Development of Daily Rainfall Simulation Model by Using Markove Chain and Preserve Spatial Correlation (Case Study: Khozestan Province)

Document Type : Research Paper


1 Ph.D. Student of Water Sciences Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

2 Professor of Water Sciences Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

3 Assistant Professor on Graduate University of advanced technology, Kerman, Iran.


Water scarcity is a big problem in many areas, especially in arid and semi-arid regions. It is rising due to the demand growth driven by increased economic activity and population growth in developing countries. Since Iran is on the world's dry belt and it has rain equivalent to 1/3 of the rain world's average, it is considered a dry country. The rain trend indicates that Iran is going to drought, so plans and measures of water resources management should be developed accordingly (Samadi Broujeni and Ebrahimi, 2010). Also rainfall in Iran is one of the main variables for assessing of water resources, but its spatial and temporal distribution is very Non-uniform. For this reason, the water resources distribution of the country is not uniform, too. Preservation and water resources management are not only a function of rainfall but also depend on the variability of rainfall. If spatial change of rainfall be small, the water resources are more homogeneity and consistency (Mirmousavi and zohrehvandi, 2011) . Hence, the rainfall variations are important in assessing water resources of rivers and the relative study of local and regional water resources. Although various approaches have been proposed for modeling of rainfall, the use of single generators can not properly reproduce the spatial correlations between different meteorological variables. In this paper, was used the first-order Markov chain(MC1), the second-order Markov chain(MC2) and the third-order Markov chain(MC3) for the occurrence of daily precipitation. The Wilks method was used to simulate the occurrence of daily precipitation by preserving the spatial correlation between stations for four synoptic stations in Khozestan province of Iran, considering the importance of preserving the spatial correlation between adjacent stations in water and agricultural studies in daily scale, which has not been studied in Iran up to now.


  • Ababaei, B., Mirzaei, F. and Sohrabi, T., 2014. Developing a Weather Generator Model to Preserve Spatial Correlations between Neighboring Stations. Water and Soil Science, 25(1),pp.181-192. (In Persian).



  • Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, pp.716–723.


  • Apipattanavis, S., Podesta, G., Rajagopalan, B. and Katz, R.W., 2007. A semiparametric multivariate and multisite weather generator. Water Resource Research, 43 (11),pp. 1-19.


  • Azhdary Moghaddam, M. and Heravi, Z., 2018. Evaluation of IDF curve production methods by relationship based on nature of combination of fractal of precipitation. Journal of Water and Soil Conservation, 24(6), pp.271-282. (In Persian).
  • Bakhtiari, B., Shahraki, N. and Ahmadi, M.M., 2014. Estimation probability of daily precipitation by using Markov chain models in different climates of Iran. Iran-Water Resources Research, 2, pp.44-55. (In Persian).


  • Bardossy, A. and Pegram, G.G.S., 2009. Copula based multisite model for daily precipitation simulation. Hydrology and Earth System Sciences, 13 (12), pp.2299–2314.


  • Brissette, F.P., Khalili, M. and Leconte, R., 2007. Efficient stochastic generation of multi-site synthetic precipitation data. Journal of Hydrology, 345, pp.121–133.


  • Byung-Jin, S., Hyun-Han, K., Dongkyun, k. and Seung, O.L., 2015. Modeling of daily rainfall sequence and extremes based on a semiparametric Pareto tail approach at multiple locations. Journal of Hydrology, 529, pp.1442-1450.


  • Daniel, S., 1985. Statistical Methods in the Atmospheric Sciences. Dep of soil, Crop and Atmospheric Sciences. ITHACA, Cornell Univ, New Yourk.


  • Darand, M., 2016. Recognition of precipitation homogeny regions of in Iran based on Aphrodite Data Base. Journal of Water and Soil Conservation, 23(2), pp.99-114. (In Persian).


  • Dastidar, A.G., Gosh, D. and Dasgupta, S., 2010 Higher order Markov chain models for monsoo rainfall over west Bengal, India. Indian Journal of Radio & Space Physics, 39, pp.39-44.



  • Ghasdi, T., Ghahreman, N. and Ghamghami, M., 2016. Comparison ofperformance of two spatial- temporal approaches for daily rainfall simulation across Iran. Iran-Water Resources Research, 12(1), pp.158-170. (In Persian).


  • Goodarzi, L., Banihabib, M.E. and Ghafarian, P., 2018. Evaluation of the WRF model performance for heavy rainfall simulation a case study of the Kan basin in Iran. Journal of Water and Soil Conservation, 25(1), pp.229-242. (In Persian).


  • Hasanalizadeh, N., Mosaedi, A., Zahiri, A.R. and Hosseinalizadeh, M., 2015. Modeling Spatio-temporal variation of monthly precipitation (Case Study: Golestan province). Journal of Water and Soil Conservation, 22(1), pp.251-269. (In Persian).


