A Pseudospectral Collocation Approach for Flood Inundation Modelling with Random Input Fields

Abstract

In this study, an efficient framework of pseudospectral collocation approach combined with the generalized polynomial chaos (gPC) and Karhunen-Loevè expansion (gPC/KLE) was introduced to examine the flood flow fields within a two-dimensional flood modelling system. In the proposed framework, the heterogeneous random input field (logarithmic Manning’s roughness) was approximated by the normalized KLE and the output field of flood flow depth was represented by the gPC expansion, whose coefficients were obtained with a nodal set construction via Smolyak sparse grid quadrature. In total, 3 scenarios (with different levels of input spatial variability) were designed for gPC/KLE application and the results from Monte Carlo simulations were provided as the benchmark for comparison. This study demonstrated that the gPC/KLE approach could predict the statistics of flood flow depth (i.e., means and standard deviations) with significantly less computational requirement than MC; it also outperformed the probabilistic collocation method (PCM) with KLE (PCM/KLE) in terms of fitting accuracy. This study made the first attempt to apply gPC/KLE to flood inundation field and evaluated the effects of key parameters (like the number of eigenpairs and the order of gPC expansion) on model performances.

Keywords: collocation, generalized polynomial chaos, Karhunen-Loevè expansion, Smolyak sparse grid, Monte Carlo