Stochastic Forecast of Flow Reservoir Behaviour

AbstractThe main advantage of stochastic forecasting of flow reservoir behaviour is the fan of a possible value, which deterministic methods of forecasting could not give us. Future development of random process is described well by first stochastic then deterministic forecasting. We can categorize the discharge in measurement profile as a random process. The contents of this article is the development of a forecasting model for the management of large open water reservoirs with supply function. The model is based on a linear autoregressive model, which forecasts values of average monthly flow from a linear combination of previous values of average monthly flow, autoregressive coefficients and random numbers. The autoregressive coefficient was calculated from the Yule-Walker equations [2,3]. The model was compiled for the forecasts in the range of 1 to 12 month with a backward correlation of 2 to 11 months. The data was freed of asymmetry with the help of the Box-Cox rule [1], the value r was found by optimization. In the next step, the data was transform to a standard normal distribution. Our data was with monthly step and forecasting was recurrent. We used a 90-year long real flow series for to compile the model. The first 75 years were used for the calibration of the model (autoregressive coefficient), the last 15 years were used only for validation. The model outputs were compared with the real flow series. For comparison between real flow series (100% successful of forecast) and forecasts, we used as values of forecast average, median, modus and miscellaneous quintiles. Results were statistically evaluated on a monthly level. The main criterion of success was the absolute error between real and forecasted flow. Results show that the longest backward correlation did not give the best results. On the other hand, the flow in months, which were forecasted recurrently, give a smaller error than flow forecasted from real flow. For each length of forecast, even for backward size of correlation, different values of quintiles were reached, for which forecasting values gave the smallest error, [4,5]. Flows forecasted by the model give very fine results in drought periods. Higher errors were reached in months with higher average flows. This higher flow was caused by floods. The floods are predictable. Due to good results in drought, periods we can use the model managed large open water reservoirs with supply function