Tropical Cyclone Compound Flood Hazard Assessment: From Investigating Drivers to Quantifying Extreme Water Levels

Abstract

Compound flooding, characterized by the co‐occurrence of multiple flood mechanisms, is a major threat to coastlines across the globe. Tropical cyclones (TCs) are responsible for many compound floods due to their storm surge and intense rainfall. Previous efforts to quantify compound flood hazard have typically adopted statistical approaches that may be unable to fully capture spatio‐temporal dynamics between rainfall‐runoff and storm surge, which ultimately impact total water levels. In contrast, we pose a physics‐driven approach that utilizes a large set of realistic TC events and a simplified physics‐based rainfall model and simulates each event within a hydrodynamic model framework. We apply our approach to investigate TC flooding in the Cape Fear River, NC. We find TC approach angle, forward speed, and intensity are relevant for compound flood potential, but rainfall rate and time lag between the centroid of rainfall and peak storm tide are the strongest predictors of compounding magnitude. Neglecting rainfall underestimates 100‐year flood depths across 28% of the floodplain, and taking the maximum of each hazard modeled separately still underestimates 16% of the floodplain. We find the main stem of the river is surge‐dominated, upstream portions of small streams and pluvial areas are rainfall dominated, but midstream portions of streams are compounding zones, and areas close to the coastline are surge dominated for lower return periods but compounding zones for high return periods (100 years). Our method links joint rainfall‐surge occurrence to actual flood impacts and demonstrates how compound flooding is distributed across coastal catchments.

1 Introduction

Tropical cyclones (TCs) are some of the costliest natural hazards worldwide (Klotzbach et al., 2018; Peduzzi et al., 2012), due to their wind‐driven storm surge and extreme rainfall, which can result in widespread coastal flooding. Although traditional coastal risk assessment approaches have solely considered storm surge (Moftakhari et al., 2019), recent events such as Hurricanes Harvey (2017) and Florence (2018) have raised awareness about the threat from TC rainfall. The co‐occurrence or consecutive occurrence in space and/or time of storm surge and rainfall can result in compound flooding, whereby the interaction of the two flood mechanisms increases the overall hazard (Santiago‐Collazo et al., 2019; Zscheischler et al., 2018). Recent research has demonstrated that the threat of compound flood events has risen across the United States (Wahl et al., 2015) and can significantly impact coastal flood risk across the globe (Couasnon et al., 2019; Ward et al., 2018). Furthermore, projections of future climate change suggest widespread increases in storm surge hazard (Lin et al., 2012; Marsooli et al., 2019), extreme rainfall hazard (Emanuel, 2017; Knutson et al., 2010), and the occurrence of compound flood events (Bevacqua et al., 2019). TCs are often identified as one of the primary drivers of observed compound flood events (Orton et al., 2018; Wu et al., 2018) and may be a significant contributor to future compound flood hazards. Thus, to accurately quantify and characterize compound flood risk, it is crucial to understand the dynamics of rainfall and storm surge during TC events.

Research efforts related to compound flooding have typically focused on either characterizing the statistical dependence between rainfall (or river flows) and storm surge (Cao et al., 2020; Couasnon et al., 2019; Hendry et al., 2019; Moftakhari et al., 2017; Ward et al., 2018; Wu et al., 2018; Zheng et al., 2014) or utilizing physics‐based models to investigate their compounding impacts on flood depths and extents (Bacopoulos et al., 2017; Herdman et al., 2018; Kumbier et al., 2018; Ray et al., 2011; Silva‐Araya et al., 2018; Torres et al., 2015). Recent work has also sought to delineate transition zones in coastal regions, where the influence of both rainfall and storm surge are important in driving total water levels (Bilskie & Hagen, 2018; Shen et al., 2019). Although numerous modeling studies have quantified interactions between rainfall‐runoff/river flows and storm surge through historical event reconstruction or synthetic scenarios, there has been considerably less work on quantifying compound flood hazard in terms of return periods of flood heights or inundation depths.

The majority of compound flood hazard studies have adopted an approach that statistically derives correlation structures between flood drivers based on observed data and then samples the joint probability distribution to develop scenarios that can be hydrodynamically modeled to produce curves/maps of flood return levels (Couasnon et al., 2018; Lian et al., 2013; Moftakhari et al., 2019; Van Den Hurk et al., 2015; Zellou & Rahali, 2019). For example, Moftakhari et al. (2019) utilized a bivariate copula to develop joint return period curves for stream flow and ocean water level for Newport Bay, CA. Compound flood heights were generated by considering specific scenarios, such as an “AND” scenario where both stream flow and ocean water level are extreme, or an “OR” scenario where at least one of the variables is extreme. Approaches that sample joint stream flow and ocean water levels to drive the estimation of compound flood hazard are limited in several ways. Since they typically rely on observed data (Couasnon et al., 2018; Moftakhari et al., 2019; Zellou & Rahali, 2019), they may not be able to accurately characterize TC‐driven compound flooding due to limited historical TC occurrences. Additionally, the timing dynamics between rainfall‐runoff and storm tides are not well captured: Peak flows are either assumed to occur at the same time as peak water levels, or a range of possible time lags are modeled (Moftakhari et al., 2019). The spatial distribution of storm tides and rainfall fields are also not captured by simplified statistical approaches that rely on point estimates of each hazard from stream/tide gauges. Previous work has demonstrated that the specific spatial patterns of TC rainfall can have significant impacts on compound water levels (Gori et al., 2020), and neglecting the spatial component could misrepresent the magnitude and location of compound impacts.

