Statistical Analysis of Rainfall Variability and Water Balance Components in Johor Districts Using Seasonal Ornstein-Uhlenbeck

Abstract

This study analyses rainfall dynamics across three key districts in Johor which are Kluang, Batu Pahat, and Senai using a water balance model integrated with Stochastic Differential Equations (SDEs). Daily rainfall data from 2005 to 2024 were examined to assess hydrological variability, seasonal behavior, and long-term rainfall trends. The water balance framework quantifies rainfall, evapotranspiration, runoff, and storage to capture the dynamic movement of water within the hydrological system. Evapotranspiration was estimated using the Penman-based method, which considers temperature, humidity, solar radiation, and wind speed to represent actual water loss. The stochastic component applies the Seasonal Ornstein–Uhlenbeck (SOU) process, a mean-reverting SDE that accounts for randomness and seasonal variation in rainfall patterns. This allows for realistic simulation of rainfall behavior under Malaysia’s biannual monsoon influence. Results show that Kluang experiences higher rainfall amplitudes and more frequent extremes, while Senai remains consistently wet and Batu Pahat exhibits moderate but increasing rainfall intensity.The integrated SOU–water balance approach effectively represents both deterministic and stochastic processes, providing a robust framework for quantifying hydrological uncertainty. By coupling stochastic rainfall modeling with physical water balance processes, the study enhances understanding of rainfall–storage dynamics and supports adaptive water resource management, particularly under changing climate conditions.