Abstract

Rainfall prediction is crucial for agricultural planning and risk management in cyclone-prone areas such as the Machinga, Phalombe, and Mulanje districts of Malawi, where farming is largely dependent on rainfed agriculture. Recent severe cyclones have highlighted the inadequacies of current predictive models, particularly in capturing extreme weather patterns influenced by tropical cyclones. This study addresses this gap by integrating the Gamma and Weibull probability distributions into stochastic differential equations (SDEs) to model rainfall with greater accuracy. These distributions are often used individually in SDEs. The Gamma distribution primarily captures the mean-reversion characteristics of data, while the Weibull distribution captures extreme rainfall patterns. Integrating them ensures that both behaviors are represented in the model. Physics-Informed Neural Networks (PINNs) are used to solve the SDEs. Stochastic simulations demonstrate the model’s ability to capture key rainfall characteristics, including seasonality, mean reversion, and extreme events. The effectiveness of the model’s normal rainfall parameter is demonstrated through its application to real data from the Machinga, Phalombe, and Mulanje districts. It reveals that lower values of the parameter correlate with increased rainfall amounts. Over several seasons, the model accurately predicted extreme rainfall events. Performance metrics validate the model’s reliability and precision.

Original language	en
Volume	11
Issue number	5
Publication status	Published - 2025