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Spatial Characteristics of Rain Fields Associated with Tropical Cyclones Landfalling over the Western Gulf of Mexico and Caribbean Sea

YAO ZHOU School of Public Administration, National Center for Integrated Coastal Research, University of Central Florida, Orlando, Florida

CORENE J. MATYAS Department of Geography, University of Florida, Gainesville, Florida

(Manuscript received 7 February 2018, in final form 30 April 2018)

ABSTRACT

The western Gulf Coast and Caribbean coast are regions that are highly vulnerable to precipitation asso- ciated with tropical cyclones (TCs). Defining the spatial dimensions of TC rain fields helps determine the timing and duration of rainfall for a given location. Therefore, this study measured the area, dispersion, and displacement of light and moderate rain fields associated with 35 TCs making landfalls in this region and explored conditions contributing to their spatial variability. The spatial patterns of satellite-estimated rain rates are determined through hot spot analysis. Rainfall coverage is largest as TCs approach the western Caribbean coast, and smaller as TCs move over the Gulf of Mexico (GM) after making landfall over the Yucatan Peninsula. The rain fields are displaced eastward and northward over the western and central Ca- ribbean Sea and the central GM. Rainfall fields have more displacement toward the west and south, which is over land, when TCs move over the southern GM, possibly as a result of the influence of Central American gyres. The area and dispersion of rainfall are significantly correlated with storm intensity and total pre- cipitable water. The displacement of rainfall is significantly correlated with vertical wind shear. Over the Bay of Campeche, TC precipitation extends westward, which may be related to the convergence of moisture above the boundary layer from the Pacific Ocean and near-surface convergence enhanced by land. Additionally, half of the storms produce rainfall over land about 48 h before landfall. TCs may produce light rainfall over land for more than 72 h in this region.

1. Introduction (NHC) tropical cyclone reports, 17 out of 42 TCs making landfalls over this region during 1998–2015 caused at least Regions along and inland of the western Gulf Coast one death, and most of these fatalities were caused by and Caribbean coast are highly vulnerable to pre- tropical cyclone precipitation (TCP) and rainfall-induced cipitation associated with tropical cyclones (TCs) from floods and landslides. Hence, a study that specifically the North Atlantic (Pielke et al. 2003; Khouakhi et al. examines the spatial distribution of TCP over the west- 2017). Some of the most devastating TCs of the past ern Caribbean Sea (CS) and Gulf of Mexico (GM) can 20 years have caused fatalities and economic damage due identify the areas experiencing TCP and determine the to widespread precipitation and induced flooding and time when rainfall begins over land and its duration. As landslides in this region, such as Hurricanes Mitch (1998), flood advisories need to be issued earlier when rainfall Stan (2005), Alex (2010), and Ingrid and Manuel (2013) extends farther ahead of the storm center, the environ- (Pasch and Roberts 2006; Pielke et al. 2003; Beven 2012; mental conditions associated with this configuration need Beven 2014). According to National Hurricane Center to be identified. Quantifying the spatial pattern of TCP can improve Denotes content that is immediately available upon publica- forecasts, which currently incorporate persistence such as tion as open access. the tropical rainfall potential (TRaP) technique (Kidder et al. 2005; Luitel et al. 2018). A variety of shape metrics Corresponding author: Corene J. Matyas, matyas@ufl.edu have been utilized to characterize spatial patterns of rain

DOI: 10.1175/JAMC-D-18-0034.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/01/21 09:49 PM UTC 1712 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 57

fields and relate them to environmental conditions. The 2. Data and methodology first application of shape analysis in tropical meteo- rology was the Dvorak technique, which uses cloud a. Data patterns in satellite imagery to estimate TC intensity The precipitation data are taken from the Tropical (Dvorak 1975; Velden et al. 2006). However, this Rainfall Measuring Mission (TRMM) Multisatellite Pre- technique does not quantify the spatial distribution of cipitation Analysis (TMPA) 3B42 precipitation prod- TC rain fields. Matyas (2007) quantified the spatial uct version 7 (Huffman et al. 2007). The TMPA product characteristics of radar-derived rain fields for TCs combines data from various spaceborne precipitation during U.S. landfall, including closure, edge rough- sensors with calibration from TRMM instruments, in- ness, elongation, and Euler number. More recently, cluding the TRMM Microwave Imager, the Special Sen- Zick and Matyas (2016) examined reanalysis data and sor Microwave Imager (SSM/I), and the Special Sensor used asymmetry, dispersiveness, and fragmentation to Microwave Imager/Sounder (SSM/IS), and also incorpo- describe rainfall structural changes during TC inten- rates rain gauge data through probability density function sity changes, landfall over the United States, and matching as ground truth. Data are available every 3 h extratropical transition. These studies analyzed U.S. since January 1998 on a 0.258 latitude–longitude grid cov- landfalling TCs and illustrated that rain field configu- ering areas from 508Sto508N(Huffman et al. 2007). The rations are related to not only storm intensity but also TMPA 3B42 dataset has been used for TCP analysis re- the storm’s location and surrounding environmental conditions. TCs passing over the western Gulf and CS gionally and globally (e.g., Shepherd et al. 2007; Lau et al. that do not interact with the midlatitude westerlies 2008; Jiang et al. 2011; Lau and Zhou 2012; Prat and experience different environmental conditions than Nelson 2013; Matyas 2014; Xu et al. 2014; Zhu and Quiring those making landfall over the United States, which 2017; Luitel et al. 2018). typically do interact with the westerlies (Elsner 2003; The TC track data are obtained from the Interna- Kimball and Mulekar 2004; Kossin et al. 2010). This tional Best Track Archive for Climate Stewardship difference in environmental conditions warrants a (IBTrACS) database (Knapp et al. 2010)andare separate study to examine TC rain field configurations plotted within a geographic information system (GIS) for TCs over the western Gulf and CS. Measuring the to identify TCs making landfall over the western Gulf area covered by rainfall, whether rainfall is spread out Coast and the Caribbean coast during 1998–2015. A or compact, and determining the side of the circulation total of 35 TCs are examined, after excluding storms center to which rainfall is displaced are key to identi- that spend less than 24 h over the ocean, or do not reach fying where and when rainfall will affect land and its tropical storm (TS) intensity during their life cycle. We duration. also exclude one extratropical storm since it experi- In this study, 35 TCs during 1998–2015 that did not ences different environmental conditions than the interact with the westerlies before making landfall over tropical storms in this region (Fig. 1). The 6-hourly the western Caribbean coast and Gulf Coast, from Texas positions and intensity of the storm are linearly in- to Nicaragua, are examined. There are three main re- terpolated to every 3 h to match the TMPA observa- search objectives. First, after measuring the area, dis- tions (Jiang et al. 2011). The storm motion speed and persion, and displacement of light and moderate rain direction are also calculated from the interpolated fields, the spatial patterns of these metrics are examined positions using the GIS. through hot spot analysis. The second goal is to determine To characterize potential influences upon the areal which TC attributes and environmental conditions are coverage and spatial configuration of the TC rain fields, associated with the spatial configuration of the TC rain deep-layer vertical wind shear and total precipitable fields. This is accomplished by comparing subareas with water (TPW) values are obtained from the Statistical distinct rain-rate spatial patterns through Mann–Whitney Hurricane Intensity Scheme (SHIPS) database, which U tests and calculating Spearman’s rank correlation co- is a product of the National Centers for Environmental efficients for the entire study region to relate the four Prediction Global Forecast System model analyses metrics and atmospheric moisture, vertical wind shear, (DeMaria et al. 2005). Within the SHIPS dataset, deep- storm motion, and storm intensity. We then utilize re- layer vertical wind shear is calculated between 850 and gression models to examine multiple factors at the same 200 hPa over the area extending 200–800 km from the time. Finally, we determine the time that rainfall reaches TC center. In this study, the 6-hourly wind shear vec- land relative to the time that the storm’s center makes tor data, which are available at 0000, 0600, 1200, and landfall and calculate the average and maximum duration 1800 UTC, are divided into southerly and westerly of rainfall from TCs over the study region. components, and linearly interpolated into 3-hourly

