters the tropical cyclone precipitation is believed to be related to the gradient wind adjustment process associated with the thermally direct circulation at the entrance region of tropical cyclones’ outflow channels (Merrill 1984; Rodgers and

Pierce 1995). Strong upper-tropospheric divergence occurs in conjunction with extratropical features, such as a stalled frontal boundary or an upper tropospheric jet streak, which can focus the precipitation regardless of whether a TC transitions into an extratropical cyclone.

Previous research has found that vertical wind shear is a dominant cause of the asymmetrical distribution of TC precipitation (Corbosiero and Molinari 2002; Chen,

Knaff, and Marks 2006; Xu, Jiang, and Kang 2014).The current study finds that when over land, vertical wind shear with a strong westerly component (e.g. > 7.5 m/s) correlates well with a larger extent in the forward quadrants of the storm. As most TCs

have a northward component to their motion, this cross-track shear pattern produces a larger extent in the downshear quadrants as expected according to the result of previous studies (Chen, Knaff, and Marks 2006; Matyas 2010b; Wingo and Cecil 2010).

Also while over land, shear with a strong southerly component correlates well with rainfall extent in the left front quadrant, which in these cases is also the downshear side.

Interestingly, our results reveal that vertical wind shear does not contribute as strongly to the prediction of rainfall area or extent as does moisture. One reason why shear might not be as strong of a predictor in individual quadrants is due to the fact that the quadrants were placed according to storm motion. To improve estimations of when rainfall will begin as a TC approaches land, it is important to predict accurately the extent of rainfall in the forward quadrants of the storm, hence the quadrants were placed according to storm motion. However, the overall TC rainfall asymmetry relates to relative location and magnitude of the storm motion and wind shear directions.

Corbosiero and Molinari (2002) noted that for the outer rainbands (100 - 300 km), the front-right quadrant is favored by storm motion and the downshear-right quadrant is favored by shear. This suggests that the storm needs to be moving approximately 0 to

90 degrees left of the shear vector, which only 50 percent of observations have this kind of situation in the current study. Motion direction with 90-180 degrees to left of shear vector has the second largest percent (~28 %) of observations. In this situation, the front-right quadrant does not overlap with the downshear-right quadrant. Moreover, the median wind shear speed in current analysis is 9.7 m/s, with more than half of observations experiencing weak to moderate wind shear (Chen, Knaff, and Marks

2006), which is another reason that vertical wind shear does not exhibit strong effect on rain field extent.

The average motion speed in this study was 4.5 m/s, which is slightly slower than average motion speed of 5.2 m/s reported by Corbosiero and Molinari (2002). This is possible because observations near and after ET completion are excluded in current study. When storm forward motion is faster (e.g. > 8.0 m/s) (Matyas 2014), TCs tend to have a larger front quadrant extent and smaller rear quadrant extent. These results generally agree with previous findings that TC translational speed is known to affect the circulation around the TC through enhanced low-level convergence in the front quadrants (Shapiro 1983), which can induce a front to front-right rainfall asymmetry. In this analysis, we further found that the TC motion to the east shows a strong linkage with rainfall extent in the left-front quadrant. The faster eastward motion suggests that

TCs are being influenced by their interaction with a middle-latitude weather system to the north or northwest side of storm, which results in a more asymmetric pattern where rainfall development might shift from the right to left side of the track (Atallah, Bosart, and Aiyyer 2007). Our results further confirm that the motion-induced asymmetric friction effect has less influence on rainfall asymmetries than deep-layer wind shear

(Corbosiero and Molinari 2003; Chen, Knaff, and Marks 2006; Wingo and Cecil 2010;

Xu, Jiang, and Kang 2014; Yu, Wang, and Xu 2015).

The biggest difference between the models to predict rainfall extent over ocean and over land are the roles of storm intensity and distance to land. The velocity of the maximum sustained wind is lower over land as expected, with a mean value of 20 m/s and standard deviation of 9.8 m/s, compared to a mean value of 31.4 m/s and standard

deviation of 14.9 m/s over the ocean. When over the ocean, coefficients of storm intensity are significant in all four extent models which implies that a more intense TC has a larger extent of rainfall in all quadrants, which also means that the total area of rainfall is larger. Although several observational analyses have found a weak correlation between intensity and TC wind size (Merrill 1984), recent research finds that intense storms have larger rainfall coverage (Matyas 2014), and more capacity to advect moisture to the left side of storm, which will result in a more symmetric rain field (Konrad and Perry 2010; Xu, Jiang, and Kang 2014; Zick and Matyas 2016). After landfall, storm intensity declines and shows a weaker influence over rainfall area and extent as expected. However, once TCs move inland, the distance between the storm center and the nearest point on the coastline becomes an important predictor of rainfall extent, especially in the rear quadrants of the storm. TCs remaining within a certain distance of coastline rather than tracking directly inland, or those moving back towards the water after turning towards the northeast have larger rain fields as the TC is likely able to keep advecting oceanic moisture into its circulation when in these locations. In this study, for the top 25 percent of observations with large rainfall area over land, the median value of distance is about 103 km to coastline, which agrees with the value of 100 km reported by Matyas (2007). Also, Matyas (2008) showed an inverse relationship between distance to the coastline and rainfall area for tropical storm Dennis (1999).

Last, we checked the standardized residuals in each model. The standardized residuals of all models do not have any spatial patterns. On an individual storm basis, we found that for the over-ocean observations, tropical storm Dennis (1999) has a relatively higher total residual when compared to other storms. As Dennis (1999) moved

northward to Carolina coastline, it interacted with a mid-latitude trough and a cold front, which caused the storm to move eastward and then southward. Meanwhile, a combination of vertical shear and cool dry air entraining into the circulation decreased the convection and weakened the cyclone (Beven 2000). Once over land, Matyas

(2008) described how dry air advection caused rainfall to become fragmented. However, the R-square values did not show a big difference after we removed this storm. For example, the r-square of area model over ocean only increases from 0.635 to 0.651 after the observations for Dennis (1999) are removed. Thus, we are confident that our models are not influenced by a single outlier storm.

Conclusions and Discussions

This study examines the size of rain fields associated with TCs making landfall over the U.S. from 1998- 2015 through a GIS-based analysis of satellite-estimated rain rates. Regions of light-to-moderate rainfall (rain rate > 2.5 mm/h) belonging to each TC are converted into polygons and measurements are made of their area and average extent in each of four quadrants placed according to storm motion (right front, left front, left rear and right rear). The results show that rain fields cover the largest area over the southern and eastern Gulf, as well as the coastal region near the Carolinas and

As TCs move inland, although the area and extent in rear quadrants decays, the rainfall in right front and left front can still extend farther than 300 km from the storm center.

These results confirm that inland regions hundreds of kilometers away from the forecasted TC track should be prepared to receive moderate rainfall well ahead of the arrival of the fastest winds, especially on the left side of the track.

We further relate the size of the rainfall field to TC attributes and environmental conditions by using Spearman’s rank Correlation tests and generalized regression models. This study reveals that: (1) total precipitable water within 400 km of storm center and upper-tropospheric divergence play the most important role in both overall coverage and extent in all quadrants, (2) the deep-layer vertical wind shear with a strong westerly component correlates well with a larger extent in the forward quadrants of the storm, (3) effects of storm motion are not as strong as wind shear, (4) storm intensity has more influence on rainfall over ocean than over land, and (5) once over land, rainfall extent is larger if TCs remain near the coastline rather than track far inland.

We also tested lag effects between environmental conditions and rainfall size and found that models with 12-hour lag variables have in best results. By applying statistical regressions on large samples of TC observations, these results reveal factors that are important to TC rain field spatial distribution, which offers useful information for TC rainfall forecasts.

In particular, this research adds to the growing number of studies that indicate the importance of incorporating data pertaining to moisture in the environment surrounding the TC when considering its potential to produce rainfall (Jiang, Halverson, and Zipser 2008; Jiang et al. 2008; Matyas and Cartaya 2009; Hill and Lackmann 2009;

Konrad and Perry 2010; Zick and Matyas 2015). Specifically, we identified the strongest links between TPW averaged 0-400 km around the storm center at lags of 12-24 hours and the area and extent of rainfall regardless of whether TCs are over the ocean or land. The Parametric Hurricane Rainfall Model (PHRaM) uses storm intensity, vertical wind shear and topography to predict radial distributions of azimuthally averaged TC rain rates derived from the TRMM Microwave Imager (Lonfat, Marks, and Chen 2004;

Lonfat et al. 2007). As the current research shows that inclusion of moisture exhibits a strong relationship with rain field extent, incorporating a variable related to moisture into

PHRaM should improve the model’s prediction of rainfall.

There are three main limitations of this study. First, due to the resolution and accuracy of TMPA dataset over land, only moderate rainfall is measured in this analysis. Heavy rainfall (e.g. rainfall > 7.5 mm/h) is more likely to contribute to high rainfall totals that can result in flooding. Thus, we recommend that future research utilize a higher-resolution dataset for rainfall over land, such as values measured by ground- based radar, to identify the regions of high rain rates that occurred when flooding was reported. Second, our regression analysis focused on observations when TCs were hurricanes or tropical storms. As revealed by existing literature, TCs undergoing the ET process could bring heavy rainfall over broad areas located hundreds of kilometers away from the landfall location. We did not specifically focus on TCs once they completed this transition as the environmental conditions would dictate the construction of a separate set of models. However, future research should examine associations between rain-field size and the conditions experienced by TCs during the entire ET process, including reintensification. Last, we only included moisture and upper-level

divergence values that represented average conditions across the region that contains the TC a region in this study. Future studies could include an analysis of the spatial distribution of moisture and upper-troposphere outflow to better explain rainfall extent around different parts of the storm.

Figure 3-1. Interpolated 3-hourly positions of tropical cyclones included in the study.

Table 3-1. Variables’ descriptions. Category Abbreviation Units Data Spatial range of source variables Latitude LAT ° IBTrACS / Longitude LON ° IBTrACS / Velocity of maximum VMAX m/s IBTrACS / sustained winds Eastward component of MotE m/s IBTrACS / motion speed Northward component MotN m/s IBTrACS / of motion speed Distance to landmass DTL km SHIPS / Average total TPW mm SHIPS 0-200 km, 0-400 km, precipitable water 0-600 km, 0-800 km, 0- 1000 km Divergence at 200 hPa D200 107/s SHIPS 0-1000 km Southerly vertical wind SHRS m/s SHIPS 200-800 km shear (850-200 hPa) Westerly vertical wind SHRW m/s SHIPS 200-800 km shear (850-200 hPa)

Figure 3-2. Measuring the extent of rainfall field of Hurricane Floyd (1999).

Table 3-2. Area and extent of rainfall fields of TCs (area unit:104 sq. km, width unit: km). Locations Variables Number Average Std. Percentile of cases Deviation 25 50 75 All Area 2085 9.58 7.68 3.66 7.71 13.74 RF extent 2085 282 168 159 270 395 LF extent 2085 228 162 104 207 319 LR extent 2085 147 125 35 124 236 RR extent 2085 224 157 93 218 342 Ocean Area 1229 11.46 8.13 5.16 9.88 16.19 RF extent 1229 295 164 182 280 400 LF extent 1229 226 150 116 212 304 LR extent 1229 184 128 78 175 270 RR extent 1229 267 146 158 272 368 Land Area 856 6.90 6.06 2.36 4.92 9.51 RF extent 856 262 170 126 250 391 LF extent 856 231 179 95 192 347 LR extent 856 94 101 0 63 151 RR extent 856 160 151 16 130 270

Figure 3-3. Spatial distribution of TC rain field area averaged in 250 km cells (Area is classified by natural break classification method).

Figure 3-4. Spatial distribution extent of TC rain fields in 250-km cells. A) Left-front quadrant.B) Right-front quadrant. C) Left-rear quadrant. D) Right-rear quadrant.

