An analytical formulation of return period of drought severity

Abstract

Planning and management of water resources systems under drought conditions often require the estimation of return periods of drought events characterized by high severities. Among the several methods proposed for describing droughts, the run method is the most suitable to provide an objective identification and characterization of drought events. According to such a method, droughts are identified as consecutive intervals where the investigated hydrological variable is continuously below a fixed threshold, and may be described by means of two characteristics, namely, drought duration and drought severity. Since both characteristics are necessary to estimate water deficit risks, frequency analysis of drought events cannot be based on the same approach generally used for flood analysis, such as maximum annual series or partial duration series of a single characteristic. In particular, the evaluation of return period for drought events needs to consider both duration and severity in order to take into account the pluriannual duration of several droughts. Very often a reliable analysis of the probabilistic structure of droughts based on the observed samples, using an inferential approach, cannot be properly carried out due to the limited number of drought events which can be identified even on quite long historical series. This problem has been faced by Shiau and Shen (2001), who have determined the conditional distribution of drought severity given a drought duration on the basis of generated hydrological series. In this paper their approach is extended by deriving analytically the parameters of the probability distribution of drought severity based on the stochastic process describing the underlying hydrological variable. More specifically, a gamma distribution is adopted to model drought severity and its parameter are theoretically determined as a function of the threshold level and the coefficient of variation of annual precipitation series assumed independent and lognormal distributed. Then, the return period of drought events with severity greater than or equal to a fixed value is computed as the mean interarrival time of drought events with a certain severity or greater. Such procedure has been applied on 88 annual series of data recorded in Sicilian rainfall stations, by computing for each series the return period corresponding to

Development of streamflow drought severity–duration–frequency curves using the threshold level method

“…Based on these definitions, various indices were proposed over the years to identify drought. Recent studies have focused on such multi-faceted drought characteristics using various indices (Palmer, 1965;Rossi et al, 1992;McKee et al, 1993;Byun and Wilhite, 1999;Tsakiris et al, 2007;Pandey et al, 2008aPandey et al, , b, 2010World Meteorological Organization, 2008;Nalbantis and Tsakiris, 2009;Wang et al, 2011;Tabari et al, 2013;Tsakiris et al, 2013).…”

“…For design purposes, rainfall intensity-duration-frequency (IDF) curves have been used for a long time to synthesize the design storm. Therefore, many studies have integrated drought severity and duration based on the multivariate theory (Bonaccorso et al, 2003;González and Valdés, 2003;Mishra and Singh, 2009;Song and Singh, 2010a, b;De Michele et al, 2013). However, these studies cannot fully explain droughts without considering the frequency, which resulted in the development of drought isoseverity curves for certain return periods and durations for design purposes.…”

Copula‐based drought severity‐duration‐frequency analysis in Iran

“…Multiple attributes of droughts have been evaluated in these studies, but significant correlation relationships are not revealed by separate consideration of correlated characteristics. Some researchers including Shiau and Shen (2001), Bonaccorso et al (2003), González and Valdés (2003), Loáiciga (2005) and Kim et al (2006aKim et al ( , 2006b, further extended the univariate analysis to explore bivariate frequency of droughts.…”

Drought Risk Analysis Using Stochastic Rainfall Generation Model and Copula Functions

“…Joint probability distribution function (Bonaccorso et al, 2003;Kim et al, 2003;Salas et al, 2005;Mirakbari et al, 2010). 또한, Gonzalez and Valdés(2003)는 수자원 시스템이 실패할 위험 정도를 해 석하는 데 있어 이변량 가뭄재현기간을 이용하였으며, 그 결과 이변량 가뭄빈도해석의 필요성을 재 증명한 바 있다.…”

“…따라서 최근에는 다양한 가뭄 특성인자 간의 관계 를 복합적으로 결합시켜 일관성이 있는 결과를 제시할 수 있는 가뭄해석방법의 필요성이 제기되고 있다. 특히 가뭄 은 지속기간과 심도를 주요 특성변수로 갖는 이변량 수문 사상이므로, 이 두 가지 변량의 발생분포 특성을 결합하 여 통계학적으로 유의한 결합분포함수의 확률을 추정하는 연구가 활발히 이루어지고 있다 (Shiau and Shen, 2001;Bonaccorso et al, 2003;Gonzalez and Valdés, 2003;Salas et al, 2005;Kim et al, 2006;Mirakbari et al, 2010).…”