Energy-Efficient Training-Free Zero-Inflation Correction for Rainfall Forecasting with Time-Series Foundation Models

Accurate rainfall forecasting is essential for climate and disaster management, but precipitation exhibits extreme zero inflation that modern time-series Foundation Models (TSFMs) fundamentally cannot represent due to their continuous regression outputs. This structural mismatch causes pervasive drizzle-like false alarms, miscalibrated nonzero intensities, and severely underdetected extremes, while retraining large TSFMs is computationally prohibitive and environmentally unsustainable for most regions. We present a training-free wrapper that corrects zero inflation for frozen TSFMs without updating any parameters. Our method restores discrete zero mass using empirical occurrence statistics, aligns positive-value distributions via probability-integral transforms, and applies Generalized Pareto tail mapping for extreme-value consistency. Experiments on South Australian rainfall show substantial gains with negligible overhead (<5,ms per forecast, compared to hundreds of GPU-hours for retraining). The proposed wrapper enables carbon-neutral, globally deployable climate services and directly advances the goals of UN SDG 13 (Climate Action).