貯水地をもつ河川の渇水確率について

Abstract

This study aims to clarify the possibility of water shortage by means of the theore-tical application of the stochastic inventory model when the water-utilization is carriedon through a reservoir.Firstly, at the time of adopting this model, inflows should be transformed into randomvariables under consideration of their seasonal variation. The seasonal randomization isdone by the prediction theory due to the linear combination of past data. Then, thestationary distribution of water stored is deduced by using of the theory of the Markov-chain of the stored water. The deduction is done in the following two cases; the onecontains fixed capacity of reservoir and demanded release of water, the other the seasonalvariation of capacity of reservoir and demanded release.Next, on the basis of this stationary distribution, the stochastic treatment to estimatethe probability of water shortage at any time and to make clear the relation betweenthe probability and the duration time is developed, and the necessary mathematicalexpressions are shown. Finally, a computational procedure applyin~ this theory to theYanagase Multi-purpose Reservoir is shown and the availability of this approach isclarified.