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2019

A Climatology of U.S. Tropical Cyclone Rainfall, Its Use in a Statistical Forecasting Technique and an Analysis of Global Forecast System Tropical Cyclone Rainfall FTriostarne J. cHallst Environments

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COLLEGE OF ARTS & SCIENCES

A CLIMATOLOGY OF U.S. TROPICAL CYCLONE RAINFALL, ITS USE IN A

STATISTICAL FORECASTING TECHNIQUE AND AN ANALYSIS OF GLOBAL

FORECAST SYSTEM TROPICAL CYCLONE RAINFALL FORECAST ENVIRONMENTS

TRISTAN HALL

A Dissertation submitted to the Department of Earth, Ocean, and Atmospheric Science in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy

2019

Henry E. Fuelberg Professor Directing Dissertation

David Van Winkle University Representative

Robert E. Hart Committee Member

Vasubandhu Misra Committee Member

Philip Sura Committee Member

The Graduate School has veriﬁed and approved the above-named committee members, and certiﬁes that the dissertation has been approved in accordance with university requirements.

ii To Catherine and Ainsley.

iii ACKNOWLEDGMENTS

This dissertation could not have been completed without the help and guidance of Dr. Henry Fuelberg. He is a craftsman of words and logical thought. Additionally, this research could not have been completed without the help of Dr. Bob Hart. His knowledge of tropical cyclones is unmatched. I thank them both immensely for their acceptance of me to pursue my Ph.D. I thank my additional committee members, Drs. Vasu Misra and Philip Sura, for taking the time to review this work and ensure its standards match those of what is expected from a Florida State Meteorologist. Thank you to Dr. Van Winkle for agreeing to be a University Representative. This work originally began as a NOAA CSTAR Grant (NA13NWS4680005). I am grateful for the support NOAA provided to complete this work. Thank you to my friends and colleagues past and present at Florida State University, especially Matthew DelCiampo, Heather Paudler, Max Marchand, Antonio Riggi, Dan Halperin, and “Steve Holt!.” These stand-up individuals were a joy to be around and provided invaluable feedback on any topic. I would also like to thank the various communities I interacted with while at Florida State: COGS members, Hart Lab members, Fuelberg Lab members, and Musicology students. Thank you for the good times and challenging discussions. A special thank you goes to Dr. Peter Souléwho gave daily weather briefings to his classes while I was a geography student at Appalachian State University. Without these briefings and discussions, I would not have pursued a graduate education in meteorology. I’d like to thank my parents, Pattie and David, for raising such a stand-up individual, and my parents-in-law, Geoff and Mary Ann for the support during this process. Thank you to my brothers, Nicholas and A.J., and my sisters-in-law, Rachel and Kaili, for the food, support, and childcare services they provided during the last days of this. Finally, I never knew I could have such love in my heart for an individual until my daughter, Ainsley Clare Hall, was born on 22 March 2018 while I was writing this dissertation. I’m sorry for the time I had to spend away from you while I finished this work. Additionally, to her mother and my partner, Catherine: you are an amazing mother and a wonderful support system. Thank you for picking me up when I needed it and supporting me through this.

iv TABLE OF CONTENTS

List of Tables ...... vii List of Figures ...... ix Abstract ...... xv

1 Introduction and Motivation 1

2 Background 5 2.1 Rainfall characteristics ...... 5 2.2 Quantitative precipitation forecast models ...... 8 2.2.1 Legacy models ...... 8 2.2.2 The Rainfall-Climatology and Persistence Model ...... 13 2.2.3 The Areal Tropical Rainfall Potential Technique ...... 14 2.2.4 The Parametric Hurricane Rainfall Model ...... 14 2.2.5 The Ensemble Tropical Rainfall Potential ...... 15 2.2.6 Numerical weather prediction models ...... 16

3 Data & Methodology 19 3.1 Data ...... 19 3.1.1 The Global Forecast System ...... 21 3.1.2 Stage IV data ...... 24 3.2 Methodology ...... 25 3.2.1 Development of the Stage IV rainfall statistical dataset ...... 25 3.2.2 Development of the statistical rainfall forecasts ...... 28 3.3 Veriﬁcation metrics and determination of forecast skill ...... 31 3.3.1 GFS environmental conditions ...... 33

4 Results 35 4.1 Regional and U.S. Stage IV TC rainfall composite analysis ...... 35 4.1.1 U.S. rainfall composites ...... 35 4.1.2 Selected regional composites ...... 44 4.1.3 Stage IV rainfall summary ...... 50 4.2 Example forecasts ...... 52 4.2.1 Stage IV statistical model forecast: Skillful ...... 53 4.2.2 Stage IV statistical model forecast: Not skillful ...... 61 4.3 Model veriﬁcation ...... 67 4.3.1 Storm-by-Storm approach ...... 68 4.3.2 Forecast-by-Forecast approach ...... 72

v 5 Analysis of Errors and Possible Improvements to the Statistical Model 77 5.1 Theoretical maximum skill of the statistical model ...... 77 5.2 Radial distributions ...... 80 5.3 Environmental analysis ...... 85 5.3.1 Mean sea level pressure and 500 hPa composites ...... 86 5.3.2 Baroclinic processes ...... 95 5.3.3 Eddy ﬂux convergence ...... 98 5.3.4 Upper-level winds ...... 101 5.3.5 Environmental summary ...... 104

6 Summary and Conclusions 107

References ...... 118 Biographical Sketch ...... 128

vi LIST OF TABLES

1 Summary of the models presented in Section 2.2 and their individual strengths and weaknesses...... 18

2 Total number of storms and 6-h locations from HURDAT2, i.e., Best Track locations (BTK) for earth-, motion-, and shear-relative coordinate systems. Numbers of six- hour locations are in brackets...... 21

3 Global Forecast System (GFS) resolution updates and grid spacing of output/working ﬁles for years used in this study. The developmental dataset is 2004 – 2012. The test years are 2013 – 2016. The “Dates Covered” column indicates the period available for thatyear...... 22

4 The number of 6 h Best Track locations and landfalls for the regions shown in Fig. 2. The number of landfalls refers to the number landfalls within the continental United States landfalls, not any landfalls on islands beyond the coastline that are included in the Best Track dataset...... 27

5 TC intensity categories. Counts of storms for each category are in Table 6. For the Strong Hurricane category (HU1), 53% were Cat 2, 16% Cat 3, 26% Cat 4, and 5% Cat5...... 28

6 Intensity and shear categories for each region’s rainfall composites after combination (e.g., from Table 5) to produce robust datasets. Each categories’ number of 6-hourly time steps and unique storms (shown in parentheses) are given...... 29

7 The nine methodologies for the Stage IV statistical rainfall model, plus R-CLIPER. Each method (except R-CLIPER) uses either the full composite or the regional composites (resulting in 18 forecasts)...... 31

8 Fractions Skill Score (FSS) categories, mean FSS for each category as well as the 95% conﬁdence interval, number of 72-h forecasts, and counts of unique storms within each category...... 34

9 Forecast and Best Track storm intensities [kt], regions (number identifier and name), shear [m s−1], and Saffir-Simpson categories for the skillful and not-skillful example forecasts discussed in Sections 4.2.1 and 4.2.2. Colors indicate Saffir-Simpson category (Blue: TS; violet: TD) for forecast intensity and correspond to colors shown in Figures. 54

10 Fractions Skill Score (FSS) for all thresholds of the regional, shear-relative method using the shear magnitude method (REG-SS; Table 7), R-CLIPER (RCP), and the Global Forecast System (GFS) for the skillful 72-h rainfall forecast of TS Ana (2015; Fig. 17) beginning at 1200 UTC 8 May 2015 and the less-skilled forecast of TS Andrea

vii (2013; Fig. 22) beginning at 1200 UTC 6 June 2013. The 95% conﬁdence interval for all thresholds is shown in the Average ﬁeld...... 55

viii LIST OF FIGURES

1 Statistics of storm-related fatalities. Recreated from Rappaport (2000, 2014)...... 2

2 The seven geographical regions. TC landfall locations are green dots for 2004 – 2012. Other 6-h locations within 300 km (grey dashed buﬀer) of the U.S. coast are shown for comparison (grey dots)...... 20

3 Example of masking technique used to limit Stage IV observations to 150 km from a coastal radar. Example shown is for TC Fay (2008). The full Stage IV dataset is shown in (a), a zoomed version is in (b), and the ﬁnal masked data is in (c)...... 26

4 Full domain Stage IV rain rate composites [in. 6 h−1] for years 2004 – 2012 for earth- relative (a), storm motion-relative (b), and shear-relative (c) coordinates with range rings shown every 200 km starting at 100 km. The latitude/longitude density (counts per 1 × 1 deg grid box) is shown in the bottom right panel (d)...... 36

5 Fractional histogram (deﬁned as the count within a bin divided by the total count of the distribution) of intensity by minimum MSLP [hPa] (line) and storm intensity [kt] (bars) for all 6-hourly Best Track storm locations within 300 km of the U.S. coastline between 2004 – 2012...... 37

6 Fractional histogram (as deﬁned in Fig. 5) of shear magnitude [m s−1] and heading [degrees from North]. The line shows shear magnitude while the bars show shear heading...... 38

7 Stage IV rain rate [in. 6 h−1] composites based on TC intensity categories: tropical depression (TD0), weak tropical storm (TS0), strong tropical storm (TS1), weak hurricane (HU0), and strong hurricane (HU1). TC intensity categories are further deﬁned in Table 5. The left panels show rainfall composites in earth-relative coordinates while the right panels show shear-relative. Range rings start at 100 km and are at intervals of 200 km...... 40

8 Azimuthally-averaged Stage IV rain rate [in. 6 h−1] with 95% conﬁdence intervals (bars) by storm intensity for all storms in the development dataset (2004 – 2012). Storm intensity categories are deﬁned in Table 5. The bin size for distance from storm center is 10 km...... 42

9 Stage IV rain rate [in. 6 h−1] for the three shear magnitude categories: Weak (< 5 m s−1); Moderate (5 – 10 m s−1); and Strong (> 10 m s−1) in earth- (top) and shear- (bottom) relative reference frames. The shear magnitude categories were based on Cecil (2007) and Wingo and Cecil (2010)...... 43

ix 10 Same as in Fig. 8 but partitioned by shear magnitude (Weak: < 5 m s−1, Moderate: 5 – 10 m s−1, and Strong: > 10 m s−1) with 95% conﬁdence intervals (bars). Shear categories are based on Cecil (2007) and Wingo and Cecil (2010)...... 45

11 Regional Stage IV rain rates [in. 6 h−1] for all storm intensities and all shear magnitudes in an earth-relative reference frame (AE; deﬁned in Table 7) for the seven geographic regions in the study. Six-hour counts can be found in Table 6...... 46

12 Median (solid lines) and Inter-Quartile Range (shaded regions, where the lower quartile is the bottom and the upper quartile is the top) for shear (blue) and TC intensity (orange) [kt]. Values are given for each of the seven geographic regions (Fig. 2) and for the composite of all regions (denoted ALL)...... 47

13 Hurricane Hermine (2016) Stage IV 6-h rainfall [in.] and GOES-13 IR (Band 4) satellite images while in the NWFL region (a; 65 kt Cat 1, 0600 UTC 02 Sept. 2016) and the MIDATL (b; 55 kt TS, 1200 UTC 03 Sept. 2016) region. Six-hourly Best Track locations are shown by black dots. Shear direction is shown by the double line pointing away from the storm at the 6-h best track location...... 48

14 Synoptic environment for Hurricane Hermine (2016) corresponding to the time in Fig. 13b (1200 UTC 03 Sept. 2016). Left panel (a) shows 850 hPa vorticity [s−1 × 10−5] and height [dam], while the right panel (b) shows 500 hPa RH [%] and height [dam]. . 49

15 As in Fig. 11 (Regional Stage IV rain rates [in. 6 h−1]), but in the shear-relative reference frame (Table 7) for the seven geographic regions. Six-hour counts can be found in Table 6...... 50

16 Scatterplot of Global Forecast System (GFS) Fractions Skill Score (FSS) and the statistical model (REG-SS; Table 7) FSS for the test dataset (2013 – 2016) using the 50 km ROI and 50-mm threshold. The blue dashed line shows the linear best ﬁt between the two FSS distributions as indicated by the equation and R2 in the bottom right...... 52

17 72-h rainfall forecast accumulation [in.] for TS Ana (2015) using the Stage IV statistical model. The regional, shear-relative using shear-magnitude composite (REG-SS Table 7 in text) was used. The forecast was initialized at 1200 UTC 8 May 2015. The date, intensity [kt], shear [m s−1], Saffir-Simpson scale category (shown as different colors for the different categories), and region the algorithm assigned (indicated by a numeric value as well as the name of the region) are shown in Table 9 corresponding 6-h locations within the accumulation plot. Best Track (HURDAT2) storm locations are shown as square markers. Start points are indicated by an “A” and the 72-h forecast point and its corresponding Best Track point are indicated by a “Z.” Shear vectors are indicated by arrows. Finally, unverified rainfall accumulations (over water) are indicated by the dashed contours. Maximum forecast accumulation is shown in the bottom right...... 56

x 18 Stage IV rain rate composites [in. 6 h−1] used in the forecast shown in Fig. 17. Weak (left), moderate (middle), and strong (right) shear relative rain rate based on shear magnitude (SS; Table 7) for the Mid-Atlantic region...... 57

19 Stage IV 72 h observed rainfall accumulation [in.] corresponding to the forecast in Fig. 17. GFS forecast 6-h locations are shown by circles (what are used as the forecast locations in Fig. 17) and corresponding Best Track locations are shown as squares. See Table 9 for veriﬁed 6-h intensities, regions, and Saﬃr-Simpson categories. Stage IV rainfall amounts are the sum of accumulations at each 6-h forecast during the total 72 h period. Maximum Stage IV accumulation is shown in the bottom right...... 58

20 R-CLIPER forecast 72 h rainfall accumulation [in.] corresponding to the forecast in Fig. 17 and the Stage IV observations in Fig. 19. GFS track is shown by circles, and Best Track is shown with squares. Dashed contoured rainfall accumulations over water were not veriﬁed. Maximum forecast amount is shown in the bottom right. See Table 9 for 6-h intensity and region values...... 59

21 Global Forecast System (GFS) 72 h rainfall accumulation forecast [in.] corresponding to the statistical model forecast in Fig. 17 and the Stage IV observations in Fig. 19. GFS track is shown by circles, and Best Track is shown with squares. Dashed contoured rainfall accumulations over water were not veriﬁed. Maximum forecast amount is shown in the bottom right. See Table 9 for 6-h intensity and region values...... 60

22 REG-SS (Table 7) forecast 72 h rainfall accumulation for TS Andrea (2013) as in Fig. 17. The forecast was initialized at 1200 UTC 6 June 2013...... 62

23 Strong shear, shear-relative regional rain rate composites [in. 6 h−1] for the four regions used to create the TS Andrea (2013) 72 h forecast shown in Fig. 22: NWFL, SATL, MIDATL, and NATL...... 63

24 Stage IV 72 h observed rainfall accumulation [in.] as in Fig. 19 but for the TS Andrea (2013) whose forecast is shown in Fig. 22...... 64

25 R-CLIPER 72 h rainfall accumulation forecast [in.] as in Fig. 20, but for TS Andrea (2013). The corresponding statistical model forecast and Stage IV observations are shown in Figs. 22 and 24, respectively...... 65

26 Global Forecast System (GFS) 72 h rainfall accumulation forecast [in.] as in Fig. 21, but for TS Andrea (2013). Forecasts and observations are shown in Figs. 22 and 24, respectively...... 66

27 Average Fractions Skill Score (FSS) per threshold for all storms within the test dataset on a storm-by-storm basis (see Section 4.3 introduction for details) for the full composite forecast methods (ALL; a) and the regional composite methods (REG; b). The individual methods are described in the text and in Table 7...... 69

xi 28 As in Fig. 27, but for those methods and thresholds whose means are statistically diﬀerent from R-CLIPER (RCP; Eq. 4.1). R-CLIPER is shown on both plots as a reference. Method label location is irrespective of FSS...... 70

29 Average rank (blue bars) with 95% conﬁdence intervals (yellow lines) of all thresholds combined for all forecast models/methods on a storm-by-storm basis (described in Section 4.3.1.2) with 95% conﬁdence intervals. Methods/Models are arranged by increasing rank (decreasing skill) from left to right. Regional (REG) and full (ALL) composites used for the statistical method (Table 7) are indicated on the abscissa by abbreviations...... 71

30 As in Fig. 27, but on a forecast-by-forecast basis...... 72

31 As in Fig. 28, but on a forecast-by-forecast basis...... 74

32 Mean Fractions Skill Score (FSS; dots) on a forecast-by-forecast basis for each method and model with 95% conﬁdence intervals (bars). Scores are aligned from best to worst with R-CLIPER (RCP) and the Global Forecast System (GFS) model scores shown in the left two positions regardless of score for reference. Scores from the regional method (REG; Table 7) are shown...... 75

33 As in Fig. 29, but on a forecast-by-forecast basis...... 76

34 As in Fig. 32, but for “perfect” forecasts which used veriﬁed shear, motion (track), and intensity values from SHIPS and Best Track analyses...... 78

35 Diﬀerence in Fractions Skill Score (FSS) between Forecasts and Best Track “Forecasts” (those that use veriﬁed 6-h locations, intensity, and shear values; BTK - FCST) for all statistical methods and R-CLIPER...... 79

36 Cross-track radial storm-total distribution of rainfall [in.] for the ALL (a) and REG (b) forecast methods. The distribution is calculated by summing the rainfall for each speciﬁc 10 km radius for a full 72-h forecast and dividing by the number of grid points summed. The procedure is described further in Section 5.2 of the text...... 80

37 A count of methods at each radius that are closer to Stage IV observations than their REG or ALL (Table 7) counterpart on a cross-track, radial accumulation basis (a; e.g., Fig. 36). The ALL-based methods that are closer to Stage IV observations than the REG-based methods are shown in the positive ordinate direction, whereas the REG-based methods are in the negative ordinate direction. Only methods that are statistically diﬀerent from their REG- or ALL-based counterpart are shown. For example, at 210 km, there are 5 REG-based methods that are closer to Stage IV observations. In panel b), the statistical variance of the methods that are closer to the Stage IV variance (similar methodology as in [a]) are shown along with the Stage IV variance (brown line; secondary axis) in the radial...... 83

xii 38 Global Forecast System (GFS) forecast positions (0 – 72 h) for the Top (a) and Bottom (b) Fractions Skill Score (FSS) categories for the environmental analysis done for the GFS (2004 – 2012; Section 5.3). The diﬀerence between the Top and Bottom FSS categories (Top – Bottom) for those grid points where data existed for both Top and Bottom is shown in (c). The six-hour locations are binned with 2 degree grid spacing. 87

39 Composites of mean sea-level pressure [hPa] at the analysis hour for the Gobal Forecast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories. Composites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel...... 88

40 Histogram of mean sea-level pressure for Top (blue), Middle (grey), and Bottom (orange) forecast categories as deﬁned in Section 5.3. Veriﬁed intensities from Best Track (BTK) analyses are shown in black. Percentages are the percent contribution to the bin for the total data set...... 89

41 Top (cyan), Middle (magenta), and Bottom (yellow) Fractions Skill Score (FSS) categories’ mean locations associated with composite environmental plots for analysis hour (a) and forecast hour 72 (b)...... 90

42 Frequency of Global Forecast System (GFS) forecasts for the Top, Middle, and Bottom Fractions Skill Score (FSS) categories as deﬁned in the text. Raw counts are shown as bars, and frequencies (normalized by the total number of forecasts in the month) are shown as dashed lines. The solid lines show the number of storms for each category and month...... 91

43 As in Fig. 39, but for 500 hPa heights [dam]...... 93

44 As in Fig. 39, but for forecast hour 72...... 94

45 As in Fig. 43, but for forecast hour 72...... 96

46 Anomalous 1000 – 500 hPa thickness [dam] composites at the analysis hour for the Global Forecast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories. Anomalies are calculated by subtracting the monthly mean (2004 – 2012) for the same month from the storm environment forecast (described further in text). Composites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel...... 97

xiii 47 As in Fig. 46, but for forecast hour 72...... 99

48 Eddy ﬂux convergence (EFC) types (Peirano et al. 2016) and the contribution of each Fractions Skill Score (FSS) category (Top, Middle, and Bottom) to each type. . . . . 101

49 300 hPa winds (vectors) and isotachs (shaded) from the Global Foreast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories at the analysis hour. Composites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel...... 103

50 Latitudinal cross-sections of winds [m s−1] centered on the TC where north is to the right of each panel. Results for the three categories of rainfall skill are shown...... 104

51 As in Fig. 49, but for 200 hPa divergence (×10−5 m s−1)...... 105

xiv ABSTRACT

While advances in tropical cyclone (TC) track forecasting have been substantial over the past few decades, and modest advances in intensity forecasting have occurred more recently, the quality of TC rainfall forecasts has not undergone the same rigorous verification. This is despite the 27% of total TC-related deaths being due to rainfall-induced flooding and that rainfall-related deaths occur more frequently than those due to any another weather-related hazard. A continual effort is needed to understand and better-forecast TC rainfall. This dissertation research seeks to contribute to this endeavor. A climatological dataset is created using 6-h Stage IV rainfall accumulations combined with Best Track 6-h locations for all TCs within 300 km of the U.S. Gulf and Atlantic coastlines during years 2004 – 2013. Stage IV data are used due to their higher spatiotemporal resolution, their extension to high latitudes, and because they have been found to be the superior option when compared to other TC rainfall data sources. The 6-h Stage IV rainfall accumulations are composited by shear magnitude and storm intensity in earth-, motion-, and shear-relative reference frames. Additionally, a full composite comprised of all storms is created. This compositing is done for TCs impacting the U.S. Gulf and Atlantic coastlines. Seven geographical regions are created within this domain to further composite the rainfall. The geographical regions are determined based on 2004 – 2013 Best Track (HURDAT2) landfall locations. Results show that some Stage IV rain rate characteristics, especially those in specific regions, are different when compared to prior findings based on satellite-derived rain rates. Results from the Stage IV-derived climatological datasets then are used together with track forecasts from the Global Forecast System (GFS) during years 2014 – 2016 to create 72-h TC rainfall forecasts. Separate forecasts are created for each 6-h TC position forecast based on shear magnitude, storm intensity, and the all-storms composites in earth-, motion-, and shear-relative reference frames. This yielded 1,290 verifiable forecasts during the 3-yr period. These statistical rainfall forecasts along with forecasts from the GFS and an R-CLIPER created from Stage IV data are verified using the Fractions Skill Score (FSS) metric. Results show that the statistical method based on shear magnitude in a shear-relative reference frame that used regional rainfall composites is the best performing of the methods. Additionally, FSSs from the statistical model are shown to

xv be larger than those from R-CLIPER. The preliminary results from the statistical model show that this method is a viable candidate to supplement R-CLIPER as a statistical baseline TC rainfall forecast method. GFS analysis and forecast environmental parameters are composited based on the skill (FSS) of each forecast. Three categories are created: Top (FSS > 0.6), Bottom (FSS < 0.3), and Middle (0.3 < FSS < 0.6). This methodology is based on the desire to provide “guidance on guidance,” i.e., suggesting to a forecaster whether the TC’s environment is conducive to a skillful or not-skillful GFS rainfall forecast, and to help determine possible factors to increase the FSS of the statistical model. Results show that some aspects of the mean sea level pressure, 1000 – 500 hPa thickness anomalies, eddy ﬂux convergence, and upper-level winds and divergence diﬀer between skillful and non-skillful TC rainfall forecasts.

xvi CHAPTER 1

INTRODUCTION AND MOTIVATION

Recent studies have focused more on the forecasting of tropical cyclone (TC) intensity, genesis location/potential, and track than on methods to better-forecast TC rainfall – one of the leading causes of deaths from TCs (Rappaport 2000, 2014). This is despite a request from the National Hurricane Center (NHC) to tackle the rainfall issue (Rappaport et al. 2009). This dissertation research investigates the climatological structure of TC rainfall in the U.S. with respect to various environmental and storm-specific parameters and develops a new statistical baseline product to improve TC rainfall prediction. The research builds on prior knowledge of TC rainfall structure and environmental characteristics. This prior knowledge also is used to investigate environmental parameters interior and exterior to a TC to better-predict when the Global Forecast System1 (GFS; Kanamitsu 1989) will have skill in forecasting TC rainfall and if these environmental parameters can be used to create a better statistical baseline product. The results from this research hopefully will help forecasters identify environmental regimes that are conducive to skillful GFS TC rainfall forecasts. The public’s perception of TC damage and deaths often relates to the devastating winds and storm surge that are associated with them (Meyer et al. 2014; Rice 2014). However, excessive rainfall also is a major cause of deaths. The rainfall can be directly related to the TC or indirectly related (an event that occurs because the storm existed, such as distant trough/ridge interaction 100s of km away from the storm; e.g., Ashley and Ashley 2008; Rappaport and Blanchard 2016). Rappaport (2000) found that 59% of all TC-related deaths between 1970 – 1999 were due to rain-related freshwater flooding. An updated report by Rappaport (2014) found that rainfall-induced floods from TCs accounted for 27% of the deaths for the years 1963 to 2012. The reduction in percentage of total deaths from 59% to 27% due to freshwater flooding was attributed to the large number of deaths from Hurricane Katrina’s (2005) storm surge. Rainfall-related flood deaths occurred more

1There is an upcoming major upgrade to the GFS. It will transition to the Finite-Volume on a Cubed-Sphere (FV3) dynamical core. However, the methods reported in this dissertation are easily applicable to any new update of the GFS.

1 Figure 1. Statistics of storm-related fatalities. Recreated from Rappaport (2000, 2014).

frequently in TCs than in any other hazard, and they are second to storm surge in total deaths (Fig. 1). During the most recent high-profile hurricane that was analyzed for rainfall-related deaths (Sandy, 2012), approximately 22% of the deaths in North America were caused by drowning from Sandy’s rainfall (Diakakis et al. 2015). Hurricane Matthew’s (2016) rainfall contributed to a portion of the 546 deaths in Haiti, the 34 deaths in the United States, and the approximately $10.0 billion in damage in the United States (NHC 2012). Rainfall is such a major contributor to death and destruction that Rezapour and Baldock (2014) created a new hurricane hazard index, one that is better-correlated to death and destruction than existing indices such as the Saffir-Simpson scale (NHC cited 2018b). Since one-quarter of the deaths in TCs are from freshwater flooding due to rainfall, it is important to understand those environments that are conducive to a skillful GFS forecast and the regional climatological characteristics of this rainfall. Tropical cyclones contribute a significant percentage of annual rainfall to portions of the United States. The seasonal (JJASON) contribution of TC precipitation in the southeastern U.S. averages 7% (Prat and Nelson 2013), and in the northeastern U.S., TCs contribute 12% and 16.8% of the total precipitation during JJA and SON, respectively (Agel et al. 2015). Larson et al. (2005) found that 20% of summertime precipitation along the U.S. Gulf Coast was from TCs, and (Jiang and Zipser 2010) corroborated these findings. Overall, TCs were found to contribute approximately 13% of the total extreme (1-in-5-yr occurrence) rainfall budget for the entire conterminous U.S.

