Explanation and Optimizing Multi‐Model Blending Algorithm Using Random Variables Theory - Yu Wang; Yong Cao; Yue Shen; Ruixia Zhao; Xiaoqing Zeng; Li Yao; Kan Dai (Geophysical Research Letters)
Abstract In this study, we modeled the multi‐model blending process using random variables and explicitly derived the distribution of the blended forecast error under the assumption of normally distributed errors. Utilizing this error distribution, we regained the scalar version of the Best Linear Unbiased Estimator. Notably, the model yielded negative weights, which contradict traditional assumptions that weights should be positive. To address this, we modified the algorithm to set negative weights to zero and compared the performance with the original algorithm. Our findings indicate that setting negative weights to zero results in a slight improvement in blending performance compared to using negative weights directly. This improvement may be attributed to modeling the actual forecast error as a normally distributed unified parameter and applying a consistent correlation coefficient across the annual data set.