Determination of Markov Chain Transition Probabilities for Daily Rainfall Data in Jordan


  • Ahmad Osama Musleh Jordan University of Science and Technology, Department of Civil Engineering, Irbid, Jordan
  • Fayez Ahmad Abdulla Jordan University of Science and Technology, Department of Civil Engineering, Irbid, Jordan


rainfall, daily rainfall, Markov chain, transition probabilities, equilibrium probabilities, spell lengths, Jordan


This study aims to determine Markov chain transition probabilities for daily rainfall data of 39 meteorological stations across Jordan. Two states were imposed to the chains, namely dry and wet, and first order was used as the dependence structure. This leads to four transition probabilities for each station in each month, namely dry-to-dry (pdd), dry-to-wet (pdw), wet-to-dry (pwd), and wet-to-wet (pww). In the end of the study, it is concluded that pdd > pdw for all stations in all months, and pww ? pwd in only 15.1% of the times, which are concentrated in the middle of the rainy season (i.e., December–March) at North of Jordan. Also, all months tend to be dry in the long term, especially October, November, April, and May. Most of the expected dry spell lengths range from 5 to 100 days, while the expected wet spell lengths range mostly from 1 to 2 days, which indicates the tendency of the Jordanian weather to be dry across the country.


A. Dahamsheh and H. Aksoy, "Markov Chain-Incorporated Artificial Neural Network Models for Forecasting Monthly Precipitation in Arid Regions," Arabian Journal for Science and Engineering, vol. 39, no. 4, pp. 2513-2524, 2014.

H. Aksoy and A. Dahamsheh, "Markov chain-incorporated and synthetic data-supported conditional artificial neural network models for forecasting monthly precipitation in arid regions," Journal of Hydrology, vol. 562, pp. 758-779, 2018.

R. W. Katz, "Precipitation as a Chain-Dependent Process," Journal of Applied Meteorology, vol. 16, no. 7, pp. 671-676, 1977.

D. Devianto, Maiyastri, U. A. Wisza, M. Wara, P. Permathasari and R. O. M. Zen, "Time Series of Rainfall Model with Markov Switching Autoregressive," in 2018 International Conference on Applied Information Technology and Innovation (ICAITI), IEEE, 2018, pp. 202-207.

V. K. Garg and J. B. Singh, "Three – State Markov Chain Approach On the Behavior Of Rainfall," New York Science Journal, vol. 3, no. 12, pp. 76-81, 2010.

J. d. S. Jale, S. F. A. X. Júnior, É. F. M. Xavier, T. Stošić, B. D. Stošić and T. A. E. Ferreira, "Application of Markov chain on daily rainfall data in Paraíba-Brazil from 1995-2015," Acta Scientiarum Technology, vol. 41, pp. 1-10, 2019.

Z. Ali, I. Hussain, M. Faisal, I. M. Almanjahie, M. Ismail, M. Ahmad and I. Ahmad, "A New Weighting Scheme in Weighted Markov Model for Predicting the Probability of Drought Episodes," Advances in Meteorology, 2018.

A. O. Ibeje, J. Osuagwu and O. R. Onosakponome, "A Markov Model for Prediction of Annual Rainfall," International Journal of Scientific Engineering and Applied Science (IJSEAS), vol. 3, no. 11, pp. 1-5, 2018.

A. Azizah, R. Welastika, A. Nur Falah, B. N. Ruchjana and A. S. Abdullah, "An Application of Markov Chain for Predicting Rainfall Data at West Java using Data Mining Approach," Conference Series: Earth and Environmental Science, vol. 303, pp. 12-26, 2019.

Á. J. Back and L. P. Miguel, "Analysis of the stochastic model of the Markov chain on daily rainfall occurrence in the state of Santa Catarina, Brazil," Management of Environmental Quality, vol. 28, no. 1, pp. 2-16, 2017.

A. F. M. K. Chowdhury, N. Lockart, G. Willgoose, G. Kuczera, A. S. Kiem and N. P. Manage, "Development and evaluation of a stochastic daily rainfall model with long-term variability," Hydrology and Earth System Sciences, vol. 21, no. 12, pp. 6541-6558, 2017.

