Volume 11, Issue 3 e2022EF002947
Research Article
Open Access

Interacting Effects of Watershed and Coastal Processes on the Evolution of Compound Flooding During Hurricane Irene

Mithun Deb

Corresponding Author

Mithun Deb

Marine and Coastal Research Laboratory, Energy and Environment Directorate, Pacific Northwest National Laboratory, Sequim, WA, USA

Correspondence to:

M. Deb,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Data curation, Writing - original draft, Visualization

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Ning Sun

Ning Sun

Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA, USA

Contribution: Conceptualization, Methodology, Software, Validation, ​Investigation, Data curation, Writing - review & editing

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Zhaoqing Yang

Zhaoqing Yang

Marine and Coastal Research Laboratory, Energy and Environment Directorate, Pacific Northwest National Laboratory, Sequim, WA, USA

Contribution: Conceptualization, Methodology, ​Investigation, Resources, Writing - review & editing, Supervision

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Taiping Wang

Taiping Wang

Marine and Coastal Research Laboratory, Energy and Environment Directorate, Pacific Northwest National Laboratory, Sequim, WA, USA

Contribution: Software

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David Judi

David Judi

Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA, USA

Contribution: Resources, Project administration, Funding acquisition

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Ziyu Xiao

Ziyu Xiao

CSIRO Oceans and Atmosphere, Brisbane, QLD, Australia

Contribution: Data curation

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Mark S. Wigmosta

Mark S. Wigmosta

Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA, USA

Contribution: Data curation

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First published: 22 March 2023
Citations: 1


In low-lying estuarine regions, compound flooding (CF) is caused by the co-occurrence of extreme precipitation, river flooding and storm surge. In recent decades, there has been a rise in the frequency and intensity of pluvial-coastal CF events in different parts of the U.S. due to the increased frequency of intense precipitation and storm surge events. However, in estuarine and deltaic regions, the CF characteristics depend mainly on the storm tide and river flow interaction. Understanding how the fluvial-coastal CF may respond to changes to watershed and estuarine characteristics is essential for future CF hazard prediction. This study examined two critical processes: (a) the interplay between antecedent soil moisture conditions and peak river flow, and (b) how the impact of sea level rise (SLR) on storm surge and river flood distribution alters the CF in complex estuaries. As the study area, we selected the Delaware Bay and River, a shallow and convergent estuary in the US Mid-Atlantic region—where flood hazards during a CF can become more significant than the surge and river flood processes occurring in isolation. For the focal event for the study, we selected Hurricane Irene (2011) because it reportedly produced the most extreme CF over the past two decades in the same region. Ultimately, our results illustrated that the potential changes to the catchment and bay characteristics from the global temperature increase and SLR could significantly modulate the fluvial-coastal CF variability. The potential increase in global temperature and rainfall intensity might not always exacerbate the CF.

Key Points

  • Future global warming-induced changes to the watershed and estuary characteristics could significantly modulate the fluvial-coastal flooding

  • The potential increase in global temperature and rainfall intensity might not always worsen the compound flooding

  • Uncertainties from the interacting processes must be carefully addressed for a comprehensive compound flood hazard projection

Plain Language Summary

Low-lying and densely populated coastal and estuarine cities are highly vulnerable to extreme coastal high tide, storm surge, precipitation, and high river discharge. Amid growing research on the risk of compound flood hazards in the future climate, this study examined the interacting flood processes in freshwater-influenced coastal systems. First, we investigated the interplay between the potential antecedent soil moisture conditions, river discharge, and compound flooding in the Delaware Bay and River (DBR). Subsequently, we evaluated the effect of sea-level rise on storm surge and river flood distribution in the same area. The study revealed that the flood depth in DBR is extremely sensitive to the watershed's antecedent soil moisture condition and sea-level rise. Studies that focus on large-scale future compound flooding hazard assessment need to adequately address the interacting watershed-coastal processes.

1 Introduction

Flooding is one of the most common natural hazards that have significant social, economic, and environmental impacts on populations living near coastal, estuarine, and riverine areas. Low-lying and densely populated coastal and estuarine cities are constantly exposed to drivers of flooding, such as extreme coastal high tide, storm surge, storm-induced precipitation, and high river discharge. The simultaneous or successive occurrences of coastal storm surges, direct runoff from heavy rainfall (pluvial), and extreme river flow (fluvial) can exacerbate the flooding more than if they were to occur individually, making it a compound event (Lai et al., 2021; Wahl et al., 2015). According to existing studies, compound flooding (CF) can be defined using a combination of two or more types of floods: (a) pluvial-coastal, (b) pluvial-fluvial, and (c) fluvial-coastal. In coastal regions during an extreme event, generally, the combination of pluvial, fluvial, and coastal flooding (i.e., pluvial-fluvial-coastal types of compounding) is characterized by a longer duration and greater spatial extent, creating a more significant impact (Ganguli & Merz, 2019; Ghanbari et al., 2021). Among these processes, pluvial-coastal flooding (e.g., Gori et al., 2020; Valle-Levinson et al., 2020) can co-occur in coastal cities with small catchment sizes where the elevated sea level blocks or slows gravity-fed stormwater drainage. In contrast, during a fluvial-coastal event (e.g., Serafin et al., 2019) or pluvial-fluvial-coastal event (e.g., Bates et al., 2021), the watershed hydrological processes (e.g., subsurface flow, evapotranspiration) control the timing and magnitude of river flooding, which affects the phase difference between the individual extremes.

Many studies related to compound flooding have focused on the pluvial-coastal interactions in various regions worldwide and how they might change over time due to climate change and sea-level rise (SLR) (e.g., Bevacqua et al., 2019; Gori et al., 2022). These studies have assessed the dependence among multiple drivers or determined the joint return periods of the extreme surge and heavy precipitation, hypothesizing that precipitation can be used as a proxy for fluvial flooding. This hypothesis is problematic as extreme precipitation and flooding can exhibit strong nonlinearity in both space and time, owing to the complex interactions of climate, land, and hydrological processes (Do et al., 2020; Sharma et al., 2018; Sun et al., 2021). To address the nonlinear issue, advances have been made in recent research to explicitly represent the fluvial component in CF modeling through observations or large-scale hydrologic model simulations, although most studies suffer from critical limitations caused by the lack of spatial observations of discharge or crude model resolution in representing spatiotemporal variability in river discharge that interacts with coastal flooding during extreme events. For instance, Moftakhari et al. (2017) analyzed the correlation between coastal water level and fluvial flooding at eight U.S. estuarine systems using observations of river discharge and water level from a limited number of gauges (generally those closest to the estuary) and showed that the inclusion of future SLR could exacerbate the compounding effects. Ghanbari et al. (2021) estimated the joint return period of CF on U.S. coasts by incorporating future SLR and projections of peak river flow using a large-scale hydrologic model (∼4 km land resolution) forced by an ensemble of downscaled global climate models from the Coupled Model Intercomparison Project Phase 5 (CMIP5) (Naz et al., 2016). Most recently, Bates et al. (2021) developed a high-resolution modeling framework to provide CF projections in future climates informed by global climate models in the contiguous United States (CONUS). The study used a spatially lumped, conceptual hydrological model for fluvial flooding simulations. Although this is considered reasonable for computational purposes in a CONUS-scale study, the lack of model fidelity can lead to high uncertainty in fluvial-coastal CF simulations for complex watersheds (Couasnon et al., 2020; Ganguli & Merz, 2019; Serafin et al., 2019).

