Review of Gould–Dincer reservoir storage–yield–reliability estimates

The Gould–Dincer suite of techniques (normal, log-normal and Gamma), which is used to estimate the reservoir capacity–yield–reliability (S–Y–R) relationship, is the only known available procedure in the form of a simple formula, based on annual streamflow statistics, that allows one to compute the S–Y–R relationship for a single storage capacity across the range of annual streamflow characteristics observed globally. Several other techniques are available but they are inadequate because of the restricted range of flows on which they were developed or because they are based on the Sequent Peak Algorithm or are not suitable to compute steady-state reliability values. This paper examines the theoretical basis of the Gould–Dincer approach and applies the three models to annual streamflow data for 729 rivers distributed world-wide. The reservoir capacities estimated by the models are compared with equivalent estimates based on the Extended Deficit Analysis, Behaviour analysis and the Sequent Peak Algorithm. The results suggest that, in the context of preliminary water resources planning, the Gould–Dincer Gamma model provides reliable estimates of the mean first passage time from a full to empty condition for single reservoirs. Furthermore, the storage estimates are equivalent to deficits computed using the Extended Deficit Analysis for values of drift between 0.4 and 1.0 and the values are consistent with those computed using a Behaviour simulation or a Sequent Peak Algorithm. Finally, a sensitivity analysis of the effect on storage of the four main streamflow statistics confirms that the influential ones are mean and standard deviation, while effects of skew and serial correlation are orders of magnitude lower. This finding suggests that the simple reduced form of the Gould–Dincer equation may profitably be used for regional studies of reservoir reliability subject to climate change scenarios based on regional statistics, without having to perform calculations based on time series, which may not be easily obtained.