  The development of surrogate models to study uncertainties in hydrologic
systems requires significant effort in the development of sampling strategies
and forward model simulations. Furthermore, in applications where prediction
time is critical, such as prediction of hurricane storm surge, the predictions
of system response and uncertainties can be required within short time frames.
Here, we develop an efficient stochastic shallow water model to address these
issues. To discretize the physical and probability spaces we use a Stochastic
Galerkin method and a Incremental Pressure Correction scheme to advance the
solution in time. To overcome discrete stability issues, we propose cross-mode
stabilization methods which employs existing stabilization methods in the
probability space by adding stabilization terms to every stochastic mode in a
modes-coupled way. We extensively verify the developed method for both
idealized shallow water test cases and hindcasting of past hurricanes. We
subsequently use the developed and verified method to perform a comprehensive
statistical analysis of the established shallow water surrogate models.
Finally, we propose a predictor for hurricane storm surge under uncertain wind
drag coefficients and demonstrate its effectivity for Hurricanes Ike and
Harvey.
