Recent severe storms on the U.S. Gulf coast have demonstrated the challenges presented by compound flooding, such as the interactions between rainfall runoff and storm surge. Historically, many studies have neglected these nonlinear interactions, but we propose to use a discontinuous Galerkin shallow water equation solver, which allows for incorporation of rainfall inputs directly onto the finite element mesh. In this work, we analyze the use of parametric rainfall for forecasting scenarios, using Hurricane Beryl (2024) as a case study. Beryl led to extensive flooding due to rainfall and storm surge along the Gulf. We use a collection of the National Oceanic and Atmospheric Administration's short-term advisories along with the best track data to demonstrate the efficacy of the parametric rainfall model for forecasting. Results show that the parametric rainfall input allowed for much more accurate inundation. Areas with heavy rainfall and low surge were affected the most, with many areas peaking over 50 cm above the baseline surge model. Almost none of the available high water marks from Beryl were captured by the standard models, but the compound flooding models capture many of them, the majority of which show relative errors under 10 percent. Results from the advisory forecast simulations were shown to be much closer to the best track hindcast simulation when rainfall forcing was used, even while early forecasts predicted the storm's trajectory much less accurately. The advisory simulations improved even further as Beryl neared the Texas coast, with sampled peak elevations most closely approximating the best track at Advisory 38, a few hours before landfall.

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