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