An alternate approach to quantifying compound flood hazard is achieved by first modeling the physical interactions of multiple flood drivers for a large number of synthetic but realistic storm events, and then statistically deriving return period curves or flood maps based on the modeled inundation depths. Few studies have adopted this approach for compound flood hazard estimation (Bass & Bedient, 2018; Orton et al., 2018), although it has been widely used to assess storm surge threat (Aerts et al., 2014; Li et al., 2018; Lin et al., 2010, 2012; Lin & Shullman, 2017; Marsooli et al., 2019). A study by Orton et al. (2018) developed synthetic TC tracks using a statistical model and estimated corresponding stream flow peak, hydrograph shape, and the time lag in the Hudson River catchment by statistically linking these parameters with TC characteristics. Then the interaction of stream flow and storm tide was modeled within a 3‐D hydrodynamic model for each synthetic storm event. This method can indirectly capture some of the spatio‐temporal dynamics associated with TC rainfall‐runoff and storm tide. Still, direct consideration of TC rainfall within numerical models remains a challenge in compound hazard assessment (Santiago‐Collazo et al., 2019).

This study poses a physics‐based method for conducting compound flood hazard assessment that explicitly models storm tides, rainfall‐runoff, and their compounding during landfalling TCs. We utilize a large number of synthetic TC tracks and simulate their rainfall fields using a simplified physics‐based model that takes into account main convective rainfall mechanisms. Synthetic tracks and rainfall fields are used as forcing in a one‐way coupled hydrodynamic modeling framework to simulate the interaction of storm tides and rainfall‐runoff in a tidal estuary. By modeling rainfall and storm tides from each of a large number of synthetic storm events, we seek to understand which types of TCs produce significant compound flooding, how rainfall hazard and storm tide hazard vary separately and jointly, and we ultimately produce probabilistic compound flood hazard maps and flood height return period curves. We apply this hazard assessment method to the Cape Fear River Estuary (CFRE) along the coast of North Carolina, USA.

2 Methods

2.1 Study Area

The Cape Fear River has its headwaters in northern North Carolina and flows southeast until it becomes a tidally influenced estuary near the coast (Figure 1a). Although the entire drainage basin encompasses more than 23,500 km² and the river stretches over 322 km, tides only propagate 100 km upstream from the mouth of the river (Famikhalili & Talke, 2016). The river flows draining the upstream portion of the Cape Fear River are unlikely to contribute to compound flooding during TC events, since upstream flows are typically lagged significantly compared to the time of peak storm tide. The primary threat of compound flooding in this area results from the interaction of intense eyewall precipitation and storm tides near the coast. However, previous work has shown that outer TC rain bands falling several hours before landfall can result in high river flows in the midstream portion of the river, which can interact with upward propagating storm tides (Gori et al., 2020). High‐resolution modeling is conducted for the portion of the catchment extending from the mouth of the river to 40 km upstream (Figure 1b), while river flows from a larger portion of the basin are captured using an empirical river model (Figure 1a).

1 Figure. (a) location of Cape Fear drainage basin (light gray), HEC‐HMS domain (medium gray), and HEC‐RAS domain (black), and (b) diagram of inundation model set up with storm tide and river boundary conditions. LiDAR elevation is relative to NAVD88 and taken from USACE's 2017 topobathy data set.

2.2 Synthetic TC Track and Rainfall Models

We apply a set of synthetic tracks generated from a statistical‐deterministic TC model that was developed in Emanuel et al. (2006). Vortices are randomly seeded according to historical genesis locations and moved according to synthetically generated environmental winds. The maximum wind speed (V_max) and radius to maximum winds (R_max) are estimated at each time step using the deterministic Coupled Hurricane Intensity Prediction System (CHIPS), which is an axisymmetric hurricane model coupled to a simplified ocean model (Emanuel et al., 2004). Synthetic tracks generated through this method have been shown to accurately reproduce observed TC statistics (Emanuel et al., 2006) and have been widely used to assess storm surge hazard (Lin et al., 2012; Lin & Shullman, 2017; Marsooli et al., 2019). Using this TC model, Marsooli et al. (2019) generated a large set of synthetic tracks across the North Atlantic basin (5,018 for the current climate) to conduct storm tide hazard assessment. We utilize a subset of these tracks for our present analysis; we select all tracks passing within 200 km of the CFRE, which results in 941 events.

Rainfall fields associated with each synthetic track are generated using the TC Rainfall (TCR) model developed by Emanuel et al. (2008). TCR is a horizontally distributed and vertically integrated model that relates precipitation rate to upward vapor flux. Vertical velocity is estimated based on a surface friction component, simplified topographic component, vortex‐stretching component, and a baroclinic component. A full description of the model formulation is detailed in Lu et al. (2018). Numerous parametric TC precipitation models have been proposed in the literature, and popular models such as R‐CLIPER (Lonfat et al., 2007) and IPET (U.S. Army Corps of Engineers, 2009) have relied on empirical relationships between rain rates and TC parameters derived from observed data. Recent work has demonstrated that these empirical models are not able to accurately reproduce spatio‐temporal patterns of TC rainfall and consequently may not be suitable for use in flood assessment (Brackins & Kalyanapu, 2020). In contrast, TCR has been shown to satisfactorily reproduce TC rainfall climatology (Zhu et al., 2013), as well as spatial patterns of rainfall totals and modeled flood peaks for TC events (Lu et al., 2018). Recent work has validated TCR using observed TC events across the U.S. Gulf and Atlantic coasts (Xi et al., 2020). Although TCR has been shown to perform well, the model does not explicitly simulate outer rain band precipitation, which results from stratified clouds that develop raindrops via complicated microphysical processes and are beyond the ability of simplified physics to capture. However, Xi et al. (2020) showed that TCR is still able to predict rainfall for locations far from the TC center, and the magnitudes are approximately correct compared to the statistics of historical observations. With awareness of the uncertainty of rainfall estimates far from the TC center, the model is a useful tool for use in risk assessment due to its ability to accurately represent rainfall return periods and rainfall accumulations. In this study, we further evaluate the performance of TCR in reproducing patterns of rainfall as well as maximum inundation depths for several historical TCs impacting the study area.