Future changes to the drainage characteristics of the watershed and the response of estuarine tidal dynamics to SLR in an evolving climate can interact and strongly modulate the compound flood potential. Recent research suggests that the trend and magnitude of peak river discharge would not necessarily follow global-warming-induced extreme precipitation in many regions of the world, and decreasing antecedent soil moisture condition (AMC) is a primary causal mechanism (Ivancic & Shaw, 2015; Sharma et al., 2018; Wasko & Nathan, 2019; Wasko & Sharma, 2017). In the future climate, even though the precipitation intensity is positively correlated with temperature increase, there is evidence that global warming could also increase periods of drought and drier soils (Berg & Sheffield, 2018; Chan et al., 2021; Sheffield & Wood, 2008). Ultimately, it will decrease soil moisture at the onset of extreme precipitation events in various places. In a large catchment, the flow response depends on the moisture it stores, and it is likely to be more affected by climate change than smaller and impervious urban catchments (Woldemeskel & Sharma, 2016). A large body of literature has reported the importance of AMC in modulating river flooding characteristics (e.g., Berghuijs et al., 2019; Nanditha et al., 2022; Nanditha & Mishra, 2022; Rajeev & Mishra, 2022). These studies have assessed the role of AMC on river peak runoff generation during heavy precipitation events and observed that a wetter AMC could significantly amplify flooding compared to drier conditions. In the context of hurricane-induced fluvial-coastal CF—when the interaction of tide, river, and storm surge dominates the along-channel flood distribution in estuarine regions, the effect of AMC and its interaction with other processes remain unexplored. Most of the recent works that examined CF at the intersection of watershed-coastal areas (e.g., Bates et al., 2021; Couasnon et al., 2020; Ganguli & Merz, 2019; Serafin et al., 2019)—have described the interaction of extreme river flow and sea levels without revealing the role of the causal land-surface processes.

The spatially varying SLR rate along U.S. coastlines is also a critical factor in increasing the amplitude and frequency of future coastal flooding, and the non-stationary and uncertain SLR projections need to be carefully addressed for flood studies (Buchanan et al., 20162017; Sweet et al., 2017; Taherkhani et al., 2020). In a convergent estuary, where the main channel width narrows exponentially from the bay entrance to the upstream river end (for example, Delaware Bay and River (DBR), U.S.), the SLR scenarios from climate change can also modulate the fluvial-coastal exchanges. In coastal modeling communities worldwide, different 2D- and 3-D hydrodynamic models have been widely used to simulate the changes in tidal dynamics and flooding due to SLR (e.g., Lee et al., 2017; Yang et al., 2014). Many have applied constant deterministic SLR values at the model boundary for simplicity. However, this simplistic approach neglects the spatial variation of the SLR, which depends on various influential processes such as the thermal expansion of ocean water, land ice loss, and changes in land water storage (Gori et al., 2022; Passeri et al., 2015). These studies have demonstrated that, for forecasting CF events with SLR, it is essential to have local projections that can accommodate various estuarine processes and cover a range of timescales. To address this problem, studies such as Kopp et al. (2014) provided localized SLR projections by considering glacier and ice sheet components, thermal expansion, ocean dynamics, and other non-climatic factors that can help reduce uncertainties in SLR projections.

In CF-related studies, additional uncertainties can still generate in estimating the joint return period of extreme sea levels and river flows by using total water surface elevation (combined SLR-induced sea surface elevation and the storm surge) in the analysis (e.g., Ganguli et al., 2020; Ghanbari et al., 2021; Moftakhari et al., 2017). This procedure does not consider the spatial variation of the storm surge or river-flow-induced flood depth on top of the elevated sea level in response to SLR. The elevated sea level can modify the wetting and drying following tide cycles in shallow and convergent estuaries if the low-lying wetlands do not keep up with the SLR (Hall et al., 2013; Lee et al., 2017). This altered embayment width and area then affects the along-channel tide and surge propagation, where the tidal amplitude and phase speed are observed to decrease with higher wetland submergence (Du et al., 2018). While the raised mean sea surface will make many new regions highly vulnerable to flooding, the flood water depth from storm surge and river flow will change based on the newly shaped estuarine geometry, ultimately affecting the compounding.

This study examined the importance of critical, interacting processes in freshwater-influenced coastal systems, including (a) the interplay between AMC and river discharge and fluvial flooding, and (b) how the SLR's impact on storm surge and river flood distribution alters the CF in complex estuaries. To properly represent the interaction between all the hydrological and hydrodynamic processes during an extreme event, it is essential to resolve all local-scale flow boundaries, including the contribution from tidal creeks and channels. To tackle this issue, various works such as Ye et al. (2020) and Ye et al. (2021) have used reanalysis products from the continental-scale National Water Model (NWM), which has almost ∼2.7 million streamflow output points in the U.S (NOAA-NWM). However, they also observed the need to improve the model's skill at capturing flow conditions during extreme events. Considering these matters and our focus in this study (river flow sensitivity to watershed AMC), we coupled two high-resolution and process-based numerical modeling frameworks: the Distributed Hydrology Soil Vegetation Model (DHSVM; Wigmosta et al., 1994) and the 3D Finite-Volume Community Ocean Model (FVCOM; Chen et al., 2003). Compared to traditional approaches where the hydrodynamic model is forced by river flow field data (e.g., streamgages), the model coupling applied here presents high-resolution flow boundary conditions that include small channels or wetland areas where observations are barely available. We selected the DBR, a shallow and convergent estuary in the U.S. Mid-Atlantic region, as a study area that is historically vulnerable to storm surges, extreme river discharge, and CF (Xiao et al., 2021). Then, we picked Hurricane Irene (2011) as the focal event for the study because it reportedly produced the most extreme CF in the DBR in the past two decades (Liu & Smith, 2016). The hydrology and hydrodynamic models are first calibrated using a large set of available flow gauges, tide gauges, tidal current profilers, and high water marks. This portion of the work has demonstrated the importance of systematically resolving different physical processes using an integrated approach to increase fidelity in CF modeling. Then, using the adequately evaluated models, we conduct sensitivity analysis of the CF distribution to various AMC and SLR scenarios. These numerical experiments tried to show the potential of the watershed AMC and future SLR conditions in changing the flood response in a converging system and why we should appropriately address the interacting watershed and coastal processes in high spatial detail when developing CF projections for the future climate.

2 Hurricane Irene

Hurricane Irene originated from a tropical wave that exited from the west coast of Africa on August 15, 2011. On August 24 12:00 UTC, it reached close to the Bahamas and became a Category 3 hurricane on the Saffir-Simpson Hurricane Wind Scale, with a peak intensity of 105 knots and a minimum central pressure of 957 mb (NHCTropicalCycloneReportHurricaneIrene). For the next few days, the hurricane gradually weakened by moving northward in the offshore direction from the east coast of Florida and Georgia. Then, on August 27 12:00 UTC, it made landfall near Cape Lookout, North Carolina, with an intensity of 75 knots and producing Category 1 hurricane-force winds (Figure 1a). Torrential rainfall amounts surpassed 20 inches in some places, while at the same time, storm surge levels reached over 10 feet, and a total of five people died in North Carolina (MiddleAtlanticRiverForecastCenter). Irene then continued north-northeastward along the coast, striking the Mid-Atlantic in Virginia, Delaware, and coastal New Jersey early on August 28. It made its final landfall in Brooklyn, New York, moved over to the northeastern United States, and became extratropical when the center was near the New Hampshire/Vermont border around August 29 00:00 UTC. Irene caused widespread heavy to extreme rainfall across the Mid-Atlantic and Northeast U.S. regions, reaching more than 10 inches total in some locations across the Delaware River Basin (Figure 1b). Interestingly, in the weeks before the arrival of Hurricane Irene, an unusual weather pattern also brought recurrent periods of heavy rainfall (∼4–8 inches) to much of New Jersey, Pennsylvania, Delaware, and northeast Maryland, leading to much higher soil moisture than usual (MiddleAtlanticRiverForecastCenter). The high AMC and heavy rainfall led to destructive river flooding in the Catskills of New York, across New Jersey, and finally in the Delaware River. The river flooding, coastal flooding from the Delaware Bay, and their compounding effect caused estimated damage of $1 billion and 11 deaths in New Jersey (Lixion & Cangialosi, 2011). This environmental and economic damage due to the concurrent coastal and fluvial flooding in the DBR during the hurricane landfall and subsequent fluvial flooding in the Delaware River from the flow accumulation in the watershed led us to select Hurricane Irene (2011) as the focal event for this study and the CF analysis.

