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.
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.
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.