SoftSEEPS relaxes the SEEPS score into a differentiable loss, letting precipitation models optimize dry/light/heavy categories directly, with SEEPS dropping by up to about 0.1 at no resolvable RMSE cost

Introduces SoftSEEPS: a sigmoid relaxation of the SEEPS dry/light/heavy categorical indicators, yielding a score s(x,y,τ)=c(x,τ)^T S c(y,τ) differentiable in the prediction, where the smoothing parameter τ trades approximation accuracy against better-conditioned gradients and the relaxation converges to the original hard classification as τ→0. SEEPS was previously a piecewise-constant assignment with no gradient signal, so ML models could only be evaluated against it, not optimized for it; the authors state that no prior work in the relevant benchmark line had developed a differentiable approximation of SEEPS, and they motivate the sigmoid relaxation by Gumbel-softmax and concrete-distribution relaxations of categorical operations. The authors report testing that SoftSEEPS converges to the reference discrete-SEEPS implementation in the scores library; during training τ is annealed automatically by a plateau scheduler tracking validation discrete SEEPS, and all reported validation SEEPS values are discrete scores.

Trains IMERGDecoder, a convolutional decoder with 54.3M parameters, to map the latent space of a frozen ArchesWeather-M backbone to IMERG daily precipitation (V07B, mm/day), predicting next-day 24-hour accumulated precipitation without any explicit precipitation input. This setup combines a well-performing yet inexpensive weather forecasting model with a limited training-compute budget; the authors note that direct comparison to existing learned downscaling methods is challenging because prior work typically focuses on regional or patch-based settings. Training uses 1998–2018, validation 2019, testing 2020; 25,000 steps with AdamW on a single A100, about 5 hours wall-clock; the decoder uses three bilinear-upsampling stages with four residual blocks each, 512 channels in the first two stages and 384 in the third.

SoftSEEPS can be combined linearly with log-normalized RMSE, and sweeping the weight traces an apparent Pareto-optimal frontier between RMSE and SEEPS: SEEPS drops by as much as about 0.1 at no resolvable cost in RMSE. The natural expectation is that SoftSEEPS can only trade off against RMSE; instead, under the joint objective SEEPS falls from 0.481 with MSE only to 0.381 while RMSE rises only from 5.316 to 5.334, whereas SoftSEEPS only reaches SEEPS 0.375 but RMSE 7.720. Appendix Table 1 gives the values: persistence RMSE 9.288/SEEPS 0.819, climatology 7.492/1.098, ERA5 interpolation 5.689/0.612; the MSE-trained decoder already exceeds all baselines.

Spatial analysis shows SEEPS improves uniformly across the globe when SoftSEEPS is added to the loss, while RMSE both improves and degrades in a spatially varying pattern, which the authors read as an indicator that including climatological information in the training objective is successful. This provides per-location evidence beyond the aggregate trade-off, indicating the gains are not merely an overall average effect but relate to climatological threshold information entering the objective. Based on the spatial evaluation in Fig. 4; the authors contrast the spatially uniform SEEPS improvement with the spatially varying RMSE pattern as the indicator.

The result targets global high-resolution precipitation forecasting with IMERG daily precipitation as the training target, and is meant for ML weather-model developers who want to optimize categorical precipitation scores directly. Methodologically, SoftSEEPS is a sigmoid relaxation of SEEPS whose smoothing parameter τ trades approximation accuracy against gradient conditioning, annealed during training by a plateau scheduler tracking validation discrete SEEPS; the authors recommend future work training larger weather models for precipitation on SoftSEEPS. Evaluation uses 2019 validation, 2020 testing, and persistence, climatology, and ERA5-interpolation baselines, and the authors note that direct comparison to existing learned downscaling methods is challenging because prior work typically focuses on regional or patch-based settings.

A careful reader would still watch: the specific τ annealing schedule and weight-sweep values are not listed numerically in the text and are only pointed to in Fig. 3; the spatial conclusion rests on the visual pattern in Fig. 4 rather than per-region statistics; the authors note direct comparison to existing learned downscaling methods is challenging, so the size of SoftSEEPS's advantage over other precipitation training objectives awaits validation in broader settings; and with SoftSEEPS only, RMSE rises to 7.720, so the intensity-error cost of using that objective alone needs weighing in applications.