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Uncertainty quantification with spectral approximations of a flood model

This work establishes a stochastic flood model based on shallow water equations (SWE) for Toce river valley in Italy by combining the deterministic SWE with a probabilistic description of some parameters that are subject to uncertainties, and approximates the model by Hermite polynomial chaos expansions (PCE) and subsequently by Karhunen-Loéve expansions (KLE) for the purposes of fast explorations of the model's probabilistic behaviour and data compressions. It is shown that to represent the model to the same accuracy of its variance, PCE and KLE approximations need to store much smaller size of data than a collocation representation.