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Improved predictions can be based on recent observed differences or errors between the best available model predictions and the actual measured data. This is possible in the predicted amount of supplies, services, sewage, transportation, power, water, heat, or gas, as well as in the predicted level of rivers. As an example, physical modeling of the dynamics of a catchment area produces models with a limited forecasting accuracy for the discharge of rivers. The discrepancies between the model and the actually observed past discharges can be used as information for error correction. With a time-series model of the error signal, an improved discharge forecast can be made for the next few days. The best type and order of the forecasting time-series model can be automatically selected. Adaptive modeling in data assimilation calculates updates of the time-series model estimated from the error data of only the last few weeks. The use of variable updated models has advantages in periods with the largest discharges, which are most important in flood forecasting.