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FIG. 1. Portions of TC tracks that made landfall during 1998–2015 over the western Carib- bean coast and/or Gulf Coast used in this study. Elevation data are obtained from the U.S. Geological Survey (https://lpdaac.usgs.gov/node/524; NASA JPL 2013). observations (Matyas 2013). TPW values incorporate gauges over land, while it has better performance in de- 2 the amount of moisture in the whole atmospheric col- tecting moderate-to-heavy TC rainfall (.100 mm day 1) umn averaged over different spatial ranges relative to over the ocean. 2 the TC’s circulation center (0–200, 0–400, 0–500, 0–600, After rain rates of 2.5 and 5 mm h 1 are used to con- 0–800, and 0–1000 km). Utilizing values over all dis- tour the TMPA data and the results are converted into tances allows us to examine the influence of moisture polygon features, we select the rainfall polygons to be over different ranges from the storm center. The vari- examined further utilizing two criteria. These criteria ables representing the environmental conditions, storm are that 1) their centroids are located within 500 km of intensity, and motion are listed in Table 1. the TC center and 2) polygons either must intersect with or be contained inside of the radius of the outmost b. Spatial analysis closed isobar (ROCI). First, the 500-km search radius is The TMPA dataset may overestimate light rain rates employed as it has been used to separate TC and non-TC 2 (e.g., ,1mmh 1) and underestimate moderate to heavy rainfall in previous TCP research (Lonfat et al. 2007; 2 rates (e.g., .5mmh 1)(Yu et al. 2009; Chen et al. 2013). Jiang et al. 2011; Hernández Ayala and Matyas 2016). Therefore, this study employs rain-rate values of 2.5 and Second, as great variability exists in storm size, previous 2 5mmh 1 as thresholds to define light-to-moderate rain- studies also use ROCI to obtain TCP, as the ROCI fall regions, as suggested by previous research (Zagrodnik typically encompasses the entire TC rain field (Matyas and Jiang 2013; Matyas 2014). It should also be noted that 2010; Zhu and Quiring 2013). Preliminary results in the the TMPA 3B42 product has different algorithms and current study show that the median ROCI in this region bias corrections for observations over land and ocean is 277 km, which might cause rainfall regions to be in- (Huffman et al. 2007; Chen et al. 2013). Rain gauge ana- cluded that are not generated by the TC’s circulation if lyses are utilized to remove bias over land. Chen et al. we use a uniform radius of 500 km for all TCs. We keep (2013) found that the TMPA has similar estimations of TC both thresholds to identify the TCP polygons because 2 light-to-moderate rainfall (50–100 mm day 1)withrain they exclude rainfall polygons that only have small parts

TABLE 1. Abbreviations, units, sources, and spatial ranges of TC attributes and environmental conditions.

Variable Abbrev Unit Data source Spatial range of variables 2 Velocity of max sustained winds VMAX m s 1 IBTrACS — 2 Eastward motion speed MOTE m s 1 IBTrACS — 2 Northward motion speed MOTN m s 1 IBTrACS — Avg total precipitable water TPW mm SHIPS 0–200, 0–400, 0–600, 0–800, 0–1000 km 2 Southerly vertical wind shear (850–200 hPa) SHRS m s 1 SHIPS 200–800 km 2 Westerly vertical wind shear (850–200 hPa) SHRW m s 1 SHIPS 200–800 km

