Assessing North Atlantic Tropical Cyclone Rainfall Hazard Using Engineered-Synthetic Storms and a Physics-Based Tropical Cyclone Rainfall Model

Dazhi Xi aDepartment of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey

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Ning Lin aDepartment of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey

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Norberto C. Nadal-Caraballo bCoastal and Hydraulics Laboratory, Engineer Research and Development Center, U.S. Army Corps of Engineers, Vicksburg, Mississippi

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Madison C. Yawn bCoastal and Hydraulics Laboratory, Engineer Research and Development Center, U.S. Army Corps of Engineers, Vicksburg, Mississippi

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Abstract

In this study, we design a statistical method to couple observations with a physics-based tropical cyclone (TC) rainfall model (TCR) and engineered-synthetic storms for assessing TC rainfall hazard. We first propose a bias-correction method to minimize the errors induced by TCR via matching the probability distribution of TCR-simulated historical TC rainfall with gauge observations. Then we assign occurrence probabilities to engineered-synthetic storms to reflect local climatology, through a resampling method that matches the probability distribution of a newly proposed storm parameter named rainfall potential (POT) in the synthetic dataset with that in the observation. POT is constructed to include several important storm parameters for TC rainfall such as TC intensity, duration, and distance and environmental humidity near landfall, and it is shown to be correlated with TCR-simulated rainfall. The proposed method has a satisfactory performance in reproducing the rainfall hazard curve in various locations in the continental United States; it is an improvement over the traditional joint probability method (JPM) for TC rainfall hazard assessment.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dazhi Xi, dxi@princeton.edu

Abstract

In this study, we design a statistical method to couple observations with a physics-based tropical cyclone (TC) rainfall model (TCR) and engineered-synthetic storms for assessing TC rainfall hazard. We first propose a bias-correction method to minimize the errors induced by TCR via matching the probability distribution of TCR-simulated historical TC rainfall with gauge observations. Then we assign occurrence probabilities to engineered-synthetic storms to reflect local climatology, through a resampling method that matches the probability distribution of a newly proposed storm parameter named rainfall potential (POT) in the synthetic dataset with that in the observation. POT is constructed to include several important storm parameters for TC rainfall such as TC intensity, duration, and distance and environmental humidity near landfall, and it is shown to be correlated with TCR-simulated rainfall. The proposed method has a satisfactory performance in reproducing the rainfall hazard curve in various locations in the continental United States; it is an improvement over the traditional joint probability method (JPM) for TC rainfall hazard assessment.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dazhi Xi, dxi@princeton.edu

1. Introduction

Recent landfalling tropical cyclone (TC) events have demonstrated their ability to produce significant rainfall flooding. For example, in 2017, Hurricane Harvey produced extreme rainfall of more than 1000 mm in the Houston, Texas, area and flooded the city, ranking itself as the wettest storm in the U.S. history (Blake and Zelinsky 2018). In Texas, 336 000 people were influenced by blackouts, and 206 fatalities were caused by Hurricane Harvey. Other examples include Hurricane Florence in 2018, which induced a total rainfall of more than 700 mm in North Carolina, and Hurricane Ida in 2021, which induced a total rainfall of 360 mm in Louisiana. Furthermore, previous research projected an increase in TC rainfall (Knutson and Tuleya 2004; Villarini et al. 2014; Wright et al. 2015), TC rainfall hazard, and associated joint hazard (Emanuel 2017; Gori et al. 2022) in the future. Continued advancement of our understanding and modeling of TC rainfall hazard is needed.

Assessing TC rainfall hazard using historical observations can be challenging due to limited data. To reliably assess TC hazard for the current and future climates, basinwide synthetic storms (Vickery et al. 2009; Emanuel et al. 2008; Lee et al. 2018; Jing and Lin 2020) and physics-based TC hazard models (Chavas et al. 2015; Lu et al. 2018; Marsooli and Lin 2018) have been developed and coupled to simulate wind, surge, rainfall, and flood hazards (Emanuel 2017; Xu et al. 2020; Marsooli et al. 2019). Though the basinwide synthetic storm models are shown to be able to reproduce large-scale climatological features of TCs, such as genesis frequency, spatial pattern of TC genesis, track density, and probability distribution of lifetime maximum intensity, they may produce bias in storm properties (intensity, duration, etc.) associated with TCs at particular geographical locations. Such bias in storm parameters can induce bias in estimated rainfall hazard. For example, Xi and Lin (2022) showed that the synthetic storm model of Jing and Lin (2020) simulates longer storm duration than the model of Emanuel et al. (2008) on the U.S. East Coast, resulting in higher estimated rainfall hazards. Also, traditional regional and global climate models may not be directly applicable to TC rainfall hazard assessment. These physics-based climate models require high resolutions and large computational resources to generate realistic TCs, so it is difficult to use the models to generate a large number of simulations to reliably estimate the return period of TC hazards, especially for extreme events.

Besides developing and bias correcting the basinwide synthetic storm models, another approach to assessing TC hazard effectively is using site-specific synthetic storms designed to capture the local climatology features of landfalling TCs (e.g., Powell et al. 2005). One way to generate site-specific storms is to first generate a large number of storms equally spaced over the range of important TC parameters (intensity, size, landfall location, bearing, etc.) and then assign probability to each generated storm to reflect local climatology (Nadal-Caraballo et al. 2020). In this paper, we refer to such storms as “engineered synthetic” storms, in contrast to the basinwide synthetic storms generated directly based on the climatology. The engineered-synthetic storms developed by the U.S. Army Corps of Engineers (USACE; Nadal-Caraballo et al. 2020) have been used in coastal storm hazard estimation with a surge-targeted joint probability method (Toro et al. 2010a,b). Specifically, to apply the engineered-synthetic storms in surge hazard assessment, each storm in the dataset is assigned a probability mass according to the joint probability distribution of storm parameters important for storm surge (Toro et al. 2010a,b). The probability distribution of surge levels is estimated based on the simulated surge level for each storm and the associated probability mass. This method is referred to as the joint probability method (JPM), which has potential advantages over basinwide synthetic storm models in local storm hazard assessment because it incorporates observed probability distributions of important storm parameters at the local scale and thus produce more accurate estimation of the local hazard (Toro et al. 2010a,b).

Though the engineered-synthetic-storms-based hazard assessment method has been extensively used in storm-surge hazard assessment, it has not yet been applied to TC rainfall hazard assessment. This study aims to develop methods that use engineered-synthetic storms for TC rainfall hazard assessment. We couple the engineered-synthetic storms (Nadal-Caraballo et al. 2020) with a physics-based TC rainfall model (TCR; Lu et al. 2018) to estimate rainfall hazard. To couple the two models, the key step is to assign a probability mass to each synthetic storm in the dataset so that the synthetic storms carry storm climatological information relevant to the TC rainfall hazard. Equivalently, here we design a resampling-based method to associate TC climatology to the synthetic storms. To avoid the difficulty of resampling from the high-dimensional probability distribution of multiple storm parameters as in JPM (Xi and Lin 2022), we develop a midway variable reflecting TC rainfall potential and resample the storms based on the distribution of this single variable.

The bias from hazard models also influences the accuracy of the hazard assessment. Previous research has reported biases in rainfall models such as TCR. For example, Feldmann et al. (2019) compared the distribution of rainfall estimated by TCR and from observation and found that the model may fail to reproduce the observed distribution in locations with complex terrain. Xi et al. (2020) coupled the model with historical U.S. landfalling TCs and found that the model overestimates rainfall in coastal areas and underestimates rainfall in inland areas. These biases of the TCR model may result in an unsatisfactory estimation of TC rainfall hazard. Thus, in this study, we also develop a bias-correction method for TCR before coupling TCR with the engineered-synthetic storms.

The paper is organized as follows: Section 2 introduces the engineered-synthetic storm dataset, TCR model, and observational data used in this study and proposes the method to bias correct TCR and the method to couple TCR with synthetic storms. Evaluation of the methods and TC rainfall hazard assessment in the coastal United States is presented in section 3. Section 4 discusses the uncertainty in the developed method and possible future directions of improvement and application. Conclusions are summarized in section 5.

