A Multimodel Weighting Decision Process for Real Time Flood Forecasting: Application to the Upper Garonne Watershed
Context This article describes a decision process for real-time flood forecasting. A method is presented which combines the results of different models with weights adapted to the state of the flood forecasting system. Each model has specific performances when it is calibrated, and has a specific sensitivity to each perturbation that can occur. The results (forecasts) of all of these models are cross-correlated. For a wide class of adequacy criteria, the best estimate of the variable to be predicted is a linear combination of these results. In that combination the weight of each model forecast is strongly linked to the model's relative performance. For a specific perturbed environment (we will call it a state of the hydrologic hydrometric system) the performance of some sensitive models decreases but others may remain stable. Optimal weights are therefore specific for each state of the system. When states can be pre-specified, the decision process splits into two different steps: diagnostic and prognostic. During a first diagnostic step, using various coherence tests among all collected data and possible external information that is not used in the model, the probability of being in each state is estimated. This step may include expert judgement as is the case in practice. During the second prognostic step, optimal weights of the model are computed, using the error covariance matrix for all models in each state of the system and the estimated probabilities of being in each state as determined during the previous diagnostic step. Such a complete decision rule needs a detailed study that cannot be done for each case, and which is based on the assumption that all perturbations can be described and modeled. A simplified procedure has thus been developed based on the basic idea that only the normal state can be easily identified. Instead of estimating state probabilities, this procedure relies on weights that evolve according to recent errors. The results of this procedure, as applied to the Vérèze catchment, have been quite as good as those obtained with the complete pond. These weighting decision procedures also proved in this case to be much more effective than any attempt to choose the best model at each time step. This very elementary result is in contradiction with classical approach of switching among multiple models. Switching procedures are in fact designed to estimate the state of the system, assuming that one must decide what is the state. For operational purpose such decisions are useless and switching procedures appear to be sub-optimal, as they lead to a discontinuous forecast decision. The interest of the multimodel approach is confirmed even if uncontrollable perturbations occur in real-time. The performances obtained since the implementation of this decision process in the flood forecasting system of the upper Garonne watershed are presented.