Table 3-3. The correlation coefficients between area and extent of TC rain fields and predictors (Correlation coefficients greater than 0.30 and significant at 0.01). Variables Over-Land Over-Ocean Correlation Quadrant Correlation Correlation Quadrant Correlation coefficient with coefficient coefficient with coefficient of area highest of extent of area highest of extent coefficient coefficient D200 0.70 RF 0.64 0.70 RF 0.70 TPW 0.60 RR 0.41 0.70 RR 0.59 VMAX 0.43 LR 0.45 0.64 RR 0.39 MotN 0.43 RF 0.43 0.45 RF 0.53 MotE / LF 0.53 / LR -0.39 SHRW 0.47 LF 0.58 / RF 0.35 SHRS 0.30 LF 0.57 0.35 LF 0.52

Table 3-4. Coefficients and model estimation of regression model to predict rainfall area over land and ocean (Variables significant at 0.1). Land Model Ocean Model Variables Coefficients p-value Coefficients p-value Intercept 10.96 < 0.001 11.42 < 0.001 TPW 0.43 < 0.001 0.30 < 0.001 D200 0.30 < 0.001 0.29 < 0.001 VMAX 0.09 0.002 0.26 < 0.001 SHRW 0.21 < 0.001 0.07 < 0.001 SHRS -0.06 0.029 -0.06 0.003 MotN 0.06 0.033 0.08 < 0.001 MotE / / 0.04 0.023 LAT / / -0.04 0.044 LON 0.15 < 0.001 0.08 < 0.001 DTL 0.18 < 0.001 / /

Number of cases 417 1086 R-square 0.703 0.635

Table 3-5. Coefficients and model estimation of extent regression models over land (Variables significant at 0.1). RF LF LR RR Variables Coeffi- p-value Coeffi- p-value Coeffi- p-value Coeffi- p-value cients cients cients cients Intercept 12.49 < 0.001 12.12 0.023 11.81 0.000 12.34 < 0.001 TPW 0.25 < 0.001 0.14 < 0.001 0.29 < 0.001 0.32 < 0.001 D200 0.11 < 0.001 0.07 0.071 0.09 0.078 0.11 0.002 VMAX / / 0.05 0.047 / / / / SHRW 0.21 < 0.001 0.21 < 0.001 / / / / SHRS -0.04 0.080 0.19 < 0.001 -0.22 < 0.001 -0.13 < 0.001 MotN 0.04 0.087 / / -0.11 0.009 / / MotE 0.08 0.004 0.21 < 0.001 -0.20 < 0.001 / / LAT / / / / 0.21 < 0.001 0.11 0.006 LON 0.08 0.004 / / / / / / DTL 0.05 0.025 / / 0.23 < 0.001 0.17 < 0.001

Number of 395 384 323 375 cases R-square 0.549 0.444 0.286 0.263

Table 3-6. Coefficients and model estimation of extent regression models over ocean (Variables significant at 0.1). RF LF LR RR Variables Coeffi- p-value Coeffi- p-value Coeffi- p-value Coeffi- p-value cients cients cients cients Intercept 12.50 < 0.001 12.29 < 0.001 12.13 < 0.001 12.43 < 0.001 TPW 0.14 < 0.001 0.24 < 0.001 0.13 < 0.001 0.14 < 0.001 D200 0.18 < 0.001 0.10 < 0.001 0.13 0.003 0.12 < 0.001 VMAX 0.04 0.006 0.09 < 0.001 0.12 < 0.001 0.06 <0.001 SHRW 0.16 < 0.001 / / -0.13 < 0.001 0.04 0.037 SHRS / / 0.13 < 0.001 / / / / MotN 0.14 < 0.001 -0.08 < 0.001 -0.05 0.036 0.07 < 0.001 MotE 0.04 0.015 0.23 < 0.001 -0.21 < 0.001 -0.05 0.018 LAT / / / / / / -0.08 < 0.001 LON / / 0.13 < 0.001 0.13 < 0.001 -0.06 0.003 DTL -0.06 < 0.001 / / 0.08 < 0.001 / /

Number of 1035 1035 1019 1058 cases R-square 0.432 0.468 0.253 0.416

CHAPTER 4 SPATIAL CHARACTERISTICS OF RAIN FIELDS ASSOCIATED WITH TROPICAL CYCLONES LANDFALLING OVER THE WESTERN GULF OF MEXICO AND CARIBBEAN SEA

Background

The western Gulf Coast and Caribbean Coast are regions that are highly vulnerable to precipitation associated with tropical cyclones (TCs) from the North

Atlantic (Pielke et al. 2003). Some of the most intense and devastating hurricanes of all time have caused numerous fatalities and economic damage due to widespread precipitation and induced flooding and landslides in this region. In 1998, Hurricane Mitch made landfall over Honduras and Nicaragua and caused more than 10,000 deaths and more than $8.5 billion in economic losses, which makes it one of most devastating hurricanes in North Atlantic history (Pielke et al. 2003). Hurricane Stan (2005) was associated with disastrous inland flooding across portions of Central America and

Mexico, and the death toll was reported as 2000 (Pasch and Roberts 2006). More recently, Tropical Storms Arlene in 2011 and Ingrid in 2013 produced wide-spread flooding and landslides over Mexico that caused large social disruption and economic losses (Brena-Naranjo et al. 2015; Pedrozo-Acuna et al. 2015). Moreover, considerable biodiversity and valuable mountain ecosystems in Mexico and Central America are particularly susceptible to hurricanes and associated flooding (McGroddy et al. 2013).

Although numerous historical hazards have been caused by tropical cyclone precipitation (TCP) in this region, the influence of TCP over this region has received less attention from scholars when compared to landfalls occurring over the U.S. Hence, studying the spatial distribution of rainfall associated with TCs making landfalls over western Caribbean and Gulf Coast could help to identify which flood-prone regions

should be evacuated in advance of the TC’s arrival. From a socioeconomic perspective, a TC with larger rain field that extends hundreds of kilometers away from storm center might require a more expansive and longer evacuation time than a storm with less rainfall area coverage (Whitehead 2003). Therefore, larger TCs tend to be more damaging and more costly. It is also important to determine the time when rainfall begins over land and durations over land as statements warning of potential flooding need to be issued earlier when rainfall extends farther ahead of the storm center.

A variety of shape metrics have been utilized to characterize spatial patterns of rain fields associated with TCs from weather radar and satellite datasets. The first application of shape analysis in tropical meteorology is the Dvorak technique (Dvorak

1975), which uses cloud patterns in satellite imagery to estimate TC intensity. Matyas

(2007) develops a set of shape metrics to describe spatial characteristics of rain fields for TCs moving over land. These studies employ three metrics: area-to-perimeter ratio, major-to-minor axis ratio, and Euler number, to capture compactness, elongation and fragmentation patterns of TC rain fields as measured through the analysis of data from ground-based radar. More recently, Zick and Matyas (2016) employ three shape metrics, including asymmetry, dispersiveness, and fragmentation, to describe rainfall structure change during TC weakening, landfall over the U.S., and extratropical transition (ET). Their analysis of accumulated rainfall from a reanalysis dataset found that before landfall, dispersiveness of TCP increases in most cases; while asymmetry and fragmentation increase more commonly in western Gulf landfalls. These previous studies also relate storm shape to TC attributes such as intensity, distance to land, and topography. They find that more intense TCs have more circular, compact and

symmetric patterns, and after landfall, TCs staying near the coastline have a more circular rainfall pattern. Moreover, although asymmetries of TC rainfall have been extensively investigated over different ocean basins by using amplitudes of Fourier components (Lonfat, Marks, and Chen 2004; Chen, Knaff, and Marks 2006; Ueno 2007) or describing asymmetries rainfall patterns extracted from satellite rainfall (Wingo and

Cecil 2010; Xu, Jiang, and Kang 2014), there are less studies measuring the displacement of rain fields from the storm center, which is useful to identify which regions will receive rainfall before TCs’ arrival and during their passage. Measuring area, dispersion, and displacement of entire rain fields associated with TCs making landfall over the Caribbean and western Gulf coasts could provide more complete information about TCP spatial configuration, helping to better predict rainfall start time and duration over specific regions.

In this study, 35 TCs making landfall over the Caribbean and western Gulf coasts during 1998- 2015 were examined. There are three main research objectives here.

First, after measuring area, dispersion, and displacement of light and moderate rain fields, spatial and temporal patterns of rainfall metrics are examined. The second goal is to determine which TC attributes and environmental conditions are associated with the spatial configuration of light and moderate rain rates for TCs. This is accomplished by comparing sub-areas with distinct rain rate spatial patterns through Mann-Whitney U

Tests and calculating Spearman’s rank correlation coefficients for the entire study region to relate the four metrics and atmospheric moisture, vertical wind shear, storm motion, and storm intensity. Finally, light and moderate rainfall polygons were used to

determine the time that rainfall reaches land relative to the time that the storm’s center makes landfall, and calculate the average and maximum duration of rainfall from TCs.

Data and Methodology

Data

The precipitation data used in this study were taken from Tropical Rainfall

Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B42 precipitation product version 7 (Huffman et al. 2007). The TMPA is a satellite-based precipitation product combining various spaceborne precipitation sensors with calibration from TRMM instruments, including the TRMM Microwave Imager, Special

Sensor Microwave Imager (SSM/I) and Special Sensor Microwave Imager/Sounder

(SSM/IS). The TRMM 3B42 dataset incorporates rain gauge data through probability density function matching as ground truth. TRMM 3B42 data are available every 3 hours since January 1998, with spatial resolution of 0.25° latitude-longitude grid covering areas from 50°S to 50°N (Huffman et al. 2007). The TRMM 3B42 dataset has been widely used for various topics of TCs rainfall analysis regionally and globally (Shepherd et al., 2007; Jiang, Liu, and Zipser 2011; Lau and Zhou, 2012; Prat and Nelson, 2013;

Xu et al., 2014; Matyas, 2014).

The TC track data were obtained from the International Best Track Archive for

Climate Stewardship (IBTrACS) database, and plotted within a GIS to identify TCs making landfall over western Gulf coast and Caribbean coast, from Texas, U.S. to

Nicaragua during 1998-2015 (Knapp et al. 2010). The landfall and demise information was obtained from the National Hurricane Center’s (NHC) storm reports

(http://www.nhc.noaa.gov/data/). A total of 35 TCs were included in this study, after excluding storms which become extratropical cyclones over the current study region,

spend less than 24 hours over the ocean, and/or do not reach tropical storm intensity during their life cycle (Figure 4-1). The 6-hourly positions and intensity of the storm were linearly interpolated to every 3 hours to match the timestamps of the TRMM observations (Jiang, Liu, and Zipser 2011). The storm motion speed and direction were also calculated from interpolated tracks using ArcGIS.

To characterize potential influences upon the areal coverage and spatial configuration of the TC rain fields, total precipitable water values and deep-layer vertical wind shear speed were obtained from the Statistical Hurricane Intensity Scheme

(SHIPS) database, which is the product of National Centers for Environmental

Prediction (NCEP) Global Forecast System (GFS) model analyses (DeMaria et al.

2005). Within the SHIPS dataset, deep-layer vertical wind shear is calculated between

850-200 hPa over the area extending from 200 km to 800 km around TC center. In the current study, the 6-hour wind shear vector data, which are available at 0000, 0600,

1200 and 1800 UTC, were divided into southerly and westerly components, linearly interpolated into 3-hourly observations, and then recombined to obtain the speed of the wind shear (Matyas 2013). Total precipitable water values incorporate the amount of moisture in the whole atmospheric column averaged over different spatial ranges relative to the TC’s circulation center (0-200 km, 0-400 km, 0-500 km, 0-600 km, 0-800 km, and 0-1000 km). Utilizing values over all distances allows us to examine the influence of moisture over different ranges from the storm center. As TCs may be smaller in this region as compared to those making landfall over the U.S., the 0-400 km distance that exhibited the highest correlation with rainfall area and extent in Chapter 3 may not be the ideal range for moisture consideration for TCs in the current study. The

variables representing the environmental conditions and storm intensity and motion are listed in Table 4-1.

Spatial Analysis

This study employed rain rate values of 2.5 mm/h and 5 mm/h as thresholds to define light to moderate rainfall regions as suggested by previous research (Zagrodnik and Jiang 2013; Matyas 2014). Previous studies state that the TRMM dataset may overestimate light rain rates (e.g. <1 mm/h) and underestimate moderate to heavy rates

(e.g. > 5 mm/ h)(Yu et al. 2009; Chen et al. 2013). Thus 2.5 mm/h and 5 mm/h were used to contour the TRMM data and the closed contour lines were converted into polygon features in ArcGIS. Next, we selected the rainfall polygons to examine further utilizing two criteria. These criteria are 1) that their centroids are located within 500 km of the TC center and 2) that polygons must either intersect with or be contained inside of the radius of outmost closed isobar (ROCI). First, the 500-km search radius was employed as it has been employed to separate TC and non-TC rainfall in previous research (Lonfat et al. 2007; Jiang, Liu, and Zipser 2011; Hernández Ayala and Matyas

2016). Second, as great variability exists in storm sizes, previous studies also use ROCI to obtain TCP, as the ROCI typically encompasses the entire TC rain field (Matyas

2010b; Zhu and Quiring 2013). Preliminary results in the current study show that median ROCI in this region is about 277 km, which might cause rainfall regions to be included that are not generated by the TC’s circulation if we use a uniform radius with

500 km for all TCs. We kept this threshold because it excludes those rainfall polygons that only have small parts that interact with ROCI, but also have large areas extending outward with centroids located outside of the 500-km range and might belong to other weather systems. Thus, we applied both spatial thresholds to identify the TCP polygons.

The Extended Best Track (EBT) dataset (Demuth, DeMaria, and Knaff 2006) provides relatively complete information about ROCI for most TCs examined in this study, though some instances of missing data have been reported in the literature (Vigh, Knaff, and

Schubert 2012; Zhu and Quiring 2013; Carrasco, Landsea, and Lin 2014). In current study, ROCI estimates are available for 84% of the observations. For observation times when the ROCI is missing, it was replaced with the available ROCI values in adjacent times. Finally, only polygons with a minimum of five pixels (~ 4,932 sq km in area) were included in our analysis.

Next, after generating rainfall fields for all TC observation times, we calculated area, dispersion, and displacement to describe the spatial patterns of the rain fields. It is important to measure the area where rainfall is occurring as larger areas mean that more locations on the ground will receive rainfall and/or rainfall will have a longer duration depending on the spatial configuration of the rainfall regions. All polygons of rainfall over 2.5 mm/h and 5 mm/h were separately summed for calculating areal coverage of light and moderate rainfall. We hypothesized that the more intense storms and/or being embedded in a more humid environment would be associated with larger rainfall size.

