Quantifying the uncertainty of precipitation forecasting using probabilistic deep learning

Precipitation forecasting is an important mission in weather science. In recent years, data-driven precipitation forecasting techniques could complement numerical prediction, such as precipitation nowcasting, monthly precipitation projection and extreme precipitation event identification. In data-driven precipitation forecasting, the predictive uncertainty arises mainly from data and model uncertainties. Current deep learning forecasting methods could model the parametric uncertainty by random sampling from the parameters. However, the data uncertainty is usually ignored in the forecasting process and the derivation of predictive uncertainty is incomplete. In this study, the input data uncertainty, target data uncertainty and model uncertainty are jointly modeled in a deep learning precipitation forecasting framework to estimate the predictive uncertainty. Specifically, the data uncertainty is estimated a priori and the input uncertainty is propagated forward through model weights according to the law of error propagation. The model uncertainty is considered by sampling from the parameters and is coupled with input and target data uncertainties in the objective function during the training process. Finally, the predictive uncertainty is produced by propagating the input uncertainty and sampling the weights in the testing process. The experimental results indicate that the proposed joint uncertainty modeling and precipitation forecasting framework exhibits comparable forecasting accuracy with existing methods, while could reduce the predictive uncertainty to a large extent relative to two existing joint uncertainty modeling approaches. The developed joint uncertainty modeling method is a general uncertainty estimation approach for data-driven forecasting applications.