Details are in the caption following the image

(a) Movement of Hurricane Irene along the U.S. east coast in 2011. The purple polygon represents the focus area of this study: Delaware River Basin. (b) Multi-sensor (radar and rain gauge) estimates of total precipitation (inches) during the hurricane by NOAA/National Weather Service/Middle Atlantic River Forecast Center. Polyline shows the track; the varying sizes of the points represent the transformation of wind intensity (knots) at every 6-hr interval.

3 Coupled Watershed-Coastal Modeling Approach

The modeling framework consists of two process-based models: DHSVM to simulate watershed hydrological processes and 3D FVCOM to simulate coastal hydrodynamics. The current configuration implements one-way coupling of DHSVM and FVCOM, in which DHSVM passes the reach-scale river boundary conditions to FVCOM at the interface between the DHSVM and FVCOM model boundary. Specifically, river conditions were represented by time series of flow simulations from 162 river reaches. In the following sections, we first describe each model component and then present model evaluation for the Hurricane Irene event.

3.1 Distributed Hydrology Soil Vegetation Model

DHSVM is a process-based, spatially distributed hydrological model. It simulates key overland and subsurface hydrological processes by solving the full energy and water balance with an explicit representation of climate, soil, and vegetation at the grid level. Core model physics and formulations have been described in detail in a large body of literature (e.g., Perkins et al., 2019; Storck et al., 1998; Sun et al., 2015; Wigmosta et al., 1994; Wigmosta et al., 2002), and only brief descriptions of DHSVM are provided here.

DHSVM represents watershed land surface with rectangular grid cells typically with a spatial resolution of 10–150 m. The model consists of a two-layer canopy model for evapotranspiration, a two-layer snowpack model for snow accumulation and melt, a multi-layer unsaturated soil model that moves infiltrated water vertically through the layers of soil based on Darcy's law, and a saturated subsurface flow routing model using a transient quasi three-dimensional model. Each grid cell exchanges saturated zone water with its eight adjacent grid cells as a function of water table depth, soil properties, and topography. For a given grid cell, the outflow rate of saturated subsurface flow is estimated as a function of the water table slope and the lateral saturated hydraulic conductivity of the soil profile. Excess surface water and intercepted subsurface flow are routed through the stream channel network to the watershed outlet. Meteorological inputs to DHSVM include precipitation, air temperature, wind speed, relative humidity, downward shortwave, and longwave radiation, commonly with a subdaily temporal resolution. As applied in this study, DHSVM was configured for the Delaware River Basin with a 90-m spatial resolution and was run at a 3-hourly timestep. The model was forced by the gridded (∼6 km) CONUS-scale meteorological data set developed by Livneh et al. (2013) after disaggregating the daily records to the 3-hourly interval. The source Livneh data set consists of daily records of precipitation, maximum and minimum air temperature, and wind speed over the period 1950–2013, obtained from about 20,000 National Climatic Data Center Cooperative Observer stations. Due to the general lack of subdaily meteorological observational records at the regional scale, the daily records were disaggregated into subdaily records of each model-required meteorological variable using the Mountain Microclimate Simulation Model (MTCLIM) algorithms (Bohn et al., 2013). MTCLIM has been used very widely to provide disaggregated climate forcing for hydrological modeling across scales (e.g., Barsugli et al., 2020; Sun et al., 2019; Sun et al., 2022). Most variables such as radiation fluxes were derived from empirical relationships, and a uniform precipitation rate was assumed throughout the day. While the omission of diurnal rainfall variations can introduce uncertainty, the effect is not significant for the DHSVM skill at the scale of this analysis, as shown later in DHSVM validation. Finally, reach-scale river discharge time series at the DHSVM-FVCOM interface were passed to FVCOM to provide the river flow boundary condition.

3.2 Finite Volume Community Ocean Model

To resolve all the complex hydrodynamic interactions in the DBR region during Hurricane Irene (2011), we selected the unstructured grid, FVCOM (Chen et al., 20032012). FVCOM has been used to model storm surges and flooding in many estuarine and coastal regions (e.g., Beardsley et al., 2013; Dukhovskoy & Morey, 2011; Rego & Li, 2010; Xiao et al., 2021; Yang et al., 2014; Yoon & Jun 2015; Zhang et al., 2020). We activated the 3D barotropic and hydrostatic version, which uses a mode-split method to solve the Reynolds-averaged Navier–Stokes equations, where an external mode solves 2D depth-integrated equations and the internal mode solves the equations in three dimensions.

The model domain extends ∼1,500 km offshore from the coast to adequately capture the storm tide generation from atmospheric-ocean interaction and ∼215 km from the Delaware Bay mouth to the river flow boundary in the upstream Delaware River (Figure 2a). To seamlessly simulate the CF from the interaction between large- and small-scale processes (open ocean to tidal creeks), the model resolution varies from 30 km along the open boundary in the open ocean to 10 m inside the smaller channels. The model grid was generated using the Surface-water Modeling System (aquaveo.com) and has approximately 1.4 million triangle elements and 700,000 nodes. Figure 2c illustrates the transition of the model grid cell size from the open ocean to the tidal creeks that followed a pre-defined size function developed by assigning different paving densities for tidal creeks, bay and river, and open ocean. We extended the floodplain boundary to 3 m elevation above the North American Vertical Datum of 1988 (NAVD88) for inland inundation, which is considered sufficient for the flood water depth for Hurricane Irene (2011). Model grid topographic and bathymetric data were collected from a combination of National Oceanic and Atmospheric Administration (NOAA) digital elevation model (DEM) sources such as the 1-arc-minute ETOPO1 and 3-arc-seconds Coastal Relief Models, Continuously Updated Digital Elevation Model (CUDEM) of ∼3.5 m resolution. More details about the elevation data sets collected for this study and their post-processing are given in Xiao et al. (2021).

Details are in the caption following the image

(a) Finite-Volume Community Ocean Model (FVCOM) unstructured grid model domain in the North Atlantic Ocean, extending ∼1,500 km offshore from the U.S. east coast shoreline; (b) Distributed Hydrology Soil Vegetation Model (DHSVM) model domain of Delaware River Basin and flow gages used for model evaluation; (c) DHSVM stream segments selected to provide river forcing at FVCOM upstream boundary (shown by golden lines); the blue circles represent the U.S. Geological Survey stream gauges available in the model domain. (d) Field data locations used for model validation. Here, green represents the current profilers, black represents tide gauges, and red represents high water marks.