Unauthenticated | Downloaded 10/01/21 09:49 PM UTC 1714 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 57 that interact with ROCI, but also have large areas with weight in the calculation. When larger regions of rainfall centroids located outside of the 500-km range. These are located near the storm center, the dispersion metric rainfall regions might belong to other weather systems. is closer to zero. If the rain fields move away from the The extended best-track (EBT) dataset (Demuth et al. storm center, rainfall near the center dissipates, and/or 2006) provides relatively complete information about more outer rainbands develop, dispersion values in- ROCI for most TCs, though instances of missing data crease (Fig. 2a): have been reported in the literature (Vigh et al. 2012;   Zhu and Quiring 2013; Carrasco et al. 2014). In the N Area r 5 å i centroid,i current study, ROCI estimates are available for 84% DISP . (1) i51 Areasum rsearch of observations. When the ROCI is missing, it is re- placed with the available ROCI values at adjacent times. The average count of rainfall polygons de- In addition to dispersion, measuring displacement creases from 2.9 per TC when we only use the 500-km provides a directional component to rainfall asymmetry search radius to 2.0 after applying both thresholds. that helps identify which region will receive TC rainfall. Last, only polygons with a minimum of five pixels are Recent observational studies have shown that vertical included. wind shear, TC motion, and moisture gradients can After defining the rainfall fields for all TC observa- cause the rain fields of TCs to become asymmetrically tions, we calculate the area, dispersion, and displace- shaped (Corbosiero and Molinari 2002; Chen et al. 2006; ment to describe the spatial patterns of the rain fields. It Lonfat et al. 2007; Matyas and Cartaya 2009; Wingo and is important to measure the area where rainfall is oc- Cecil 2010). These previous researchers have shown that curring as larger areas mean that more locations on the the rainfall is enhanced in the downshear direction and ground will receive rainfall and/or rainfall will have a the right-of-motion direction. When TCs approach land, longer duration depending on the spatial configuration friction enhances convergence on the side of the storm of the rainfall regions. All polygons of rainfall over 2.5 near land, which can also cause asymmetry of the rain 21 and 5 mm h are summed separately for calculating the fields. Here, we develop a new method to calculate the areal coverage of light and moderate rainfall. Although displacement of all polygons of rainfall, which is based previous research shows that the rainfall area is posi- on the dispersion calculation and relative location of tively correlated with the environmental moisture, there individual polygons to the storm center. In this calcula- is a disagreement about the relationship between storm tion, ui is the heading of the vector from the storm center intensity and rainfall size (Jiang et al. 2008; Konrad and to the individual polygon centroid (Fig. 2b): Perry 2010; Matyas 2010; Lin et al. 2015). Here, we hy-   pothesize that the more intense storms and/or being N Area r 5 å i centorid,i u embedded in a more humid environment tend to be DISE sin i (2) i51 Area r associated with larger rainfall size. sum search The dispersion metric is used to measure the spread of and the centers of precipitation clusters away from the TC   circulation center. The calculation of dispersion is taken N Area r 5 å i centorid,i u from Zick and Matyas (2016), who established a search DISN cos i . (3) i51 Area r radius of 600 km in light of the many extratropical sum search transition cases in their study. In the current study, the c. Statistical analysis ratio of the centroid radius (rcentroid) to the search radius of rainfall polygons (rsearch 5 500 km) represents the First, a moving average method is applied over every measure of dispersion [see Eq. (1)]. Since only polygons five observations (;15 h) of the entire life cycle to that have centroids located within 500 km of the storm smooth the data. We then employ optimized hot spot center are included, the theoretical range of this metric analysis to examine the spatial pattern of the area, dis- is from 0 to 1. Our calculations also differ from those of persion, and displacement of TC rain fields. This tool Zick and Matyas (2016), as we consider all complete identifies statistically significant spatial clusters of high rainfall polygons over the rain-rate thresholds instead of values (hot spots) and low values (cold spots) by em- truncating pixels at the search radius boundary. When ploying the Getis–Ord Gi* statistic (Ord and Getis precipitation fragments into multiple clusters, the dis- 1995). The Getis–Ord Gi* statistic measures the in- persion is calculated individually for each rainfall poly- tensity of the clustering of high or low values (i.e., area gon, and then the values of all polygons are summed to of rain field) in a point feature relative to its neighboring get the final value, with larger polygons receiving more point features in the entire dataset. In the current study,

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FIG. 2. (a) A comparison of light rain fields from Tropical Storm Arlene (2011) [area: 19 3 104 km2; displacement (DISP): 0.58] and Hurricane Dean (2007) (area: 17 3 104 km2; DISP: 0.17). (b) A comparison of displacement of rain fields and wind shear from Hurricane Mitch (1998) [dispacement to the east (DISE): 66km; displacement to the north (DISN): 2 2 100 km; SHRW: 6.4 m s 1;SHRS:23.4 m s 1) and Hurricane Ernesto (2012) (DISE: 276 km; 2 2 DISN: 2155 km, SHRW: 20.5 m s 1;SHRS:25.0 m s 1).

the optimal fixed-distance band is based on the average there is a statistically significant hot (cold) spot of rain- distance to the 30 nearest neighbors, which is about fall metrics at a significance level of p value less than 156 km. The sum for a point and its neighbors is com- 0.01. The false discovery rate (FDR) correction is also pared proportionally to the sum of all features. The null applied to reduce the critical p value thresholds and hypothesis is that the values associated with the features account for multiple testing and the spatial dependence are randomly distributed. The Getis–Ord Gi* statistic in the analysis. generates z scores (standard deviations) and p values To determine the factors affecting rain fields, first a (statistical probabilities) for each point feature that in- set of Mann–Whitney U tests is applied to examine dicate whether the rain field metric of a given point whether environmental and storm conditions are sig- feature is statistically clustered compared to the rain nificantly different when comparing observations that field metric in a neighboring point feature, as well as the occurred within hot and cold spots of area, dispersion, rainfall area across the entire analysis domain. The and displacement. The null hypothesis is that there is no larger z score suggests that there is more intense clus- difference between conditions in hot spot and cold spot tering of values. A z score above 1.65 (below 21.65) clusters. The null hypothesis is rejected if the p value of means that there is a statistically significant hot (cold) the test result is less than 0.05. We then apply a set of spot of rainfall metrics at a significance level of p value correlation tests and regression methods to explore the less than 0.10. A z score above 1.96 (below 21.96) means relationships between the size of TCP fields and the that there is a statistically significant hot (cold) spot of TC attributes and environmental conditions. First, rainfall metrics at a significance level of p value less than Spearman’s rank correlations are calculated to identify 0.05. A z score above 2.58 (below 22.58) means that the preliminary correlation between variables and the

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4 2 TABLE 2. Numbers of features and statistics of metrics for all observations, hot spots, and cold spots of light rainfall [area (10 km ) and displacement (km)].

