A Multivariate Scaling System Is Essential to Characterize the Tropical Cyclones' Risk
Abstract
The current Tropical Cyclones (TCs) scaling system, Saffir-Simpson Hurricane Wind Scale (SSHWS), characterizes the hazardousness of these events solely based on wind speed. This is despite the fact that TCs are classic examples of compound hazards during which multiple hazard drivers that are wind, storm surge, and intense rainfall interact and yield in impacts greater than the sum of individuals. Studies have shown that people's decision to evacuate is highly related to the estimated SSHWS category. Thus, the current SSHWS -based classification of TCs yields an underestimation of the hazardousness of TCs and so may misguide the threatened communities. Here, we propose a new scaling system that uses Copulas for categorizing TCs based on the likelihood of a given set of severity for rainfall, surge, and wind speed. We use a variety of data sources to obtain the timing and intensity of wind speed, rainfall along the track, and the associated maximum surge for 102 TCs that have made landfall in the United States' Atlantic and Gulf coasts between 1979 and 2020. Comparing the outputs of our scaling system with official damage reporting for the costliest TCs in the history of the United States, we show that the proposed approach significantly improves TC hazard communication and can be useful for informing decision makers and emergency responders.
Key Points
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The current Tropical Cyclones (TCs) scaling system solely based on wind speed, underestimates the hazardousness of events
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We propose a new scaling system that takes into account the compound hazard of TCs and uses Copulas to categorize them
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The proposed approach can significantly improve TCs' hazard communication
1 Introduction
Tropical cyclones (TCs) are among the most devastating natural disasters in the world. Despite the tremendous national governments' protection efforts, they still result in loss of lives and properties ( Karimiziarani et al., 2022; Klotzbach et al., 2018; Munoz et al., 2021; Sebastian et al., 2017; Song et al., 2022; Tennant & Gilmore, 2020). Tropical Cyclones are compound hazards, during which a combination of climate processes and hazards (i.e., torrential rainfall, intense winds, and abnormal surge) lead to significant societal impacts greater than the impacts each can produce in isolation (de Ruiter et al., 2020; Leonard et al., 2014; Zscheischler et al., 2018).
Current TC hazard characterization frameworks are incomprehensive and lack the systematic consideration of compounding effects of hazards. Although TCs cause compound events, Saffir-Simpson Hurricane Wind Scale (SSHWS), the current scaling system used for classifying the level of hazardousness of TCs in the Atlantic, eastern and central Pacific, relies only on wind speed. Studies indicated that people's decision to evacuate is heavily related to the SSHWS category (Lazo et al., 2010; Morss & Hayden, 2010). While intensive winds associated with TC cause severe property damage and casualty, torrential rainfall accompanied with weakened wind speed, cause extensive flooding (Alipour et al., 2022; Oldenborgh et al., 2017; Touma et al., 2019). Slow moving TCs in coastal areas result in massive flooding due to heavy rainfall amount and destructive surges (Kossin, 2018). Rappaport (2014) investigated the causes of loss of life from Atlantic TCs in the United States from 1963 to 2012. He identified that storm surge is responsible for about half of the fatalities (49%) followed by heavy precipitation and strong winds with 27% and 8%, respectively. Due to climate change and sea-level rise, TC-driven flooding in coastal areas is expected to increase in the future (Elsner et al., 2008; Marsooli et al., 2019; Woodruff et al., 2013). Recent tree-ring–based analysis on extreme precipitation attributed to TC shows the increasing trend in precipitation amount as a result of slowing TC translation speed (Maxwell et al., 2021). The increasing frequency of TC rainfall and surge joint hazard (Gori et al., 2022) and the fact that TCs are one of the largest drivers of coastal flood losses across U.S. Atlantic and Gulf coasts (Hallegatte et al., 2013; Peduzzi et al., 2012), raise the need for an enhancement in TC hazard assessments.