To represent all the essential processes responsible for CF during a hurricane, we enforced three primary lateral and sea surface boundary conditions: (a) tidal forcing at the open ocean boundary, (b) river flow conditions at the coastal land-channel boundary, and (c) meteorological forcing with wind stress and atmospheric pressure. The tidal forcing at the open boundary is specified as a time series of the water surface elevation (WSE) obtained from the TPXO8.0 global ocean tide model (Egbert & Erofeeva, 2002). To inject water at the river flow boundary, we selected the tracer control element method described in Chen et al. (2012). Among a couple hundred DHSVM streams that intersect the FVCOM land boundary, we picked 162 stream segments that have identifiable channel widths with the FVCOM grid resolution and bathymetry representation from publicly available data sets (Figure 2c). We also placed the historically available 23 U.S. Geological Survey (USGS) stream gage locations in DBR on the same map (shown as blue circles) to illustrate the enhanced density of smaller channels and creeks when a high-resolution hydrology model is incorporated. Finally, the sea surface wind stress and atmospheric pressure field of Hurricane Irene (2011) were collected from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5), a global atmospheric reanalysis model that provides the highest resolution available in public repositories for this event—a spatial resolution of 30 km.

We used five layers in the sigma vertical coordinate for all the model runs. To parameterize the horizontal and vertical eddy viscosity, a horizontal diffusion coefficient of 0.2 m2/s and a vertical diffusion coefficient of urn:x-wiley:23284277:media:eft21265:eft21265-math-0001 m2/s are specified. More importantly, Xiao et al. (2021) have shown that the along-channel tidal amplitude in the DBR is sensitive to the spatially varying bottom roughness length-scale. We assigned roughness length-scales of 0.0005 m for the coastal ocean to lower bay and 0.0001 m for the middle and upper bay based on Xiao et al. (2021). We also limited the minimum drag coefficient urn:x-wiley:23284277:media:eft21265:eft21265-math-0002 value to 0.0018 and used a minimum depth of 10 cm as the criteria for simulating the wetting/drying process.

4 Model Validation

4.1 DHSVM Evaluation of Irene Flooding

Because of the considerable topographic complexity and land heterogeneity of the Delaware River Basin, it is crucial to evaluate the hydrological model for its robustness in capturing the spatial and temporal variability of flow responses (i.e., river boundary conditions). As applied for simulating river flooding during Irene, DHSVM simulated daily flows (averaged from the 3-hourly flows) were evaluated against USGS daily flow observations at six gage locations representing a range of drainage areas from 4,118 to 17560 km2 along the longitudinal profile (upstream–downstream) of the mainstem of the Delaware River (Figure 2b). The model performance was measured by the Nash-Sutcliffe efficiency (NSE) and the Kling–Gupta efficiency (KGE; Gupta et al., 2009) calculated over the duration of Irene. NSE is commonly used for measuring hydrological model performance:
where urn:x-wiley:23284277:media:eft21265:eft21265-math-0004 and urn:x-wiley:23284277:media:eft21265:eft21265-math-0005 are simulated and observed daily flow, respectively, urn:x-wiley:23284277:media:eft21265:eft21265-math-0006 is the total number of days used in metric calculations, and urn:x-wiley:23284277:media:eft21265:eft21265-math-0007 is observed daily mean flow over urn:x-wiley:23284277:media:eft21265:eft21265-math-0008 days. KGE measures the goodness-of-fit by analyzing the correlation, variability, and bias between simulations and observations:
where r is the linear correlation, 𝛼 is the viability error, and 𝛽 is the bias between observed and simulated daily flows. Both NSE and KGE range from -∞ to 1, and a value of 1 indicates perfect agreement between simulation and observations. Comparison between simulations and observations of daily streamflow suggests strong agreement (Figure 3). NSE daily ranges are from 0.73 to 0.92 and KGE ranges are from 0.60 to 0.94 (Table 1). Although the model captured the timing of peak river discharge during Hurricane Irene for all evaluated gages, at USGS-01428500 and USGS-01463500, we observed a higher peak flow bias. In addition to other sources of uncertainties, such as climate input and topography, the uncertainty in stage-discharge rating curves and streamflow records can contribute to this bias in the simulated flow.
Details are in the caption following the image

Evaluation of daily streamflow simulations of Distributed Hydrology Soil Vegetation Model during Hurricane Irene against USGS gauge observations along the upstream–downstream direction of the Delaware River.

Table 1. Distributed Hydrology Soil Vegetation Model (DHSVM) Performance Statistics at USGS Gauge Locations in the Delaware River
Model Metrics/USGS streamgage NSE KGE Bias Bias in peak flow
DHSVM 01427510 0.89 0.89 9.2% −1.2%
01428500 0.92 0.94 1.7% −14.3%
01434000 0.89 0.85 5.1% −2.9%
01438500 0.88 0.85 7.9% −5.2%
01446500 0.92 0.91 4.6% −6.8%
01463500 0.73 0.60 21.2% 24.0%

4.2 FVCOM Evaluation of Irene Coastal and Riverine Flooding

To accurately represent the estuarine hydrodynamics in the entire DBR region during Hurricane Irene, we collected field data sets of the bay and river WSE, tidal current velocity, and high water marks from the low-lying wetlands. These were obtained from various sources for the storm period, covering both coastal and fluvial flooding. The WSE was collected from the NOAA Tides & Currents database (tidesandcurrents.noaa.gov), and we chose a 15-min interval for the time series. NOAA's National Ocean Service (C.MIST) maintained three current profilers—one acoustic Doppler current profiler (ADCP) (db0201) and two acoustic Doppler profilers (ADPs) (db0301 and db0501)—in the lower Delaware Bay to the upstream Delaware River near Philadelphia that covered the entire period of the hurricane. These instruments have a varying sensor frequency range where db0201 operated at 1,200 kHz, db0301 at 500 kHz, and db0501 at 1,500 kHz, and they sampled and stored data at 6-min intervals. Finally, the high water marks in the study area during Hurricane Irene were collected from the Delaware Geological Survey (dgs.udel.edu). Figure 2d shows the locations of these gauges along the DBR, and we can see that the high water mark points are limited to the left side of Delaware Bay for this particular storm period.

Figures 4-6 compare the model and in situ WSE, current datasets, and high water marks, respectively, where we observed good model performance. To quantify model error statistics, we computed the linear correlation coefficient, average bias index, and model skill as
Details are in the caption following the image

(a) Water surface elevation comparison between model results and in situ (in meters) at NOAA tide gauge locations in Delaware Bay and River. (b) Scatter comparison and statistics at four locations that represent different bay and river zones, going from upstream river to the bay entrance.

Details are in the caption following the image

(a) Depth-averaged principal component velocity comparison between model results and in situ (in m/s) at NOAA C-MIST profiler locations. (b) Scatter comparison and statistics at same locations.

Details are in the caption following the image

High water mark comparison between model results and in situ (in meters) in the low-lying wetlands of the State of Delaware.

In Figure 4a, we can see that the model WSE and phase match very well with the in situ WSE in the bay region (Cape May to Delaware City). The model also shows a strong ability to predict the peak surge elevation. When storm tide propagates upstream from Delaware City to Newbold, the relative error increases due to the more significant decrease in channel width and greater influence of river discharge. Even though the model peak surface amplitude agrees well, even in Philadelphia, there is a slightly elevated phase error in the upstream portion of the Delaware River. The major rivers, along with numerous tidal channels and creeks, are significant contributors to the non-linear interaction in the region, and the model flooding and draining are highly sensitive to it. The error estimates are shown in the scatter plot (Figure 4b), where we only included gauges representing different bay and/or river dominant zones. In the mid and upper bay—Ship John Shoal and Delaware City, the model shows higher correlation coefficients of 0.98 and 0.97, respectively, and a skill of 0.99 for both. The correlation coefficient decreases to 0.92 and the skill scores decrease to 0.95 and 0.96 at the upstream gauges (Philadelphia and Newbold), respectively. Overall, the averaged bias index indicates a negligible model underprediction in the bay area and then increases slowly near the river flow boundary during the fluvial flooding.

