DOI: 10.25349/d9jp4x
title: Variations in the Intensity and Spatial Extent of Tropical Cyclone Precipitation

description: The intensity and spatial extent of tropical cyclone precipitation (TCP)
 often shapes the risk posed by landfalling storms. Here we provide a
 comprehensive climatology of landfalling TCP characteristics as a function
 of tropical cyclone strength, using daily precipitation station data and
 Atlantic US landfalling tropical cyclone tracks from 1900-2017. We analyze
 the intensity and spatial extent of ≥ 1 mm/day TCP (Z1) and ≥ 50 mm/day
 TCP (Z50) over land. We show that the highest median intensity and largest
 median spatial extent of Z1 and Z50 occur for major hurricanes that have
 weakened to tropical storms, indicating greater flood risk despite weaker
 wind speeds. We also find some signs of TCP change in recent decades. In
 particular, for major hurricanes that have weakened to tropical storms,
 Z50 intensity has significantly increased, indicating possible increases
 in flood risk to coastal communities in more recent years.
description: 1. Station precipitation and
 tropical cyclone tracks We
 use daily precipitation data from the Global Historical Climatology
 Network (GHCN)-Daily station dataset (Menne et al., 2012) and TC tracks
 archived in the revised HURricane DATabase (HURDAT2) database (Landsea
 & Franklin, 2013). HURDAT2 is a post-storm reanalysis that uses
 several datasets, including land observations, aircraft reconnaissance,
 ship logs, radiosondes, and satellite observations to
 determine tropical cyclone track locations, wind speeds and central
 pressures (Jarvinen et al., 1984; Landsea & Franklin, 2013). We
 select 1256 US stations from the GHCN-Daily dataset that have observations
 beginning no later than 1900 and ending no earlier than 2017 (though most
 station records are not continuous throughout that period). These 1256
 land-based stations are well distributed over the southeastern US and
 Atlantic seaboard (see Supporting Figure S1). We
 use the HURDAT2 Atlantic database to select locations and windspeeds of TC
 tracks that originated in the North Atlantic Ocean, Gulf of Mexico and
 Caribbean Sea, and made landfall over the continental US. Though tracks
 are determined at 6-hourly time steps for each storm (with additional
 timesteps that indicate times of landfall, and times and values of maximum
 intensity), we limit our analysis to track points recorded at 1200 UTC, in
 order to match the daily temporal resolution and times of observation of
 the GHCN-Daily precipitation dataset (Menne et al., 2012), as well as the
 diurnal cycle of TCP (Gaona & Villarini, 2018). Although this
 temporal matching technique may omit high values of precipitation from the
 analysis, it reduces the possibility of capturing precipitation that is
 not associated with a TC.   2. Tropical cyclone and Lifetime
 Maximum Intensity (LMI) categories For
 each daily point in the tropical cyclone track, we use the maximum
 sustained windspeed to place the storm into one of three Extended
 Saffir-Simpson categories: tropical storms (“TS”; 34-63 knots), minor
 hurricanes (“Min”; categories 1 and 2; 64-95 knots), and major hurricanes
 (“Maj”; categories 3 to 5; &gt; 96 knots) (Schott et al., 2012).
 Additionally, for each track, we record the category of the lifetime
 maximum intensity (LMI), based on the maximum windspeed found along the
 whole lifetime of the track (i.e., using all available track points). LMI
 is a standard tropical cyclone metric, and is considered a robust measure
 of track intensity through time and across different types of data
 integrated into the HURDAT2 reanalysis (Elsner et al., 2008; Kossin et
 al., 2013, 2014). Therefore, for each track point, a dual category is
 assigned: the first portion of the classification denotes the category of
 the storm for a given point (hereafter “point category”), while the second
 denotes the LMI category. The combination of the two can thus be
 considered a “point-LMI category”. For example, the point on August 27,
 2017 at 1200 UTC along Hurricane Harvey’s track is classified as TS-Maj
 because it is a tropical storm (TS) at this point but falls along a major
 hurricane LMI track (see starred location in Supporting Figure S2a). Given
 that the LMI category for a given point cannot be weaker than the point
 category itself, the set of possible point-LMI category combinations for
 each track point is TS-TS, TS-Min, TS-Maj, Min-Min, Min-Maj, and Maj-Maj.
