Ensemble predictions in hydrology: necessity, preparation and using in water management decision processes

During the flood the decision maker, who decides about water outflow from the reservoir which closes a small mountain catchment (the area more or less 1000 km2), wants exact hydrograph forecasts for next 3 days. During the drought the decision maker needs exact forecasts for next 2 - 3 months. Above expectations are unrealistic because of lack of precise quantitative precipitation forecasts (QPF), even for 1 day. Mezoscale COSMO-LM14 model (operated in Poland) gives the QPF biased by error similar to the " naive forecast " errors similar to observed precipitation. In our opinion, expectation that in the close future the important progress in the QPF quality will be possible is unrealistic because of chaotic nature of the atmosphere and impossibility of precise estimating of initial conditions. QPF biased by substantial errors causes large errors in hydrograph forecasts. Uncorrected hydrographs used as a categorical forecast (only one possible realization of the future hydrograph) can cause inadmissible losses in decision processes. We need ensemble of hydrological forecasts represents uncertainty of forecast and. the proper decision algorithm. Unfortunately, up to this day in Poland, the QPF are formulated in a categorical form. Then some part of our work was devoted to prepare such algorithms that enable to transform one categorical QPF to a QPF ensemble. To develop decision algorithms that could transform ensemble hydrological forecasts into an optimal decision is the main part of our work. It is difficult problem because. in the stochastic control problem the result of the control is a random variable. Usually an optimization criteria is formulated as maximization (or minimization) of an expected value of this variable. But this criteria is not synonymous because there is infinite number of different random distributions with the same expected values. Then we have to use an additional criteria which eliminates unacceptable results of the control, for example increase of the flood peak (it is possible in the case of the flood overestimation). Conclusion is, that in the stochastic control the optimization problem always becomes multicriterial. The most important result of our researches we can formulate as follows : using the ensemble hydrological predictions and the proper decision algorithm we achieve the important progress in the reservoir control based on the same imperfect forecast system. This effect we can achieve without additional costs