Model performance was further assessed for the velocity at the three ADCP/ADP locations. We computed the depth-averaged quantity of the principal velocity component from both in situ and model results, shown in Figures 5a and 5b. Similar to surface comparison, we observed a higher correlation and skill scores of 0.98 and 0.99, respectively, at the bay entrance. In the upper bay Delaware City gauge, located near the opening of the Chesapeake canal, both correlation and skill decrease to 0.94 and 0.97. From this location to the most upstream profiler in Philadelphia, we noticed an increase in the phase error during peak river discharge conditions that contributed to the model skill score decrease to 0.94. Moreover, the model slightly underpredicts the ebb flow during the same period (Figure 5a, top panel), illustrated by the averaged bias index value of −0.16 m/s.

Finally, we also validated the model using high water marks in the low-lying wetlands collected by the State of Delaware during Hurricane Irene (Figure 2b). The water marks represent a combination of bottom elevation and water depth, where the error is sensitive to many factors such as the topographic DEM data set, model grid resolution, and river inputs through the land boundary. Model results in Figure 6 show an overprediction in some locations, with the largest error observed being 0.59 m. The actual surveyed bottom elevation is missing from the field data, which obstructed the evaluation of percent error coming from the bottom elevation differences. Also, the higher bias detected here falls near the vertical accuracy limit of the DEM data set—a maximum of 0.5 m (CUDEM-1/3Arc-Second). Considering all these complexities, overall, we have good model performance over the wetlands; the difference is well within limits compared to similar studies by Ye et al. (2020) and Huang et al. (2021) for compound flood analysis.

5 Numerical Experiments—Storyline Approach

Using the physically consistent approach with the coupled modeling framework, we constructed two sets of numerical experiments to evaluate how fluvial-coastal flooding induced by Hurricane Irene may evolve under changing conditions: (a) AMC scenarios that represent a range of plausible soil moisture conditions corresponding to a drier to wetter future of the basin, and (b) SLR scenarios based on localized projections of SLR that represent spatial variations at the ocean boundary (Figure 7). Through this storyline approach, we investigated the interacting watershed and coastal processes that dominate the spatial and temporal evolution of Hurricane Irene flooding at river-coastal interfaces.

Details are in the caption following the image

Sketch of the storyline approach designed based on a hurricane event and different watershed AMC and SLR scenarios.

The AMC scenarios (i.e., initial soil moisture condition, prescribed at the pixel level at the beginning of a simulation) were created to reflect the range of variations in simulated basin-wide soil moisture in historical climates. Because soil moisture is physically limited by soil porosity, which changes with different soils, for each model pixel we applied a spatially uniform scaling factor to its soil porosity that varies with the local soil type. We used the scaling factors 0.8, 0.85, 0.9 and 0.95 to represent moderately dry to nearly saturated AMC scenarios, based on the probability distribution of DHSVM simulated basin-average soil moisture from 1955 to 2013 forced by the Livneh climate data set (described in Section 3). Different AMC scenarios were prescribed to DHSVM on August 21, 2011, about a week before Irene landfall reached the peak daily volume for the whole basin.

We also incorporated probabilistic, localized SLR projections from Kopp et al. (2014) for 2100, considering four Shared Socioeconomic Pathway (SSP) scenarios (sealevel.nasa.gov/ipcc-ar6-sea-level-projection-tool). These scenarios are defined based on future greenhouse gas emission rates and globally averaged surface air temperature as (a) SSP1-2.6: low emission rate (1.3°C–2.4°C increase in 2081–2100 compared to 1850-1900), (b) SSP2-4.5: intermediate (2.1°C–3.5°C), (c) SSP3-7.0: high (2.8°C–4.6°C), and (d) SSP5-8.5: very high (3.3°C–5.7°C). We extracted the spatially varying sea levels in 2100 for these conditions at the ocean boundary and integrated them with the present-day tidal surface elevation. Then, we performed the model simulations with two different setups—(a) SLR + tide only and (b) SLR + tide, surge, and river—to estimate the changes to the flood water depth for various SLR conditions.

6 Results

6.1 Effect of Different AMC and Fluvial Conditions on Compounding

This section assesses the interaction among tide, surge, and river discharge (TSR) during Hurricane Irene and how it changes the CF throughout the DBR. Additionally, we have analyzed the sensitivity of the compounding to different river discharge conditions under various AMC scenarios of the watershed during the hurricane event.

Analysis of basin-wide river discharge under different AMC scenarios shows that AMC has a substantial effect on peak river discharge during Hurricane Irene that also varies spatially across the basin. Figure 8 demonstrates the river discharge during the hurricane event under different AMC scenarios for two key locations: the Delaware River upstream boundary near Trenton, NJ (referred to as Delaware River hereafter), and the outlet of the Schuylkill River basin. The Delaware River upstream flow boundary covered the drainage area consisting of six sub-watersheds of the Delaware River Basin and represented accumulated upstream flow processes during the event. Schuylkill Valley, a sub-watershed of the Delaware River Basin, covers some of the northwest counties near Philadelphia, and suffered from intense precipitation during the peak surge from the bay side, which is reflected in the Schuylkill River discharge (Figure 8b). In contrast, the Delaware River peak discharge shows a 2-day lag with the storm surge peak (Figure 8a). Looking at the different AMC and river flux conditions, we observed nonlinear sensitivity of peak river discharge across the basin to changing AMC. For instance, the peak river discharge at selected locations shows a higher sensitivity when the watershed AMC decreases to 90% of the Hurricane Irene baseline event, as shown in Figure 8. Other scenarios: AMC 85% and 80% showed a similar decrease in volume flux at both river flow boundaries.

Details are in the caption following the image

(a) River discharge (in m3/s) at the upstream Delaware River flow boundary (Trenton, NJ) for different AMC scenarios during Hurricane Irene. (b) Similar comparison at a secondary channel, Schuylkill River, which converges with the Delaware River near Philadelphia, PA.

To estimate the hurricane-induced flood depth, we first identified the peak tidal WSE for the entire model domain and then located the peak WSE for the combination of TSR during the hurricane. The difference between these two provided a flood water depth for the selected period of the hurricane event. Figure 9 shows the changes in channel properties from the entrance of Delaware Bay to the upstream Delaware River flow boundary at Trenton, NJ. The locations of the NOAA tide gauge are placed on top of the transect to show the distance along the transect (Figure 9, left). Channel thalweg depth, cross-section averaged depth, and surface width are also estimated (Figure 9, right) to illustrate the role of channel properties (i.e., convergence/divergence) in changing the tidal wave and storm surge characteristics in the DBR.

Details are in the caption following the image

Left: The along-channel transect following Delaware Bay and River thalweg, collected from the Delaware River Basin Commission (state.nj.us/drbc/). NOAA tide gauge locations - Brandywine Shoal Light (BSL), Ship John Shoal (SJS), Reedy Point (RP), Marcus Hook (MH), Philadelphia (PHL), Burlington (BU), and Newbold (NB)—are placed along top of the transect (red circles) with the distance from the bay entrance (in km). Right: The along-channel thalweg bottom elevation from NAVD88 (in meters), cross-section averaged bottom elevation, and channel width for a still water level condition are shown from top to bottom, respectively.

