Efficient estimates of uncertainties in tsunami inundation forecasts

We present a methodology for efficient variance estimation of nonlinear tsunami inundation forecasts. The tsunami inundation dataset is produced using a numerical nonlinear shallow water equation solver with an initial deformation of the sea surface. We introduce a set of perturbation equations to the nonlinear shallow water equations, which use the dataset as the reference case. Perturbations to the initial condition of the inundation event are imposed to simulate an ensemble of outcomes. The linearized version of the shallow water perturbation equations is used to precalculate numerical Green’s functions for a sparse grid of points within the domain. The Green’s function approach allows for efficient calculations of ensembles of perturbations. Variances are computed from the ensembles, and the resulting statistical summaries are interpolated to the entire domain using the universal kriging. It is demonstrated that variance estimates, for the entire domain or a select grid points of interest, can be made with a much lower computational complexity than other traditional approaches, as well as exposing the task to simple parallelization. This methodology is applicable to other similar dynamic problems.