Percentile Metric Variable No. of obs Mean Std dev 25 50 75 AREA All 1304 10.0 7.5 4.9 8.3 13.2 Hot spots 326 14.2 9.6 7.1 12.0 18.9 Cold spots 251 5.6 4.4 2.2 4.8 7.7 DISP All 1304 0.31 0.17 0.18 0.30 0.42 Hot spots 270 0.42 0.17 0.30 0.41 0.52 Cold spots 242 0.22 0.14 0.11 0.20 0.30 DISE All 1304 23 101 242 15 86 Hot spots 354 90 88 25 84 152 Cold spots 478 233 95 292 237 16 DISN All 1304 20 93 234 22 71 Hot spots 343 74 85 18 74 120 Cold spots 442 223 89 276 221 34

variables with the highest correlations to area and con- indicates that light and moderate rainfall fields have a figurations are selected to enter the regression models. similar spatial configuration. Therefore, we mainly dis- Second, we utilize linear regression models and gener- cuss spatial patterns of light rainfall fields. When con- alized linear models (GLMs) with standardized co- sidering all observations, the rainfall areal coverage efficients to examine the relative contributions of each averages 10.0 3 104 km2 for light rainfall. The light rain- predictor to the area, dispersion, and displacement of fall area in the current study is larger than that for U.S. the TC rainfall (Jagger and Elsner 2002; Jiang et al. 2008; landfalls, which is 9.58 3 104 km2. For moderate rainfall, Matyas 2010). the median value of 4.1 3 104 km2 is similar to that of TCs Finally, we analyze the times that light and moderate before and after landfall over Florida (Matyas 2014). This rainfall begin to reach land prior to landfall of the storm finding is interesting because previous studies show that center, as well as average rainfall duration per storm. To many U.S. landfalling TCs experience extratropical estimate the rainfall start time, we determine the time transition, which results in increasing the TC rainfall ex- that rain fields first intersect with continental landmasses tent (Atallah et al. 2007; Matyas 2013). The median value along the western Gulf Coast and Caribbean Sea coast, of dispersion is about 0.30 with a skew to the left side, and count the hours between this time and the time of which indicates that light-to-moderate rain fields of most landfall. To determine rainfall duration, a grid with cell observations are relatively cohesive and symmetric size of 100 km 3 100 km is placed over the study region. (Table 2). The range of dispersion of light rainfall is All light and moderate rainfall fields every 3 h are 0–0.81, which is smaller than the 0–1 range of disper- overlapped with the grid and the frequency of TCP re- siveness values associated with U.S. landfalling TCs es- ceipt at each cell is counted. The average TCP duration timated by Zick and Matyas (2016), who used a 600-km per storm is calculated by first multiplying the total search radius. This result is likely because many of the number of TCP hits by 3 h, and then dividing by the TCs in their study experienced extratropical transition, number of storms influencing this cell. The historical during which rainfall is known to expand away from the maximum duration of rainfall from the TCs is also es- storm center (Atallah et al. 2007; Matyas 2010; Evans timated. The output of this analysis includes four maps et al. 2017). For displacement, about 52% (48%) of ob- with grids featuring the average and maximum duration servations have displacement to the east (west), and light/moderate rainfall in each cell. about 60% (40%) have displacement to the north (south). Considering most storms have a strong westward 3. Results and discussion component in motion and major landmasses are located on the western or southwestern side of a storm, dis- a. Overview of rain field metrics and environmental placement to the west and/or south suggests that rainfall conditions fields extend toward the front–left and landward side of a First, the statistics of the area, dispersion, and dis- storm, which might result in an earlier rainfall start time placement of light rainfall of all observations are exam- and/or longer rainfall duration over land. ined (Table 2). All four metrics have high correlations Next, the statistics of storm intensity, motion, moisture, (r . 0.7) between light and moderate rainfall, which and vertical wind shear are summarized in Table 3,and

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TABLE 3. Names, units, and statistics of variables over the entire region. Missing data in the SHIPS dataset result in fewer observations.

Percentile Variable No. of obs Unit Avg Std dev 25 50 75 2 VMAX 1360 m s 1 29 16 15 23 36 2 MOTE 1329 m s 1 23.8 3.1 25.9 23.5 21.5 2 MOTN 1329 m s 1 1.3 1.5 0.0 1.4 2.4 2 SHRW 1104 m s 1 3.3 5.0 0.3 3.4 6.3 2 SHRS 1104 m s 1 20.2 4.5 23.4 21.0 2.6 TPW (0–200 km) 1230 mm 63.2 4.1 60.3 62.9 66.0 TPW (0–400 km) 1230 mm 60.4 4.3 57.3 60.5 63.4 TPW (0–600 km) 1230 mm 58.1 4.5 55.2 58.5 60.8 TPW (0–800 km) 1230 mm 56.1 44.0 53.7 56.5 58.8 TPW (0–1000 km) 1230 mm 54.5 4.3 52.4 54.8 57.1

Fig. 3 shows their spatial distributions. The median max- The majority of storms have westward or northwest- 2 imum wind speed is about 23 m s 1, which falls between ward motion with slow-to-moderate speed (e.g., less than 2 2 the thresholds of a tropical storm (17 m s 1) and a hurri- 8.0 m s 1). Zonally, about 75% of storms have a westward 2 2 cane (33 m s 1), and about 40% of storms reach hurricane trajectory at about 3.5 m s 1. The northward component of intensity. Storm intensity has a clear spatial pattern the speed is slower, as expected, with a median value of 2 (Fig. 3a). The TCs over the CS are more intense than 1.4 m s 1. As TCs tend to develop rainfall asymmetries those over the GM, which is likely because when related to their motion when moving fast, the relatively TCs develop over the GM, they have limited space to slow speeds occurring in the current study’s observations intensify before land interaction. This pattern agrees might not be an important factor affecting rainfall patterns. with previous research (Fraza and Elsner 2014). Multiple The average TPW decreases as expected when the intense Atlantic basin hurricanes occurred over the spatial region it is averaged over increases from 0–200 to CS, including Hurricanes Mitch (1998), Emily (2005), 0–1000 km (Table 3). Here, TPW over 0–400 km is used Wilma (2005), Dean (2007), and Felix (2007), all of to compare with TCs over other regions examined by which reached category 5 on the Saffir–Simpson scale previous researchers. When considering all observations (Guiney and Lawrence 2000; Franklin and Brown 2006; in the current study, the average value of TPW over Pasch et al. 2006; Beven 2008; Franklin 2008). Storm in- 0–400 km is 60.4 mm, with a standard deviation value of tensity quickly decays within 24 h of landfall as expected. 4.3 mm. This value is much higher than the average for

FIG. 3. Distribution of: (a) storm intensity, (b) average TPW over 0–400 km, (c) SHRW, and (d) SHRS.

