Data for Variations in the Intensity and Spatial Extent of Tropical Cyclone Precipitation
From Touma et al. (in review at GRL) Methods Section
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; available for download here: https://www.ncdc.noaa.gov/ghcnd-data-access) and TC tracks archived in the revised HURricane DATabase (HURDAT2) database (Landsea & Franklin, 2013; available for download here: https://www.aoml.noaa.gov/hrd/hurdat/Data_Storm.html). 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; > 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, Z1(x) and Z50(x), 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.
We use the relaxed moving neighborhood and semivariogram framework developed by Touma et al. (2018) to quantify the spatial extent of Z1 and Z50 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 (Z(x) = 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(h), for each station pair selected for that track point (Eq. 1):
γ(h)=(1/2)[Zx+h-Zx]2, Eq. 1
where h 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 (Z(x) = Z(x+h) = 1) have a semivariogram value of 0, and all pairs with one threshold station and one non-threshold station (Z(x) = 1 and Z(x+h) = 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):
γ(h) = 0 ⇒ h = 0
γ(h) = c + b[(3/2)(h/α) - (1/2)(h/α)3] ⇒ 0 < h ≤ α
γ(h) = c + b ⇒ h ≥ α, 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.