Subgrid Corrections in Storm-Driven Coastal Flooding

Coastal flooding models based on the numerical solution of the 2D shallow water equations are used widely to predict the timing and magnitude of inundation during storms, both in real-time forecasting and long-term design. Constraints on computing time, especially in forecasting, can limit the models’ spatial resolution and hence their accuracy. However, it is desirable to have fast flooding predictions that also include the best-available representation of flow pathways and barriers at the scales of critical infrastructure. This need can be addressed via subgrid corrections, which use information at smaller scales to ‘correct’ the flow variables (water levels and current velocities) averaged over the model scale.

In this dissertation, subgrid corrections have been added to the ADvanced CIRCulation (ADCIRC) model, a widely used, continuous-Galerkin finite-element based, shallow water flow model. This includes the full derivation of averaged governing equations, closure approximations, and subgrid implementation into the source code. Testing of this new model was first performed on 3 domains: an idealized winding channel, a tidally influenced bay in Massachusetts, and a regional storm surge model covering Calcasieu Lake in Southwestern Louisiana with forcing from Rita (2005). By pre-computing the averaged variables from high-resolution bathy/topo data sets, the model can represent hydraulic connectivity at smaller scales. This allows for a coarsening of the model and thus faster predictions of flooding, while also improving accuracy. The implementation permits changing a logic-based wetting and drying algorithm to a more desirable logic-less algorithm, and requires averaging correction factors on both an elemental and vertex basis. This new framework further increases efficiency of the model, and is general enough to be used in other Galerkin-based, finite-element, hydrodynamic models. It is shown that the flooding model with subgrid corrections can match the accuracy of the conventional model, while offering a 10 to 50 times increase in speed.

Next, higher level corrections to bottom friction and advection were incorporated into the subgrid model, and the framework was expanded and tested at the ocean-scale. It was hypothesized that by adding higher-level corrections to the model and applying them to ocean-scale domains, accurate predictions of storm surge at the smallest coastal scales can be obtained. To accomplish this, higher-level corrections were derived and implemented into the governing equations and extensive elevation and landcover data sets were curated to cover the South Atlantic Bight region of the U.S. Atlantic Coast. From there, the subgrid model was tested on an ocean-scale domain with tidal and meteorological forcing from Matthew (2016). The improvements in water level prediction accuracy due to subgrid corrections are evaluated at 218 observation locations throughout 1500 km of coast along the South Atlantic Bight. The accuracy of the subgrid model with relatively coarse spatial resolution (RMSE = 0.41 m) is better than that of a conventional model with relatively fine spatial resolution (RMSE = 0.67 m).By running on the coarsened subgrid model, we improved the accuracy over efficiency curve for the model, and as a result the computational expense of the simulation was decreased by a factor of 13.

Finally, subgrid corrections were systematically tested on a series of five ocean-scale meshes with minimum nearshore resolutions ranging from around 60 m on the highest resolution mesh to 1000 m on the coarsest mesh. This study aimed to find the mesh resolution that offered the best trade-off between accuracy and efficiency. The limitations of the subgrid model were explored and guidelines for future users were established. In all, it was found that the primary limitation to the subgrid model came from the aliasing of important flow-blocking features such as barrier islands in the coarsest resolution meshes. However, in areas without these features subgrid corrections can offer tremendous advantages while running on very coarse meshes.

The work completed in this dissertation moves the science of subgrid corrections forward by integrating the corrections into a widely used ocean-circulation and storm surge model. This work offers improvements to both hurricane storm surge forecasting and long-term design by allowing for reduced run-times and increased accuracy on coarsened numerical meshes.

JL Woodruff (2023). “Subgrid Corrections in Storm-Driven Coastal Flooding,” North Carolina State University.