2.3 Hydrodynamic Modeling

Our floodplain modeling approach utilizes a one‐way coupled framework across three models, whereby models exchange information through inputs/outputs, but each model is run independently (Santiago‐Collazo et al., 2019). Storm tides at the coastline are simulated within a basin‐scale hydrodynamic model: The ADvanced CIRCulation (ADCIRC) model (Luettich et al., 1992; Westerink et al., 1992) that covers the entire U.S. Atlantic and Gulf coasts (Marsooli & Lin, 2018). The ADCIRC formulation adopted here employs the 2‐D depth‐integrated shallow water equations. The ADCIRC mesh terminates at the coastline and has resolution varying from >50 km in the deep ocean to ~1 km near the coast. Astronomical tide is simulated using eight tidal constituents, and TC pressure and wind fields are represented using physics‐based parametric equations. Full details of the ADCIRC mesh, tidal forcing, and wind/pressure fields are detailed in Marsooli and Lin (2018). Wave forcing is not considered in this analysis due to the computational expense of coupling ADCIRC with the wave model SWAN, and previous coastal flood hazard studies have typically neglected the contributions of wave forcing (Lin et al., 2012; Marsooli et al., 2019). Previous work has also shown wave setup to be relatively small at the study area (Marsooli & Lin, 2018), suggesting that storm tides can be reasonably estimated by using surge plus astronomical tide forcing alone. Each synthetic event is simulated within ADCIRC starting when the TC enters within 800 km of the coastline and ending when the TC moves more than 300 km inland from the coast.

River flows from the greater Cape Fear River (i.e., the region outside the coastal study area) are estimated using the Hydrologic Modeling System (HEC‐HMS), which is an empirical rainfall‐runoff model developed by the U.S. Army Corps of Engineers (HEC, 2010). HEC‐HMS utilizes the Soil Conservation Society (SCS) dimensionless hydrograph approach (Soil Conservation Service, 1972) for estimating basin runoff and the Green and Ampt equation (Green & Ampt, 1911) for simulating infiltration. Full details of the HEC‐HMS model set up and data sources are documented in Gori et al. (2020). The HEC‐HMS model covers the midstream portion of the drainage area (dark gray in Figure 1a), while flows from the upper catchment (light gray in Figure 1a) are set as the average monthly baseflow recorded by three USGS stream gauges. The upper contributions are fixed as the baseflow across each simulation since accounting for the river baseflow is important for accurately estimating total flow, but additional rainfall‐runoff generated in the upper drainage basin during each storm event would be lagged significantly after the time of peak storm tide and thus would not contribute to overall maximum water elevations in the coastal zone.

Water elevation time series are extracted from ADCIRC along the coastline at points spaced roughly 500 m apart. At each time step, interpolated water levels from the coastline points serve as boundary conditions for a high‐resolution inundation model. Storm tides are propagated across the coastal plain and upward through the Cape Fear River within a coupled 1‐D/2‐D HEC‐RAS model (HEC, 2016), where the main Cape Fear River is modeled using 1‐D cross sections and the coastal plain is modeled using 60 m rectangular cells. River flows from HEC‐HMS serve as an upstream boundary condition for the river portion (1‐D component) of the HEC‐RAS model, and the TCR fields are applied directly to the 2‐D HEC‐RAS grid after subtracting infiltration according to Green and Ampt (1911). The inundation model set up is illustrated in Figure 1b, and full details of the loosely coupled framework are presented in Gori et al. (2020), where the framework was validated against National Oceanic and Atmospheric Administration (NOAA) tidal gauges and USGS high water marks for six historical TC events. For each synthetic event modeled here, the simulation time starts 12 hr before rainfall begins or 24 hr before peak storm tide (whichever is earlier) and ends 12 hr after the end of rainfall or 24 hr after peak storm tide (whichever is later). These restrictions are implemented to increase computational efficiency by minimizing simulation time.

To compare compound flood maps with flood maps that consider solely rainfall‐runoff or storm surge, we model the following scenarios for each synthetic event: surge + astronomical tide (storm tide), rainfall + astronomical tide (rainfall + tide), and rainfall + surge + astronomical tide (rainfall + storm tide). For the scenarios that include rainfall forcing, this includes rainfall over both the downstream (HEC‐RAS domain) and midstream (HEC‐HMS domain) portions of the drainage basin. For the scenario that solely considers storm tide, the upstream river flow is simply set as the monthly average baseflow. Maximum water elevations across the study area are extracted for each synthetic event and each of the hazard scenarios.

2.4 Compound Flood Hazard Assessment

We investigate the marginal and joint distributions of TC rainfall and storm tides. Since we employ a relatively large set of events, the marginal distribution of each flood driver is represented using smoothed estimates of the empirical distribution (rather than fitting a theoretical distribution). The joint distribution of area‐averaged peak storm tide (S) and area‐averaged peak rainfall intensity (R) is estimated using a bivariate copula. According to Sklar's Theorem (Sklar, 1959), there exists a unique bivariate copula C_S,R that generates the joint cumulative distribution function (CDF) F_S,R given the continuous marginal CDFs F_S and F_R. Copulas have been widely implemented to assess compound flood hazard between storm tides and rainfall (Sebastian et al., 2017; Wahl et al., 2015; Xu et al., 2018; Zellou & Rahali, 2019). Rather than fitting a parametric copula to the synthetic data, we simply represent the copula structure using a non‐parametric kernel density estimate. We choose this approach because the upper tail behavior of the data is significantly different compared to the rest of the distribution, and fitting a parametric copula to the entire data set could bias the tail estimate.

