Probabilistic Modeling of Flow Over Rough Terrain

Abstract

This paper presents a method for the propagation of uncertainty, modeled in a probabilistic framework, through a model-based simulation of rainflow on a rough terrain. The adopted model involves a system of conservation equations with associated nonlinear state equations. The topography, surface runoff coefficient, and precipitation data are all modeled as spatially varying random processes. The Karhunen-Loeve expansion is used to represent these processes in terms of a denumerable set of random variables. The predicted state variables in the model are identified with their coordinates with respect to the basis formed by the Polynomial Chaos random variables. A system of linear algebraic deterministic equations are derived for estimating these coordinates.