A dissertation submitted in partial fulfillment of the requirements for the Degree of Doctor of Technical Science, Asian Institute of Technology, Bangkok, Thailand.

Thesis (Ph.D.) - Asian Institute of Technology, 1978

The present study comprises an investigation of the storage problem of reservoirs using analyses of range, adjusted range, and maximum depletion. The storage capacity was assumed to be infinite for the case of the range and adjusted range analyses, and semi-infinite for the case of the maximum depletion analysis. The related random variables considered are the partial sum and adjusted partial sum, the surplus and adjusted surplus, the deficit and adjusted deficit, the range and adjusted range, and the maximum depletion. The annual inflows used in the analysis were assumed to be independent and identically distributed as normal variables or as gamma variables. In addition, a scheme for investigating the capacity of a reservoir for within- the-year regulation was formulated and illustrated by means of case studies. Analytical solutions were obtained for the distributions of the partial sum and adjusted partial sum, for the first four moments of the surplus and deficit, for the expected values of the adjusted surplus, adjusted deficit, range and adjusted range. Additionally, analytical derivation was made for covariance between the partial sum in the entire period and each of the three variables: surplus, deficit and range, Due to the complexity of the derivation to obtain the analytical formulas, the Monte Carlo method was used to compute the higher moments of the adjusted surplus, adjusted deficit, range and. adjusted range, and the moments of· the maximum depletion. Finally, the distributions' of the surplus, adjusted surplus, deficit, adjusted deficits, range, adjusted range and maximum .depletion were. fitted using the Pearson criterion.