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.

Historical trends and variability of meteorological droughts in Taiwan / Tendances historiques et variabilité des sécheresses météorologiques à Taiwan

“…Drought duration, as used in this work, is a discrete variable, and is fitted as a geometric distribution by Kendall & Dracup (1992) and Mathier et al (1992). However, if drought duration is considered a continuous variable, it can be described by an exponential distribution (Zelenhasic & Salvai, 1987;Shiau, 2006). On the other hand, drought magnitude is usually fitted as a gamma distribution (Zelenhasic & Salvai, 1987;Mathier et al, 1992;Shiau, 2006).…”

Multivariate assessment of droughts: Frequency analysis and dynamic return period

“…VV., 2011], for the selection of the drought events of interest, we use here the discharge threshold ''Q300,'' equal to 824 m 3 /s, indicated by the CR as the ''alarm threshold.'' In addition, following Zelenhasić and Salvai [1987] and AA. VV.…”

“…[14] In the following, we consider a hydrological drought as an episode, or a period of time, during which the discharge values are smaller than a given threshold [Yevjevich, 1967;Zelenhasić and Salvai, 1987]-for other approaches see e.g., the literature cited in the Introduction. Each episode is characterized by two variables : the Duration D (in days), and the average intensity I (in m 3 /s), defined as the average of all the volumes below the threshold (i.e., the average of all the differences between the threshold and the actual daily streamflows).…”

“…The threshold is assumed to be equal to a given percentile of the flow-duration curve (generally, the 95-, 90-, 80-, 70-, or 60-percentile). Among others, see Sen [1977]; Dracup et al [1980b]; and Clausen and Pearson [1995] for the application of the run method at a yearly time scale, and Zelenhasić and Salvai [1987] ; Tallaksen et al [1997] ; Demuth and K€ ulls [1997]; Demuth and Heinrich [1997]; Kjeldsen et al [2000]; Engeland et al [2004]; Byzedi and Saghafian [2009] ;and Byzedi [2010] at a daily time scale.…”

“…[6] Zelenhasić and Salvai [1987] have modified the run method, to cope with the possible dependence of drought periods, introducing two additional conditions: (i) two consecutive drought events, separated by a relatively short interval (interevent time) during which the flow is slightly above the threshold, have to be considered as just one drought event with duration and severity equal to the sum of the two events duration and severity, respectively ; (ii) all droughts with severity less than 0.5% of maximum severity are neglected. Similar investigations are carried out by Tallaksen et al [1997]; Demuth and K€ ulls [1997]; Kjeldsen et al [2000]; Engeland et al [2004]; Byzedi and Saghafian [2009];and Byzedi [2010].…”