Assessment and modelling of uncertainty in precipitation forecasts from TIGGE using fuzzy probability and Bayesian theory

The precipitation forecasts from numerical weather prediction have a variety of potential uses in flood forecasting and reservoir operation, but suffer from relatively poor performance due to the uncertainty of the hydrometeorological system. In this study, the control forecasts of four global weather centres were selected and assessed against the measured data using several verification metrics during the flood season (May-September) over the Shihe River catchment in the Huaihe River basin of China. The results show that the daily rainfall forecasts have low prediction ability and cannot meet the demand of reservoir regulation. To describe the uncertainty of precipitation forecasts for the safety of flood control, a new model was proposed using fuzzy probability and Bayesian theory on the basis of the generalized probability density function (GPDF). The performance of the new model is examined by using various probability measures and compared with the ensemble forecasts generated by the weather centres. It is proved that the fuzzy Bayesian model can generate the conditional probability distribution of actual precipitation from a single predicted value based on the historical observation and forecast data, and has strong generalization ability. Compared with the ensemble forecasts, although the fuzzy Bayesian model shows a slightly improvement in accuracy, it has better performance in sharpness and reliability. Meanwhile, the new model is easy to update with new samples by modifying its likelihood function, which is favourable for real-time reservoir regulation. In addition, the uncertainty of the precipitation forecast was analysed with the model in different lead times. Generally, the uncertainty increases with the growth of lead time, and the probability distribution of the rainfall forecast within 3 days is an acceptable result for a risk and benefit analysis of the flood control system. To be more specific, a fuzzy Bayesian model based on the GPDF is an efficient way to generate the probability distribution of the precipitation with forecast data for the uncertainty analysis, and makes it possible to provide a reference for reservoir managers to plan regulation strategies with a lead time of at least 3 days.