Uncertainty analysis for water supply reservoir yields

- Generalized analytical equation for evaluating variance of yield estimates was derived.
- First order variance approximation (FOVA) was found to be the best method.
- Covariance between the input stochastic random variables plays a significant role.
- Coefficient of variation of yields depends on variability and length of the inflows.
- Long inflow records are required for small margin of error of yields from reservoirs.

SummaryUnderstanding the variability of water supply reservoir yields is central for planning purposes. The basis of this study is an empirical global relationship between reservoir storage capacity, water supply yield and reliability based on a global database of 729 rivers. Monte Carlo simulations reveal that the coefficient of variation of estimates of water supply reservoir yields depend only on the length of streamflows record and the coefficient of variation of the streamflows used to estimate the yield. We compare the results of those Monte Carlo experiments with an analytical uncertainty method First Order Variance Approximation (FOVA). FOVA is shown to produce a general, accurate and useful expression for estimating the coefficient of variation of water supply reservoir yield estimates. We also document how the FOVA analytical model can be used to determine the minimum length of streamflow record required during the design of water supply reservoirs so as to ensure that the yield delivered from reservoir falls within a prespecified margin of error.