Reservoir storage with dependent, periodic net inputs

Let Rn denote the range of cumulative sums of the net inputs to a reservoir during n time intervals. For periodic net inputs possessing a wide variety of covariance structures, the asymptotic behavior of Rn is given by limn→∞ P[Rn/γn½ ≤ r] = FR(r), where γ is a function of the dependence and periodicity assumptions on the net inputs and FR is the cumulative distribution function of the range of a standard Brownian motion process. Analogous results hold for the adjusted range, rescaled adjusted range, and maximum deficit. (The last quantity is the storage obtained upon application of the sequent peak algorithm.) As previous authors have argued, the n½ behavior of the rescaled adjusted range is not inconsistent with H. E. Hurst's empirical findings if it is assumed that the so-called Hurst phenomenon is a preasymptotic property of reservoir behavior. Useful representations for the parameter γ may be obtained for many of the net input sequences employed in hydrologic modeling, such as mth-order autoregressive (stationary or periodic) and log autoregressive processes.