Tropical cyclones hazard categories are effective risk communication tools that can help people with their disaster-related behaviors and actions. Therefore, using an enhanced TC scaling system that accounts for different TC hazard components can improve residents' preparedness and their response decision. In a previous study, we proposed a new TC categorization scale that considers the joint probability of cumulative precipitation and wind speed (Song et al., 2020). We compared our results with those from SSHWS's (based on wind speed only) and concluded that including the precipitation in TCs scaling system improves TCs hazard characterization and risk estimation. Although informative, the proposed scale did not account for the hazard of a potential surge. Senkbeil and Sheridan (2006) and Bloemendaal et al. (2021) proposed alternative TC hazard categories that consider the wind speed, surge, and precipitation simultaneously, by using physical concepts and dividing the possible range of each driver into different categories. These studies ignored the correlation among TCs drivers and considered them independently.
Here, we propose a novel approach for comprehensive risk assessment of TCs based on joint probability of all hazard components (i.e., rainfall severity, wind speed, and surge height). We gather the required information of the Atlantic and Gulf TCs from a variety of publicly available data sources including HURricane DATa 2nd generation (HURDAT2), the world's storm SURGE DATa (SURGEDAT), Phase 2 of the North American Land Data Assimilation System (NLDAS-2), and National Hurricane Center (NHC) reports. We characterize the joint likelihood of TC-driven hazards using Copula functions and then define new TCs hazard categories considering the estimated joint exceedance probability of extreme winds, torrential rainfall, and surges during TC events. We integrate the estimated hazard of the 36 costliest TC in the U.S. history using SSHWS categories and our proposed multi-hazard scaling with the vulnerability of the affected areas to estimate the risk of these historic events and compare it with the official reported damage. This comparison helps evaluate the usefulness of our novel scaling system with the current practices.
2 Data and Methods
In this study, we propose a new TC hazard scaling that takes into account each event's associated wind speed, rainfall severity, and surge height. We gather the information of 102 Atlantic TCs that made landfall in the CONUS between 1979 and 2020 and then fit the marginal and joint distributions to data to estimate the joint probabilities of the compound events. We integrate the inverse normal of the compound hazard probability with the Social Vulnerability Index (SVI) to generate a risk proxy for each event and compare it with the officially reported damages. The detail of the data sets and the methodology are explained in the following subsections.
2.1 HURDAT2
The revised Atlantic TC database, HURricane DATa 2nd generation (HURDAT2), is a NOAA data set that provides all the six-hourly information of TCs and subtropical cyclones into a comma-delimited, text file. This information includes, but is not limited to, location, maximum winds, and central pressure of all known TC events between 1851 and 2020 (Landsea & Franklin, 2013). We linearly interpolated data to construct an hourly data set in order to be consistent with the NLDAS-2 hourly precipitation. We use the date, time, location, and maximum sustained wind speed data from 1979 to 2020.
2.2 NLDAS-2
The hourly precipitation data from Phase 2 of the North American Land Data Assimilation System (NLDAS-2) is available at 1/8th-degree spatial resolution (about 12 km) for the period of January 1979 to the present (Xia et al., 2012). This hourly precipitation data is generated from multiple in situ and remotely sensed data sources (Alipour, Ahmadalipour, & Moradkhani, 2020; Yu et al., 2017). Although the radius to maximum wind speeds is often less than 100 km, the precipitation radius can be much larger. For instance, for the case of hurricane Harvey 2017 and hurricane Irma 2017, the maximum precipitation rate has been observed in the radius of 350–400 km and 400–550 km, respectively (Pérez-Alarcón et al., 2021). To sample the precipitation associated with TCs at time t, in our previous study (Song et al., 2020), we extracted the cumulative precipitation within a 5-degree radius buffer area of the eye of TCs over 3 hours window of time t-1, t, and t+1. Although using this method improved the characterization of TC hazards, it does not indicate if TCs rain over the same area over the 3 hours (slow moving TCs that result in extensive flooding like Hurricane Harvey 2017) or affect different areas with fewer overlaps impacts (fast moving TCs). Here, the date, time, and location of TC acquired from our constructed hourly HURDAT2 are utilized to extract the 3-hourly cumulative precipitation (i.e., the total precipitation for times t − 1, t, and t + 1) using a 5-degree radius buffer area from the center point of the TC at time t. Estimating the precipitation amount from the same location represents the magnitude of slow moving TCs that can cause heavy rain due to their duration of influence (Yamaguchi et al., 2020). Since we used a 5-degree radius as the approximation of TC size in our study area, we sampled wind and precipitation from those parts of the TCs that are within 5 degrees of shorelines.