After constructing the marginal and joint distributions of rainfall and storm tide, we compute marginal and joint return period curves by modeling TC occurrence as a Poisson process with arrival rate λ per year. TC arrival rate λ is estimated by the TC model and is equal to 0.63 events per year for the study area. Assuming a Poisson structure, the return period (T) is related to the hazard exceedance probability (P_T) as follows: [Image Omitted. See PDF]

For univariate return periods, P_T is simply equal to P(X_≥x_T), where X is the value of any single hazard (rainfall or storm tide), and x_T is the T‐year hazard magnitude. For each return period T, Equation 1 can be solved to find the corresponding T‐year storm tide (s_T) or rainfall (r_T). Joint return period curves may be defined by considering two scenarios (Salvadori et al., 2016): (1) both rainfall and storm tide exceed a certain quantile (the “AND” scenario; P_T = P(S_≥s_T, R_≥r_T)) or (2) at least one hazard exceeds a certain quantile (the “OR” scenario; P_T = P(S_≥s_T or R_≥r_T)). As it is bivariate, each T‐year return period corresponds to a contour line of possible storm tide and rainfall combinations that all have the same P_T. Given that P_T is related to the marginal and joint CDFs, for each return period T, Equation 1 can be solved to find the corresponding combinations of T‐year storm tide (s_T) and rainfall (r_T).

After examining the distribution of the flood drivers, the distribution of maximum water levels is analyzed. For each grid cell in the high‐resolution model domain, the empirical distribution of maximum water levels is estimated based on the modeled depths of each synthetic event. The T‐year water level is computed according to Equation 1 to produce 50‐, 100‐, and 250‐year flood maps. At selected locations, full return period curves are calculated to show how different TC hazards can dominate for varying ranges of flood return periods.

3 Results

3.1 TCR Model Validation

TCR is evaluated by comparing simulated rainfall fields with radar rainfall observations for three historical TCs: Fran (1996), Floyd (1999), and Matthew (2016). Also, each TC is modeled within HEC‐RAS using TCR forcing compared to using radar rainfall forcing. Comparisons of area‐averaged time series of rainfall rates and maximum inundation depths across the study domain are shown in Supporting Information S1. In general, TCR can reproduce the evolution and magnitude of rainfall. TCR predicts the time of peak rainfall to occur 4–5 hr later than the observed peak for both Fran (1996) and Matthew (2016) but accurately predicts the time of peak rainfall for Floyd (1999). Additionally, Floyd (1999) displayed significant antecedent rainfall before its peak eyewall precipitation, and the TCR model did not capture this antecedent rainfall. Based on the three events, TCR struggles to predict the exact time of peak rainfall but can capture the temporal evolution of each rain event. Additionally, the absolute average inundation depth difference across all storms between TCR forcing and radar rainfall forcing is only 0.05 m and over 92% of the model domain is estimated within 0.2 m by TCR forcing. Maps showing the depth differences between TCR and radar rainfall for each event are depicted in Supporting Information Figure S2.

3.2 Rainfall and Storm Tide Marginal and Joint Distributions

Analyzing rainfall and storm tide hazard distributions as well as their dependence structure can provide insight about the likelihood of observing compound flooding in the study area. Figures 2a–2c depict extreme storm tides along the coastline for 50–250 year return periods, and Figures 2d–2f similarly depict 50‐ to 250‐year rainfall intensity (mm/hr) across the study area. The storm tide distribution looks spatially homogenous for lower return periods (50‐year) but displays increasing heterogeneity with increasing hazard severity. This is likely due to a shift in the distribution of approach angle for high‐intensity storms compared to the total storm set or differences in the frequency of landfall location for extreme events. In contrast, the spatial pattern of rainfall intensity looks similar across all return periods, displaying a band of high‐intensity rainfall that follows the shape of the coastline. The rainfall pattern is expected, since the abrupt change in ground friction associated with moving from ocean to land typically results in increased rainfall (Liu et al., 2018). These return period maps illustrate how each hazard varies spatially across the study domain; however, the marginal distributions do not yield insights about the extent to which these hazards co‐occur.

2 Figure. Extreme storm tides along the coastline for (a) 50‐, (b) 100‐, and (c) 250‐year levels, and peak rainfall intensity across the greater CFRE region for (d) 50‐, (e) 100‐, and (f) 250‐year levels. The white box in (d)–(f) indicates the geographic extent shown in (a)–(c).

Figures 3a and 3c depict marginal return period curves for (a) peak storm tide averaged across the coastline and (c) peak rainfall intensity averaged over the study area. The marginal 100‐year peak storm tide is roughly 1.75 m and peak rainfall intensity is 16.5 mm/hr. Figure 3b depicts the joint cumulative probability distribution of peak storm tide and rainfall (shaded from blue to yellow) with each synthetic storm event plotted as a black dot. The green contour lines correspond to the “AND” return period scenario while red contours correspond to the “OR” scenario. By examining the scatter plot of synthetic storms, it appears that storm tide and rainfall are less correlated for non‐extreme values but become increasingly correlated with increasing hazard magnitude. The tail dependence, which quantifies the extent to which two variables are dependent in their upper limit (Coles et al., 2000) is calculated to be 0.48 at the 10% level. This means that if one hazard exceeds its 90th percentile, there is a 48% chance that the other hazard also exceeds its 90th percentile. Significant upper tail dependence implies that compounding impacts may be higher for severe events compared to lower magnitude storms.

