Modeling the Impact of Tropical Cyclone Intensity on Rainfall under Stochastic Processes

Abstract Rainfall prediction is crucial for agricultural planning and risk management in cyclone-prone areas like Malawi's Machinga district, where farming largely depends on rain-fed 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 Gamma and Weibull probability distributions into stochastic differential equations (SDEs) to model rainfall with greater accuracy. Physics-Informed Neural Networks (PINNs) are used to solve the SDE. The models have successfully demonstrated the ability to capture key rainfall characteristics, such as seasonality, mean reversion, and extreme values, through rigorous numerical simulations. Simulation results confirm the model's effectiveness, showing distinct behaviors as a normal rainfall parameter varies, indicating its critical role in scaling the impact of cyclones on rainfall. Application to real data from Machinga district revealed that lower values of the parameter correlate with increased cyclone activity and abnormal rainfall patterns. Over several seasons, the model accurately predicted extreme rainfall events, with performance metrics such as \(R^2\) values consistently exceeding 0.55, validating the model’s reliability and precision.