Résumé
In flood forecasting systems the uncertainties generally propagate from an atmospheric model through a rainfall-runoff model. Thus it appears to be difficult to isolate the errors that stem from the individual model components. In this study, the integrated flood forecasting system uses the rainfall and temperature forecast of the American atmospheric GFS model (deterministic run) as forcing data in a conceptual hydrological model (deterministic run) coupled with an autoregressive error model in order to predict river discharge. The auto-regressive error model is added to the hydrologic model, in order to take advantage of the correlation in time between forecasting errors, thereby enabling the reduction of errors that arise from hydrologic simulation. To assess the predictive uncertainty (total uncertainty) of the coupled models, the method makes use of a bivariate meta-gaussian density. The latter allows estimating the probability distribution of the integrated model errors conditioned on predicted river discharge values. The technique is based on the application of a standard Normal Quantile Transform that makes the distribution of the model outputs and the model errors Gaussian in order to render straightforward the computation of confidence intervals. In forecasting mode, the model makes use of the known error distributions to account for bias in the predicted discharge values and to estimate the upper and lower confidence intervals. The proposed methodology is applied to the case study of the Alzette river located in the Grand Duchy of Luxembourg. Confidence limits are computed for various lead times of prediction and compared with the respective observations of river discharge.