2.3 SURGEDAT
The world's storm SURGE DATa (SURGEDAT) developed in the Louisiana State University is an archive of the location and height of more than 700 TC surge around the world since 1880 (Needham et al., 2015). This information is gathered from multiple sources including government reports, historic maps, academic papers, books, and newspapers. To match NLDAS-2 data availability, we use SURGEDAT to extract all the tropical surges along the U.S. Gulf and Atlantic coasts since 1979. The SURGEDAT available information does not include the storm surges after 2014; therefore we use NHC reports to obtain those hurricanes surge data that hit the U.S. coasts between 2014 and 2020. As we only had maximum surges available for each event, after using time series of precipitation and wind to conduct two-way sampling over the wind speed and precipitation for the events, instead of using a threshold to select multiple samples from the time series, we only used a maximum of two samples from each event that were associated to the reported maximum surge.
2.4 Multivariate Hazard Categories
there always exists a copula such that
(1)Here, to estimate the marginal distribution for each variable, that is, TCs windspeed, surge, and precipitation, we evaluate 17 different continuous distribution functions that previously have been used to fit skewed data (Sadegh et al., 2018). First, we employ the chi-square goodness-of-fit test to see whether data is sampled from distributions at a 5% significance level. From those distributions that pass the test, we select the one that minimizes the distance (root mean square error) between empirical probability values and the estimated values.
bivariate copulas densities using 
linked trees (Equation 2).
(2)
, denote the marginal densities, and 
refers to the bivariate copula densities with 
.In this paper, to construct and fit a vine copula model to our data we use the R VineCopula package that provides 48 bivariate copula families including Elliptical copulas (Gauss, t-), one-parametric Archimedean copulas (Clayton, Gumbel, Frank, Joe, …), two-parametric Archimedean copulas (BB1, BB7, etc.), and rotated versions of one-parametric and two-parametric Archimedean. Since there is a huge number of possible vines, this package selects the structure of trees using Czado et al.’s (2012) approach for finding optimal C-vines structure, Traveling Salesman Problem for D-vines, and Maximum Spanning Tree for R-vines Dissmann et al. (2012) structure selection. In addition, the package uses either Akaike's Information Criterion (AIC), Bayesian's Information Criterion (BIC), or log-likelihood as the bivariate copula selection criteria and Maximum likelihood estimation for estimating their parameters, simultaneously. To assess if the selected vine copula function can represent the distribution of our sample, we test the estimated CDFs versus the joint empirical CDFs using the two-sample Kolmogorov-Smirnov test at the 5% significance level.
) using the non-exceedance probability from the vine copula model as follows:
(3)
is the inverse normal function, variables 
, 
, and 
represent values of wind speed, rainfall severity, and surge, respectively. MHI at the wind speed margin (when the events are associated with minimal precipitation and surge) is consistent with SSHWS as we use the non-exceedance probability of 0.703, 0.867, 0.927, 0.968, and 0.99 corresponding to SSHWS wind speed thresholds of 74, 96, 111, 130, and 156 mph to divide the MHI to different multivariate hazard categories. While this methodology results in similar SSHWS and MHI categories at the wind speed margin, it alters the MHI categories when the amount of precipitation and surge are considerable. We use the terminologies of SSHWS for MHI categories to be consistent with the public's perception of hazardous events.2.5 Social Vulnerability Index (SVI)
The Centers for Disease Control and Prevention's (CDC) SVI is based on 15 census variables that consider unemployment, minority status, disability, housing, and transportation and aims to identify communities that may need support before, during, or after natural or human-caused disasters, or disease outbreaks (Flanagan et al., 2011). This data set is available for the years 2000, 2010, 2014, 2016, and 2018 at both U.S. census tract and county level resolutions. For simplicity, accuracy, and consistency, we use the 2018 SVI at the county level to evaluate the U.S. counties' vulnerability to TC events (Alipour, Ahmadalipour, Abbaszadeh et al., 2020). To identify the most affected areas, we use a 3-degree radius buffer area of which the center point is the middle point of TC reported surge and the associated maximum wind location. We examined the correlation between 15 vulnerability factors and the TC actual damage reported by National Centers for Environmental Information (NCEI) and found the largest correlation value (0.55) in integrating factors namely, people who speak intermediate, households with people either older than 65, younger than 16, single parents or with disabilities, and housing units with more than one occupant per room. The integrated vulnerability index later will be used to produce a TC risk proxy and assess the MHI performance.