The dispersion metric was used to measure the spread of the centers of precipitation clusters away from the TC circulation center. The calculation of dispersion was taken from Zick and Matyas (2016), who established a search radius of 600 km in light of the many extratropical transition cases in their study (Equation 4-1). In the current study, the ratio of the centroid radius (rcentroid) to the search radius of rainfall polygons (rsearch = 500 km) represents the measure of dispersion. Since only polygons

which have centroids located within 500 km of storms are included, the theoretical range of this metric will be (0, 1). Our calculations also differed from Zick and Matyas

(2016) as we considered all complete rainfall polygons over certain rain rate thresholds instead of truncating pixels at the search radius boundary. When precipitation fragmented into multiple clusters, the dispersion was calculated individually for each rainfall polygon, and then the values of all polygons were summed to get the final dispersion value at each observation time. When larger regions of rainfall are located near the storm center, the dispersion metric is closer to zero. If the rain fields move away from the storm center, rainfall near the center dissipates, and/or more outer rain bands develop, dispersion values increase (Figure 4-2).

푁 퐴푟푒푎𝑖 푟푐푒푛푡푟표𝑖푑,𝑖 DISP = ∑푖=1 ( ) (4-1) 퐴푟푒푎푡표푡푎푙 푟푠푒푎푟푐ℎ

Recent observational studies have shown that vertical wind shear, TC motion and moisture gradients can cause the rain fields of TCs to become asymmetrically- shaped (Corbosiero and Molinari 2002; Chen, Knaff, and Marks 2006; Lonfat et al.

2007; Matyas and Cartaya 2009; Wingo and Cecil 2010). These previous researchers have shown that the rainfall is enhanced in the downshear direction and right of motion direction. When TCs approach land, friction enhances convergence on the side of storm near land, which can also cause asymmetry of the rain fields. In addition to dispersion, measuring displacement provides a directional component to rainfall asymmetry that helps identify which region will receive TC rainfall. Here, we developed a new method to calculate the displacement of all polygons of rainfall, which is based on the dispersion calculation and relative location of individual polygons to the storm center (Equation 4-2

and Equation 4-3). In this calculation, 휃푖 is the heading of vector from the storm center to the individual polygon centroid (Figure 4-3).

푁 퐴푟푒푎𝑖 푟푐푒푛푡표푟𝑖푑,𝑖 DISE = ∑푖=1 ( ) sin 휃푖 (4-2) 퐴푟푒푎푠푢푚 푟푠푒푎푟푐ℎ

푁 퐴푟푒푎𝑖 푟푐푒푛푡표푟𝑖푑,𝑖 DISN = ∑푖=1 ( ) cos 휃푖 (4-3) 퐴푟푒푎푠푢푚 푟푠푒푎푟푐ℎ

Statistical Analysis

First, to examine the spatial pattern of rainfall metrics, we employed Optimized

Hot Spot Analysis, which executes the Hot Spot Analysis tool using parameters derived from characteristics of area, dispersion, and displacement of TC rain fields. This tool identifies statistically significant spatial clusters of high values (hot spots) and low values (cold spots) by employing the Getis-Ord Gi* statistic (Ord and Getis 1995). First, the Getis-Ord Gi* statistic measures the intensity of clustering of high or low values (i.e. area of rain field) in a point feature relative to its neighboring point features in the entire dataset. In current study, the optimal fixed distance band was based on the average distance to 30 nearest neighbors, which is about 156 km. The sum for a point feature and its neighbors is compared proportionally to the sum of all features. The null hypothesis is that the values associated with features are randomly distributed. The

Getis-Ord Gi* statistic generates z- scores (standard deviations) and p- values

(statistical probabilities) for each point feature that indicate whether rain field metric of a given point feature is statistically clustered compared to rain field metric in neighboring point feature, as well as rainfall area across the entire analysis domain. The larger a feature’s z-score, the more intense the clustering of values (hot spot). A z-score above

1.65 (below -1.65) means that there is a statistically significant hot (cold) spot of rainfall metrics at a significance level of p-value less than 0.10. A z-score above 1.96 (below -

1.96) means that there is a statistically significant hot (cold) spot of rainfall metrics at a significance level of p-value less than 0.05. A z-score above 2.58 (below - 2.58) means that there is a statistically significant hot (cold) spot of rainfall metrics at a significance level of p-value less than 0.01. The False Discovery Rate (FDR) Correction parameter was also applied, where the critical p-values determining confidence levels were reduced to account for multiple testing and spatial dependence.

To determine the temporal trend of rainfall field spatial patterns, a moving average method was applied firstly over every five observations (~15 hours) of the entire life cycle to smooth the data and remove temporal trends due to the diurnal cycle, and then a moving Mann-Kendall analysis was applied over every 7 observations (~21 hours) to test whether significant increasing or decreasing trends exist. Although the most common trend analysis method is linear regression, a non-parametric statistical test is more robust when the number of observations is limited in the test (only 7 observations). The Mann-Kendall test, an application of Kendall’s rank order correlation test to time series data, is a nonparametric test for zero slope of the linear regression of time-ordered data versus time (Mann 1945).

To determine the factors affecting rain fields, first a set of Mann-Whitney U tests were applied to examine whether environmental and storm conditions are significantly different when comparing observations that occurred with hot and cold spots of area, dispersion and displacement of light rainfall. The null hypothesis is that there is no difference between conditions in hot spot and cold spot clusters. The null hypothesis is rejected if the p-value of the test result is less than 0.05. We then considered the relationships between rainfall characteristics and conditions across the entire study area

by calculating Spearman’s rank correlation coefficients between area, distribution metrics, and environmental conditions of moisture and wind shear speed as well as storm conditions of intensity and speed of motion for all observations. If the test is significant at a level of 0.01, there is a robust correlation between rainfall metrics and environmental or storm conditions.

Last, after generating all rainfall fields of TCs every three hours, we analyzed the times that light and moderate rainfall begin to reach land prior to landfall of the storm center, as well as average rainfall duration per storm over land. To estimate the rainfall start time, we determined the time that rain fields first interested with Mexico and

Central American countries using a GIS, and counted the hours between this time and the time of landfall. To determine rainfall duration, a grid with cell size of 100 km was created covering the entire study region. All light and moderate rainfall fields every 3 hours were overlapped with the grid and count the frequency of TCP receipt at each cell. The average TCP duration per storm was calculated by firstly multiplying total TCP hits by 3 hours, and then dividing by the number of storms influencing this cell. The historical maximum duration of rainfall from TCs was also estimated. The outputs of this analysis include four maps with grid with average and maximum duration light/moderate rainfall in each cell.

Overview of Rain Field Metrics and Environmental Conditions

First, the statistics of area, dispersion and displacement of light rainfall of all observations are examined (Table 4-2). Since all four metrics have high correlations

(ρ > 0.7) between light and moderate rainfall, which indicates that these two rainfall fields have similar spatial configuration, we mainly discuss spatial-temporal pattern of light rainfall fields. When considering all observations in the current study region, the

rainfall areal coverage is 10.0×104 and 4.1×104 sq. km on average for light and moderate rainfall, respectively. Comparing with rainfall area above 2.5 mm/h of U.S. landfalling TCs examined in Chapter 3, the light rainfall area in current study is larger than that for U.S. landfalls, which is 9.58×104 sq. km (Table 3-2). For moderate rainfall, the median value is similar to that of TCs before and after landfall over Florida (Matyas

2014). The median value of light or moderate dispersion is about 0.30 with a skew to the left side, which indicates that light to moderate rain fields of most observations in the current study are relatively cohesive and symmetric (Table 4-2). The average dispersion value is about 0.31, with indicates that when considering all rainfall polygons, their area- weighted distance from storm center to rainfall centroids is about 150 km. The range of diversion of light rainfall is (0, 0.81) in current study which is relative smaller than a range of dispersiveness values of rain field associated with U.S. landfalling TCs estimated by Zick and Matyas (2016), which is about (0,1). For displacement, slightly more rain fields have displacement to north (east) than to the south (west). About 52

(48) percent of observations have displacement to east (west), and about 60 (40) percent of observation have displacement to north (south).

To understand how the TC attributes and synoptic-scale environment influences the rainfall patterns in TCs before, during and after landfall over the western Caribbean

Coast and Gulf Coast, we examined the storm intensity, motion, TPW and wind shear, and their influence on spatial pattern of TCP. The statistics of storm intensity, motion speed, moisture, and wind shear are summarized in Table 4-3, and the Figure 4-4 shows spatial distribution of storm intensity, average TPW over 0-400 km, SHRW, and

SHRS.

Two TC attributes, including intensity and motion, are first discussed. The average maximum wind speed is about 23 m/s, which falls between the thresholds of tropical storm (17 m/s) and hurricane (33 m/s), and about 40 % of storms reach hurricane intensity. Storm intensity has a clear spatial pattern (Figure 4-4A). The TCs over Caribbean Sea (CS) are more intense than those over Gulf of Mexico (GM), which might because when TCs develop over Gulf of Mexico, they have limited space to intensify before land interaction. Some of most intense Atlantic basin hurricanes can be found over the Caribbean Sea, including Hurricanes Mitch (1998), Emily (2005), Wilma

(2005), Dean (2007) and Felix (2007), all of which reached Category 5 on the Saffir-

Simpson scale (Guiney and Lawrence 1999; Franklin and Brown 2006; Pasch et al.

2006; Franklin 2008; Beven 2008). Storm intensity quickly decays within 24 hours of landfall. When considering motion speed, the majority of storms have westward or northwestward motion with slow to moderate speed (less than 8.0 m/s) (Matyas 2014).

Zonally, about 75 % of storms have a westward trajectory at about 3.5 m/s. In the north- south direction, the northward speed is even slower with a median value of 1.4 m/s. As

TCs tend to develop rainfall asymmetries related to their motion when moving fast, the relatively slow speeds occurring in the current study’s observations might not be an important factor affecting rainfall patterns.

Table 4-3 lists TPW averaged over different spatial regions. The average TPW decreases when the spatial region increases from 0-200 km to 0-1000 km. Here TPW over 0-400 km is taken as an example to describe the moisture environment and compare with other regions examined by previous researchers. When considering all observations in the current study, the average value of TPW over 0-400 km is 60.4 mm,

with a standard deviation value of 4.3 mm. This value is much higher than average TPW of TCs within 500 km of Puerto Rico which is about 45 mm (Hernández Ayala and

Matyas 2016) and average TPW of U.S. landfalling TCs with median value of 47 mm

(Xu, Jiang, and Kang 2014). These higher moisture values are likely due to evaporation of warm ocean water over the Gulf of Mexico, Caribbean Sea and western tropical

North Atlantic, which are referred to as the Atlantic warm pool (AWP). The AWP has sea surface temperatures (SSTs) >28.5-degree C during summer and fall (Wu et al.

2012; Wang and Enfield 2003; Wang and Lee 2007). The distribution of TPW shows the highest values over the southern Gulf of Mexico, especially the Bay of Campeche

(Figure 4-4B). In the western CS, the TCs are embedded within an environment that has higher amounts of moisture than the central and eastern CS. These spatial patterns are possibly due to seasonal variation of the AWP region. Wang and Enfield (2003) illustrated that early in the hurricane season (July - August), the AWP mainly covers the

Gulf of Mexico and northwestern Caribbean Sea. The AWP reaches its maximum size around September, when it covers both the Gulf of Mexico and entire Caribbean Sea. In

October, the AWP shifts southward and covers the Caribbean Sea but not the Gulf of

Mexico. Since 10 out of 11 TCs originated over the Gulf of Mexico in July-September and 11 out of 15 TCs originated over the western CS in September-October, they experienced much higher moisture compared to the storms that moved over the central and eastern CS in July and August. Figure 4-4B shows that most TCs did not experience large decreases in moisture (less than 10 mm) after landfall as they stayed within 200 km of the coastline and could still advect high amounts of moisture from

coastal and off-shore regions into their circulations from both eastern Pacific and

Atlantic sides (Enfield and Alfaro 1999; Brena-Naranjo et al. 2015).

Previous studies utilized 5 and 10 m/s to classify vertical wind shear speed as weak, moderate or strong (Corbosiero and Molinari 2002; Wingo and Cecil 2010).

Regardless of direction, the wind shear speed of the entire study area has a median value of 5.9 m/s, with about 38 % of observations experiencing light shear (0-5 m/s),

46% moderate shear (5-10 m/s), and 16% of strong shear (> 10 m/s). The median absolute magnitude of meridional wind shear is 3.1 m/s, which is weaker than the zonal shear absolute magnitude, with a median value of 4.1 m/s. The dominant wind shear direction is eastward or northeastward over the Caribbean Sea, and southeastward over

Gulf of Mexico (Figure 4-4). This spatial pattern of wind shear is consistent with a climatological study of wind shear patterns (June - October) by Chen, Knaff, and Marks

(2006). The northerly wind shear environment of storms over the Gulf of Mexico is also mentioned by several tropical storm reports from NHC (e.g. Hurricane Bret

(1999)(Lawrence and Kimberlain 2001), Tropical Storm Dolly (2014)(Beven 2015)). This northerly wind shear is possibly due to Central American gyres (CAGs) and/or the

Madden-Julian oscillation (MJO). The MJO is a large-scale episodic modulation of tropical winds and precipitation that travels eastward from Asia to America, with a characteristic repeat time of 30 to 60 days. A previous study showed that when MJO wind anomalies in the lower troposphere of the eastern Pacific are westerly, Gulf of

Mexico and western Caribbean hurricane genesis is four times more likely over the Gulf of Mexico and western Caribbean than when the MJO winds are easterly (Maloney and

Hartmann 2000). CAGs are large, closed, cyclonic circulations that occur during the

rainy season (May–November). Papin (2017) classified CAGs into tropical CAGs and trough CAGs, and found that about 50% of CAGs are related with at least one TC over the Gulf of Mexico and Caribbean Sea during 1980-2010. He found that during CAG periods, there are more northeasterly winds at 850 hPa and more westerly winds at 200 hPa over southern Gulf of Mexico region, which results in a northerly wind shear and likely explains the tendency for northerly wind shear in our study.