2 (Kunkel et al. 2012) and up to 10% of the total rainfall budget along the Gulf and Atlantic Coasts (Rodgers et al. 2001). These percentages show that TCs contribute a considerable portion of overall rainfall in the United States, and, in extreme rainfall scenarios, an even greater contribution. Therefore, understanding regional aspects of TC rainfall is imperative to further understanding TC rainfall structure and its influence on TC rainfall forecasts. Rappaport et al. (2009) stated that one of the high priority, near-term specific needs of the NHC is improved guidance for TC precipitation amount and distribution. The Weather Prediction Center (WPC) is responsible for creating the U.S. TC rainfall forecasts that are included in NHC advisories (Rappaport et al. 2009). The WPC forecast, known as the “rainfall statement,” is is- sued for all TCs that are expected to make landfall (WPC 2018). Graphical QPFs (Quantitative Precipitation Forecasts) from the WPC also are provided on the NHC website. If the NHC discon- tinues following a storm because it loses tropical characteristics, but the storm still poses a threat in terms of rainfall, WPC begins to issue Tropical Public Advisories. These advisories provide detailed information about the remnants of the TC and its precipitation field (WPC 2018). The NHC currently uses satellite-derived rainfall estimates (SREs) to provide operational quantitative precipitation estimates (QPEs) in tabular form. The QPEs contain 6-h estimates derived from both the Naval Research Laboratory (NRL) Blend SRE Technique (Vicente et al. 1998, 2002; Turk et al. 2010) and NOAA’s Climate Prediction Center (CPC) QMORPH, a variation of the CPC-Morph (CMORPH) SRE technique (Ferraro 1997; Ferraro et al. 2000; Kummerow et al. 2001; Joyce et al. 2004). Values from the most-recent run of the GFS also are included in the table (NHC cited 2018a). Accurate TC rainfall forecasts are imperative to mitigate the loss of life and property. Although current techniques provide TC QPEs (those outlined above and described in Chapter 2), verifications indicate that each technique has limitations. This research proposes a new statistical baseline method for QPFs, seeks to understand the skill of GFS TC rainfall forecasts and the environments that are associated with well-forecast and poorly-forecast TCs, and provides a detailed climatological perspective of U.S. regional TC rainfall characteristics. Providing a new and different statistical baseline method that can be used as a comparison of skill to existing forecast products is needed. While existing efforts are useful and necessary, the development of a new product based

3 on a diﬀerent methodology provides the research community with a more robust analysis of TC rainfall skill.

4 CHAPTER 2

BACKGROUND

2.1 Rainfall characteristics

Four physical processes have been associated with precipitation in a TC: water vapor flux convergence near 850 hPa, upward vertical motion, potential instability, and boundary layer convergence (Elsberry 1995). The four processes are interconnected: boundary layer convergence leads to upward vertical motion, and potential instability is related to low-level moisture transport. TC motion, intensity, and structure, and therefore rainfall, are modulated by vertical wind shear (e.g., Shapiro 1983; Jones 1995; Bender 1997; Frank and Ritchie 1999, 2001; Reasor et al. 2013). When a hurricane experiences weak shear, its vortex tilts downshear. This tilt creates a horizontally asymmetric vertical velocity field. Jones (1995), using a barotropic model, and Frank and Ritchie (1999), using a baroclinic model, described the effects of vertical shear on TC structure and vertical motion. These papers found that a downshear-tilted vortex creates a thermal wind imbalance. A secondary circulation develops to restore the imbalance. From a potential vorticity (PV) viewpoint, the downshear-titled vortex projects a positive PV anomaly toward the surface in the downshear direction. To maintain constant PV downshear, the isentropes must slope upward. The opposite is true in the upshear portion of the storm. A cold (warm) potential temperature anomaly was found to develop downshear (upshear) in both the baroclinic and barotropic models, confirming the creation of the sloped isentropes. Since both models showing this relationship were dry, the primary circulation associated with the vortex created ascent (descent) downshear (upshear) along the isentropes. After several hours of model integration, both studies found that maximum upward motion was located in the downshear-right quadrant. However, after several more hours of integration, barotropic effects caused the vertical velocity to rotate about the center of the storm (Jones 1995), whereas the vertical velocity in the baroclinic model from Frank and Ritchie (1999) remained in the downshear right quadrant. Frank and Ritchie (1999) performed moist simulations to incorporate diabatic effects. Contrary to the dry simulations, upward motion and convection were located in the downshear-left quadrant. The rainwater associated with this convection was

5 advected to the left of the shear vector. The authors concluded that once moist processes began, the adiabatic lifting processes were destroyed, and the secondary circulation was due to differential vorticity advection. The location of precipitation and convection in a TC is the result of several processes (Black et al. 2002; Hence and Houze 2011). First, updrafts are initiated primarily in the downshear-right quadrant (Black et al. 2002; Hence and Houze 2011; Reasor et al. 2013), as found in the modeling studies of Jones (1995) and Frank and Ritchie (1999). Observationally, a lightning maximum, an indicator of deep convection, was found in the downshear-right quadrant (Corbosiero and Molinari 2003). Next, the rotating, tangential winds of the TC advect the updrafts cyclonically around the storm, and rainfall occurs in the downshear-left side of the TC. By the time the updraft reaches the upshear side, it is at a higher altitude than the 0◦C isotherm, and the low-levels become dominated by downdrafts. Finally, the remaining frozen condensate falls out, the updrafts accelerate upward and detach from the eyewall, and exit the storm near the tropopause on the right side of the shear vector (Black et al. 2002). Storm-specific processes can modify the distribution of rainfall in a TC. Vertical wind shear is the dominant factor organizing precipitation and convection (Corbosiero and Molinari 2003; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013; Xu et al. 2014). Using satellite (Chen et al. 2006; Wingo and Cecil 2010; Xu et al. 2014) and radar (Marks et al. 1992; Reasor et al. 2013) observations, greatest precipitation asymmetries have been found in the downshear-left quadrant. The amplitude of the asymmetry increases with increasing strength of the shear (Rogers et al. 2003; Chen et al. 2006; Wingo and Cecil 2010; Xu et al. 2014). However, when shear is minimal, Chen et al. (2006) found that the effect of storm motion is comparable to the effect of shear in explaining TC precipitation asymmetries. Cline (1926) noted a front-right quadrant favor- ability with respect to motion for storms along the northern Gulf Coast. Similarly, Schoner (1968) found that maximum rainfall generally is located to the right of storm motion for specific regions and translational directions over the U.S. For storms entering the coastal regions, precipitation generally is greater on the right side of the storm than the left (Goodyear 1968). Studying landfalling storms in Florida using gauge data, Miller (1958) observed that rainfall rates were greater ahead of a storm than behind but found minimal differences between the right and left sides. A wavenumber-1 asymmetry was noted by Lonfat et al. (2004), with maximum precipitation located

6 in the front quadrants with respect to storm motion. The maximum asymmetry shifts from the forward left to the forward right quadrant as storm intensity increases. As the translation speed of the storm increases, the front-to-back asymmetry also increases. These effects are caused by increased asymmetrical frictional forcing due to increased storm motion and tangential wind speed (Shapiro 1983). This effect also can be seen with increasing storm motion (Frank and Ritchie 1999). External to the TC, synoptic-scale flow patterns affect TC rainfall. Specifically, mid-latitude troughs have adverse effects on TC intensity, but not necessarily rainfall (DeMaria et al. 1993; Peirano et al. 2016). Troughs can enhance the upper-level outflow of a TC. Additionally, the juxtaposition of the trough and the TC can enhance the TC’s convection (Molinari and Vollaro 1989). Atallah and Bosart (2003) found that an approaching trough interacting with Hurricane Floyd (1999) created a strong baroclinic zone to the left of the storm. The trough enabled the enhancement of rainfall within the baroclinic zone. A deep middle-latitude trough also can elongate precipitation in the region between the trough axis and the TC. Conversely, a weak trough can aggregate precipitation to the northeast, near the ridge downstream of the TC (Atallah et al. 2007). A proven metric to identify the influence of a trough on a TC is eddy flux convergence (EFC) in the upper troposphere, typically around 200 hPa (Molinari and Vollaro 1990; DeMaria et al. 1993; Hanley et al. 2001; Peirano et al. 2016). This dissertation research employs EFC arguments to determine the effects of approaching troughs on GFS TC rainfall forecasts. Although vertical wind shear is the dominant factor for organizing precipitation and convection within a TC, additional environmental and storm-related factors are important. Topographic effects play a key role on a TC’s rainfall distribution and amount (Haggard et al. 1973; Simpson and Riehl 1981; Rogers et al. 2009; Lonfat et al. 2007). The basic concept is similar to that occurring in synoptic-scale systems: upslope winds can lead to condensation and precipitation on the windward side of a mountain. The degree to which topography affects rainfall depends on several factors including the angle of incidence between the storm winds and the land surface, fetch (moisture supply), and the width of the mountain on which the winds are impinging (Smith and Barstad 2004). Xu et al. (2014) found that steeper mountains enhance rainfall in TCs more than gently sloped mountains. Sea surface temperature (SST) also can affect the structure and amount of rainfall (Rodgers et al. 1994; Hence and Houze 2011; Xu et al. 2014). A smaller probability of greater reflectivity was found in storms experiencing a cooler SST (Hence and Houze 2011).

7 To summarize, TC-related rainfall accumulation depends on all the factors mentioned above, as well as storm track (Rogers et al. 2003; Rogers et al. 2009). For example, vertical shear can realign the rainfall, but the orientation of the shear and motion vectors can create diﬀerent rainfall patterns (Rogers et al. 2003; Lonfat et al. 2007). The previously mentioned studies primarily focused on observations from radar or satellites. These platforms provide instantaneous rain rates that can be integrated over time to provide accumulated rainfall. The studies using satellite data provide a useful climatology, but primarily considered TCs over water (e.g., Lonfat et al. 2004). However, rainfall patterns over land can be diﬀerent from those over water due to the interaction with the land surface (Simpson and Riehl 1981). This study only considers QPEs on land.

2.2 Quantitative precipitation forecast models

Although operational QPFs for TCs have improved in recent years, they still exhibit limitations. This section outlines the many different models that have been created for TC QPFs. “Legacy” models are those proposed during the 20th century, prior to the development of R- CLIPER (Marks et al. 2002, the widely accepted TC rainfall persistence model) or were created prior to knowing the effects of shear on TC precipitation. Nonetheless, they are the foundation on which multiple 21st century models were built. Every model created after R-CLIPER is highlighted below in its own subsection. The current research seeks to build on the methods of prior research to create a new and different statistical baseline forecast product to supplement the insight provided from R-CLIPER on TC rainfall forecast skill.

2.2.1 Legacy models

Schoner and Molansky (1956) developed a climatology of landfalling tropical systems from 1900 – 1955 in preparation for the 1956 hurricane season. Their goal was a ﬁrst step to “investigating correlations of hurricane quantitative rainfall forecasting methods for use in connection with general hurricane forecasting activities.” Their climatology consisted of an analog look-up table for storms making landfall in three regions: the North Atlantic, South Atlantic (including Florida), and Gulf Coast (excluding Florida). It provided storm-total, 12-, and 24-h rainfall accumulations. Additionally, it reported a brief synopsis of rainfall accumulations with respect to storm motion on a quadrant-speciﬁc basis. The regional approach for investigating TC rainfall was used in this

8 research to separate the U.S. Gulf and Atlantic coastlines into seven geographic regions (described in Chapter 3) to gain insight on regional TC rainfall structure. The regional datasets then were used as input to the statistical model created for this dissertation. Riehl and Malkus (1961) found a radial relationship of precipitation in Hurricane Daisy (1958). The relationship was logarithmic with respect to storm motion, with precipitation decaying radially outward from the center of the storm. Simpson and Riehl (1981) found this relationship to be consistent across several storms. The relationship constituted the ﬁrst maximum rainfall prediction equation for TCs (Pfost 2000). Using the results of Riehl and Malkus (1961) and Simpson and Riehl (1981), Pfost (2000) formulated an equation that relates maximum precipitation accumulation to storm speed:

y = 31.1(0.915)x (2.1) where x is storm speed [mph] and y is the predicted rainfall [in.]. Thus, if a storm’s speed decreases, the maximum rainfall potential increases. The concept is simple since if a storm is moving slowly, it remains longer over an area, and therefore, should produce a greater rainfall accumulation. However, an inherent problem with this technique is that as a storm approaches 0 mph, the greatest possible rainfall is 31.1 in. Like Pfost (2000), the “Kraft Rule of Thumb” provided an estimate of maximum rainfall in inches:

100 R = (2.2) max V where V is the storm’s motion [kt] (attributed to Kraft; Pfost 2000). The result that TC rainfall can be aﬀected by storm motion and that storm motion can be used as a forecasting parameter was motivation to create rainfall datasets based on ranges of storm motion as input into the statistical model created for this work. Schoner (1968) used the Schoner and Molansky (1956) dataset of storms whose radial wind was 75 mph or greater. They chose this threshold because “storms of less than hurricane intensity often lose their compact wind circulation prior to, or shortly after landfall, which often results in an area of disassociated showers, whereas a well-deﬁned hurricane maintains its circulation and produces a more uniform rainfall pattern with respect to its center after landfall.” This approach is limiting since storms of tropical storm strength or less often produce heavy rainfall (Schoner

9 and Molansky 1956). Schoner (1968) separated the U.S. Gulf and Atlantic coasts into six different regions: the Texas Coast, Middle Gulf Coast, Florida West Coast, Florida East Coast, South Atlantic Coast, and North Atlantic Coast. Their analysis, like Schoner and Molansky (1956), provided a climatological look-up table for TC precipitation. However, it was more in-depth than the earlier study and included the impacts of regional factors. Schoner’s (1968) work is additional motivation to create several geographic regions to gain insight into regional effects on TC rainfall. In an attempt to improve the results of Schoner (1968), the storm-intensity dataset created for this work used storms whose radial wind was > 20 kt (∼23 mph; instead of only > 75 mph) with the intent to provide a more-comprehensive analysis with respect to storm intensity (Chapter 3). Goodyear (1968) is perhaps the first study to quantify the average amount and probability of TC rainfall occurring on the right side of the storm track. They found a 48-h average accumulation of 5.75 in. located approximately 35 mi. to the right of the track. Additionally, the probability of the greatest 6-h rainfall was 7% at approximately 25 – 50 mi. to the right of track (using a grid spacing of 25 miles). Haggard et al. (1973) performed a statistical study of the probability of maximum rainfall from TCs passing over the Appalachian Mountains. Their data, consisting of rain gauge measurements, were modeled using a gamma distribution. Probabilities of rainfall exceeding specified amounts and rainfall amounts at specific probability levels were tabulated. Their research provided forecasters with a maximum rainfall potential for TCs crossing the Appalachian Mountains. The seven geographic regions of the present study are an attempt to account for topographical influences on TC rainfall in the statistical model. Griffith et al. (1978) reported the first results from an empirical scheme that provided a QPE based on geosynchronous visible and infrared satellite data. The scheme classified cloud or reflectivity regions as having certain amounts of precipitation associated with them. Their QPE equation was: X Rv = IAE × ∆t × aibi (2.3)

3 2 where Rv is rain volume [m ], I rain rate, AE area [km ], ∆t the time diﬀerence between subsequent images [h], a the fraction of the cloud system covered by each brightness contour, b an empirically derived rainfall weighting factor that is a function of brightness or temperature, and i indexes for

10 the brightness levels. The research also defined a rainfall potential for approaching hurricanes: D¯d¯ RP = (2.4) v¯ where RP is the mean total rain potential for a point directly in the path of the storm, D the satellite-inferred daily average storm rainfall [mm day−1], d the mean cross section [km] of the storm as measured from the satellite image in the direction of motion, and v the mean storm speed [km day−1]. Equation (2.4) does not provide the location for the expected precipitation, other than directly in the storm’s path, just its mean amount. Unlike the satellite-derived QPEs used by Griffith et al. (1978), the statistical model presented here uses climatological Stage IV data (gauge and radar-derived rainfall observations; described further in Chapter 3) to create its rainfall forecasts. Spayd and Scofield (1984) created the Tropical Cyclone Precipitation Estimation Technique which employed visible and infrared geostationary satellite data to calculate the Rainfall Potential (RP) for “any number of projected points passing through the TC”: R D + R D R D + R D RP = CDO CDO WC WC + OBA OBA ECT ECT (2.5) V V

−1 where RCDO, RWC , ROBA, and RECT are rainfall rates [in. h ] for the central dense overcast area, wall cloud, significant bands in the outer banding area, and embedded cold convective tops, respectively, D is the diameter of these features in the direction of motion, and V is the speed of the TC [deg lat h−1]. This technique required a user to actively select criteria to create a rainfall forecast and manually draw isohyets for locations within the storm’s projected path. The analyst had to consider the change in size of cloud features, upslope/downslope components, and onshore/offshore flow characteristics. The technique was highly subjective since Spayd and Scofield (1984) recommended that the analyst somehow adjust the rainfall potential if there were projected changes in storm speed or cloud features. Similarly, the classification of cloud features was left to the discretion of the analyst. Unlike Spayd and Scofield (1984), which used analyst input, the statistical model created for this work is algorithmically based where rainfall composites used as input are determined by storm location, shear, and motion characteristics (described further in Chapter 3). Attempting to create a relationship between storm motion and storm total rainfall, Pfost (2000) studied storms impacting the Northern Gulf Coast and Florida Peninsula. They developed

11 two regression equations which calculated a storm-maximum rainfall, one for each region, and then assumed the location of the maximum rainfall location based on Goodyear (1968) and “plots of the position of observed maximum rainfall relative to the coastline where the center of the tropical cyclone crosses the coast.” The two regional regression equations were:

R = 9.75 − 0.039V (2.6a)

R = 9.37 − 0.063V (2.6b) where R is storm total rainfall [in.], V is storm movement [kt] and Eq. (2.6a) is for the Northern Gulf Coast and Eq. (2.6b) is for the Florida Peninsula. Pfost (2000) described these regression equations as providing “first guesses” for each respective region. They show that a forecaster can expect a maximum storm total rainfall between 9 and 10 in. for storms making landfall within the region of study. Pfost also plotted maximum rainfall amounts with respect to storm motion for landfalling TCs. As noted in the previously mentioned studies, maximum rainfall generally was found to the right of storm motion. The study highlights the importance of creating regionally specific regression models and analyses, as was done with the creation of our statistical model (Chapter 3). Since these two regions, which were relatively close to each other, produced different regression equations, it is likely that differences in rainfall will be found in the seven regions used in this study. After the launch of the NOAA-15 satellite in 1998, containing the first Advanced Microwave Sounding Unit (AMSU), Kidder et al. (2000) proposed an experimental tropical rainfall potential (TRaP) algorithm using moisture data from AMSU. This model used data from either the operational SSM/I (Special Sensor Microwave/Imager) at 14 km × 16 km resolution (Ferraro et al. 1998) or the AMSU 48-km resolution to provide rain rates (Grody et al. 1999) that could yield an aerial extent of rain and average rain rate in the direction of storm motion:

RD T RaP = (2.7) V where R is the average rain rate along a line in the direction of motion, D is the distance of that line, and V is the speed of the TC. The AMSU-derived rain rates were found to be small compared to observations at Key West during Hurricane Georges (1998), but of suﬃcient accuracy to be useful for forecasters. The statistical model created for this work used Stage IV rainfall data (described in

12 Chapter 3), a radar- and gauge-derived product, to create TC rainfall forecasts. Using land-based QPEs instead of satellite-based methods likely will give additional insight into forecasting rainfall.

2.2.2 The Rainfall-Climatology and Persistence Model

The 21stcentury, the modern era of TC QPFs, began with the Rainfall-Climatology and Persistence model (R-CLIPER; Marks et al. 2002). R-CLIPER provides a baseline persistence forecast based on a climatology of satellite observations. The climatology provides a mean rain rate and a probability distribution of rain rate in a storm-centered coordinate system composed of 50, 10-km wide annuli in four quadrants (Marks et al. 2002). R-CLIPER stratifies storms by their intensity using relationships by Lonfat et al. (2004) out to 500 km and can be used with any automated tropical cyclone forecast (ATCF; Sampson and Schrader 2000) track: ( (R ) + (R − R )(r/r ) r < r R (r) = 0 m 0 m m (2.8) Rm exp (− (r − rm) /re) r > rm where R(r) is the rain rate, r the radius, rm the radius of maximum rainfall, re is 500 km, R0 the mean rainfall rate at re, and Rm the mean rainfall rate at rm. Thus, R-CLIPER is sensitive to changes in storm track, motion, and intensity. A curving storm can accumulate more precipitation on the inside of a curved track than the outside due to: 1) a decrease in the speed of the storm, which extends the duration of the rain on the inside, and 2) an increase in duration on the inside of the curve due to the shape of the track (Marks et al. 2002). Although R-CLIPER serves as a baseline estimate for other models, it does not consider all environmental influences. Its symmetrical nature does not account for the many environmental conditions which make a TC’s precipitation asymmetric. Marks et al. (2002) indicated that “more than a simple rain model with a peak along the track is needed (e.g., one with asymmetries).” The model developed in this dissertation builds on the foundation of R-CLIPER, but instead of approaching the TC rainfall forecast problem from a parameterized perspective, the approach is a statistical frequentist method. Raw data are used and combined to create seven unique regional composites with respect to shear, motion, and intensity. These composites can be placed on any ATCF track similar to R-CLIPER (described further in Chapter 3). Additionally, R-CLIPER used the variability of TC rainfall with respect to storm intensity to modulate the forecast rainfall. This work uses that prior knowledge, but also adds the effects of storm speed, geographic region, and shear strength.

13 2.2.3 The Areal Tropical Rainfall Potential Technique

Kidder et al. (2005) improved the model presented in Kidder et al. (2000). Their updated model automated the earlier TRaP technique, but instead of assuming that a storm moved in a constant direction, it included oﬃcial track forecasts. This new technique used AMSU-B rain rate estimates (Weng et al. 2003). The time of the closest approach of the satellite over a TC was used as the time of the observation, and a cubic spline interpolation was applied to create storm positions every 15 min from oﬃcial forecast tracks. Twenty-four-hour rainfall accumulations are computed using the following:

96 X T RaP (xj, yj) ≈ wiR (xj − ∆xi, yi − ∆yi) ∆t (2.9) i=0 where T RaP is the 24-h rainfall [mm], ∆t is 0.25 h, ∆xi and ∆yi are 15-min offsets calculated as the difference between time ti and tobs (as part of a cubic spline calculation to determine the relative position of the TC), wi are the trapezoidal-rule weights: 0.5 for i = 0 or 96, 1.0 otherwise, and R is the satellite-estimated rain rate [mm]. Several assumptions are made in the Areal TRaP technique: the forecast track is accurate, satellite-estimated rain rates are correct, and the spatial pattern of rain rates does not change (Kidder et al. 2005). Validating the technique with TRMM Microwave Imager (TMI) observations, Ferraro et al. (2005) found that TRaP using TMI produced the best results compared to TRaPs created with SSM/I- and AMSU-derived rain rates, and even outperformed the Eta model (Black 1994). The technique was found to work best for storms that were 12 and 18 h from landfall. Persistence forecasts provide a good benchmark for a storm in its current state; however, it is rare for a storm’s rainfall pattern to remain constant over a 24-h period. One reason is that topography and shear affect the rainfall. The model created for this dissertation research includes the effects of shear and topography by a using a composite analysis of land-based historical TC QPEs.

2.2.4 The Parametric Hurricane Rainfall Model

Lonfat et al. (2007) updated R-CLIPER by adding the eﬀects of topography and shear to create the Parametric Hurricane Rainfall Model (PHRaM):

RP HRaM = RR−CLIP ER + Rshear + Rtopo (2.10)

14 where RP HRaM is the total spatial rainfall field generated by PHRaM, RR−CLIP ER is the rain field generated by R-CLIPER (Marks et al. 2002, Eq. 2.8), Rshear is the rain field associated with the effects of vertical shear, and Rtopo is the rain field modulated by topography. To calculate Rshear, statistical relationships were created as a function of storm intensity and various amplitudes of shear. The rainfall distribution was modeled using wavenumber-1 and -2 Fourier coefficients:

X X Rshear (r, θ) = ai (r) cos (iθ) + bi (r) sin (iθ) (2.11) where r is the radial distance from the center of the storm, θ is the azimuthal angle around the storm, ai and bi are Fourier coeﬃcients for wavenumber i. The cosine and sine functions allow asymmetries across the left/right and front/back quadrants, respectively. Rtopo was calculated as an amount proportional to the low-level, ﬂow-dependent gradient of ground elevation:

Rtopo = cV~s · ∇~ hs (2.12) where c is a constant of proportionality, V~s is the 10 m wind field, and hs is the ground elevation. Therefore, if a grid cell within the model is located at an increasingly higher (lower) elevation, its rainfall accumulation will increase (decrease) proportionally to the change in elevation. This places more precipitation on the windward side of mountains, and less on the leeward side. Lonfat et al. (2007) found that this modified R-CLIPER, which accounts for shear and topography, significantly improved rainfall forecasts. However, the model did not produce the strong asymmetries associated with vertical shear. They conceded that many additional processes need to be included in the model, including convergence along a coastline, extratropical transition (ET), and moisture supply. The model created for this work builds on the success of PHRaM, but through the lens of frequentist instead of parameterized statistics. Additionally, it seeks to add the influences of storm motion as well as the effects of varying regional characteristics on TC rainfall to provide a new and different baseline statistical model.

2.2.5 The Ensemble Tropical Rainfall Potential

A further improvement to the TRaP technique was developed by Ebert et al. (2011): the ensemble TRaP (eTRaP). The eTRaP technique synthesizes multiple satellite QPEs and track forecasts and applies the same QPF technique as TRaP (Section 2.2.3). In addition, eTRaP

15 creates probabilistic rainfall forecasts exceeding certain thresholds. Each 6-h TRaP is weighted by its expected accuracy, which is a function of the age of the TRaP forecast and the sensor being used. These weights are determined by validating 6-h observations with Stage IV rainfall data. The 24-h eTRaP forecast is computed as follows:

n X wiRi i=1 R = n (2.13) X wi i=1

th where R is the ensemble mean, Ri the areal rainfall of the i TRaP ensemble member, wi the weight (deﬁned in Ebert et al. 2011), and n the number of ensemble members. Probabilistic forecasts are created using:

n X wiIi ( i=1 0,Ri < RT P (R ≥ RT ) = n ,Ii = (2.14) X 1,Ri ≥ RT wi i=1 where P is the probability of R being greater than RT , and RT is the threshold rain amount described in Ebert et al. (2011). The eTRaP model was found to create better QPFs and probabilistic forecasts than the one-sensor TRaP technique (Ebert et al. 2011). However, it still was subject to the pitfalls of the assumptions in Kidder et al. (2005). Nonetheless, Ebert et al. (2011) showed that probabilistic rainfall forecasts can be used in a climatological sense.

2.2.6 Numerical weather prediction models

With the development of sophisticated numerical weather prediction (NWP) models, the need for analog and statistical techniques may seem unnecessary. However, an NWP model’s precipitation forecast is subject to the biases and deficiencies of the model. Additionally, while a storm is offshore, few, if any, land-based rainfall observations are available, causing the assimilation of precipitation into the model to be imprecise (Kidder et al. 2005; Marchok et al. 2007). Statistically based methods allow the determination of skill of NWP models, and the previously mentioned statistical models (R-CLIPER, PHRaM, (e)TRaP) isolate key TC-specific parameters which am- plify or modulate TC rainfall. Therefore, the results of statistically derived rainfall forecasts can

16 be compared to those of an NWP forecast to identify key features and any possible irregularities within the NWP forecast. When compared to the North American Mesoscale model (NAM; Janjic et al. 2005) and the Geophysical Fluid Dynamics Laboratory model (GFDL; Kurihara et al. 1995), the GFS model performed best in three categories related to TC rainfall: the ability to match QPF patterns, ability to match the mean value and volume of observed rainfall and reproduce the rainfall distribution, and the ability to produce extreme rainfall amounts (Marchok et al. 2007). No work to the author’s knowledge has investigated those environmental parameters conducive to a skillful GFS TC rainfall forecast. This dissertation seeks to fill that void by investigating a composite analysis of skillful and not skillful GFS TC rainfall forecast environments. The methodology of this analysis could easily extend to any future NWP model. Table 1 summarizes the strengths and weakness of each model described in this section. The model created for this dissertation incorporates the strengths of some models (e.g., the intensity- based methods of R-CLIPER and PHRaM and the regional approaches of Schoner [1968]) and attempts to improve on the weaknesses of others (e.g., by including motion- and shear-relative rainfall, shear magnitude, or inherent topographical features) to create a new baseline TC rainfall forecast product. R-CLIPER is the widely accepted method for comparing skill between other forecast methods. However, the only parameter in the R-CLIPER equation (Equation 2.8) that increases or decreases rainfall amount is storm intensity (Marks et al. 2002). The effects of stronger shear or slower storm motion are not included. The model created for this dissertation research incorporates these different parameters and seeks to provide another baseline method from which to determine TC rainfall skill.

