Long‐memory flow models in reservoir analysis: What is their practical value?

The theoretical value of long‐memory stochastic models lies in their ability to generate time series that resemble long historic records of some geophysical processes better than do short‐memory models. Since the use of short‐memory streamflow models has become standard practice in reservoir design, it is worth asking whether the suspected theoretical superiority of long‐memory models justifies a change in this practice; in other words, whether their theoretical appeal can be translated into better design of storage reservoirs. This paper analyzes the problem from the point of view of the differences in reservoir performance reliability obtained on the basis of long‐ and short‐memory models fitted to the same historic streamflow record of a length typically encountered in reservoir design. It appears that the differences in reliability resulting from the replacement of one model by the other (shorter memory yields higher reliability) are small compared both to (1) the accuracy of measurement of the socioeconomic impact of reliability changes and (2) the accuracy of estimating the reliability itself on the basis of available streamflow records and for economically relevant lengths of reservoir operation periods. Thus it is argued that given the socioeconomic and hydrologic data typically available for reservoir planning and design, the replacement of short‐memory models with long‐memory models in reservoir analyses cannot be objectively justified. It is suggested that for a long time to come the use of long‐memory models will, in principle, remain equivalent to the use of a small safety factor in the intrinsically inaccurate estimate of reservoir performance reliability.