2. Data and method development

a. Engineered-synthetic storms

In this study, we use synthetic storm datasets generated by the USACE as part of the Coastal Hazards System (CHS) (Nadal-Caraballo et al. 2020). We used four regional datasets consisting of TCs covering the U.S. North Atlantic region (Nadal-Caraballo et al. 2015), Texas (Nadal-Caraballo et al. 2019), Louisiana (Nadal-Caraballo et al. 2022), and the U.S. South Atlantic region, including the Gulf Coast, as shown in Fig. 1.

Fig. 1.
Fig. 1.

Synthetic tracks generated for this study: (a) Texas, (b) Louisiana, (c) South Atlantic, and (d) North Atantic.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

The synthetic storms are characterized by storm parameters including 1-hourly track reference location and heading direction θ, central pressure deficit Δp, radius of maximum winds Rmax, and forward translation speed Vt. The synthetic TCs are generated with 60-km spacing between master tracks (MTs) and an average of 7.5–8.1 unique TCs (with various Δp and Rmax) per MT. Figure 1 shows the generated synthetic tracks used in this study for the four regional TC datasets. The size of each TC dataset and the range of TC parameters covered per region are listed in Table 1.

Table 1.

Total number of synthetic storms in each region and the range of TC parameters. The spacings of θ and Δp are 20° and 5 hPa, respectively. The convention of θ is 0° from north (clockwise). Specifically in the current study, we added storms to each MT with one-half of the minimal intensity shown in the range to better cover low-rainfall events. Here, ITCS indicates initial TC suite.

Table 1.

TC genesis for these synthetic storms generally occur in the eastern Caribbean Sea, near the Antilles, or in the Gulf of Mexico. To characterize relevant along-track variation of TC parameters, reference values for θ, Δp, Rmax, and Vt are established at offshore reference points 250 km from landfall or designated bypassing location. The intensity of TCs is estimated from Δp using the physics-based planetary boundary layer TC vortex model of Cardone et al. (1976), Thompson and Cardone (1996), and Cox et al. (2017). For each TC track, θ and Vt are held constant beginning at the reference point and until the TC makes landfall or, in the case of bypassing storms, when the TC reaches the point of closest approach. Prelandfall filling is applied starting at each reference point based on empirical relationships derived from the analysis of historical TCs in the International Best Track Archive for Climate Stewardship (IBTrACS) archive (Knapp et al. 2010). The prelandfall filling analysis considers TC parameters within 500 km prior to landfall or within a 48-h period before reaching the bypassing reference location. The development of these synthetic TC tracks also involves a postlandfall filling model by Vickery (2005). For details of the engineered-synthetic storm modeling, see Nadal-Caraballo et al. (2020).

b. Physics-based TC rainfall model

The detailed formulation of the TCR model can be found in Lu et al. (2018), and here we briefly summarize the model. The model calculates the TC rain rate as the product of precipitation efficiency and the vertical transport of water vapor across the TC boundary layer. The model estimates the water vapor transport as the product of the saturation specific humidity at the top of the boundary layer and the vertical velocity across the TC boundary layer. The vertical velocity is calculated as the summation of vertical velocities caused by frictional effect, vortex stretching, baroclinic forcing, topographic forcing, and radiative cooling. All the parameters in the model are set following Xi et al. (2020). We apply TCR to observed storms in IBTrACS and engineered-synthetic storms, and only rainfall within 300 km to the TC center is simulated following Emanuel (2017), Feldmann et al. (2019), and Xi and Lin (2022). To run the TCR simulation, we linearly interpolate the observed 6-hourly storm location and intensity to hourly time step. The environmental fields needed were obtained from ERA5 reanalysis (Hersbach et al. 2020).

c. Gauge observation of TC rainfall

The Parameter–Elevation Regression on Independent Slopes Model (PRISM) rainfall product from the Climate Group at Oregon State University (Daly et al. 1994, 2000, 2002; Daly 2006) is used as the observation for both bias correction of TCR and evaluation of the coupled rainfall assessment framework. PRISM provides gridded 4-km-resolution daily rainfall observation from 1981 to 2018. The data are linearly interpolated into hourly temporal resolution to be consistent with the temporal resolution of the synthetic storms. The linear interpolation has limited influence on our analysis because we investigate event total rainfall. For each point of interest, the observed event total rainfall is calculated as the total rainfall during the period when TC is within 300 km of the point of interest, to be consistent with the simulations. The reason we choose to use PRISM is because it has a long period of observation and relatively fine resolutions, which are important for TC rainfall hazard analysis.

d. Bias-correction method for TCR

Previous research indicates that TCR has intrinsic biases (Feldmann et al. 2019; Xi et al. 2020). For example, Xi et al. (2020) showed that TCR overestimates rainfall in coastal areas and underestimates rainfall farther inland. In this study, to better estimate TC rainfall hazard, we aim to first bias correct TCR itself statistically. We focus on reducing the bias of the event total rainfall simulated by TCR itself, so we compare the TCR simulation based on historical IBTrACS (1981–2018) storms (IBTrACS-TCR) with gauge observations. Our goal is to minimize the L2 distance (sum of all squared differences) between the cumulative distribution functions (CDFs) fitted by the gauge observed and the IBTrACS-TCR-simulated event total rainfall for each point of interest:
L2=10thpercentileofgaugeobservation90thpercentileofgaugeobservation[Fgauge(x)FIBTrACS-TCR(x)]2dx,
where x represents the event total rainfall, Fgauge is the CDF of event total rainfall fitted with gauge observations, and FIBTrACS-TCR is the CDF of event total rainfall fitted with IBTrACS-TCR simulation. We focus from the 10th percentile to the 90th percentile to take advantage of the most reliable range of the rain gauge observation. We exclude the CDF beyond 90th and 10th percentile because the extreme events (>90th) are difficult to estimate reliably using limited historical data and the weak rainfall event may be too strongly influenced by non-TC factors.

We hypothesize that the bias in IBTrACS-TCR is mainly caused by two factors. First, the parameterization of drag coefficient Cd, which determines the main rainfall mechanism (frictional effect) in TCR, induces uncertainties. In the TCR model, the drag coefficient is estimated from surface roughness using a classical expression for momentum in the Ekman boundary layer and an arbitrary height for the boundary layer (Esau 2004). In this study, a height of 500 m is used to calculate the drag coefficient for the slab boundary following Feldmann et al. (2019), which may introduce bias. Second, as a TC rainfall model, TCR lacks the representation of rainfall caused by other synoptic systems (background rainfall) especially for weak TCs, because TCR is developed assuming the TC has a mature and compact/coherent structure, which is invalid for weak TCs. Feldmann et al. (2019) showed that adding background rainfall will help capture the probability distribution of rainfall in the low-rainfall regime. To correct the bias of simulated event total rainfall caused by the first factor, we aim to find a multiplicative factor A that can be applied to the TCR-simulated event total rainfall. We use the multiplicative factor to correct the inaccuracy caused by the parameterization of Cd because it is a multiplicative parameter in the (dominate) frictional term in TCR (Lu et al. 2018). Previous research suggests that rainfall can cause the drag in the TC boundary layer to increase (Caldwell and Elliott 1972), so we assume that the multiplicative factor is a linear function of the simulated event total rainfall, or ETR (A = αETR + b). To correct the bias caused by the second factor, we assume that the background rainfall follows an exponential distribution (Rodriguez-Iturbe et al. 1999), and it can be directly added to the TCR-simulated rainfall (Feldmann et al. 2019).