3 Figure. (a) Marginal peak storm tide return period curve. (b) Joint empirical cumulative distribution (shaded blue to yellow) with “AND” (green) and “OR” (red) return period contours. Black dots show storm events. (c) Marginal max rainfall intensity return period curve.

As expected, the “AND” return period contours contain lower values of rainfall and storm tide compared to the “OR” contours. The rainfall and storm tide values along the 100‐year “AND” contour are lower than the marginal 100‐year values (although the contour converges to the marginal values at its edges). Conversely, values on the 100‐year “OR” contour are generally higher than the marginal 100‐year values (again converging to the marginal values at the edges of the contour). Previous work has suggested utilizing the point on each return period isoline with the highest joint probability density to represent a “most likely” multi‐hazard scenario for a given exceedance probability (Moftakhari et al., 2019; Salvadori et al., 2014). Adopting this criterion, the most likely 100‐year “OR” scenario corresponds to a peak storm tide of 1.97 m and/or a peak rainfall intensity of 18.4 mm/hr. These joint estimates are higher than the marginal estimates because the “OR” condition takes into account that high‐intensity rainfall can occur both in the absence of high storm tide as well as co‐occurring with high storm tide (and similarly with the storm tide probability).

3.3 Analyzing Characteristics of Compounding Events

To understand which types of TC events are capable of inducing significant compound impacts, we investigate the characteristics of storms that produce large storm tide, intense rainfall, or significant compounding. We define top rainfall events as the top 10% of storms producing highest total rainfall across the study area, and top storm tide events as the top 10% of storms producing highest storm tides averaged over the study area. To quantify the magnitude of compounding for each storm event, here we consider the area (in km²) where the combination of rainfall and storm tides increases total water levels by at least 0.2 m compared to the maximum of the two hazards modeled separately (referred to as the “max scenario”) and call this the compounding area (A_C). Top compound events are defined as the top 10% of storms that result in the largest A_C.

Figure 4 shows distributions of top rainfall (green), storm tide (blue), and compound (pink) events, and the distribution of the total storm set (purple) for TC characteristics of (a) approach angle, (b) forward speed, (c) maximum wind speed (V_max), and (d) radius of maximum wind (R_max), at landfall or time of passing closest to the study area. The distributions of V_max for rain, storm tide, and compound events look similar and are shifted to high values compared to that of the total population. We expect this behavior since storm intensity is a significant predictor of inner core TC rainfall and is also correlated with the peak storm tide. Consistently, the top events in each category tend to have smaller R_max values compared to the total population (Figure 4d), as intense storms tend to have smaller R_max. However, the distribution of the top storm tide events is wider since large (and possibly less intense) storms can also produce high storm tides (Irish et al., 2008). It is important to note that the distribution of R_max values for top rainfall and compound events presented here indicates that high rainfall is associated with small R_max values. This is because smaller, more intense storms typically produce higher eyewall precipitation, which is the rainfall mechanism simulated by TCR. However, real storms can also produce intense outer rain bands, which are not accounted for here, and storms with a large R_max could still produce intense rainfall via outer rain bands even if they produce moderate eyewall rainfall.

4 Figure. Distributions for top rainfall (green), top storm tide (blue), top compound (pink), and total population (purple) for (a) approach angle, (b) forward speed, (c) max wind speed, (d) and radius to max wind at the time of landfall or nearest approach to study area.

The distribution of approach angles illustrates that top rainfall, storm tide, and compound events tend to make landfall differently compared to the total storm population. All of the top events display a bimodal distribution of approach angles, where the first peak (~−40° for top compound and rain events and ~−20° for top storm tide) corresponds to an angle slightly offset from parallel with the coastline, and the second peak (~70° for top compound and rain events and ~80 for top storm tide) corresponds to an approach almost perpendicular to the coastline. The first peak may produce high storm tides by pushing water along the coastline and toward the mouth of the Cape Fear River. Additionally, since there are a larger number of total storms with an approach angle of −20° to −40°, there is a higher chance to observe events with both high storm tide and high rainfall. Storms approaching along the second angle may have higher intensities overall that generate high storm tides and intense eyewall precipitation. The top rainfall events are more likely to occur along the second peak, indicating that storms approaching from the open ocean are more likely to induce significant rainfall. Finally, the forward speed of the storm also varies across different types of events. Top rain events tend to move slowly since a slower‐moving storm has time to drop more rainfall over the study area. The forward speed of top storm tide events has a bimodal distribution, but the distribution does not shift from that of the total population. Compound storms have moderate forward speed, representing a balance between inducing high storm tides and being near the study area long enough to drop significant rainfall. In general, TCs that can produce significant compound impacts tend to be high intensity, smaller storms that approach the study area either along the coastline or nearly perpendicular to it, and move with moderate forward speed.

