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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2509.08369 |
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| _version_ | 1866918138693550080 |
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| author | Hunt, Kieran M. R. |
| author_facet | Hunt, Kieran M. R. |
| contents | 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 propose 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 for $y>0$, matching observed precipitation characteristics. We (i) estimate $p$ from the variance--mean power law and show that precipitation across temporal aggregations is far from Gaussian, with the Tweedie power $p$ increasing with accumulation length towards a Gamma limit; and (ii) demonstrate consistent skill gains when training deep data-driven models with Tweedie deviance in place of RMSE. In diffusion-model downscaling over Beijing, Tweedie loss improves wet-pixel MAE and extreme recall ($\sim0.60$ vs $0.50$ at the 99th percentile). In ConvLSTM nowcasting over Kolkata, Tweedie loss yields improved wet-pixel MAE and dry-pixel hit rates, with improvements that compound autoregressively with lead time (for MAE, $\sim2%$ at $t{+}1$ growing to $\sim16%$ at $t{+}4$). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stop using root-mean-square error as a precipitation target! Hunt, Kieran M. R. Atmospheric and Oceanic Physics 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 propose 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 for $y>0$, matching observed precipitation characteristics. We (i) estimate $p$ from the variance--mean power law and show that precipitation across temporal aggregations is far from Gaussian, with the Tweedie power $p$ increasing with accumulation length towards a Gamma limit; and (ii) demonstrate consistent skill gains when training deep data-driven models with Tweedie deviance in place of RMSE. In diffusion-model downscaling over Beijing, Tweedie loss improves wet-pixel MAE and extreme recall ($\sim0.60$ vs $0.50$ at the 99th percentile). In ConvLSTM nowcasting over Kolkata, Tweedie loss yields improved wet-pixel MAE and dry-pixel hit rates, with improvements that compound autoregressively with lead time (for MAE, $\sim2%$ at $t{+}1$ growing to $\sim16%$ at $t{+}4$). 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. |
| title | Stop using root-mean-square error as a precipitation target! |
| topic | Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2509.08369 |