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

TL;DR

This paper introduces a modified loss function for data-driven weather forecasting models that reduces smoothing effects, leading to sharper forecasts, higher resolution, and improved tropical cyclone and wind extreme predictions.

Contribution

A simple, parameter-free modification to the mean squared error loss function that separates decorrelation and spectral amplitude errors, enhancing forecast sharpness and resolution.

Findings

Effective resolution increased from 1,250km to 160km

Improved ensemble spread and forecast sharpness

Enhanced predictions of tropical cyclone strength and wind extremes

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.