Risk analysis of raising reservoir flood limited water level based on Bayes theorem and flood forecast error

Abstract: The development of hydrometeorological forecast technology offers important opportunities for reservoir dynamic control of flood limited water level. Economic benefits can be improved by raising the flood limited water level, but there is certain flood control risk. The purpose of this study was to propose a risk analysis method of upper bound of dynamic control of flood limited water level in order to provide the support for the development of dynamic control of flood limited water level. The proposed risk analysis method was based on Bayes theorem and flood forecast error characteristics. Qinghe reservoir, located in the northeast of China, was taken as an example. 21 flood events of actual and forecast runoff from the year 1964 to 2013 were used. For large reservoirs that has the ability for multi-year regulation, decision makers of flood control operation concern a lot about runoff forecast accuracy because the design flood is controlled by the flood volume. First, maximum entropy method was selected to simulate the runoff prediction error probability density function of 21 flood events, also forecast error range was calculated. According to the actual need of runoff forecast error in Qinghe reservoir, the range was divided into 6 zones, and distribution probabilities of runoff forecast errors in each zone, namely the prior probability distributions of flood forecasting errors were obtained by integrating the density function. Then, the probabilities of the highest water levels being higher than corresponding designed levels within different flood forecast error bounds were studied, and the risks of different flood forecast errors were inferred by Bayes theorem when the highest water level in flood regulation met with the design flood frequency. Based on the risk analysis method, risks of each design water level considering flood forecast information were compared with risks of conventional mode. The proposed risk analysis method of upper bound of dynamic control of flood limited water level was compared with the conventional mode risk calculation results, which could be concluded that upper bound of dynamic control of flood limited water level considering forecast errors was safe and feasible. The risk method of single condition calculation was compared with Bayesian risk, which could be concluded that the proposed method was reasonable. The results showed that for the design flood level of 138.06 m, the risk rate of raising the flood limited water level as 127.80 m for flood forecast operation was 0.00077%, smaller than the original design risk rate (0.01%). It demonstrated that the risk of taking flood forecast results as discriminant index to raise the reservoir flood control level was smaller than the original routine operation risk. It was also fully proved that the Qinghe reservoir forecast operation mode used to determine the water level of reservoir flood control was safe and feasible. The upper bound of dynamic control of flood limited water level 127.80 m according to forecast operation mode in Qinghe reservoir is safe. The calculation results of single condition risk were smaller than the Bayesian posterior probability calculation, and the sum probability of mutually exclusive events was not equal to 1. Because the single condition of the completeness of time was irrespective, and the risk was calculated under the condition of incomplete calculation results. In addition, the distribution probability of flood forecast error multiplying the design flood frequency was lack of rationality. Using Bayesian formula to calculate the posterior probability had not only considered the conditions of mutually and complete event occurrence, but also combined the weighted probability, which was more reasonable than conventional irrespective of the posteriori probability calculation results. Above all, the proposed risk analysis method has certain theoretical meaning and practical value, and it can be used as the reference of the same type reservoir.