3 Results
There exists a statistically significant correlation (at 5% significance) between the three TC-driven hazards considered here. In this study, we used Kendall's tau rank correlation coefficient to evaluate the dependencies between the TC hazard components. Based on our analysis, the correlation varies from strong correlation between surge and wind (0.48) to a weaker correlation between wind and rainfall (0.14) and rainfall and surge (0.28; Figure 1). To estimate the distribution of each variable, we evaluated 17 different continuous marginal distribution functions and ended up fitting the inverse Gaussian distribution to the wind speed data, and generalized extreme value distribution to the rainfall severity and surge data.
The histogram and the fitted distribution of the three tropical cyclone hazard components (a–c) and scatterplots and the linear trend line corresponding to each pair (d–f).
We use the marginal distributions to estimate each variable probability/cumulative distribution function (CDF) and construct a C-vine copula that models the joint probabilities of three TC hazard components. C-vine copula has a star structure that uses surge as the root node and fits a Gaussian copula to wind speed and surge pairs and a Frank copula to rainfall severity and surge pairs at the first tree and then fits an Independent copula to the variables at the second tree. In this study, Copulas are employed to obtain the events' non-exceedance probabilities and categorize them based on the multivariate hazard index, which is defined as the inverse normal of non-exceedance probability. Figure 2a shows the joint probability values across the three factors space using the C-vine copula model. The multivariate TC hazard categories are based on the inverse normal values corresponding to SSHWS wind speed thresholds. SSHWS considers the wind speeds ranges of 74–95, 96–110, 111–130, 131–155, and ≥156 mph as a hurricane category 1–5, respectively, and events associated with wind speed less than 74 mph as tropical storm/depression. We use the same thresholds to classify the multivariate hazard index. This includes 0.533, 1.112, 1.454, 1.852, and 2.33 values, which correspond to the inverse normal of the non-exceedance probabilities of 74, 96, 111, 131, 156 mph wind speed at the margin, respectively. Figure 2b displays multivariate TC hazard categories. The different colors in this figure represent different categories, with yellow representing MHI tropical storms or depressions and dark red representing MHI hurricane category 5, the most severe TC events. This figure indicates TCs that are associated with low wind speed, but large surge or rainfall severity are categorized with a more severe ranking.
Subplot (a) displays the joint cumulative distribution of wind speed, rainfall severity, and surge, with blue representing lower non-exceedance probabilities and red denoting higher values. Subplot (b) shows the distribution of Tropical Cyclone categories based on the multivariate hazard index.
Figure 3 displays some of the TCs that are characterized by severe surges or torrential rainfall but with low wind speed. Figure 3a depicts a few of the TCs with reported wind speeds from 74 to 95 mph, which fall within the range that SSHWS considers being a hurricane category 1. For example, using our proposed multivariate hazard index, Irene in 2011, which was associated with extreme rainfall, can now be considered a MHI category 4 hurricane. Similarly, Sandy in 2012, with a storm surge of more than 12 feet, can be classified as a MHI category 2 hurricane. Figure 3b also depicts some of the most devastating TCs in U.S. history, which were associated with winds ranging from 96 to 110 mph, the range of wind speed that SSHWS classifies as a hurricane category 2, but brought severe surge and rainfall amounts. For example, Ike in 2008 was associated with wind speeds ranging from 96 to 110 mph and was classified as a hurricane category 2 based on SSHWS, but it turned out to be a much more devastating storm and is now the seventh costliest Atlantic TC on the U.S. record. Ike is classified as a MHI category 5 hurricane due to the significant rainfall severity and surge.
The multivariate hazard categories for some of the most devastating Tropical Cyclone in the U.S. history that were associated with low wind speed (<74 mph for subplot [a] and 74 to 95 mph for subplot [b]).