Although compound TC events tend to have the characteristics discussed above, the strongest single predictor of compounding magnitude (A_C) is the maximum rainfall intensity (P_max, in mm/hr) observed over the study area. The Kendall rank correlation between the A_C and P_max is 0.73, compared to correlations of 0.36, −0.5, and 0.39 between A_C and peak storm tide (ST), closest distance from the storm center to the CFRE (Min_D), and relative time lag between centroid of rain and storm tide (T_Lag), which are the next three strongest predictors. Figure 5 shows a plot of P_max versus A_C with different color points referring to T_Lag. Positive T_Lag values indicate rainfall occurring before peak storm tide, while negative values indicate rainfall occurring after peak storm tide. The shape of the scatter plot suggests the existence of a rainfall rate threshold after which significant compound impacts start to occur (shown as the black horizontal line). The minimum P_max that produces significant compounding is around 13 mm/hr, and the threshold behavior of the plot makes sense since low rainfall rates can more easily be infiltrated or attenuated by the basin, but once rain exceeds a certain intensity it can produce significant runoff peak flows. Although the exact rainfall threshold depends on the basin characteristics of the study area, future work could examine whether similar behavior is observed in other coastal catchments. To characterize different types of events, Figure 5 is subset into three regions (labeled I–III in the plot) that correspond to different magnitudes of rainfall and compounding. In addition to the threshold of 13 mm/hr separating low‐intensity versus high‐intensity rain events, a vertical line at 8 km² separates low versus high compound impacts, and it corresponds to A_C greater than 5% of the 100‐year floodplain area. Region I corresponds to high rainfall, low impact, Region II corresponds to high rainfall, high impact, and Region III corresponds to low rainfall and low impact events. As discussed above, Region III events result in low/no compound impacts because the rainfall intensity is too low to induce significant rainfall‐runoff.

5 Figure. Scatter plot of maximum rainfall intensity versus AC in km2. Horizontal and vertical dashed lines separate three regions of storm types.

Region I contains events that have high rainfall intensity but low compound impacts. This is because although rainfall intensity is the most important predictor of compounding, other variables are important as well. More than 40% of Region I events have T_Lag values greater than 2 hr or negative values. T_Lag values that deviate significantly from zero indicate that the bulk of the rainfall‐runoff is missing the peak storm tide, and consequently compound impacts are low. Some events have both high P_max and low T_Lag, but the total amount of rainfall is too small to result in widespread flooding. Finally, some events result in low compounding because the storm tide for these events is extreme (>100 years) and consequently surge flooding dominates flood depths across most of the study area. In contrast to Region I, Region II events have both high rainfall intensity and high compound impacts. All of these events have T_Lag values between 0–2 hr, and total rainfall accumulations >90 mm. Additionally, these events have similar severity levels of storm tide and rainfall rates, with the most severe storm tide events corresponding to the most severe rainfall events. Thus, while rainfall intensity is the primary indicator of compound magnitude, the impact is also determined by factors such as the time lag, total rainfall, and relative severity of each hazard.

3.4 Delineating Flood Zones

Based on Figure 5, the magnitude of compounding can vary greatly across different storm events. Although characteristics of TC hazards can determine compounding potential, characteristics of the basin also influence the magnitude of rainfall‐surge interaction and determine where compound impacts will occur. Infiltration capacity, land use, topography, flow paths, and catchment size determine how rainfall‐runoff is generated and conveyed downstream and how storm surge propagates upstream, which ultimately determines their interaction effect. Portions of the study area can be surge dominated, rainfall dominated, or display significant interaction where both hazards contribute to total water levels. There is no consensus about how to delineate transition regions in coastal areas, and different approaches for classifying flood zones have been presented in the literature. Bilskie and Hagen (2018) define transition zones as areas where storm tide elevations are below rainfall‐runoff elevations but neither hazard is dominant compared to the combined rainfall + storm tide elevations. Shen et al. (2019) define transition zones as areas where rainfall + storm tide elevations are at least 0.01 m higher than simulations of either hazard alone. Here, to focus on the compounding effect of the two drivers, we adopt a similar approach as Shen et al. (2019) but define transition zones as areas where combined elevations are >0.2 m higher than elevations from either hazard alone (consistent with A_C defined above). Surge‐dominated zones are areas where storm tide elevations are within 0.2 m of the combined scenario, and rainfall‐dominated zones as areas where rainfall + tide elevations are within 0.2 m of the combined scenario. It is hypothesized that flood hazard may be significantly underestimated in transition areas if storm tide and rainfall are modeled separately, or if rainfall is neglected entirely.

The distribution of flood zones may vary significantly across different storm events due to differing magnitudes and temporal overlap of rainfall and storm tide; here we investigate the average over all synthetic events producing more than 10 mm of net rainfall (after subtracting infiltration) to understand the typical basin response. For each event, flood zones are delineated across the study area based on the criteria explained above. Rainfall‐dominated regions are set equal to 1, transition zones equal to 0, and surge‐dominated zones equal to −1. Flood zones are estimated by averaging across all events and are shown in Figure 6. On average, storm tide is dominant within and along the banks of the Cape Fear River and the coastline (dark blue), while inland areas far from either the coastline or river are rainfall‐dominated (red). Along tributaries of the river and small coastal streams, well‐defined transition zones are evident (light green).

6 Figure. Flood zone map based on average of all simulations with >10 mm net rainfall.

3.5 Flood Hazard Maps

We generate compound flood hazard maps based on the modeled maximum depths of the synthetic events. Figure 7 shows flood hazard maps under a range of return periods (50, 100, and 250 years) and different hazard scenarios. For the 50‐year maps, storm tide is dominant across the study area, as the storm tide map looks similar to rainfall + storm tide map. However, with increasing storm severity, the contributions of rainfall‐runoff become increasingly important (as shown in the 100‐ and 250‐year flood maps). Storm tide dominates water levels in the main stem of the Cape Fear River since the depths modeled by the storm tide scenario closely match the depths of the combined scenario. However, along the coastline and smaller tributaries, the importance of rainfall‐runoff is evident.

7 Figure. Flood return period maps under a range of hazard levels (vertical) and different hazard scenarios (horizontal).