17 Table 1: Summary of the models presented in Section 2.2 and their individual strengths and weaknesses.

Model Name Strengths Weaknesses

Schoner and General analog forecasting technique with Because it is analog, assumes current Molansky - 55 years of storms. storm is similar to those in the database. (1956)

Riehl and Radial relationship; “ﬁrst maximum Malkus (1961); Only ﬁnds maximum accumulation, not - rainfall prediction equation for TCs Simpson and location. (Pfost 2000).” Riehl (1981)

“Kraft Rule of “Kraft Only ﬁnds maximum accumulation, not Relationship of storm motion to total Thumb” (Pfost Rule of location; does not consider shear, rainfall. 2000) Thumb” topography, or other factors.

Only considers storms with > 75 mph intensity; because it is analog, assumes Schoner (1968) - Regional approach; analog look-up table. current storm is similar to those in the database.

Only ﬁnds probability of maximum Goodyear - Motion-relative. location, not amount; does not consider (1968) shear, topography, or other factors.

Only ﬁnds maximum accumulation, not Haggard et al. Probability of maximum rainfall due to - location; does not consider shear, motion, (1973) topography. or other factors.

Assumes persistence of storm rainfall; Griﬃth et al. - Satellite-derived QPF. only ﬁnds maximum accumulation, not (1978) location.

Spayd and Satellite-derived QPF; ﬁnds location and Assumes persistence of storm rainfall; - Scoﬁeld (1984) amount of maximum rainfall. human intervention required.

Relationship of storm motion to total Assumes maximum location based on Pfost (2000) - rainfall for two regions; provides a Goodyear (1968). reasonable “ﬁrst guess.”

Assumes persistence of storm rainfall and Kidder et al. Satellite-derived QPF; provides maximum TRaP motion; does not give maximum location (2000) rainfall accumulation guess. of rainfall.

Parameterized approached based on storm intensity; assumes linear rainfall Parameterized approach; does not Marks et al. R- within radius of maximum rain and consider shear, topography, explicitly (2002) CLIPER exponential decay beyond said radius; motion, or other storm factors. provides maximum location of rainfall.

Satellite-derived QPF; includes oﬃcial Kidder et al. Areal Assumes forecast track is correct; rainfall forecast track; provides maximum (2005) TRaP will persist from previous times. location and amount of rainfall.

Updated R-CLIPER that includes eﬀects Lonfat et al. Assumes forecast track and shear are PHRaM of shear and topography; provides (2007) correct. maximum location and amount of rainfall.

Ebert et al. Same as Areal TRaP but includes eTRaP Same as Areal TRaP. (2011) multiple satellite-derived QPEs.

Dynamical model with parameterized or explicitly resolved convection; feedback Inaccuracies within the model itself due - NWPs processes between environment and TCs; to assumptions made for satellite-derived QPEs can enhance parameterizations. forecasts via assimilation.

18 CHAPTER 3

DATA & METHODOLOGY

3.1 Data

The revised Atlantic hurricane database (HURDAT2, aka “Best Track”; HRD 2018) was used to locate all tropical cyclones (> 20 kt sustained wind speed) within 300 km of the United States coastline, whether inland or offshore, during the years 2004 – 2012 (Fig. 2). This 300 km distance is the typical location when TCs begin to influence coastal rainfall (e.g., Corbosiero and Molinari 2003; Lonfat et al. 2004; Wingo and Cecil 2010). It also allows the analysis of TCs that have retained their tropical characteristics after making landfall. Once a storm has moved inland, beyond the 300 km buffer, it is no longer considered. Best Track TCs inland of the 300 km U.S. coastal buffer also were used to constrain the GFS forecasts to dates/times when the storm existed. For example, if a storm existed in the Best Track dataset from 0000 UTC 23 March to 0000 UTC 1 April, and a GFS forecast initiated at 0000 UTC 30 March forecast the storm to continue through 0000 UTC 2 April, the last day of the GFS forecast was not used. Each 6-h location from every storm meeting the above criteria was used as if it were a unique storm. This assumption, used regularly in TC precipitation studies, considers all forecasts as unique timesteps to increase the number of data points (e.g., Corbosiero and Molinari 2003; Lonfat et al. 2004; Chen et al. 2006; Wingo and Cecil 2010; Xu et al. 2014). The total number of storms and individual 6-h locations within 300 km of the U.S. coast in both the GFS and Best Track datasets is listed in Table 2. GFS forecast TC locations during the study period were obtained from the NHC Automatic Tropical Cyclone Forecast (ATCF) archive (Sampson and Schrader 2000). Forecast hours 0 – 72 from each model run were used, regardless of the model’s accuracy in terms of intensity, track, or environment. Only those times when Best Track data existed were considered. This choice allowed the inclusion of times when GFS forecast precipitation was available (accurate or inaccurate), even if the track was incorrect. The GFS forecast tracks were used for the Stage IV statistical rainfall model and for the analysis of favorable GFS TC environments (both described below). Using the

19 Figure 2. The seven geographical regions. TC landfall locations are green dots for 2004 – 2012. Other 6-h locations within 300 km (grey dashed buﬀer) of the U.S. coast are shown for comparison (grey dots).

GFS forecast tracks allowed a one-to-one comparison of rainfall skill between the statistical rainfall model and GFS TC rainfall. The Stage IV precipitation dataset (described below) provided the TC rainfall composites that were used in the statistical forecast product. It also was used to validate the GFS precipitation forecasts and statistical rainfall forecasts. The complete Stage IV dataset was divided into two categories. The developmental dataset included years 2004 – 2012, while the test dataset consisted of years 2013 – 2016.

20 Table 2: Total number of storms and 6-h locations from HURDAT2, i.e., Best Track locations (BTK) for earth-, motion-, and shear-relative coordinate systems. Numbers of six-hour locations are in brackets.

Total Storms [Locations]

Year Earth-Relative Motion-Relative Shear-Relative

GFS BTK GFS BTK GFS BTK

2004 9 [803] 9 [124] 9 [764] 9 [119] 9 [803] 9 [124]

2005 12 [846] 10 [131] 12 [795] 10 [128] 12 [843] 10 [131]

2006 4 [297] 4 [47] 4 [281] 4 [47] 4 [297] 4 [47]

2007 8 [341] 8 [64] 8 [324] 7 [59] 8 [341] 8 [64]

2008 9 [856] 9 [93] 9 [817] 8 [88] 9 [856] 9 [91]

2009 6 [173] 4 [21] 6 [166] 3 [13] 6 [152] 4 [21]

2010 8 [410] 8 [72] 8 [384] 8 [71] 8 [410] 8 [70]

2011 7 [308] 5 [46] 7 [289] 5 [42] 7 [308] 5 [46]

2012 7 [654] 5 [69] 7 [619] 5 [67] 7 [653] 5 [69]

2013 6 [223] 4 [29] 6 [207] 4 [29] 6 [223] 4 [29]

Total 76 [491] 66 [696] 76 [4646] 63 [663] 76 [4886] 66 [692]

3.1.1 The Global Forecast System

The GFS underwent numerous modifications between 2004 – 2016 which could affect the TC precipitation forecasts. For example, changes were made to GFS’s resolution, physics, radiation scheme, and/or data assimilation techniques at least once per year since 2004 (the beginning of the study period). This section highlights changes to the GFS which likely would impact the quality of its precipitation forecasts for the CONUS during the period of study. The first major upgrade to the GFS after 2004 occurred during May 2005 when its horizontal resolution was increased from T254L64 (∼55 km grid spacing) to T382L64 (∼38 km grid spacing) in both the analysis and forecasts out to 180 h. The forecast dataset used for this study between 2004 through 2006 were available at a 1 × 1 deg (∼111 km) grid spacing (Table 3). After the upgrade, WPC forecasters were unable to reach a consensus about the overall performance of the new GFS-derived QPF. However, they did determine that it performed with less skill at day 1 and greater skill at days 2 and 3 compared to the previous implementation. This lack of consistently improved QPF performance was addressed in June 2005, and the model’s positive precipitation bias then decreased (EMC cited 2018). During 2006, a new orographic configuration was implemented

21 Table 3: Global Forecast System (GFS) resolution updates and grid spacing of output/working ﬁles for years used in this study. The developmental dataset is 2004 – 2012. The test years are 2013 – 2016. The “Dates Covered” column indicates the period available for that year.

Horizontal Year Grid Type File Grid Dates Covered Resolution Spacing T254 2002 Eulerian 1 × 1 N/A (∼55 km) 2003 - - - N/A 2004 - - - 20 Jul–30 Nov T382 2005 - - 7 May–30 Nov (∼38 km) 2006 - - - 6 Jun–30 Nov 2007 - - 0.5 × 0.5 21 May–30 Nov 2008 - - - 31 May–30 Nov 2009 - - - 18 May–30 Nov T574 2010 - - 1 Jun–30 Nov (∼23 km) 2011 - - - 1 Jun–30 Nov 2012 - - - 1 May–30 Nov 2013 - - - 1 May–30 Nov 2014 - - - 1 May – 31 Dec T1534 2015 Semi- - 1 May - 30 Nov (∼13 km) Lagrangian 2016 - - - 1 May - 30 Nov that changed parameterizations of mountain blocking and vertical diffusion. However, this update had negligible effects on precipitation verification (Iredell 2006). The 2007 upgrade changed the vertical coordinate to a hybrid sigma-pressure system that reduced the positive precipitation bias and increased skill (Iredell 2007). The associated forecast data files were changed to 0.5 deg grid spacing, remaining the same through the end of the study period. The major upgrade during 2010 included an increase in horizontal resolution to T574L64 (∼23 km grid spacing) and updated the shallow and deep convection schemes for the 0 – 192 h forecasts. The 2011 GFS Performance Review (Yang 2013) showed that the equitable threat score (ETS) decreased with increasing precipitation threshold. It also revealed a ∼1.25 bias score for 0 – 72 h total precipitation amounts between 0.01 and 0.10 in. This bias decreased nearly linearly to ∼0.8 at 2 in., indicating that the model underestimates precipitation at higher thresholds. During 2012 the land surface look-up table was updated, which improved the 0-to-3-day

22 precipitation forecasts (McClung 2012). The 2012 Performance Review (Yang 2014) noted that the ETS score for the 0 – 72 h GFS precipitation forecast now was better than that of the NAM. Although the GFS still did not outperform forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF), United Kingdom Met Office (UKMO), Canadian Meteorological Center (CMC), and Japan Meteorological Agency (JMA) in terms of ETS, the upgraded GFS did exhibit a better bias score than most of these models. The 2013 Performance Review (Yang 2014) showed that QPFs for the summers (JJA) of the previous two years (2011 – 2012) exhibited a lower ETS and greater bias for light rain events. The last change in model resolution during our study period occurred during January 2015 when it was upgraded from a T574 Eulerian (∼23 km grid spacing) to a T1534 Semi-Lagrangian (∼13 km grid spacing) resolution. The technical bulletin describing the upgrade did not contain commentary about any increase in precipitation skill (McClung 2016). Notable additional upgrades in 2015 included the implementation of higher resolution SST data and an improvement to reduce a sharp decrease in cloud water during the first model time step. Finally, during May 2016, the GFS data assimilation technique was upgraded from a 3D to a 4D Hybrid Ensemble-Variational algorithm (McClung 2014). An hourly tropical cyclone relocation technique was implemented. Again, the technical bulletin for this upgrade contained no information whether these model changes increased rainfall skill. In nearly all the GFS technical implementation notices described above where precipitation was mentioned, the precipitation skill was improved over the entire CONUS. It is important to note that none of the reviews specifically analyzed rainfall skill or bias in TC environments. Instead, they considered the entire CONUS during the summer and/or winter seasons. However, Marchok et al. (2007) did compare the GFS-derived precipitation within TC environments to that of other models (NAM, R-CLIPER, GFDL). Results showed that GFS performed better than the other models in terms of matching QPF patterns (by using ETS as a metric), matching the mean volume and distribution of observed rainfall, and reproducing observed extreme rainfall amounts. Although the GFS has been modified and enhanced during the study period, the GFS products during years 2004 – 2012 (developmental period) will be treated as a single data set; a similar approach is followed for years 2013 – 2016 (test period).

23 3.1.2 Stage IV data

The Stage IV dataset (Lin and Mitchell 2005) is a national mosaic of hourly radar- and gauge-derived rainfall measurements on a 4 × 4 km grid. The two data sources are combined in a statistically optimal way. Although Stage IV rainfall data are accumulated over 1, 6, and 24 h periods, the 6-h accumulations were used in this study to match the Best Track and GFS forecast 6-h locations. Each of the twelve National Weather Service River Forecast Centers (RFCs) chooses the algorithm for their region that produces the best rainfall estimates (QPEs) that will comprise the national Stage IV product. Fortunately, eight of the nine RFCs whose areas of responsibility overlap the study area (West Gulf, Lower Mississippi, Southeast, Middle Atlantic, Northeast, Ohio, North Central, and Missouri Basin) use the same technique: the multi-sensor precipitation estimator (MPE). The remaining RFC, Arkansas-Red River Basin, uses the P3 algorithm (Young et al. 2000; Seo and Breidenbach 2002). The biases associated with each of these RFC selections (and therefore their QPE techniques) during JJA and SON are comparable, except over the Missouri Basin during JJA where rainfall is overestimated compared to the other regions within the study domain (Nelson et al. 2016). This difference is most likely due to decreased gauge and radar density in the western portions of that RFC’s domain. After each RFC creates its regional rainfall product, each applies its own manual quality control (QC) procedure whose result is input to the national Stage IV dataset. Faulty rainfall estimates at a radar site often are due to the use of unsuitable reflectivity- rainfall (Z-R) relationships (Fulton et al. 1998). The correlation between Z and R has been found to be greatest at locations close to the radar (Villarini and Krajewski 2010). Medlin et al. (2007) found that both gauges and radar underestimated Hurricane Danny’s (1997) rainfall due to inappropriate Z-R relationships, gauge collection errors, and storm-force winds. There also are radar-specific uncertainties and errors that can adversely impact QPEs, such as poor radar calibration, attenua- tion, ground clutter, and beam blockage. Villarini et al. (2011) recommended using the Stage IV dataset only out to 150 km offshore of a coastal radar. Finally, TC-strength winds can affect the ability of a gauge to correctly collect rainfall. Specifically, the accuracy of a gauge decreases with increasing wind speed (e.g., Miller 1958; Simpson and Riehl 1981). Wootten and Boyles (2014) found a latitudinal gradient in Stage IV root mean square error (RMSE), with greater RMSEs in

24 the southern U.S. They also showed that Stage IV overestimates low rainfall intensities by small amounts and underestimates higher intensities by larger amounts. The Stage IV dataset has been used in numerous TC studies. For example, it has been employed to validate TRaP techniques (a snapshot TC rainfall persistence model; Ferraro et al. 2005; Lonfat et al. 2007; Habib et al. 2009; Ebert et al. 2011; Zagrodnik and Jiang 2013), to evaluate model- or satellite-derived TC precipitation (Marchok et al. 2007; Villarini et al. 2011), and to highlight inter-storm diﬀerences (Jiang et al. 2008). Despite the limitations of Stage IV data described above, it still was the superior option compared to other CONUS precipitation datasets (e.g., the TRMM Multiple Satellite Precipitation Analysis [TMPA] and the North American Land Data Assimilation System [NLDAS]) for landfalling TCs (Villarini et al. 2011). Stage IV data also were chosen because they extend to higher latitudes than TRMM.

3.2 Methodology

The GFS and Stage IV data were used in several ways to achieve the goals of the research. This section highlights the methods used to analyze these data. The individual 6-h Stage IV precipitation accumulations were composited with respect to storm motion, shear, and intensity. This compositing was done for the entire eastern U.S. and Gulf Coasts (denoted the “full” composites) and for speciﬁc geographic regions (denoted the “regional” composites). These Stage IV composites served as input to the statistical rainfall forecast model that is derived in the following sections. Finally, the GFS forecast data also were composited based on whether the GFS produced a skillful or not-skillful TC rainfall forecast. Details of the compositing methodology follow.

3.2.1 Development of the Stage IV rainfall statistical dataset

To develop the new method for forecasting TC rainfall and to help identify errors in the GFS TC rainfall forecasts, the Stage IV rainfall data were composited with respect to environmental vertical shear, TC motion, and TC intensity during the years 2004 – 2012 for all Best Track storms within 300 km of the U.S. coastline. However, only Stage IV data within 150 km of each coastal radar site (Fig. 3) were used to maintain data quality (Villarini et al. 2011). These composited data served as the rainfall grids for the statistical rainfall forecasts.

25 Figure 3. Example of masking technique used to limit Stage IV observations to 150 km from a coastal radar. Example shown is for TC Fay (2008). The full Stage IV dataset is shown in (a), a zoomed version is in (b), and the ﬁnal masked data is in (c).

3.2.1.1 Aggregation of Stage IV rainfall data. To account for regional effects on TC precipitation, such as the orientation of the coastline and latitude, the U.S. Gulf and Atlantic coastlines were divided into seven geographic regions based on a cluster analysis of Best Track landfall locations (Fig. 2). Thiessen polygons (Thiessen 1911) were used to determine the boundaries of each region by selecting the polygons that were closest to clustered landfall locations. This approach of using clustered TC locations is similar to that used for compositing TCs by Schoner (1968) who investigated climatological patterns of rainfall, and Jagger and Elsner (2006) who created three regions to study extreme hurricane winds near the U.S. Observed TC tracks along the U.S. coast were used to determine boundaries of the seven regions. For example, storms in the Southern Texas region (denoted STX, see Fig. 2) primarily translate from east to west, whereas those in the Northern Gulf primarily track south to north and possibly recurve into the mid-latitude synoptic flow. If a storm was located within 300 km of the U.S. coastline, the Stage IV data out to 500 km from storm center were binned on an equidistant cylindrical grid with a 10 × 10 km spacing (provided the data were within the 150 km coastal radar buffer as discussed in Section 3.2.1; e.g.,

26 Table 4: The number of 6 h Best Track locations and landfalls for the regions shown in Fig. 2. The number of landfalls refers to the number landfalls within the continental United States landfalls, not any landfalls on islands beyond the coastline that are included in the Best Track dataset.

Region N 6-h BTK N Landfalls Southern Texas 53 5 Northern Gulf 190 19 Northwestern Florida 60 6 Southern Florida 109 11 Southern Atlantic 80 3 Middle Atlantic 148 7 Northern Atlantic 105 6

Fig. 3). This grid spacing was chosen so that each grid box within each of the seven regions would have a sufficient sample size. The latitude-longitude location of each 10 × 10 km grid cell was converted to an x-y distance coordinate from the center of the storm on the equidistant cylindrical grid. Table 4 shows the number of 6-h Best Track and landfall locations for each of the regions shown in Fig. 2. Each region contains a considerable number of 6 h Best Track locations and total landfalls. Because there is a reasonable distribution of 6 h locations in each region, the bias in the methodology used to determine the regions is minimized. Additionally, the distribution helps ensure that the regional boundaries are representative of the historical location of TC tracks and landfalls along the U.S. Atlantic and Gulf of Mexico Coasts. Earth-, motion-, and shear-relative rainfall composites were created for each of the seven geographic regions and the entire U.S eastern and Gulf coasts. Storm motion was defined as the storm’s previous 6-h forward speed and heading. Shear was calculated at 6-h timesteps using the same procedure in the Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria et al. 2005) in which vector wind differences between 200 and 850 hPa are averaged within an annulus of 200 – 800 km. SHIPS-derived shear was not used since SHIPS does not necessarily contain all 6-h timesteps for all storms within the dataset. Each of the three relative grids (at each time) was rotated so the rotated heading (for motion) and shear angle (downshear; in the direction of the vector) and rainfall field pointed toward the top of the grid domain (denoted “up”). For example, a storm moving to the northeast, with a previous 6-h heading of 45◦ east of north (or with the shear vector pointing toward the northeast) was rotated left 45◦.

27 Table 5: TC intensity categories. Counts of storms for each category are in Table 6. For the Strong Hurricane category (HU1), 53% were Cat 2, 16% Cat 3, 26% Cat 4, and 5% Cat 5.

Category Name Wind Speed [kt] TD0 Tropical Depressions < 34 TS0 Weak Tropical Storms 34 – 45 TS1 Strong Tropical Storms 46 – 63 HU0 Weak Hurricanes 64 – 82 HU1 Strong Hurricanes > 82

In addition to the directional compositing described above, each region and the full composite was further composited based on the magnitude of environmental shear and storm intensity. Shear categories were based on Cecil (2007) and Wingo and Cecil (2010): weak, < 5 m s−1; moderate, 5 – 10 m s−1; and strong > 10 m s−1. Storm intensity categories in Table 5 were either Tropical Depressions, Weak Tropical Storms, Strong Tropical Storms, Weak Hurricanes, or Strong Hurricanes. These additional categorizations sometimes contained too few storms to be statistically robust. Therefore, rainfall composites for adjacent intensity categories within their respective regions were combined. The resulting combinations are shown in Table 6. Similarly, some shear categories in some regions did not exhibit a suﬃcient number of storms to be statistically robust. In that case adjacent shear categories were combined based on like-patterns and magnitudes of rainfall (Table 6). Unlike the TC intensity categories’ rainfall composites, some regions did not contain any periods within a respective Low, Moderate, or High shear environment. For example, the Northern Atlantic region rarely exhibited low-shear environments; therefore, the Low and Moderate shear categories were not combined.

3.2.2 Development of the statistical rainfall forecasts

A major goal of the research was to better-predict TC rainfall using a statistical framework by employing higher-resolution data than previous studies and similar but improved methods for compositing rainfall. The model developed here is similar to R-CLIPER and PHRaM in that it approaches the forecasting problem from a climatological perspective (described in Chapter 2). PHRaM was developed to improve R-CLIPER by including the effects of shear and topography. However, the current approach creates different regional climatological datasets that include the effects of topography, as well as interactions with coastlines and differing synoptic-scale features due to latitudinal differences. As will be shown in Chapter 4, a simple parameterized approach

28 Table 6: Intensity and shear categories for each region’s rainfall composites after combination (e.g., from Table 5) to produce robust datasets. Each categories’ number of 6-hourly time steps and unique storms (shown in parentheses) are given.

Storm Intensity and Shear Magnitude Rainfall Composite Categories

Region Storm Intensity Categories Shear Magnitude Categories

Weak Strong Weak Strong Low Moderate High All TD TS TS HU HU (< 5 m s−1) (5–10 m s−1) (> 10 m s−1)

STX TD TS+ Low Moderate+

NGULF TD TS Cat 1+ Low Moderate High

NWFL TD TS+ No Data Moderate High

SFL TD TS Cat 1+ Low Moderate High

SATL TD TS+ No Data Moderate High

MIDATL TD TS Cat 1+ Low Moderate High

Weak NATL TD Strong TS+ (> 45 kt) No Data Moderate High TS (34–45 kt) 6-h timestep and unique storm counts

All 268 (57) 247 (61) 149 (49) 70 (28) 63 (19) 82 (28) 327 (58) 312 (57)

STX 31 (7) 41 (11) 17 (7) 34 (13)

NGULF 102 (24) 85 (26) 37 (12) 18 (9) 90 (27) 74 (18)

NWFL 26 (12) 42 (12) N/A 34 (12) 28 (12)

SFL 31 (11) 47 (16) 34 (10) 20 (9) 59 (17) 31 (14)

SATL 38 (12) 50 (14) N/A 34 (10) 37 (16)

MIDATL 38 (13) 87 (19) 25 (7) 27 (6) 60 (15) 52 (21)

NATL 32 (12) 48 (15) 33 (13) N/A 17 (8) 89 (23)

29 oversimplifies regional TC rainfall characteristics, whereas the frequentist approach used here includes them. Specifically, the current method is two-dimensional in that it contains a mechanism that reorients the rainfall (using TC motion and vertical shear vectors) and a mechanism to modify the magnitude of the rainfall (using the magnitude of TC shear and TC intensity). An additional utility of the present rainfall model is to identify areas where the GFS poorly replicated observed (Stage IV) TC rainfall. This methodology allows a direct comparison of GFS rainfall forecasts based on shear, forward motion, and intensity. The statistical rainfall forecasting scheme being developed used the composited Stage IV data (described above) placed on a GFS TC track forecast. ATCF track forecasts for the GFS between 2013 – 2016 were used to locate 6-hourly forecast TC locations. A nearest neighbor approach was used to locate the position of a grid point on the composite grid with the corresponding latitude/longitude grid point of the forecast. Simply stated, “where on the globe is the composited grid point located when the point is placed on a TC track?” There were 18 different rainfall forecast methods (shear- and intensity-based plus all shears/intensities; each with three rotations for each individual region and all regions combined) for each 72-h forecast track (Table 7). An R-CLIPER forecast also was created by using the equation from Marks et al. (2002, Eq. (2.8) in Section 2.2.2). The individual parameters in Eq. (2.8) were determined using data from the Stage IV development dataset. The goal of each method was to out-perform the R-CLIPER forecasts. If a forecast method could not beat an R-CLIPER forecast, it was deemed not useful. When applied to a forecast, the shear- and motion-relative datasets were rotated with respect to the shear or motion vector. For example, if the shear vector pointed 45◦ east of north, the shear-relative dataset (either AS/IS/SS; Table 7) would be rotated 45◦ counterclockwise such that the “up” direction in the statistical dataset always pointed downshear. Or, when using the motion-relative dataset (either AM/IM/SM; Table 7), it was rotated by the previous 6-h motion vector such that “up” was forward. Finally, 6-h rainfall from each geographic region along the storm track was accumulated over the 72-h forecast period out to 500 km from the storm center. As an example of the methodology above, consider a hypothetical storm translating through the STX and NGULF regions. If the shear-magnitude/shear-relative (SS; Table 7) forecast method were being employed, the SS rainfall dataset from the STX region was used initially. Then, as the storm translated through the STX region and into the NGULF region, the NGULF SS rainfall

30 Table 7: The nine methodologies for the Stage IV statistical rainfall model, plus R-CLIPER. Each method (except R-CLIPER) uses either the full composite or the regional composites (resulting in 18 forecasts).

Rotational Ensemble Reference Description Basis Member Frame

RCP - Stage IV R-CLIPER Marks et al. (2002)

IE Earth Lonfat et al. (2004); Based on storm intensity. Chen et al. (2006); IM Motion Varies from region to region. Xu et al. (2014) IS Shear AE Earth Black et al. (2002); Based on all intensities Rogers et al. (2003); AM Motion and shear magnitudes. Lonfat et al. (2004); AS Shear Chen et al. (2006) SE Earth Based on shear magnitude Chen et al. (2006); SM Motion (< 5, 5 – 10, and > 10 m s−1). Wingo and Cecil (2010) SS Shear dataset was used. If shear could not be calculated for any reason (or did not have a climatological composite, such as the < 5 m s−1 category in the NATL region), the model used the all-storms/motion-relative (AM) dataset. If the motion could not be calculated (say for forecast hour 0), the all-storms/earth-relative (AE) data set was employed. Consider another hypothetical storm in the MIDATL region. The storm remained in this region during its entire 72 h forecast. If the all-storms/motion-relative (AM; Table 7) dataset were being employed, the MIDATL AM rainfall dataset would be used initially. However, since no previous six-hour motion at initialization is calculated, the MIDATL AE (all-storms/earth-relative) rainfall dataset was used. At the second forecast time (+6 h), the MIDATL AM method was used since there was a previous six-hour motion.

