Numerical Analysis of Storage-Level Probability Distribution and fist Passage Probability in A Reservoir with Correlated Inflows

Abstract

A numerical analysis method is developed to estimate storage-level probability distributions in an actual reservoir with correlated inflows. A bivariate probability density model is adopted in order to estimate cumulants of a probability distribution for sum of two variables (inflows) mutually correlated. Using transition probability matrices obtained from the probability distribution functions for the sum variables, a calculation procedure of storage-level probability distributions for each period of five days through a year is shown. Moreover, the first passage probability and first passage time from an normal storage-level to a drought level are formulated and demonstrated for an actual reservoir.