To illustrate the impact of considering each hazard separately, Figure 8 shows difference maps between the 100‐year (a) rainfall + tide scenario, (b) storm tide scenario, (c) the “max” scenario, which considers the maximum of (a) and (b) at each point in the study area, and the 100‐year rainfall + storm tide scenario. The rainfall + tide scenario significantly underestimates the water elevation in the main stem of the Cape Fear River and along the coastline (areas in red), where storm tide is the dominant hazard, but produces similar results as the combined scenario in the overland areas (areas in blue). Along the main stem of the Cape Fear River, the storm tide scenario does not significantly underestimate the water levels compared to the combined scenario. However, along the coastline and in the overland areas the storm tide scenario underestimates the water levels by up to 0.3 m and greater than 0.5 m, respectively. The max scenario illustrates that there are also regions of the study area where the compounding of rainfall‐runoff and storm tide plays an important role in overall water elevations. In particular, the “max” flood levels are still significantly lower than the total, compound flood levels in parts of the coastline and tributaries.

8 Figure. Difference maps between 100‐year rainfall + storm tide and (a) rainfall + tide, (b) storm tide, and (c) max (rainfall + tide, storm tide).

Table 1 shows the percent of floodplain where water levels are significantly underestimated (i.e., underestimated by more than 0.2 m) for each return period and each hazard scenario. The rainfall + tide scenario underestimates water levels across the majority of the study area for all return periods and thus is not shown in Table 1. The storm tide scenario accurately characterizes water levels for lower severity storms, such as the 25‐year and up to the 50‐year event. However, for more severe events like the 100–250‐year water levels, the storm tide scenario underestimates depths across a significant portion of the floodplain, resulting in up to 28% of the floodplain being underestimated for the 100‐year level. The max scenario produces similar results as the combined scenario for both moderate severity (25–75 years) and very extreme (250‐year) water levels; for these return periods, the max scenario only underestimates water levels across less than 4.5% of the floodplain. However, for the 100‐year event, the max scenario significantly diverges from the combined scenario, underestimating water levels across 16% of the floodplain. This suggests that the compounding of rainfall‐runoff and storm tides varies significantly across storm severities and may be significant for a specific range of flood return periods.

1 TablePercent of Floodplain Where Water Levels Are Underestimated by at Least 0.2 m Compared to Combined Scenario

	Return period
25	50	75	100	150	200	250
Storm tide	0.35	8.65	11.8	27.9	18.9	21.9	19.4
Max	0.04	0.47	1.15	16.1	6.09	8.11	4.43

3.6 Flood Height Return Period Curves

We further investigate how rainfall, storm tide, and compound hazards vary across the study area and hazard levels by quantifying flood height return period curves at select locations. Return period curves for three locations of a tributary to the Cape Fear River (indicated by red dots in Figure 6 box 2) are shown in Figures 9a–9c, with red indicating the rainfall + tide scenario, blue the storm tide scenario, and purple the rainfall + storm tide scenario. At the downstream location (a) storm tide is dominant across all return periods, but at the midstream location (b) both hazards are important. At (b) storm tide is the most important hazard for return periods less than 60 years, and rainfall is the most important hazard for return periods greater than 60 years (although storm tide still contributes to the overall water levels). The upstream location shows that both rainfall and storm tide are equally important for return periods less than 40 years, but rainfall is the dominant hazard for greater return periods. Figures 9d and 9e similarly show return period curves for two locations along a coastal stream (shown in Figure 6 box 1). The downstream location (d) displays surge dominance across all return periods. In the upstream location both rainfall and storm tide are important for return periods less than 100 years (e), but for return periods greater than 100 years, storm tide becomes an increasingly dominant component of total flood heights. Figure 9 demonstrates that in their extreme upper tail, compound water levels converge to being either rainfall dominated or storm tide dominated. This explains why the magnitude of compounding peaks at the 100‐year return period, and then decreases for higher return period levels (shown in Table 1).

9 Figure. Return period curves for storm tide (blue), rainfall + tide (red), and rainfall + storm tide (purple) at (a) downstream, (b) midstream, (c) upstream locations on the tributary shown in Figure 6 box 2, and (d) downstream and (e) upstream locations along a coastal stream shown in Figure 6 box 1.

4 Discussion

4.1 Overall Picture of Compound Flooding

Figure 3b illustrates dependence between TC rainfall intensity and storm tide especially for the upper tail, suggesting there is significant potential for compound flooding during extreme TC events. The flood zone map in Figure 6 confirms that the average response of the basin to concurrent rainfall and storm tides results in transition areas along tributaries of the main river and along coastal streams. Both the hazard distributions and the basin response determine the ultimate return period flood height shown in Figure 7, and the compounding of rainfall and storm tide significantly increases water levels across 16% of the 100‐year floodplain (Table 1). Although the locations of rainfall‐surge interaction for the 100‐year water levels (Figure 7) generally match the transition areas outlined in Figure 6, the areas close to the coastline also depicts significant compounding that is not predicted by Figure 6. This discrepancy suggests that for extreme events, the location of compounding can differ from the average basin response. Furthermore, the return period curves in Figure 9 demonstrate that the relative importance of each hazard in driving total water levels can vary significantly across return periods so that a single location may be dominated by different hazards for different storm severities. In general, water levels at midstream locations of coastal tributaries are dominated by storm tides for lower return periods due to more frequent occurrence of mild TC events that produce non‐negligible storm tides but are not intense enough to produce significant eyewall precipitation (Figures 2a and 2c). However, more rare events (higher return period) have more extreme rainfall rates (Figures 2b and 2c), resulting in increasing importance of rainfall‐runoff in driving total water levels. Based on Figures 6–9, we can characterize the main stem of the river as surge dominated, the upstream portions of smaller streams and the disconnected pluvial areas as rainfall dominated, but the midstream portions of smaller streams as compounding zones, and the areas close to the coastline as surge dominated for lower return periods but compounding zones for high return periods (100 years).

