Daily Rainfall-State Forecasting in Medan Using a First-Order Markov Chain

Abstract

This study examines daily rainfall-state transitions in Medan using a first-order Markov chain fitted to historical rainfall observations from the Belawan station of Indonesia’s Meteorology, Climatology, and Geophysics Agency. The observation period extends from 1 January 2020 to 31 December 2024. Rainfall amounts were assigned to three states: zero rainfall, 0.1–0.99 mm, and at least 1 mm. These categories are rainfall-based proxies and do not independently describe cloud cover. Of 1,827 calendar days, 1,725 were classified and 102 records marked 8888 were excluded. The reported transition matrix indicates persistence probabilities of 0.600, 0.172, and 0.487 for the three states, respectively. The stationary distribution is approximately 0.477, 0.138, and 0.385. In the seven-day illustration, the zero-rainfall state has the largest forecast probability at every horizon, although its probability declines toward 0.477. Comparison with six valid observations yields three correct classifications, equivalent to 50% accuracy; all three observed days with rainfall of at least 1 mm are missed. The model provides an interpretable local example of rainfall-state dynamics, but this short evaluation does not establish operational forecast skill. Reproducible transition estimation, confirmed temporal separation of estimation and evaluation data, and longer benchmark comparisons are needed before practical forecasting use.