Research papersCharacterization of the diurnal cycle of maximum rainfall in tropical cyclones
Introduction
Tropical cyclones (TCs) are phenomena of paramount importance not only for the rain they produce but also for the havoc they unleash, both in coastal and inland areas (e.g., Czajkowski et al., 2017, Khouakhi et al., 2017). They are also considered the deadliest type of weather-related disasters, as the death toll from ∼2000 storms (from 1995 through 2015) amounts to ∼242,000 fatalities (UNISDR and CRED, 2017) or 251,384 (roughly equivalent to 40% of the total casualties from weather-related disasters) from 1980 to 2000 according to UNDP (2004, p.37). For instance, in 2017 Hurricane Harvey brought almost 125,000 m3 of rain, spread over four U.S. states (Fritz and Samenow, 2017). Averaged over the Houston area, the lowest total precipitation in seven days brought by Hurricane Harvey was 700.2 mm, which is more than double of any previous record (315.8 mm for seven days of rainfall) between 1950 and 2016 (Risser and Wehner, 2017). Put into perspective, this amount of rainfall is the equivalent to the yearly average precipitation in Houston (Burian and Shepherd, 2005, Fritz, 2017). Overall, Hurricane Harvey produced the largest rainfall ever recorded of any hurricane affecting the United States, e.g., Emanuel, 2017, NOAA-WPC, 2017, and Samenow (2017). The number of fatalities caused by this storm is reported to be ∼80 people (e.g. Moravec, 2017, van Oldenborgh et al., 2017).
The impact exerted by TCs comes from the high-wave storm surges, extreme winds, and floods and landslides associated with the torrential rains they produce (e.g. Mendelsohn et al., 2012, Peduzzi et al., 2012). Out of these three factors, we devote our attention to the characterization of heavy rainfall from TCs given its direct relation to flooding, which in the last two decades has affected ∼2.3 billion people (UNISDR and CRED, 2017). This is equivalent to 56% of the people affected by weather-related disasters. Hence, the characterization of heavy rainfall from TCs provides essential information to assess and evaluate the impact from landfalling TCs, helping thus potential affected communities to be more resilient against such natural hazards. Several studies have focused on TC-rainfall characterization. For instance, Prat and Nelson (2016) studied the contribution of TCs to extreme daily rainfall, whereas Prat and Nelson (2013) established the contribution of TC-rainfall to the seasonal precipitation totals for the southeastern United States. Jiang et al. (2008) analyzed the rainfall distribution from landfalling TCs in the north Atlantic basin. All of the above studies were based on about one decade of satellite data. Lonfat, 2004, Rios Gaona et al., 2018 are global studies in which TC-rainfall is characterized and stratified by basin and intensity (among other features) also from global satellite data.
