Building Drag Model for Porous Shallow-Water Equations

Porous shallow-water equations (PSWEs) predict the depth and velocity of urban flooding without resolving individual buildings in the grid, which can reduce computational costs by a factor of 10 or more and thereby streamline large-scale modeling of urban flood hazards. However, PSWEs require a drag coefficient to account for building form drag and bottom shear, and its estimation has been challenging and a source of significant uncertainty in previous studies. Here, we use statistical mechanics, dimensional analysis, and classical shallow-water equations (CSWEs) to develop a new, closed-form equation for the drag coefficient that can be computed using globally available building footprints and topographic slope data. Considering both idealized building configurations and the layouts of numerous cities, and using the new equation for the drag coefficient, we show that coarse-grid PSWE predictions are consistent with fine-grid CSWE predictions at street width and larger scales. This work thus offers a pathway for full closure of the PSWEs for accurate and efficient urban flood prediction.