Stop Using Root-Mean-Square Error as a Precipitation Target!
- 1Department of Meteorology, University of Reading, Reading, United Kingdom
- 2National Centre for Atmospheric Sciences, University of Reading, Reading, United Kingdom
Abstract
Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semicontinuous, zero inflated, strictly nonnegative, and heavy tailed. This Gaussian-implied objective misspecifies the data-generating process because it tolerates negative predictions, underpenalizes 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 ) = μ p . 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 toward 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 convolutional long short-term memory (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, from 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.
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BibTeX
@article{hunt2026stop,
title = {{Stop Using Root-Mean-Square Error as a Precipitation Target!}},
author = {Kieran M. R. Hunt},
journal = {Artificial Intelligence for the Earth Systems},
year = {2026},
month = jul,
doi = {10.1175/aies-d-25-0083.1},
url = {https://doi.org/10.1175/aies-d-25-0083.1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Stop Using Root-Mean-Square Error as a Precipitation Target!
AU - Kieran M. R. Hunt
PY - 2026
DA - 2026/07/29
JO - Artificial Intelligence for the Earth Systems
DO - 10.1175/aies-d-25-0083.1
UR - https://doi.org/10.1175/aies-d-25-0083.1
AB - Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semicontinuous, zero inflated, strictly nonnegative, and heavy tailed. This Gaussian-implied objective misspecifies the data-generating process because it tolerates negative predictions, underpenalizes 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 ) = μ p . 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 toward 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 convolutional long short-term memory (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, from 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.
SN - 2769-7525
ER -