The probability of Duration and frequency of rainy and non-rainy periods Case study: Karaj County

In this research, the probability of duration and frequency of rainy and non-rainy periods of Karaj station were studied using two-state first order Markov chain model. Daily rainfall data of Karaj station were sorted based on number of rainy and non-rainy day matrix, during a given statistical period (1985-2008) for 24 years and then probability matrix was measured on the basis of maximum of likelihood. The results of this study show that Probability of daily raining was 0.2470 and lack of raining was 0.7869. But, the highest probability of rainy in Karaj County was October that marked 0.53. March had the lowest return period for 2 and 3 days raining, that is, 4.5 and 13.5 days, and September had 27.08 days for 2 days raining and 705.25 days for 3 days raining, respectively in return period. The January, February, March, April, May and December were of highest probability of raining in p(x=4) base on computing probability of occurrence of rainy days via Poisson distribution.