3.3 Veriﬁcation metrics and determination of forecast skill

The GFS, R-CLIPER, and Stage IV statistical rainfall models were verified against Stage IV observations using the Fractions Skill Score (FSS; Roberts and Lean 2008). Its “fuzzy-logic” approach (Ebert 2008) permits minor deviations in the exact locations of QPFs. Thus, the FSS evaluation is not as harsh as comparing individual grid points as is done with the Equitable Threat Score or Critical Success Index (Wilks 2006). The FSS requires the specification of a radius of influence (ROI, search radius) around the grid point for which the score is being computed. Several

31 ROIs generally are applied so the change in skill with respect to radius is shown. ROIs of 25, 50, 75, and 100 km were used here. Since forecasts were verified using a 10 × 10 km grid spacing, there were 19, 78, 176, and 314 grid boxes in each ROI, respectively. Different rainfall thresholds also were employed to identify at what thresholds the various forecast methods and the GFS either had skill or no skill. The fraction of grid points within the ROI that exceed the specified threshold was computed for every onshore grid point within the domain. The FSS then was computed from these fractions. A score of 1 represents a perfect score, while 0 indicates that no forecast points verified. A score of 0.5 indicates that the QPF verified at 50% of the grid points comprising the rainfall threshold within the designated ROI. Thirteen thresholds were chosen: 1 mm, 5 mm, 10 – 100 mm (with an interval of 10 mm), and 150 mm. This provided a large range that allowed the determination of skill for low, ∼1 – 30 mm, moderate, ∼30 – 60 mm, and heavy ∼70 – 150 mm rainfall accumulations. Skill of the statistical model (or the GFS) was assessed by comparing its FSS to that from R-CLIPER. If the statistical model had an FSS greater than that from R-CLIPER, the statistical model was deemed more skillful. If the statistical model could provide a better or comparable FSS than R-CLIPER, then it could be used as a supplement to R-CLIPER. Results (discussed in Chapter 4) showed that FSS changes little (∼0.05 FSS) between ROIs regardless of threshold for the statistical model. Therefore, the 50 km ROI was selected as the primary ROI for analysis. Several caveats about the verification process should be discussed. The Stage IV data were downscaled and interpolated from their native 4 × 4 km grid to the same 10 × 10 km grid as the statistical model. This results in a smoothing of the rain fields and decreases maximum rain amounts. It allows the possibility of better verified forecasts from the statistical model since the statistical model, by its design, struggles at forecasting high rain threshold amounts (discussed in Chapter 4). For example, assume that an earth-relative, all shears/all intensities (Table 7) 6 h rainfall composite has a maximum rain rate of 0.5 in. 6 h−1 and is used to create a 72-h forecast. The maximum amount of rain that the forecast can achieve is 6 in. (152 mm) – approximately the maximum threshold studied. This maximum would occur if the storm remained stationary. This scenario is highly unlikely. Since the earth-relative all shear/all intensities approach is being used, shear and motion will not affect the composite.

32 The GFS was verified similarly on the same 10 × 10 km grid as the statistical model. Each GFS forecast (whether it had a native grid spacing of 0.5 deg or 1 deg, see Table 3) was interpolated to a 10 × 10 km grid spacing. This interpolation modifies the resulting FSS calculation and is more favorable to smaller rainfall thresholds. This occurs because the GFS data files being used, due to their coarse resolution struggle at recreating typical high-resolution TC rainfall structures such as the moat-rain-moat (a feature that can be much smaller than 50 – 100 km). When the forecast files are interpolated from their native resolution to a lower resolution for analysis, the result best- represents the average, or most-representative rainfall, within the lower resolution grid box. This reduction in resolution will generally suppress larger rainfall amounts due to their scarcity more than smaller rainfall amounts. The common method for producing a one-to-one comparison of skill is to reduce all higher- resolution grids to the coarsest grid being studied. However, this is not done here since the primary concern is evaluating the skill of the statistical model compared to R-CLIPER. Comparison of the statistical techniques to a full-scale dynamical model is accomplished using the GFS. Since the statistical model was created from Stage IV data that were reduced in resolution from 4 km to 10 km, we determined that evaluating skill on a 10 x 10 km grid was sufficient.

3.3.1 GFS environmental conditions

To investigate the environmental conditions that are conducive to skillful or not skillful GFS forecasts, and to gain insight into whether additional parameters could be added to the statistical model, the FSS was computed for all GFS forecast storms from 2004 – 2012. The dataset then was divided into three categories based on the value of FSS (Table 8): Top performing (FSS > 0.66), Middle performing (0.33 < FSS < 0.66), and Bottom performing (FSS < 0.33) forecasts. The Middle category served as a “sanity check” to ensure that diﬀering environments did indeed exist between the Top and Bottom categories, and to ensure that the Top and Bottom categories are representative of the full dataset and not just dominated by one or two storms. Therefore, if the Top and Bottom forecasts occurred in greatly diﬀerent environments, Middle should be between them. Mean environmental values were computed at each forecast hour for the forecasts in the Top, Middle, and Bottom categories.

33 Table 8: Fractions Skill Score (FSS) categories, mean FSS for each category as well as the 95% conﬁdence interval, number of 72-h forecasts, and counts of unique storms within each category.

Bottom Middle Top FSS Thresholds < 0.33 0.33 – 0.66 > 0.66 Mean FSS ± 95% CI 0.06 ± 0.02 0.51 ± 0.02 0.81 ± 0.01 72-h Forecast Counts 123 68 113 Counts, Unique Storms 35 26 22

34 CHAPTER 4

RESULTS

The results are organized into three sections: 1) composite analyses of Stage IV rainfall distributions near TCs, 2) example TC rainfall forecasts from the GFS and the newly created Stage IV statistical model, and 3) veriﬁcation of forecasts from the models (the GFS, R-CLIPER, and the statistical model). An analysis of errors within the model and an investigation of possible improvements to the model are presented in Chapter 5.

4.1 Regional and U.S. Stage IV TC rainfall composite analysis

The previous TC-related rainfall studies outlined in Chapter 2 primarily analyzed satellite- derived QPEs with respect to shear, motion, and/or intensity. This research, instead, uses Stage IV rainfall data to investigate these characteristics. It also compares the current results to those of the earlier studies. Both similarities and diﬀerences are found. The diﬀerences are shown to be more pronounced when considering TC rainfall on a regional basis.

4.1.1 U.S. rainfall composites

4.1.1.1 All storm intensities and vertical shear magnitudes. Figure 4 shows Stage IV-derived mean 6-h rain rate composites during years 2004 – 2012 in earth-, storm motion-, and 200 – 850 hPa vertical shear-relative reference frames.1 The composites generally are consistent with the ﬁndings of previous shear- and motion-relative TC rainfall studies which used satellite-derived QPEs (e.g., Black et al. 2002; Rogers et al. 2003; Lonfat et al. 2004; Chen et al. 2006; Wingo and Cecil 2010; Xu et al. 2014). However, several striking diﬀerences are revealed by the Stage IV data. For example, the principal rainband in the earth-relative plot (Fig. 4a) appears as a broad, arcing rainfall maximum that extends northeast to southeast from the center of the storm. This orientation of the principal rainband was not seen in previous composite-based studies, probably due to their including storms which were not near land. However, Willoughby

1The color scheme and color scale for Fig. 4 and the following composite ﬁgures all have a range from 0.2 in. to 2.2 in. to remain consistent among all ﬁgures.

35 Figure 4. Full domain Stage IV rain rate composites [in. 6 h−1] for years 2004 – 2012 for earth- relative (a), storm motion-relative (b), and shear-relative (c) coordinates with range rings shown every 200 km starting at 100 km. The latitude/longitude density (counts per 1 × 1 deg grid box) is shown in the bottom right panel (d).

et al.’s (1984) observational study revealed that the orientation of the principal rainband shown in Fig. 4a was dominant in weaker hurricanes and in strongly sheared storms. In the present dataset, the distribution of storm intensities within 300 km of the coastline (Fig. 5) reveals that most of the 6-hourly locations correspond to storms that are less than or equal to tropical storm strength. The distribution of current storm intensities in Fig. 5 is consistent with those of prior studies (e.g., Wingo and Cecil 2010). Stage IV rain rate composites with respect to storm motion (Fig. 4b) exhibit a general right-of-motion maximum that is somewhat more pronounced in the forward-right quadrant. This orientation is consistent with the results of Cline (1926), Goodyear (1968), Parrish et al. (1982), Burpee and Black (1989), Rodgers et al. (1994), Lonfat et al. (2004), and Kimball (2008). The right-of-motion signature is attributed to the increased asymmetrical frictional forcing on the right side of a storm’s track (Shapiro 1983). The right-side maximum also could be associated with the stabilization of the left side due to dry air intrusion as a storm approaches land (Kimball

36 Figure 5. Fractional histogram (deﬁned as the count within a bin divided by the total count of the distribution) of intensity by minimum MSLP [hPa] (line) and storm intensity [kt] (bars) for all 6-hourly Best Track storm locations within 300 km of the U.S. coastline between 2004 – 2012.

2008). Since most of the 6-h storm-center locations comprising the present dataset are over water (72.5%), and all are within 300 km of the U.S. coastline, the right-of-track maximum and therefore subsequent stabilization of the left side is consistent with Kimball (2008). Figure 6 shows the distribution of 200 – 850 hPa vertical shear directions and magnitudes for the present dataset. The majority of 6-hourly storm locations are in environments with shear < 10 m s−1 (moderate to weak shear), and most shear headings (the direction the shear vector is pointing) are toward the NNE to ENE. These characteristics (Fig. 6) are much like those of previous rainfall composite studies (e.g., Fig. 6 of Chen et al. 2006 and Fig. 2 of Wingo and Cecil 2010). The results of Willoughby et al. (1984), showing the existence of the principal rainband in stronger sheared storms, also should be observed with the Stage IV dataset because of the current distribution of shear strengths, and that is indeed the case. The 200 – 850 hPa shear-relative rain rate pattern (Fig. 4c) exhibits a general downshear-left (DSL) maximum, consistent with previous research (Black et al. 2002; Rogers et al. 2003; Chen et al. 2006; Wingo and Cecil 2010; Reasor et al. 2013; Xu et al. 2014). However, the current rainfall pattern is more asymmetric than in prior studies. Speciﬁcally, when comparing our rainfall pattern to Wingo and Cecil (2010, their Fig. 3), the asymmetric rainfall structure seen in Fig. 4c is more elongated in the downshear direction.

37 Figure 6. Fractional histogram (as deﬁned in Fig. 5) of shear magnitude [m s−1] and heading [degrees from North]. The line shows shear magnitude while the bars show shear heading.

This difference is attributed to the exclusion of storms beyond 300 km from the U.S. coastline. Storms located this far from the coast are unlikely to be influenced by the distant land mass which could contribute to the asymmetric structure of rainfall due to enhanced frictional forcing or the entrainment of dry continental air (e.g., Kimball 2008). Instead, the present DSL maximum is attributed to the processes described in Chapter 2 (e.g., Black et al. 2002). Specifically, it occurs because the counterclockwise winds of the TC advect rain falling in the convectively initiated side (downshear-right) toward the DSL quadrant. The more elongated asymmetric shear-relative rainfall structure seen in Fig. 4c also could be associated with having more-available Stage IV data at higher-latitudes than previous studies which used TRMM data. TCs in the higher latitudes expe- rience stronger-sheared environments that can lead to an increased asymmetric rainfall structure (discussed in detail below). To summarize, the earth-, motion-, and shear-relative rain rate composites in Fig. 4 have many similarities with previous research based on satellite-derived rainfall. However, several important features that differ from previous findings become apparent when the Stage IV dataset is employed. Examples are the location of the principal rainband in the earth-relative reference frame (Fig. 4a) and the more asymmetric rainfall structure in the shear-relative reference frame (Fig. 4c).

38 Thus, the Stage IV rainfall data appear to be as acceptable, if not superior to, TRMM data in analyzing TC rainfall. Stage IV rainfall data previously were found to be superior to satellite- derived TC rainfall when performing a one-to-one comparison of three diﬀerent storms during the 2004 hurricane season (Villarini et al. 2011). The rain rate composites in Fig. 4 will be used as input to the statistical forecast model being developed. Since the model will be used to forecast TC rainfall over land, we believe that the previously mentioned features will enhance the utility of the model, further showing the usefulness of using Stage IV data in TC rainfall composite studies. The Stage IV data also will be used to produce additional TC rainfall composites and to verify both the statistical rainfall model and the GFS predicted rainfall.

4.1.1.2 Rainfall composites by storm intensity. The Stage IV rain rate data next were composited by storm intensity: Tropical Depressions (TD0), Weak Tropical Storms (TS0), Strong Tropical Storms (TS1), Weak Hurricanes (HU0), and Strong Hurricanes (HU1; Table 5) based on Rodgers et al. (1994), Lonfat et al. (2004), Chen et al. (2006), Wingo and Cecil (2010), and Xu et al. (2014). Figure 7 shows rain rate composites for these intensity categories in earth- (left) and shear-relative (right) reference frames. Results show that as storm intensity increases, the rain rate pattern in both reference frames becomes more symmetric. Although this pattern change is somewhat more apparent in the earth-relative frame (Fig. 7, left, e.g., compare TD0 with HU1), it is best explained using the shear-relative reference frame (Fig. 7, right). As environmental vertical shear increases in magnitude, storm intensity usually decreases, and vice versa. The shear-relative plots in Fig. 7 show a well-defined DSL rain rate maximum for intensity categories TD0 through TS1. These weak storms most likely are occurring in stronger-sheared environments. However, as storm intensity increases to hurricane strength (HU1, again assuming that shear is weakening), the storm’s rainfall becomes more symmetric as the effects of shear diminish. Thus, the HU1 shear-relative intensity storms exhibit a slight DSL maximum of rain rate, although the pattern is more symmetric about the center of the storm compared to TD0. Rodgers et al. (1994) observed that as storm intensity increases, the heavier rainfall shifted toward the TC center. Additionally, Chen et al. (2006) found that the wavenumber-1 asymmetry with respect to the 200 – 850 hPa vertical shear decreases (becomes more symmetric) as storm intensity increases (their Fig. 4). The composites shown in Fig. 7 are consistent with their results. However, later sections will show that differences do arise when viewed from a regional perspective.

39 Figure 7. Stage IV rain rate [in. 6 h−1] composites based on TC intensity categories: tropical depression (TD0), weak tropical storm (TS0), strong tropical storm (TS1), weak hurricane (HU0), and strong hurricane (HU1). TC intensity categories are further deﬁned in Table 5. The left panels show rainfall composites in earth-relative coordinates while the right panels show shear-relative. Range rings start at 100 km and are at intervals of 200 km.

40 Figure 7 revealed that as storm intensity increases, the associated rain rate also increases. Figure 8, showing mean 6-h azimuthally averaged rain rates and their 95% confidence intervals, also highlights this relationship. For example, at 50 km from the center of the storm, the TD0 rain rate is ∼0.4 in. 6 h−1, while the HU1 rain rate is more than quadruple this value (∼1.8 in. 6 h−1). These results agree with those of Rodgers et al. (1994) and Lonfat et al. (2004) and are due to the contraction of areas of maximum rain rates associated with increasing storm intensity. Specifically, as intensity increases, the primary circulation becomes stronger and more symmetric (Lonfat et al. 2004). The relationship between increasing rain rate with increasing storm strength also was seen in Fig. 7 where the HU1 composites exhibited a much greater rain rate than the TD0 composites. The Stage IV rain rate maxima at the inner core (radius of 0 – 5 km, Fig. 8) for TD0, TS0, TS1, HU0, and HU1 are approximately 12, 19, 35, 45, and 70 mm 6 h−1, respectively. The radial distributions (Figs. 8 and 10) do not exhibit a typical eyewall/eye rainfall structure due to two characteristics of the Stage IV data. First, they were accumulated at 6-h intervals and are not instantaneous rain rates. These characteristics allow rain to be accumulated as the storm progresses over the Best Track center location (what we are defining as storm center; 0 km; see Fig. 13 for an example [discussed later]). Second, the grid size of the Stage IV data (4 km × 4 km) is smaller than that of the binning interval (5 km) in the radial plots. This allows rain to be indicated in the 0 – 5 km bin. When viewing the data at 1 km resolution (not shown), an eye-type feature with minimal rainfall is seen, with an increase in rain rate several kilometers from storm center. However, since the 1-km plots were noisy and less legible, they were not used in the compositing process. Rodgers et al. (1994) found TRMM-derived rain rate maxima of approximately 23.4 mm (0.92 in.) 6 h−1, 27.6 mm (1.09 in.) 6 h−1, and 38.4 mm (1.51 in.) 6 h−1for their Depression, Storm, and Hurricane rain rate categories, respectively, in the Atlantic Basin (their Fig. 2, converted to 6-hourly). If we average the current TS0/TS1 or HU0/HU1 categories or just the TS1 and HU1 categories to obtain tropical storm and hurricane rain rate categories that are consistent with Rodgers et al. (1994), current rain rates are greater than found in their research. However, Lonfat et al. (2004) also found global (e.g., all oceanic basins) mean rain rate maxima of approximately 18.6 mm (0.73 in.), 42 mm (1.65 in.), and 75.6 mm (2.98 in.) 6 h−1, respectively, for the same categories. The Stage IV results are similar to their global values. The Stage IV rainfall accumulations are

41 Figure 8. Azimuthally-averaged Stage IV rain rate [in. 6 h−1] with 95% conﬁdence intervals (bars) by storm intensity for all storms in the development dataset (2004 – 2012). Storm intensity categories are deﬁned in Table 5. The bin size for distance from storm center is 10 km.

primarily over land, while TRMM data are over both land and water. This suggests that the Stage IV data are superior to TRMM over land.

4.1.1.3 Rainfall composites by vertical shear magnitude. Vertical shear of suf- ﬁcient strength (e.g., > 5 m s−1) is the primary mechanism that orients precipitation patterns in TCs (Corbosiero and Molinari 2003; Ueno 2007; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013; Xu et al. 2014). Therefore, the Stage IV rainfall data were composited into three shear categories following Cecil (2007) and Wingo and Cecil (2010): Weak, < 5 m s−1; Moderate, 5 – 10 m s−1; and Strong > 10 m s−1 (Fig. 9). The rainfall pattern in weak shear environments (Fig. 9; left panels) is more symmetric about the storm center and is less organized than in strong shear environments (Fig. 9; right panels) due to the TC’s response to vertical shear. Numerous studies have found a relationship between convection, rainfall, and the vertical tilt of a TC vortex due to diﬀerential advection by deep-layer environmental shear. A vertically sheared vortex will tilt downshear. This tilt initiates a thermal couplet between the upshear and downshear sides. In an adiabatic state (e.g., Jones 1995; Frank and Ritchie 1999) a parcel moves downwind along the cyclonic rotation of the TC and ascends downshear along an isentropic surface. The parcel then descends isentropically on the upshear side. This partially explains the rain rate

42 Figure 9. Stage IV rain rate [in. 6 h−1] for the three shear magnitude categories: Weak (< 5 m s−1); Moderate (5 – 10 m s−1); and Strong (> 10 m s−1) in earth- (top) and shear- (bottom) relative reference frames. The shear magnitude categories were based on Cecil (2007) and Wingo and Cecil (2010).

minimum seen upshear in the shear-relative composites (Fig. 9; bottom). However, once condensation occurs the ascent path of the parcel is no longer on an isentropic surface. The secondary circulation forced by the vertical shear then is due to differential vorticity advection (Frank and Ritchie 1999). Convection initiates in the DSR quadrant, and the subsequent hydrometeors are advected downwind one shear quadrant (DSL; e.g., Hence and Houze 2011; Reasor et al. 2013). Therefore, weakly-sheared storms will have a weaker secondary circulation (due to vertical shear and the thermal couplet) and a less-organized rainfall pattern (Fig. 9; left) due to the erosion of the thermal couplet due to condensation (since some parcels begin to condense at different times than others). Strongly sheared storms, with the effects of differential vorticity advection exerting an important role in the secondary circulation, will initiate more convection in the DSR quadrant which will subsequently create more rainfall that is advected to the DSL quadrant. Therefore, the displacement and asymmetry of TC rainfall in weakly-sheared environments is less than in environments with stronger shear. The control run of the moist simulations experiment of Frank

43 and Ritchie (1999), when neither zonal flow nor shear were induced on a baroclinic vortex, did not produce greater rainfall than simulations when zonal flow and/or vertical shear were induced. Instead, the rainfall was more concentrated within the eyewall region. Thus, any increase in rainfall magnitude was due to the reorientation of rainfall, not the increased production of it. The variation in magnitude of shear-relative rain rate is opposite that found in the composites categorized by storm intensity. Specifically, the composites categorized by storm intensity (Fig. 7) reveal an increase in rain rate with storm intensity (an increase in storm intensity is usually inversely related to the magnitude of vertical shear in the storm environment), while the weak-shear storms (Fig. 9; left panels) exhibit smaller rain rates than the strong-shear storms (Fig. 9; right panels). This is further exemplified in Fig. 10 which shows azimuthally averaged 6-h rain rate by shear category. Readers should recall from the previous section that a minimum is not expected in the 0 – 5 km bin due to the methodology being used. From the storm center out to 500 km, the stronger-sheared storms produce greater azimuthally-averaged rain rates, except near ∼50 – 70 km where the moderate shear category exhibits greater rates. Since shear tilts the vortex, stabilizes the storm, and decreases convection (DeMaria 1996), strongly sheared storms are more likely to be weaker in intensity. The control runs (non-sheared) and variable runs (sheared) of Frank and Ritchie (1999) produced the same total accumulated rainfall. However, their control run exhibited more rainfall concentrated in the eyewall region (meaning less rainfall than outside the eyewall region). Therefore, using the Stage IV observations, the increased rain rates in the shear magnitude composites (Figs. 9 and 10) must be due to the ability of vertical shear to reorient rainfall instead of creating more rainfall (as was found with Frank and Ritchie [1999]). In stronger-sheared storms, the effect of shear is strong enough to consistently align rainfall DSL (Fig. 9, right panels).

4.1.2 Selected regional composites

The previous discussion highlighted the characteristics of TC rainfall based on the magnitude of vertical shear, storm intensity, and earth- and shear-relative reference frames for the entire Atlantic and Gulf of Mexico coasts. The following discussion focuses on seven speciﬁc geographic regions comprising the overall domain (Fig. 2). Due to the large number of categories (seven regionally speciﬁc datasets, three rotational reference frames, shear magnitude, and intensity, totaling 42 unique composites), only selected regions will be discussed in detail. To maintain statistical ro-

44 Figure 10. Same as in Fig. 8 but partitioned by shear magnitude (Weak: < 5 m s−1, Moderate: 5 – 10 m s−1, and Strong: > 10 m s−1) with 95% conﬁdence intervals (bars). Shear categories are based on Cecil (2007) and Wingo and Cecil (2010).

bustness, those regions that did not exhibit clear signals in either of the composites were combined or discarded (Table 6). To gain an overall perspective of regional differences in TC rainfall, Fig. 11 shows earth- relative rain rates for each of the seven geographic regions (Fig. 2) for the combination of all storm intensities and shear magnitudes. Although there are some similarities among the regions (Fig. 11), such as a preferred maximum in the northeast quadrant (similar to the full composite, Fig. 4), there also are some important differences. For example, the NWFL, MIDATL, and NATL regions exhibit an elongated southwest to northeast rain rate maximum. Also, the STX, NGULF, and SFL regions are more axially symmetric than the Atlantic regions (SATL, MIDATL, and NATL). These differences in patterns are due to the different storm environments of the regions. The southern storms are more axially symmetric due to their more tropical environments, whereas the higher-latitude storms occur in more baroclinic environments and thus are more influenced by the effects of shear. Figure 12 shows the median distribution of shear magnitude and storm intensity for the seven geographic regions. The SFL region contains the strongest storms, with a median intensity of 50 kt and an upper quartile of 75 kt. Consequently, its rain rate composite (Fig. 11) exhibits the greatest magnitudes, consistent with the stronger intensity storms occurring

45 Figure 11. Regional Stage IV rain rates [in. 6 h−1] for all storm intensities and all shear magnitudes in an earth-relative reference frame (AE; deﬁned in Table 7) for the seven geographic regions in the study. Six-hour counts can be found in Table 6.

there (Fig. 12). Conversely, the NATL region contains the greatest shear (Fig. 12) and therefore has the most asymmetric structure (Fig. 11). These differences show the importance of studying TC rainfall on regional scales. The differing regional characteristics of TC rainfall are exemplified by Hurricane Hermine (2016; Fig. 13). Only Stage IV rainfall accumulations within 150 km of the nearest coastal radar (Chapter 3) are shown. Hermine at 30 min past landfall (i.e., 0600 UTC 2 September [Fig. 13a]) is located over the Florida Panhandle based on HURDAT2 (HRD 2018). The storm still retains a typical tropical rainfall structure. For example, the effects of enhanced frictional convergence to produce increased rainfall can be seen over northern Florida and southern Georgia, as well as a remnant eyewall signature southwest of the 6 h best track location (Stage IV accumulations are for the previous 6 h). Figure 13 also is an example of why the azimuthally averaged rain rate graphs (Figs. 8 and 10) did not show a minimum at 0 km radius. Specifically, the Stage IV “eye” is

46 Figure 12. Median (solid lines) and Inter-Quartile Range (shaded regions, where the lower quartile is the bottom and the upper quartile is the top) for shear (blue) and TC intensity (orange) [kt]. Values are given for each of the seven geographic regions (Fig. 2) and for the composite of all regions (denoted ALL).

located southwest of the 6-h Best Track location. By 1200 UTC 3 September, 30 h later (Fig. 13b), Hermine has moved northeast. If one assumes that the region of cold IR-derived cloud tops over the Atlantic Ocean is associated with rainfall, there is now a greater gap between the western and eastern sides of the precipitation field. This is due to the entrainment of mid-level dry air from a ridge over the Ohio River Valley (Fig. 14). During the 30-h period between Figs. 13a and b the dry air interacted with the storm and altered its rainfall pattern. Specifically, the TC entrained the dry air cyclonically around the storm causing a minimum in rainfall east and southeast of the storm, assumed by the lack of clouds in GOES IR imagery (Fig. 13b) and by the drier air at 500 hPa (Fig. 14b). The synoptic flow associated with the dry air entrainment simultaneously moved the eastern rainband further away from the storm, out to approximately 400 km. Thus, the rainfall pattern has shifted from a typical tropical rainfall orientation (Fig. 13a) to a more elongated, widespread signature to the west and north with a far-removed rainband to the east. The cloud band east of Hermine in Fig. 13b corresponds well to the band of rainfall in the MIDATL composite at a range of approximately 300 km (Fig. 11), further showing the usefulness of viewing TC rainfall in a regional manner. This type of detail is not seen in the full composites (Fig. 4) or

47 Figure 13. Hurricane Hermine (2016) Stage IV 6-h rainfall [in.] and GOES-13 IR (Band 4) satellite images while in the NWFL region (a; 65 kt Cat 1, 0600 UTC 02 Sept. 2016) and the MIDATL (b; 55 kt TS, 1200 UTC 03 Sept. 2016) region. Six-hourly Best Track locations are shown by black dots. Shear direction is shown by the double line pointing away from the storm at the 6-h best track location.

in prior research. The temporal change in rainfall patterns (Fig. 13) appears related mostly to the entrainment of dry air from the west into and around the storm, but also to the increase in vertical shear. At 0600 UTC 2 September, the SHIPS-derived vertical shear over Hermine is ∼10 m s−1 (with a heading of 71 deg east of north), whereas 30 h later, it is ∼21 m s−1 (with a heading of 56 deg east of north). A mid-level cyclone starts to build west of the storm over the Appalachians around 0600 UTC 3 September and eventually merges with the storm around 1200 UTC 3 September (shown as an elongated trough that is oriented east to west from the center of the storm in Fig. 14b). This mid-level cyclone increases the environmental shear on Hermine while also aiding the entrainment of dry air. The eﬀect of increased vertical shear on rainfall can be visualized: If one imagines rotating the MIDATL shear-relative rainfall composite (Fig. 15; discussed below) clockwise by 71 deg (the angle of the shear heading at this time; shown by the double line in Fig. 13b), the rainfall observations at 1200 UTC 3 September (Fig. 13b) are mostly realized. This type of analysis is crucial to understanding and better-forecasting TC rainfall.

