Uncertainty Analysis for Synthetic Streamflow Generation

Synthetic streamflow generation has been widely used in hydrology and water resources since the 1960's for a number of practical problems such as determining the capacity of a reservoir and assessing the long-term behavior of an existing reservoir. Synthetic streamflows can be obtained using parametric and non-parametric approaches. The former assumes that a certain mathematical model describes the stochastic behavior of the underlying process, e.g. streamflow. And the mathematical model hinges on a number of parameters that must be estimated from historical data. If the available historical data would be sufficiently long (e.g. hundreds of years), the model parameters could be estimated with a good precision, the synthetic samples produced from the model would reflect the expected variability of the process under consideration, and consequently the expected variability of the design variables obtained from them (e.g. the size of the needed storage capacity for a reservoir). However, the usual lengths of historical streamflow records are short which means that the model parameters are uncertain and consequently the variability of the design variables may be uncertain beyond what is expected. A number of approaches have been proposed in literature to tackle the problem of parameter uncertainty in simple stochastic models. In the paper described herein we take an approach based on the asymptotic distribution of the parameter estimators of an AR(1) model and investigate in some detail the effect of the uncertainty in one or more parameters on the design variables such as the reservoir size and reliability. Our analysis has been conducted based on simulation studies of an AR(1) model for a wide range of parameters. The paper includes an example to illustrate the applicability of the concepts obtained in the study.