Markov chain analysis of southwest monsoon rainfall time-series data from 1951 to 2021 in areas with Type I Philippine climate

Abstract

Time-series rainfall data of the southwest monsoon were analyzed using the Markov chain to determine the tendencies of rainfall states in the areas with a Type I Philippine climate. We analyzed 71 years of rainfall data from June to September 1951 to 2021. Based on the computed stationary distribution, time-series rainfall data from Type I climate zones tend to lie in state R₁ (0 mm to 5 mm) with long-term transition probability from any possible state to state R₁ of π_R1 = 0.551775 during the season. The long-term transition probability from any possible state to state R₂ (6 mm to 25 mm) is π_R2 = 0.28182, about half of the value for state R₁. Classified rainfall states R₃ to R₆ have negligible long-term transition probabilities. These values correspond to the long-term tendencies of the rainfall state for the entire study period. Thus, daily rainfall from June to September mostly took place between the threshold of 0 mm to 5 mm for the past 71 years. This implies that the bulk of rainfall in Type I climate is concentrated on certain days, leaving the majority of remaining days to have dry to light rain weather.