Spectral Sampling Method for Uncertainty Propagation in Long-Wave Runup Modeling

Abstract

This paper presents a stochastic approach to model input uncertainty with a general statistical distribution and its propagation through the nonlinear long-wave equations. A Godunov-type scheme mimics breaking waves as bores for accurate description of the energy dissipation in the runup process. The polynomial chaos method expands the flow parameters into series of orthogonal modes, which contain the statistical properties in stochastic space. A spectral projection technique determines the orthogonal modes from ensemble averages of systematically sampled events through the long-wave model. This spectral sampling method generates an output statistical distribution using a much smaller sample of events comparing to the Monte Carlo method. Numerical examples of long-wave transformation over a plane beach and a conical island demonstrate the efficacy of the present approach in describing uncertainty propagation through nonlinear and discontinuous processes for flood-hazard mapping.