Improved first-order second moment method for uncertainty estimation in flood forecasting

The first-order second moment (FOSM) method is widely used in uncertainty analysis. This method uses a linearization of the function that relates the input variables and parameters to the output variables. This simplification occasionally leads to problems when the mean value of the input variable is close to a local or global maximum or minimum value of the function. In this case, the FOSM computes artificially a zero uncertainty because the first derivative of the function is equal to zero. An improvement to the FOSM is proposed, whereby a parabolic reconstruction is used instead of a linear one. The improved FOSM method is applied to a flood forecasting model on the Loire River (France). Verification of the method using the Monte Carlo technique shows that the improved FOSM allows the accuracy of the uncertainty assessment to be increased substantially, without adding a significant burden in computation. The sensitivity of the results to the size of the perturbation is also analysed.