S. Deka, "Determination of the Order of a Markov Chain for Daily Rainfall Data of North East India: "Application AIC criterion"," Journal of Applied and Natural Science, vol. 10, no. 1, pp. 80-87, 2018.

S. Mahmud and M. Ataharul Islam, "Predictive ability of covariate-dependent Markov models and classification tree for analyzing rainfall data in Bangladesh," Theoretical and Applied Climatology, vol. 138, no. 1, p. 335–346, 2019.

P. Gogumalla and S. K. Tripathi, "Evaluation of Markov Chain Model for Forecasting Precipitation of Uttarakhand Districts," HCTL Open International Journal of Technology Innovations and Research (IJTIR), vol. 6, no. 5, pp. 142-151, 2018.

M. Tettey, F. T. Oduro, D. Adedia and D. A. Abaye, "Markov chain analysis of the rainfall patterns of five geographical locations in the south eastern coast of Ghana," Earth Perspectives, vol. 4, no. 1, pp. 6-16, 2017.

P. Thwe, E. K. Win and H. P. M. Wai, "A Markov Chain Approach on Daily Rainfall Occurrence," International Journal of Trend in Scientific Research and Development (IJTSRD), vol. 3, no. 6, pp. 280-282, 2019.

C. Yoo, J. Lee and Y. Ro, "Markov Chain Decomposition of Monthly Rainfall into Daily Rainfall: Evaluation of Climate Change Impact," Advances in Meteorology, vol. 2016, no. 3, pp. 1-10, 2016.

R. D. Stern and R. Coe, "A Model Fitting Analysis of Daily Rainfall Data," Journal of the Royal Statistical Society. Series A (General), vol. 147, no. 1, pp. 1-34, 1984.

F. H. Chiew, R. Srikanthan, A. J. Frost and E. G. Payne, "Reliability of daily and annual stochastic rainfall data generated from different data lengths and data characteristics," in In MODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings, Melbourne, Victoria, Australia, 2005.

T. Berhane, N. Shibabaw, G. Awgichew and T. Kebede, "Option pricing of weather derivatives based on a stochastic daily rainfall model with Analogue Year component," Heliyon, vol. 6, no. 1, 2020.

B. Getachew and M. Teshome, "Markov chain modeling of daily rainfall in Lay Gaint Woreda, South Gonder Zone, Ethiopia," Journal of Degraded and Mining Lands Management, vol. 5, no. 2, pp. 1141-1152, 2018.

J. Jaafar, A. M. Baki, I. Abu Bakar, T. Wardah, H. Awang and F. Ismail, "Evaluation of Stochastic Daily Rainfall Data Generation Models," 2016, pp. 203-220.

J. Mahanta, S. Dey and P. Khosro, "Analyzing Rainfall Condition of Bangladesh: An Application of Markov Chain," Thailand Statistician, vol. 16, no. 2, pp. 203-212, 2018.

K. Mammas and D. F. Lekkas, "Rainfall Generation Using Markov Chain Models; Case Study: Central Aegean Sea," Water, vol. 10, no. 7, pp. 856-866, 2018.

R. Y. Adam, "Stochastic Model for Rainfall Occurrence Using Markov Chain Model in Kurdufan State, Sudan," American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), vol. 17, no. 1, pp. 272-286, 2016.

A. Mitra, "Bayesian Approach to Spatio-Temporally Consistent Simulation of Daily Monsoon Rainfall over India," New York, NY, USA, 2017.

A. Dahamsheh and H. Aksoy, "Structural Characteristics of Annual Precipitation Data in Jordan," Theoretical and Applied Climatology, vol. 88, pp. 201-212, 2007.

H. Aksoy and A. Dahamsheh, "Artificial neural network models for forecasting monthly precipitation in Jordan," Stochastic Environmental Research and Risk Assessment, vol. 23, pp. 917-931, 2009.




How to Cite

Ahmad Osama Musleh, & Fayez Ahmad Abdulla. (2022). Determination of Markov Chain Transition Probabilities for Daily Rainfall Data in Jordan. American Scientific Research Journal for Engineering, Technology, and Sciences, 88(1), 233–247. Retrieved from