A linearized approach to flow resistance uncertainty in a 2-D finite volume model of flood flow

A linearized approach to quantifying predictive uncertainty in a 2-D model of shallow water flow in response to uncertainty in friction parameterization is presented. The resulting uncertain finite volume (UFV) method is tested against Monte Carlo simulations for uncertain models over channel only, floodplain only and channel and floodplain meshes. The results show that the UFV model performs well in predicting mean and standard deviations of water depths, for problems with two independent Manning's n values, with standard deviations of up to 0.02 m1/3 s−1 with a mean value of 0.03 m1/3 s−1. For depth averaged velocities, mean values are well represented, but standard deviations are poorly predicted by UFV. UFV also performs well when modelling flow over an uneven fractal topography and for a distributed (11 degrees of freedom) parameterization. A computation time advantage of >50 when compared to the Monte Carlo method is observed.