NOAA's NCEI, in collaboration with the NHC, has provided damage estimates for the 50 costliest TCs to hit the United States (NCEI, 2021). The NCEI data set is provided using both insured and uninsured losses that would not have been incurred had the event not taken place. National Centers for Environmental Information determines the total loss of events using multiple sources including the National Weather Service, the Federal Emergency Management Agency, U.S. Department of Agriculture, U.S. Army Corps of Engineers, individual state emergency management agencies, state and regional climate centers, media reports, and insurance industry estimates. Among the 50 costliest TC reported by NCEI, 36 of them made landfall over the CONUS between 1979 and 2020. We use the reported damage of these TC to evaluate the proposed multivariate hazard index. Figure 4 depicts the track of 102 TCs that were used in this study to construct the MHI along with the multivariate category and the location of the 36 costliest TC related storm surges. These storm surges were associated with strong wind speed and widespread rainfalls. The area near these points can be considered as the potentially affected areas from the TC compound hazard. We refer the readers to supplementary material (Figure S1) for more information on the comparison of TCs categorization between the SSHWS and the MHI.
The track of 102 tropical cyclones that made landfall in the U.S. Atlantic and Gulf coasts between 1979 and 2020. Circles show the location of 36 costliest tropical cyclones according to National Centers for Environmental Information report 2021 adjusted cost. The colors represent hurricane categories based on the proposed multivariate Tropical Cyclone hazard index.
The multivariate hazard scale, which considers storm surge, wind speed, and rainfall severity simultaneously, can significantly improve the TC hazard communication. To assess the usefulness of our method and compare it with the SSHWS, we multiply the estimated hazard levels with the integrated SVI vulnerability index. With this, we generated a proxy of the associate risk for each event that enables us to compare the results with the actual damage. The hazard levels are the inverse normal of the non-exceedance probability of a given event estimated from either the Copulas (for the multivariate approach) or the inverse Gaussian distribution (for the univariate approach i.e., only based on wind speed). We use the Spearman's ranking correlation coefficient to measure the association between the estimated risks and NCEI reported damage. Figure 5 shows the result of multivariate categories versus SSHWS scale where colors represent categories for both SSHWS and multivariate categories. Overall, while the SSHWS has a good correlation with NCEI reported damage (0.59), using the multivariate hazard scale can significantly strengthen the correlation (0.78). These 36 TCs are the most devastating storms on record, while the SSHWS classifies seven events as category 4 and above hurricanes, the multivariate hazard scale classifies 19 of them as MHI category 4 and 5. Katrina as the most devastating TC on record with the maximum wind speed in the range of 111–130 mph (SSHWS category 3), is classified as MHI hurricane category 5 (Figure 5c).
Comparison of damage ranks using both univariate and multivariate hazard indices. Subplot (a) is the adjusted damage of 36 costliest tropical cyclones to impact the U.S. Atlantic and Gulf coasts between 1979 and 2020. Subplots (b, c) are estimated products of hazard and vulnerability.
4 Discussion and Conclusion
In this paper, we propose a new TCs hazard scaling system that takes into account the compound hazard of TCs. Our findings revealed that taking into account the rainfall severity and surge associated with TCs as well as their wind speed, could significantly improve TC hazard communication. TC is the major cause of compound flooding in the Gulf of Mexico and North America (Lai et al., 2021). The current TC scaling system solely based on wind speed underestimates the hazardousness of events such as Sandy 2012, Irene 2011, and Matthew 2016, which are associated with either torrential rainfall, severe surge, or both but weakened wind speeds. Furthermore, as the frequency of TC-driven intensive rainfall is increasing (Knutson et al., 2010) and TC translation speed is expected to decrease (Maxwell et al., 2021; resulting in higher rainfall severities), our new scaling system can be a helpful tool to inform communities prone to TC risk.
The rain-gauged data have limitations due to their spatial coverage, and satellite-based precipitation, available for 1979–2020, have relatively coarse spatial or temporal resolution and are subject to the inherent systematic biases and uncertainties in their retrieval algorithms (Shi & Song, 2015; Wang et al., 2019). Spatial homogeneity and temporally consistent precipitation estimate of reanalysis precipitation products make them a valuable source for historical analyses (Dollan et al., 2022). Considering the relatively fine temporal and spatial resolution of NLDAS-2, in addition to the data availability, we used this data set to extract the precipitation during the events. However, as NLDAS-2 combines different data resources and disaggregation methodology, it results in underestimating extreme precipitation (Behnke et al., 2016). Using more accurate precipitation can improve the characterization of precipitation associated with TCs and the dependency structure of TCs hazard drivers, which in turn result in improving TCs hazard categorization and communication. It should be noted that the sample size for our analysis is limited to the available TCs surge data. We obtained the surge data from the world's storm surge data center, which included a limited record of Atlantic TCs between 1979 and 2020 (less than 100). Considering a more comprehensive surge data would enhance the proposed TC hazard scaling skill.
