Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions

The initial data and bottom topography, used as inputs in shallow water models, are prone to uncertainty due to measurement errors. We model this uncertainty statistically in terms of random shallow water equations. We extend the Multi-Level Monte Carlo (MLMC) algorithm to numerically approximate the random shallow water equations efficiently. The MLMC algorithm is suitably modified to deal with uncertain (and possibly uncorrelated) data on each node of the underlying topography grid by the use of a hierarchical topography representation. Numerical experiments in one and two space dimensions are presented to demonstrate the efficiency of the MLMC algorithm.