The focus of this work is to delve into the diurnal cycle of TC-rainfall maxima. The number of studies about the diurnal cycle of TC-rainfall have grown in recent years due to the widespread development and availability of satellite rainfall estimates. Bowman and Fowler (2015) carried out statistical analyses over 15 years of TMPA 3B42 (Tropical Rainfall Measurement Mission - TRMM Multisatellite Precipitation Analysis) and IBTrACS (International Best Track Archive for Climate Stewardship) data to investigate the diurnal cycle of TC-rainfall, which they see as one potential component of precipitation variability in these storms. Wu et al. (2015) studied the diurnal variations of oceanic TC-rainfall in their inner core and outer rainbands. Their study was also based on 15 years (1998–2012) of TMPA 3B42 data (1401 TCs), and focused only on oceanic storms (i.e., beyond 300 km from coastlines). Leppert II and Cecil (2016) used TRMM's Microwave Imager (TMI) and Precipitation Radar (PR) to study the diurnal cycle of 208 storms in the Atlantic basin during the period 1998–2011. They stratified their analyses by radii (from 100 to 1000 km, every 100 km), by intensity (wind speed larger than 34 kt, and 64 kt), and by height (2, 8, and 10 km). More recently, O’Neill et al. (2017) examined cloud-resolving TC simulations to understand the wavelike diurnal cycle responses on quasi-steady TCs. They found evidence of diurnal wave propagation in the upper troposphere in eddy-temperature fields. Tang et al. (2017) studied the sensitivity of hurricane Secondary Eyewall Formation (SEF) to solar insolation. Through a numerical simulation, Navarro et al. (2017) determined the impact of periodic diurnal heating on a balanced vortex, highlighting the importance of clouds. The introductions of Bowman and Fowler, 2015, Leppert and Cecil, 2016, and O’Neill et al. (2017) provide extensive literature (and recounted details) on the diurnal cycle of oceanic precipitation (e.g. Frank, 1977, Hai-Long et al., 2013), of TC-rainfall (e.g. Jiang et al., 2011, Wu et al., 2015), and of cloud-tops changes (e.g. Browner et al., 1977, Dunion et al., 2014, Kossin, 2002). Studies on the diurnal cycle of TC-rainfall contribute to the characterization and understanding of TC-rainfall variability from the diurnal insolation cycle on TCs. Such a variation is key to improve storm intensity prediction, and TC modelling on global climate systems, for instance.
Our work advances the knowledge of the diurnal cycle of maximum TC-rainfall because we use high-resolution satellite data and circular statistics. IMERG (Integrated Multi-satellitE Retrievals for GPM - Global Precipitation Measurement mission) is a follow-up on almost two decades on continuous rainfall monitoring at global scales from TRMM and its equivalent TMPA products (Huffman et al., 2007). IMERG is a gridded rainfall product with a spatiotemporal resolution of 0.1° × 0.1° every 30 min (Hou et al., 2014). Rainfall monitoring at high resolution from space nowadays serves as a key tool to develop and enhance societal applications such as fresh water availability, flood forecasting, landslide warning, water-borne disease propagation, and storm-tracking (Kirschbaum and Patel, 2016, Stanley et al., 2017). The main advantage with regard to storm-tracking is that from global rainfall estimates such IMERG one can track the precipitation path of such large scale storms that often are difficult to even quantify from ground-based sensors like gauges and weather radars. The IBTrACS data set offers a detailed record of TC-tracks and maximum sustained windspeed (MSW) of all the TCs worldwide since 1842 (and up to March 2017). By combining these two data sets, we can obtain a detailed and accurate description of the spatiotemporal variability of rainfall from TCs. This allows us to study the diurnal cycle of maximum rainfall for all the TCs (259) worldwide in a span of 3 years (GPM launched its core satellite on February 2014).
In addition to high-resolution satellite data, we use circular statistics, which represents the appropriate statistical framework for analyses of this kind. In circular statistics the data under analysis is represented as points over a unit circle, which is the support for “circular” variables (Pewsey et al., 2013). In a circular space, all data is equally likely to be distributed over a segment equivalent to 2π. This abstraction has the unique advantage to account for the intrinsic periodicity of circular and/or directional variables, such as time of the day at which rainfall occurs or the azimuthal direction of the maximum sustained windspeed of a hurricane, for instance. A basic example is that of the average of a random variable that took place at 01:00 and 23:00, for instance. A linear analysis will tell us that the average time of such a random variable is 12:00. Due to the proximity of 01:00 and 23:00 in a 24-h circular space, the circular analysis will yield an average time of 00:00, which is a more correct approximation of the true nature of the random variable under analysis.