We estimate the multiplicative factor and background rainfall distribution by minimizing L2 in Eq. (1). We pose restrictions in the optimization process so that the product of the multiplicative factor and Cd (i.e., the corrected Cd) is less than 6 × 10−3, and the mean of the background rainfall is less than 25 mm. The Cd threshold is the maximum value calculated based on the surface roughness for the continental United States in Feldmann et al. (2019), and the threshold of background rainfall is set so that the maximum background rainfall is smaller than the minimal TC rainfall considered in TCR simulations (Emanuel 2017). We perform the optimization using the algorithm of greedy search.

e. TC rainfall potential parameter

To couple TCR with engineered-synthetic storms, we need to assign a probability mass to each storm in the synthetic dataset, or we can resample the synthetic storms. We define a parameter called TC rainfall potential (POT) to be a midway variable for resampling in order to avoid the difficulty of resampling from the high-dimensional probability distribution of a number of storm parameters as in previous research (Xi and Lin 2022). The POT should have the following properties to be a reasonable midway variable. First, POT should be a highly condensed form of information related to the TC track, intensity, and environmental humidity when the storm moves around the point of interest. Second, POT should be able to capture the essential features of TCR and be positively correlated with TCR-simulated event total rainfall at each point of interest. We thus develop the POT (mm) as
POT=L<300kmpot(rs,t)=L<300kmA(rs)exp[B(rs)Vmax(t)C(rs)]q(t),
where L (km) is the distance from the storm center to the point of interest and rs is the rescaled distance from point of interest to the TC center (distance divided by the radius of maximum wind. The radius of maximum wind is estimated using an empirical equation following Xi et al. (2020) if the observation is not available in IBTrACS. Vmax(t) (m s−1) and q(t) (kg kg−1) are the intensity and saturation specific humidity of the storm at time t, respectively; A, B, C are model parameters, which depend on the rescaled distance; pot(rs, t) (mm h−1) is the rainfall potential in a specific time step t and from the storm at the rescaled distance rs. To know the exact expression of pot(rs, t), we fit the model parameters A, B, and C in Eq. (2) using idealized TCR simulations with only the frictional term (with Cd set to be a constant of 1 × 10−3 to focus on the variability from storm parameters). Thus, POT can be viewed as a parametric statistical TC rainfall model that considers only TC rainfall caused by frictional convection but ignores the asymmetry induced by TC translation and environmental wind shear.

To calculate POT, in addition to storm parameters, we need saturation specific humidity [Eq. (2); the saturation specific humidity is assumed to be constant following Lu et al. (2018)]. For the historical storms, we obtain the environmental 600-hPa air temperature from ERA5 reanalysis by averaging the temperature within the 500–800-km annulus centered at storm center and calculate the saturated low-level saturation specific humidity following Emanuel (2017) and Xi and Lin (2022) for each time step for each storm. For the synthetic storms, we randomly assign an environmental temperature from ERA5 reanalysis according to the historical observation based on the month and the location of the simulated synthetic storm in each time step and calculate the saturation specific humidity using the same method.

We selected nine points of interest in the United States (Fig. 2) to investigate the relationship between obtained POT and event total rainfall from IBTrACS-TCR (Fig. 3). These representative locations were chosen to cover the U.S. East and Gulf Coasts as well as inland areas (represented by Atlanta, Georgia). POT has good correlations with IBTrACS-TCR-simulated event total rainfall (R2 > 0.75). The slope between POT and event total rainfall varies from location to location, which is a result of the spatial variation of drag coefficient as we set a constant drag coefficient when developing the POT. We also noticed that the correlations in some locations (e.g., New Orleans, Louisiana, and Savannah, Georgia) are higher than that of others (e.g., Tampa, Florida, and Jackson, Mississippi). One possible explanation is that because POT is developed based on the symmetric field of TC rainfall, if the storms impacting the point of interest have systematic asymmetric structure, the correlation between POT and event total rainfall would be weak.

Fig. 2.
Fig. 2.

Locations of the nine points of interest for evaluation.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

Fig. 3.
Fig. 3.

Correlation between POT and TCR-simulated event total rainfall (before bias correction) in nine selected points of interest. The dashed black lines are the ETR-is-equal-to-POT lines.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

f. Resampling method for hazard assessment

We perform a resampling of storms to result in the same probability distribution of POT in the synthetic dataset as in the historical observation. However, based on the design of POT, it is clear that POT will not capture the asymmetric component of TC rainfall; thus, in the resampling method, we account for this systematic difference between event total rainfall and POT. The resampling method can be summarized in the following steps:

  1. We fit the probability distribution of POT of historical events using kernel density estimation plus a generalized Pareto distribution (GPD) for tails.

  2. We fit a linear regression model between the IBTrACS-TCR-simulated event total rainfall and historical POT.

  3. We randomly draw a sample from the fitted distribution of POT and find the storms in the synthetic storm dataset that have the POT value within ±15 (mm) of the random sample we just drew. We call these synthetic storms “the pool.”

  4. We predict the event total rainfall of the synthetic storms in the pool, using the linear regression model we fitted in step 2. We calculate the mean of the predicted event total rainfall and variance of the residuals. If there are not enough (<5) events in the pool, we use the variance of residuals of the linear regression model in step 2.

  5. We randomly draw an event total rainfall value from its Gaussian distribution, with mean and variance from step 4, and select the event in the pool that has the closest event total rainfall value to be the sample.

  6. We repeat steps 3–5 until reaching the sample number we desire (1000 in this study).

In this resampling process, we achieve two goals. First, because of step 3, the resampled rainfall potential follows the historical (target) probability distribution of POT (observation data obtained from 1981 to 2018 assuming stationary climatology). Second, because of steps 4–5, we capture overall differences between event total rainfall and POT caused mainly by the asymmetric feature of the rainfall. Before resampling, we first apply the multiplicative bias-correction factor to both IBTrACS-TCR and synthetic-storm TCR simulations. After the resampling, we add the background rainfall, randomly drawn from the fitted exponential distribution described in section 2d, to the TCR rainfall estimates to obtain the total rainfall estimates.

3. Results

a. Bias correction of TCR

The bias correction described in section 2d is performed for each 0.1 × 0.1 grid point in the continental United States. In Fig. 4 we show the comparison of the probability distributions of IBTrACS-TCR rainfall before and after bias correction with rain gauge observations in the nine selected points of interest. The proposed method can significantly improve TCR performance. For example, in Orlando, Florida, IBTrACS-TCR significantly overestimates TC rainfall hazard, while in Atlanta IBTrACS-TCR underestimates TC rainfall hazard. After we apply the bias correction, the hazard curve matches well with the gauge observation. For some locations (e.g., New Orleans; Raleigh, North Carolina), the bias-corrected hazard curve matches the observation in the low-rainfall regime well, but it does not match the observation in the high-rainfall regime. However, for extreme rainfall, the exceedance probability estimated from the rain gauge observation has high uncertainties due to data limitation. Thus, in general, the proposed bias-correction method improves the performance of TCR. We also show the separate effect of bias correcting background rainfall and drag coefficient in Figs. S1 and S2 in the online supplemental material, respectively, and it is shown that for most locations, bias correcting drag coefficient helps the most, but for inland locations such as Atlanta, bias correcting background rainfall will significantly improve the performance of overall estimation of TC rainfall hazard.

Fig. 4.
Fig. 4.

Exceedance probability of event total rainfall in observation (black dots), IBTrACS-TCR simulations (green dots), and bias-corrected IBTrACS-TCR simulations (purple line), for selected points of interest. The number of storms in the analysis is shown in the title of each figure.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

Figures 5a and 5b examine the spatial distribution of the bias-correction parameters. The mean of the multiplicative factors and the mean of the additive bias-correction parameters are both higher in inland regions and lower in coastal regions. The highest values are shown in inland Georgia, which can be explained by the example in Fig. 4f that IBTrACS-TCR significantly underestimates TC rainfall in Atlanta. Xi et al. (2020) show that TCR overestimates the annual mean TC rainfall in the coastal areas while it underestimates the annual mean TC rainfall in inland areas, and our results consistently indicate the same spatial pattern of TCR bias (Figs. 5c,d). The dashed lines in Figs. 3c and 3d show the exponential-fitted relations between the bias-correction factors and the distance to coastline. The exponential fittings show a better match than the linear fittings, indicating the bias of TCR is higher in inland areas. The correlation between the bias and the distance to the coast indicates that the causation of the bias is mostly related to the model assumption of compact structure of TCs as TCs in inland areas are usually weaker and the coherent structure of the ocean-generated systems is destroyed.

Fig. 5.
Fig. 5.

Spatial pattern of bias-correction factors in the continental United States: (a) mean multiplicative bias-correction parameter, (b) mean additive bias-correction parameter, (c) relationship between mean multiplicative bias-correction parameter and the distance to coast, and (d) relationship between mean additive bias-correction parameter and the distance to coast.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

b. Evaluation of the hazard assessment method

With a bias-corrected TCR model developed in section 3a, the next step in the rainfall assessment framework is resampling the synthetic storms and performing TCR simulations for these synthetic events. After the resampling, we first examine the POT–event total rainfall (ETR) relationship, as the successful reproduction of the historical POT–ETR relationship not only proves the success of the resampling process but also results in lower bias in the estimated rainfall hazard (detailed in section 4). Figure 6 shows that after the resampling process, the synthetic POT–ETR relationship is close to the historical POT–ETR relationship. The successful reproduction of the averaged POT–ETR relationship (dashed red line) is a basis for the correct estimation of probability of event total rainfall using the POT-targeted resampling method.