For the results analysis, we evaluated the role of river discharge in amplifying peak WSE for two separate time windows due to the compounding nature of the event. First, the flood water depth was calculated along the transect during storm-surge-induced flooding from the open ocean. Subsequently, we picked another time window from the period when Hurricane Irene moved inland, weakened, and produced higher river discharge from the torrential rains. These extreme coastal and fluvial conditions and their relative phase lag control the compounding for a specific portion of the DBR. In Figure 8, they are shown separately using dashed lines. Even though there is a 2-day lag between the peaks, during Hurricane Irene's peak storm surge period, the river discharge reached nearly 1,500 m3/s, contributing to the non-linear interaction between TSR. The hydrodynamic model results in Figure 10 are separated for the abovementioned flooding periods. The maximum WSE along the bay and river in a shallow-convergent estuary is primarily controlled by the system's geometry, tidal characteristics, and the atmospheric properties of the hurricane (wind, precipitation, etc.). To understand the along-channel flood gradient in the DBR during Hurricane Irene and for the AMC scenarios, we briefly describe the tidal dynamics in Section 10.

Details are in the caption following the image

(a) Along-channel peak water surface elevation (WSE) with different AMC scenarios separated for two different time windows; left panel: during peak storm surge from the bay side (between 08/28/2011 and 08/29/2011), right panel: during peak Delaware River discharge (between 08/29/2011 and 08/31/2011). (b) Flood water depth (in meters) estimated by removing peak tidal WSE from the WSE with tide, surge, and river forcings; left and right panels are separated similarly to the panel separation in (a).

6.1.1 Tidal Dynamics in the Delaware Bay and River

Various studies such as Parker (1984), Friedrichs and Aubrey (1994), Wong and Sommerfield (2009), and more recently Pareja-Roman et al. (2020), Ye et al. (2020), and Xiao et al. (2021), have examined the changes to the tidal constituents' amplitude and phase along the DBR thalweg transect. These studies have specifically shown the varying nature of the largest tidal constituent urn:x-wiley:23284277:media:eft21265:eft21265-math-0013 amplitude: increasing from ∼0.6 to ∼0.85 m for the first 60 km (near SJS; station names are defined in Figure 9), ∼0.1 m damping for the next ∼80 km (near MH), and then increasing again to ∼1.1 m for the remaining 60–70 km (near NB). This spatial variation of urn:x-wiley:23284277:media:eft21265:eft21265-math-0014 and other major semi-diurnal constituents (urn:x-wiley:23284277:media:eft21265:eft21265-math-0015, urn:x-wiley:23284277:media:eft21265:eft21265-math-0016, urn:x-wiley:23284277:media:eft21265:eft21265-math-0017, and urn:x-wiley:23284277:media:eft21265:eft21265-math-0018) has mainly resulted from a complex contribution from the converging width, length of the estuary relative to the tidal wavelength, and the non-linear frictional effects (Friedrichs & Aubrey, 1994; Parker, 1984). This study focuses mainly on the flood analysis, and to serve this purpose, we identified the peak tidal WSE for the entire duration of the Hurricane Irene simulation, represented by a blue solid line in Figure 10a. Without any atmospheric and river boundary forcing, the model results depicted a similar along-channel distribution of peak tidal WSE compared to the existing studies. Especially around MH (∼140 km from entrance), the model peak tidal WSE also shows a local minimum of ∼1.0 m, a quasi-node generated from the superposition of the frictionally damped incident wave and the reflected wave from the head of the tide [see Parker (1984) for more details].

6.1.2 Changes to Non-Linear Interactions and Compound Flooding

In Figure 10, the red solid line and the black dashed lines represent peak WSE for the baseline Hurricane Irene simulation with TSR and TSR with different AMC scenarios, respectively. During surge-induced flooding, while the Hurricane Irene storm tide shows an along-channel peak WSE gradient similar to the peak tidal WSE, there is an increased elevation from the river flow boundary (∼215 km, Delaware River flow boundary) to RP (∼100 km) due to river discharge. For the baseline case, starting from ∼50 km to the end of the reach, the non-linear interaction from TSR produced a spatially varying peak WSE, where the large flow from tributaries and creeks near Philadelphia due to the intense precipitation during hurricane landfall contributed substantially to the elevated water level. Figure 10b shows the resulting compound flood water depth. It indicates how a local stream, the Schuylkill River, between MH and PHL exacerbates the flooding to 0.8 m for a portion of the Delaware River, while the main river flux increases the flood depth for the remaining stretch to 1.0 m. Then, for different AMC scenarios, we observed a decrease in the flood level of more than 0.2 m near PHL and 0.4 m close to the river flow boundary (near NB), even with the less extreme wet AMC of 90%. The flow in the small channels and tributaries has decreased by almost 40%, along with an increased phase lag in the peak discharge signal, shown in Figure 8. Other scenarios: AMC 80% and 85% produced an order of magnitude lower volume flux that is insignificant for elevating the flood level and compounding (Figure 10a). Interestingly, with a minimum river discharge, AMC 80%, we still notice a higher along-channel flood elevation gradient between MH and PHL (around ∼150 km). This shows the potential contribution of channel properties such as width and depth convergence (Figures 9b and 9c) and the interaction of the incident and reflected tidal waves in amplifying local flood water levels.

During Delaware River peak river discharge (Figure 8), the bay water level returns to the regular mean sea level in the absence of the storm surge. As shown in Figure 10a, the peak WSE is even lower than the tidal peak WSE at the downstream end of the bay (entrance to ∼75 km). When Hurricane Irene passed through the Delaware Bay region, the local wind field had a southwest and southeast movement for multiple days (https://tidesandcurrents.noaa.gov/met.html?id=8537121), pushing some of the water out of the bay and reducing the sea level. Although the tide-river interaction controls the flooding for this period, the flooding extent for the baseline case still reaches RP (∼100 km), similar to the surge-dominated period. The main difference between the two is in the gradient of the flood level, where it is significantly higher close to the river flow boundary for the peak river discharge. As the cross-section area of the river slowly expanded from the river boundary to RP, the flood water depth also decreased from 1.3 m to near zero. Parker (1984), Pareja-Roman et al. (2020), and Xiao et al. (2021) have demonstrated that from PHL (∼160 km) to the river flow boundary, the tidal amplitude and range dampens with higher Delaware River runoff; however, the sea-level increases at the same time at a much larger rate. In Figure 10b, we can see a rapid decline of 0.5 m within a 12-km distance from the boundary (∼215 km) to NB (∼203 km) due to the doubling of the channel depth and flow diversion toward other tidal creeks. Then, the flood level decreases gradually following the river width expansion for the remaining portion. For different AMC and river flux conditions, the flood water depth decreased to 0.8 m when the AMC decreased to 90%, a reduction of nearly 38% for a 33% change in river discharge. For the other scenarios, the changes in flood level followed a similar trend. To show the spatial distribution of the compounding, we have provided horizontal 2D maps of the flooding in Figure 11 that focus mainly on the river portion—from RP to the river flow boundary. In the subplot for the surge-induced flooding and baseline case, Figure 11a, we can see the along- and across-channel changes, where from MH the flooding starts to increase more significantly. The results show a substantial decrease in flood amplitude and extent starting with AMC 90%. Similarly, Figure 11b illustrates the 2D distribution of the fluvial flood water depth, which shows a more significant change closer to the river flow boundary.

