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The development of surrogate models to study uncertainties in hydrologicsystems requires significant effort in the development of sampling strategiesand forward model simulations. Furthermore, in applications where predictiontime is critical, such as prediction of hurricane storm surge, the predictionsof system response and uncertainties can be required within short time frames.Here, we develop an efficient stochastic shallow water model to address theseissues. To discretize the physical and probability spaces we use a StochasticGalerkin method and a Incremental Pressure Correction scheme to advance thesolution in time. To overcome discrete stability issues, we propose cross-modestabilization methods which employs existing stabilization methods in theprobability space by adding stabilization terms to every stochastic mode in amodes-coupled way. We extensively verify the developed method for bothidealized shallow water test cases and hindcasting of past hurricanes. Wesubsequently use the developed and verified method to perform a comprehensivestatistical analysis of the established shallow water surrogate models.Finally, we propose a predictor for hurricane storm surge under uncertain winddrag coefficients and demonstrate its effectivity for Hurricanes Ike andHarvey.

Cross-mode Stabilized Stochastic Shallow Water Systems Using Stochastic Finite Element Methods