Regional Variations of Rain Rates and Corresponding Environmental Conditions

Before examining conditions across the entire study region, we identify regions where rainfall patterns exhibit spatial similarities using a hotspot analysis (Figure 4-5).

These maps indicate clusters of larger area, higher values of dispersion and displacement as hot spots and clusters of smaller area and lower values as cold spots at confidence levels of 90%, 95% and 99%. The hotspot analysis is also applied to examine where significant increasing (hotspot) and decreasing (cold spot) trends tend to occur (Figure 4-6). These spatial patterns of rainfall size and configuration are likely due to different TC attributes and environmental conditions. Mann-Whitney U tests are applied to test for differences in storms and environmental conditions between groups of hot and cold spots of area, dispersion and displacement of light rainfall. The results of significant tests are listed in Table 4-4.

For the area, the largest hotspot cluster is over the western Caribbean Sea (west of

78˚W) about 500 km west of land, which comprises all TCs making landfall over the

Yucatan Peninsula, Belize, and Honduras (Figure 4-5A). There are three small hot spot clusters over the coastal regions of Honduras and Mexico, which are related to

Hurricane Mitch (1998), Hurricane Stan (2005), Tropical Storm Arlene (2011), Tropical

Storm Barry (2013), and Tropical Storm Dolly (2014). According to the tropical storm

reports, these storms produced extreme rainfall accumulations (at least 150 mm) over

Mexico, Belize, Honduras, or Nicaragua (Guiney and Lawrence 1999; Pasch and

Roberts 2006; Beven 2012; Stewart 2013; Beven 2015). This finding supports our assertion that a larger raining area is associated with rainfall that can lead to flooding.

The cold spots of area mainly are associated with storms moving over the southeastern

Yucatán Peninsula and adjacent eastern Bay of Campeche, as well as after landfall over Texas, U.S. However, significant changing trends of area show a different spatial pattern (Figure 4-6A). Most TCs decrease in rainfall area before and during landfall over western Caribbean Sea coast and Texas, U.S, while increases in rainfall area occur when moving over the central Caribbean Sea and Yucatan Peninsula and back to the

Bay of Campeche. The Mann-Whitney U tests show that larger rainfall area is related to higher storm intensity and higher moisture content 0-600 km from the storm center

(Table 4-4). Although both tests produce statistically significant results, there is a larger difference between hot spot and cold spot intensity values than for moisture, which indicates that intensity has the strongest association with rainfall area.

The spatial configurations of rainfall fields are discussed next. First, displacement has higher number of significant hot/cold spots and clearer spatial pattern than dispersion (Figure 4-5 C and D). More rainfall fields have displacement to west and north side of storm center over the western Caribbean Sea south of Cuba before landfall over the Yucatan Peninsula and central Gulf of Mexico. The rainfall has more displacement to the south and west over coastal region of Belize, Nicaragua, Honduras, and Bay of Campeche, which indicates that rainfall in this region shifts toward land.

Mann-Whitney U tests reveal that both motion and wind shear have differing

100

distributions between groups of hot and cold spots (Table 4-4). Larger displacement to east is related to faster westward and northward speed, as well as stronger southerly and westerly shear. Larger displacement to north is related to faster northward speed and stronger southerly shear. These combined results indicate that the rain fields shift to the downshear or downshear right side of the storm, and agree with results from

Corbosiero and Molinari (2002), which noted that for the outer rainbands (100 - 300 km), the front-right quadrant is favored by storm motion and the downshear-right quadrant is favored by shear.

The clusters of hot and cold spots of dispersion are more scattered (Figure 4-5

B). The hot spot regions include the western Caribbean Sea region about 500 km west of western Caribbean Coast, coastal region of Honduras and Nicaragua, southeastern

Yucatán Peninsula and adjacent eastern Bay of Campeche. The average dispersion value of hot spots is about 0.42, with indicates that the area-weighted distance from storm center to rainfall centroids is about 200 km for these observations (Table 4-2).

The average dispersion value of observations in cold spot zones is 0.22. The cold spots of dispersion are distributed over the eastern Caribbean Sea, ocean region adjacent to eastern coast of Yucatan Peninsula, and ocean region before landfall over southern

Gulf coast. Mann-Whitney U tests reveal that a more dispersed pattern is related to increased storm intensity, but less moisture (Table 4-4). These results agree with Zick and Matyas (2016) that more intense storms have more cohesive structure, while further imply that as in drier environment, the outer rain bands might be depressed and results in a less dispersive rainfall pattern.

101

Last, there are few clusters of significant increasing or decreasing trends of dispersion and displacement (Figure 4-6). There are two possible reasons for this outcome. First, since the change of spatial configuration might occur quickly, these changes might not be captured in the trend analysis over a 21-hour period. Second, as shown in the Mann-Whitney U tests, the spatial configuration metrics are related to different environmental conditions, which might also have different time lags. For example, the wind shear might take 0-24 hours to influence displacement of rainfall, while the lag effect might be also related to the magnitude of wind shear (Wingo and

Cecil 2010).

Overall Variations of Rain Rates and Corresponding Environmental Conditions

In this section, we determine the conditions that are most correlated with the total areal coverage and spatial configurations of rain fields associated with TCs through the calculation of Spearman’s rank correlation coefficients. Values of area, dispersion, and displacement of light and moderate rainfall fields were smoothed over 5 observations.

Table 4-5 shows the correlation coefficients of Spearman's rank correlation tests of TCs attributes (VMAX, MotE and MotN) and environmental conditions (TPW, SHRW and

SHRS). Only correlations with coefficients greater than 0.30 and that are significant at a level of 0.01 are listed.

First, as storms intensify, both light and moderate rainfall coverage enlarge, with decreasing dispersion values (Table 4-5). These combined results of area and dispersion further confirm previous research which states that, as the storm intensity increases, the TC circulation gets stronger and larger, which results in a larger rainfall area a more cohesive pattern with major rainfall regions located close to the storm center (Dvorak 1975; Kimball and Mulekar 2004; Matyas 2014; Zick and Matyas 2016).

102

Next, the dispersion of rainfall is negatively correlated with storm intensity, but positively correlated with moisture (Table 4-5). Previous studies show that a relatively moist environment within a broad region surrounding storm center is essential to sustain or increase TC size and rainfall production (Trenberth and Fasullo 2007; Jiang,

Halverson, and Zipser 2008; Hill and Lackmann 2009; Konrad and Perry 2010; Lin,

Zhao, and Zhang 2015; Matyas 2017). Previous studies also employed observational and numerical methods to examine environmental humidity’s influence on TC rainfall structure. Matyas and Cartaya (2009) analyzed Hurricanes Frances and Jeanne (2004), and determined that the precipitation distribution was influenced by the degree of outer rain band activity, which was in turn related to environmental humidity. Hill and

Lackmann (2009) employed numerical modeling to test the environmental humidity’s influence on the extent of its rain fields. They found that relatively moist environments are conducive to more widespread precipitation at larger radial distances and greater lateral extent of spiral bands (Hill and Lackmann 2009). The current study adds to these numerical modeling and case studies by employing a large sample size from satellite- based estimates of rainfall and statistical methods to associate larger rain fields that are highly dispersed with higher values of moisture.

We further determine which extent of moisture has the highest correlations with light and moderate rainfall and analyze time lag effects. The rainfall area and dispersion values have significant correlations with average TPW over ranges from 200 km up to

800 km from the storm center. For area and dispersion of light rainfall, the highest correlation exists between rainfall metrics and with TPW averaged over 0-400 km. For moderate rainfall, the area has the highest correlation with TPW averaged over 0-200

103

km, while the dispersion has the highest correlation with TPW averaged over 0-600 km.

These results are generally consistent with previous research that shows the cyclonic convergent inflow is within a 4°-6°radius of the TC center (Frank 1977, Evans and Hart

2003). Moreover, as identified by previous research, there should be a lag-effect between the onset of environmental conditions and change in rain field structures

(Jiang, Halverson, and Zipser 2008; Matyas 2010b). Here the time lag is identified as the time with significant correlation with the highest coefficient. Although the correlation tests are significant when utilizing the current time and lags out to 30 hours, the highest correlation coefficients exist between light (moderate) rainfall area and current (6 hours previous) TPW, and the coefficients gradually decrease as lag increases. This result agrees with Jiang, Halverson, and Zipser (2008), who also found similar correlations of moisture and rainfall volume between 0 hours and 12 hours. The correlation coefficient for moisture and dispersion gradually increases as time lag increases, and reaches highest correlation coefficient at about 24-30 hours, which is much longer than the lag between rainfall area. A possible explanation is that dispersion of entire fields gradually changes, while area responds more directly. The rain fields can grow in size without a change in dispersion if the growth is symmetrical about the storm center. Also, a large change in the radial extent of rain rates is needed to change dispersion given the 500- km search radius.

Last, we examined the conditions related with displacement of light and moderate rainfall. In general, the TC rainfall asymmetry has larger amplitudes with respect to vertical wind shear than to TC motion. The westerly wind shear has a stronger correlation with displacement to the east, and southerly wind shear is also

104

positively correlated with displacement to north, especially for light rainfall (Table 4-5).

Wingo and Cecil (2010) concluded that the asymmetry coverage is predominately downshear left, regardless of motion speed and direction, while Corbosiero and Molinari

(2002) found that outer rainbands shift to downshear right direction. Here we found that downshear direction is more dominant in our sample. When considering the lag effect, the westerly wind shear takes about 18-24 hours for changes in rainfall displacement, and the southerly wind shear takes about 30 hours for changes in rainfall displacement.

This difference might be because the southerly wind shear is much weaker than westerly wind shear (Table 4-3), since the previous study also found that weaker wind shear takes longer to change storm structure (Wingo and Cecil 2010). The displacement is only weakly correlated with eastward and northward motion speed. This result is possible because most TCs have slow to moderate forward speed, so that shear is a more dominant force. Also, the dominant TCs motion is to the west, which opposes the dominant wind shear direction. In this situation, the effect of motion speed on rainfall asymmetry tends to be reduced (Corbosiero and Molinari 2002; Chen, Knaff, and Marks 2006; Ueno 2007; Wingo and Cecil 2010; Xu, Jiang, and Kang 2014).

Although the correlation test over all observations indicates that rainfall fields are displaced towards the downshear direction, displacement in the upshear direction occurs over the southern Gulf of Mexico and coastal region adjacent to Belize. Here, most rainfall was displaced to the western or southwestern side of the storm while it was experiencing westerly shear. As a TC approaches land, increased surface friction enhances convergence on the side of the storm near land (Powell 1982; Kimball 2008;

Xu, Jiang, and Kang 2014). Increased surface friction and induced low-level

105

convergence over land could help a large region of rainfall to occur in the entire front half of the storm (Kimball 2008). In addition, due to the short land distance of Central

America, TCs making landfall over the southern Gulf Coast and moving towards the

Pacific coast of Mexico could advect moisture from the eastern Pacific Ocean. This moisture advection could explain the existence of large rainfall areas on the west (front) side of storm. An example of this rainfall pattern can be found from Hurricane Ernesto

(2012) (Figure 4-3).

Rainfall Start Time and Average Duration

According to the NHC, tropical storm or hurricane watches/warnings are issued

48/36 hours prior to the anticipated arrival of tropical-storm-force winds, without considering rainfall start time. The times that light and moderate rainfall begin over the western Caribbean coast or Gulf coast is summarized in 12-hour periods before landfall

(Figure 4-7). First, for TCs landfalling over the western Caribbean or Gulf coast, the median light rainfall start time is about of 36-48 hours before landfall over both regions.

However, the range of light rainfall start times has a large difference when these two regions are compared. The earliest that light rainfall reaches land is about 180 hours, which occurs during Hurricane Keith (2000). Hurricane Keith originated over the western

Caribbean Sea 135 km away from the coastline. As it formed, it produced rainfall left of the storm center over the coastal region of Honduras. For Gulf of Mexico region, the storm that has the earliest rainfall start time is Tropical Storm Ingrid (2013) that formed in Bay of Campeche. It produced rainfall over land at the time of formation, which is 120 hours before landfall. Due to the TCs in Gulf of Mexico being closer to the coastline when they form (Figure 4-1), they make landfall earlier in their lifecycle when compared to TCs that form over the Caribbean Sea. Although rainfall over the Gulf of Mexico is

106

smaller in areal coverage, it is more displaced to the west and south, which is the side of the storm that is closest to land. The median moderate rainfall start time shows about

12 hours of difference between CS and GM landfalls. About half of storms have moderate rainfall reaching land 12-24 hours before landfall over Caribbean coast, while about half storms making landfall from the Gulf coast region have moderate rainfall reaching land about 24-36 hours before landfall. Therefore, people along the Gulf Coast should evacuate from flood-prone areas two days before landfall is anticipated.

