Propagation of uncertainties in coupled hydro-meteorological forecasting systems: A stochastic approach for the assessment of the total predictive uncertainty

The pressure on the scientific community to provide medium term flood forecasts with associated meaningful predictive uncertainty estimations has increased in recent years. A technique for assessing this uncertainty in hydro-meteorological forecasting systems is presented. In those, the uncertainties generally propagate from an atmospheric model through a rainfall-runoff model. Consequently, 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 7-day rainfall and temperature forecast of the American atmospheric GFS model (deterministic run) as forcing data in a conceptual hydrologic model (deterministic run) coupled with a linear error model in order to predict river discharge. The linear error model is added to the hydrologic model run, in order to take advantage of the correlation in time between forecasting errors, thereby reducing errors that arise from hydrologic simulations. To assess the predictive uncertainty (total uncertainty) of the coupled models, the method makes use of a bivariate meta-gaussian probability density function. The latter allows estimating the probability distribution of the integrated model errors conditioned by the predicted river discharge values. 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 observations of river discharge.