Drought length properties for periodic‐stochastic hydrologic data

Abstract

[1] Extreme droughts may be characterized by their duration, severity (magnitude or intensity), spatial extent, and frequency or return period. Comparing the time series of water supply and water demand and analyzing droughts based on the theory of runs may determine these characteristics. This study is focused on drought analysis where the underlying water supply process is periodic stochastic, such as for monthly streamflows. The probability mass function (pmf) of drought length and associated low-order moments are derived assuming a periodic simple Markov chain. The derived pmf allows estimating the occurrence probability of droughts of a given length and its return period. The applicability of the drought formulations has been illustrated using a variety of water supply series such as monthly and weekly precipitation, monthly streamflows, the Palmer hydrologic drought index, and the standardized precipitation index. The results obtained confirm the validity of the analytical derivations for drought lengths and associated return periods. The overall conclusion of the study is that simple definitions of droughts enables one characterizing droughts using stochastic approaches and analytical derivations. They are particularly useful for drought analysis because the limited hydrologic records that are generally available do not allow observing many drought events of a particular duration and, in fact, extremely long droughts may not even be observable from the historical sample. This hinders the applicability of an inferential approach for finding the probability distributions of drought lengths and their associated return periods because it is either impractical or not feasible.

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

“…A significant amount of research (Gupta and Duckstein, 1975;Sen, 1980;Dracup et al, 1980;Zelenhastic and Salvai, 1987;Frick et al, 1990;Kendall and Dracup, 1992;Loáiciga and Leipnik, 1996;Chung and Salas, 2000;Cancelliere and Salas, 2004) has developed probabilistic methods to investigate properties of droughts. Multiple attributes of droughts have been evaluated in these studies, but significant correlation relationships are not revealed by separate consideration of correlated characteristics.…”

Drought Risk Analysis Using Stochastic Rainfall Generation Model and Copula Functions

“…그러나 가뭄의 특성인 자를 무엇으로 선정하여 분석했는가에 따라 가뭄빈도해석 의 결과는 서로 상이하게 나타난다 (Fernandez and Salas, 1999;Chung and Salas, 2000;Cancelliere and Salas, 2004). 따라서 최근에는 다양한 가뭄 특성인자 간의 관계 를 복합적으로 결합시켜 일관성이 있는 결과를 제시할 수 있는 가뭄해석방법의 필요성이 제기되고 있다.…”

An Analysis of the Occurrence Probabilities of Wet and Dry Periods through a Stochastic Monthly Rainfall Model

“…Moreover, complete data are strictly required to perform the analysis of wet and dry periods, because missing values may significantly influence estimates of event duration and the character of their alternation [49]. In order to overcome such a difficulty, the probabilistic behavior of dry and wet periods characteristics can be derived analytically, assuming a given stochastic structure of the underlying hydrological and meteorological series [24,[50][51][52][53][54][55][56][57][58][59]. This has led to the development of stochastic models frequently used to produce long rainfall series that are statistically similar to historical records (e.g., [60]).…”