Correlations and Crossing Rates of Periodic-Stochastic Hydrologic Processes

Abstract

When a continuous valued hydrological series such as monthly stream flows is clipped by a constant or variable threshold series (such as water demand), a binary series may be obtained. Such a series may be useful for analyzing and modeling a variety of hydrological processes such as the occurrences of wet and dry days, deficit and surplus series, and water quality series that exceed or not exceed a certain allowable level. In addition, they are also useful for analyzing the occurrence of periods of low flows and droughts, and periods of surpluses and floods. A method that relates the correlation functions of a periodic continuous valued series and the corresponding clipped periodic binary series is proposed. Based on this method the parameters of a periodic discrete autoregressive process, PDAR(1), as a function of the parameters of the underlying continuous valued periodic autoregressive process, PAR(1), are derived. Furthermore, the relationship between the periodic crossing rates of a discrete binary series and the autocorrelation function of the continuous valued series is derived. The proposed relationships have been tested using data of monthly stream-flow series for several streams as well as simulated data based on the PAR(1) and PDAR(1) models. The results obtained indicate the validity of the derived relationships and their applicability for analyzing and modeling periodic-stochastic hydrological series.