Probabilistic collocation method for uncertainty analysis of soil infiltration in flood modelling

The probabilistic collocation method (PCM) based on the Karhunen-Loeve expansion (KLE) and Polynomial chaos expansion (PCE) is applied for uncertainty analysis of flood inundation modelling. The floodplain hydraulic conductivity (KS) is considered as one of the important parameters in a 2-dimensional (2D) physical model FLO-2D (with Green-Ampt infiltration method) and has a nonlinear relationship with the flood simulation results, such as maximum flow depths (hmax). In this study, due to the spatial heterogeneity of soil, log-transformed Ks was assumed a random field in spatiality with normal distribution and decomposed with KLE in pairs of corresponding eigenvalues and eigenfuctions. The hmax random field is expanded by a second-order PCE approximation and the deterministic coefficients in PCE are solved by FLO-2D. To demonstrate this method, a simplified flood inundation case was used, where the mean and variance of the simulation outputs were compared with those from direct Monte Carlo Simulation. The comparison indicates that PCM could efficiently capture the statistics of flow depth in flood modelling with much less computational requirements.