Fig. 6.
Fig. 6.

Evaluation of the POT–ETR relationship after resampling for the nine selected points of interest. Black dots are observation, red dots are synthetic storms after resampling, the black dashed line is the fitted relationship between POT and ETR in the observation, and the red dashed line is the fitted relationship between POT and ETR in the synthetic datasets after resampling.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

To evaluate the performance of the resampling method designed for TC rainfall hazard assessment, we examine the return period of TC rainfall in the nine selected points of interest (Fig. 7). For all locations, the return periods estimated from resampled synthetic storms match well with the estimation from the rain gauge observation in the low-return-period regime, proving that the bias correction and the resampling method together can satisfactorily reproduce the probability distribution of event total rainfall. The differences between the synthetic storm estimated return period and observed return period can be attributed to two sources: TCR modeling (even after the bias correction) and synthetic storm modeling and resampling. For example, in Tallahassee, Florida, the synthetic storm overestimates rainfall hazard in the high-return-period regime when compared with the gauge observation but matches well with IBTrACS-TCR (bias corrected) results. This difference shows that in Tallahassee, the bias of the final estimated hazard curve comes mainly from the TCR modeling (even after bias correction). In New Orleans, however, the IBTrACS-TCR estimated hazard curve matches the gauge observation, but the resampled hazard curve is higher than both the rain gauge observation and IBTrACS-TCR simulation, indicating that the bias comes mainly from the synthetic storm modeling and resampling.

Fig. 7.
Fig. 7.

Return-period estimation of TC rainfall hazard (represented by ETR) for the nine selected point of interest. Red dots are estimated ETR return period from resampled synthetic storms, black dots are estimated ETR return period from the observation, purple dots are estimated ETR return period using the three-parameter joint probability method, the red curve is the GPD fitted by ETR simulated by synthetic storms, and the blue curve is the estimated ETR return period from IBTrACS-TCR simulation (after bias correction). The λ in the title shows the annual occurrence rate of TCs in the selected location.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

We compare the POT-based resampling method with the three-parameter-based (i.e., intensity, distance, duration) resampling method, a JPM method developed in Xi and Lin (2022), by showing the estimated hazard curve obtained by the three-parameter-based resampling method (purple dots in Fig. 7). Although at some locations (e.g., Jackson, Tallahassee, and Savannah), the three-parameter-based resampling method can reproduce the hazard curve as well as the POT-based method, in some other locations (e.g., New Orleans, Tampa, and New York City), the hazard curve estimated by the three-parameter-based resampling method has large discrepancies from the observation and the estimation based on the POT method. For all locations, the POT-based method has satisfactory results, implying that the POT-based method is more reliable than the JPM-based method for TC hazard assessment using engineered-synthetic storms.

c. TC rainfall hazard assessment of coastal United States

Section 3b shows that the resampling method can capture the probability distribution of event total rainfall of TCs in different points of interest well. In this section, we apply the developed method for TC rainfall hazard assessment in U.S. coastal regions. Following Jing and Lin (2020), we define mileposts along the North American coastline and calculate the return period of event total rainfall at these mileposts. To validate the estimation of TC rainfall hazards along the U.S. coastline, we selected nine locations along the coastline and examine the exceedance probability of event total rainfall estimated from the synthetic storm-TCR coupled model (Fig. 8). We select these locations from milepost 50 (near Houston) to milepost 170 (Maine) with 15-milepost spacing (Fig. 9a). At all nine locations, the estimated probability distributions of event total rainfall are close to the observed probability distributions and IBTrACS-TCR simulation in the low-rainfall regime. (Fig. 8). The designed method extends the reliable estimation of TC rainfall hazard to higher rainfall regime and extreme events by incorporating synthetic storms with a larger sample size. We noted that for some locations the estimations are more continuous (e.g., mileposts 140, 155, 170) while for some other locations the estimations are noncontinuous (e.g., milepost 110) for the extreme events (exceedance probability smaller than 0.1). One possible explanation is that there are very few synthetic storms generating extreme rainfall impacting those locations where the estimation is noncontinuous. As Fig. 7 shows, the estimations of 10-yr return level and 50-yr return level compare well to the observation. For the 100-yr return level, the observational data are too limited to fully support the robustness of TC rainfall hazard. Since the fitting of POT (or JMP parameters) is based on the observational data, it is worth conducting future research (e.g., employing large ensembles of simulations) to evaluate whether the resampling method can correctly estimate the return levels for high return periods (>100 years).

Fig. 8.
Fig. 8.

Exceedance probability of ETR from gauge observation (black dots), TCR simulation on historical TCs (after bias correction; blue line), and that simulated by synthetic storm-TCR coupled model (red dots). The black dashed lines are the confidence intervals of 0.05 significant level for the observation. All TCs that enter the 300-km circle centered on the milepost of interest are included in the estimation.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

Fig. 9.
Fig. 9.

(a) Milepost locations following Jing and Lin (2020). (b) The 10- (blue), 50- (green), and 100-yr (red) return levels of ETR at coastal mileposts.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

We then apply the hazard assessment method to all U.S. mileposts (Fig. 9b). We found that the rainfall hazard is most significant on the border of the Gulf Coast and Florida coast (around milepost 70), border of Florida and the East Coast (around milepost 105), and North Carolina’s coast (around milepost 120). TC rainfall hazard on the Northeast coastline is significantly lower than other coastal regions, due to weaker and less frequent storms in this region and possible underestimation of TC rainfall by TCR due to the model’s limited capability in capturing the effect of TC extratropical transition. We also found that the proportional difference between the 10-yr return level and 50-yr return level is more significant than the proportional difference between the 50-yr return level and 100-yr return level. The 100-yr return level may be underestimated due to the uncertainty of the extremes estimated by the engineered-synthetic storms (section 4).

4. Discussion

The synthetic storm modeling and resampling are not bias-free, and here we discuss where the bias may come from and how we might improve and understand the bias of the hazard assessment method developed in this study. Because the performance of the resampling process depends on whether the synthetic storms have enough data around the observed ETR–POT regression relationship (steps 4–5), the statistical relationship between event total rainfall and POT in the synthetic storm dataset may profoundly influence the accuracy of the results of rainfall hazard assessment. From Fig. 6, we see that in general the resampling process can produce high correlations between event total rainfall and POT when compared with the observation, but these relationships are imperfect. The imperfect ETR–POT relationship may induce uncertainty in the event total rainfall estimation. Since we based our resampling method on POT, if the relationships between event total rainfall and POT differ in the synthetic storm dataset (after resampling) and observation, we can end up with resampled synthetic storms that have a similar probability distribution of POT as in the observation but a different probability distribution of event total rainfall. This uncertainty may be particularly important for extremes because there exist fewer synthetic storm data that we can resample from.

To test if the abovementioned understanding of the uncertainty is correct and to better infer the bias of the rainfall hazard assessment method using the ETR–POT relationship, we design an idealized statistical test. In the statistical testing, we first create a mock observation with limited data (50 data points) to mimic the historical observation. We create the mock observation by setting a constant ETR–POT relationship (black lines in Figs. 10a,d,g), randomly draw the POT in the range of POT in the historical observation (Fig. 6), and calculate the mock observed event total rainfall based on the ETR–POT relationship (Figs. 10a,d,g; black dots). We also create an extended mock observation (5000 data points; green dots) to compare with the estimated rainfall hazard. We create a larger set of mock observations to establish a reliable estimation of the tail so that we can evaluate the ability of the resampling process to reproduce the probability of extreme events. Then we create three sets of mock synthetic storm simulations that have different ETR–POT relationships (blue lines in Figs. 10a,d,g), to cover different types of intrinsic bias in the synthetic storm dataset. We then perform the resampling and exceedance probability calculation as described in section 2f. We find that the bias in the final assessment of rainfall hazard (Figs. 10c,f,i) is modulated by the initial bias of the ETR–POT relationship in the synthetic storm dataset. When the slope of the ETR–POT relationship in the synthetic dataset is smaller than that of the historical observation (Fig. 10a), there is still enough data to be resampled in the low POT region. However, in the high POT region (extreme event), all of the event total rainfall values that we can resample from are below the observed ETR–POT relationship, so the event total rainfall values resampled are smaller than they should be (Fig. 10b), which leads to the underestimation of the tail of the rainfall hazard distribution (Fig. 10c). On the contrary, if the slope of the ETR–POT relationship in the original synthetic dataset is larger than that of the historical observation (Fig. 10d), the tail of rainfall hazard will be overestimated (Fig. 10f). If the ETR–POT relationship is similar in the original synthetic dataset and the observation (Fig. 10g), the bias in the tail is negligible (Fig. 10i).