48 Figure 14. Synoptic environment for Hurricane Hermine (2016) corresponding to the time in Fig. 13b (1200 UTC 03 Sept. 2016). Left panel (a) shows 850 hPa vorticity [s−1 × 10−5] and height [dam], while the right panel (b) shows 500 hPa RH [%] and height [dam].

When viewing regional TC rain rates in a shear-relative reference frame, major diﬀerences become apparent when compared to the full coastal composites (Fig. 4) and prior studies (e.g., Corbosiero and Molinari 2003; Chen et al. 2006; Ueno 2007; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013; Xu et al. 2014). Figure 15 shows shear-relative rain rates for the seven geographic regions, and Table 6 gives the number of storms and unique forecasts that contributed to each regional composite. All regions except MIDATL exhibit a DSL maximum, while MIDATL exhibits more of a left-of-shear maximum (as in the Hermine example in Fig. 13b). The MIDATL composite still favors the DSL quadrant, but it is more symmetric about the front-to-back axis and to the left of the shear vector. This result diﬀers from Xu et al. (2014, their Fig. 2) whose SUSA region (NGULF in this research) primarily was symmetric about the downshear vector. However, Xu et al.’s SEUSA composite did exhibit a left-of-shear maximum like the MIDATL region. The STX rain rate composite (which has the weakest shear of the geographic regions) is more symmetric than the NATL (which has the strongest shear; Fig. 12). The SFL shear-relative composite exhibits the greatest mean 6-h rain rate. This is attributed to storm intensities in the

49 Figure 15. As in Fig. 11 (Regional Stage IV rain rates [in. 6 h−1]), but in the shear-relative reference frame (Table 7) for the seven geographic regions. Six-hour counts can be found in Table 6.

region. The NATL region has the most radially expansive and asymmetric rain rate structure of the regions (Fig. 15) due to its more baroclinic environment. That is, as TCs reach the northern latitudes, they increasingly interact with mid-latitude, synoptic-scale weather features such as mid- level troughs. The troughs enhance vertical shear on the storm causing its rainfall ﬁeld to become less tropically symmetric and elongating it to make it more radially expansive (e.g., Atallah et al. 2007).

4.1.3 Stage IV rainfall summary

The Stage IV composites described above emphasize the importance of investigating regional aspects of TC rainfall. The full composites (Fig. 4) reveal that Stage IV TC rain rates are consistent with previous satellite-derived results. However, the Stage IV observations reveal a banding signature in the earth-relative reference frame that was not apparent in prior composite- based research. The Stage IV rain rate structures also are more asymmetric compared to those of

50 prior research – an important finding revealing that rain rate maxima, when viewed in different reference frames, can be more elongated than previously found. An additional finding is that interesting variations in rain rate are observed when individual geographic regions are compared. Specifically, the U.S. Gulf and Atlantic coastlines were separated into seven geographic regions based on Best Track landfall locations. The Stage IV regional rainfall data were further composited based on storm intensity and the magnitude of environmental 850 – 200 hPa vertical shear, and were oriented in earth-, motion-, and shear-relative reference frames. This type of analysis with Stage IV TC rainfall has not, to the author’s knowledge, been done before. The regional composites reveal rain rate characteristics that do not appear in the full composites. All regions except the MIDATL exhibit shear-relative rain rate patterns that generally are consistent with prior research. That is, maximum rain rate primarily is concentrated in the DSL quadrant (Fig. 15). Although the MIDATL region also exhibits a DSL maximum, it is more symmetric about the downshear/upshear axis. This is attributed to asymmetric frictional forcing inland of the coastline. Its motion-relative rain rate structure contains a left-of-motion maximum (which is opposite that of previously described TC rainfall structures that showed a right-of-motion maximum). Similarly, a left-of-motion structure is apparent in the SATL and NATL regions. Rain rate composites separated into intensity categories reveal that as storm intensity increases, so does rainfall. This is observed across all regions (not shown). The NATL region exhibits an expansive rain field that is related to its enhanced baroclinicity. Conversely, the more southern regions (NGULF, STX, SFL) exhibit rainfall structures that are more tropical looking in nature. One of the primary research goals was to determine whether TC rainfall fields viewed from a regional perspective exhibit different rainfall signatures. Results show that Stage IV data are ideal for this purpose because of their greater spatiotemporal resolution and their ability to detect rainfall at higher latitudes than TRMM observations (thus revealing unique regional characteristics, e.g., NATL). These results next will be used to develop a statistical rainfall forecast model whose results will be compared to the GFS model using Stage IV data from 2013 to 2016 as truth. The statistical model hopefully will provide forecasters an additional resource that supplements existing products. Because of the interesting and new findings above, it is hypothesized that an update to R-CLIPER is appropriate, revisiting the analysis of Lonfat et al. (2004) from which R-CLIPER’s

51 Figure 16. Scatterplot of Global Forecast System (GFS) Fractions Skill Score (FSS) and the statistical model (REG-SS; Table 7) FSS for the test dataset (2013 – 2016) using the 50 km ROI and 50-mm threshold. The blue dashed line shows the linear best ﬁt between the two FSS distributions as indicated by the equation and R2 in the bottom right.

methodology is based (Section 2.2.2), but instead using Stage IV data. This approach could produce more-accurate results and provide a better baseline persistence forecast than current methods. However, that is beyond the scope of this research.

4.2 Example forecasts

I first compare the skill of the statistical model and the GFS using the test data during 2013 – 2016. Figure 16 plots the FSSs of the GFS and the REG-SS model based on a radius of influence (ROI) of 50 km and a 50-mm rainfall threshold. Other ROI and thresholds were investigated; however, varying ROI does not provide notably different results, and the 50 mm threshold (as will be shown) is the value at which the GFS and the statistical models diverge in skill. Therefore, it was chosen as the threshold shown here. Results show a positive correlation between skillful forecasts from the REG-SS statistical method and the GFS. The statistically significant (α = 0.5) correlation of 0.48 indicates that as the FSS of the GFS increases, so does that of the statistical model. However, one should note the great deal of scatter in the figure that seriously degrades its

52 usefulness. Thus, it is not appropriate to use the forecast FSS of one model to predict the skill of another. Additional comparisons between GFS and the statistical model will follow. This section highlights selected forecasts of the statistical model, R-CLIPER, and the GFS (for comparison) that either were skillful or not skillful. A full veriﬁcation of the statistical model and its methodology follows. A detailed analysis of environmental characteristics favorable for skilled or not skilled forecasts of the GFS and whether these parameters could be used in the statistical model is given in Chapter 5. Comparisons to GFS forecasts for the same forecast hour also are described.

4.2.1 Stage IV statistical model forecast: Skillful

An example 72 h total rainfall forecast from the test dataset beginning at 1200 UTC 8 May 2015 is given in Fig. 17 for TS Ana (2015). The regional statistical composites used during the 72-h forecast period were those from the REG-SS method, in which rainfall was composited by shear magnitude in a shear-relative reference frame (Table 7; Fig. 18). The GFS TC forecast track was used to place the rainfall composites. Shear was determined by calculating the difference in wind vectors in the GFS forecast between the 200 and 850 hPa surfaces, similar to SHIPS (Chapter 3). The corresponding Stage IV observations are shown in Fig. 19. Table 9 shows the 6-h forecast and Best Track intensities, shears, and regions used. The average FSS for the REG-SS method from the statistical model for all rainfall thresholds combined is 0.73 (Table 10). TS Ana is an example of when the statistical model performs well, i.e., it is a skillful forecast based on the regional SS method. The results for Ana suggest that a simple statistical forecast model can provide a reasonably good forecast (compare Fig. 17 with Fig. 19). The two figures show that the forecast and observed locations of maximum rainfall are collocated in southeastern NC with values of 8.52 in. and 7.59 in., respectively. Over land, where the forecasts can be verified, the observations show a right-of-track maximum (Fig. 19), while the forecast shows a more symmetrical pattern across the storm track (Fig. 17). Over water, in the unverifiable area of the forecast, indicated by dashed contours, the forecast produces maximum rainfall right of the track. The maximum value of 8.52 in. also is located just right of the track in southeastern NC. The reasons for these patterns are discussed below. The hierarchical approach of the REG-SS statistical method selects composite rainfall datasets based on the magnitude of shear. The forecast rainfall accumulation for TS Ana is due

53 Table 9: Forecast and Best Track storm intensities [kt], regions (number identifier and name), shear [m s−1], and Saffir-Simpson categories for the skillful and not-skillful example forecasts discussed in Sections 4.2.1 and 4.2.2. Colors indicate Saffir-Simpson category (Blue: TS; violet: TD) for forecast intensity and correspond to colors shown in Figures.

TS Ana (2015) Forecast Values Best Track Values Intensity S-S Shear Intensity S-S Shear Date Region Region [kt] Category [m s−1] [kt] Category [m s−1] 2013060612 48 TS 13.4 3 NWFL 55 TS 13.45 3 NWFL 2013060618 39 TS 12.86 3 NWFL 55 TS 11.7 3 NWFL 2013060700 35 TS 13.04 3 NWFL 40 TS 12.06 3 NWFL 2013060706 41 TS 12.02 5 SATL 40 TS 11.93 5 SATL 2013060712 38 TS 13.61 6 MIDATL 40 TS 13.83 6 MIDATL 2013060718 36 TS 17.48 6 MIDATL 40 TS 15.63 6 MIDATL 2013060800 36 TS 19.83 7 NATL 40 TS 18.63 7 NATL 2013060806 48 TS 20.56 7 NATL 40 TS 21.47 7 NATL 2013060812 40 TS 24.43 7 NATL 40 TS 24.19 7 NATL 2013060818 35 TS 28.8 7 NATL 40 TS 28.43 7 NATL TS Andrea (2013) Intensity S-S Shear Intensity S-S Shear Date Region Region [kt] Category [ m s−1] [kt] Category [ m s−1] 2015050812 35 TS 2.59 6 MIDATL 40 TS 2.63 6 MIDATL 2015050818 35 TS 4.95 6 MIDATL 45 TS 5.4 6 MIDATL 2015050900 35 TS 7.87 6 MIDATL 50 TS 7.23 6 MIDATL 2015050906 35 TS 9.41 6 MIDATL 50 TS 10.29 6 MIDATL 2015050912 34 TS 9.63 6 MIDATL 50 TS 12.08 6 MIDATL 2015050918 33 TD 8.79 6 MIDATL 45 TS 10.23 6 MIDATL 2015051000 36 TS 9.41 6 MIDATL 45 TS 8.97 6 MIDATL 2015051006 33 TD 9.44 6 MIDATL 40 TS 9.96 6 MIDATL 2015051012 30 TD 8.71 6 MIDATL 35 TS 8.4 6 MIDATL 2015051018 26 TD 6.21 6 MIDATL 30 TD 6.44 6 MIDATL 2015051100 27 TD 7.19 6 MIDATL 30 TD 6.07 6 MIDATL 2015051106 32 TD 6.31 6 MIDATL 30 TD 6.12 6 MIDATL 2015051112 30 TD 4.78 6 MIDATL 30 TD 4.36 6 MIDATL to persistent northerly shear combined with the TC’s slowing and turning ﬁrst to the northwest and later to the northeast. Therefore, the rain accumulation occurs right of the track over water, and somewhat symmetric about the track over land, where the observed large accumulations are located. The storm remained within the MIDATL during the entire forecast period. Its rain rate composite (Fig. 18) exhibits a general left-of-shear rainfall maximum for all three shear categories

54 Table 10: Fractions Skill Score (FSS) for all thresholds of the regional, shear-relative method using the shear magnitude method (REG-SS; Table 7), R-CLIPER (RCP), and the Global Forecast System (GFS) for the skillful 72-h rainfall forecast of TS Ana (2015; Fig. 17) beginning at 1200 UTC 8 May 2015 and the less-skilled forecast of TS Andrea (2013; Fig. 22) beginning at 1200 UTC 6 June 2013. The 95% conﬁdence interval for all thresholds is shown in the Average ﬁeld.

Threshold [mm] Method 1 5 10 20 30 40 50 60 SS 0.65 0.74 0.85 0.88 0.85 0.81 0.80 0.74 FSS Ana RCP 0.55 0.36 0.30 0.23 0.19 0.16 0.16 0.15 GFS 0.85 0.62 0.48 0.20 0.03 0.00 0.00 0.00 SS 0.88 0.90 0.90 0.80 0.71 0.53 0.23 0.01 FSS Andrea RCP 0.85 0.77 0.74 0.71 0.72 0.62 0.31 0.00 GFS 0.91 0.93 0.90 0.73 0.58 0.43 0.33 0.23

Threshold [mm] Model 70 80 90 100 150 Average SS 0.69 0.66 0.67 0.64 0.49 0.73 ± 0.07 FSS Ana RCP 0.15 0.15 0.15 0.14 0.11 0.22 ± 0.14 GFS 0.00 0.00 0.00 0.00 0.00 0.17 ± 0.38 SS 0.00 0.00 0.00 0.00 0.00 0.38 ± 0.36 FSS Andrea RCP 0.00 0.00 0.00 0.00 0.00 0.36 ± 0.33 GFS 0.15 0.07 0.01 0.00 0.00 0.41 ± 0.31

(weak, moderate, and strong) instead of the primary DSL maximum seen in the full composite (Fig. 9). The forecast rainfall pattern shows the effects of changing from weak to strong shear. The weaker shear composite (Fig. 18; left panel) exhibits a more symmetric rainfall structure than the stronger shear categories. Furthermore, as shear increases, the rainfall field radially expands. Further examining the effects of shear, although the shear vector primarily pointed south (i.e., northerly shear) during Ana’s 72 h forecast period, its magnitude changed. The GFS-derived shear at initialization was 2.6 m s−1 (the weak category). Twelve hours later, shear increased to 7.9 m s−1 (the moderate shear category) and remained so until forecast hour 72, when it decreased to 4.8 m s−1. Thus, the beginning of the forecast used the weak shear category MIDATL composite (Fig. 18) which exhibited an arcing rainfall structure from downshear, to left of shear, to upshear within 300 km of the storm center. This arcing rainfall structure contributed to the large rain accumulation over water. Additionally, since the shear vector became oriented toward the southeast during the first few timesteps of the forecast, the accumulation along the track increased due to the weak shear composite having a pronounced downshear (along track in this example) signal. More intense accumulation occurred when the model switched to the moderate shear composite near the

55 Figure 17. 72-h rainfall forecast accumulation [in.] for TS Ana (2015) using the Stage IV statistical model. The regional, shear-relative using shear-magnitude composite (REG-SS Table 7 in text) was used. The forecast was initialized at 1200 UTC 8 May 2015. The date, intensity [kt], shear [m s−1], Saffir-Simpson scale category (shown as different colors for the different categories), and region the algorithm assigned (indicated by a numeric value as well as the name of the region) are shown in Table 9 corresponding 6-h locations within the accumulation plot. Best Track (HURDAT2) storm locations are shown as square markers. Start points are indicated by an “A” and the 72-h forecast point and its corresponding Best Track point are indicated by a “Z.” Shear vectors are indicated by arrows. Finally, unverified rainfall accumulations (over water) are indicated by the dashed contours. Maximum forecast accumulation is shown in the bottom right.

middle of the forecast period. Now, with the shear vector pointing primarily toward the southwest and south, the moderate shear composite accumulated rainfall to the right of and along TS Ana’s track. When TS Ana made landfall, its forecast track recurved toward the northeast (Fig. 17; numbered 6-h locations) which led to forecast rainfall accumulation to the right of and along the track (southeastern NC/eastern SC), including the maximum accumulation of 8.52 in. in southeast

56 Figure 18. Stage IV rain rate composites [in. 6 h−1] used in the forecast shown in Fig. 17. Weak (left), moderate (middle), and strong (right) shear relative rain rate based on shear magnitude (SS; Table 7) for the Mid-Atlantic region.

NC. The last 6-hourly location of the 72-h forecast (marked by a “Z” in Fig. 17) produced little accumulation over northeastern NC (compared to southern NC) due to the faster forward speed (less time to accumulate rainfall) and the transition of the model to the weak shear composite (individual 6-h accumulation not shown). In summary, the distinct SS rainfall characteristics of the MIDATL region (Fig. 18) lead to the well-placed forecast maximum in southeastern NC and the reasonable forecast (compare Figs. 17 and 19). Rainfall forecasts from the current statistical model now are compared to those from R- CLIPER (Chapter 3; Fig. 20). The average threshold FSS for the R-CLIPER forecast is 0.22 (Table 10). This is smaller than the 0.73 FSS from the statistical model. The maximum R-CLIPER forecast rainfall is 6.6 in. (∼1 in. less than observed and ∼1.9 in. less than the statistical model). The location of R-CLIPER’s maximum rainfall is near the coastal North Carolina/South Carolina border, close to the observed maximum location (Fig. 19). R-CLIPER’s maximum is located on the forecast track due to the track structure and the symmetry of the R-CLIPER forecast method (Eq. 2.8). The track forecast pivots and turns from its westward orientation to a more northward direction during the forecast. Because R-CLIPER is designed to be symmetric about the storm track, maxima should be along straight segments of the storm track. These maxima will transition

57 Figure 19. Stage IV 72 h observed rainfall accumulation [in.] corresponding to the forecast in Fig. 17. GFS forecast 6-h locations are shown by circles (what are used as the forecast locations in Fig. 17) and corresponding Best Track locations are shown as squares. See Table 9 for veriﬁed 6-h intensities, regions, and Saﬃr-Simpson categories. Stage IV rainfall amounts are the sum of accumulations at each 6-h forecast during the total 72 h period. Maximum Stage IV accumulation is shown in the bottom right.

to near curves in the track (if there are any) or near areas where a storm moves slowly (if the storm changes speed; Marks et al. 2002). This is seen in Fig. 20 where the maximum is located on the inward side of the curved forecast track. The magnitude of forecast rainfall is similar to that of the observed and statistical model because of the speed of the storm. Speciﬁcally, as Ana approached the coast, its speed was relatively slow (as indicated by the closely grouped 6-h GFS forecast positions, circles) compared to the faster motion during the latter half of the forecast period. The slow speed led to the large rainfall accumulation near the coast. Overall, R-CLIPER produced a forecast with a broad rainfall ﬁeld that was not as detailed as the statistical model.

58 Figure 20. R-CLIPER forecast 72 h rainfall accumulation [in.] corresponding to the forecast in Fig. 17 and the Stage IV observations in Fig. 19. GFS track is shown by circles, and Best Track is shown with squares. Dashed contoured rainfall accumulations over water were not veriﬁed. Maximum forecast amount is shown in the bottom right. See Table 9 for 6-h intensity and region values.

These results highlight the potential of the statistical model to be a new baseline forecast product. Rainfall forecasts from the statistical model now are compared to those from the GFS (Fig. 21). The GFS performed considerably less skillfully than the statistical model, yielding an average FSS of only 0.17 for the combination of all rainfall thresholds (Table 10). The GFS produced less rain than the statistical (REG-SS) forecast with a maximum of only 2.04 in. near southeast SC and did not forecast the large accumulations in eastern NC seen in both the REG-SS forecast and the Stage IV observations (Fig. 19). The overall area of GFS’s maximum rainfall also was smaller than the REG-SS forecast and the observations. In the context of the REG-SS composites (Fig. 15), the GFS does not appear to have produced a rainfall pattern that is consistent with

59 Figure 21. Global Forecast System (GFS) 72 h rainfall accumulation forecast [in.] corresponding to the statistical model forecast in Fig. 17 and the Stage IV observations in Fig. 19. GFS track is shown by circles, and Best Track is shown with squares. Dashed contoured rainfall accumulations over water were not veriﬁed. Maximum forecast amount is shown in the bottom right. See Table 9 for 6-h intensity and region values.

the DSL maximum (Fig. 17). Instead, its maximum is left of track, perhaps due to dynamical characteristics internal to the simulated storm. Internal TC dynamical characteristics of the GFS are beyond the scope of this research. To summarize, the statistically derived forecast for TS Ana (speciﬁcally the REG-SS method) is considered very good. The average FSS for all rainfall thresholds was 0.73, with the individual FSS of each threshold ranging from 0.64 to 0.88 for thresholds between 1 and 100 mm (Table 10). The model accurately predicted the location of maximum rainfall (albeit over-forecasting by approximately 1 in.). The skill of this forecast highlights the importance of understanding regional rainfall characteristics. Comparing the FSS of the statistical model forecast to that of the R-

60 CLIPER forecast (threshold average of 0.22 with a range of 0.14 – 0.55 between the 1- and 100-mm thresholds), it appears that the statistical model is a reasonable approach and can serve as a new and diﬀerent baseline product. Additionally, it is instances such as this that show that the statistical model can provide a good supplement to the GFS in forecasting rainfall. However, the next section will show that these good results do not always occur.

4.2.2 Stage IV statistical model forecast: Not skillful

Not all forecasts produced by the statistical model were as skillful as the one for TS Ana. Figure 22 shows the 72-h forecast rainfall accumulation for TS Andrea (2013) using the REG-SS method. Shear-relative rainfall composites from four geographic regions were used in creating the total accumulation forecast (Fig. 23). The 72-h observed Stage IV rainfall is shown in Fig. 24. Table 9 shows the 6-h forecast and Best Track intensities, shears, and regions used. The average FSS for the combination of all accumulation thresholds is 0.38, with individual FSS values for each threshold shown in Table 10. The REG-SS method produces a maximum 72 h accumulation of 2.83 in. near north-central NC (Fig. 22) compared to the observed value of 8.17 in. over the Delmarva Peninsula (Fig. 24). One should note the numerous small-scale maxima in Fig. 22 whose cause is described below. Several potential reasons for the accumulation discrepancies are explored. TC track error between the GFS forecast and Best Track contributed some to the location error in rainfall. For example, if one mentally shifts the forecast track (indicated by circles in Fig. 24) to the observed track (squares), the maximum accumulation remains the same, but the rainfall pattern is shifted further east. Although this mental shifting provides better spatial agreement between the two forecasts, the accumulations still exhibit poor agreement. A second potential cause of the discrepancies is how the observed and forecast forward speeds of Andrea compare. However, results show that these speeds are similar since the 6-h positions are near the same latitudes, and the storm was moving primarily with a northward component. Therefore, track error does not contribute signiﬁcantly to the poor rainfall forecast shown in Fig. 22. Although forecast shear magnitude and direction that comprise the REG-SS method rainfall forecast could contribute to faulty rainfall accumulations, both were fairly constant during the forecast. Figure 22 shows that most 6-h intervals exhibit a shear vector pointing toward the northeast in the > 10 m s−1 range.

61 Figure 22. REG-SS (Table 7) forecast 72 h rainfall accumulation for TS Andrea (2013) as in Fig. 17. The forecast was initialized at 1200 UTC 6 June 2013.

The rapid forward speed at which Andrea moved is the major factor leading to the poor skill of the forecast. If a storm hovers over the same area for an extended period as does Ana in Fig. 17, the Stage IV 6 h composites are adequate, and the model can accumulate large amounts of rainfall. However, Andrea’s forward motion (Fig. 22) increased from about 9 m s−1 (20 mph) at forecast hour 6 to 40 m s−1 (89 mph) at forecast hour 54 as it became embedded in a mid-latitude trough. This rapid motion prevented the 6 h rainfall composites from accumulating the heavy rainfall that was occurring (Fig. 24), thereby causing the REG-SS method to perform poorly. Stated diﬀerently, the 6 h rain rate composites used to create the forecast were inadequate for depicting changes in rain rate during such rapid motion. An alternative would have been to linearly interpolate between 6-h forecast positions to “ﬁll in” the accumulations between 6-h TC positions, i.e., dividing the 6-h rainfall accumulations by 6 to create hourly accumulations. However, that would have been

62 Figure 23. Strong shear, shear-relative regional rain rate composites [in. 6 h−1] for the four regions used to create the TS Andrea (2013) 72 h forecast shown in Fig. 22: NWFL, SATL, MIDATL, and NATL.

“unfair” to the 6-h composites. The only reasonable alternative would have been to create the original composites at hourly intervals since Stage IV observations do provide hourly accumulations. However, that is a topic for future research. The results for Andrea show that the unique characteristics of each regional composite are important to understanding TC rainfall. However, a limiting factor, at least for Andrea, is the storm’s speed. The regional, shear-relative composites used for the forecast (Fig. 23) display the expanding area of rainfall for strongly sheared storms (> 10 m s−1) when moving northward from the NWFL to SATL to MIDATL to the NATL regions. As the storm’s latitude increases,

63 Figure 24. Stage IV 72 h observed rainfall accumulation [in.] as in Fig. 19 but for the TS Andrea (2013) whose forecast is shown in Fig. 22.

the left-of-shear radial extent widens, and the rainfall field becomes more expansive within the NATL region. However, because of the different radial distributions of rainfall from MIDATL to NATL, the rainfall is less organized into a dominant maximum (compare MIDATL and NATL in Fig. 23). This is reflected in the forecast (Fig. 22) where maxima > 2 in. are located from Florida to Virginia. North of Virginia, where the NATL composite was used (indicated by a “7” east of Maine in Fig. 22), the rainfall maximum begins to decrease, but the areal extent of > 1 in. rainfall expands. TS Andrea is an example of where the statistical model would not add useful information to a forecaster. The FSS of the R-CLIPER forecast (Fig. 25) for TS Andrea was 0.36, approximately the same as that of the statistical model (Table 10). Like the statistical model, the R-CLIPER forecast struggled at the larger rainfall thresholds, thus resulting in a relatively small overall FSS. This is

64 Figure 25. R-CLIPER 72 h rainfall accumulation forecast [in.] as in Fig. 20, but for TS Andrea (2013). The corresponding statistical model forecast and Stage IV observations are shown in Figs. 22 and 24, respectively.

partially due to the speed at which TS Andrea translated. However, unlike the statistical model, R- CLIPER also could not replicate the maximum rainfall accumulations seen through North Carolina, Virginia, and the Delmarva peninsula. Its maximum rainfall was near the Florida/Georgia border near Tallahassee, FL and was approximately 2.2 in. Because TS Ana did not signiﬁcantly change direction during the forecast period, the maximum is positioned symmetrically on the TC track. Even though the FSS between R-CLIPER and the REG-SS method are similar, the detail provided by the REG-SS forecast provides a better understanding of what we can expect in the TC’s rainfall pattern. The similarities in the rainfall structure (DSL/left-of-track maximum) between the REG- SS method (Fig. 22) and observations (Fig. 24) is more detailed than the generic R-CLIPER forecast (Fig. 25). This insight provided by the statistical model shows its capability as a new statistical

65 Figure 26. Global Forecast System (GFS) 72 h rainfall accumulation forecast [in.] as in Fig. 21, but for TS Andrea (2013). Forecasts and observations are shown in Figs. 22 and 24, respectively.

baseline method. The GFS also performed poorly during Andrea (Fig. 26), with a threshold-averaged FSS of 0.41 (Table 10) compared to 0.38 for the statistical model. The GFS, like the statistical model, placed maximum accumulations left of the storm track, which also was left of shear. The GFS’s maximum rainfall of 5.27 in. (while greater than the REG-SS method of 2.83 in.) still was less than the 8.17 in. that was observed (Fig. 24). However, the location of this maximum, in central VA, is closer to the observed maximum over the Delmarva Peninsula than the REG-SS method. Since the GFS and the REG-SS statistical method created relatively similar forecast rainfall patterns for TS Andrea (compare Figs. 22 and 26) and both exhibited poor skill, there must be additional factors contributing to the poor skill. . If one assumes that the typical rainfall pattern of a storm should be similar to that of the REG-SS composites (the best performing statistical

66 method as will be shown in Section 4.3), then the GFS created a forecast for TS Andrea that generally matches this ideology. That is, a “real” TC should produce rainfall, on average, that is similar to the accumulations created by the REG-SS method. However, recalling the GFS (Fig. 21) and REG-SS (Fig. 17) forecast examples for TS Ana, this was not the case for the GFS. The GFS did not create shear-relative signatures consistent with the observations and the REG-SS forecast over land. In short, the GFS replicated the REG-SS method in one forecast (Andrea) but not in another (Ana). It is instances such as this—where a core understanding of TC rainfall is violated or not consistent (the REG-SS method)—that naturally lead the research to an additional step: To understand this type of variability by studying storm environments during skillful or not skillful rainfall forecasts. This major objective of the research will be discussed in Section 5.3. The preceding discussion highlighted the ability of the REG-SS forecast method to sometimes perform well and sometimes poorly. It indicated that the slower a storm moves, the more skill the model will have since it was derived from data at 6-h time intervals (e.g., TS Ana, Figs. 17 – 21). The forecast for rapidly moving TS Andrea (Figs. 22 – 26) is an example of when the 6-h composite data were inadequate. A detailed analysis of this and other environmental characteristics will be presented later. In the meantime, a detailed analysis of model skill is presented for all forecasts and all storms within the test dataset.