Although here we used the historical data for our analysis, the constructed MHI (shown in Figure 2) is designed to be used in the operational setting as well. For this purpose, hazard data shall be retrieved from TC forecasts. NHC provides the forecast of the cyclone's center location and maximum 1-min surface wind speed using multiple weather numerical models (https://www.nhc.noaa.gov/modelsummary.shtml). This information can be linearly interpolated to have an hourly estimate of the track and maximum wind speed. The 3 hourly cumulative precipitation forecasts can be also retrieved from weather forecast models such as the Global Forecast System (GFS; https://www.ncei.noaa.gov/products/weather-climate-models/global-forecast). And finally, the NHC provides storm surge forecasts using the Sea, Lake and Overland Surges from Hurricanes (SLOSH) model (https://www.nhc.noaa.gov/surge/slosh.php). Sea, Lake, and Overland Surges from Hurricanes is a numerical model developed by the NWS to estimate storm surge heights resulting from TCs using a different set of parameters. Recent advancements in more detailed hydrodynamic simulation and operational coastal ocean forecasting enables predictions such as CERA (https://cera.coastalrisk.live/) that can be considered as possible alternatives for an accurate surge forecasting. Given the possible availability of precipitation, wind speed, and storm surge forecasts, one can estimate their corresponding MHI and inform the potentially affected communities of the TC MHI-based category. Like other available scales, the performance of the MHI is subject to the quality of the forecast data. NHC provides yearly verification reports of its past track and wind speed forecasts (https://www.nhc.noaa.gov/verification/verify3.shtml). Each year the level of forecast error is different. In some years, such as 2018, they were more accurate. The precipitation forecasts for landfalling TCs have been also evaluated in some studies (e.g., Luitel et al., 2018; Marchok et al., 2007). It has been indicated that depending on the weather forecast model and lead time, the skill of numerical weather forecasts systems is different. In addition, it has been shown that the SLOSH model can be a reliable tool for storm surge prediction (Forbes et al., 2014; Glahn et al., 2009). The MHI can categorize TC at any time and location during the event given the expected wind speed, precipitation, and surge as it is based on the union of the non-exceedance probabilities of all the factors (please see Equation 3). In other words, if the storm is close to the shoreline, based on the expected value of surge, precipitation, and wind speed, it can be scaled from a tropical storm to a hurricane with different categories. However, if it is far from the shoreline, where the impact from the surge is minimal to none, it still can scale the events to any category (due to the concept of the union in MHI formulation). For the same reason, we still can use the MHI solely considering the wind speed, which will result in the Saffir-Simpson Hurricane Wind Scale category. This means MHI design is flexible enough to categorize the event as it moves along its path and so can be helpful both for event categorization and warning. It is noted that although the multihazard TC scaling system developed here is proposed and applied for the U.S. Gulf and Atlantic TC, the framework is applicable to other regions as well.
Acknowledgments
This work was financially supported by USACE award no. A20-0545-001. We would like to acknowledge the data provided by the North American Land Data Assimilation Systems (NLDAS-2).
Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Open Research
Data Availability Statement
Phase 2 of the North American Land Data Assimilation System (NLDAS-2) product can be accessed from https://ldas.gsfc.nasa.gov/nldas/v2/forcing. The world's storm SURGE DATa (SURGEDAT) is available at http://surge.climate.lsu.edu/data.html. Atlantic TCs data (HURDAT2) can be downloaded from the NHC Data Archive (https://www.nhc.noaa.gov/data/#hurdat). The NHC full record of TCs details is available at (https://www.nhc.noaa.gov/data/tcr/index.php). The SVI can be retrieved from the Centers for Disease Control and Prevention's (CDC) website at https://www.atsdr.cdc.gov/placeandhealth/svi/data_documentation_download.html.