A slow-moving storm with a large and dispersed pattern of rainfall would result in a longer duration of TCP over land. Figure 4-8 shows average durations of light and moderate rainfall per storm. Overall, two regions receive longer duration of light and moderate per storm, namely the western Caribbean Sea adjacent to central America and Bay of Campeche, which is due to large rainfall area and/or rainfall displaced to the side of the storm nearest the coast (Figure 4-5). These long duration TCP events are likely to result in higher rainfall totals. The average duration of light rainfall is above 24 hours for light rainfall, and 12 hours for moderate rainfall, which might result in rainfall totals exceeding 60 mm for one storm. It is important to note that due to the size of each pixel, this represents an average rainfall total over an area of 1024 sq. km with higher values likely to occur within each pixel. Moreover, there is an abrupt shift from 1-12 h per storm to 12-24 h per storm in the middle of the Caribbean. It is because that rain fields of TCs are smaller and more cohesive over the eastern than western Caribbean

Sea. Moreover, storm motion is faster over eastern Caribbean Sea, which causes shorter duration of rainfall. We also estimate the maximum duration of TCP for individual storms in history (Figure 4-9). The coastal region over Belize, Nicaragua and

107

Honduras, as well as southern coast of Bay of Campeche received more than 72 hours of light rainfall and 49 hours of moderate rainfall during one storm period. The longest duration of TCP over Mexico and Central America region is caused by Hurricane Mitch

(1998), where 698 mm of rain fell during 41 hours in southern Honduras (Hellin, Haigh, and Marks 1999).

Conclusions and Future Research

In this study, we have documented the spatial patterns of rain fields associated with landfalling TCs over the western Caribbean and Gulf coasts between 1998 and

2015 based on estimates of rain rates available from a satellite-derived dataset. Area, dispersion and displacement are calculated for the entire rain field as delineated by the edges of light (2.5 mm/h) and moderate (5 mm/h) rain rates. The spatial and temporal pattern of area, dispersion, and displacement of TCP are determined by hot spot analysis and Mann-Kendall analysis. The factors that contribute to the spatial patterns of rainfall are also examined by using Mann-Whitney U tests and Spearman’s rank correlation tests, including TC storm intensity, motion speed and direction, TPW, and vertical wind shear speed and direction. Finally, light and moderate rainfall polygons were used to determine the time that rainfall reaches land relative to the time that the storm’s center makes landfall, average duration, and maximum duration of rainfall from

TCs

There are three major findings of this study in terms of rain field area, spatial patterns, and corresponding environmental conditions. (1) The rainfall coverage is largest as TCs approached the western CS coast, and rainfall area enlarges as TCs move back over the Gulf of Mexico after making landfall over the Yucatan Peninsula. (2)

108

In terms of displacement, rain fields have more displacement to east and north over western and central Caribbean Sea and central Gulf of Mexico. Rainfall fields have more displacement to west and south when TCs move over the southern Gulf of

Mexico. (3) The area and dispersion of light/moderate precipitation field of TCs are mainly correlated with storm intensity and TPW, and the displacement of rainfall is significantly correlated with vertical wind shear (displacement to the downshear direction). The rainfall displacement of TCs to the west is observed over Bay of

Campeche, which may be related to the convergence of moisture above the boundary layer from the Pacific Ocean and near-surface convergence enhanced by land.

Last, after generating light and moderate rainfall polygons, we determined the time that rainfall reaches land relative to the time that the storm’s center makes landfall, average duration, and maximum duration of rainfall from TCs. The larger and dispersed rainfall fields result in early rainfall start time and longer durations over land. About half of storms have their light and moderate rainfall reaching land about 48 hours before landfall. The duration of TCP over the western Caribbean and Gulf coast is about 12-24 hours per storm, and the historical maximum light rainfall duration could be longer than

72 hours for individual storm. Knowledge of rainfall start time before landfall and possible duration of rainfall is useful for hazard mitigation and to identify time and regions might receive rainfall from storm.

Future studies can extend this research in two main directions. First, to further examine heavy rainfall and its possible influence on flooding, the rainfall magnitude and the higher rainfall threshold (e.g. > 8.0 mm/h) produced by TCs need to be identified from radar-based products as well as surface observations, especially for cases which

109

caused extreme flooding. As we noted, the spatial resolution of the TRMM observations can greatly underestimate local rainfall maxima. Second, we found that large-scale atmospheric features like the Central American Gyre and MJO could affect environmental conditions over Gulf of Mexico and Caribbean Sea, which in turn influences tropical cyclone precipitation. Future studies should explore the interaction of

CAG, MJO and tropical cyclones in this region and how tropical cyclone rainfall changes under the differing configurations of vorticity, wind flow, and moisture.

110

Figure 4-1. Tracks of 35 tropical cyclones that made landfall in 1998–2015 over the western Caribbean and/or Gulf coasts. Elevation data were obtained from USGS.

Figure 4-2. A comparison of rain fields from Tropical Storm Arlene (2011) (Area: 19× 104 sq km, DISP: 0.58) and Hurricane Dean (2007) (Area: 17 × 104 sq km, DISP: 0.17).

111

Figure 4-3. A comparison of displacement of rain fields and wind shear from Hurricane Mitch (1998) (DISE: 66 km, DISN: 100 km, SHRW: 6.5m/s, SHRS: -3.4 m/s) and Hurricane Ernesto (2012) (DISE: -76 km, DISN: -157 km, SHRW: 0.5 m/s, SHRS: -5.1 m/s).

Table 4-1. Abbreviations, units, source, and spatial range of TC attributes and environmental conditions. Variables Abbreviation Units Data source Spatial range of variables Velocity of maximum VMAX m/s IBTrACS / sustained winds Eastward component of MotE m/s IBTrACS / motion speed Northward component of MotN m/s IBTrACS / motion speed Average total precipitable TPW mm SHIPS 0-200 km, 0-400 km, 0-600 water km, 0-800 km, 0- 1000 km Southerly vertical wind shear SHRS m/s SHIPS 200-800 km (850-200 hPa) Westerly vertical wind shear SHRW m/s SHIPS 200-800 km (850-200 hPa)

112

Table 4-2. Number of features and statistics of metrics for all observations, hot spots, and cold spots of light rainfall (area unit:104 sq km, width unit: km). Metrics Variables Number of Average Std. Percentile observations deviation 25 50 75 AREA All 1304 10.0 7.5 4.9 8.3 13.2 Hot spots 326 14.2 9.6 7.1 12.0 18.9 Cold spots 251 5.6 4.4 2.2 4.8 7.7 DISP All 1304 0.31 0.17 0.18 0.30 0.42 Hot spots 270 0.42 0.17 0.30 0.41 0.52 Cold spots 242 0.22 0.14 0.11 0.20 0.20 DISE All 1304 23 101 -42 15 86 Hot spots 354 90 88 25 84 152 Cold spots 478 -33 95 -92 -37 16 DISN All 1304 20 93 -34 22 71 Hot spots 343 74 85 18 74 120 Cold Spots 442 -23 89 -76 -21 34

Table 4-3. Name, unit and statistics of variables over entire region. Different number of observations is due to the missing data in SHIPS. Variables Number of Unit Average Std. Percentile observations deviation 25 50 75 VMAX 1360 m/s 29 16 15 23 36 MotE 1329 m/s -3.8 3.1 -5.9 -3.5 -1.5 MotN 1329 m/s 1.3 1.5 0.0 1.4 2.4 SHRW 1104 m/s 3.3 5.0 0.3 3.4 6.3 SHRS 1104 m/s -0.2 4.5 -3.4 -1.0 2.6 TPW 1230 mm 63.2 4.1 60.3 62.9 66.0 (0-200 km) TPW 1230 mm 60.4 4.3 57.3 60.5 63.4 (0-400 km) TPW 1230 mm 58.1 4.5 55.2 58.5 60.8 (0-600 km) TPW 1230 mm 56.1 44.0 53.7 56.5 58.8 (0-800 km) TPW 1230 mm 54.5 4.3 52.4 54.8 57.1 (0-1000 km)

113

Figure 4-4. Distribution of storm intensity, average TPW over 0-400 km, SHRW, and SHRS. A) Storm intensity. B) Average TPW over 0-400 km. C) SHRW. D) SHRS.

114

Figure 4-5. Hotspots maps of area, dispersion, and displacement of light rainfall. A) Area. B) Dispersion. C) Displacement to east. D) Displacement to north.

Figure 4-6. Hotspots maps of change of area, dispersion, and displacement of light rainfall.A) Area. B) Dispersion. C) Displacement to east. D) Displacement to north.

115

Table 4-4. Mann-Whitney U Tests results of conditions related to hot and cold spots of area, dispersion and displacement of light rainfall. Metrics Variables Variable statistics P-value Higher Median Lower value Median value group group AREA VMAX(m/s) hot spots 27 cold spots 18 <0.001* TPW(mm) hot spots 59 cold spots 58 0.011* (0-600 km) DISP VMAX(m/s) cold spots 31 hot spots 21 <0.001* TPW(mm) hot spots 61 cold spots 59 0.002* (0-600 km) DISE MotE(m/s) cold spots -3.4 hot spots -2.5 <0.001* MotN(m/s) hot spots 1.5 cold spots 1.0 <0.001* SHRW(m/s) hot spots 4.3 cold spots 1.3 <0.001* SHRS(m/s) hot spots 0.2 cold spots -1.7 <0.001* DISN MotN(m/s) hot spots 1.6 cold spots 1.0 <0.001* SHRS(m/s) hot spots 2.2 cold spots -2.8 <0.001* * Significant at level of 0.05

Table 4-5. Spearman’s rank correlation coefficients, time lags and spatial range between area, shape metrics and environmental conditions (Correlation coefficients greater than 0.3 and significant at 0.01). Variables Variables Light rainfall Moderate rainfall AREA DISP DISE DISN AREA DISP DISE DISN VMAX Coefficient 0.43 -0.36 / / 0.41 -0.30 / / MotE Coefficient / / / / -0.14 / / / MotN Coefficient / / / 0.33 / / / 0.30 TPW Coefficient 0.52 0.33 / / 0.49 0.39 / / Time lag(h) 0 24 / / 0 24 / / Range(km) 0-400 0-400 / / 0-200 0-600 / / SHRW Coefficient / / 0.60 / / / 0.61 / Time lag(h) / / 18-24 / / / 18-24 / SHRS Coefficient / / / 0.54 / / / 0.56 Time lag(h) / / // 30 / / / 30

116

25 Light TCP A

20 Moderate TCP

10 Frequency

0 -180 -168 -156 -144 -132 -120 -108 -96 -84 -72 -60 -48 -36 -24 -12 Hours prior to landfall

30 B Light TCP 25 Moderate TCP 20

Frequency 10

0 -120 -108 -96 -84 -72 -60 -48 -36 -24 -12 Hours prior to landfall

Figure 4-7. Start time of light and moderate rainfall relative to landfall. A) CS landfall. B) GM landfall.

117

Figure 4-8. Average duration of light and moderate rainfall associated with TCs. A) Light rainfall. B) Moderate rainfall.

Figure 4-9. Maximum duration of light and moderate rainfall associated with TCs. A) Light rainfall. B) Moderate rainfall.

118

CHAPTER 5 CONCLUSIONS

Summary

The main purpose of this dissertation is to quantify the spatial characteristics of precipitation associated with TCs making landfall over eastern U.S., Mexico and other

Central American countries. After these patterns are identified, different TCs attributes and environmental conditions associated with these spatial patterns are investigated through statistical methods. Toward these objectives, this dissertation addresses three primary research questions.

1. What are the spatial characteristics of storm total rainfall swaths for TCs

making landfall over U.S.?

2. What is the spatial variation in the size of TC rain fields in each quadrant of

the storm before and after landfall over the U.S. and which storm attributes

and environmental conditions can predict of TC rain field?

3. For TCs making landfall over the western Gulf of Mexico and Caribbean Sea

coastlines, are there preferred locations where TC rain fields grow in area

and/or become more dispersed and displaced so that they affect land sooner

and what TC and environmental conditions are associated with these

characteristics?

All of these questions are explored in three different chapters and their main findings are summarized below.

The first question was examined in Chapter 2, which develops a Geographic

Information System method to delineate rainfall swaths for 257 U.S. landfalling TCs during 1948 to 2014 using a daily gridded dataset. We then describe spatial patterns of

119

TCP using three methods. First, we measure the rainfall swath areas and average widths over land, and find that TCs that spend longer periods over land have wider average widths so that rainfall swaths cover larger areas. Second, trends in the change of left extent of TCP swaths are analyzed and TC attributes related to these trends are explored. Seventy of 85 TCs have rain swaths that expand on the left side at some points as they move inland. The TCs exhibiting expansion were hurricanes at landfall, re-intensifying over land, undergoing extra-tropical transition, and/or moving near the coastline. Last, we construct a series of maps with return intervals and frequency distributions for inland TCP and tropical storm-force winds. The results show that 94 % of 2435 counties over the eastern U.S. are more frequently exposed to rainfall than wind from TCs. While cumulative rainfall shows a gradual decrease from southeastern coast inland, many inland regions have received 5-6 TCP events in a single season, which confirms that TCP should be a concern for people living inland as well as near the coast. This study’s analysis of the spatial characteristics of TCP inland extent from a climatological perspective should benefit forecasting, hydroclimatological studies and risk analysis of TC hazards posed by TC rainfall.

