A method of streamflow drought analysis

Abstract

A method of completely describing and analyzing the stochastic process of streamflow droughts has been recommended. All important components of streamflow droughts such as deficit, duration, time of occurrence, number of streamflow droughts in a given time interval [0, t], the largest streamflow drought deficit, and the largest streamflow drought duration in a given time interval [0, t] are taken into consideration. A streamflow drought is related here to streamflow deficit. Following the theory of the supremum of a random number of random variables a stochastic model is presented for interpretation and analysis of the largest streamflow drought deficit below a given reference discharge and the largest streamflow drought duration concerning a time interval [0, t], at a given location of a river. The method is based on the assumption that streamflow droughts are independent, identically distributed random variables and that their occurrence is subject to the Poisson probability law. This paper is actually a continuation of the previous E. Zelenhasić (1970, 1979, 1983) and P. Todorović (1970) works on the extremes in hydrology. Application of the method is made on the 58‐year record of the Sava River at Sr. Mitrovica and on the 52‐year record of Tisa River at Senta, Yugoslavia, and good agreement is found between the theoretical and empirical distribution functions for all analyzed drought components for both rivers. Only one complete example, the Sava River at Sr. Mitrovica, is given in the paper. The proposed method deals with hydrograph recessions of daily or instantaneous discharges in the region of low flows, and not with mean annual flows which were used by other investigators.