Modeling Weekly Rainfall Dynamics Using Markov Chains: Evidence from Biswanath District, Assam, India

Abstract

Rainfall variability is important for agricultural production and water resource management in rain-fed regions. This study examined weekly rainfall dynamics in Biswanath district, Assam, using a first-order Markov Chain model based on weekly rainfall data from 1971 to 2022. Rainfall observations were classified into No Rain, Light Rain, Moderate Rain, and Heavy Rain states, and a transition probability matrix was estimated to assess movement among these states. Steady-state probabilities were used to describe the long-term distribution of rainfall conditions, while mean recurrence time and mean first passage time were considered to evaluate persistence and accessibility among rainfall states. The results showed that No Rain and Light Rain were the dominant long-term states, whereas Heavy Rain exhibited the highest one-step persistence. The stationary probabilities were 0.334 for No Rain, 0.263 for Light Rain, 0.239 for Moderate Rain, and 0.164 for Heavy Rain. Mean first passage time results indicated that Heavy Rain was reached in approximately 3.08–3.17 weeks from the other states, while Light Rain required approximately 5.79–6.05 weeks. These findings show that long-term rainfall frequency and short-term state persistence provide complementary information. The Markov Chain framework therefore provides a structured description of weekly rainfall behaviour that may support rainfall assessment, crop planning, irrigation scheduling, and water resource management in Biswanath district.