Deterministic, Dynamic Model Forecasts of Storm-Driven Erosion

The U.S. Atlantic and Gulf coasts are vulnerable to storms, which can cause significant erosion of beaches and dunes that otherwise protect coastal communities. One example is Hurricane Ian (2022), which impacted Florida’s Gulf coast and then again the southeast U.S. Atlantic coast, resulting in significant beach and dune scarping and breaches in multiple locations. Models can be used for real-time forecasts of storm-driven erosion, which can support decision-making, but are limited due to demands for computational resources and uncertainties in dynamic coastal systems. Current methods for erosion forecasts are based on empirical equations for wave run-up, which do not represent sediment transport during the storm, and on surrogate models, which also must rely on simplified representations of the system. However, with continued advancements in high-resolution geospatial data and computational efficiencies, there is an opportunity to apply morphodynamic models for deterministic forecasts of beach and dune erosion as a stormapproaches the coast. Real-time morphodynamic model implementation is challenging because the framework must be accurate and efficient while maintaining versatility to account for forecast uncertainties. Additionally, the evaluation and post-processing for the model needs to effectively communicate the results, including the timing and scale of coastal change during an extreme event when temporal observations are unavailable.

In this study, we apply the state-of-art model eXtreme Beach (XBeach) to predict coastal erosion due to Hurricanes Michael (2018) and Ian (2022). Sandy beaches along the U.S. Atlantic and Gulf coasts are represented with thousands of one-dimensional transects, which are sampled for real-time forecasts based on the storms’ tracks and projected landfall locations. The morphodynamic model is initialized with high-resolution digital elevation models of the present-day conditions and forced with hydrodynamics from high-resolution wave and circulation models, and its predictions are categorized based on impacts to the primary dune. A key contribution of this study is the semi-automation of the modeling system, so the modeling framework can be applied to different regions of the coast as the landfall location shifts.

To demonstrate this, forecasts for Ian (2022) were initiated several days before the initial landfall location in Punta Gorda, Florida, and continued as the track made a secondary landfall near Georgetown, South Carolina. About 1800 transects are selected for each of the 25 advisories. The simulations are monitored, evaluated, and visualized to communicate the XBeach predictions of coastal change. The framework produces results in less than an hour and then publishes visualizations in less than 10 minutes. Results are compared spatially and temporally to qualitative post-Ian observations and total water level predictions. XBeach can predict dune impact compared to an established coastal change forecasting model while providing additional morphodynamic information not typically available, such as timing and magnitude of volume change. The addition of fully resolved ground surface information and morphodynamics in the model makes it possible to better understand the storm evolution and how that translates into erosion of beaches and dunes.

JF Gorski (2023). “Deterministic, Dynamic Model Forecasts of Storm-Driven Erosion,” North Carolina State University.

Numerical Extensions to Incorporate Subgrid Corrections in an Established Storm Surge Model

Inundation models represent coastal regions with a grid of computational points, often with varying resolution of flow pathways and barriers. Models based on coarse grid solutions of shallow water equations have been improved recently via the use of subgrid corrections, which account for information (ground surface elevations, roughness characteristics) at smaller scales. In this work, numerical approaches of an established storm surge model are extended to include subgrid corrections. In an attempt to maintain continuity with existing users and results, model extensions were limited to those needed to provide basic subgrid capabilities, and included two major additions. First, a finite volume method is used to incorporate corrections to the mass and momentum equations using high-resolution ground surface elevations. Second, the no-slip condition imposed on the B-grid wet/dry interface in the model is modified to a slip condition to enable flows in channels with widths comparable to cell size. Numerical results demonstrate these numerical extensions can significantly enhance the accuracy of the model’s predictions of coastal flooding, with low additional computational cost.

A Begmohammadi, D Wirasaet, AC Poisson, JL Woodruff, JC Dietrich, D Bolster, AB Kennedy (2023). “Numerical extensions to incorporate subgrid corrections in an established storm surge model.” Coastal Engineering Journal, 65(2), 175-197, DOI: 10.1080/21664250.2022.2159290.

