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Journal article

Modeling Rainfall State Transitions in Tropical Monsoon Climates: A Discrete-Time Markov Chain Approach with Application to Central Kerala, India

Abstract

This study presents a comprehensive stochastic analysis of daily rainfall patterns at four meteorological stations in Central Kerala over a 23-year period (2000–2023) using a first-order Markov chain (MC) model. Preliminary diagnostics, including autocorrelation and partial autocorrelation functions, confirmed the predominance of lag-1 dependence across all seasons and locations, justifying the application of the first-order MC framework. Rainfall was classified into six discrete states based on the Indian Meteorological Department (IMD) thresholds, and transition probability matrices were constructed for annual and seasonal scales. The results revealed a clear seasonal variability. The southwest monsoon exhibited greater persistence and more frequent transitions to higher-intensity rainfall states, whereas the winter and pre-monsoon seasons were dominated by dry or light rainfall. Model reliability was evaluated by comparing the theoretical and observed wet/dry spell lengths, with strong agreement observed across the stations. To assess the influence of large-scale climate variability, the data were stratified according to El Niño–Southern Oscillation (ENSO) phases. Notable shifts in transition dynamics were detected, particularly during the monsoon season, with enhanced rainfall persistence during La Niña events and suppressed rainfall under El Niño conditions. A sensitivity analysis, including the merging of high-intensity states, was conducted to address data sparsity and evaluate the robustness of the transition probabilities. While the model effectively captures key rainfall dynamics, limitations remain related to sub-daily variability and state boundary definitions. Nonetheless, the findings offer valuable insights for water resource planning and climate adaptation in the region and underscore the utility of Markov chain models under non-stationary climate conditions.Graphical abstractThis study aimed to examine the spatiotemporal patterns of daily rainfall in Central Kerala using a Discrete-Time Markov Chain (DTMC) model. The graphical abstract shows the study area, which includes four districts: Malappuram, Palakkad, Thrissur, and Ernakulam. These districts are marked on the map to illustrate the spatial extent of the investigation. Time-series rainfall data from 2000 to 2023 are presented for each station, considering both ENSO and seasonal effects. The core methodology is outlined, beginning with the determination of model order using ACF and PACF plots. Daily rainfall is classified into six distinct states, as per the Indian Meteorological Department’s guidelines: Dry, Light, Moderate, Rather Heavy, Heavy, and Very Heavy. Each station’s rainfall sequence is analyzed using a first-order Markov chain to determine transition probabilities, which describe the likelihood of moving between rainfall states. Goodness-of-fit tests and model validation are applied to ensure model validity. A sensitivity analyses, including the merging of high-intensity states, was conducted to address data sparsity and evaluate the robustness of the transition probabilities. The final section presents heatmaps of transition matrices analysis, revealing strong seasonal persistence and highlighting the dominance of rainfall transitions during the Southwest Monsoon and dry/light states in drier seasons. This workflow captures the study's main findings, providing a solid foundation for understanding how the monsoons and ENSO influence rainfall in Kerala. This approach offers valuable insights for planning water resources that can withstand climate change, mitigating the impact of disasters, and informing future research on how changing monsoon patterns will affect the region's hydrology.

Authors

David A; Abdelaal A; Hassini S; Guo Y

Journal

Earth Systems and Environment, , , pp. 1–18

Publisher

Springer Nature

Publication Date

January 1, 2025

DOI

10.1007/s41748-025-00755-3

ISSN

2509-9426

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