Approximate reliability and resilience indices of over-year reservoirs fed by AR(1) Gamma and normal flows

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Abstract
Approximate storage-reliability-resilience-yield (S-R-R-Y) relationships are derived for over-year water supply systems fed by autoregressive lag one Gamma and normal inflows. It is shown that a two-state Markov model may be exploited along with S-R-R-Y relationships to describe the general behaviour of over-year water supply systems. The two-state Markov model is also used to relate the probability of n-year no-failure operations (the concept of reliability used in the USA) to the steady-state probability of a system failure (the concept of reliability used in Australia and elsewhere) yielding a unified view of system reliability. Resiliency criteria are introduced which indicate whether or not a reservoir system is likely to return to normal operations once a failure has set in. These criteria indicate that the resilience of an over-year water supply system is generally independent of its steady-state reliability. The conditions under which finite reservoir systems behave like semi-infinite reservoir systems are also documented, and a factor is derived which describes the impact of the serial correlation of the inflows on the derived S-R-R-Y relationship.