Autocorrelation structure of monthly streamflows

Abstract

The autocorrelation structure of monthly streamflows, a nonstationary process, is developed from a mathematical model that assumes that monthly precipitation is an independent series and that the base flow of the stream is derived from a linear aquifer. Under these assumptions the first-order autocorrelation coefficients of streamflow are found to vary seasonally, as do other statistics such as monthly means and standard deviations. Comparison of the autocorrelation coefficients predicted by the model with those computed from an actual streamflow record of 58 years indicates that the seasonality of streamflow is well represented by the model. The effects of autocorrelation of streamflows onhydrologic analysis have been demonstrated in many investigations. Among these are the studies of LeopoM [1959], Matalas and Langbein [1962], and Lloyd [1963], which have shown that autocorrelation reduces the reliability of the estimates of other statistical parameters of streamflow and increases the storage requirements for regulation of a stream. These two facets working in unison demonstrate the important role that information concerning the magnitude of autocorrelation plays in the development of the water resource. In spite of its importance, very little has been done to increase understanding of the controlling mechanisms of autocorrelation. I'gemelsfelder [1960] hypothesized that carry-over storage in the groundwater phase of the hydrologic cycle is one of the prime sources of persistence, a positive form of autocorrelation, in streamflows. He developed a descriptive model [Wemelsfelder, 1964] of streamflow that accounts for this component of autocorrelation, but no attempt was made to derive predictive relations. However, Fiering [1967], using a similar model, developed an estimator of the autocorrelation function of annual streamflow. One of the assumptions imbedded in Fiering's analysis is that the time series of streamflows is a stationary process. Because of the seasonality exhibited by monthly series of streamflows the requirement of stationarity negates the use of Fiering's function in the estimation of the autocorrelation coefficients of monthly series.This paper presents a model of streamflow that accounts for the nonstationarity of the monthly series. The model parameters yield estimates of the autocorrelation coefficients of the streamflows of contiguous months. MODEL OF DiSCRETIZED STREAMFLOWThe usual taxonomy of stochastic processes has an initial division of all processes into two classes: discrete parameter processes, in which a process is described or observed only at discrete time intervals, and continuous parameter processes, in which a process is defined at any time during the interval in which the process is functioning. Streamflow is a phenomenon that is a member of the latter class. In dealing with streamflow, however, hydrologists invariably use discrete series of observations, usually either the average rates or the volumes of discharge during specified intervals of time, Copyright (b !974 by the...

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