Fig. 10.
Fig. 10.

Idealized statistical testing of the resampling method: (a),(d),(g) Relationship between POT and ETR in mock observation and mock synthetic storm dataset. Black and blue lines are linear regressions between ETR and POT in mock observation and mock synthetic storms, respectively. (b),(e),(f) Relationship between POT and ETR in mock synthetic dataset after resampling. (c),(f),(i) Exceedance probability of ETR in mock observation (black dots), resampled mock synthetic storms (blue dots), and extended mock observations (green dots). The first row corresponds to the test in which the synthetic storms have lower ETR given the same POT relative to observations. The second row corresponds to the test in which the synthetic storms have higher ETR given the same POT relative to observations. The third row corresponds to the test in which the synthetic storms have a similar ETR given the same POT in comparison with observations.

Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0131.1

Some potential applications of this analysis exist. First, the relationship between the bias of rainfall hazard estimation and the bias in the ETR–POT relationship after resampling (Figs. 10b,e,h) can be used to infer the bias of the hazard assessment. For example, the ETR–POT relationship after resampling is underestimated in Atlanta (Fig. 6). Although in the comparison of low-return-period events the resampling matches the gauge observation well in Atlanta (Fig. 7), it is likely that the resampling process underestimates the extreme events (that are beyond the observation and cannot be evaluated directly with the observation). Also, the relationships between the initial bias of the ETR–POT relationship in the synthetic dataset and the bias in rainfall hazard estimation can aid the design of better synthetic storm datasets that have a similar initial ETR–POT relationship as in the observation for TC rainfall hazard assessment.

5. Conclusions

In this study, we couple a recently developed physics-based TC rainfall model (TCR) with engineered-synthetic storms to perform TC rainfall hazard assessment. We first bias correct TCR by matching the probability distributions of event total rainfall simulated by TCR coupled with historical TCs and event total rainfall observed by the rain gauge. Then we develop a parameter named rainfall potential (POT) to act as the base parameter for resampling as a way to assign probability mass to each synthetic storm. POT is designed to contain information from both TC tracks and environmental humidity and is shown to have a linear correlation with event total rainfall. The synthetic modeling and resampling of synthetic storms based on POT is shown to render similar probability distribution of event total rainfall as from the gauge observation, proving the developed method is suitable for TC rainfall hazard assessment. The resampling method can drastically increase the sample size for rainfall hazard estimation, which provides reliable estimation of the return period of extreme events. The developed method is then used to assess TC rainfall hazard in the coastal United States, and the analysis shows that the coastal areas in the east Gulf Coast, north Florida, and North Carolina are most prone to landfalling TC rainfall risk, which is consistent with previous research (Bregy et al. 2020; Knight and Davis 2009; Stansfield et al. 2020; Jiang and Zipser 2010).

The engineered-synthetic storm-based TC rainfall hazard assessment method has several potential applications. As shown in this study, if it is coupled with the observed storm climatology information (e.g., that obtained from IBTrACS), the synthetic storm can be used to assess landfalling TC rainfall hazard in the current climate. Following a similar method, if the explicitly simulated TCs are available from regional or global climate simulations, the engineered-synthetic storms can be coupled with the simulated storm climatology in climate models to assess the effect of climate change on landfalling TC rainfall hazards.

The developed method has some limitations that are worth addressing in future work. First, as mentioned in section 4, the bias of the developed hazard assessment method is related to the design of the synthetic storms. Future work could reduce the bias of the hazard assessment by designing synthetic storm models for the specific purpose of hazard assessment. Also, the developed method is designed to match the probability distribution of event total rainfall. Similar to previous methods designed for surge hazard assessment (e.g., Toro et al. 2010b), the method may not render the correct probability distribution of other hazard components related to TCs, so its application in joint hazard assessment is limited. Future research could consider developing resampling methods that target joint hazards (Gori et al. 2022) or modifying the current method to consider other hazard components.

Acknowledgments.

This material is based upon work supported by the National Science Foundation (NSF Award 1854993) and by the U.S. Army Corps of Engineers (USACE) Flood and Coastal Systems R&D Program through the Oak Ridge Institute for Science and Education (ORISE) Research Participation Program as part of an interagency agreement between the U.S. Department of Defense (DOD) and the U.S. Department of Energy (DOE). ORISE is managed by ORAU under DOE Contract DE-SC0014664. All opinions expressed in this paper are the authors’ and do not necessarily reflect the policies and views of NSF, USACE, DOD, DOE, or ORAU/ORISE. Author Xi thanks Prof. Dan Chavas of Purdue University for his useful suggestions.

Data availability statement.

The database of synthetic tropical cyclones used in this study is part of the USACE CHS program and can be accessed through the CHS website (https://chs.erdc.dren.mil). The IBTrACS data (https://www.ncdc.noaa.gov/ibtracs/), PRISM rainfall product (https://prism.oregonstate.edu/), and ERA5 reanalysis dataset (https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5) can be obtained online.

REFERENCES

  • Blake, E. S., and D. A. Zelinsky, 2018: National Hurricane Center tropical cyclone report: Hurricane Harvey. NOAA/NWS Rep. AL092017, 45 pp., https://www.nhc.noaa.gov/data/tcr/AL092017_Harvey.pdf.

  • Bregy, J. C., J. T. Maxwell, S. M. Robeson, J. T. Ortegren, P. T. Soulé, and P. A. Knapp, 2020: Spatiotemporal variability of tropical cyclone precipitation using a high-resolution, gridded (0.25° × 0.25°) dataset for the eastern United States, 1948–2015. J. Climate, 33, 18031819, https://doi.org/10.1175/JCLI-D-18-0885.1.

    • Search Google Scholar
    • Export Citation
  • Caldwell, D. R., and W. P. Elliott, 1972: The effect of rainfall on the wind in the surface layer. Bound.-Layer Meteor., 3, 146151, https://doi.org/10.1007/BF02033915.

    • Search Google Scholar
    • Export Citation
  • Cardone, V. J., W. J. Pierson, and E. G. Ward, 1976: Hindcasting the directional spectra of hurricane-generated waves. J. Pet. Technol., 28, 385394, https://doi.org/10.2118/5484-PA.

    • Search Google Scholar
    • Export Citation
  • Chavas, D. R., N. Lin, and K. Emanuel, 2015: A model for the complete radial structure of the tropical cyclone wind field. Part I: Comparison with observed structure. J. Atmos. Sci., 72, 36473662, https://doi.org/10.1175/JAS-D-15-0014.1.

    • Search Google Scholar
    • Export Citation
  • Cox, A. T., B. T. Callahan, M. Ferguson, and M. A. Morrone, 2017: Tropical cyclone wind field analysis for ocean response modeling: Hurricane Harvey (2017). First Int. Workshop on Waves, Storm Surges and Coastal Hazards, Liverpool, United Kingdom, National Oceanography Centre, P14, https://www.oceanweather.com/about/papers/Harvey.pdf.

  • Daly, C., 2006: Guidelines for assessing the suitability of spatial climate data sets. Int. J. Climatol., 26, 707721, https://doi.org/10.1002/joc.1322.

    • Search Google Scholar
    • Export Citation
  • Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140158, https://doi.org/10.1175/1520-0450(1994)033<0140:ASTMFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Daly, C., G. H. Taylor, W. P. Gibson, T. W. Parzybok, G. L. Johnson, and P. A. Pasteris, 2000: High-quality spatial climate data sets for the United States and beyond. Trans. ASAE, 43, 19571962, https://doi.org/10.13031/2013.3101.