Storm Surge Predictions from Ocean to Subgrid Scales

The inland propagation of storm surge caused by tropical cyclones depends on large and small waterways to connect the open ocean to inland bays, estuaries, and floodplains. Numerical models for storm surge require these waterways and their surrounding topography to be resolved sufficiently, which can require millions of computational cells for flooding simulations on a large (ocean scale) computational domain, leading to higher demands for computational resources and longer wall-clock times for simulations. Alternatively, the governing shallow water equations can be modified to introduce subgrid corrections that allow coarser and cheaper simulations with comparable accuracy. In this study, subgrid corrections are extended for the first time to simulations at the ocean scale. Higher-level corrections are included for bottom friction and advection, and look-up tables are optimized for large model domains. Via simulations of tides, storm surge, and coastal flooding due to Hurricane Matthew in 2016, the improvements in water level prediction accuracy due to subgrid corrections are evaluated at 218 observation locations throughout 1500 km of coast along the South Atlantic Bight. The accuracy of the subgrid model with relatively coarse spatial resolution (ERMS = 0.41 m) is better than that of a conventional model with relatively fine spatial resolution (ERMS = 0.67 m). By running on the coarsened subgrid model, we improved the accuracy over efficiency curve for the model, and as a result, the computational expense of the simulation was decreased by a factor of 13.

JL Woodruff, JC Dietrich, D Wirasaet, AB Kennedy, D Bolster (2023). “Storm surge predictions from ocean to subgrid scales.” Natural Hazards, published online, DOI: 10.1007/s11069-023-05975-2.

Emulator for Eroded Beach and Dune Profiles due to Storms

Dunes and beaches are vulnerable to erosion during storm events. Numerical models can predict beach response to storms with fidelity, but their computational costs, the domain-specific knowledge necessary to use them, and the wide range of potential future storm and beach conditions can hinder their use in forecasting storm erosion for short- and long-term horizons. We develop an emulator, which is an efficient predictive model that behaves like a numerical model, to predict the morphologic response of the subaerial beach to storms. Specific emphasis is placed on providing antecedent beach states as an input to the emulator and predicting the post-storm profile shape. Training data include beach profiles at multiple stages in a nourishment life cycle to assess if such a framework can be applied in locations that nourish as a coastal defense policy. Development and application of the emulator is focused on Nags Head, North Carolina, which nourishes its beaches to mitigate hazards of storm waves, flooding, and erosion. A high-fidelity, process-based morphodynamic model is used to train the emulator with 1250 scenarios of sea-storms and beach profiles. The post-storm beach state is emulated with a parameterized power-law function fit to the eroded portion of the subaerial profile. When the emulator was tested for a sequence of real storms from 2019, the eroded beach profiles were predicted with a skill score of 0.66. This emulator is promising for future efforts to predict storm-induced beach erosion in hazard warnings or adaptation studies.

A Gharagozlou, DL Anderson, JF Gorski, JC Dietrich (2022). “Emulator for Eroded Beach and Dune Profiles due to Storms.” Journal of Geophysical Research: Earth Surface, 127(8), e2022JF006620, DOI: 10.1029/2022JF006620.

Improved Wave Predictions with ST6 Physics and ADCIRC+SWAN

The Simulating WAves Nearshore (SWAN, Booij et al. 1999) model is used widely for predictions of waves in coastal regions. Like other spectral wave models, SWAN uses parameterizations to represent wave evolution due to sources (e.g. wind), sinks (e.g. whitecapping, bottom friction, depth-limited breaking), and resonance (e.g. quadruplet and triad wave-wave interactions). Each parameterization is based typically on observational data to represent the transfer of energy to, from, and between waves. It is necessary for each term to represent its physical process, but it is also necessary for the terms to be calibrated collectively to represent their combined effects on wave evolution. The calibrated wave predictions can then be coupled with models for circulation and coastal flooding, e.g. ADvanced CIRCulation (ADCIRC, Luettich et al. 1992).

SWAN release version 41.20 included a new “package” of wave physics (referred to as ST6 physics). This package has new parameterizations of wind input, whitecapping, swell dissipation, wind speed scaling, and other processes (Rogers et al. 2012). The ST6 physics have been adopted by other wave models (e.g. NOAA’s WaveWatch III, Liu et al. 2019), and it may become the preferred physics package for SWAN. However, because the ST6 physics package has changes to so many parameterizations, it is necessary to quantify its effects on wave predictions. Recent studies (e.g. Aydogan and Ayat 2021) have demonstrated the benefits of using the ST6 physics in the standalone version of SWAN, but its effects have not been quantified for the coupled ADCIRC+SWAN (Dietrich et al. 2011a), which is used for real-time forecasts during impending storms. Do the ST6 physics improve the ADCIRC+SWAN wave predictions?