The results presented here raise open questions about how to delineate regions susceptible to compound flooding. Should transition zones be delineated using a single event, an average of many events, or by using an extreme scenario (with a high return period)? On the one hand, averaging over many events (as in Figure 6) can account for the fact that different storms may produce different extents of rainfall‐surge interaction. However, this approach could miss areas that only exhibit compounding for extreme events, which is more relevant for floodplain management efforts. Furthermore, what threshold should be used to determine significant hazard interaction/compounding? In this study, we arbitrarily choose 0.2 m as the threshold indicating a significant increase in water levels. However, future work should investigate how different thresholds or classification criteria impact the delineation of transition/compound zones. Given that hydrodynamic modeling of combined rainfall‐surge events is computationally costly, clear delineation of transition zones would aid in understanding which coastal areas require compound flood models and which areas can be reasonably estimated using a single flood hazard.

4.2 Characterizing Joint Occurrence Versus Mapping Flood Hazard

Section 3.2 investigated the joint occurrence of TC storm tide and rainfall by characterizing the marginal and joint probability distributions of the hazards, and section 3.3 examined the characteristics of TCs that produce significant compound flood impacts. In contrast, sections 3.5 and 3.6 presented flood hazard maps based on the distribution of the overall modeled maximum water levels. We argue that examining both the occurrence of TC hazards as well as quantifying the overall flood heights is crucial to fully understanding the compound flood phenomenon. Understanding which TC characteristics and hazard patterns are associated with compound impacts could aid in real‐time forecasting efforts by allowing future storms to be classified as surge events, rain events, or compound events. Additionally, these characteristics can be examined under future climate scenarios to better understand how compounding flooding will be driven in the future. Studying the joint probability distribution of multiple flood hazards can reveal whether rainfall and storm tides have significant dependence, particularly for extreme events, and can provide a first estimate of the compound flood potential. On the other hand, examining compound flood hazard maps allows us to link compound event occurrence to actual flood impacts. Since return period maps are the primary metric used to assess flood risk, and because U.S. flood policy is centered on the 100‐year floodplain, it is crucial to understand how the interaction of multiple flood mechanisms could alter flood hazard maps. Finally, compound flood maps provide valuable information to engineers and city planners about how to design structures located in flood‐prone regions so that they are robust to a combination of potential hazards.

5 Conclusions

This study has investigated the co‐occurrence and compound impacts TC rainfall and storm tide. Drawing on a large data set of synthetic TC events and rainfall fields generated from a simplified physical model, we simulated compound flooding from storm tides and rainfall‐runoff within a loosely coupled physical modeling framework. We investigated the characteristics of TCs that may result in compound flood impacts, finding that storm characteristics such as storm intensity, approach angle, and forward speed are relevant indicators, but that maximum rainfall intensity and relative time lag between storm tide and peak rainfall are the main predictors of compound flood severity. We also investigated how our coastal catchment responded to co‐occurring flood mechanisms and delineated flood zones across the study area. Finally, we produced compound flood hazard maps as well as return period curves. We found that neglecting rainfall hazard could underestimate water levels across 28% of the study area for the 100‐year event, and consideration of both hazards separately (i.e., taking the maximum) would underestimate the 100‐year flood heights across 16%. These results demonstrate that not only is it important to consider both rainfall and storm tide in flood hazard assessment but for certain return periods, the compound hazard cannot be accurately estimated by simply taking the max of every single hazard.

Although this study has sought to investigate compound flooding in multiple ways, it is not able to capture all the flood mechanisms associated with TC landfall. In particular, the exclusion of outer TC rain bands is a limitation of this study, since they may also contribute to compound impacts. Outer rain bands falling several hours before landfall could cause high flows within the lower Cape Fear River and interact with storm tides (Gori et al., 2020), and neglecting this possibility could result in an underestimation of the compound hazard. However, existing parametric rainfall models are unable to simulate outer rain band structure (Xi et al., 2020), and the relative importance of outer rain bands compared to inner core rainfall varies greatly across different TC events and locations. Although the TCR model is not able to simulate outer rain bands for single TC events, the model produces accurate outer rainfall estimates compared to historical averages. Additionally, our approach does not account for antecedent rainfall conditions or simulate TC interaction with other weather systems that could produce additional rainfall. Exclusion of antecedent rainfall could also lead to underestimation of compound impacts. Finally, in the comparison of TCR with historical TC events (Supporting Information S1), we found that TCR often predicts the peak rainfall to occur later than the observed peak. Since the relative time lag between rainfall centroid and peak storm tide plays an important role in observed compound impacts (Figure 5), we may underestimate true compound impacts if TCR consistently predicts late arrival of the peak rainfall. Despite these limitations, this study represents an important step forward in simulating the impacts of TC rainfall on coastal flood hazard by directly incorporating physics‐based, spatially varied rainfall fields in our hydrodynamic modeling framework.

Acknowledgments

This work was supported by a National Defense Science & Engineering Graduate (NDSEG) fellowship from DoD and National Science Foundation (NSF) grant Nos. 1520683 and 1854993.

Data Availability Statement

All data used in this study are available through public repositories. Radar rainfall data can be accessed through either NCAR's EOL data repository (https://rda.ucar.edu/datasets/ds507.5/) or NOAA's National Severe Storm Laboratory (NSSL) (at https://www.nssl.noaa.gov/projects/mrms/). Stream discharge data can be obtained from USGS's National Water Information System (https://waterdata.usgs.gov/nwis).