Enhancing Machine Learning Models for Nowcasting and Short‐Term Forecasting of Precipitation With a Novel Probability‐Matching Loss Function

Yuan Cao, Shuaiyi Li, Jie Feng, Lei Chen, Hao Li, Yijun Zhang

Geophysical Research Letters · 16 December 2025 · China Meteorological Administration (CMA), Fudan University (FuXi)

In one sentence. A probability-matching loss replaces MSE for ML precipitation nowcasting, reducing smoothing and heavy-rain underestimation and better matching the observed intensity distribution.

Abstract

Abstract Machine learning (ML) precipitation forecasting models typically employ a mean squared error (MSE) loss function for optimization. However, due to the well‐known “double penalty” effect, MSE‐based losses often lead to overly smoothed prediction fields and a systematic underestimation of the frequency of heavy rainfall. To address this limitation, we propose a novel probability‐matching (PM) based loss for ML precipitation nowcasting and short‐term forecasting, comparing its performance with other classical losses. Comprehensive skill evaluation demonstrates that PM‐based loss offers relatively more balanced and consistent performance across metrics, particularly its lower forecast bias from light to heavy rainfall intensities. Spectral power analysis further indicates that PM‐based loss better preserves small‐scale precipitation variability throughout the forecast period. Additionally, it results in a forecast frequency distribution of precipitation that more closely aligns with the observed distribution. These findings indicate consistent improvements in predictive skill and reliability of ML precipitation forecasts when trained with the PM‐based loss.

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