A thesis submitted in partial fulfillment of the requirement for the Degree of Master of Science at the Asian Institute of Technology, Bangkok, Thailand.

Thesis (M.Sc.) - Asian Institute of Technology, 1976

Under the assumption that the reservoir is of infinite capacity, the mean or expected value of the storage required to maintain the long term mean inflow is investigated when the annual inflow is distributed as independent gamma variable. This is done by introducing the range of partial sums of the fluctuations of the inflow around its mean. The inflow is first standardized, and by means of the data generation method, an approximate equation of the mean range is then obtained. It is expressed in terms of Cs, the skewness coefficient of the inflow distribution, and of n, the number of years, in the following form: 10' E (R ) 1. 65 n = I 3_ exp (- 0.0475Cs ) O.7(n-l)0.6+ 2 n E i-1/2 i=l In the case when n=l, this expression approximates well the exact formula which is derived mathematically: E(R1) = 2/a [l( /a , a-1)- I (-a - ,a) /ci+1 in which a is the shape parameter of the gamma distribution, and I(u,p) is the incomplete gamma function. The mean storage required for regulating the mean inflow is then obtained by multiplying E(Rn ) by the standard deviation of the inflow discharges.