Details are in the caption following the image

Spatial map of the flood water depth (in meters) estimated by removing peak tidal WSE from the WSE with tide, surge, and river forcings for different AMC scenarios. Two time windows are given using (a) peak storm surge period from the bay side (between 08/28/2011 and 08/29/2011) and (b) peak Delaware River discharge (between 08/29/2011 and 08/31/2011).

6.2 Response of Compound Flooding to Future Sea-Level Rise

This section describes the effect of different future SLR scenarios on the DBR along-channel changes in CF and non-linear interaction of TSR. Though the SLR scenarios have a spatially varying hydrodynamic response throughout the entire North Atlantic Basin, we focused only on the changes in the DBR region in this study. Model results for different scenarios with Hurricane Irene's atmospheric and river forcing are shown in Figure 12. Figure 12a represents the along-channel peak WSE, and the flood water depth is shown in Figure 12b, which is estimated by removing the SLR + tide peak WSE from SLR + TSR peak WSE. The along-channel peak WSE increased uniformly during surge-induced flooding following the elevated mean sea level from SLR. While the peak WSE during fluvial flooding shows a similar response, the along-channel gradient became milder with the higher SLR cases, especially at the river portion (RP to the head, Figure 12b). At the same time, the flood water depth remained nearly identical for all SLR scenarios and decreased compared to the baseline case starting from MH to the river flow boundary. During surge-induced flooding, the flood depth is reduced by more than 0.2 m between MH and PHL, indicating a weakened TSR interaction and compounding under SLR scenarios. The most significant difference is observed at the river flow boundary, where the flood depth is reduced by nearly 0.4 m during peak river discharge.

Details are in the caption following the image

(a) Along-channel peak water surface elevation (WSE) with different SLR scenarios separated for two different time windows; left panel: during peak storm surge from the bay side, right panel: during peak Delaware River discharge. (b) Flood water depth (in meters) estimated by removing peak SLR + tidal WSE from the WSE with SLR + tide, surge and river forcings; left and right panels are separated similarly to the panels in (a).

To understand this decrease in the along-channel flood water depth, we examined the changes to the tidal wave characteristics from the SLR-induced altered embayment width, depth, and area. Figures 13a and 13b show the inundation (wetting and drying) areas in the entire DBR region following a regular tidal forcing (without SLR) and tidal forcing with the most conservative SLR case (SSP1 2.6). In the mid and lower Delaware Bay, many low-lying land areas comprising agricultural land and wetland/salt-marsh systems lie within 1 m of the present-day mean sea level (Lee et al., 2017). Even the SSP1 2.6 based mean sea level increase of ∼0.7 m submerges most of these areas during high tide, causing a much more dramatic variation in estuary width following the tidal cycles (Figure 13b). This increased embayment width and frictional drag play a critical role in reducing the phase speed of the tidal wave and along-channel amplitude decay [see Friedrichs, 2010 for more details]. We observed a similar trend in bay water level variation for the applied SLR cases, as shown in Figure 13c. With SLR scenarios, the tidal water surface fluctuates from a higher sea level (Figure 13a). We removed this elevated sea level using a tide-averaging method and extracted the surface oscillation for comparison. In the absence of storm surge and river discharge, the tidal range decreases as the waves propagate upstream, more prominently when the water surface overtops most low-lying areas (PHL WSE in Figure 13c). Recent studies, such as Hall et al. (2013), Lee et al. (2017), and Du et al. (2018), have observed a similar along-channel tidal energy dissipation when the wetlands are allowed to be submerged by SLR-induced higher tidal elevation. Specifically, Lee et al. (2017) has shown that the increased inundated area with higher sea level causes significant dissipation and reduces the tidal range in the DBR region. Although they only describe the changes in the tidal range without identifying the surface flood/ebb asymmetry, these studies support our model results shown in Figure 13c.

Details are in the caption following the image

Comparison of tidal flooding and draining in the Delaware Bay and River. (a) Tidal surface elevation at RP for two scenarios: without SLR and with SLR SSP1 2.6. Red circles show the instantaneous time periods used for mapping the estuary width change in (b). (b) Top panels: extent of wet area (or estuary width) during a rising and a low slack tide using SLR scenario SSP1 2.6 and present-day bathymetry conditions; bottom panels: a similar comparison but without SLR. (c) Comparison of the tidal surface variation from a mean sea level (in meters) with and without SLR scenarios at two along-channel locations: BSL (bay entrance) and PHL (upstream end).

Friedrichs and Aubrey (1994) provided analytical solutions for surface elevation and cross-sectionally integrated channel velocity when tidal waves propagate in a strongly convergent estuary. By keeping all the first- and second-order terms in the continuity and momentum equations, a tidal amplitude growth factor is derived as
where urn:x-wiley:23284277:media:eft21265:eft21265-math-0020; urn:x-wiley:23284277:media:eft21265:eft21265-math-0021 represents the tidal wave number, urn:x-wiley:23284277:media:eft21265:eft21265-math-0022 is the e-folding length-scale of area convergence. The tidal wave phase speed, urn:x-wiley:23284277:media:eft21265:eft21265-math-0023 and frictionless gravity wave speed, urn:x-wiley:23284277:media:eft21265:eft21265-math-0024, are
Here, urn:x-wiley:23284277:media:eft21265:eft21265-math-0027 and urn:x-wiley:23284277:media:eft21265:eft21265-math-0028 represent time-averaged channel cross-section area and width, urn:x-wiley:23284277:media:eft21265:eft21265-math-0029 is the frictional drag coefficient, urn:x-wiley:23284277:media:eft21265:eft21265-math-0030 is the tidal amplitude to channel depth ratio, and urn:x-wiley:23284277:media:eft21265:eft21265-math-0031 is the tidal radian frequency. Now, using Equations 7 and 8 in Equation 6, we can obtain the tidal amplitude growth factor as
By implementing this scaling analysis on several realistic convergent estuaries, Friedrichs and Aubrey (1994) showed that for urn:x-wiley:23284277:media:eft21265:eft21265-math-0033, the tidal amplitude increases along the channel, whereas for urn:x-wiley:23284277:media:eft21265:eft21265-math-0034, it decays.

We can use Equation 9 for a simple mechanistic explanation of the tidal amplitude damping for SLR cases seen in Figure 13c. Figure 13b shows the dramatic increase in embayment width in the mid and lower Delaware Bay with SLR scenarios. The rate of width increase is much faster than the cross-section area increase due to the shallow conditions in the newly flooded wetlands/salt-marsh systems. The decrease in urn:x-wiley:23284277:media:eft21265:eft21265-math-0035 or cross-section averaged depth along with the amplified drag coefficient urn:x-wiley:23284277:media:eft21265:eft21265-math-0036 from shallow bathymetry and vegetation roughness can alter the value of urn:x-wiley:23284277:media:eft21265:eft21265-math-0037 and make it less than zero. Ultimately, the rising sea level from SLR conditions slows down the along-channel tidal wave phase speed, urn:x-wiley:23284277:media:eft21265:eft21265-math-0038, and increases amplitude damping in the DBR, more noticeably during the flood tide. During storm tide conditions, when surge elevation is added to the SLR sea level, the same processes can cause higher energy dissipation and reduce the along-channel surge amplification. In addition, the increase in DBR surface area from urn:x-wiley:23284277:media:eft21265:eft21265-math-0039 km2 for baseline case to urn:x-wiley:23284277:media:eft21265:eft21265-math-0040 km2 for SSP1 2.6 (11.72% increase) and the increase in DBR water volume from urn:x-wiley:23284277:media:eft21265:eft21265-math-0041 to urn:x-wiley:23284277:media:eft21265:eft21265-math-0042 m3 (10.4% increase) have limited the influence of river discharge on TSR interaction and generating CF from the river flow boundary to MH (Figure 12b).

