21-A comparative study of rainfall simulation using transitional probability matrix methods.

Abstract

Daily rainfall values of North-East monsoon from, September to 'December (122 days} are used for the formulation of Transitional Probability Matrices. Sixteen raingauge stations of Bhavani basin in India with lengths of record ranging from 23 years to 32 years are analysed.Synthetic generation is carried out using three different methods.

Daily rainfall values are converted into states by selecting suitable class intervals. Using the states thus arrived at transitional frequency and hence cumulative transitional probability is worked out for each station. In the first method, the class interval includes zero rainfall values as state 1. Generation is done with rectangular distributed random numbers in conjunction with the transitional probability matrices obtained continuously for one year.

In the second approach conditional probabilities are worked out for dry /wet days being followed by dry /wet days. The transitional probability matrix is arrived at taking into account only days with rainfall values greater than 0. 1 mm. Synthetic generation is done in two parts. First part decides whether a particular day is dry or wet using conditional probability and rectangularly distributed random number. The second part decides the state of a wet day using cumulative transitional probability matrix.

In the third approach, wet and dry spells are identified in the historic sequence and fitted with geometric distributions. The transitional frequency matrix used in method 2 is used to fit two-parameter gamma distributions. Generation is done in two steps. First wet or dry spells are generated using the wet or dry spell distribution function. For wet spell duration the state for each day is determined from the cumulatives transitional probability matrix and rectangularly distributed random number. The rainfall states generated are converted into rainfall values using mid value of the corresponding class interval . Synthetic generation is done for 100 years. The historic and synthetic rainfall values are compared by the Chi-square test, the F-test. Students' t-test and the median test and the results are discussed. The first method gives best results except for the fact that the variance of the generated series is less. The fact that wet and dry spell sequences follow geometric distribution needs to be locked into as the same is not true for many of the stations.