4.3 Model veriﬁcation

The skills of the statistical TC rainfall model (i.e., the different permutations or methods in Table 7) and the GFS in predicting TC rainfall now are evaluated using the test (independent) dataset (forecasts during years 2013 – 2016). The metric Fractions Skill Score (FSS, where 0 indicates that no forecast grid points verified and 1 indicates that all forecast grid points verified; Roberts and Lean 2008) again is used to calculate the skill of 72-h forecast rainfall accumulations. The 72-h period was chosen to be consistent with prior TC rainfall verification studies (e.g., Marchok et al. 2007) and to minimize errors due to forecast track error. Each 72-h forecast is verified against corresponding Stage IV observations at several accumulation thresholds. The full composite coastline methods denoted “ALL,” the individual regional composite methods denoted “REG,” and the GFS are compared to R-CLIPER (RCP).

67 Two different approaches for describing skill are used: a storm-by-storm basis and a forecast- by-forecast basis. The storm-by-storm approach computes the FSS of each storm for each rainfall threshold for each of its 72 h forecasts. Stated differently, the FSS equation includes all 72-h values (hits/misses) for each threshold per storm. Thus, each storm has one FSS for each rainfall threshold. Finally, all the individual storm scores are averaged to obtain one value per accumulation threshold. This method provides insight on how a model performed for each storm. Storm environments can change between forecasts, and this method removes some of that possible variability. In the second approach, the forecast-by-forecast method computes the skill of each 72-h forecast individually and then averages the results. Each forecast within the dataset has its own FSS. This method, while subject to more variability, provides insight into how the models/methods perform compared to one another on a forecast-by-forecast basis. If a forecaster is assessing model performance in real-time, the forecast-by-forecast method would be more beneficial. Conversely, post-season assessments would benefit from the storm-by-storm analysis.

4.3.1 Storm-by-Storm approach

4.3.1.1 FSS by rain threshold. Figure 27 shows the average FSS of all storms in the testing dataset as a function of rainfall threshold. The overall trend is decreasing FSS with increasing rainfall threshold, regardless of the forecast method used (defined in Table 7). Although most FSS values are tightly clustered at all thresholds, nearly all the statistical forecast methods and the GFS exhibit a greater FSS than R-CLIPER (RCP, blue diamonds) for thresholds less than 90 mm. At even greater rainfall thresholds, such as 100 and 150 mm, several statistical methods exhibit slightly less skill than R-CLIPER, with the GFS (blue rectangles) having the largest FSS. One or sometimes several techniques have an FSS that is slightly superior to the GFS between 5 and 50 mm, whether using the regional composites (REG) or the full composite (ALL). Statistical differences in methods for each threshold are discussed in Section 4.3.2. FSS values for the GFS and all the statistical techniques begin to diverge at the 50-mm threshold, with the GFS becoming superior to all the statistical methods. Various aspects of different forecast rainfall patterns could be tested for statistical significance. However, this research determined statistical significance using a difference of means test between the FSSs of the R-CLIPER and both the REG/ALL methods at each rainfall threshold (Fig. 27). It was computed at the α = 0.05 level (Wilks 2006):

68 (a) ALL forecast methods. (b) REG forecast methods.

Figure 27. Average Fractions Skill Score (FSS) per threshold for all storms within the test dataset on a storm-by-storm basis (see Section 4.3 introduction for details) for the full composite forecast methods (ALL; a) and the regional composite methods (REG; b). The individual methods are described in the text and in Table 7.

x¯ − x¯ z = 1 2 . (4.1) h s2 s2 i1/2 1 + 2 n1 n2 The numerator in Eq. (4.1) denotes the difference we are testing (whether the sample mean of FSS from sample 1 [REG or ALL] is different from that of sample 2 [RCP]), while the denominator is the sum of the two samples’ variances. Figure 28 shows which statistical methods (both REG and ALL) have a statistically significant difference in mean threshold FSS compared to RCP. If a statistical method is shown in the figure, its mean FSS can be either more- or less-skillful than RCP at the given threshold. Or, stated differently, if a method is not shown this indicates that the mean RCP FSS is not statistically different from that method at that threshold. The RCP FSSs (compared to the Stage IV data) are shown as a reference. Results (Fig. 28) show that RCP does not produce forecasts that are significantly different in skill from those of virtually all the methods developed here or the GFS on a storm-by-storm basis. The exceptions are at the 5 mm threshold for the statistical model (Fig. 28a). When FSS means of the REG forecast methods are compared to that of RCP (Fig. 28b), the results are the same as with the ALL forecasts, but with the addition of the AE method at 5 mm and the SS and AS methods at 10 mm. Thus, Figs. 27 and 28 show that RCP and the numerous ALL/REG methods are statistically indistinguishable – using either method or model does not provide a statistical

69 (a) ALL forecasting methods. (b) REG forecasting methods.

Figure 28. As in Fig. 27, but for those methods and thresholds whose means are statistically diﬀerent from R-CLIPER (RCP; Eq. 4.1). R-CLIPER is shown on both plots as a reference. Method label location is irrespective of FSS.

advantage over the other on a storm-by-storm basis when comparing skill using FSS. Additionally, these figures show that the various methods within the statistical model, on a storm-by-storm basis are not that different from one another. There is no statistical difference in means between the ALL and REG forecast methods at each respective threshold (not shown). This finding is discussed in more detail in Section 4.3.2 and in Chapter 5. R-CLIPER is a widely used statistically derived TC rainfall forecasting tool. However, results (Fig. 28) show that rainfall forecasts from GFS and R-CLIPER are statistically different only at the 1-, 5-, 70-, and 80-mm thresholds. That is, R-CLIPER statistically has the same skill as the GFS at thresholds > 5 mm and < 70 mm and for thresholds > 80 mm. The GFS only provides a statistically different forecast that is greater in FSS than R-CLIPER for light rain accumulations and a narrow range of moderate-to-heavy rain accumulations on a storm-by-storm basis (Fig. 28).

4.3.1.2 FSS rank. To determine which model performs best on a storm-by-storm basis for all thresholds combined, the average rank at each threshold was computed between the ALL/REG methods, the GFS, and RCP with a lower number (higher rank; 1 being best) indicating a more-skilled forecast. For example, if the REG-SS, GFS, and RCP methods/models have FSS values of 0.3, 0.6, and 0.9, respectively, at the 20 mm threshold, then their rank would be 3, 2, and 1, respectively, at that threshold. This calculation was run at every threshold for all methods/models. Then, the average and 95% conﬁdence intervals of these ranks for all the thresholds combined was

70 Figure 29. Average rank (blue bars) with 95% conﬁdence intervals (yellow lines) of all thresholds combined for all forecast models/methods on a storm-by-storm basis (described in Section 4.3.1.2) with 95% conﬁdence intervals. Methods/Models are arranged by increasing rank (decreasing skill) from left to right. Regional (REG) and full (ALL) composites used for the statistical method (Table 7) are indicated on the abscissa by abbreviations.

computed for each respective method/model to get a consensus of relative performance. The results are shown in Fig. 29. Figure 28 showed that there were few statistically different skills among the models. Nonethe- less, the findings of rank (Fig. 29) show that the regional shear-relative by shear magnitude method (REG-SS) is the best performing approach. The second best average ranked approach (second best-performing in terms of FSS) is the full composite shear-relative by shear magnitude method (ALL-SS). It is not surprising that the two highest-ranking statistical forecast methods are those that employ shear since it has been shown to be the dominant mechanism that modifies TC rainfall (Corbosiero and Molinari 2003; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013; Xu et al. 2014). However, it is surprising that the GFS is only the fifth best-performing model. Since the GFS is a dynamical model with complex routines to solve for rainfall (and even explicitly resolve rain), one would expect it to be ranked highest in a majority of instances. Surprisingly, this is not the case. This is explained by Fig. 27 which shows that the GFS only outperforms the other statistical models in the ≥ 60 mm range. R-CLIPER ranks third from the bottom (Fig. 29). Based on these results, the statistical model displays viability as a good supplement (not a replacement)

71 (a) ALL forecasting methods. (b) REG forecasting methods.

Figure 30. As in Fig. 27, but on a forecast-by-forecast basis.

to the GFS and, more importantly, it shows that it can compete as a new baseline forecast product alongside R-CLIPER.

4.3.2 Forecast-by-Forecast approach

Recall that the forecast-by-forecast approach provides insight on how a model performs for each forecast for each storm. The skill of each 72-h forecast is calculated individually. This method provides insight into how the models/methods perform compared to one another on a forecast-by-forecast basis. If a forecaster is assessing model performance in real-time, this method is beneﬁcial.

4.3.2.1 FSS by rain threshold. Results using the forecast-by-forecast basis are somewhat diﬀerent than those just described using the storm-by-storm approach. The average FSSs for a homogenous set of forecasts for all methods (both ALL/REG permutations) are shown in Fig. 30. The term “homogenous” means that only those forecasts where all methods/models had an FSS for all thresholds were included in the calculations. Results show that the skills of the methods/models generally are less than those using a storm-by-storm approach (compare Figs. 27 and 30) at the smaller thresholds but slightly greater at the larger thresholds. This occurs because the storm-by- storm approach used more data points to calculate the average value than being used now. This is especially true at the smaller thresholds since these accumulations are most common (see discussion on the ability of the statistical model to accumulate rainfall in Section 4.2.2). The greater number of samples renders the storm-by-storm FSS averages less critical to a relatively small number of

72 inaccurate rainfall values than when using the forecast-by-forecast approach, thereby producing a greater FSS. Like the storm-by-storm approach (Fig. 27), results from the forecast-by-forecast approach (Fig. 30) show that all forecasting methods exhibit greater skill at smaller rainfall thresholds and decreasing skill at larger thresholds. The GFS is not the superior performing model until thresholds exceed 40 mm. At thresholds < 30 mm, all methods (both REG and ALL) are superior to R- CLIPER (Fig. 30, diamonds). For thresholds between 30 and 70 mm, the two worst-performing methods are the motion-relative methods IM and AM, confirming what has been found in prior research, that motion-relative rainfall forecasting is not a preferred approach. Investigating whether there are statistically significant differences in FSS threshold means between the statistical model and RCP on a forecast-by-forecast basis also reveals different results than when using the storm-by-storm approach (Fig. 31). Statistically significant differences were computed in a similar manner as with the storm-by-storm method (Fig. 28) using Eq. (4.1). There are more statistical methods whose threshold means are statistically different than RCP than found using the storm-by-storm basis. This is expected since there are more data points (each storm has numerous forecasts). The REG-SS method (Fig. 31b) exhibits a larger FSS than RCP for thresholds ≤ 60 mm. Beyond 60 mm, there is no difference between the mean threshold FSSs of the various forecasting techniques. These findings further highlight the capability of the statistical method developed here to be a supplement to RCP as a baseline forecasting technique. Providing improved FSSs in the majority of the thresholds studied is evidence of the need for this new forecasting technique. The differences between RCP and the GFS occur between thresholds of 1 – 10 mm and ≥ 60 mm (Fig. 31). This finding can be interpreted as the GFS outperforming RCP at these thresholds since it has a larger FSS. The only statistically significant difference in means between REG and ALL is at the 150 mm threshold between the IE and IM methods (not shown). Figure 32 shows the mean FSS on a forecast-by-forecast basis of each method/model for six different thresholds: 10, 30, 50, 70, 90, and 150 mm. These thresholds were chosen to simplify the figure, still provide a full range of thresholds, and because the results of the thresholds not shown are similar to those shown for adjacent thresholds. At the 10 mm threshold, the statistical model has a larger mean FSS than RCP and GFS. As threshold increases, GFS has a larger mean FSS (as

73 (a) ALL forecasting methods. (b) REG forecasting methods.

Figure 31. As in Fig. 28, but on a forecast-by-forecast basis.

seen in Fig. 30) than any other method. Additionally, as threshold increases, the statistical model initially has a larger FSS than RCP. However, for thresholds > 90 mm, the FSSs of the RCP and the statistical model become very similar, and the 95% conﬁdence intervals begin to overlap more. More importantly, Fig. 32 primarily reveals that each of the statistical methods developed from the numerous ideologies are nearly indistinguishable from each other. With such a large overlap in 95% conﬁdence intervals, it can be concluded that over an extended period of time, each statistical method will produce a similar FSS. This means that although the statistical model is proving to be a viable new baseline model, it still has limitations. These are discussed further in Chapter 5.

4.3.2.2 FSS rank. The average rank for the combined thresholds of all forecasts within the test dataset was computed as done in Section 4.3.1.2 using the same homogenous dataset described in that section. Figure 33 reveals that once again the REG-SS method is the top performer, with the ALL-IS method in second place, the REG-IS method in third, and the GFS in fourth. R-CLIPER ranks last, indicating that all the statistical forecast methods improve on it when evaluating on a forecast-by-forecast basis. These results show that the REG-SS method consistently out-performs the GFS whether on a forecast-by-forecast or storm-by-storm basis as well. This suggests that it is a viable candidate as a supplement to the GFS and as a statistical baseline method to determine forecast skill. These results are more informative than those from the storm-by-storm method since, at least in a real-time setting, a forecaster may only care about how a model is performing for a particular forecast.

74 Figure 32. Mean Fractions Skill Score (FSS; dots) on a forecast-by-forecast basis for each method and model with 95% conﬁdence intervals (bars). Scores are aligned from best to worst with R- CLIPER (RCP) and the Global Forecast System (GFS) model scores shown in the left two positions regardless of score for reference. Scores from the regional method (REG; Table 7) are shown.

To summarize, the regional, shear magnitude by shear-relative statistical forecast method (REG-SS) consistently outperforms all other statistical methods (see Figs. 29 and 33). The statistical model, regardless of method, has a larger FSS than R-CLIPER indicating that it is a reasonable candidate as a new statistical baseline model. Additionally, whether comparing the skill of the forecast methods on a storm-by-storm basis or on a forecast-by-forecast basis, the 50 mm rainfall threshold appears to be the common value at which the skill of the statistical methods

75 Figure 33. As in Fig. 29, but on a forecast-by-forecast basis.

(ALL/REG) becomes inferior to the GFS (see Figs. 27 and 30). Therefore, this threshold and the REG-SS method are chosen as the parameters used in the upcoming analyses comparing the statistical model and the GFS. In other words, instead of comparing all the statistical approaches with the GFS, only the REG-SS method will be used. This will help determine what factors, if any, could be added to the model to improve its baseline score.

76 CHAPTER 5

ANALYSIS OF ERRORS AND POSSIBLE IMPROVEMENTS TO THE STATISTICAL MODEL

This chapter seeks to identify deﬁciencies and errors in the statistical model which was developed for this dissertation and provides methods and thoughts in which the model could be improved. GFS forecasts are used to compute environmental characteristics and provide insight into possible mechanisms which could improve the statistical model forecasts.

5.1 Theoretical maximum skill of the statistical model

Chapter 4 showed that the statistical model had larger Fractions Skill Scores than R- CLIPER at numerous thresholds indicating that it could provide value in the continual effort to improve TC rainfall forecast skill. However, to get an understanding of the limitations of the statistical model, we first show mean threshold FSS for 6 different thresholds (10, 30, 50, 70, 90, and 150 mm; similar to Fig. 32) for “perfect” forecasts (Fig. 34). Verified 6-h location and intensity analyses were used from Best Track as “forecast” locations and intensity and verified shear analyses from SHIPS were used as shear input. The results from using the verified parameters gives a theoretical maximum on the FSS of the statistical model. Stated differently, if the statistical model was given a perfect forecast in terms of shear, motion, and intensity, the resultant FSS (Fig. 34) is the best the model could do with the way it is designed. A larger 95% confidence interval is shown in Fig. 34 than compared to Fig. 32 due to the smaller number of forecasts (N=11). “Forecasts” for this analysis, were just the number of storms in the test dataset. Best Track FSSs (Fig. 34) exhibit the same behavior as the forecast FSSs (Fig. 32), i.e., FSS decreases with increasing threshold. The statistical model, regardless of method, has a larger FSS than RCP through the 70 mm threshold. The SS method only has the greatest FSS at the 50 mm threshold, whereas the IS method has the greatest FSS for all other thresholds shown. However, the overlap of the 95% confidence interval at all thresholds once again shows that results of the individual methods, whether shear-, motion-, or intensity-based, are nearly indistinguishable. Thus,

77 Figure 34. As in Fig. 32, but for “perfect” forecasts which used veriﬁed shear, motion (track), and intensity values from SHIPS and Best Track analyses.

forecasting TC rainfall is much more complex than reducing its nature down to shear-, motion-, or intensity-based ideologies. The Best Track forecasts are superior to those of the statistical model, but they are far from perfect. Diﬀerences between Best Track forecasts (with veriﬁed 6-h shear, intensity, and track) and the actual statistical model forecasts are shown in Fig. 35 (Best Track minus Forecast). The results reveal that errors in shear, intensity, motion, and track contribute to the reduction in the overall FSS of the forecasts by ∼0.2 near 30 mm, ∼0.1 near 70– 90 mm, and less than ∼0.05 at 1 mm and 150 mm for some or most methods. The reduction is due to the inaccuracies of the intensity, shear,

78 Figure 35. Diﬀerence in Fractions Skill Score (FSS) between Forecasts and Best Track “Forecasts” (those that use veriﬁed 6-h locations, intensity, and shear values; BTK - FCST) for all statistical methods and R-CLIPER.

and/or motion forecasts. Shear, intensity, motion, and track contribute to the reduction of FSS for RCP by ∼0.1 for thresholds ≤ 30 mm and ∼0.05 for thresholds > 30 mm. The greater variability between FSSs of the Best Track and forecast values when compared to R-CLIPER indicates that the methodology of the statistical model introduces additional error into the forecast. Meaning, since R-CLIPER has fewer variables, there is less that can contribute to the errors in a forecast compared to the statistical model. This does not mean that the statistical model performs more poorly than R-CLIPER (the results in Chapter 4 indicate otherwise). Instead it shows that the statistical model, due to its methodology, creates forecasts with more variability than R-CLIPER. Best Track FSSs of the statistical model (Fig. 34) still are not perfect. This is due to the methodology of the statistical model which uses climatological values to forecast a dynamic weather feature. TC rainfall is not consistent during an entire forecast period. The statistical model assumes that the rainfall is the same structure as a climatological composite (e.g., based on shear, intensity, or motion). This is not the case. Additionally, it assumes that the composite rain rates are consistent for the ranges of shear or intensity magnitudes we chose to separate them (Table 6). These assumptions introduce error into every statistical model forecast. However, the results of Chapter 4 indicate that this new method still is an improvement on R-CLIPER FSS and

79 (a) ALL forecast methods. (b) REG forecast methods.

Figure 36. Cross-track radial storm-total distribution of rainfall [in.] for the ALL (a) and REG (b) forecast methods. The distribution is calculated by summing the rainfall for each speciﬁc 10 km radius for a full 72-h forecast and dividing by the number of grid points summed. The procedure is described further in Section 5.2 of the text.

can provide value to the research community.

5.2 Radial distributions

We next evaluate the statistical model, RCP, and the GFS based on their radial distributions of rainfall (Fig. 36). The radial distribution was computed on the test dataset (2013 – 2016) and compared to Stage IV observations (blue asterisks). It is the cross-track, mean radial distribution for a 72-h storm-total accumulation similar to Marchok et al. (2007). Meaning, a cross-track accumulation was performed on the 72-h storm-total forecasts. At each 6-h track location of the forecast a line was drawn from the center of the storm perpendicular to the track, and the closest grid points at 10-km intervals out to 500 km, both left and right of the TC center, were recorded as the radial accumulation. The cross-track mean accumulation then was calculated. This method is chosen so no along-track bias is introduced due to the continual accumulation of rainfall along the track. At radii less than 120 km (Fig. 36a) the ALL intensity-based methods (squares; ALL-IE, IM, and IS) better replicate the Stage IV observations (blue asterisks) than the other methods. The regional intensity-based methods (Fig. 36b; squares; REG-IE, IM, IS) are closer to Stage IV observations at radii < 120 km when compared to other REG methods in this range except near ∼10 km from storm center. Beyond 120 km, the results of each statistical method are virtually

80 indistinguishable from those of any other statistical method (Figs. 36a and b). Rodgers et al. (1994) showed that TC rain rates shift toward the center of a storm as its intensity increases. This suggests that near the storm center, storm-intensity can regulate the rain rate, i.e., by the area of rainfall either contracting or becoming more radially expansive depending on the intensity of the TC (Rodgers et al. 1994, their Fig. 2). Therefore, when considering radial rainfall distributions, the intensity-based statistical methods shown here (squares) seem able to account for these changes and thereby perform better than either the shear-magnitude (prefix S; straight lines) methods or the all shear magnitude/storm intensity (prefix A; circles) composites at radii < 120 km. The effects of shear and storm intensity on the radial distribution of rainfall are further examined by comparing Figs. 7 and 9. The intensity-based composites (Fig. 7) show that as intensity increases, rain rate increases much more than with varying shear magnitude (Fig. 9). Thus, varying the magnitude of shear appears to rearrange TC rainfall more than increase its magnitude. The greatest differences between the ALL and REG radial distributions occur at radii < 100 km where the regional, intensity-based methods (Fig. 36b) produce greater rainfall than the ALL (Fig. 36a) distributions. This finding that the intensity-based methods are superior to other methods in terms of radial distributions does not contradict the previous results regarding the superiority of the shear-based approaches when considering spatial rainfall (Figs. 29 and 33. They simply indicate that the intensity-based methods can regulate rainfall better in the radial (for radii < 120 km) and align them closer with Stage IV observations than the other methods. Since rainfall patterns are not revealed by radial plots, the results of Figs. 29 and 33 still hold true. This finding indicates that the error in the methods that are not intensity-based may occur because these methods do not consider storm intensity. Comparing the statistical model to RCP (Fig. 36) reveals that the statistical model creates radial rain rates that are closer to observations than RCP. R-CLIPER greatly over-estimates radial rain rates at nearly all radii. This radial distribution from RCP is not what is expected from its defining equation (Eq. 2.8). The equation produces a linear rain rate from the storm center out to the radius of maximum rain (which is defined for different intensity categories) which then switches to an exponential decay beyond this radius. The results in Fig. 36 do not show this linear and exponential decay radial rain rate structure. The radial structure shown in Fig. 36 is after 72 h of rain accumulation. The total accumulated rainfall after a 72-h forecast is different

81 (e.g., Fig. 25) than a 6-h rain rate snapshot. The accumulation of rain can lead to poorly verified forecasts and radial accumulations. For example, the accumulated rainfall distribution in Fig. 25 is less realistic than what is seen from the statistical model (Fig. 22), the GFS (Fig. 26), and observations (Fig. 24). Specifically, RCP exhibits a wet bias beyond the radius at which maximum rainfall is observed (Fig. 36). This wet bias is due to the overlap of the radial accumulation from the R-CLIPER forecast over the 72-h period. Compared to the Stage IV observations, the GFS (Figs. 36a or b) under forecasts at all radii, with a maximum difference of ∼0.4 in. at approximately 20 – 40 km. The dry bias decreases with increasing radius. To help explain the radial performance of the model, Fig. 37 shows the number of REG and ALL methods at each radius that are closer to Stage IV observations than their REG or ALL counterpart. Meaning, a REG-based method (e.g., REG-SE/SM/SS) was compared to its ALL-based counterpart (e.g., ALL-SE/SM/SS). Only radii where the REG and ALL methods are statistically significantly different (Eq. 4.1) are counted. For example, if an AIE (All Intensity- Based; Earth-Relative) composite had a mean radial rainfall of 5 in. at a radius of 130 km, and the REG-IE method (Regional Intensity-Based; Earth-Relative) had 4 in. at the same radius, both values were compared to the hypothetical Stage IV observation of 3 in. at 130 km. Since the difference between the REG-IE and the Stage IV observations is smaller compared to the difference between the Stage IV observations and ALL-IE, the REG-IE method would get a count in its bin if the means between these two ALL and REG methods are statistically different. This methodology highlights those radii where either the REG or ALL composite approach, as well as which method (intensity/shear/or rotation), are closer to observations. In addition, since the plot shows those radii where a statistically significant difference exists between ALL/REG, it reveals those radials where each method performs best (i.e., closer to Stage IV observations). Differences between the REG- or ALL-based methods and Stage IV observations (Fig. 37a) indicate that the core and banded areas of the TC exhibit the greatest variability in rainfall among the forecast methods since only a few methods are statistically different from their REG- or ALL- based counterpart in these regions. Conversely, the region between 60 and 180 km is void of statistically different methods meaning the REG- or ALL-based methods produce similar forecasts at these radials. At radii < 60 km, only the intensity-based methods differ statistically from their

82 (a) (b)

Figure 37. A count of methods at each radius that are closer to Stage IV observations than their REG or ALL (Table 7) counterpart on a cross-track, radial accumulation basis (a; e.g., Fig. 36). The ALL-based methods that are closer to Stage IV observations than the REG-based methods are shown in the positive ordinate direction, whereas the REG-based methods are in the negative ordinate direction. Only methods that are statistically diﬀerent from their REG- or ALL-based counterpart are shown. For example, at 210 km, there are 5 REG-based methods that are closer to Stage IV observations. In panel b), the statistical variance of the methods that are closer to the Stage IV variance (similar methodology as in [a]) are shown along with the Stage IV variance (brown line; secondary axis) in the radial.

REG- or ALL-based counterpart (green shades). It is only in this range that the ALL methods outperform any REG method. Between 180 km and ∼370 km, various REG methods are significantly different from their ALL counterparts and perform better than ALL at several different radii. The 60 – 180 km radial range is statistically similar between ALL- or REG-based methods. These results suggest that there is no advantage to using either a regional or full composite approach within this radial range. However, when studying inner-core rainfall radial accumulations, using the ALL composite is more advantageous since values are closer to the Stage IV data (compare Figs. 36a and b) and are statistically different than their REG counterpart. Conversely, when studying and forecasting radial bands ≥ 180 km and ≤ 350 km, using the REG methods provide a better forecast. The results of Fig. 37a indicate that the ALL forecast methods are more skillful at radials near the TC’s core. Therefore, a forecaster can have more confidence in the ALL forecast methods in this region of the TC when viewing rainfall from a radial perspective. Conversely, outside the core, in the banded and dense-overcast regions of a TC, more-specialized methods of forecasting, such as the REG methods shown in Fig. 37a are better. This suggests that at these larger radii

83 the finer-detailed composites provided by the REG-based method are better at forecasting rainfall than those of the more-generalized ALL composites. Comparing Fig. 4 (ALL-AE/M/S) to either Fig. 11 (REG-AE) or Fig. 15 (REG-AS) is evidence of this hypothesis. The ALL composites generally produce an inner-core rainfall structure that is tightly packed towards the center of the TC, whereas the REG composites show more variability. At larger radii, the ALL composites exhibit similar rain rate magnitudes and distributions, whereas the REG composites show more detail. At first glance, it may seem that the ALL forecast methods and REG forecast methods produce similar results in terms of which is better (one performs well near the TC center, and the other performs well at larger radii), and that the results shown with Figs. 29 and 33 (which showed the ranks of each forecast method compared to the others) are inaccurate. However, Figs. 36 and 37 are radial distributions, and if one considers the scale at which the different radii impact the overall TC rainfall forecast, the REG methods are justified as being considered the superior approach. That is, superior ALL forecast methods are constrained to radii < 60 km (or 11,304 km2). Conversely, superior REG forecast methods occur between radii ≥ 180 km and ≤ 350 km (or 282,914 km2) – a 2,400% increase in area compared to the ALL methods. A large area with a superior FSS is more impactful than a small area with a superior FSS. Figure 37b considers the evaluation from the perspective of comparing statistical variances in radial rainfall accumulations from the Stage IV observations and both the REG- and ALL-based methods. Observations in the TC core generally have a larger statistical variance than at larger radii (Fig. 37b, line). If we compare differences in statistical variance between the REG and ALL methods and Stage IV, the hypothesis that the REG methods are better at larger radii and the ALL methods are better at smaller radii again is supported (Fig. 37b, bars). Within the core (< 60 km) only the ALL methods have a statistical variance that is closer to Stage IV than do the REG methods (i.e., more counts in the positive ordinate direction). Conversely, at larger radii more REG methods have a variance that is closer to Stage IV observations than ALL methods (more counts in the negative ordinate direction). A forecast that can replicate the radial variance of the observations will be superior to one that does not. This is the case for ALL methods in the core and REG methods in the banded and dense overcast regions of the TC at larger radii.

