Stop Using Root-Mean-Square Error as a Precipitation Target!

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.