  • Katz, R.W., 1981. On some criteria for estimating the order of a Markov chain. Technometrics, 23, pp.243–249.


  • Khalil, A.F., Kwon, H.H., Lall, U. and Kaheil, Y.H., 2010. Predictive downscaling based on non-homogeneous hidden Markov models. Hydrological Sciences Journal, 55 (3), pp.333–350.


  • Khalili, A., 1997. Integrated water plan of Iran. Meteorological studies, Ministry of power, Iran.



  • Li, C., Singh, V.P. and Mishra, A.K., 2013. A bivariate mixed distribution with a heavytailed component and its application to single-site daily rainfall simulation. Water Resource Research, 49 (2), pp.767–789.



  • Mandal, K.G., Padhi, J., Kumar, A., Ghosh, S., Panda, D.K., Mohanty, R.K. and Raychaudhuri, M., 2015. Analyses of rainfall using probability distribution and Markov chain models for crop planning in Daspalla region in Odisha, India. Theoretical applied and climatology, 121, pp.517-528.


  • Mhanna, M. and Bauwens, W., 2011. A stochastic space-time model for the generation of daily rainfall in the Gaza Strip. International Journal of Climatology, pp.1-15.


  • Mirmousavi, H. and Zohrehvandi, H., 2011. Modeling of weekly rainfall probabilities to analyze consecutive dry days (Case to study: Nahavand Meteorological Station of Hamedan Province. In 2the National Conference on Applied Research in Water Resources of Iran, 18-19 May, Zanjan Regional Water Authority, Zanjan, Iran. (In Persian).


  • Moon, S.E., Ryoo, S.B. and Kwon, J.G., 1994. A Markov Chain Model for Daily Precipitation Occurrence in South Korea. International Journal of Climatology, 14, pp.1009-1016.


  • Moradi, H.R., Rajabi, M. and faragzade, M., 2011. Investigation of meteorological drought characteristics in Fars province, Iran. CATENA, 84, pp.35-46.


  • Mouelhi, S., Nemri, S., Jebari, s. and Slimani, M., 2016. Using the Markov chain for the generation of monthly rainfall series in a semi-arid zone. Open Journal of Modern Hydrology, 6, pp.51-65.


  • Mozafari, Gh.A., Mazidi, A. and Shafie, Sh., 2017. Analysis and determining the threshold of extreme precipitation of Western Iran through using general extreme value distribution. Journal of Water and Soil Conservation, 24(2), pp.107-125. (In Persian).


  • Nadi, M. and Baziyarpoor, h., 2017. Evaluation and modification of Aphrodite daily precipitation network in Golestan province. Journal of Water and Soil Conservation, 24(4), pp.273-286. (In Persian).


  • Rahimi, J., Ghahreman, N. and Rahimi, A., 2011. Markov chain model probability of dry, wet weeks and statistical analysis of weekly rainfall for Agricultural Planning at Varamin plain. In 1the National Conference on agrometeorology and agricultural water management, 22-23 november, Tehran university, Iran. (In Persian).


  • Salarijazi, M., 2017. Determination of distributional changes of annual rainfall in some semi-northern stations in Iran. Journal of Water and Soil Conservation, 24(4), pp.143-159. (In Persian).


  • Samadi Broujeni, H. and Ebrahimi, A.S., 2010. Drought consequences and ways to deal with it in Chaharmahal va Bakhtiari province. Shahrekord University, pp.460. (In Persian).




  • Senthilvelan, A., Ganesh, A. and Banukumar, K., 2012. Markov Chain Model for Probability of Weekly Rainfall in Orathanadu Taluk, Thanjavur District, Tamil Nadu. International Journal Geomatics and Geosciences, 3(1), pp.191-203.


  • Srikanthan, R. and Pegram, G.G.S., 2009. A nested multisite daily rainfall stochastic generation model. Journal of Hydrology, 371, pp.142–153.


  • Srikanthan, R., 2005. Stochastic generation of daily rainfall data at a number of sites. Cooperative Research Centre for Catchment Hydrology. Technical Rep. 05/7.


  • Thompson, C.S., Thompson, P.J. and Zheng, X., 2007. Fitting a multisite daily rainfall model to New Zealand data. Journal of Hydrology, 340, pp.25-39.



  • Wilks, D.S., 1998. Multisite generalization of a daily stochastic precipitation generation model. Journal of Hydrology, 210, pp.178–191.


  • Wilks, D.S., 1999. Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agricultural and Forest Meteorology, 93 (3), pp.153– 169.


Volume 46, Issue 2
September 2023
Pages 15-29
  • Receive Date: 22 April 2018
  • Revise Date: 30 May 2019
  • Accept Date: 01 June 2019
  • Publish Date: 23 August 2023