    • Search Google Scholar
    • Export Citation
  • Daly, C., W. P. Gibson, G. H. Taylor, G. L. Johnson, and P. Pasteris, 2002: A knowledge-based approach to the statistical mapping of climate. Climate Res., 22, 99113, https://doi.org/10.3354/cr022099.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., 2017: Assessing the present and future probability of Hurricane Harvey’s rainfall. Proc. Natl. Acad. Sci. USA, 114, 12 68112 684, https://doi.org/10.1073/pnas.1716222114.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., R. Sundararajan, and J. Williams, 2008: Hurricanes and global warming: Results from downscaling IPCC AR4 simulations. Bull. Amer. Meteor. Soc., 89, 347368, https://doi.org/10.1175/BAMS-89-3-347.

    • Search Google Scholar
    • Export Citation
  • Esau, I. N., 2004: Parameterization of a surface drag coefficient in conventionally neutral planetary boundary layer. Ann. Geophys., 22, 33533362, https://doi.org/10.5194/angeo-22-3353-2004.

    • Search Google Scholar
    • Export Citation
  • Feldmann, M., K. Emanuel, L. Zhu, and U. Lohmann, 2019: Estimation of Atlantic tropical cyclone rainfall frequency in the United States. J. Appl. Meteor. Climatol., 58, 18531866, https://doi.org/10.1175/JAMC-D-19-0011.1.

    • Search Google Scholar
    • Export Citation
  • Gori, A., N. Lin, D. Xi, and K. Emanuel, 2022: Tropical cyclone climatology change greatly exacerbates US extreme rainfall–surge hazard. Nat. Climate Change, 12, 171178, https://doi.org/10.1038/s41558-021-01272-7.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Jiang, H., and E. J. Zipser, 2010: Contribution of tropical cyclones to the global precipitation from eight seasons of TRMM data: Regional, seasonal, and interannual variations. J. Climate, 23, 15261543, https://doi.org/10.1175/2009JCLI3303.1.

    • Search Google Scholar
    • Export Citation
  • Jing, R., and N. Lin, 2020: An environment‐dependent probabilistic tropical cyclone model. J. Adv. Model. Earth Syst., 12, e2019MS001975, https://doi.org/10.1029/2019MS001975.

    • Search Google Scholar
    • Export Citation
  • Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS): Unifying tropical cyclone data. Bull. Amer. Meteor. Soc., 91, 363376, https://doi.org/10.1175/2009BAMS2755.1.

    • Search Google Scholar
    • Export Citation
  • Knight, D. B., and R. E. Davis, 2009: Contribution of tropical cyclones to extreme rainfall events in the southeastern United States. J. Geophys. Res., 114, D23102, https://doi.org/10.1029/2009JD012511.

    • Search Google Scholar
    • Export Citation
  • Knutson, T. R., and R. E. Tuleya, 2004: Impact of CO2-induced warming on simulated hurricane intensity and precipitation: Sensitivity to the choice of climate model and convective parameterization. J. Climate, 17, 34773495, https://doi.org/10.1175/1520-0442(2004)017<3477:IOCWOS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2018: An environmentally forced tropical cyclone hazard model. J. Adv. Model. Earth Syst., 10, 223241, https://doi.org/10.1002/2017MS001186.

    • Search Google Scholar
    • Export Citation
  • Lu, P., N. Lin, K. Emanuel, D. Chavas, and J. Smith, 2018: Assessing hurricane rainfall mechanisms using a physics-based model: Hurricanes Isabel (2003) and Irene (2011). J. Atmos. Sci., 75, 23372358, https://doi.org/10.1175/JAS-D-17-0264.1.

    • Search Google Scholar
    • Export Citation
  • Marsooli, R., and N. Lin, 2018: Numerical modeling of historical storm tides and waves and their interactions along the U.S. East and Gulf Coasts. J. Geophys. Res. Oceans, 123, 38443874, https://doi.org/10.1029/2017JC013434.

    • Search Google Scholar
    • Export Citation
  • Marsooli, R., N. Lin, K. Emanuel, and K. Feng, 2019: Climate change exacerbates hurricane flood hazards along US Atlantic and Gulf Coasts in spatially varying patterns. Nat. Commun., 10, 3785, https://doi.org/10.1038/s41467-019-11755-z.

    • Search Google Scholar
    • Export Citation
  • Nadal-Caraballo, N. C., J. A. Melby, V. M. Gonzalez, and A. T. Cox, 2015: Coastal storm hazards from Virginia to Maine. U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-15-5, 221 pp., https://apps.dtic.mil/sti/pdfs/ADA627157.pdf.

  • Nadal-Caraballo, N. C., V. M. Gonzalez, and L. Chouinard, 2019: Storm recurrence rate models for tropical cyclones: Report 1. U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-19-4, 137 pp., https://apps.dtic.mil/sti/pdfs/AD1073835.pdf.

  • Nadal-Caraballo, N. C., M. O. Campbell, V. M. Gonzalez, M. J. Torres, J. A. Melby, and A. A. Taflanidis, 2020: Coastal hazards system: A probabilistic coastal hazard analysis framework. J. Coastal Res., 95, 12111216, https://doi.org/10.2112/SI95-235.1.

    • Search Google Scholar
    • Export Citation
  • Nadal-Caraballo, N. C., and Coauthors, 2022: Coastal Hazards System–Louisiana (CHS-LA). U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-22-16, 189 pp., https://apps.dtic.mil/sti/pdfs/AD1178936.pdf.

  • Powell, M., G. Soukup, S. Cocke, S. Gulati, N. Morisseau-Leroy, S. Hamid, N. Dorst, and L. Axe, 2005: State of Florida hurricane loss projection model: Atmospheric science component. J. Wind Eng. Ind. Aerodyn., 93, 651674, https://doi.org/10.1016/j.jweia.2005.05.008.

    • Search Google Scholar
    • Export Citation
  • Rodriguez-Iturbe, I., A. Porporato, L. Ridolfi, V. Isham, and D. R. Coxi, 1999: Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation. Proc. Roy. Soc. London, A455, 37893805, https://doi.org/10.1098/rspa.1999.0477.

    • Search Google Scholar
    • Export Citation
  • Stansfield, A. M., K. A. Reed, C. M. Zarzycki, P. A. Ullrich, and D. R. Chavas, 2020: Assessing tropical cyclones’ contribution to precipitation over the eastern United States and sensitivity to the variable-resolution domain extent. J. Hydrometeor., 21, 14251445, https://doi.org/10.1175/JHM-D-19-0240.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, E. F., and V. J. Cardone, 1996: Practical modeling of hurricane surface wind fields. J. Waterw. Port Coastal Ocean Eng., 122, 195205, https://doi.org/10.1061/(ASCE)0733-950X(1996)122:4(195).

    • Search Google Scholar
    • Export Citation
  • Toro, G. R., A. W. Niedoroda, C. Reed, and D. Divoky, 2010a: Quadrature-based approach for the efficient evaluation of surge hazard. Ocean Eng., 37, 114124, https://doi.org/10.1016/j.oceaneng.2009.09.005.

    • Search Google Scholar
    • Export Citation
  • Toro, G. R., D. T. Resio, D. Divoky, A. W. Niedoroda, and C. Reed, 2010b: Efficient joint-probability methods for hurricane surge frequency analysis. Ocean Eng., 37, 125134, https://doi.org/10.1016/j.oceaneng.2009.09.004.

    • Search Google Scholar
    • Export Citation
  • Vickery, P. J., 2005: Simple empirical models for estimating the increase in the central pressure of tropical cyclones after landfall along the coastline of the United States. J. Appl. Meteor. Climatol., 44, 18071826, https://doi.org/10.1175/JAM2310.1.

    • Search Google Scholar
    • Export Citation
  • Vickery, P. J., D. Wadhera, L. A. Twisdale Jr., and F. M. Lavelle, 2009: U.S. hurricane wind speed risk and uncertainty. J. Struct. Eng., 135, 301320, https://doi.org/10.1061/(ASCE)0733-9445(2009)135:3(301).

    • Search Google Scholar
    • Export Citation
  • Villarini, G., D. A. Lavers, E. Scoccimarro, M. Zhao, M. F. Wehner, G. A. Vecchi, T. R. Knutson, and K. A. Reed, 2014: Sensitivity of tropical cyclone rainfall to idealized global-scale forcings. J. Climate, 27, 46224641, https://doi.org/10.1175/JCLI-D-13-00780.1.