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TCs within 500 km of Puerto Rico, which is about 45 mm (1999), Lawrence and Kimberlain (2001); Tropical Storm (Hernández Ayala and Matyas 2016), and average for Dolly (2014), Beven (2015)]. This northerly wind shear is southern U.S. landfalling TCs of 47 mm (Xu et al. 2014). possibly due to the Madden–Julian oscillation (MJO) These higher moisture values are likely due to the and/or Central American gyres (CAGs). The MJO is a evaporation of warm ocean water over the GM, CS, and large-scale episodic modulation of tropical winds and western tropical North Atlantic, which are referred to as precipitation that travels eastward from Asia to America, the Atlantic warm pool (AWP). The AWP has sea sur- with a characteristic repeat time of 30–60 days. Maloney face temperatures (SSTs) . 28.58C during summer and and Hartmann (2000) showed that when there are low- fall (Wang and Enfield 2003; Wang and Lee 2007; Wu level westerly MJO wind anomalies over the eastern et al. 2012). The distribution of TPW shows the highest Pacific, hurricane genesis in the GM and western CS is values over the southern GM, especially the Bay of 4 times more likely than when there are easterly MJO Campeche (Fig. 3b). In the western CS, the TCs are winds. CAGs are large, closed, cyclonic circulation pat- embedded within an environment that has higher terns that occur during May–November. Papin (2017, amounts of moisture than the central and eastern CS. 74–76) found that during 1980–2010 about 50% of trop- These spatial patterns may be due to seasonal variations ical CAGs were related with at least one TC over the GM in the AWP region. Wang and Enfield (2003) illustrated and CS. During CAG periods, there are more north- that early in the hurricane season (July–August), the easterly winds at 850 hPa and more westerly winds at AWP mainly covers the GM and northwestern CS. The 200 hPa over the southern GM region, which results in a AWP reaches its maximum size around September, northerly wind shear and likely explains the tendency for when it covers both the GM and the entire CS. In northerly wind shear in our study. Furthermore, a pre- October, the AWP shifts southward and covers the CS vious study also found that CAGs have anomalous but not the GM. Since 10 out of 11 TCs originated over moisture and precipitation surrounding their centers, the GM in July–September and 11 out of 15 TCs origi- which might also contribute higher TPW over the Gulf nated over the western CS in September–October, TCs and western CS (Papin et al. 2017). from these regions experienced much higher moisture b. Regional variations of rain rates and compared to the storms that moved over the central and corresponding environmental conditions eastern CS during July and August. Figure 3b shows that most TCs experience a decrease in moisture that is less We first identify regions where rainfall patterns exhibit than 5 mm after landfall as they stayed within 200 km of spatial similarities using a hot spot analysis (Fig. 4). These the coastline and could still advect high amounts of maps indicate clusters of larger area and higher values of moisture from coastal and offshore regions into their dispersion and displacement as hot spots, and clusters of circulation patterns from both the eastern Pacific and smaller area and lower values as cold spots at confidence Atlantic sides (Enfield and Alfaro 1999; Brena-Naranjo levels of 90%, 95%, and 99%. These spatial patterns of et al. 2015). rainfall size and configuration are likely due to different TC Previous studies utilized threshold values of 5 and attributes and environmental conditions. Mann–Whitney U 2 10 m s 1 to classify the vertical wind shear speed as tests are applied to test for differences in storms and envi- weak, moderate, or strong (Corbosiero and Molinari ronmental conditions between groups of hot and cold spots 2002; Wingo and Cecil 2010). Regardless of direction, of area, dispersion, and displacement of light rainfall. The the wind shear speed of the entire study area has a results of significance tests are listed in Table 4. 2 median value of 5.9 m s 1, with about 38% of observa- For area, the largest hot spot cluster is over the 2 tions experiencing light shear (0–5 m s 1), 46% moder- western CS (west of 788W), which comprises all TCs 2 2 ate shear (5–10 m s 1), and 16% strong shear (.10 m s 1). making landfall over the Yucatan Peninsula, Belize, and The median absolute magnitude of meridional wind Honduras (Fig. 4a). There are three small hot spot 2 shear is 3.1 m s 1, which is weaker than the zonal shear clusters over the coastal regions of Honduras and 2 absolute magnitude, with a median value of 4.1 m s 1. Mexico, which are related to Hurricanes Mitch (1998) The dominant wind shear direction is eastward or and Stan (2005), as well as Tropical Storms Arlene northeastward over the CS, and southeastward over the (2011), Barry (2013), and Dolly (2014). According to the GM (Figs. 3c,d). This spatial pattern of wind shear is NHC reports, these storms produced extreme rainfall consistent with a climatological study of wind shear accumulations (at least 150 mm) over Mexico, Belize, patterns (June–October) by Chen et al. (2006). The Honduras, or Nicaragua (Guiney and Lawrence 2000; northerly wind shear environment of storms over the Pasch and Roberts 2006; Beven 2012; Stewart 2013; GM is also mentioned in several storm reports from Beven 2015). This finding supports our assertion that a the National Hurricane Center [e.g., Hurricane Bret larger rain area is associated with higher rainfall

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FIG. 4. Hot spot maps of (a) area, (b) dispersion, (c) displacement to the east, and (d) displacement to the north of light rainfall field. accumulations that can lead to flooding. The cold spot the area-weighted distance from the storm center to the areas are mainly associated with storms moving over the rainfall centroids is about 200 km for these observations southeastern Yucatan Peninsula and adjacent eastern (Table 2). The average dispersion value of the obser- Bay of Campeche, as well as after landfall over Texas. vations in cold spot zones is 0.22. The cold spots of dis- The Mann–Whitney U tests show that the larger rainfall persion are distributed over the eastern CS, the ocean area is related to higher storm intensity and higher region adjacent to the eastern coast of the Yucatan moisture content 0–600 km from the storm center Peninsula, and the ocean region before landfall over the (Table 4). southern Gulf Coast. Mann–Whitney U tests reveal The clusters of hot and cold spots of dispersion are that a less dispersed pattern is related to increased storm more scattered (Fig. 4b). The hot spot regions include intensity but less moisture (Table 4). These results agree the western CS region about 500 km west of the west- with Zick and Matyas (2016) that more intense storms ern Caribbean coast, coastal region of Honduras and have a cohesive structure, while further implying that Nicaragua, southeastern Yucatan Peninsula, and adja- while in a drier environment, the outer rainbands re- cent eastern Bay of Campeche. The average dispersion main closer to the storm center and result in a less dis- value of the hot spots is about 0.42, which indicates that persive rainfall pattern.

