A study of the occurance of rain fall in Raipur district with the help of Markov chain model

Abstract

In order to study the pattern of occurrence of rainfall, data relating to 21 rain-gauge stations located in different parts of Raipur district were collected from Meteorological Department, Poona. The number of years for which the data were available varied from station to station, the variation being from 39 to 60 years. For the purpose this study, a day was taken as dry if the amount of rainfall was found to be below 3 mm per day. On the contrary, it was taken as a wet day. A sequence of wet and dry days for each center and for each year during the period 1st June to 30th September was obtained. Replicating the sequence over years the probability for the day being wet when the immediately preceding day is dry (P12) as well as the probability of the day being wet when the immediately preceding day is wet (P12) were worked out for each center separately. It was observed that that these probabilities are not equal in respect of each center. This suggested the dependence of the weather of a day on the weather conditions of the immediately preceding day. As such a Markov chain model was fitted for each center. The results indicated that 10 of the centers have similar pattern of the occurrence of rainfall while the remaining 11 centers are different. The results of the 10 similar centers were pooled. The value of P12 varied from 0.257 to 0.309 while that of P22 varied 3.25 to 3.88 days while that of the wet runs varied from 1.71 to 2.42 days. The system was found to settle down after about 6 to 8 days to a condition of statistical equilibrium in which the state occupation probabilities were independent of the initial conditions. The expected number of cry days varies from 70 to 78 whereas the number of wet days varies from 44 to 52 days.