The second question was the focus of Chapter 3. Here, we looked at the area and extent of rain fields associated with TCs making landfall over U.S. coastline and built regression models to predict rain field size before and after landfall. This study examines the size of rain fields associated with TCs making landfall over the U.S. from

1998- 2015 through a GIS-based analysis of satellite-estimated rain rates. Regions of moderate rainfall (rain rate > 2.5 mm/h) belonging to each TC are converted into polygons and measurements are made of their area and average extent in each of four

120

quadrants placed according to storm motion (right front, left front, left rear and right rear). A grid is constructed to delineate spatial distributions of TC rain field size before and after U.S. landfall. The results show that rain fields cover the largest area over the southern and eastern Gulf, as well as the coastal region near the Carolinas and

Delaware. As far as extent, the left sides of TC rain fields remain closer to the storm center when located over the western Gulf of Mexico. The right rear quadrant has the largest extent when located over the eastern Gulf of Mexico, while the right front quadrant has the largest extent overall, and large extents can occur both over the ocean and over land. As TCs move inland, although the area and extent in rear quadrants decays, the rainfall in right front and left front can still extend farther than 300 km from the storm center, meaning that rainfall can begin hours before the circulation center approaches. The size of the rainfall field is related to TC attributes and environmental conditions by using Spearman’s rank correlation Tests and generalized linear regression models. The results reveal that total precipitable water within 400 km of storm center and upper-tropospheric divergence play the most important role in both overall coverage and extent in all quadrants. The deep-layer vertical wind shear with a strong westerly component correlates well with a larger extent in the forward quadrants of the storm, while effects of storm motion are not as strong as wind shear which is possibly due to the relatively moderate to strong wind shear over study area. Last, storm intensity has more influence on rainfall over ocean than over land, while distance to coastline have more influence on rainfall after landfall. By applying statistical regressions on large samples of TC observations, these results reveal factors that are

121

important to TC rain field spatial distribution, which offers useful information for TC rainfall forecasts.

The third question measured area, dispersion and displacement of light and moderate rain fields associated with 35 TCs making landfalls over the western Gulf and

Caribbean Coasts during 1998-2015 and explored different conditions contributing to their spatial characteristics in this region. Four metrics characterize the spatial configurations of light and moderate rainfall fields (rain rate > 2.5 mm/h and 5.0 mm/h), including area, dispersion and displacement to east/north. The spatial and temporal pattern of area, dispersion, and displacement of TCP are determined by hot spot analysis and Mann-Kendall analysis. The results show that the rainfall coverage is largest as TCs approached the western Caribbean coast, while rainfall area increases as TCs move back over the Gulf of Mexico after making landfall over the Yucatan

Peninsula. The rain fields have more displacement to east and north over western and central Caribbean Sea and central Gulf of Mexico. Rainfall fields have more displacement to west and south which is over land when TCs move over the southern

Gulf of Mexico. The area and dispersion of light/moderate precipitation field of TCs are mainly correlated with storm intensity and total precipitable water. The displacement of rainfall is significantly correlated with vertical wind shear, while significate influence of moisture source and land interaction on rainfall displacement can also be observed over

Bay of Campeche. The larger and dispersed rainfall fields result in early rainfall start time and longer durations over land. About half of storms have their light and moderate rainfall reaching land about 48 hours before landfall. The duration of TCP over the

122

western Caribbean and Gulf coast is about 12-24 hours per storm, and the historical maximum light rainfall duration could be longer than 72 hours for individual storm.

As summary, this dissertation describes spatial patterns of precipitation associated with Atlantic TCs making landfall over U.S. coastline, western Gulf coast and western Caribbean coast, and investigate the contributing factors to rainfall patterns.

The area of TCP reaches largest before making landfall, while after landfall the rainfall extent could still extend in left and/or front side of TCs after U.S. landfalls, or displace to left and/or front side of TCs after landfalling over southern Gulf coast, which indicate inland area still need be informed of TCs. Thus, people located to the left or front of the projected storm track should monitor conditions closely as they may receive TCP. We also found that rainfall area above 2.5 mm/h of U.S. landfalling TCs is relative smaller than that for western Gulf and Caribbean coast. The factors that contribute to larger rainfall area or wider extent include stronger storm intensity and higher moisture both over ocean and over land, as well as closer distance to coastline after landfall. The deep-layer vertical wind shear has stronger effect than storm motion on rainfall asymmetry. ET processes contribute to the expansion of left side of rainfall as TCs move over inland U.S. Last, we provide a climatological view of the areas of eastern

U.S., Mexico and Central American countries that have been most affected by TCs or received longer duration of TCP. While cumulative rainfall shows a gradual decrease from coastal regions to inland areas, many inland U.S. regions have received 5-6 TCP events in a single season, and inland locations of Mexico and Central American countries experienced maximum duration of TCP over 48 hours during one storm, which

123

confirms that TCP should be a concern for people living inland as well as near the coast.

Future Directions

There are three aspects for my future work in the area of tropical cyclone precipitation First, I will keep improving my GIS spatial technique for extracting various thresholds of rainfall over a variety of gridded precipitation datasets. Based on extracted rainfall fields, a variety of geometrics, including geometrics used in current research, including area, extent, displacement, and dispersion, as well as additional shape metrics, such as fragmentation, or elongation, will be used to measures the spatial characteristics of rainfall fields. The application of various geometrics will offer a more complete understanding of spatial characteristics of TC rain fields. An extension of this study is to apply the spatial analysis method to characterize the rain fields of TCs in different ocean basins around the world. Spatial statistics methods like space-time cluster analysis and spatial regressions will be used to explore the spatial-temporal pattern of TCP and reveal the correlations of all geometrics to synoptic-scale environmental conditions (e.g. moisture, upper-level divergence, wind shear) for observations over ocean and over land, and land surface conditions (e.g. elevation and roughness). Although spatial variation is acknowledged to be of crucial importance within physical geography, there is a wide array of geospatial techniques that have yet to be utilized by weather and climate researchers. Moreover, although there have been numerous research that investigates the magnitude of precipitation of different precipitation datasets by statistical analysis, uncertainties associated with spatial patterns of rainfall as detected by different satellite and weather radar datasets are not well researched. I also plan to quantitatively compare the performance of spatial pattern

124

of TCP as detected by different gridded precipitation datasets, such as TMPA,

Integrated Multisatellite Retrievals for GPM (IMERG), and Stage IV radar data, which for example, could provide errors in pattern and location attributes when incorporating those datasets in distributed hydrologic modeling.

Second, heavy/extreme precipitation is more directly related to inland flooding.

An extended study is to examine storm-relative heavy rainfall thresholds are first identified based on a gridded precipitation dataset. A set of long-term precipitation datasets can also be identified as Parameter-elevation Regressions on Independent

Slopes Model (PRISM), Livneh daily CONUS near-surface gridded meteorological dataset (Livneh et al. 2014), and Climate Hazards Group InfraRed Precipitation with

Stations data (CHIRPS)(Funk et al. 2015). After identifying which long-term gridded precipitation dataset has better estimations of heavy rainfall values and patterns from

TCs, the location and area of heavy rainfall regions will be identified by using both absolute rainfall value and storm-relative heavy rainfall thresholds to reveal where these heavy rainfall regions are prone to occur. A large sample of tropical cyclones will be investigated to provide climatological links between the heavy precipitation areas with

TC attributes, environmental conditions, or topography. The results of this dissertation and other recent studies (Takakura et al. 2017; Matyas 2017) reveal the importance of a connection to moisture from the deep tropics to sustain high rain rates, thus the spatial patterns of moisture should be closely examined in future research.

Last, I plan to extend my dissertation research into the realm of social and environmental consequences of tropical cyclones. For example, I plan to use combined

TC rainfall and wind swaths to identify the exposure of the population, urbanized areas,

125

and the ecological system to TC conditions, which may be useful to local officials when determining where to concentrate and fund hazard mitigation measures. I also plan to combine hazard conditions with social and medical vulnerability to further explore the disaster risk. Another extension of my doctoral research is that the geometrics of TCP

(e.g. area, extent, and displacement, etc.) can be input into hazard models like FEMA's

HAZUS, which can improve the accuracy of risk assessment for flooding. The arrival time and duration of storm conditions can be better predicted, and this improved information could be disseminated to the general public in a format they can understand and use in their personal decision-making processes.

126

LIST OF REFERENCES

Andersen, T., and J. Shepherd. 2014. A global spatiotemporal analysis of inland tropical cyclone maintenance or intensification. International Journal of Climatology 34 (2):391-402.

Arndt, D., J. Basara, R. McPherson, B. Illston, G. McManus, and D. Demko. 2009. Observations of the overland and reintensification of tropical storm Erin (2007). Bulletin of the American Meteorological Society 90 (8):1079-1094.

Atallah, E., and L. Bosart. 2003. The extratropical transition and precipitation distribution of hurricane Floyd (1999). Monthly Weather Review 131 (6):1063-1081.

Atallah, E., L. Bosart, and A. Aiyyer. 2007. Precipitation distribution associated with landfalling tropical cyclones over the eastern United States. Monthly Weather Review 135 (6):2185-2206.

Barrett, B., E. Sanabia, S. Reynolds, J. Stapleton, and A. Borrego. 2016. Evolution of the upper tropospheric outflow in Hurricanes Iselle and Julio (2014) in the Navy Global Environmental Model (NAVGEM) analyses and in satellite and dropsonde observations. Journal of Geophysical Research-Atmospheres 121 (22):13273- 13286.

Beven, J. 2000. Tropical Cyclone Report Hurricane Dennis. NOAA/National Hurricane Center, Miami, Florida.

Beven, J. 2008. Tropical Cyclone Report Hurricane Felix. NOAA/National Hurricane Center, Miami, Florida.

———. 2012. Tropical Cyclone Report Tropical storm Arlene. NOAA/National Hurricane Center, Miami, Florida.

Beven, J. I. 2014. Tropical Cyclone Report Tropical Storm Dolly. NOAA/National Hurricane Center, Miami, Florida.

Blacutt, L., D. Herdies, L. de Goncalves, D. Vila, and M. Andrade. 2015. Precipitation comparison for the CFSR, MERRA, TRMM3B42 and Combined Scheme datasets in Bolivia. Atmospheric Research 163:117-131.

Braun, S., J. Sippel, and D. Nolan. 2012. The impact of dry midlevel air on hurricane intensity in idealized simulations with no mean flow. Journal of the Atmospheric Sciences 69 (1):236-257.

Brena-Naranjo, J., A. Pedrozo-Acuna, O. Pozos-Estrada, S. Jimenez-Lopez, and M. Lopez-Lopez. 2015. The contribution of tropical cyclones to rainfall in Mexico. Physics and Chemistry of the Earth 83-84:111-122.

127

Brun, J., and A. Barros. 2014. Mapping the role of tropical cyclones on the hydroclimate of the southeast United States: 2002-2011. International Journal of Climatology 34 (2):494-517.

Carrasco, C., C. Landsea, and Y. Lin. 2014. The influence of tropical cyclone size on Its intensification. Weather and Forecasting 29 (3):582-590.

Cecil, D. 2007. Satellite-derived rain rates in vertically sheared tropical cyclones. Geophysical Research Letters 34 (2): L02811.

Cerveny, R., and L. Newman. 2000. Climatological relationships between tropical cyclones and rainfall. Monthly Weather Review 128 (9):3329-3336.

Chen, L., Y. Li, and Z. Cheng. 2010. An overview of research and forecasting on rainfall associated with landfalling tropical cyclones. Advances in Atmospheric Sciences 27 (5):967-976.

Chen, S., J. Knaff, and F. Marks. 2006. Effects of vertical wind shear and storm motion on tropical cyclone rainfall asymmetries deduced from TRMM. Monthly Weather Review 134 (11):3190-3208.

Chen, Y., E. Ebert, K. Walsh, and N. Davidson. 2013. Evaluation of TRMM 3B42 precipitation estimates of tropical cyclone rainfall using PACRAIN data. Journal of Geophysical Research-Atmospheres 118 (5):2184-2196.

Corbosiero, K., M. Dickinson, and L. Bosart. 2009. The contribution of eastern North Pacific tropical cyclones to the rainfall climatology of the southwest United States. Monthly Weather Review 137 (8):2415-2435.

Corbosiero, K., and J. Molinari. 2002. The effects of vertical wind shear on the distribution of convection in tropical cyclones. Monthly Weather Review 130 (8):2110-2123.

———. 2003. The relationship between storm motion, vertical wind shear, and convective asymmetries in tropical cyclones. Journal of the Atmospheric Sciences 60 (2):366-376.

Croke, M. 2005. Examining planetary, synoptic and mesoscale features that enhance precipitation associated with landfalling tropical cyclones in North Carolina, Master thesis, North Carolina State University.

Czajkowski, J., K. Simmons, and D. Sutter. 2011. An analysis of coastal and inland fatalities in landfalling US hurricanes. Natural Hazards 59 (3):1513-1531.

DeMaria, M., and J. Kaplan.1999. An updated statistical hurricane intensity prediction scheme (SHIPS) for the Atlantic and eastern North Pacific basins. Weather and Forecasting 14 (3):326-337.

128

DeMaria, M., M. Mainelli, L. Shay, J. Knaff, and J. Kaplan. 2005. Further improvements to the statistical hurricane intensity prediction scheme (SHIPS). Bulletin of the American Meteorological Society 86 (9):1217-1217.

Demuth, J., M. DeMaria, and J. Knaff. 2006. Improvement of advanced microwave sounding unit tropical cyclone intensity and size estimation algorithms. Journal of Applied Meteorology and Climatology 45 (11):1573-1581.

Dunn, G., W. Davis, and P. Moore. 1955. Hurricane of 1955. Monthly Weather Review:315-326.

Dvorak, V. 1975. Tropical cyclone intensity analysis and forecasting from satellite imagery. Monthly Weather Review 103 (5):420-430.

Enfield, D., and E. Alfaro. 1999. The dependence of Caribbean rainfall on the interaction of the tropical Atlantic and Pacific oceans. Journal of Climate 12 (7):2093-2103.

Ensor, L., and S. Robeson. 2008. Statistical characteristics of daily precipitation: Comparisons of gridded and point datasets. Journal of Applied Meteorology and Climatology 47 (9):2468-2476.

