A Perturbance Moment Point Estimate Method for Uncertainty Analysis of the Hydrologic Response

A robust hydrological modelling framework must include a quantitative assessment of the uncertainties affecting the accuracy of model results. This is important both to quantify the relative importance of the uncertainty sources, a necessary step toward the reduction of the overall uncertainty, and to adequately support decision-making processes. Here we consider a new uncertainty estimation method, the Perturbance Moment Point Estimate Method (PMM), based on a discrete representation of the probability distribution functions of the stochastic input variables. We apply the method to a geomorphological model of the hydrologic response of the Brenta River (North-East Italy) and compare its performance with those from a traditional, more computationally-intensive, Monte Carlo Simulation (MCS) approach. We show that the PMM method is significantly more efficient in terms of computational time and offers an accuracy that is appropriate for hydrological applications. We also show how the use of Point Estimate Methods allows the analysis of the effects of individual sources of uncertainty without the need for additional simulations. The PMM application shows that for the particular basin under study, the uncertainty in calibrated model parameters is a major contributor to the overall uncertainty which is not necessarily a novelty in the hydrologic literature. However, we also find that the imperfect knowledge of forcing inputs and particularly measurement error in rainfall observations plays a comparably important role and induces, in our study, a large uncertainty in the estimated discharge. Finally, we observe a somewhat compensative interaction among different sources of uncertainty, which may lead to an overall model uncertainty that differs from the sum of the uncertainties associated with the individual sources.