Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function

Christopher Subich, Syed Zahid Husain, Leo Separovic, Jing Yang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57191-57211, 2025.

Abstract

Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a “double penalty” effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model’s effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-subich25a, title = {Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function}, author = {Subich, Christopher and Husain, Syed Zahid and Separovic, Leo and Yang, Jing}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57191--57211}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/subich25a/subich25a.pdf}, url = {https://proceedings.mlr.press/v267/subich25a.html}, abstract = {Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a “double penalty” effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model’s effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.} }
Endnote
%0 Conference Paper %T Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function %A Christopher Subich %A Syed Zahid Husain %A Leo Separovic %A Jing Yang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-subich25a %I PMLR %P 57191--57211 %U https://proceedings.mlr.press/v267/subich25a.html %V 267 %X Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a “double penalty” effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model’s effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.
APA
Subich, C., Husain, S.Z., Separovic, L. & Yang, J.. (2025). Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57191-57211 Available from https://proceedings.mlr.press/v267/subich25a.html.

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