Forecasting Return Time of Extreme Precipitation by Large Deviation Theory
Abstract
Forecasting extreme precipitation is essential yet challenging due to its rarity and complexity. We develop a large deviation framework to estimate the return times of extreme precipitation events. We first find that the Landau distribution, originally introduced in plasma physics, accurately captures extreme precipitation at approximately 93% of global locations, outperforming conventional extreme value distributions with 76% matched locations under the same accuracy criterion. Enriching rare event samples by the fitted Landau distribution, we obtain more accurate estimates of large deviation rate functions and return times, enabling forecasts beyond historically observed precipitation intensities. Mapping historical return times to future projections from the Coupled Model Intercomparison Project Phase 6 (CMIP6), we show that return time curves under different emission scenarios collapse onto a unified relation, revealing a sharply increased lifetime exposure to extreme precipitation for 21st-century birth cohorts under most future emission scenarios.
Cite
@article{arxiv.2604.10890,
title = {Forecasting Return Time of Extreme Precipitation by Large Deviation Theory},
author = {Haotian Xie and Haoxian Liu and Jingfang Fan and Ying Tang},
journal= {arXiv preprint arXiv:2604.10890},
year = {2026}
}