84 5.3 Environmental analysis

The final goal of this research is to determine whether there are specific environmental characteristics that are conducive to skillful or not skillful GFS rainfall forecasts and if so whether these environmental fields might serve as parameters in a revised statistical model. This approach is desirable because of the growing need for “guidance on guidance.” That is, if we know in advance whether a model will perform well or not, we can either have or not have confidence in what it is predicting. The analysis hopefully will provide guidance to identify environments/forecasts where one expects the GFS to perform well or poorly in terms of TC rainfall. It also lays the groundwork for applying the methodology to models other than the GFS. Finally, the analysis can serve as a “next step” in statistical TC rainfall forecasting. Unlike a dynamic model like the GFS, the statistical model contains no direct feedback from the storm to its environment or vice versa which could affect a rainfall forecast. However, if shear, for example, is forecast to be large over a storm due to an approaching upper level trough, that information already is mostly contained within the shear relative composite grids on which the statistical model is based. Similarly, feedback from the TC to the environment also should be contained within the composite grids (e.g., Figs. 4, 7, 9, 11, or 15). Therefore, other environmental parameters possibly could be found that could contribute to the statistical model similar to what was previously studied with respect to shear, motion, and intensity. Following an approach similar to Atallah and Bosart (2003), Atallah et al. (2007), Kimball (2008), Milrad et al. (2009), and others, we examine the composite synoptic environments in cases of skillful and non-skillful TC rainfall forecasts. However, unlike previous studies, the present analysis is not done for a specific storm (e.g., a case study), but for all TCs in our dataset between 2004 – 2012. It is performed with GFS forecasts in addition to its 0-h analysis. The methodology was to first separate each of the GFS forecasts and analyses into “Top Skill” (FSS ≥ 0.66) and “Bottom Skill” (FSS < 0.33) categories. A “Middle Skill” category also was examined since the environments of the Middle category would be expected to be between the Top and Bottom categories. The methodology then composited various dynamic and thermodynamic environmental parameters within each skill category. This approach allowed us to isolate and identify environmental features that the statistical model possibly is missing or would not benefit from using.

85 A geographical representation of all 6-h locations (analysis through 72 h forecast) of the Top and Bottom ATCF GFS forecasts, as well as their difference, for years 2004 – 2012 is given in Fig. 38. Results reveal that the best performing forecasts are well-dispersed across the southeastern United States and portions of the Gulf of Mexico (Fig. 38a). Locations of the worst performing (Bottom) forecasts (Fig. 38b) have many similarities to those of the top performers. However, their most frequent locations are over the Gulf of Mexico and off the coast of the Carolinas. The differences in locations between the Top and Bottom categories are shown in Fig. 38c.

5.3.1 Mean sea level pressure and 500 hPa composites

Mean sea level pressure (MSLP) at the analysis hour is the first meteorological variable examined (Fig. 39). For this and the variables that follow, the number of storms and forecasts within each skill category is given at the top of the plots. The composites were computed on a standard 0.5 × 0.5 deg grid (Section 3.2) with the center at the TCs’ ATCF GFS position. The top of the plot faces north. Hatched areas denote regions whose difference between the Top and Bottom mean MSLP (or other mean variable shown) is statistically different (Eq. 4.1). At each grid point in the Top and Bottom composites respectively, the statistical variances and means were computed and used as input into Eq. (4.1) as sample 1 (Top) and sample 2 (Bottom). The statistical model considers intensity in one of its permutations (Table 7). Therefore, it is useful to determine whether the GFS also shows that intensity is a contributor to TC rainfall forecast skill. If a model (the GFS in this instance) forecasts the intensity of a TC well, not only will this benefit those in the path of the storm in terms of wind damage, but it also can be used as an indicator on the threat of rainfall. A clear difference between the Top and Bottom skill categories (Fig. 39) is that TCs comprising the Top forecasts are stronger in intensity (lower MSLP) than the Bottom ranked TC forecasts. There is a -0.46 statistically significant correlation (α = 0.05) between the GFS MSLP and FSS, indicating that as the GFS minimum pressure in a storm decreases (intensifies), the FSS of the forecast generally increases. To confirm this finding, the distribution of forecast and verified Best Track intensities is shown in Fig. 40, where bars indicate total counts and the dashed lines illustrate the percentage contribution for a specific category to each bin. The Top skill category has a greater percentage of total counts in the lower pressure (stronger TC) bins, whereas the Bottom skill category overwhelmingly has more forecasts in the highest-pressure bin (weaker storms). As

86 Figure 38. Global Forecast System (GFS) forecast positions (0 – 72 h) for the Top (a) and Bottom (b) Fractions Skill Score (FSS) categories for the environmental analysis done for the GFS (2004 – 2012; Section 5.3). The diﬀerence between the Top and Bottom FSS categories (Top – Bottom) for those grid points where data existed for both Top and Bottom is shown in (c). The six-hour locations are binned with 2 degree grid spacing.

storm intensity increases, rainfall asymmetry decreases (Xu et al. 2014), and the radius of maximum rain decreases (Lonfat et al. 2004). Thus, if there is less asymmetry, one expects fewer outliers in the rainfall distributions at the analysis hour – the rainfall ﬁeld is becoming more circular about the center of the storm. Current results of the GFS, based on a composite analysis of rainfall, does show the rainfall becoming more symmetric as intensity increases (not shown). However, the contraction of the radius of maximum rainfall as intensity increases is not seen. Therefore, in terms

87 Figure 39. Composites of mean sea-level pressure [hPa] at the analysis hour for the Gobal Forecast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories. Com- posites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel.

of forecast skill, the ability of the GFS to create a rainfall forecast that becomes more symmetric as intensity increases may contribute more to its skill than the reduction in the radius of maximum rain. It appears that the GFS is simulating this symmetry and therefore can create more-skillful rainfall forecasts as storm intensity increases. However, a much more thorough analysis is needed to conﬁrm tentative results.

88 Figure 40. Histogram of mean sea-level pressure for Top (blue), Middle (grey), and Bottom (orange) forecast categories as deﬁned in Section 5.3. Veriﬁed intensities from Best Track (BTK) analyses are shown in black. Percentages are the percent contribution to the bin for the total data set.

Additional insight into what comprises a skillful or non-skillful GFS rainfall forecast can be gained by looking beyond the TC itself at the overall synoptic environment around the storm. Further inspection of Fig. 39 suggests that the sub-tropical anticyclone may influence the skill of the GFS analyses. The Bottom ranked forecasts occur with a stronger anticyclone to the east of the TC than do the Top forecasts. Figure 41 shows the mean TC locations for the analysis times used in the composites for the Top, Middle, and Bottom categories. Results show that the locations of the TCs comprising the composited analyses do not appear to be the cause of the differing skills since there is only an approximately 3◦ longitude difference between the Bottom and Top tiered forecasts (Fig. 41a). If either the Top or Bottom analysis locations were shifted east or west, it would not explain the difference in the strength of the sub-tropical anticyclone. I tested the correlation between the FSS of the GFS rainfall forecasts and the strength of the sub-tropical anticyclone to investigate if it should be used as a parameter in a revised statistical model. This was done by computing the areal maximum and average MSLP within a box situated over the anticyclone (between 25◦ N and 45◦ N and 20◦ W and 55◦ W). The procedure was followed for each 72-h forecast, yielding one areal maximum and average MSLP value per forecast. When all months with a TC are considered, there is a 0.09 and 0.05 (N=230) statistically insignificant correlation between FSS and both the areal maximum and average MSLP of the anticyclone, respectively. Thus, the strength of the anticyclone does not appear to be related to the skill of TC

89 Figure 41. Top (cyan), Middle (magenta), and Bottom (yellow) Fractions Skill Score (FSS) categories’ mean locations associated with composite environmental plots for analysis hour (a) and forecast hour 72 (b).

GFS rainfall forecasts. The exception is when considering forecasts only during August when there is a statistically signiﬁcant correlation of 0.32 between the forecast areal-average intensity of the anticyclone and FSS (N=83 forecasts of the 230 total). It does not appear that the strength of the anticyclone can be a useful input to the statistical model To determine if a monthly relationship exists, the Top, Middle, and Bottom skill categories were separated by month. The results show variability between months, including an inverse relationship in raw counts (bars) and percent totals (dashed lines) between Top and Bottom forecasts during the months of August and September (Fig. 42). Since the Top/Middle/Bottom category divisions were empirically based (an objective 0.33 FSS division), the number of storms (solid lines) is relatively similar between all three categories. Meaning, an individual storm could have an equal number of skillful (Top category) or not-skillful (Bottom category) forecasts. Raw forecast counts (solid bars) and normalized monthly percent-totals (dashed lines; Fig. 42) of the Top and Bottom forecasts reveal that during August, the GFS has less skill than in September. This is indicated by the larger number of Bottom forecasts compared to Top forecasts during August, compared to the

90 Figure 42. Frequency of Global Forecast System (GFS) forecasts for the Top, Middle, and Bottom Fractions Skill Score (FSS) categories as deﬁned in the text. Raw counts are shown as bars, and frequencies (normalized by the total number of forecasts in the month) are shown as dashed lines. The solid lines show the number of storms for each category and month.

larger number of Top forecasts compared to Bottom forecasts during September. The result that August has fewer skillful forecasts than September is consistent with Chan and Chan (2012) who found that TC size is positively correlated with TC strength and that the largest TCs occurred in September. To conclude the preceding discussion about the relation between anticyclone strength and forecast skill, readers should recall from Figs. 39 and 40 that stronger storms are correlated with more-skillful rainfall forecasts. If TC size and strength are related to the position of the sub-tropical anticyclone, if the largest TCs occur during September (Chan and Chan 2012), and if the most skillful forecasts occur during September, this suggests that the GFS accurately predicts the sizes of TCs in relation to the strength of the sub-tropical anticyclone as shown by the larger, more intense storms in Fig. 39. This is expected to lead to more-skilled rainfall forecasts during September. Additionally, during July, when fewer large storms occur (Chan and Chan 2012), the Bottom forecasts dominate the monthly spread (Fig. 42). These results could be a byproduct of under sampling. However, since Chan and Chan (2012) found monthly relationships with sub-tropical anticyclone position and TC strength, the current results (Fig. 42) are supported by this monthly

91 methodology. Due to the sub-tropical anticyclone’s influence on storm size and the relationship of storm size to intensity, a forecaster may be able to use this information to gain insight on whether skillful or not skillful rainfall forecasts will occur. However, the current results (Figs. 39 and 40) only relate TC strength and size to skillful rainfall forecasts. Depending on the validity of Chan and Chan (2012) that the position of the sub-tropical anticyclone is a proxy for TC size, forecasting skillful forecasts by using the position of the sub-tropical anticyclone may or may not be useful. If any of the above conditions (the “ifs”) are not met, the relationship of storm strength (intensity) and rainfall skill still can be used (Fig. 40). Additionally, since Fig. 39 shows that Top tiered forecast storms are larger than Bottom tiered forecast storms, the size of the storm also could be an indicator of rainfall skill. This topic requires much additional study for it to be useful guidance on guidance. Because the statistical model already employs intensity arguments for some of its methods, the size of the TC also already may be incorporated within the model. However, it is a subject of future research to create a method which categorizes rainfall fields by TC size. This new method may further use intensity in conjunction with TC size to increase the overall FSS of the statistical model forecasts. Looking higher in the atmosphere, Fig. 43 shows mean 500 hPa heights for the Top, Middle, and Bottom ranked forecasts at the time of GFS initialization. This level is expected to be better associated with the steering flow than MSLP. As observed with MSLP (Fig. 39), the Top forecasts are associated with lower 500 hPa heights near the storm center than the Bottom forecasts. The plots show that at GFS forecast initialization, both the Top and Bottom forecasts are, on average, embedded within a mid-level ridge. However, the Top forecasts exhibit a weaker mid-level ridge west of the TCs than the Bottom forecasts, which might explain their stronger intensity and better FSS. These results indicate again the importance of intensity on forecasting TC rainfall. Because the statistical model already incorporates intensity, these results can be beneficial to the “guidance on guidance” effort of using GFS forecasts. Additionally, improvements on the intensity methods in the statistical model may create better forecasts than the other methods. By forecast hour 72 (Fig. 44), the MSLP size and intensity relationships with FSS found at the analysis hour (Fig. 39) remain, but the relative position of the TCs to the sub-tropical anticyclone has changed. The Top tiered forecasts are associated with a high-pressure feature

92 Figure 43. As in Fig. 39, but for 500 hPa heights [dam].

north of the composite TC, whereas the Bottom forecasts have tracked along the western edge of the sub-tropical anticyclone. Again, as was seen at the analysis hour, the relative mean geographical TC location between the skill groups (Fig. 41b) does not contribute to the differences in the strength of the anticyclone. The higher pressure north of the TC in the Top forecasts could contribute to a steering flow that helps keep the TC in the easterlies. This continual westward movement can contribute to a greater chance of rainfall over the United States. Therefore, if forecasters see a TC with a well-defined low-level ridge to the north, a skillful forecast might be expected. Further research is needed. At 500 hPa at forecast hour 72 (Fig. 45), TCs of both the Top and Bottom skilled forecasts

93 Figure 44. As in Fig. 39, but for forecast hour 72.

are located on the western side of the sub-tropical anticyclone at 500 hPa. Although there are no statistically significant differences at any grid point in the mean heights between the Top and Bottom forecasts (no hatching), small scale differences are apparent. These more subtle pattern differences could be important to successful TC forecasts even though mean grid point values of the two plots are statistically similar. On the other hand, the subtle differences could be artifacts of the compositing process. The Top ranked forecasts occur with a deeper trough immediately west of the TC (yellow lines, Figs. 45a and b); this trough is farther west of the TC in the Bottom forecasts. The upstream ridge (blue line) of the Bottom forecasts exhibits considerably smaller amplitude than the Top forecasts. Looking northeast of the TC, the downstream ridge in the Bottom forecasts is

94 stronger, with higher heights farther north and a tighter gradient than the Top’s downstream ridge, indicative of an environment that is more baroclinic and has been related to possible extratropical transition (ET; e.g., Atallah and Bosart 2003; Abraham et al. 2004; Atallah et al. 2007). However, the extent to which ET may or may not be a factor is beyond the scope of this research. These results suggest that a forecaster could look at a 72-h forecast of 500 hPa height patterns and have some idea whether a rainfall forecast will have skill or not. However, much additional study is needed to conﬁrm these suggestions. In terms of the statistical model and how 500 hPa heights could contribute to better FSS, a wave analysis could be undertaken to use amplitudes of approaching short-wave troughs as an indicator of their eﬀects on rainfall structure. Additionally, since ET may be a contributor to GFS forecast skill (indicated by the downstream ridge), it also could be used as a parameter in the statistical model using the methods of indicating ET discussed in Hart and Evans (2001), Atallah and Bosart (2003), and others. This is a topic of future research.

5.3.2 Baroclinic processes

Baroclinic processes can affect a TC’s circulation, moisture supply, and environment (e.g., Hart and Evans 2001; Ritchie and Elsberry 2001; Atallah and Bosart 2003), and they could affect the skill of a rainfall forecast. To discern whether a skillful or not skillful GFS TC rainfall forecast can be distinguished based on baroclinic processes, and whether these processes can be used as parameters in the statistical model, we next investigate 1000 – 500 hPa mean thickness anomalies at the analysis time (Fig. 46). The anomalies were calculated by subtracting the 2004 – 2012 individual monthly means (Aug., Sept., etc.) from those of the storm environment at the GFS model initialization or individual forecast time. For example, if a forecast was valid at 0000 UTC 12 August, then the August climatological mean thickness field was subtracted from the field at that 6-h time step. Results (Fig. 46) show that the magnitude of the positively anomalous thickness region centered over the TCs in the Top forecast category and its overall size are much larger in areal extent than the Bottom category. Greatly different thickness also exists between the Top and Bottom categories near the northwest boundary of the study domain: The top forecasts are within a negative anomalously thick (cooler) environment, whereas the Bottom forecasts are within an anomalously positive thick (warmer) environment. The Top forecasts exhibit an anomalously thick environment that extends northward from the storm to the edge of the domain. Conversely, the

95 Figure 45. As in Fig. 43, but for forecast hour 72.

Bottom forecasts exhibit an anomalously thick environment that extends from west of the storm toward the northeast where the greatest values are located. This pattern of the Bottom tiered forecasts is representative of the enhanced thickness ﬁelds found downstream of a TC in Atallah and Bosart (2003) and is often representative of ET. The results shown in Fig. 46 further indicate that TC size could be a reasonable parameter to use in the statistical model because larger storms are related to top-tiered GFS forecasts, and smaller storms are related to bottom-tiered forecasts. Additionally, the downstream ridge building seen in the bottom-tiered forecasts (Fig. 46b), and its representativeness of ET, indicate again that ET could contribute to increased FSS from a revised statistical model.

96 Figure 46. Anomalous 1000 – 500 hPa thickness [dam] composites at the analysis hour for the Global Forecast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories. Anomalies are calculated by subtracting the monthly mean (2004 – 2012) for the same month from the storm environment forecast (described further in text). Composites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel.

At forecast time 72 hours (Fig. 47), the region of enhanced thickness north of the TC in the Top skilled forecasts (Fig. 47a) has decreased in magnitude and is now oriented northeast of the TC. The negative thickness anomaly near the northwest corner of the domain has become more negatively anomalous (shown by dark purple) in the Top category, whereas the positive thickness

97 anomaly in the Bottom tiered forecasts in the same region has become weaker (but still positively anomalous). Northwest of the TC in the Bottom forecasts, a strong negatively anomalous thickness region has developed. A negative anomalous thickness environment is similarly located in the Top forecasts, but it is much stronger (more negative) in the Bottom forecasts. Atallah and Bosart (2003) studied cases of ET in baroclinic environments for only a few TCs during 1999. They found that the GFS (then called the AVN) performed poorly in creating rainfall forecasts with Floyd (1999; a storm undergoing ET) due to inadequately building the downstream ridge associated with Floyd’s outflow. Additionally, they stated that poorly forecast rainfall was attributed to the GFS “fail[ing] to simulate the sharpness of the trough-ridge couplet and the associated synoptic-scale forcing.” The current results (Fig. 47b) show a discernable trough-ridge couplet in the Bottom tiered forecasts that is indicated by negative/positive thickness anomalies. In additional, northeast of the Bottom tiered forecasts’ TC is a larger-amplitude anomalous thickness ridge than the Top tiered forecasts. This ridge could be a signature of “strong ET” (Atallah and Bosart 2003) and is likely attributed to the diabatic ridging from broad slant-wise ascent ahead of the storm. Therefore, the environment of the Bottom tiered forecasts appears to be associated with ET or ET-like environments. However, the results of Atallah and Bosart (2003) were based on only one storm which produced up to 50 cm of rain along its path. Hart and Evans (2001) found that 46% of TCs in the North Atlantic Basin had transitioned to an ET phase since 1950. Therefore, it is possible that the Bottom tiered forecasts are undergoing some form of ET and that the GFS cannot accurately simulate the rainfall field associated with this phase change. Much more research is needed to confirm the extent to which ET affects GFS rainfall forecast skill. Because the statistical model depends on GFS forecasts as input for intensity, shear, and track, using ET as a parameter in the model, may introduce additional error due to the present GFS’s inability to forecast ET well. However, a future model that better forecasts ET could be used to create the forecasts. Further analysis is needed to test the difference in FSS of the statistical model when using the GFS or another NWP model.

5.3.3 Eddy ﬂux convergence

Sawyer-Eliassen (Eliassen 1951) relationships state that a TC in gradient wind balance responds to a momentum source (e.g., an approaching trough) by enhancing upper level outﬂow that will increase the removal of mass from the storm. This leads to a decrease in the TC’s pressure

98 Figure 47. As in Fig. 46, but for forecast hour 72.

and an increase in TC intensity. However, trough interactions with a TC have been found to more likely decrease the TC’s intensity, in contrast to what is expected from Sawyer-Eliassen relationships (DeMaria et al. 1993; Peirano et al. 2016). One should recall that a change in storm intensity is related to a change in rainfall structure, (Fig. 4) and forecast skill (Fig. 40). Using a more limited methodology than Peirano et al. (2016), Hanley et al. (2001) found that TC/trough interactions were more likely to increase TC intensity. However, the arguments presented by Peirano et al. (2016) are thought to be more reliable than those of Hanley et al. (2001). To quantify the impact of an increased baroclinic environment on GFS TCs and their resultant rainfall ﬁelds and skill, eddy ﬂux convergence (EFC) was analyzed (e.g., DeMaria et al.

99 1993; Hanley et al. 2001; Peirano et al. 2016). Figure 48 shows the contribution of all three FSS categories (Top, Middle, and Bottom) to the three EFC types defined in Peirano et al. [2016]): “Superposition,” “Distant Interaction,” and “No Interaction.” EFC was calculated at the 200 hPa level, consistent with Peirano et al. (2016). Superposition is defined as an EFC interaction that is greater than or equal to the upper quartile of the full distribution of EFC calculations (3.5 m s−1 day−1 here) for two consecutive 6-h time periods in an annulus of 300 – 600 km around the storm center. Distant Interaction uses the same methodology as Superposition (upper quartile of 2.7 m s−1 day−1), but within an annulus of 500 – 900 km. No Interaction is defined as any EFC occurring between +/- 20 percentiles of 0 m s−1 day−1 for 18 consecutive hours in both the Superposition and No Interaction annuli. Results in Fig. 48 show that forty percent (35%) of the Superposition cases and 46% (32%) of the Distant Interaction cases were contributed by the Bottom (Top) forecasts. More notably, 50% of the No Interaction cases came from the Top forecast category, whereas 20% came from the Bottom tier. These results suggest that through the lens of EFC, well-forecast hurricane rainfall events are those not associated with an upper level trough and enhanced EFC interaction. The proposed hypothesis is that when an upper level trough (and therefore enhanced EFC) is interacting with a TC, a GFS forecast will be less skilled in terms of rainfall. Because of the relationship between GFS FSS and EFC, it is possible that EFC could be used as input to a revised statistical model. Shear and EFC are related since shear is calculated as the difference in wind vectors between the 200 and 850 hPa surfaces, while EFC is calculated using winds at the 200 hPa surface. Therefore, using EFC may not significantly increase the FSS of the statistical model, but it might be a replacement for shear magnitude. Shear is an important mechanism that reorients rainfall (Fig. 9) around the storm with maxima seen in the DSL quadrant. However, it is possible that EFC may be a better indicator of the magnitude of rain seen in shear- relative composites (compare weak, moderate, and strong categories in Fig. 9 and visualize replacing with Superposition, Distant Interaction, and/or No Interaction EFC categories). This hypothesis needs much further investigation and should be the topic of future research. Trough interactions with a TC have been found to either strengthen or weaken storm intensity. Specifically, interactions of any sort (whether Superposition or Distant) make the weakening of a TC more likely and strengthening less likely compared to storms without a trough interaction

100 Figure 48. Eddy ﬂux convergence (EFC) types (Peirano et al. 2016) and the contribution of each Fractions Skill Score (FSS) category (Top, Middle, and Bottom) to each type.

(Peirano et al. 2016). This ﬁnding, coupled with the results of the current research where Top forecasts are found to be more intense than Bottom forecasts (Figs. 39 and 40), give credence to the hypothesis that GFS rainfall forecasts will have poor skill when an upper level trough (more- speciﬁcally, a Superposition trough) is interacting with the TC.

5.3.4 Upper-level winds

Upper-tropospheric wind patterns, especially divergent regions above a TC, can play an important role in strengthening or weakening the storm. Figure 49 shows mean 300 hPa winds at the analysis hour for the Top, Middle, and Bottom tiered forecasts. The location of an upper level jet stream north of the TC center is different between the Top and Bottom forecasts. The jet streak associated with the Top forecasts is positioned farther east of the TC than in the Bottom forecasts. In addition, the jet streak is much stronger with the Bottom tiered forecasts than with the Top. Applying the simple four-quadrant jet streak theory (Bjerknes 1951) provides a reasonable understanding about the impact of jet interactions on TC intensity and therefore rainfall forecast skill. The location of the jet streak in the Top forecasts places the TC center in its right entrance region. This region typically has divergent flow due to transverse ageostrophic circulations that induce ascent below. The upper level divergent flow can aid in strengthening the TC due to the

101 secondary circulation interacting with convection near the storm center (DeMaria et al. 1993; Shi et al. 1990; Hanley et al. 2001; Leroux et al. 2016). Conversely, the stronger jet streak of the Bottom tiered forecasts is positioned almost immediately north of the storm with the TC center positioned only slightly within the right-entrance quadrant. This TC/jet streak orientation is less conducive to upper-level divergent flow than the Top forecasts and therefore any subsequent deepening/increasing of convection of the TC. Further analysis of the jet feature in the Top forecasts (Fig. 49a), reveals a southward extension of the stronger winds (greens and warmer colors) to within 10 degrees north of the TC. This momentum source interacts with the TC and further aids in the intensification of the storm (e.g., Molinari and Vollaro 1989) by increasing upper level divergence. To ensure that the southward extension is not an artifact, all 300 hPa products used in the study were examined. The extension was seen in a large portion of the dataset and therefore appears to be a common feature and not a byproduct of averaging. The extension feature is not seen in the Bottom tiered forecasts (Fig. 49b). Since this momentum feature is prominent in the Top forecasts, it has the potential to assist a forecaster in assessing whether a GFS rainfall forecast likely will have skill or not. The strength and contribution of the jet stream north of the TC (Fig. 49) and its influence on upper-level divergence and GFS rainfall skill is further explored with Figs. 50 and 51. Figure 50 shows latitudinal cross-sections of wind centered on the TC for the Top, Middle, and Bottom forecast categories. Figure 51 is a spatial field of 200 hPa divergence at the analysis hour. A skillful forecast at initialization is associated with a TC located near the right-entrance region of a jet streak (Fig. 49a). Figure 50a reveals the interaction of the TC with this jet and that the northern side (right side of the figure) of the storm’s outflow is somewhat connected to the southern edge of the jet. This is not seen with the Bottom forecasts (Fig. 50b). The interaction with the upper-level jet causes an enhanced area of divergence (colored darker blues/yellow) over the storm for the skillful forecasts (Fig. 51a). Conversely, the Bottom ranked forecasts (Fig. 51b) exhibit a smaller region of upper-level divergence than the Top forecasts consistent with the smaller-sized TCs within the Bottom category as shown in Fig. 39. The enhanced upper-level divergence of the Top forecasts aids in the intensification of the storm (e.g., DeMaria et al. 1993; Shi et al. 1990; Hanley et al. 2001; Leroux et al. 2016), which was found to be related to a better rainfall forecast (e.g., Figs. 39 and 40 and the statistically significant correlation of -0.46 between GFS MSLP and FSS).

102 Figure 49. 300 hPa winds (vectors) and isotachs (shaded) from the Global Foreast System (GFS) for Top (a), Bottom (b), and Middle (c) Fractions Skill Score (FSS) categories at the analysis hour. Composites are computed using environmental fields at every GFS 6-h forecast location on a 0.5 × 0.5 deg grid spacing. The Middle category is shown as a “sanity check” between the Top and Bottom categories. Hatched areas between Top and Bottom are areas that are statistically different (by computing a difference of means test (Eq. 4.1). The number of storms (NS) and forecasts (NF) are shown in the top right of each panel.

