A Mutual Information Theory-Based Approach for Assessing Uncertainties in Deterministic Multi-Category Precipitation Forecasts

Abstract

Copyright © 2022 The Authors. The very nature of weather forecasts and verifications and the way they are used make it impossible for one single or absolute standard of evaluation. However, little research has been conducted on verifying deterministic multi-category forecasts, which is based on the attribute of uncertainty. The authors propose a new approach using two mutual information theory-based scores for assessing the comprehensive uncertainty of all categories and the uncertainty for a certain category in deterministic multi-category precipitation forecasts, respectively. Specifically, the comprehensive uncertainty is defined as the average reduction in uncertainty about the observations resulting from the use of a predictive model to provide all categories forecasts; the uncertainty of a certain category is defined as the reduction in uncertainty about the observations resulting from the use of a predictive model to provide a certain category forecast. By applying the proposed approach and traditional verification methods, the four precipitation forecasting products from the China Meteorological Administration, European Centre for Medium-Range Weather Forecasts, National Centers for Environmental Prediction, and United Kingdom Meteorological Office were verified in the Dahuofang Reservoir Drainage Basin, China. The results indicate that: (a) the proposed approach can better capture the changing patterns of uncertainties with lead times and distinguish the forecasting performance among different forecast products; (b) the proposed approach is resistant to the extreme bias; (c) the proposed approach needs a careful choice of bin width; and (d) the bias analysis is necessary before verifying the uncertainties in precipitation forecasts.