TABLE 4. Mann–Whitney U-test results of conditions related to hot and cold spots of the area, dispersion, and displacement of light rainfall.

Variable statistics Group of higher-value Group of lower-value Metric Variable variables Median variables Median p value 2 AREA VMAX (m s 1) Hot spots 27 Cold spots 18 ,0.001 TPW (mm) Hot spots 59 Cold spots 58 0.011 (0–600 km) 2 DISP VMAX (m s 1) Cold spots 31 Hot spots 21 ,0.001 TPW (mm) Hot spots 61 Cold spots 59 0.002 (0–600 km) 2 DISE MOTE (m s 1) Cold spots 23.4 Hot spots 22.5 ,0.001 2 MOTN (m s 1) Hot spots 1.5 Cold spots 1.0 ,0.001 2 SHRW (m s 1) Hot spots 4.3 Cold spots 1.3 ,0.001 2 SHRS (m s 1) Hot spots 0.2 Cold spots 21.7 ,0.001 2 DISN MOTN (m s 1) Hot spots 1.6 Cold spots 1.0 ,0.001 2 SHRS (m s 1) Hot spots 2.2 Cold spots 22.8 ,0.001

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TABLE 5. Spearman’s rank correlation coefficients, time lags, and the spatial range between the area, shape metrics, and environmental conditions. The correlations that are significant at 0.01 are set in boldface.

Light rainfall Moderate rainfall Variable Coef AREA DISP DISE DISN AREA DISP DISE DISN VMAX Coef 0.43 20.41 0.02 0.09 0.43 20.14 0.02 0.10 MOTE Coef 20.03 0.22 20.02 0.01 20.09 0.10 20.03 0.03 MOTN Coef 20.09 20.01 0.07 0.30 20.04 20.12 0.05 0.30 TPW Coef 0.52 0.33 20.01 20.15 0.49 0.39 0.05 20.12 Time lag (h) 0 24 24 30 0 24–30 0, 30 30 Range (km) 0–400 0–400 0–400 0–400 0–200 0–600 0–200 0–200 SHRW Coef 0.09 0.04 0.60 0.15 0.08 0.04 0.61 0.15 Time lag (h) 30 24 18–24 24 24 24 18–24 18–24 SHRS Coef 20.14 0.05 0.23 0.54 20.15 20.05 0.23 0.56 Time lag (h) 12–18 30 18 30 12–18 30 18–24 30

Next, displacement has a higher number of significant with TPW averaged over 0–600 km. These results are hot–cold spots and a clearer spatial pattern than dis- generally consistent with previous research that shows persion (Figs. 4c,d). Rainfall tends to be displaced to the the cyclonic convergent inflow is within a 48–68 radius of eastern and northern sides of the storm center over the the TC center (Frank 1977; Evans and Hart 2003). western CS south of Cuba before making landfall over Moreover, as identified by previous research, there the Yucatan Peninsula and central GM. Rainfall has should be a lag effect between the onset of environ- more displacement to the south and west over the mental conditions and changes in the rain field struc- coastal regions of Belize, Nicaragua, Honduras, and the tures (Jiang et al. 2008; Matyas 2010). Moving forward, Bay of Campeche, which indicates that rainfall in this we utilize the time-lagged variable that produces the region shifts toward land. Mann–Whitney U tests reveal highest statistically significant correlation coefficient. that both motion and wind shear have differing distri- Although the correlation tests are significant when uti- butions between groups of hot and cold spots (Table 4). lizing the current time and lags out to 30 h, the highest Larger eastward displacement is related to faster west- correlation coefficients exist between the light (moder- ward and northward wind speeds, as well as stronger ate) rainfall area and current (6 h previous) TPW and southerly and westerly shears. Larger displacement the coefficients gradually decrease as lag increases. This to the north is related to faster northward wind speed result agrees with Jiang et al. (2008), who also found and stronger southerly shear. These combined results similar correlations of moisture and rainfall volume indicate that the rain fields shift to the downshear or between 0 and 12 h. However, the correlation coefficient downshear-right side of the storm, and agree with the for moisture and dispersion gradually increases as the results of Corbosiero and Molinari (2002), who noted time lag increases, and reaches its highest correlation that for the outer rainbands (100–300 km) the front- coefficient at about 24–30 h. A possible explanation is right quadrant is favored by storm motion and the that the dispersion gradually changes, while the area downshear-right quadrant is favored by shear. responds more directly. The rain fields can grow in size without a change in dispersion if the growth is sym- c. General connections between rain rates and metrical about the storm center. Also, a large change in contributing factors the radial extent of rain rates is needed to change the In this section, we first use Spearman rank correlation dispersion given the 500-km search radius. Matyas et al. tests to explore to what extent moisture has the highest (2018) found that higher rainfall regions showed a rel- correlations with light and moderate rainfall and we atively sudden increase in dispersion as the inner core then analyze time-lag effects (Table 5). The results show eroded and convection increased in the outer rainbands, that the rainfall area and dispersion values have signif- which also indicates that it takes a large change in storm icant correlations with average TPW over ranges from structure to alter the dispersion. Finally, the westerly 200 up to 800 km from the storm center (p value , 0.01). wind shear takes about 18–24 h for changes in rainfall For the area and dispersion of light rainfall, the highest displacement, and the southerly wind shear takes about correlation exists between rainfall metrics and TPW 30 h for changes in rainfall displacement. This difference averaged over 0–400 km. For moderate rainfall, the area might be because the southerly wind shear is much has the highest correlation with TPW averaged over weaker than the westerly wind shear (Table 3), since 0–200 km, while dispersion has the highest correlation previous research also found that weaker wind shear

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TABLE 6. Coefficients and model estimations of light and moderate rain field regression models. Symbols specify significance levels: ***, significant at the 0.01 level; **, significant at the 0.05 level.

