Dinamika dan Probabilitas Transisi Curah Hujan Harian di MKG Itera Menggunakan Model Rantai Markov
Abstract
This study aims to analyze the characteristics of daily rainfall in the Meteorology, Climatology, and Geophysics (MKG) Itera region during the period from January to October 2025 using a Markov Chain model. Daily rainfall data are classified into four states based on rainfall intensity, namely No Rain, Light Rain, Moderate Rain, and Heavy Rain. The analysis begins with descriptive statistics to identify general characteristics of the data. The average daily rainfall is 6.50 mm/day, with the highest recorded intensity reaching 82.8 mm on February 21, 2025, and a rainfall variance of 195.68 mm². Subsequently, a transition probability matrix is constructed to model the dynamics of rainfall condition changes between states from day to day. In addition, the steady-state probabilities are calculated to determine the long-term tendencies of rainfall conditions. The results indicate that daily rainfall exhibits a fluctuating pattern with relatively high variability. Most observations fall into the No Rain (48%) and Light Rain (40%) states, indicating that more than 88% of rainfall conditions are of low intensity. The transition probability matrix shows that the highest transition probability occurs from Moderate Rain to Light Rain at 66.7%, suggesting that moderate rainfall tends to decrease to light rainfall on the following day. Furthermore, the probabilities of remaining in the No Rain and Light Rain states are relatively high, at 61.1% and 46.7%, respectively, indicating persistence in dry or low-intensity rainfall conditions. The steady-state distribution shows that, in the long run, the probabilities are 47.6% for No Rain, 40.4% for Light Rain, 8.9% for Moderate Rain, and 3.0% for Heavy Rain. These findings suggest that rainfall patterns in the MKG Itera region are predominantly characterized by dry to low-intensity conditions. Overall, the Markov Chain model is capable of effectively representing the dynamics of daily rainfall and provides a comprehensive description of long-term rainfall characteristics in the MKG Itera region.
Downloads
References
N. Sunarmi et al., “Analisis faktor unsur cuaca terhadap perubahan iklim di Kabupaten Pasuruan pada tahun 2021 dengan metode Principal Component Analysis,” Newton-Maxwell J. Phys., vol. 3, no. 2, hal. 56–64, 2022.
T. Zera, A. R. Fauziah, M. Nafian, dan A. Ramadhani, “Mapping of Peak Ground Acceleration (PGA) Values using the Donovan Model for Sumatran,” J. Phys. Conf. Ser., vol. 2243, no. 1, hal. 012031, Jun 2022, doi: 10.1088/1742-6596/2243/1/012031.
R. Sandi, B. Sujatmoko, dan M. Sebayang, “Simulasi Data Curah Hujan Harian Menggunakan Stokastik Rantai MArkov dengan Orde 3 X 3 (Studi Kasus: Daerah Aliran Sungai Kampar).” Riau University.
S. K. Nasib, N. Nurwan, E. D. D. Yanuari, dan T. Macmud, “Karakteristik rantai markov pada data curah hujan bulanan stasiun djalaluddin,” JMPM J. Mat. dan Pendidik. Mat., vol. 7, no. 2, hal. 81–89, 2022.
R. D. Stern dan R. Coe, “A model fitting analysis of daily rainfall data,” J. R. Stat. Soc. Ser. A Stat. Soc., vol. 147, no. 1, hal. 1–18, 1984.
D. S. Wilks, “Interannual variability and extreme-value characteristics of several stochastic daily precipitation models,” Agric. For. Meteorol., vol. 93, no. 3, hal. 153–169, 1999.
L. Zhang dan V. P. Singh, “Bivariate flood frequency analysis using the copula method,” J. Hydrol. Eng., vol. 11, no. 2, hal. 150–164, 2006.
F. Yusof, L. M. Yung, dan Z. Yusop, “Tropical daily rainfall amount modelling using Markov Chain-Mixed Exponential (MCME),” J. Teknol. (Sciences Eng., vol. 74, no. 11, 2015.
M. Tettey, F. T. Oduro, D. Adedia, dan D. A. Abaye, “Markov chain analysis of the rainfall patterns of five geographical locations in the south eastern coast of Ghana,” Earth Perspect., vol. 4, no. 1, hal. 6, 2017.
N. Mawaddah, D. Permana, N. Amalia, dan A. Salma, “Analisis Pola Curah Hujan Di Kota Bengkulu Menggunakan Model Rantai Markov,” Imajiner J. Mat. dan Pendidik. Mat., vol. 7, no. 4, hal. 352–359, 2025.
E. M. Wimalasiri dan A. D. Ampitiyawatta, “Markov chain probability models to describe bi-modal rainfall pattern in Sri Lanka,” J. Agric. Sci. Lanka, vol. 17, no. 2, 2022.
D. S. Wilks, Statistical methods in the atmospheric sciences, vol. 100. Academic press, 2011.
H. Ihsan, W. Sanusi, dan H. Hasriani, “Peramalan Pola Curah Hujan di kota makassar menggunakan model rantai markov,” J. Math. Comput. Stat., vol. 2, no. 1, hal. 19–30, 2019.
R. Douc, E. Moulines, P. Priouret, dan P. Soulier, Markov chains, vol. 4. Springer, 2018.
M. Charles, J. Grinstead, dan L. Snell, “Introduction to probability,” Am. Math. Soc., 1997.
U. F. Arshinta dan D. Ahmad, “Analisis Curah Hujan di Kota Padang dengan Menggunakan Rantai Markov,” J. Math. UNP, vol. 2, no. 4, hal. 45–50, 2019.
S. M. Ross, Introduction to probability models. Academic press, 2014.
R. Michels dan R. Langrock, “Nonparametric estimation of bivariate hidden Markov models using tensor-product B-splines,” Stat. Modelling, hal. 1471082X251335431, 2025.
P. C. Stern, B. K. Sovacool, dan T. Dietz, “Towards a science of climate and energy choices,” Nat. Clim. Chang., vol. 6, no. 6, hal. 547–555, 2016.
Copyright (c) 2026 Indonesian Journal of Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