    • Search Google Scholar
    • Export Citation
  • Wright, D. B., T. R. Knutson, and J. A. Smith, 2015: Regional climate model projections of rainfall from U.S. landfalling tropical cyclones. Climate Dyn., 45, 33653379, https://doi.org/10.1007/s00382-015-2544-y.

    • Search Google Scholar
    • Export Citation
  • Xi, D. and N. Lin, 2022: Investigating the physical drivers for the increasing tropical cyclone rainfall hazard in the United States. Geophys. Res. Lett., 49, e2022GL099196, https://doi.org/10.1029/2022GL099196.

    • Search Google Scholar
    • Export Citation
  • Xi, D., N. Lin, and J. Smith, 2020: Evaluation of a physics-based tropical cyclone rainfall model for risk assessment. J. Hydrometeor., 21, 21972218, https://doi.org/10.1175/JHM-D-20-0035.1.

    • Search Google Scholar
    • Export Citation
  • Xu, H., N. Lin, M. Huang, and W. Lou, 2020: Design tropical cyclone wind speed when considering climate change. J. Struct. Eng., 146, 04020063, https://doi.org/10.1061/(ASCE)ST.1943-541X.0002585.

    • Search Google Scholar
    • Export Citation

Supplementary Materials

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  • Blake, E. S., and D. A. Zelinsky, 2018: National Hurricane Center tropical cyclone report: Hurricane Harvey. NOAA/NWS Rep. AL092017, 45 pp., https://www.nhc.noaa.gov/data/tcr/AL092017_Harvey.pdf.

  • Bregy, J. C., J. T. Maxwell, S. M. Robeson, J. T. Ortegren, P. T. Soulé, and P. A. Knapp, 2020: Spatiotemporal variability of tropical cyclone precipitation using a high-resolution, gridded (0.25° × 0.25°) dataset for the eastern United States, 1948–2015. J. Climate, 33, 18031819, https://doi.org/10.1175/JCLI-D-18-0885.1.

    • Search Google Scholar
    • Export Citation
  • Caldwell, D. R., and W. P. Elliott, 1972: The effect of rainfall on the wind in the surface layer. Bound.-Layer Meteor., 3, 146151, https://doi.org/10.1007/BF02033915.

    • Search Google Scholar
    • Export Citation
  • Cardone, V. J., W. J. Pierson, and E. G. Ward, 1976: Hindcasting the directional spectra of hurricane-generated waves. J. Pet. Technol., 28, 385394, https://doi.org/10.2118/5484-PA.

    • Search Google Scholar
    • Export Citation
  • Chavas, D. R., N. Lin, and K. Emanuel, 2015: A model for the complete radial structure of the tropical cyclone wind field. Part I: Comparison with observed structure. J. Atmos. Sci., 72, 36473662, https://doi.org/10.1175/JAS-D-15-0014.1.

    • Search Google Scholar
    • Export Citation
  • Cox, A. T., B. T. Callahan, M. Ferguson, and M. A. Morrone, 2017: Tropical cyclone wind field analysis for ocean response modeling: Hurricane Harvey (2017). First Int. Workshop on Waves, Storm Surges and Coastal Hazards, Liverpool, United Kingdom, National Oceanography Centre, P14, https://www.oceanweather.com/about/papers/Harvey.pdf.

  • Daly, C., 2006: Guidelines for assessing the suitability of spatial climate data sets. Int. J. Climatol., 26, 707721, https://doi.org/10.1002/joc.1322.

    • Search Google Scholar
    • Export Citation
  • Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140158, https://doi.org/10.1175/1520-0450(1994)033<0140:ASTMFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Daly, C., G. H. Taylor, W. P. Gibson, T. W. Parzybok, G. L. Johnson, and P. A. Pasteris, 2000: High-quality spatial climate data sets for the United States and beyond. Trans. ASAE, 43, 19571962, https://doi.org/10.13031/2013.3101.

    • Search Google Scholar
    • Export Citation
  • Daly, C., W. P. Gibson, G. H. Taylor, G. L. Johnson, and P. Pasteris, 2002: A knowledge-based approach to the statistical mapping of climate. Climate Res., 22, 99113, https://doi.org/10.3354/cr022099.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., 2017: Assessing the present and future probability of Hurricane Harvey’s rainfall. Proc. Natl. Acad. Sci. USA, 114, 12 68112 684, https://doi.org/10.1073/pnas.1716222114.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., R. Sundararajan, and J. Williams, 2008: Hurricanes and global warming: Results from downscaling IPCC AR4 simulations. Bull. Amer. Meteor. Soc., 89, 347368, https://doi.org/10.1175/BAMS-89-3-347.

    • Search Google Scholar
    • Export Citation
  • Esau, I. N., 2004: Parameterization of a surface drag coefficient in conventionally neutral planetary boundary layer. Ann. Geophys., 22, 33533362, https://doi.org/10.5194/angeo-22-3353-2004.

    • Search Google Scholar
    • Export Citation
  • Feldmann, M., K. Emanuel, L. Zhu, and U. Lohmann, 2019: Estimation of Atlantic tropical cyclone rainfall frequency in the United States. J. Appl. Meteor. Climatol., 58, 18531866, https://doi.org/10.1175/JAMC-D-19-0011.1.

    • Search Google Scholar
    • Export Citation
  • Gori, A., N. Lin, D. Xi, and K. Emanuel, 2022: Tropical cyclone climatology change greatly exacerbates US extreme rainfall–surge hazard. Nat. Climate Change, 12, 171178, https://doi.org/10.1038/s41558-021-01272-7.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Jiang, H., and E. J. Zipser, 2010: Contribution of tropical cyclones to the global precipitation from eight seasons of TRMM data: Regional, seasonal, and interannual variations. J. Climate, 23, 15261543, https://doi.org/10.1175/2009JCLI3303.1.

    • Search Google Scholar
    • Export Citation
  • Jing, R., and N. Lin, 2020: An environment‐dependent probabilistic tropical cyclone model. J. Adv. Model. Earth Syst., 12, e2019MS001975, https://doi.org/10.1029/2019MS001975.

    • Search Google Scholar
    • Export Citation
  • Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS): Unifying tropical cyclone data. Bull. Amer. Meteor. Soc., 91, 363376, https://doi.org/10.1175/2009BAMS2755.1.

    • Search Google Scholar
    • Export Citation
  • Knight, D. B., and R. E. Davis, 2009: Contribution of tropical cyclones to extreme rainfall events in the southeastern United States. J. Geophys. Res., 114, D23102, https://doi.org/10.1029/2009JD012511.

    • Search Google Scholar
    • Export Citation
  • Knutson, T. R., and R. E. Tuleya, 2004: Impact of CO2-induced warming on simulated hurricane intensity and precipitation: Sensitivity to the choice of climate model and convective parameterization. J. Climate, 17, 34773495, https://doi.org/10.1175/1520-0442(2004)017<3477:IOCWOS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2018: An environmentally forced tropical cyclone hazard model. J. Adv. Model. Earth Syst., 10, 223241, https://doi.org/10.1002/2017MS001186.

    • Search Google Scholar
    • Export Citation
  • Lu, P., N. Lin, K. Emanuel, D. Chavas, and J. Smith, 2018: Assessing hurricane rainfall mechanisms using a physics-based model: Hurricanes Isabel (2003) and Irene (2011). J. Atmos. Sci., 75, 23372358, https://doi.org/10.1175/JAS-D-17-0264.1.

    • Search Google Scholar
    • Export Citation
  • Marsooli, R., and N. Lin, 2018: Numerical modeling of historical storm tides and waves and their interactions along the U.S. East and Gulf Coasts. J. Geophys. Res. Oceans, 123, 38443874, https://doi.org/10.1029/2017JC013434.

    • Search Google Scholar
    • Export Citation
  • Marsooli, R., N. Lin, K. Emanuel, and K. Feng, 2019: Climate change exacerbates hurricane flood hazards along US Atlantic and Gulf Coasts in spatially varying patterns. Nat. Commun., 10, 3785, https://doi.org/10.1038/s41467-019-11755-z.

    • Search Google Scholar
    • Export Citation
  • Nadal-Caraballo, N. C., J. A. Melby, V. M. Gonzalez, and A. T. Cox, 2015: Coastal storm hazards from Virginia to Maine. U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-15-5, 221 pp., https://apps.dtic.mil/sti/pdfs/ADA627157.pdf.