Esnard, A., A. Sapat, and D. Mitsova. 2011. An index of relative displacement risk to hurricanes. Natural Hazards 59 (2):833-859.

Estrada, F., W. Botzen, and R. Tol. 2015. Economic losses from US hurricanes consistent with an influence from climate change. Nature Geoscience 8 (11): 880- 884.

Evans, C., K. Wood, S. Aberson, H. Archambault, S. Milrad, L. Bosart, K. Corbosiero, C. Davis, J. Dias Pinto, J. Doyle, C. Fogarty, T. J. Galarneau, C. Grams, K. Griffin, J. Gyakum, R. Hart, N. Kitabatake, H. Lentink, R. McTaggart- Cowan, W. Perrie, J. Quinting, C. Reynolds, M. Riemer, E. Ritchie, Y. Sun, and F. Zhang. 2017. The extratropical transition of tropical cyclones. Part I: cyclone evolution and direct impacts. Monthly Weather Review 145(11), 4318-4344.

Frank, W. 1977. The structure and energetics of the tropical cyclone I. Storm structure. Monthly Weather Review 105 (9):1119–1135.

Frank, W., and E. Ritchie. 2001. Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Monthly Weather Review 129 (9):2249-2269.

Franklin, J. 2008. Tropical Cyclone Report Hurricane Dean. NOAA/National Hurricane Center, Miami, Florida.

Franklin, J., and D. Brown. 2006. Tropical Cyclone Report Hurricane Emily. NOAA/National Hurricane Center, Miami, Florida.

129

Funk, C., P. Peterson, M. Landsfeld, D. Pedreros, J. Verdin, S. Shukla, G. Husak, J. Rowland, L. Harrison, A. Hoell, and J. Michaelsen. 2015. The climate hazards infrared precipitation with stations-a new environmental record for monitoring extremes. Scientific Data 2: 150066.

Groisman, P., R. Knight, and T. Karl. 2012. Changes in intense precipitation over the central United States. Journal of Hydrometeorology 13 (1):47-66.

Guiney, J., and M. Lawrence. 1999. Tropical Cyclone Report Hurricane Mitch. NOAA/National Hurricane Center, Miami, Florida.

Guo, Q., and C. Matyas. 2016. Comparing the spatial extent of Atlantic basin tropical cyclone wind and rain fields prior to land interaction. Physical Geography 37 (1):5- 25.

Hart, R., D. Chavas, and M. Guishard. 2016. The arbitrary definition of the current Atlantic major hurricane landfall drought. Bulletin of the American Meteorological Society 97 (5):713-722.

Hart, R., and J. Evans. 2001. A climatology of the extratropical transition of Atlantic tropical cyclones. Journal of Climate 14 (4):546-564.

Hellin, J., H. Haigh, and F. Marks. 1999. Rainfall characteristics of hurricane Mitch. Nature 399 (6734):316-316.

Hernández Ayala, J., D. Keellings, P. Waylen, and C. Matyas. 2017. Extreme floods and their relationship with tropical cyclones in Puerto Rico. Hydrological Sciences Journal 62 (13):2103-2119.

Hernández Ayala, J., and C. Matyas. 2016. Tropical cyclone rainfall over Puerto Rico and its relations to environmental and storm-specific factors. International Journal of Climatology 36 (5):2223-2237.

Higgins, R., and V. Kousky. 2013. Changes in observed daily precipitation over the United States between 1950-79 and 1980-2009. Journal of Hydrometeorology 14 (1):105-121.

Higgins, R., V. Silva, W. Shi, and J. Larson. 2007. Relationships between climate variability and fluctuations in daily precipitation over the United States. Journal of Climate 20 (14):3561-3579.

Hill, K., and G. Lackmann. 2009. Influence of environmental humidity on tropical cyclone size. Monthly Weather Review 137 (10):3294-3315.

Holland, G., and P. Webster. 2007. Heightened tropical cyclone activity in the North Atlantic: natural variability or climate trend? Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences 365 (1860):2695-2716.

130

Hou, A., R. Kakar, S. Neeck, A. Azarbarzin, C. Kummerow, M. Kojima, R. Oki, K. Nakamura, and T. Iguchi. 2014. The global precipitation measurement mission. Bulletin of the American Meteorological Society 95 (5):701-722.

Houze, R. 2010. Clouds in tropical cyclones. Monthly Weather Review 138 (2):293-344.

Huffman, G., R. Adler, D. Bolvin, G. Gu, E. Nelkin, K. Bowman, Y. Hong, E. Stocker, and D. Wolff. 2007. The TRMM multisatellite precipitation analysis (TMPA): Quasi- global, multiyear, combined-sensor precipitation estimates at fine scales. Journal of Hydrometeorology 8 (1):38-55.

Jagger, T., and J. Elsner. 2006. Climatology models for extreme hurricane winds near the United States. Journal of Climate 19 (13):3220-3236.

———. 2009. Modeling tropical cyclone intensity with quantile regression. International Journal of Climatology 29 (10):1351-1361.

———. 2012. Hurricane clusters in the vicinity of Florida. Journal of Applied Meteorology and Climatology 51 (5):869-877.

Jiang, H., J. Halverson, J. Simpson, and E. Zipser. 2008. On the differences in storm rainfall from Hurricanes Isidore and Lili. Part II: Water budget. Weather and Forecasting 23 (1):44-61.

Jiang, H., J. Halverson, and E. Zipser. 2008. Influence of environmental moisture on TRMM-derived tropical cyclone precipitation over land and ocean. Geophysical Research Letters 35(17): L17806.

Jiang, H., C. Liu, and E. Zipser. 2011. A TRMM-based tropical cyclone cloud and precipitation feature database. Journal of Applied Meteorology and Climatology 50 (6):1255-1274.

Jiang, H., E. Ramirez, and D. Cecil. 2013. Convective and rainfall properties of tropical cyclone inner cores and rainbands from 11 years of TRMM data. Monthly Weather Review 141 (2):431-450.

Jones, S., P. Harr, J. Abraham, L. Bosart, P. Bowyer, J. Evans, D. Hanley, B. Hanstrum, R. Hart, F. Lalaurette, M. Sinclair, R. Smith, and C. Thorncroft. 2003. The extratropical transition of tropical cyclones: Forecast challenges, current understanding, and future directions. Weather and Forecasting 18 (6):1052-1092.

Jones, T., and D. Cecil. 2007. SHIPS-MI forecast analysis of hurricanes Claudette (2003), Isabel (2003), and Dora (1999). Weather and Forecasting 22 (4):689-707.

Kaplan, J., and M. Demaria. 1995. A simple empirical-model for predicting the decay of tropical cyclone winds after landfall. Journal of Applied Meteorology 34 (11):2499- 2512.

131

Keim, B., and R. Muller. 2007. Spatiotemporal patterns and return periods of tropical storm and hurricane strikes from Texas to Maine. Journal of Climate 20 (14):3498- 3509.

Kimball, S. 2006. A modeling study of hurricane landfall in a dry environment. Monthly Weather Review 134 (7):1901-1918.

———. 2008. Structure and evolution of rainfall in numerically simulated landfalling Hurricanes. Monthly Weather Review 136 (10):3822-3847.

Kimball, S., and M. Mulekar. 2004. A 15-year climatology of North Atlantic tropical cyclones. Part I: Size parameters. Journal of Climate 17 (18):3555-3575.

Klein, P., P. Harr, and R. Elsberry. 2000. Extratropical transition of western North Pacific tropical cyclones: An overview and conceptual model of the transformation stage. Weather and Forecasting 15 (4):373-395.

Klotzbach, P., and W. Gray. 2003. Forecasting September Atlantic basin tropical cyclone activity. Weather and Forecasting 18 (6):1109-1128.

Knaff, J., C. Sampson, and G. Chirokova. 2017. A global statistical-dynamical tropical cyclone wind radii forecast scheme. Weather and Forecasting 32 (2):629-644.

Knapp, K., M. Kruk, D. Levinson, H. Diamond, and C. Neumann. 2010. The international best track archive for climate stewardship (IBTrACS) unifying tropical cyclone data. Bulletin of the American Meteorological Society 91 (3):363-376.

Knight, D., and R. Davis. 2007. Climatology of tropical cyclone rainfall in the southeastern United States. Physical Geography 28 (2):126-147.

———. 2009. Contribution of tropical cyclones to extreme rainfall events in the southeastern United States. Journal of Geophysical Research-Atmospheres 114, D23102.

Knutson, T., T. Delworth, K. Dixon, I. Held, J. Lu, V. Ramaswamy, M. Schwarzkopf, G. Stenchikov, and R. Stouffer. 2006. Assessment of twentieth-century regional surface temperature trends using the GFDL CM2 coupled models. Journal of Climate 19 (9):1624-1651.

Knutson, T., J. McBride, J. Chan, K. Emanuel, G. Holland, C. Landsea, I. Held, J. Kossin, A. Srivastava, and M. Sugi. 2010. Tropical cyclones and climate change. Nature Geoscience 3 (3):157-163.

Konrad, C., M. Meaux, and D. Meaux. 2002. Relationships between tropical cyclone attributes and precipitation totals: Considerations of scale. International Journal of Climatology 22 (2):237-247.

132

Konrad, C., and L. Perry. 2010. Relationships between tropical cyclones and heavy rainfall in the Carolina region of the USA. International Journal of Climatology 30 (4):522-534.

Kovach, M., and C. Konrad. 2014. The spatial distribution of tornadoes and high wind impacts associated with inland-moving tropical cyclones in the southeastern United States. Physical Geography 35 (3):245-271.

Kruk, M., E. Gibney, D. Levinson, and M. Squires. 2010. A climatology of inland winds from tropical cyclones for the eastern United States. Journal of Applied Meteorology and Climatology 49 (7):1538-1547.

Kunkel, K., D. Easterling, D. Kristovich, B. Gleason, L. Stoecker, and R. Smith. 2010. Recent increases in U.S. heavy precipitation associated with tropical cyclones. Geophysical Research Letters 37(24): L24706.

Kunkel, K., T. Karl, D. Easterling, K. Redmond, J. Young, X. Yin, and P. Hennon. 2013. Probable maximum precipitation and climate change. Geophysical Research Letters 40 (7):1402–1408.

Larson, J., Y. Zhou, and R. Higgins. 2005. Characteristics of landfalling tropical cyclones in the United States and Mexico: Climatology and interannual variability. Journal of Climate 18 (8):1247-1262.

Lau, K., and H. Wu. 2011. Climatology and changes in tropical oceanic rainfall characteristics inferred from Tropical Rainfall Measuring Mission (TRMM) data (1998-2009). Journal of Geophysical Research-Atmospheres 116(D17): D17111.

Lau, W., and Y. Zhou. 2012. Observed recent trends in tropical cyclone rainfall over the North Atlantic and the North Pacific. Journal of Geophysical Research- Atmospheres 117(D3): D03104.

Lawrence, M., and T. Kimberlain. 2001. Tropical Cyclone Report Tropical storm Bret. NOAA/National Hurricane Center, Miami, Florida.

Li, H., Y. Wei, and K. Korinek. 2017. Modelling urban expansion in the transitional Greater Mekong Region. Urban Studies.

Lin, Y., M. Zhao, and M. Zhang. 2015. Tropical cyclone rainfall area controlled by relative sea surface temperature. Nature Communications 6, 6591.

Livneh, B., E. Rosenberg, C. Lin, B. Nijssen, V. Mishra, K. Andreadis, E. Maurer, and D. Lettenmaier. 2014. A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States: Update and extensions. Journal of Climate 27 (1):477-486.

133

Lonfat, M., F. Marks, and S. Chen. 2004. Precipitation distribution in tropical cyclones using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager: A global perspective. Monthly Weather Review 132 (7):1645-1660.

Lonfat, M., R. Rogers, T. Marchok, and F. Marks. 2007. A parametric model for predicting hurricane rainfall. Monthly Weather Review 135 (9):3086-3097.

Maggioni, V., P. Meyers, and M. Robinson. 2016. A review of merged high-resolution satellite precipitation product accuracy during the Tropical Rainfall Measuring Mission (TRMM) Era. Journal of Hydrometeorology 17 (4):1101-1117.

Mainelli, M., M. DeMaria, L. Shay, and G. Goni. 2008. Application of oceanic heat content estimation to operational forecasting of recent Atlantic category 5 hurricanes. Weather and Forecasting 23 (1):3-16.

Maloney, E., and D. Hartmann. 2000. Modulation of hurricane activity in the Gulf of Mexico by the Madden-Julian oscillation. Science 287 (5460):2002-2004.

Mann, H. 1945. Nonparametric tests against trend. Econometrica 13 (3):245-259.

Matyas, C. 2007. Quantifying the shapes of US landfalling tropical cyclone rain shields. Professional Geographer 59 (2):158-172.

Matyas, C. 2008. Shape measures of rain shields as indicators of changing environmental conditions in a landfalling tropical storm. Meteorological Applications 15 (2):259-271.

———. 2009. A spatial analysis of radar reflectivity regions within Hurricane Charley (2004). Journal of Applied Meteorology and Climatology 48 (1):130-142.

———. 2010a. A geospatial analysis of convective rainfall regions within tropical cyclones after landfall. International Journal of Applied Geospatial Research 1 (2):71-91.

———. 2010b. Associations between the size of hurricane rain fields at landfall and their surrounding environments. Meteorology and Atmospheric Physics 106 (3- 4):135-148.

———. 2013. Processes influencing rain-field growth and decay after tropical cyclone landfall in the United States. Journal of Applied Meteorology and Climatology 52 (5):1085-1096.

