A subgrid approach for unresolved topography in shallow water hydrodynamic modeling
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This study develops methods to represent the effect of subgrid scale topography for shallow water hydrodynamic models using Cartesian grids. Neglect of subgrid scale topographic variability is recognized as causing misrepresentation of wetting and drying processes (Defina, 2000). Subgrid topography has been previously parameterized at model-resolved grid scales using data from high-resolution digital elevation models to capture flow area and volume effects (e.g. Casulli, 2009), but proposed approaches have neglected key aspects of flow resistance. Form drag exerted by unresolved subgrid features cannot be arbitrarily neglected for shallow flow dynamics as it introduces complexity through directional variability. That is, the conventional approach to modeling subgrid frictional effects is through drag coefficients that apply identically to all flow directions through a grid cell; however, subgrid features can introduce directional bias through form drag, e.g. an embankment that blocks flow in only one direction. In the present work, two new model schemes were developed to address the frictional forcing on subgrid scale. These schemes are extensions of the subgrid modeling ideas of Volp et al. (2013) and Casulli (2009). The first new scheme is a subgrid drag model that determines directional drag coefficients representing the integrated and directionally-biased effects of subgrid drag. The second new scheme is a subgrid momentum model using the integrated fluxes through faces of a grid cell to represent subgrid forces and acceleration at the resolved-scale interface between two grid cells. The combination of these two methods is demonstrated to provide an approach to representing subgrid physical processes that have been missing in prior models. The new subgrid models were implemented in the Fine Resolution Environmental Hydrodynamics Model (Frehd) and validated using model-model comparisons at fine and coarse grid resolution. The validation test cases use real-world estuarine topography of a section from a 1×1 m lidar survey of the Nueces River Delta (Texas, USA). The new subgrid models are shown to reduce discrepancies between coarse-grid and fine-grid simulations over the time-space domain. Of key importance is that the new models can represent the flow deflection by subgrid topographic obstructions that cannot be captured without directional drag coefficients. This study indicates that application of the new subgrid modeling approaches can reduce grid-scale dependency that otherwise requires finer grid resolution to adequately capture flow physics.