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A Pseudospectral Collocation Approach for Flood Inundation Modelling with Random Input Fields
In this study, an efficient framework of pseudospectral collocation approach combined with the generalized polynomial chaos (gPC) and Karhunen-LoevÃ¨ 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 Manningâ€™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-LoevÃ¨ expansion, Smolyak sparse grid, Monte Carlo
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