Investigation of Probability of Occurrence and Persistence of Rainy Days by Using Markov Chain Model (Case Study: Lamerd City)

Document Type : Original Article

Authors

1 Ph.D. Candidate in Water Engineering Department, Faculty of Agriculture, Shiraz University

2 Associate Professor, Department of Water Engineering, Faculty of Agriculture, Shiraz University

Abstract

In the present study, using available records of daily rainfall of 22 years (1995-2016) of the Lamerd (Fars Province) weather station, frequencies and durations of rainy days were studied by using the Markov chain model. In this study, the months of May to October were disregarded due to the insignificant number of daily precipitations. The daily rainfall data were arranged based on the transition matrix of occurrence of dry and wet days, while the transition matrix was calculated based on the maximum likelihood method. In all studies done in Iran, in order to forecast precipitation by using the Markov chain, only the first order of the Markov chain was used which may not be in good agreement with data and resulted to incorrect results. But in this study, by using an accurate statistical method, the appropriate order of the Markov chain was diagnosed to be used. Matrices of stationary probability and the return periods of rainy days for 2 to 5-day precipitations were determined for the studied months in this research. The results showed that the probability of precipitation per day is 0.126, and the probability of absence of precipitation is 0.874.

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Main Subjects


Akan AO, Houghtalen RJ (2003) Urban hydrology, hydraulics, and storm water quality. John Wily & Sons,Inc,U.S.A, 392 p
Akyuz DE, Bayazit M, Onoz B (2012) Markov chain models for hydrological drought characteristics. Journal of Hydrometeorology 13(1):298-309
Asakereh H (2008) Analysis of frequency and spell of rainy days using Markov chain model for city of Tabriz. Journal of Iran Water Resources Research 4(2):46-56 (In Persian)
Bigdeli A, Eslami A (2010) Analysis of wet and dry periods by Markov chain model in southern of Caspian sea. In: Proc. Of International Conference on Environmental Engineering and Applications, 10-12 Sept, Singapore, Singapore, 96-99
Cox DR, Miller H D (1977) The theory of stochastic processes. Chapman and Hall/CRC, 408 p
Dash PR (2012) A Markov chain modeling of daily precipitation occurrences of Odisha. International Journal of Advanced Computer and Mathematical Science 3:482-486
Dastidar AG, Gosh D, Dasgupta S (2010) Higher order Markov chain models for monsoon precipitation over west Bengal, India. Indian Journal of Radio & Space Physics 39:39-44
Gabriel KR, Neumann J (1962) A Markov chain model for daily precipitation occurrence at Tel Aviv. Journal of the Royal Meteorological Society 88(375):90-95
Grace RA, Eagleson PS (1966) The synthesis of short-time-increment precipitation sequences, Hydrodynamics Laboratory, Massachusetts Institute of Technology, Cambridge, USA (No. 91). Report
Hejazizade Z, Shirkhani A (2005) Statistical analysis and prediction of short-term drought and dry periods in Khorasan province. Journal of Geographical Researches 52:3-20 (In Persian)
Hoaglin DC, Mosteller F, Tukey JW (2011) Exploring data tables, trends, and shapes. John Wiley & Sons, 527p
Jalali M, Kargar H, Soltani S (2011) Probability of rainy days occurrence in Urmia city by using Markov chain model. Journal of Geographic Space 35:235-257 (In Persian)
Khanal NN, Hamrick RL (1971) A stochastic model for daily precipitation data synthesis. Central and Southern Florida Flood Control District, 1-28
Mirmousavi H, Zohreh Vandi H (2011) Modeling of weekly precipitation probabilities to analysis of sequent dry days (Case study: Nahavand weather station). In: Proc. of Second National Conference of Applied Research of Water Resources of Iran, 18-19 May, Iran, 73-84 (In Persian)
Rahimi J, Ghahraman N, Rahimi A (2011) Statistical analysis of weekly wet and dry periods using Markov chain for agricultural programming in Varamin plain. In: Proc. of First National Conference of Meteorology and Agricultural Water Management, 22-23 November, Iran, 54-63 (In Persian)
Raziei T, Shokoohi AR, Saghafian B (2003) Prediction of drought severity, duration and frequency using probabilistic and time series methods (Case study: Sistan and Baloochestan province). Journal of Desert 8(2):292-310 (In Persian)
Salami R, Ramezanpour M, Ebrahimi L (2012) Analysis of wet and dry periods using Markov chain (Case study: Ardebil, Iran). M. Sc. Thesis in Natural Geography (Environmental planning), Islamic Azad University, Chaloos Branch
Sariahmed A (1969) Synthesis of sequences of summer thunderstorm volumes for the Atterbury watershed in the Tucson area. M.Sc. thesis, university of Arizona
Sedaghat Kerdar A, Fattahi A (2008) Drought forecast indices in Iran. Journal of Geography and Development 11:59-76 (In Persian)
Selvaraj RS, Selvis T (2010) Stochastic modelling of daily precipitation at ADUTHURAI. International Journal of Advanced Computer and Mathematical Sciences 1(1):52-57
Yusefi N, Hejam S, Irannezhad P (2007) Estimation of wet year and drought probabilities by using Markov chain and normal distribution (case study of Qazvin). Journal of Geographic Research 60:121-128 (In Persian)
Zarei A (2006) Engineering statistics. Danesh Parvar, Tehran, 820 p (In Persian)