  • Nadal-Caraballo, N. C., V. M. Gonzalez, and L. Chouinard, 2019: Storm recurrence rate models for tropical cyclones: Report 1. U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-19-4, 137 pp., https://apps.dtic.mil/sti/pdfs/AD1073835.pdf.

  • Nadal-Caraballo, N. C., M. O. Campbell, V. M. Gonzalez, M. J. Torres, J. A. Melby, and A. A. Taflanidis, 2020: Coastal hazards system: A probabilistic coastal hazard analysis framework. J. Coastal Res., 95, 12111216, https://doi.org/10.2112/SI95-235.1.

    • Search Google Scholar
    • Export Citation
  • Nadal-Caraballo, N. C., and Coauthors, 2022: Coastal Hazards System–Louisiana (CHS-LA). U.S. Army Engineer Research and Development Center Tech. Rep. ERDC/CHL TR-22-16, 189 pp., https://apps.dtic.mil/sti/pdfs/AD1178936.pdf.

  • Powell, M., G. Soukup, S. Cocke, S. Gulati, N. Morisseau-Leroy, S. Hamid, N. Dorst, and L. Axe, 2005: State of Florida hurricane loss projection model: Atmospheric science component. J. Wind Eng. Ind. Aerodyn., 93, 651674, https://doi.org/10.1016/j.jweia.2005.05.008.

    • Search Google Scholar
    • Export Citation
  • Rodriguez-Iturbe, I., A. Porporato, L. Ridolfi, V. Isham, and D. R. Coxi, 1999: Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation. Proc. Roy. Soc. London, A455, 37893805, https://doi.org/10.1098/rspa.1999.0477.

    • Search Google Scholar
    • Export Citation
  • Stansfield, A. M., K. A. Reed, C. M. Zarzycki, P. A. Ullrich, and D. R. Chavas, 2020: Assessing tropical cyclones’ contribution to precipitation over the eastern United States and sensitivity to the variable-resolution domain extent. J. Hydrometeor., 21, 14251445, https://doi.org/10.1175/JHM-D-19-0240.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, E. F., and V. J. Cardone, 1996: Practical modeling of hurricane surface wind fields. J. Waterw. Port Coastal Ocean Eng., 122, 195205, https://doi.org/10.1061/(ASCE)0733-950X(1996)122:4(195).

    • Search Google Scholar
    • Export Citation
  • Toro, G. R., A. W. Niedoroda, C. Reed, and D. Divoky, 2010a: Quadrature-based approach for the efficient evaluation of surge hazard. Ocean Eng., 37, 114124, https://doi.org/10.1016/j.oceaneng.2009.09.005.

    • Search Google Scholar
    • Export Citation
  • Toro, G. R., D. T. Resio, D. Divoky, A. W. Niedoroda, and C. Reed, 2010b: Efficient joint-probability methods for hurricane surge frequency analysis. Ocean Eng., 37, 125134, https://doi.org/10.1016/j.oceaneng.2009.09.004.

    • Search Google Scholar
    • Export Citation
  • Vickery, P. J., 2005: Simple empirical models for estimating the increase in the central pressure of tropical cyclones after landfall along the coastline of the United States. J. Appl. Meteor. Climatol., 44, 18071826, https://doi.org/10.1175/JAM2310.1.

    • Search Google Scholar
    • Export Citation
  • Vickery, P. J., D. Wadhera, L. A. Twisdale Jr., and F. M. Lavelle, 2009: U.S. hurricane wind speed risk and uncertainty. J. Struct. Eng., 135, 301320, https://doi.org/10.1061/(ASCE)0733-9445(2009)135:3(301).

    • Search Google Scholar
    • Export Citation
  • Villarini, G., D. A. Lavers, E. Scoccimarro, M. Zhao, M. F. Wehner, G. A. Vecchi, T. R. Knutson, and K. A. Reed, 2014: Sensitivity of tropical cyclone rainfall to idealized global-scale forcings. J. Climate, 27, 46224641, https://doi.org/10.1175/JCLI-D-13-00780.1.

    • Search Google Scholar
    • Export Citation
  • Wright, D. B., T. R. Knutson, and J. A. Smith, 2015: Regional climate model projections of rainfall from U.S. landfalling tropical cyclones. Climate Dyn., 45, 33653379, https://doi.org/10.1007/s00382-015-2544-y.

    • Search Google Scholar
    • Export Citation
  • Xi, D. and N. Lin, 2022: Investigating the physical drivers for the increasing tropical cyclone rainfall hazard in the United States. Geophys. Res. Lett., 49, e2022GL099196, https://doi.org/10.1029/2022GL099196.

    • Search Google Scholar
    • Export Citation
  • Xi, D., N. Lin, and J. Smith, 2020: Evaluation of a physics-based tropical cyclone rainfall model for risk assessment. J. Hydrometeor., 21, 21972218, https://doi.org/10.1175/JHM-D-20-0035.1.

    • Search Google Scholar
    • Export Citation
  • Xu, H., N. Lin, M. Huang, and W. Lou, 2020: Design tropical cyclone wind speed when considering climate change. J. Struct. Eng., 146, 04020063, https://doi.org/10.1061/(ASCE)ST.1943-541X.0002585.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Synthetic tracks generated for this study: (a) Texas, (b) Louisiana, (c) South Atlantic, and (d) North Atantic.

  • Fig. 2.

    Locations of the nine points of interest for evaluation.

  • Fig. 3.

    Correlation between POT and TCR-simulated event total rainfall (before bias correction) in nine selected points of interest. The dashed black lines are the ETR-is-equal-to-POT lines.

  • Fig. 4.

    Exceedance probability of event total rainfall in observation (black dots), IBTrACS-TCR simulations (green dots), and bias-corrected IBTrACS-TCR simulations (purple line), for selected points of interest. The number of storms in the analysis is shown in the title of each figure.

  • Fig. 5.

    Spatial pattern of bias-correction factors in the continental United States: (a) mean multiplicative bias-correction parameter, (b) mean additive bias-correction parameter, (c) relationship between mean multiplicative bias-correction parameter and the distance to coast, and (d) relationship between mean additive bias-correction parameter and the distance to coast.

  • Fig. 6.

    Evaluation of the POT–ETR relationship after resampling for the nine selected points of interest. Black dots are observation, red dots are synthetic storms after resampling, the black dashed line is the fitted relationship between POT and ETR in the observation, and the red dashed line is the fitted relationship between POT and ETR in the synthetic datasets after resampling.

  • Fig. 7.

    Return-period estimation of TC rainfall hazard (represented by ETR) for the nine selected point of interest. Red dots are estimated ETR return period from resampled synthetic storms, black dots are estimated ETR return period from the observation, purple dots are estimated ETR return period using the three-parameter joint probability method, the red curve is the GPD fitted by ETR simulated by synthetic storms, and the blue curve is the estimated ETR return period from IBTrACS-TCR simulation (after bias correction). The λ in the title shows the annual occurrence rate of TCs in the selected location.

  • Fig. 8.

    Exceedance probability of ETR from gauge observation (black dots), TCR simulation on historical TCs (after bias correction; blue line), and that simulated by synthetic storm-TCR coupled model (red dots). The black dashed lines are the confidence intervals of 0.05 significant level for the observation. All TCs that enter the 300-km circle centered on the milepost of interest are included in the estimation.

  • Fig. 9.

    (a) Milepost locations following Jing and Lin (2020). (b) The 10- (blue), 50- (green), and 100-yr (red) return levels of ETR at coastal mileposts.

  • Fig. 10.

    Idealized statistical testing of the resampling method: (a),(d),(g) Relationship between POT and ETR in mock observation and mock synthetic storm dataset. Black and blue lines are linear regressions between ETR and POT in mock observation and mock synthetic storms, respectively. (b),(e),(f) Relationship between POT and ETR in mock synthetic dataset after resampling. (c),(f),(i) Exceedance probability of ETR in mock observation (black dots), resampled mock synthetic storms (blue dots), and extended mock observations (green dots). The first row corresponds to the test in which the synthetic storms have lower ETR given the same POT relative to observations. The second row corresponds to the test in which the synthetic storms have higher ETR given the same POT relative to observations. The third row corresponds to the test in which the synthetic storms have a similar ETR given the same POT in comparison with observations.

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