Work on TC-rainfall via circular statistics has not been carried out so far. The common approach is to apply linear statistics to draw the cyclic patterns, e.g., Hu et al. (2017). Recent and related work on the implementation of circular analysis in hydrometeorological topics include those of Dhakal et al., 2015, Masseran, 2015, and Villarini (2016). Dhakal et al. (2015) developed a non-parametric (circular statistics) approach that optimizes the bandwidth(s) of a Von Mises distribution (Section 2). Their approach assessed the non-stationarity of 60 years of maximum daily precipitation at ten locations in the northeastern United States. Masseran (2015) used non-parametric circular statistics to better characterize the wind regime in the northern region of Borneo (Malaysia). From almost one year of hourly wind direction data (one station only), they found that the finite mixture of Von Mises–Fisher approach (Section 2) systematically outperforms the one based on non-negative trigonometric sums. From annual maximum instantaneous peak discharges (∼7500 gage stations with at least 30 years of data), Villarini (2016) applied circular statistics to study the seasonality of flooding across the continental United States. Other examples of developments and implementations of circular statistics in earth sciences (including mixtures of Von Mises–Fisher probability density functions - MvMF-PDFs) include those by Lark et al. (2014), and Oliveira et al. (2012). To the best of our knowledge, our work is the first of its kind that offers a comprehensive and quantitative characterization of the diurnal cycle of TC-rainfall maxima, analyzed via the circular statistics framework.
A detailed presentation of the theoretical framework of circular statistics is beyond the scope of this paper. For that matter, we point the interested reader to previous works carried out by Fisher, 1993b, Mardia, 1972b, Mardia and Jupp, 2000, and Pewsey et al. (2013), where deep and comprehensive formulations, details, and references on the theory of circular statistics can be found. Our approach relies on the R-packages (Hornik and Grün, 2014), (Agostinelli and Lund, 2017), and (Tsagris et al., 2017). R is a computing language and environment for statistical analysis (R Core Team, 2018).
We stratify our analysis by TC duration, maturity, and intensity, basin of origin, distance from the center, and whether the storm is over the ocean or land. A thorough analysis of yet another characteristic of TC-rainfall such as the diurnal cycle of maximum TC-rainfall gets us closer to more realistic representations and models of the rainfall associated with TCs. We consider our approach a better assessment of the diurnal cycle because not only the available high-resolution data we use but also the circular framework offers a more accurate and appropriate approach for the statistical description of TC-rainfall maxima.
This paper is organized as follows: Section 2 briefly describes the data we use and introduces the conceptual framework of circular statistics, and its implementation. Section 3 presents the results and discussion alongside. Summary and conclusions are provided in Section 4.
Section snippets
Data and methodology
Our data set is similar to that of Rios Gaona et al. (2018), in which they analyzed 166 TCs for the period of March 2014 through March 2016. Hence, the analysis comes from the merging of two data sets: IBTrACS, and IMERG V04 Final.
The IBTrACS (v03r10) is a worldwide collection of TC best-track data (Knapp et al., 2010). Developed by the National Climatic Data Center (NCDC) jointly with the World Data Center for Meteorology, it is a comprehensive project that gathers information from all the
Results and discussion
The summary statistics for the sample of 1024 unit vectors that represent the LSTs at which maximum precipitation (per storm for all the 259 TCs under analysis) occurs are: = 1.952 h or 0.5111 rad (sample mean direction), =0.131 (sample mean resultant length), and = 0.8693 (sample circular variance). The concentration parameter () is 0.26375. Bear in mind that as the sample of average rainfall per TC is really large (multiple radii per several TC-centers), each storm can potentially
Summary and conclusions
The goal of this work was to quantitatively assess the diurnal cycle of maximum TC-rainfall by means of non-parametric circular statistics. To do so, we cross-referenced the IBTrACS (v03r10) and IMERG (V04) data sets to accurately account for high-resolution rainfall within a 2000 km-wide swath along the path of a given TC. We analyzed 259 TCs that occurred from March 2014 through February 2017 (∼3 years of data). The IMERG data set is a gridded satellite product of high spatiotemporal rainfall
Acknowledgements
This material is based in part upon work supported by the National Science Foundation under CAREER Grant AGS-1349827, and Award NA14OAR4830101 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.
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