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.
The U.S. Atlantic and Gulf of Mexico coasts are vulnerable to storms, which can cause significant erosion of beaches and dunes that protect coastal communities. Real-time forecasts of storm-driven erosion are useful for decision support, but they are limited due to demands for computational resources and uncertainties in dynamic coastal systems and storm forcings. Current methods for coastal change forecasts are based on empirical calculations for wave run-up and conceptual models for erosion, which do not represent sediment transport and morphological change during the storm. However, with continued advancements in high-resolution geospatial data and computational efficiencies, there is an opportunity to apply morphodynamic models for forecasts of beach and dune erosion as a storm approaches the coast. In this study, we implement a forecast system based on a deterministic, dynamic model. The morphodynamic model is initialized with digital elevation models of the most up-to-date conditions and forced with hydrodynamics from wave and circulation model forecasts, and its predictions are categorized based on impact to the primary dune, defined in this study as the first ridge of sand landward of the beach. Results are compared spatially to the observed post-storm topography using changes to dune crest elevations and volumes, and temporally to the predicted total water level at the forecasted moment of dune impact.
With sea-level rise, flooding in coastal communities is now common during the highest high tides. Floods also occur at normal tidal levels when rainfall overcomes stormwater infrastructure that is partially submerged by tides. Data describing this type of compound flooding is scarce and, therefore, it is unclear how often these floods occur and the extent to which non-tidal factors contribute to flooding. We combine measurements of flooding on roads and within storm drains with a numerical model to examine processes that contribute to flooding in Carolina Beach, NC, USA — a community that chronically floods outside of extreme storms despite flood mitigation infrastructure to combat tidal flooding. Of the 43 non-storm floods we measured during a year-long study period, one-third were unexpected based on the tidal threshold used by the community for flood monitoring. We introduce a novel model coupling between an ocean-scale hydrodynamic model (ADCIRC) and a community-scale surface water and pipe flow model (3Di) to quantify contributions from multiple flood drivers. Accounting for the compounding effects of tides, wind, and rain increases flood water levels by up to 0.4 m compared to simulations that include only tides. Setup from sustained (non-storm) regional winds causes deeper, longer, more extensive flooding during the highest high tides and can cause floods on days when flooding would not have occurred due to tides alone. Rainfall also contributes to unexpected floods; because tides submerge stormwater outfalls on a daily basis, even minor rainstorms lead to flooding as runoff has nowhere to drain. As a particularly low-lying coastal community, Carolina Beach provides a glimpse into future challenges that coastal communities worldwide will face in predicting, preparing for, and adapting to increasingly frequent flooding from compounding tidal and non-tidal drivers atop sea-level rise.
Compound flooding, the concurrence of multiple flooding mechanisms such as storm surge, heavy rainfall, and riverine flooding, poses a significant threat to coastal communities. To mitigate the impacts of compound flooding, forecasts must represent the variability of flooding drivers over a wide range of spatial scales while remaining timely. One approach to develop these forecasts is through subgrid corrections, which utilize information at smaller scales to “correct” water levels and current velocities averaged over the model scale. Recent studies have shown that subgrid models can improve both accuracy and efficiency; however, existing models are not able to account for the dynamic interactions of hydrologic and hydrodynamic drivers and their contributions to flooding along the smallest flow pathways when using a coarse resolution. Here, we have developed a solver called CoaSToRM (Coastal Subgrid Topography Research Model) with subgrid corrections to compute compound flooding in coastal systems resulting from fluvial, pluvial, tidal, and wind-driven processes. A key contribution is the model’s ability to enforce all flood drivers and use the subgrid corrections to improve the accuracy of the coarse-resolution simulation. The model is validated for Hurricane Eta 2020 in Tampa Bay, showing improved prediction accuracy with subgrid corrections at 42 locations. Subgrid models with coarse resolutions (R2 = 0.70, 0.73, 0.77 for 3-, 1.5-, 0.75-km grids) outperform standard counterparts (R2 = 0.03, 0.14, 0.26). A 3-km subgrid simulation runs roughly 50 times faster than a 0.75-km subgrid simulation, with similar accuracy.
In this research, we implemented a neural network to predict peak values for total water level (tides and storm surge) at multiple stations, considering astronomical tides and storm tracks of any duration as inputs. To create the training library, we simulated 1,813 synthetic tropical cyclones based on historical data in the North Atlantic Ocean, with a specific focus on storms that affect North Carolina. These simulations used a full-physics hydrodynamic model with variable spatial resolution of about 50 m near the coast. The outputs were downscaled to grayscale images with a higher and constant resolution of 15 m, enhancing the flood predictions by considering small-scale topographic features, and then used as training data for the neural network. The many-to-one deep learning model predicts a single peak total water level in time at multiple locations in space using time series of the offshore astronomical tide and track parameters as inputs. We used the model to make probabilistic predictions of peak total water levels for observed and perturbed tracks of several historical storms that affected North Carolina.
We showed that the neural network performed well (with errors ranging from 8 to 43 cm) in predicting peak total water levels at nine locations in North Carolina. We applied the neural network to make probabilistic predictions of peak total water levels for observed and perturbed tracks of historical storms. For each storm, the neural network predicted at nine stations for 101 storm scenarios (the true/historical storm and 100 perturbations) in less than 10 seconds. The performance for the observed historical storms was similar to those obtained in process-based simulations, but with a significant gain in computational runtime.
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.
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.
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.