The jet streak seen in Figs. 49 and 50 and its associated upper-level divergence (Fig. 51) could be considered proxies for storm intensity. As discussed previously, these features can increase storm intensity due to the secondary circulation induced by the jet interacting with convection near the storm center (DeMaria et al. 1993; Shi et al. 1990; Hanley et al. 2001; Leroux et al. 2016). However, using upper level jet streaks and divergence to increase the FSS of the statistical

103 Figure 50. Latitudinal cross-sections of winds [m s−1] centered on the TC where north is to the right of each panel. Results for the three categories of rainfall skill are shown.

model may be too complex. If these features contribute to intensity, then intensity should be the parameter used in the statistical model.

5.3.5 Environmental summary

The investigations of this section suggest several tentative hypotheses regarding how a TC’s environment impacts the skill of the GFS on forecasting the TC’s rainfall. Since these environmental characteristics aﬀect a GFS rainfall forecast, they possibly could be used as new parameters in the statistical model. Each of the hypotheses requires additional research to conﬁrm.

104 Figure 51. As in Fig. 49, but for 200 hPa divergence (×10−5 m s−1).

To summarize, the GFS appears to provide better TC rainfall forecast skill for the more intense storms. An inverse relationship between TC minimum MSLP and FSS was found (-0.46 correlation, Figs. 39 and 40). This parameter is already included in the statistical model. In addition, results showed a possible relationship between TC size and forecast rainfall skill (Fig. 39). This parameter, while linked to TC intensity, could prove useful in improving the FSS of the statistical model. The results also suggest a relationship between 1000 – 500 hPa thickness and Top vs. Bottom ranked forecast skill (Figs. 46 and 47). Bottom forecast storms appear to be interacting more with an anomalous thickness region immediately over and north/northeast of the storm than

105 do the Top forecasts. A strong negatively anomalous thickness region west of the TC in the Bottom forecasts, in addition to a 500 hPa height ridge building to the northeast of the storm, is suggestive of an extratropical transition event. The eﬀects of ET on rainfall are signiﬁcant (e.g., Atallah and Bosart 2003). Therefore, ET is a prime candidate to be explored for inclusion in the next version of the statistical model. Based on Peirano et al. (2016), EFC calculations were done to quantify the impact of upper-level troughs on the TC. Superposition and Distant Interaction cases were found to be more associated with Bottom ranked forecasts than Top. This suggests, in general, that a GFS forecast often will have poor rainfall skill if an upper level trough is interacting with the TC. EFC could be a replacement or supplement to shear magnitude in the statistical model because of the relationship between EFC and upper-level shear. In addition, a jet stream or jet streak interacting with a TC might provide a forecaster with insight on the expected skill of a TC rainfall forecast. A jet positioned northeast of the TC center, such that the TC is in the jet’s right-entrance region, will provide divergence aloft that could enhance convection and lead to a possible increase in TC intensity. The more intense TCs were shown to be associated with more skillful rainfall forecasts (Figs. 39 and 40).

106 CHAPTER 6

SUMMARY AND CONCLUSIONS

This dissertation research had three major goals: (1) Create a unique TC-specific Stage IV rainfall composite dataset based on shear magnitude, storm intensity, and all shear magnitudes/storm intensities in shear-, motion-, and earth-relative reference frames. Research objective (2): Use the results of (1) to create a new statistical baseline TC rainfall forecast product to supplement R-CLIPER and other current forecasting techniques. And, (3): Use the results of (2) to determine when the GFS is expected to follow or not follow our current knowledge of TC rainfall, and then determine those environmental regimes that either will be conducive to skillful or not-skillful GFS forecasts GFS forecasts. The findings in (3) are considered possible future improvements to the statistical model presented here. Past research has created TC rainfall composites. However, none have used Stage IV data on such a large sample size and in such a specifically composited manner. Comparisons of the current composites (Objective 1) with those of prior research revealed differences. Many efforts have strived to better-forecast TC rainfall (see Chapter 2). However, except for dynamic models, most were parameterized methods, whereas this study approached the problem from a frequentist approach specialized by the storms’ shear magnitude and intensity, viewed in earth-, motion-, and shear-relative reference frames using Stage IV data – something not done before to the author’s knowledge. The results of the statistical model were compared to forecasts from R-CLIPER and GFS using the metric Fractions Skill Score (FSS; Roberts and Lean 2008). Finally, environmental features for skillful and non-skillful GFS forecasts were analyzed with the intent of supporting efforts to provide “guidance on guidance.” This type of analysis of TC rainfall also has not been performed to the author’s knowledge. The public’s perception of TC damage usually relates to storm surge or the TC’s devastating winds (Meyer et al. 2014; Rice 2014). However, Rappaport (2014) found that deaths from TC rain- induced floods accounted for 27% of TC-related total deaths for years 1963 – 2012. Additionally, rainfall-related deaths occur more frequently than from any other hazard (Fig. 1). Therefore, it is

107 important to better understand hurricane rainfall and increase efforts to more skillfully forecast it. This dissertation strived to address these concerns. To aid in the ongoing efforts to better understand TC rainfall and forecast it with greater skill, the Stage IV dataset was used as input to a newly developed statistical baseline TC rainfall model. Stage IV data have higher spatiotemporal resolution and can record rainfall at higher latitudes than TRMM, the staple of prior TC rainfall composite-based research. The Stage IV data allowed an analysis of TC rainfall over land – where individuals are most impacted. Since the rainfall composites were to be used in the statistical rainfall model (research objective 2), these characteristics of Stage IV attracted us to them. The Stage IV data were categorized by storm intensity and shear magnitude, with the results compared to previous research based on TRMM-derived rainfall (Black et al. 2002; Rogers et al. 2003; Lonfat et al. 2004; Chen et al. 2006; Cecil 2007; Wingo and Cecil 2010; Xu et al. 2014). The storm-motion and shear-relative datasets were prepared by rotating the storm’s previous 6- h motion and the 850 – 200 hPa vertical shear, respectively. This approach provided a two- dimensional analysis: one reoriented the TC rainfall (using TC motion and vertical shear vectors), and the second modified the magnitude of the rainfall (using the magnitude of TC shear and TC intensity). Data from 2004 – 2012 were composited on a 10 × 10 km equidistant grid and used as the development dataset. The goal of compositing the Stage IV dataset in this manner was to retain as much detail as possible from the higher-resolution data to achieve research goal (1). In addition, the higher-resolution data served as input to develop the statistical model for research goal (2). The composite analyses showed some similarities with prior findings that employed TRMM data. However, rainfall features found in the prior research often were enhanced when using the Stage IV data. Compositing the dataset regardless of shear magnitude or shear intensity was shown to highlight the unique characteristics of using Stage IV data (Fig. 4). Earth-relative Stage IV results showed a rainband signature east of the storm that was not indicated in prior composite-based work. This likely was attributed to the location of Stage IV data, since they were primarily over land, and the distribution of storm intensities (Fig. 5). Willoughby et al. (1984) found that rainband signatures are more apparent in weaker storms. This research corroborated their findings by using composited data (e.g., Fig. 7) for five TC intensity categories. A right-of-motion rainfall

108 maximum, similar to prior research (Fig. 4) was attributed to asymmetrical frictional forcing between the surface and the translating TC (Shapiro 1983). However, the approaching land surface also could contribute to the Stage IV motion-relative asymmetry. Kimball (2008) showed that an approaching land surface stabilized the left side of the TC which then enhanced rainfall asymmetry. This stabilization likely is more apparent in Stage IV data than in the previously used TRMM data since those studies primarily accumulated TC rainfall over open water. The shear-relative rain rate composites showed a more asymmetrical and radially expansive pattern than found previously (e.g., Wingo and Cecil 2010). The Stage IV data next were aggregated by storm intensity (Fig. 7). Results showed that as storm intensity increased, the rain rate pattern became more symmetric in the earth- and shear-relative reference frames. Figure 7 corroborated the findings of Shapiro (1983) who found that rainband signatures were primarily found in weaker storms. The reduction in asymmetry with increasing storm intensity (Fig. 7) was attributed to strong TCs generally occurring in environments of weak shear and vice versa. Results showed that rain rate asymmetry and vertical shear were positively correlated, i.e., increased shear led to increased asymmetry as in (Wingo and Cecil 2010). Therefore, weaker storms, generally occurring with larger magnitudes of environmental shear, are more influenced by the effects of that shear, thus rendering the storm more asymmetric. However, in stronger storms, vertical shear generally is weaker, and its effects diminish, thereby reducing asymmetry (Fig. 7). The effects of shear on TC rain rate asymmetry also were shown in Fig. 9. Jones (1995) and Frank and Ritchie (1999) showed that a TC experiencing environmental vertical shear exhibits a tilted vortex. This induces a secondary circulation on the storm that is manifested by a potential temperature (θ) couplet. This couplet provides a mechanism on an isentropic surface for ascent on the downshear (direction of vertical tilt) side of the storm and descent on the upshear side. However, once condensation occurs, parcels ascend at different rates and no longer on isentropic surfaces. The secondary circulation then becomes dominated by differential vorticity advection. The composites in Fig. 9 showed rain rates in three different shear magnitude environments (weak, moderate, and strong). As vertical shear strengthened, results showed that rain rates became more asymmetric and organized. A 10 m s−1 change in the magnitude of shear produced a much different rain rate pattern. This finding highlighted the importance of understanding rainfall asymmetry

109 with respect to shear. The transitional state of the secondary circulation from an isentropic path to one where condensation occurs was revealed by the weak shear composite (Fig. 9a) in which the rainfall pattern was less organized. Conversely, with increased shear a well-defined DSL maximum appeared (Fig. 9c). Seven geographic regions were created to ascertain whether there were any differences in regional TC rainfall characteristics. The methodologies of Schoner and Molansky (1956), Schoner (1968), and Jagger and Elsner (2006) were used to separate the U.S. coastline into discreet regions. For each of these regions, composites were created based on shear magnitude, storm intensity, and all shear magnitude/storm intensities. This was done in earth-, motion-, and shear-relative frameworks, producing a total of 42 composites. When compositing TC rainfall in this regional manner, characteristics not previously found in prior work became apparent (Figs. 11 and 15). Rain rates in the STX, NGULF, and SFL regions were found to be more axially symmetric than in the Atlantic regions (SATL, MIDATL, and NATL). Results showed that these differences were due to the different environments of the geographic regions. Higher-latitude storms occur in regions where the environment is more baroclinic; therefore, they are more impacted by the effects of shear. For example, the NATL region had the greatest shear (Fig. 12) and had the most asymmetric structure of rain rate (Figs. 11 and 15). The SFL region contained the strongest storms, and its rain rate composites contained the greatest rainfall. The currently observed detail in the regional U.S. TC rainfall composites has not been reported in prior research due to their use of TRMM-derived rainfall estimates. The unique features of the regional rain rate composites highlight the complexity of TC rainfall and the importance of understanding its structure in a regional manner. The results of the composites helped accomplish research goal (1) and were used to achieve research goal (2). Two, 72-h TC rainfall forecasts, skillful and unskillful in terms of FSS, were described to demonstrate the utility and deficiencies of the statistical model. The statistically derived forecasts also were compared to forecasts from the GFS. The REG-SS method (Table 7) was employed for these example forecasts from the test dataset (2013 – 2016). The skillful forecast was for TS Ana (2015) using the 1200 UTC 8 May 2015 initialization. Results showed that the statistical model can create a skillful forecast with a threshold averaged FSS of 0.73 (Figs. 17 and 18 and Table 10). Not only was the FSS large, but the location and magnitude of maximum rainfall were similar

110 to observations. The REG-SS method created a maximum accumulation of 8.52 in. compared to the 7.59 in. from observations. The REG-SS method also replicated the observed rainfall patterns, with maximum rainfall oriented right of track. The GFS produced a considerably diﬀerent forecast for the same period. Its average threshold FSS was only 0.17, and it produced a rainfall maximum of 2.04 in. that was located farther away from the observed maximum than the REG-SS method (compare Figs. 17, 19, and 21). The TS Ana forecast was a good example of when the statistical model can be a viable candidate to supplement the GFS rainfall forecasts. The R-CLIPER forecast (Fig. 20) produced an average FSS of 0.22 (Table 10). Its forecast rainfall was mostly symmetric about the forecast track with a maximum of 6.6 in. near the inward bend of the track. Because of R-CLIPER’s methodology (Section 2.2.2), this forecast structure was expected. The greater- detailed forecast from the statistical model, coupled with a better-located maximum and larger FSS than R-CLIPER, indicate that the newly developed statistical model can be a supplement to R-CLIPER as a new baseline method. Not all forecasts from the statistical model were as skillful as the one for TS Ana (2015). An unskillful 72 h forecast from TS Andrea (2013), initialized at 1200 UTC 6 June 2013 (Figs. 22 – 26), was presented. The REG-SS forecast produced a threshold average FSS of 0.38 (Table 10). The maximum accumulated rainfall was 2.83 in. – approximately 5.3 in. less than observed (8.17 in.) even though the overall rainfall pattern from REG-SS was similar to that observed (Figs. 22 and 24). Results revealed that discrepancies between the REG-SS forecast and observations were due to the storm’s rapid forward speed which ranged from 9 m s−1 at forecast hour 6 to 40 m s−1 at forecast hour 54. The forecast track speeds used by the statistical model were accurate (forecast 6-h locations were collocated with Best Track 6-h locations); however, the 6-h rainfall composites used by REG-SS simply did not have suﬃcient time to accumulate the amount of observed rainfall. The GFS and R-CLIPER performed similarly poorly during TS Andrea with an average threshold FSS of 0.41 and 0.36, respectively (Table 10). Both the GFS and the REG-SS method replicated shear-relative rainfall patterns. Since shear has been shown to be the primary mechanism that modulates rainfall amount and placement (e.g., Corbosiero and Molinari 2003; Chen et al. 2006; Ueno 2007; Wingo and Cecil 2010; Hence and Houze 2011; Reasor et al. 2013; Xu et al. 2014), one might expect the GFS to produce the shear-induced rainfall characteristics. However, the GFS did not follow the rainfall

111 patterns of the REG-SS method during TS Ana, whereas it did follow the expected patterns with TS Andrea. Research goal (3) sought to develop a new method for investigating TC rainfall forecast skill with respect to a storm’s broader synoptic environment. The results of verifying 72-h rainfall forecasts from all methods and models were sum- marized. Accumulations from each method comprising the statistical model and the GFS were verified against Stage IV observations using the test dataset (years 2013 – 2016) at 13 different rainfall thresholds ranging from 1 to 150 mm using FSS as the statistical metric. Various radii of influence (ROI) were explored, but results from the 50 km ROI were presented since its results were similar to those from the other ROIs (not shown). Seventy-two-hour forecasts were verified to reduce potential errors due to GFS forecast track error. Two different approaches were taken: an aggregate analysis on a storm-by-storm basis, and an aggregate based on a forecast-by-forecast basis. Results from both methods proved useful in analyzing the verification results. If a seasonal analysis of skill is desired, the storm-by-storm approach should be used since it minimizes noise between forecasts and only reports how an individual storm performs. Conversely, if a specific TC analysis is desired, the forecast-by-forecast method should prove useful since a forecaster can assess model performance in near real time. The overall trend of both the storm-by-storm and forecast-by-forecast methods was decreasing FSS with increasing rainfall threshold (Figs. 27, 28, 30, and 31). Both the GFS and the statistical model outperformed R-CLIPER (RCP). However, at thresholds > 100 mm, several of the statistical methods exhibited a lower skill than RCP. For rainfall thresholds < 50 mm, several, sometimes all statistical methods, produced a greater FSS than the GFS and R-CLIPER. This finding occurred whether viewing on a storm-by-storm basis, a forecast-by-forecast basis, or whether using the ALL (full composites) or REG (regional) composites. However, for thresholds ≥ 50 mm, the GFS had a slightly greater FSS compared to all statistical methods (both ALL and REG) regardless of how the FSS was aggregated. When viewing FSS by individual rainfall thresholds (Fig. 32), the differences, if any, between the individual statistical models and R-CLIPER became apparent. At lower thresholds, the statistical model had a larger FSS than R-CLIPER, but similar FSSs to the other methods. This indicates that the difficulty in forecasting TC rainfall is much greater than reducing forecast techniques down to a few parameters. It is likely that additional parameters must be included.

112 At larger thresholds, differences between R-CLIPER and any of the statistical methods became minimal, indicating that they struggled at larger FSSs. Comparisons were made between the overall forecast skill of all the methods and models (Figs. 29 and 33). Whether on a forecast-by-forecast or storm-by-storm basis, the REG-SS method was the top ranked performing method. This result showed that the statistical model might be a helpful complement to the GFS and that it can routinely out-score R-CLIPER. A simple question was posed: If the GFS performed poorly, will the statistical model also perform poorly or vice versa? The question was answered using the REG-SS method since results showed it to be the best statistical method developed. Figure 16 showed a weak positive linear relationship between the GFS and the REG-SS method. However, since the relationship was quite weak (R2 = 0.23) and contained a great deal of scatter, one cannot confidently state that there is a meaningful relationship between results of one forecast method and another. Radial distributions of rainfall accumulations (Fig. 36) showed that the GFS had a dry bias at most radii, whereas the statistical models exhibited a wet bias at most radii. R-CLIPER exhibited a greater wet bias than any other method. Near the TC center, the ALL intensity-based methods (ALL-IE/M/S) were found to have a smaller difference with Stage IV observations than any REG-based method (Fig. 37a). Similarly, near the TC center these methods also had statistical variances that were closer to Stage IV statistical variances than any REG-based method (Fig. 37b). For radii between approximately 190 and 350 km, various REG methods were found to align better with Stage IV observations. The 60 – 180 km range showed no distinctions between methods. The superiority of the REG-based methods over the ALL-based methods in the range 190 – 350 km covered a much greater area than the superiority of the ALL-based methods over the REG-based in the much smaller core area. Contributions to errors in the statistical model were explored. Results revealed that errors in forecast shear, motion (track), and intensity could contribute as much as a ∼0.2 difference in FSS compared to “perfect” forecasts (those that used verified shear, track, and intensity from SHIPS and Best Track analyses). The maximum difference in FSS from R-CLIPER “perfect” forecasts and actual forecasts was ∼0.1. This smaller difference from R-CLIPER compared to the statistical model was due to the greater number of degrees of freedom in the statistical model. Simply stated, since more variables are input to the statistical model, there are more variables that

113 can introduce error to it. Nonetheless, the larger Best Track and forecast FSSs from the statistical model compared to R-CLIPER show that it is a viable solution as a new statistical baseline method. The final goal of the research (goal 3) was to determine whether any specific environmental characteristics were conducive to skillful or not skillful GFS TC rainfall forecasts and if these environments would be useful additions to an updated statistical model. Determining in advance whether a GFS forecast would be skillful or not is consistent with the current emphasis of providing guidance on guidance. The methodology used here for that purpose could be extended to any forecasting model. The first step was to categorize each 72-h rainfall forecast into one of three categories according to its FSS: Top (FSS ≥ 0.66), Middle (0.33 – 0.66), and Bottom (< 0.33). The environmental composites of the Top and Bottom categories were expected to be different, and the Middle category was expected to fall between the two. The composite analysis of each category was done on the 0.5 × 0.5 deg grid that is native to the GFS forecasts being used. Composites of mean sea-level pressure (MSLP) showed that TCs comprising the Top tiered forecasts are stronger in intensity (lower MSLP) than TCs comprising the Bottom tiered forecasts (Figs. 39 and 44). This was verified by the distribution of intensity and skill categories (Fig. 40) and a -0.46 statistically significant correlation (α = 0.05) between GFS MSLP and FSS. In addition, a stronger sub-tropical ridge was found at the analysis hour of the Bottom forecasts than for the Top forecasts. By forecast hour 72, the relationship of a better FSS being related to stronger storms remained, but the location of the TC with respect to the sub-tropical anticyclone had changed. TCs of the Top forecasts appeared to be passing through a portion of the anticyclone, causing local high pressure north of the storm. Conversely, TCs of the Bottom forecasts were located on the western side of the anticyclone at forecast hour 72. Thus, rainfall forecasts of more intense storms appear to be more skillful at the analysis hour through forecast hour 72 (Figs. 39a and 44a). Conversely, forecasts of weaker TCs that translate to the west of the anticyclone are expected to be less skillful (Figs. 39b and 44b). These results should be considered tentative, requiring additional research to confirm. Higher in the atmosphere, 500 hPa heights revealed that both the Top and Bottom tiered forecasts were located in a broad mid-level ridge at initialization (Figs. 43 and 45). However, the Bottom forecasts resided in a much stronger ridge. Relatively minor ridge/trough interactions with the TC were found at forecast hour 72 in both the Top and Bottom forecasts. Specifically,

114 upstream, to the west of the storm, the Top forecasts were associated with a higher-amplitude ridge west of a trough. A similar layout was observed in the Bottom forecasts (Figs. 45a and b). However, the trough in the Bottom forecasts was located farther from the storm and was not as strong. Downstream and northeast of the TC, the Bottom forecasts were associated with a stronger ridge than the Top forecasts. This placement previously has been associated with ET since the downstream ridge in the Bottom forecasts matched patterns in Atallah and Bosart (2003), Abraham et al. (2004), Atallah et al. (2007). The extent to which the current ridge can be attributed to ET was not explored and is beyond the scope of this research. However, it is a topic of future exploration. It was hypothesized that a wave analysis could be performed to calculate impacts of the trough/ridge structure around the TC and, if results are favorable, used as input to the next version of the statistical model. Thickness anomalies in the 1000 – 500 hPa layer were investigated to ascertain whether baroclinic processes contributed to skillful or unskillful TC rainfall forecasts. Results showed that this was indeed the case. At the analysis time, positively anomalous thickness located over TCs of the Top ranked forecasts was much larger in areal extent than that found in the Bottom ranked forecasts (Fig. 46). Thickness patterns in the vicinity of the TCs also were diﬀerent. The Top forecasts exhibited a positive thickness anomaly extending due north from the TC’s center. Con- versely, the Bottom forecasts’ positive thickness anomaly extended from west of the storm to its northeast and was greater in magnitude. By forecast hour 72 (Fig. 47), the Bottom forecast thickness anomaly directly over the storm had increased in size and extended northeast from the center of the storm. The top forecast’s thickness anomaly to the north had shifted northeast and became weaker. A negative thickness anomaly to the west developed in both the Top and Bottom forecasts. However, the Bottom forecasts’ anomaly was more negative than the Top’s. Therefore, an unskillful forecast might be expected if the anomalous thickness environment of a TC is forecast to change from one that is small, positive, and directly over the storm to one that is even more positively anomalous and extending from the center of the storm to the northeast with a strong negative thickness anomaly to the immediate west of the storm. The anomalous thickness couplet shown in Fig. 47 was indicative of ET. Therefore, it was suggested that the impact of ET on TC rainfall be investigated further. Its impacts on TC rainfall could lead to increasing the FSS of the statistical model.

115 To quantify the impact of an increased baroclinic environment on GFS TC rainfall skill, an analysis of eddy flux convergence (EFC) at 200 hPa was performed (e.g., DeMaria et al. 1993; Hanley et al. 2001; Peirano et al. 2016). Results in Fig. 48 showed that the Bottom forecasts consisted of 40% Superposition EFC interactions and 46% of Distant Interaction cases. Alternatively, the Top forecasts consisted of 35% and 32%, respectively. More notably, 50% of the No Interaction cases corresponded to the Top forecast category, whereas 20% came from the Bottom. Therefore, well- forecast rainfall events do not appear to be associated with an upper-level trough and enhanced EFC. It is more likely that when an upper level trough (and therefore enhanced EFC) is interacting with a TC, the GFS forecast of it will exhibit relatively small FSS. Trough interactions with a TC can either strengthen or weaken storm intensity. Specifically, Superposition or Distant Interaction EFC events make the weakening of a TC more likely (and strengthening less likely) compared to storms with no EFC interaction (Peirano et al. 2016). This result from Peirano et al. (2016), coupled with the findings of the current research where Top forecasts were stronger than those of the Bottom forecasts (Figs. 39 and 40), suggests that it is likely that the GFS will have less skill at forecasting TC rainfall when an upper level trough (more-specifically, a Superposition trough) interacts with the TC. The results in Fig. 48 indicated that EFC impacts skill. EFC and vertical shear both use 200 hPa winds in their calculations. Therefore, it was hypothesized that EFC categories could be used instead of shear magnitude categories to increase the FSS of the statistical model. This is likely from a theoretical perspective since EFC is more comprehensive because it is calculated over several annuli instead of one annulus as done for shear. Upper-tropospheric wind features also were found to differ between the Top and Bottom GFS forecasts (Fig. 49). An upper-level jet stream was found in both categories; however, the location of the jet stream differed. The Top forecasts exhibited a jet stream whose axis was positioned more northeast of the TC than in the Bottom forecasts. Based on the simple four- quadrant jet model, the right entrance region of the Top forecasts was in a more-favorable position than the Bottom forecasts to produce enhanced upper-level divergence over the TC. This placement could aid the intensification of the storm (e.g., DeMaria et al. 1993; Shi et al. 1990; Hanley et al. 2001; Leroux et al. 2016). Figures 39 and 40 revealed that more intense storms resided within the Top forecast category. Therefore, if an enhanced upper-level jet feature is positioned as seen

116 in Fig. 49 such that it causes the storm to intensify, a skillful forecast might be expected. The contribution of jet streaks and upper-level outflow were already incorporated to some extent in the intensity-based versions of the statistical model since upper-level winds and storm intensity are closely related. This dissertation research sought to contribute to an improved understanding of TC rainfall forecasts and rainfall climatology. Stage IV data composited in a manner not done previously showed distinct characteristics not seen before (research goal 1). These climatological rainfall composites were used to develop a new statistical rainfall baseline model (similar to R-CLIPER). Verification of the model showed that it can be a viable candidate to assist in current forecasting efforts in some situations (research goal 2). Finally, using knowledge from goals (1) and (2), environments conducive to skillful and unskillful GFS-derived TC rainfall forecasts were determined. This is consistent with current efforts to provide guidance on guidance (research goal 3). This type of analysis to the author’s knowledge has not been done before. Additionally, the findings in research goal 3 were considered as possible future implementations into revised versions of the statistical model. While much research remains to be done to create better TC rainfall forecasts, this research hopefully provides insight toward that goal. It also hopes to serve as a steppingstone from which to continue exploring unique and sustainable methods to better-forecast TC rainfall.

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127 BIOGRAPHICAL SKETCH

Tristan Hall was raised in the one-horse town of Genoa, Ohio. His parents are Pattie and David Hall. He has two older brothers and they are all very close. In elementary school, his advisor asked him what he wanted to be when he grew up. He answered simply “doctor,” as many children do, and “storm chaser.” After high school Tristan, without a plan, followed his brothers to Appalachian State University. Not a smart decision as an 18 year old, but all the brothers wanted to be together and his life only only got better. During his time at Appalachian State, he met and fell hopelessly in love with a brilliant violinist named Catherine Williams. As he progressed in his studies, Tristan became increasingly interested in meteorology. One of his professors would give a daily weather synopsis that sparked more and more interest in meteorology from Tristan. Unfortunately, Appalachian State did not have a meteorology degree program. Instead, Tristan decided to double major in physics and geography with concentrations in the atmosphere. Additionally, he earned a minor in mathematics to supplement his work in the sciences. When it was time to apply for graduate school, Tristan had only one institution in mind: Florida State University. He applied to Florida State and was accepted in 2010. He completed his master’s in 2014 and continued at Florida State for his Ph.D. During Tristan’s time at Florida State, his daughter was born. She is the deﬁnition of happiness. Tristan loves to spend as much time as possible with her. She loves blueberries, her Cozy Coupe, and terrorizing the cats. Tristan currently resides with his family in Raleigh, North Carolina.

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