Stop using root-mean-square error as a precipitation target!

Hunt, K. M. R. ORCID: https://orcid.org/0000-0003-1480-3755 (2026) Stop using root-mean-square error as a precipitation target! Artificial Intelligence for the Earth Systems. ISSN 2769-7525 doi: 10.1175/AIES-D-25-0083.1

Abstract/Summary

Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semi-continuous, zero-inflated, strictly non-negative, and heavy-tailed. This Gaussian-implied objective misspecifies the data-generating process because it tolerates negative predictions, underpenalises rare heavy events, and ignores the mass at zero. We suggest replacing RMSE with the Tweedie deviance, a likelihood-based and differentiable loss from the exponential–dispersion family, with variance function V(μ) = μᵖ. For 1 < p < 2, it yields a compound Poisson–Gamma distribution with a point mass at zero and a continuous density over y > 0, matching observed precipitation characteristics. In this paper, we (i) estimate p from the variance–mean power law and show that precipitation across temporal aggregations is far from Gaussian and that the Tweedie power p increases with accumulation length towards a Gamma limit; and (ii) demonstrate consistent skill gains when training deep data-driven models with Tweedie deviance instead of RMSE. In diffusion-model downscaling over Beijing, Tweedie loss improves wet-pixel MAE and extreme recall (∼0.611 vs 0.566 at the 99th percentile). In ConvLSTM nowcasting over Kolkata, Tweedie loss yields improvements in wet-pixel MAE and dry-pixel hit rates, with improvements autoregressively compounding over lead time (for MAE, 3.5% at t+1 growing to 8.7% at t+4). Extreme recall at the 99.9th percentile is not significantly higher at t+1 but becomes significantly higher by t+3 and t+4. Because the Tweedie deviance is continuous in p, it adapts smoothly across scales, offering a statistically justified, practical replacement for RMSE in precipitation-based learning tasks.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/131168
Identification Number/DOI	10.1175/AIES-D-25-0083.1
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > NCAS Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Meteorological Society
Download/View statistics	View download statistics for this item