Estimation of Reservoir Storage Capacity Using the Gould-Dincer Formula with the Aid of Possibility Theory

Abstract

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271×106 m3, and that for D = 0.5 was 634.5×106 m3. On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [315,5679]×106 m3 and for D = 0.5 the value is interval [158,2839]×106 m3, with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions.

Keywords

• reservoir capacity
• probability
• fuzzy logic
• confidence intervals
• fuzzy estimators
• possibility theory