7 Discussion

Our results in Section 10 show that the CF is highly sensitive to the AMC scenarios, subsequent river discharge, and tidal and surge elevation. A reduced river/creek discharge can decrease the compounded flood water depth during the surge-induced flooding, mainly at the ocean-river interaction zone (between MH and PHL). The more significant change can be seen at the river flow boundary during fluvial flooding, which generally affects the previously flooded river areas again after a certain period. At the onset of Hurricane Irene, the AMC was near the maximum saturation for the upper Delaware River Basin (MiddleAtlanticRiverForecastCenter), which led to increased flooding during surge-induced and fluvial peak conditions. Using temperature and precipitation projections from the CMIP5 global climate models for the Delaware River Basin, Hawkins and Woltemade (2019) found that the annual temperature is projected to increase from 2.0 to 4.5°C by 2080–2099, depending on representative concentration pathways (RCPs) 2.6 to 8.5. Then, based on a calibrated hydrology model, they also showed a basin-wide 7%–18% decrease in the summer subsurface moisture capacity by 2080–2099 due to the increased evapotranspiration in the area. Despite likely significant spatial variability in hydrologic behaviors across the Delaware River Basin in the future climate, such a temporally and spatially averaged representation provided a general idea about the soil moisture trend. Based on the predicted soil moisture range and our sensitivity analysis, it is likely that for the worst future climate condition (RCP 8.5), an extreme event similar to Hurricane Irene could see a reduced compound flood depth in the Delaware River.

Lastly, key limitations of this study should be noted. The analysis only showcases the impact of AMC scenarios without accounting for other essential watershed processes that can modulate fluvial flooding potential, such as future changes in hurricane precipitation and distribution and runoff from snowmelt (Hawkins & Woltemade, 2019). If tropical cyclone tracks become slow-moving and landfall becomes more intense for a longer duration in the future as projected (Emanuel, 2017; Knutson et al., 2020; Li & Chakraborty, 2020), AMC may have a weakened effect on flood characteristics when soil is more likely to be saturated with longer-duration and especially high-intensity rainfall in advance of peak discharge. The results of this study primarily reflect responses from a complex and specific coastal estuarine region, DBR; other systems in different parts of the world might show an opposing trend where the AMC increases and accelerates flooding in the future (e.g., Khatun et al., 2022). However, the integrated modeling and analysis approach can be readily transferred to analyze CF in other distinct coastal regions, except for coastal regions with gentle bed slopes. The backwater effect from storm surges on upstream river processes is not simulated here due to the relatively steep bed slopes of the DBR, although we acknowledge that neglecting the backwater effect would be a limiting factor for modeling coastal systems with gentle gradients. A two-way coupling approach between DHSVM and FVCOM has been identified as a future research direction.

While the SLR scenarios have shown that the tidal flooding extent and duration will increase almost linearly along the DBR, the surge and river-flow-induced flood depth will decrease. Our model results are based on the existing bathymetry and land elevation data, which might create additional uncertainties. The low-lying wetland areas could potentially keep up with the SLR (Kirwan et al., 2016), in which case the estuary width will reflect the current tidal flooding and draining, where the changes will mainly occur in terms of the bay/channel water depth. Hall et al. (2013) and Lee et al. (2017) have shown that if a hard shoreline approach (e.g., a sea wall at the shoreline) is implemented in the future, it would restrict the wetlands from submergence and increase the tidal amplitude in the river portion where the channel is much narrower (from MH to the river flow boundary). This means that the tidal energy dissipation in the lower bay region would not occur anymore, and the convergence effect would increase the tidal amplitude and surge along the channel. A coupled hydrodynamic and geomorphology model is needed to predict the dynamic changes in the estuary morphology and wetland elevation by applying the rising sea level and long-term future climate variations. However, it is a challenging task and a matter of ongoing research that falls outside the scope of this study.

Ultimately, this study has shown that the CF is not dominated by one system or a single flood driver; it is driven by complex non-linear interactions between watershed and coastal flood drivers. In a changing climate, disentangling the drivers of compound flooding would be a promising topic for future research.

8 Concluding Remarks

Amid growing research on the risk of compound flood hazards in the future climate, in this study, we focused on the sensitivity of fluvial (river flow) and coastal (storm surge) interaction to changing catchment and estuarine properties. We selected a shallow and convergent estuarine system in the U.S. Mid-Atlantic region—Delaware Bay and River—that historically has suffered both economically and socially from deadly extreme events, and is also expected to be vulnerable to climate change. Two high-resolution numerical modeling frameworks, DHSVM and FVCOM, are integrated and fully evaluated using a variety of field data sets to properly represent the interaction between the hydrological and hydrodynamic processes, reaching a ∼10 m resolution in the small tidal creeks in the Delaware Bay. It also illustrates the necessity of regional-scale model nesting to enhance fidelity in hazard analysis of extreme events. Then, we designed a sensitivity study to shed light on the response of fluvial-coastal CF to two essential variables: (a) potential future changes to the AMC and (b) future SLR. We observed that the along-channel flood depth and compounding are highly sensitive to catchment AMC and future SLR. A 20% decrease in AMC before Hurricane Irene (2011) entirely diminishes the river discharge at the upstream river flow boundary, leading to an indistinguishable CF at the river reach. Similarly, even the most conservative SLR case (SSP1 2.6) submerges most low-lying agricultural lands and wetlands, changes the tidal dynamics, and decreases the flood water depth on top of the higher sea level. This study revealed that, in estuarine systems, the changes in catchment and bay characteristics would play a critical role, and an increase in global temperature and rainfall intensity might not always lead to a higher CF. Studies that implement fluvial-coastal flood projection in the comprehensive prediction of future compound flood hazards need to improve the modeling accuracy by considering uncertainties from the critical processes and their interactions more adequately.


This work was supported by the MultiSector Dynamics area of the United States Department of Energy, Office of Science, Office of Biological and Environmental Research as part of the multi-program, collaborative Integrated Coastal Modeling (ICoM) project. All model simulations were performed using resources available through Research Computing at Pacific Northwest National Laboratory.

    Conflict of Interest

    The authors declare no conflicts of interest relevant to this study.

    Data Availability Statement

    The 3D ocean model FVCOM code is available from the MEDM Lab (http://fvcom.smast.umassd.edu/fvcom/). The Distributed Hydrology Soil Vegetation Model (DHSVM) code is available at https://www.pnnl.gov/projects/distributed-hydrology-soil-vegetation-model. Model unstructured grid is developed using different bathymetry and topographic data sets from ETOPO1 Global Relief Model (https://www.ngdc.noaa.gov/mgg/global/), Coastal Relief Model (https://www.ngdc.noaa.gov/mgg/coastal/crm.html), Continuously Updated Digital Elevation Model (https://coast.noaa.gov/htdata/raster2/elevation/NCEI_ninth_Topobathy_2014_8483/), and NOAA Continually Updated Shoreline Product (https://shoreline.noaa.gov/data/datasheets/cusp.html). Hydrodynamic model lateral and surface boundary conditions are assigned using OSU TPXO Tide Models (https://www.tpxo.net/home) and ECMWF ERA5 (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5), and model validations are performed using tidal water level and current measurements from NOAA tides and currents (https://tidesandcurrents.noaa.gov/) and C. MIST (https://cmist.noaa.gov/cmist/), respectively. They are provided here at https://zenodo.org/record/6609261 (https://doi.org/10.5281/zenodo.6609261).