A Distributional Regression Network With Data Transformation for Calibrating Rainfall Forecasts

• Published in: Journal of geophysical research. Machine learning and computation Vol. 2; no. 2
• Main Authors: Huang, Zeqing, Schepen, Andrew, Bennett, James C., Robertson, David E., Zhao, Tongtiegang, Im, Eun‐Soon, Wang, Quan J.
• Format: Journal Article
• Language: English
• Published: Wiley 01.06.2025
• Subjects: data transformation; forecast calibration; forecast skill; machine learning; rainfall forecast
• ISSN: 2993-5210; 2993-5210
• DOI: 10.1029/2025JH000635

Machine learning methods provide a promising approach for exploiting relationships between raw forecasts and observations for forecast calibration. This paper highlights the role of data transformation in rainfall forecast calibration with neural networks. We develop a distributional regression network that accounts for the positive skewness and zero bound of rainfall by incorporating a normalizing transformation (log‐sinh) in both the input and output stages. A unified loss function is formulated based on the negative log‐likelihood function for parameter optimization. To test the role of data transformation, we conduct five calibration experiments: one that does not use transformation at all (the baseline) while the others use the log‐sinh transformation in different ways. All experiments are based on 10‐day rainfall forecasts from the European Centre for Medium‐range Weather Forecasts (ECMWF) from 2011 to 2022. Overall, the calibration methods effectively correct spatiotemporally varying biases in raw forecasts and improve reliability, yielding mean skill improvements of approximately 2%–11% and in the best case reducing forecast biases to less than 2%. Without transformation, the baseline method suffers from forecast biases ranging from −30% to 50%, due to its limited ability to characterize the uncertainty of rainfall forecasts. Of the four experiments that use the log‐sinh transformation, the optimal performance is achieved by the combined use of transforming raw forecasts for the input layer and utilizing fixed transformation parameters for generating calibrated forecasts in the output layer. We show that this method marginally outperforms an advanced existing Bayesian Ensemble Model Output Statistics method in reducing forecast biases. Plain Language Summary Rainfall forecasts generated by numerical weather prediction models are often subject to systematic biases and insufficient representation of uncertainty in their ensemble spread. Machine learning methods, which exhibit general effectiveness in capturing non‐linear relationships, offer a promising approach for forecast calibration to improve rainfall forecasts. This paper presents a neural network architecture for rainfall forecast calibration that explicitly handles the feature of non‐normal distributions, including positive skewness and the zero bound of rainfall data. Specifically, a normalizing transformation (log‐sinh) is incorporated into the distributional regression networks; and a unified loss function is formulated for parameter optimization based on the negative log‐likelihood function. Five comparative experiments are devised to test the different implementations of data transformation using 10‐day rainfall forecasts from the European Centre for Medium‐range Weather Forecasts. The results show that the calibration method without data transformation inadequately corrects spatiotemporally varying biases in raw forecasts, with forecast bias ranging from −30% to 50%. The distributional regression networks incorporating data transformation effectively reduce forecast biases to less than 2% and achieve mean skill improvements of about 2%–11% compared to raw forecasts. Overall, this paper highlights the effectiveness of the neural networks with data transformation in rainfall forecast calibration. Key Points A neural network architecture for rainfall forecast calibration is developed by introducing a normalizing transformation and a unified loss function Five comparative experiments based on 10‐day rainfall forecasts are devised to investigate the importance of data transformation The neural networks with data transformation effectively correct biases in raw forecasts and yield mean skill improvements of about 2%–11%