———. 2014. Conditions associated with large rain-field areas for tropical cyclones landfalling over Florida. Physical Geography 35 (2):93-106.

134

———. 2017. Comparing the spatial patterns of rainfall and atmospheric moisture among tropical cyclones having a track similar to Hurricane Irene (2011). Atmosphere 8 (9), 165.

Matyas, C., and M. Cartaya. 2009. Comparing the rainfall patterns produced by Hurricanes Frances (2004) and Jeanne (2004) over Florida. Southeastern Geographer 49 (2):132-156.

Maxwell, J., J. Ortegren, P. Knapp, and P. Soule. 2013. Tropical cyclones and drought amelioration in the Gulf and southeastern coastal United States. Journal of Climate 26 (21):8440-8452.

McGroddy, M., D. Lawrence, L. Schneider, J. Rogan, I. Zager, and B. Schmook. 2013. Damage patterns after Hurricane Dean in the southern Yucatan: Has human activity resulted in more resilient forests? Forest Ecology and Management 310:812-820.

Mendelsohn, R., K. Emanuel, S. Chonabayashi, and L. Bakkensen. 2012. The impact of climate change on global tropical cyclone damage. Nature Climate Change 2 (3):205-209.

Merrill, R. 1984. A comparison of large and small tropical cyclones. Monthly Weather Review 112 (7):1408-1418.

———. 1988. Characteristics of the upper-tropospheric environmental flow around hurricanes. Journal of the Atmospheric Sciences 45 (11):1665-1677.

Mueller, K., M. DeMaria, J. Knaff, J. Kossin, and T. Vonder Haar. 2006. Objective estimation of tropical cyclone wind structure from infrared satellite data. Weather and Forecasting 21 (6):990-1005.

Nogueira, R., and B. Keim. 2010. Annual volume and area variations in tropical cyclone rainfall over the eastern United States. Journal of Climate 23 (16):4363-4374.

———. 2011. Contributions of Atlantic tropical cyclones to monthly and seasonal rainfall in the eastern United States 1960-2007. Theoretical and Applied Climatology 103 (1-2):213-227.

Ord, J., and A. Getis. 1995. Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis 27 (4):286-306.

Papin, P. 2017. A climatology of Central American gyres. Master thesis, University at Albany, State University of New York.

Pasch, R., E. Blake, H. I. Cobb, and D. Roberts. 2006. Tropical Cyclone Report Hurricane Wilma. NOAA/National Hurricane Center, Miami, Florida.

135

Pasch, R., and D. Roberts. 2006. Tropical Cyclone Report Hurricane Stan. NOAA/National Hurricane Center, Miami, Florida.

Pedrozo-Acuna, A., J. Rodriguez-Rincon, M. Arganis-Juarez, R. Dominguez-Mora, and F. Gonzalez Villareal. 2015. Estimation of probabilistic flood inundation maps for an extreme event: Panuco River, Mexico. Journal of Flood Risk Management 8 (2):177-192.

Pielke, R. 2007. Future economic damage from tropical cyclones: sensitivities to societal and climate changes. Philosophical Transactions of the Royal Society a- Mathematical Physical and Engineering Sciences 365 (1860):2717-2729.

Pielke, R., J. Rubiera, C. Landsea, M. Fernandez, and R. Klein. 2003. Hurricane Vulnerability in Latin America and the Caribbean: Normalized damage and loss potentials. Natural Hazards Review 4 (3):101-114.

Powell, M. 1982. The transition of the Hurricane Frederic boundary-layer wind field from the open Gulf of Mexico to landfall. Monthly Weather Review 110 (12):1912-1932.

Powell, M. 1987. Changes in the low-level kinematic and thermodynamic structure of Hurricane Alicia (1983). Monthly Weather Review 115 (1):75-99.

Prat, O., and B. Nelson. 2013. Precipitation contribution of tropical cyclones in the southeastern United States from 1998 to 2009 using TRMM satellite data. Journal of Climate 26 (3):1047-1062.

———. 2016. On the link between tropical cyclones and daily rainfall extremes derived from global satellite observations. Journal of Climate 29 (17):6127-6135.

Quiring, S., A. Schumacher, C. Labosier, and L. Zhu. 2011. Variations in mean annual tropical cyclone size in the Atlantic. Journal of Geophysical Research-Atmospheres 116.

Rappaport, E. 2000. Loss of life in the United States associated with recent Atlantic tropical cyclones. Bulletin of the American Meteorological Society 81 (9):2065- 2073.

———. 2014. Fatalities in the United States from Atlantic tropical cyclones. Bulletin of the American Meteorological Society 95 (3):341-346.

Rezapour, M., and T. Baldock. 2014. Classification of hurricane hazards: The importance of rainfall. Weather and Forecasting 29 (6):1319-1331.

Rodgers, E., and H. Pierce. 1995. Environmental influence on Typhoon-Bobbie precipitation distribution. Journal of Applied Meteorology 34 (11):2513-2532.

136

Romero-Lankao, P., J. Smith, D. Davidson, N. Diffenbaugh, P. Kinney, P. Kirshen, P. Kovacs, and L. Villers Ruiz. 2014. Climate Change 2014: Impacts, adaptation, and vulnerability. Part B: Regional aspects. Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, 1439-1498. Cambridge, United Kingdom and New York, NY, USA.

Santer, B., T. Wigley, P. Gleckler, C. Bonfils, M. Wehner, K. AchutaRao, T. Barnett, J. Boyle, W. Bruggemann, M. Fiorino, N. Gillett, J. Hansen, P. Jones, S. Klein, G. Meehl, S. Raper, R. Reynolds, K. Taylor, and W. Washington. 2006. Forced and unforced ocean temperature changes in Atlantic and Pacific tropical cyclogenesis regions. Proceedings of the National Academy of Sciences of the United States of America 103 (38):13905-13910.

Shapiro, L. 1983. The asymmetric boundary-layer flow under a translating hurricane. Journal of the Atmospheric Sciences 40 (8):1984-1998.

Smith, A., and R. Katz. 2013. US billion-dollar weather and climate disasters: data sources, trends, accuracy and biases. Natural Hazards 67 (2):387-410.

Stewart, S. 2013. Tropical Storm Report Tropical Storm Barry. NOAA/National Hurricane Center, Miami, Florida.

Sugg, A. 1968. Beneficial aspects of tropical cyclone. Journal of Applied Meteorology 7 (1):39-45.

Takakura, T., R. Kawamura, T. Kawano, K. Ichiyanagi, M. Tanoue, and K. Yoshimura. 2017. An estimation of water origins in the vicinity of a tropical cyclone’s center and associated dynamic processes. Climate Dynamics 50 (1-2):555–569.

Trenberth, K., and J. Fasullo. 2007. Water and energy budgets of hurricanes and implications for climate change. Journal of Geophysical Research-Atmospheres 112 (D23):D23107.

Ueno, M. 2007. Observational analysis and numerical evaluation of the effects of vertical wind shear on the rainfall asymmetry in the typhoon inner-core region. Journal of the Meteorological Society of Japan 85 (2):115-136.

Vigh, J., J. Knaff, and W. Schubert. 2012. A Climatology of hurricane eye formation. Monthly Weather Review 140 (5):1405-1426.

Villarini, G., R. Goska, J. Smith, and G. Vecchi. 2014. North Atlantic tropical cyclones and U.S. flooding. Bulletin of the American Meteorological Society 95 (9):1381- 1388.

Villarini, G., and J. Smith. 2010. Flood peak distributions for the eastern United States. Water Resources Research 46(6):W06504.

137

Villarini, G., J. Smith, M. Baeck, T. Marchok, and G. Vecchi. 2011. Characterization of rainfall distribution and flooding associated with US landfalling tropical cyclones: Analyses of Hurricanes Frances, Ivan, and Jeanne (2004). Journal of Geophysical Research-Atmospheres 116(D23): D23116.

Villarini, G., J. Smith, R. Vitolo, and D. Stephenson. 2013. On the temporal clustering of US floods and its relationship to climate teleconnection patterns. International Journal of Climatology 33 (3):629-640.

Visser, H., A. Petersen, and W. Ligtvoet. 2014. On the relation between weather-related disaster impacts, vulnerability and climate change. Climatic Change 125 (3-4):461- 477.

Wang, C., and D. Enfield. 2003. A further study of the tropical Western Hemisphere warm pool. Journal of Climate 16 (10):1476-1493.

Wang, C., and S. Lee. 2007. Atlantic warm pool, Caribbean low-level jet, and their potential impact on Atlantic hurricanes. Geophysical Research Letters 34 (2): L02703.

Whitehead, J. 2003. One million dollars per mile? The opportunity costs of Hurricane evacuation. Ocean & Coastal Management 46 (11-12):1069-1083.

Wingo, M., and D. Cecil. 2010. Effects of vertical wind shear on tropical cyclone precipitation. Monthly Weather Review 138 (3):645-662.

Wright, D., T. Knutson, and J. Smith. 2015. Regional climate model projections of rainfall from US landfalling tropical cyclones. Climate Dynamics 45 (11-12):3365- 3379.

Wu, L., H. Su, R. Fovell, B. Wang, J. Shen, B. Kahn, S. Hristova-Veleva, B. Lambrigtsen, E. Fetzer, and J. Jiang. 2012. Relationship of environmental relative humidity with North Atlantic tropical cyclone intensity and intensification rate. Geophysical Research Letters 39(20): L20809.

Xu, G., T. Osborn, and A. Matthews. 2017. Moisture transport by Atlantic tropical cyclones onto the North American continent. Climate Dynamics 48 (9-10):3161- 3182.

Xu, W., H. Jiang, and X. Kang. 2014. Rainfall asymmetries of tropical cyclones prior to, during, and after making landfall in South China and Southeast United States. Atmospheric Research 139:18-26.

Yaukey, P. 2011. Wind speed changes of North Atlantic tropical cyclones preceding landfall. Journal of Applied Meteorology and Climatology 50 (9):1913-1921.

138

Yu, Z., Y. Wang, and H. Xu. 2015. Observed rainfall asymmetry in tropical cyclones making landfall over China. Journal of Applied Meteorology and Climatology 54 (1):117-136.

Yu, Z., H. Yu, P. Chen, C. Qian, and C. Yue. 2009. Verification of tropical cyclone- related satellite precipitation estimates in mainland China. Journal of Applied Meteorology and Climatology 48 (11):2227-2241.

Zagrodnik, J., and H. Jiang. 2013. Investigation of PR and TMI Version 6 and Version 7 rainfall algorithms in landfalling tropical cyclones relative to the NEXRAD Stage-IV multisensor precipitation estimate dataset. Journal of Applied Meteorology and Climatology 52 (12):2809-2827.

Zandbergen, P. 2009. Exposure of US counties to Atlantic tropical storms and hurricanes, 1851-2003. Natural Hazards 48 (1):83-99.

Zhang, F., and Y. Weng. 2015. Predicting hurricane intensity and associated hazards: A five-year real-time forecast experiment with assimilation of airborne doppler radar observations. Bulletin of the American Meteorological Society 96 (1):25-33.

Zhou, Y., W. Lau, and G. Huffman. 2015. Mapping TRMM TMPA into average recurrence interval for monitoring extreme precipitation events. Journal of Applied Meteorology and Climatology 54 (5):979-995.

Zhou, Y., and C. Matyas. 2017. Spatial characteristics of storm-total rainfall swaths associated with tropical cyclones over the eastern United States. International Journal of Climatology 37 (S1):557–569.

Zhu, L., and S. Quiring. 2013. Variations in tropical cyclone precipitation in Texas (1950 to 2009). Journal of Geophysical Research-Atmospheres 118 (8):3085-3096.

Zhu, L., S. Quiring, and K. Emanuel. 2013. Estimating tropical cyclone precipitation risk in Texas. Geophysical Research Letters 40 (23):6225-6230.

Zick, S., and C. Matyas. 2015. Tropical cyclones in the North American Regional Reanalysis: The impact of satellite-derived precipitation over ocean. Journal of Geophysical Research-Atmospheres 120 (17):8724-8742.

———. 2016. A Shape metric methodology for studying the evolving geometries of synoptic-scale precipitation patterns in tropical cyclones. Annals of the American Association of Geographers 106 (6):1217-1235.

139

BIOGRAPHICAL SKETCH

Yao Zhou is a physical geographer that focuses on extreme weather and climate events in here research at the Department of Geography at the University of Florida.

Yao Zhou holds a Bachelor of Science in geographic information system from Wuhan

University, China in 2009. Yao also has a Master of Science degree in physical geography from Beijing Normal University, China, 2012. At this institution, Yao worked in several projects that incorporated natural hazard risk analysis and mapping. After graduating from Beijing Normal University in 2012, Yao entered the PhD program at

Department of Geography at the University of Florida and worked with her advisor, Dr.

Corene Matyas.

At the University of Florida, Yao worked on her dissertation entitled “Estimating

Spatial Characteristics of Precipitation Associated with Tropical Cyclones Originating over the North Atlantic”. The second chapter of dissertation has been published in

International Journal of Climatology. In 2017, Yao received the Supplemental Retention

Scholarship from Graduate School, to aid with research and dissertation in her final year of study. Yao taught several courses at the Department of Geography, including physical geography lab, GIS lab, and maps and graphs. Yao also worked as a research assistant with Dr. Matyas on a project funded by the National Science Foundation. Yao graduated with her PhD in geography with a certificate in applied atmospheric science in Spring 2018 and will work as a Postdoc at the University of Central Florida after graduation.

140