Simple Stochastic Model for Annual Flows

Persistence is a phenomenon greatly influencing hydrologic time series. An explanation of its nature has been attempted in different ways, including transitory behavior or infinite memory of the process, and nonstationary process mean. An operational stochastic model for annual discharges is studied in this paper; its purpose is to reproduce the altemance of periods, sometimes called cycles, observed in hydrology. The model is of almost immediate application, being defined by parameters that can be estimated easily through the analysis of the autocorrelation function of the observed data. The model is expressed in two forms that are valid for the cases of normal and lognormal distributions of the variables, respectively. The dependence of the parameters of the variables distribution on the operating parameters of the process is graphically represented by curves interpolated from a large number of sampling points. The performance of the model is also evaluated with respect to its behavior in accordance to Hurst's phenomenon, by verifying the values assumed by Hurst's coefficient during the simulations.