Coef Variable Area DISP DISE DISN Light rainfall Intercept 11.41*** 21.22*** 23.87*** 16.57*** VMAX 0.28*** 20.21*** 24.40** 8.82*** MOTE — — — — MOTN 20.05*** — 6.62*** 17.56*** TPW 0.30*** 0.18*** 4.24** — SHRW — 0.02** 47.14*** 23.77** SHRS — 0.05*** 12.66*** 35.48*** No. of cases 928 928 928 928 Adjusted R2 0.525 0.325 0.420 0.376 Moderate rainfall Intercept 10.49*** 21.32*** 20.144*** 10.58*** VMAX 0.31*** 20.12*** — 9.39*** MOTE 20.05** — 26.57*** — MOTN 20.06*** 20.06*** 6.57*** 20.26*** TPW 0.32*** 0.21*** 6.10*** 6.05*** SHRW — 0.03** 40.89*** — SHRS 0.06** — 10.59*** 27.37*** No. of cases 907 907 907 907 Adjusted R2 0.398 0.263 0.337 0.270

takes longer to change the storm structure (Frank and the displacement is also impacted by factors like the Ritchie 2001). convergence of moisture and near-surface conver- gence enhanced by land. When considering the influ- d. Results of generalized linear regression models ence of higher moisture and upper-level divergence on In this section, a total of eight regression models are the extent of rainfall, the locations of these conditions applied to link the variables to the area, dispersion, and relative to storm are important. Moreover, the light displacement to the east and north of light and moderate rainfall model shows better performance than the rainfall. The generalized linear regressions are applied moderate rainfall model. This is likely because the for area and dispersion metrics that follow a gamma moderate rainfall has a smaller variability with a stan- distribution. As suggested by the correlation results, we dard deviation of 3.1 3 104 km2 than the light rainfall use current TPW (0–400 km) in the area model of light area among individual storms, which cannot be pre- and moderate rainfall, and TPW (0–400 km) from 24 h dicted as well. Finally, the standardized residuals of all earlier in the dispersion and displacement models. The models do not demonstrate any spatial patterns. wind shear values 24 h earlier are used in the area, dis- As storms intensify, both light and moderate rainfall persion, and displacement models. The linear re- coverages grow, with decreasing dispersion values and gressions are applied for displacement to the east and expansion toward the north–northwest side of the storm north, which follows a normal distribution. As a stepwise center (Table 6). These combined results of area and method is applied, the variables that are significant at a dispersion further confirm previous research, which level of 0.05 are included in the models (Li et al. 2017). states that, as the storm intensity increases, the TC All VIF values are less than 5, which confirms that col- circulation gets stronger and larger, which results in a linearity is unlikely in these models. The variables’ larger rainfall area and a more cohesive pattern with coefficients and regression estimations of the area, dis- major rainfall regions located close to the storm center persion, and displacement models of light and moderate (Dvorak 1975; Kimball and Mulekar 2004; Matyas 2014; rainfall are listed in Table 6. Zick and Matyas 2016; Matyas et al. 2018). Moreover, We first compare the R2 values of the models to de- since motion has a strong west or northwest component termine how well the observations are predicted. The for most observations, the relationship of intensity and model estimations show that the area models have a displacement shows that as a storm intensifies, the better performance than models of dispersion and dis- rainfall tends to shift to the left/left-front side of the placement for both light and moderate rainfall. This storm center. These results agree with previous studies result is possibly because dispersion has a different that conclude intense storms have more capacity to ad- relationship with storm intensity and moisture, and vect moisture to the left or left-front side of storm, which

Unauthenticated | Downloaded 10/01/21 09:49 PM UTC 1722 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 57 will result in a more symmetric rain field (Matyas 2007; Although our results indicate that rainfall fields are Konrad and Perry 2010). displaced toward the downshear direction in many cases, Next, the dispersion of rainfall is negatively correlated displacement in the upshear direction occurs over the with storm intensity, but positively correlated with southern GM and coastal region adjacent to Belize. Here, moisture (Table 6). Previous studies show that a rela- most rainfall is displaced to the western or southwestern tively moist environment within a broad region sur- side of the storm while it is experiencing westerly shear. rounding a storm center is essential to sustain or increase As a TC approaches land, increased surface friction en- TC size and rainfall production (Trenberth and Fasullo hances convergence on the side of the storm near land 2007; Jiang et al. 2008; Hill and Lackmann 2009; Konrad (Powell 1982; Kimball 2008; Xu et al. 2014). Increased and Perry 2010; Lin et al. 2015; Matyas 2017). Previous surface friction and induced low-level convergence over studies also employed observational and numerical land could lead to the occurrence of a large region of methods to examine the environmental humidity’s influ- rainfall across the entire front half of the storm (Kimball ence on the TC rainfall structure (Ying and Zhang 2012). 2008). In addition, because of the narrow landmass of Matyas and Cartaya (2009) analyzed Hurricanes Frances Central America and CAGs occurring throughout this and Jeanne (2004), and determined that the precipitation region, TCs making landfall over the southern Gulf distribution is influenced by the degree of outer-rainband Coast and moving toward the Pacific coast of Mexico activity, which is in turn related to environmental hu- could advect moisture from the eastern Pacific Ocean. midity. Hill and Lackmann (2009) employed numerical This moisture advection could explain the existence of modeling to test the environmental humidity’s influence large rainfall areas on the west (front) side of storm. An on the extent of its rain fields. They found that relatively example of this rainfall pattern can be found from ex- moist environments are conducive to more widespread amination of Hurricane Ernesto (2012) (Fig. 2b). precipitation at larger radial distances and greater lateral e. Rainfall start time and duration extent of spiral bands. Moreover, dispersion has a rela- tively weak and positive correlation with wind shear. According to the NHC, tropical storm or hurricane Stronger wind shear shifts the rain fields to the down- watches (warnings) are issued 48 (36) hours prior to the shear direction, which also increases dispersion. The anticipated arrival of TS-force winds, without consid- current study adds to these case studies by employing a ering the rainfall start time. However, Guo and Matyas large sample size from satellite-based estimates of rainfall (2016) indicated that the rainfall extends beyond TS- and statistical methods to associate larger rain fields that force winds for some TCs over the GM, which suggested are highly dispersed with higher values of moisture and/or that the rainfall might arrive earlier than the wind and stronger wind shear. needs to be examined separately. The times when light Finally, we examine the conditions related to the and moderate rainfall begin over the western Caribbean displacement of light and moderate rainfall. In general, coast or Gulf Coast are summarized in 12-h periods the TC rainfall asymmetry has larger amplitudes with before landfall (Fig. 5). First, for TCs landfalling over respect to vertical wind shear than to TC motion. The the western Caribbean coast or Gulf Coast, the median westerly wind shear has a stronger correlation with dis- light rainfall start time is about of 36–48 h before landfall placement to the east, and southerly wind shear is over both regions. Thus, in many cases, watches will also positively correlated with displacement to north, have already been issued for wind-related conditions especially for light rainfall (Table 6). Previous re- although the lead time before onset of rainfall will be search concluded that the asymmetry coverage is pre- smaller than for the onset of winds. However, the range dominately downshear left, regardless of motion speed of light rainfall start times has a large difference when and direction, and downshear–downshear right in the these two regions are compared. The earliest that light outer rainbands (100–300 km) (Corbosiero and Molinari rainfall reaches land is about 171 h, which occurs during 2002; Wingo and Cecil 2010). This result is possible be- Hurricane Mitch (1998) (Fig. 5a). For the GM region, cause most TCs have slow-to-moderate forward speed the storms that have the earliest rainfall start time are so that shear is a more dominant force. Displacement to Hurricanes Bret (1999), Nate (2011), and Ingrid (2013), the north is positively correlated with northward motion which formed over the Bay of Campeche. They all speed. Also, the dominant TCs motion is to the west, produced rainfall over land at the time of formation, which opposes the dominant wind shear direction. In which is about 102–120 h before landfall. As a result of this situation, the effect of motion on rainfall asymmetry the TCs in the GM being closer to the coastline when tends to be reduced (Corbosiero and Molinari 2002; they form (Fig. 1), they make landfall earlier in their Chen et al. 2006; Ueno 2007; Wingo and Cecil 2010; Xu life cycle when compared to TCs that form over the et al. 2014). CS. Although rainfall over the GM is smaller in areal

