Computer simulation and approximate expression for the mean range of reservoir storage with GAR(1) inflows

Reservoir storage capacity has been investigated for independent and first-order dependent normal inflows. Besides the normal distribution, annual streamflows have also been found to follow the gamma distribution[4],[11] it is then useful to consider this situation. In the work of Phien[10], the inflows are assumed to follow the gamma distribution, and the mean value of the range (or the storage capacity) was derived analytically, and compared very well with the empirical formula obtained from Monte Carlo experiments in his earlier study. This paper considers the distribution of the storage capacity of reservoirs where the inflows are assumed to follow the first-order autoregressive model for gamma variables, denoted GAR(1) model. By means of computer simulation method, the annual inflows are generated, then the data for the partial sums and range are obtained for any given value of n, the life time (in years) of the reservoir under consideration. By theoretical analysis, a closed form formula for the variance of the sum of GAR(1) variables is derived. This formula is then used along with the empirical formula of Phien[10] to obtain an approximate expression for the mean value of the reservoir storage. The results computed from the approximate expression can be compared very well with those obtained from generated data. This means that the approximate expression obtained can be used to determine the mean range (or mean reservoir capacity) for any value of the parameters of the GAR(1) model found in practice.