CC Day, JC Dietrich (2022). “Improved wave predictions with ST6 Physics and ADCIRC+SWAN.” Shore & Beach, 90(1), 59-61, DOI: 10.34237/1009016.

Effects of Model Resolution and Coverage on Storm-Driven Coastal Flooding Predictions

Predictions of storm surge and flooding require models with higher resolution of coastal regions, to describe fine-scale bathymetric and topographic variations, natural and artificial channels, flow features, and barriers. However, models for real-time forecasting often use a lower resolution to improve efficiency. There is a need to understand how resolution of inland regions can translate to predictive accuracy, but previous studies have not considered differences between models that both represent conveyance into floodplains and are intended to be used in real time. In this study, the effects of model resolution and coverage are explored using comparisons between forecast-ready and production-grade models that both represent floodplains along the US southeast coast, but with typical resolutions in coastal regions of 400 and 50 m, respectively. For two storms that impacted the US southeast coast, it is shown that, although the overall error statistics are similar between simulations on the two meshes, the production-grade model allowed a greater conveyance into inland regions, which improved the tide and surge signals in small channels and increased the inundation volumes between 40% and 60%. Its extended coverage also removed water level errors of 20–40 cm associated with boundary effects in smaller regional models.

A Thomas, JC Dietrich, CN Dawson, RA Luettich (2022). “Effects of Model Resolution and Coverage on Storm-Driven Coastal Flooding Predictions.” Journal of Waterway, Port, Coastal, and Ocean Engineering, 148(1), 04021046, DOI: 10.1061/(ASCE)WW.1943-5460.0000687.

Impact of Storm Events on Density Stratification in the Pamlico and Albemarle Estuarine System

Tropical cyclones and other coastal storms have multiple effects on estuaries. They create storm surge, or the rise of water levels above the normal tides, which can cause flooding of coastal areas, including communities near estuaries. They can also alter ecosystems, including in estuaries with changes to nutrient loading and regeneration, abrupt changes in salinity, increases in the mixed-layer depth, decreases in sea-surface temperature, and breakdowns in water column stratification. The interactions between surge and estuarine circulation can enhance the storm effects. And with the increasing intensity of tropical cyclones, these effects will be further enhanced.

Numerical models can represent the coastal environment and its response to the combined effects of tides, river flows, and winds. It is especially challenging for numerical models to represent the response of estuaries to storms, due to the complex interactions of fresh and saline waters, and thus relatively few studies have used models to represent both storm- and density-driven circulation in estuaries. These few studies have shown that salinities and temperatures of estuaries can change significantly during storms and may require weeks to recover, depending on the amount of freshwater discharge. However, these studies have been limited in number and geographic coverage, relied on coupling to other models for baroclinic inputs, did not have the estuarine mixing and stratification as a focus, or were missing physics. Much is still uncertain about how estuarine circulation evolves during a storm event. How quickly do the horizontal salinities respond to the storm? How does the salinity transport vary through an estuary? How do freshwater discharges due to rainfall affect the mixing? Another uncertainty is the salinity response after the storm. How quickly does a system recover? Do the freshwater discharges interrupt the recovery? In this thesis, it is hypothesized that, for a large and shallow estuarine system with minimal connections to the open ocean, the storm forcing will cause large brackish and freshwater intrusions and recoveries that vary through the system.

To investigate this hypothesis, we developed a three-dimensional model of storm- and density-driven circulation in the Albemarle-Pamlico Estuarine System (APES) in North Carolina. Irene (2011) was used as the basis for storm event simulations to examine the evolution of the horizontal salinity distribution. Included in this model were hurricane-strength winds and pressures, tides, river discharges, and density circulation. Using this model, it was determined that during Irene, APES experienced movements of brackish water into the estuaries and saline water into the sounds. These movements were heavily dependent on the winds. After the stormsimulation, the large river discharges produced intrusions of fresher water into major areas of the sound, and after two weeks, the system was not fully regulated.

From this research, we have developed a better understanding of the horizontal salinity distribution of APES as well as how the system reacts to a single storm event. This research allows for future studies to consider different types of storms along with refinement of the river forcings, to understand better the full range of estuarine responses.

BA Rumbaugh (2021). “Impact of storm events on density stratification in the Pamlico and Albemarle Estuarine System,” North Carolina State University.