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FIG. 5. Cumulative frequency of TCs having light (blue bars) and moderate (orange bars) rainfall over land prior to landfall for the (a) CS and (b) GM. coverage, it is more displaced to the west and south, are higher. The average duration of light rainfall is which is the side of the storm that is closest to land. about 24 h, and 12 h for moderate rainfall, which might The median moderate rainfall start time shows about a result in rainfall totals exceeding 60 mm for one storm. 12-h difference between CS and GM landfalls (Fig. 5b). It is important to note that because of the size of each About half of the storms have moderate rainfall pixel, this represents an average rainfall total over an reaching land 12–24 h before landfall over the Carib- area of 104 km2 with higher values likely to occur bean coast, while about half of the storms making within each pixel. Moreover, there is an abrupt shift landfall from the Gulf Coast region have moderate from 1–12 h per storm to 12–24 h per storm in the rainfall reaching land about 24–36 h before landfall. middle of the Caribbean. This is because the rain fields Therefore, people along the Gulf Coast should avoid of the TCs are smaller and more cohesive over the flood-prone areas beginning 2 days before landfall is eastern than the western CS. Moreover, storm motion anticipated. is faster over the eastern CS, which causes a shorter A slow-moving storm with a large and dispersed pat- duration of rainfall. We also estimate the maximum tern of rainfall should result in a longer duration of TCP. duration of TCP for individual storms (Figs. 6b,d). The Figures 6a and 6c show average durations of light and coastal regions over Belize, Nicaragua, and Honduras, moderate rainfall per storm. Overall, two regions re- as well as the southern coast of the Bay of Campeche, ceive a longer duration of light and moderate rainfall received more than 72 h of light rainfall and 49 h of per storm, namely the western CS adjacent to Central moderate rainfall during one storm period. The longest America and the Bay of Campeche, which is due to a duration of TCP over Mexico and Central America large rainfall area and/or rainfall that is displaced to the was caused by Hurricane Mitch (1998), when 698 mm side of the storm nearest the coast. These long-duration of rain fell during 41 h in southern Honduras (Hellin TCP events are likely to result when the rainfall totals et al. 1999).

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FIG. 6. (left) Average and (right) maximum duration of (a),(b) light and (c),(d) moderate rainfall associated with TCs.

4. Conclusions and future research the central GM. Rainfall fields have more displacement to west and south, which is close to or over land, when In this study, we have documented the spatial patterns TCs move over the southern GM. 3) The area and dis- of rain fields associated with landfalling TCs over the persion of light-to-moderate precipitation fields of TCs western Caribbean coast and Gulf Coast between 1998 are mainly correlated with storm intensity and TPW, and and 2015 based on estimates of rain rates available from a the displacement of rainfall is significantly correlated with satellite-derived dataset. The area, dispersion, and dis- vertical wind shear (displacement in the downshear di- placement are calculated for the entire rain field as de- 2 lineated by the edges of light (2.5 mm h 1) and moderate rection). The rainfall displacement of TCs to the west is 2 (5 mm h 1) rain rates. The spatial patterns of the area, observed over the Bay of Campeche, which may be re- dispersion, and displacement of TCP are measured by hot lated to the convergence of moisture above the boundary spot analysis. The factors that contribute to the spatial layer from the Pacific Ocean and near-surface conver- patterns of rainfall—including TC storm intensity, mo- gence enhanced by land. tion speed, and direction; TPW; and vertical wind shear Finally, after generating light and moderate rainfall speed and direction—are also examined by using Mann– polygons, we determined the times that the rainfall Whitney U tests, Spearman’s rank correlation test, and reaches land relative to the time that the storm’s center regression models. Finally, light and moderate rainfall makes landfall, the average duration, and the maximum polygons are used to determine the time that rainfall duration of rainfall from TCs. The larger and dispersed reaches land relative to the time that the storm’s center rainfall fields result in early rainfall start times and makes landfall, the average duration, and the maximum longer durations over land. For about half of the storms, duration of rainfall. their light and moderate rainfall reaches land about 48 h There are three major findings of this study in terms of before landfall. The duration of TCP over the western rain field area, spatial patterns, and corresponding envi- Caribbean coast and Gulf Coast is about 12–24 h per ronmental conditions. 1) The rainfall coverage is largest storm, and the historical maximum light rainfall dura- as TCs approach the western CS coast, and the rainfall tion has been as high as 721 h for an individual storm. area is smaller as TCs move back over the GM after Knowledge of rainfall start time before landfall and its making landfall over the Yucatan Peninsula. 2) In terms possible duration of rainfall is useful for hazard mitiga- of displacement, rain fields have more displacement to tion and for identifying the timing when regions might east and north over the western and central CS, as well as receive rainfall from a TC.

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