Quantifying multiple uncertainties in modelling shallow water-sediment flows: A stochastic Galerkin framework with Haar wavelet expansion and an operator-splitting approach

Abstract

The interactive processes of shallow water flow, sediment transport, and morphological evolution constitute a hierarchy of multi-physical problems of significant interests in a spectrum of engineering and science areas. To date, modelling shallow water hydro-sediment-morphodynamic (SHSM) processes is subject to multiple sources of uncertainty arising from input data and incomplete understanding of the underlying physics. A stochastic SHSM model with multiple uncertainties has yet to be developed as most SHSM models still concern deterministic problems and only one has been recently extended to a stochastic setting, but is restricted to a single source of uncertainty. Here we first present a new probabilistic SHSM model incorporating multiple uncertainties within the stochastic Galerkin framework using a multidimensional tensor product of Haar wavelet expansion to capture local, nonlinear variations in joint probability distributions and an operator-splitting-based method to ensure that the modelling system remains hyperbolic. Then, we verify the proposed model via benchmark probabilistic numerical tests with joint uncertainties introduced in initial and boundary conditions, matching established experiments of flow-sediment-bed evolutions driven by a sudden dam break and by a landslide dam failure and large-scale rapid flow-sediment-bed evolution in response to flash flood. The present work facilitates a promising modelling framework for quantifying multiple uncertainties in practical shallow water hydro-sediment-morphodynamic modelling applications.