 This dual classification allows us to explore climatological TCP spatial
 extents and intensities during the tropical cyclone lifetime. Our dual
 classification does not account for the timing of the point category
 relative to the LMI category for a given point along a track (i.e., the
 time-lag between the LMI and point in consideration). However, the
 majority of points selected in our analysis occur after the TC has reached
 its LMI and are in the weakening stage (see Supporting Table S1 for more
 details). This could be expected, as our analysis is focused on land-based
 precipitation stations, and TCs weaken over land. However, a small
 fraction of TC points analyzed occur over the ocean before making
 landfall, but are close enough to land for precipitation gauges to be
 impacted.   3. Moving neighborhood method for
 TCP spatial extent and intensity  We
 first find the distribution of tropical cyclone precipitation (TCP)
 intensity using all daily land precipitation values from all available
 stations in a 700 km-radius neighborhood around each point over land on
 each tropical cyclone track (Figure 1a and Supporting Figure S2). We then
 create two new binary station datasets,
 <i>Z<sub>1</sub>(x) </i>and<i>
 Z<sub>50</sub>(x)</i>, which indicate whether or not a
 station meets or exceeds the 1 mm/day or 50 mm/day precipitation
 threshold, respectively, on a given day. The 50 mm/day threshold is
 greater than the 75th percentile of TCP across all tropical cyclone
 categories (Figure 1a), allowing us to capture the characteristics of
 heavy TCP while retaining a robust sample size. The 1 mm/day threshold
 captures the extent of the overall TCP around the TC track
 point. We
 use the relaxed moving neighborhood and semivariogram framework developed
 by Touma et al. (2018) to quantify the spatial extent of
 <i>Z<sub>1</sub></i> and
 <i>Z<sub>50</sub></i><sub> </sub>TCP
 for each track point. Using a neighborhood with a 700 km radius around
 each track point, we select all station pairs that meet two criteria: at
 least one station has to exhibit the threshold precipitation on that given
 day (<i>Z(x)</i> = 1; blue and pink stations in Supporting
 Figure S2b), and at least one station has to be inside the neighborhood
 (black and pink stations in Supporting Figure S2b). We then calculate the
 indicator semivariogram, g<i>(h),</i> for each station pair
 selected for that track point (Eq. 1): <i>γ</i><i>h</i><i>=0.5*</i><i>[Z(</i><i>x+h)</i><i>-Z(</i><i>x)</i><i>]</i><sup><sup><i><sup>2</sup></i></sup></sup>,                                                                                               Eq. 1 where <i>h</i> is the separation distance between the stations in the station pair. The indicator semivariogram is a function of the separation distance, and has two possible outcomes: all pairs with two threshold stations (<i>Z(x)</i> = <i>Z(x+h)</i> = 1) have a semivariogram value of 0, and all pairs with one threshold station and one non-threshold station (<i>Z(x)</i> = 1 and <i>Z(x+h)</i> = 0) have a semivariogram value of 0.5. We then average the semivariogram values for all station pairs for equal intervals of separation distances (up to 1000 km) to obtain the experimental semivariogram (Supporting Figure S2c). To quantify the shape of the experimental semivariogram, we fit three parameters of the theoretical spherical variogram (nugget, partial sill, and practical range) to the experimental semivariogram (Eq. 2): <i>γ(</i><i>h) </i><i>= </i><i>0, for h=0</i> <i>γ(</i><i>h) </i><i>= </i><i>c+b*((</i><i>3/</i><i>2)(</i><i>h/</i><i>α)</i><i>-(</i><i>1/2)(</i><i>h/</i><i>α)</i><sup><sup><i><sup>3</sup></i></sup></sup><sup><i>), for 0</i></sup><i>&lt;h≤α</i> <i>γ(</i><i>h) </i><i>= </i><i>c+b, for h≥α</i>,                                                                                                   Eq. 2 where c is the nugget, b is the partial sill, and a is the practical range (Goovaerts, 2015). The nugget quantifies measurement errors or microscale variability, and the partial sill is the maximum value reached by the spherical semivariogram (Goovaerts, 2015). The practical range is the separation distance at which the semivariogram asymptotes (Supporting Figure S2c). At this separation distance, station pairs are no longer likely to exhibit the threshold precipitation (1 mm/day or 50 mm/day) simultaneously (Goovaerts, 2015; Touma et al., 2018). Therefore, as in Touma et al. (2018), we define the length scale – or spatial extent – of TCP for that given track point as the practical range. There are some subjective choices of the moving neighborhood and semivariogram framework, including the 700 km radius of neighborhood (Touma et al. 2018). Previous studies found that 700 km is sufficient to capture the extent to which tropical cyclones influence precipitation (e.g., Barlow, (2011), Daloz et al. (2010), Hernández Ayala & Matyas (2016), Kim et al. (2014), Knaff et al. (2014), Knutson et al. (2010) and Matyas (2010)). Additionally, Touma et al. (2018) showed that although the neighborhood size can slightly impact the magnitude of length scales, it has little impact on their relative spatial and temporal variations.   4. Analysis of variations and trends We use Mood’s median test (Desu & Raghavarao, 2003) to test for differences in the median TCP intensity and spatial extent among point-LMI categories, adjusting <i>p</i>-values to account for multiple simultaneous comparisons (Benjamini & Hochberg, 1995; Holm, 1979; Sheskin, 2003). To test for changes in TCP characteristics over time, we divide our century-scale dataset into two halves, 1900-1957 and 1958-2017. First, the quartile boundaries are established using the distributions of the earlier period (1900-1957), with one-quarter of the distribution falling in each quartile. Then, we find the fraction of points in each quartile in the later period (1958-2017) to determine changes in the distribution. We also report the<i> p</i>-values of the Kolmogorov-Smirnov (K-S) test to quantify the differences in the full distributions of TCP intensity and extent between the earlier and later periods (Sheskin, 2003) (see Supporting Text S1 for more details). Further, to determine the effect of multi-annual variability on the changes between the earlier and later periods of our dataset, we calculate changes in TCP intensity and extent using midpoint years ranging from 1947 to 1967.
description: See README file.