Probabilities and return periods of multisite droughts/Probabilités et périodes de retour de sécheresses multi-sites

Abstract

Because droughts cover extensive areas, it is important to consider multisite droughts in a region. Probability distribution of joint droughts at a number of sites is derived assuming that flows are cross-correlated first-order Markov processes. A geometric distribution is found with a parameter that depends on the threshold probability, lag-one autocorrelation coefficients, and the multivariate probability of remaining below the threshold. Computation of the parameter of the geometric distribution is discussed. An expression is obtained for the return period of multisite droughts. Application of the derived expression is shown in an example.Key words autocorrelation; multisite droughts; probability distribution; return period Probabilités et périodes de retour de sécheresses multi-sitesRésumé Parce que les sécheresses couvrent des surfaces étendues, il est important de considérer les sécheresses multi-sites sur une région. La distribution de probabilité des sécheresses conjointes en plusieurs sites est déduite en supposant que les écoulements présentent une corrélation croisée selon un processus de Markov de premier ordre. Une distribution géométrique est mise en évidence avec un paramètre qui dépend du seuil de probabilité, des coefficients d'autocorrélation avec décalage de 1, et de la probabilité multivariée en deçà du seuil. Le calcul du paramètre de la distribution géometrique est discuté. Une expression est obtenue pour la période de retour des sécheresses multi-sites. Une application de l'expression obtenue est présentée sur un exemple.

Combined analysis of precipitation and water deficit for drought hazard assessment

“…They assumed that the binary process consisting of dry years (D: X t < x 0 ) and wet years (W: X t ≥ x 0 ) follows a simple (first-order) Markov chain with two states (dry and wet). Bayazit and Önöz (2005) analysed the probability distribution and return periods of joint droughts at a number of sites assuming that streamflows are cross-correlated first-order Markov processes. The stochastic properties of the SPI time series were explored for predicting drought class transitions using Markov chain modelling (Paulo et al 2005, Paulo andPereira 2007).…”

“…Various authors investigating return periods of droughts have found different levels of persistence in precipitation as well as in streamflow data. The identified order of Markov chain depended on the applied thresholds to distinguish between wet and dry conditions, the analysed time interval and the type of the indicator (Chin 1977, Roldan and Woolhiser 1982, Şen 1990, Fernández and Salas 1999, Cancelliere and Salas 2004, Bayazit and Önöz 2005, Schoof and Pryor 2008, Sharma and Panu 2008, Akyuz et al 2012. Time series of SPI-SRI indicator for the 1966-2006 period were analysed as a discrete-state, discrete-time variable with five possible states S = {0,1,2,3,4}.…”

Bi-site Analysis of Meteorological Drought Duration: Theoretical Modeling and Application

“…The first approach adopts the proportion of the area covered by the drought deficit to characterize regional droughts (Santos 1983;Shin and Salas 2000;Hisdal and Tallaksen 2003;Bonaccorso et al 2003;Loukas and Vasiliades 2004;Paulo and Pereira 2008). The second approach relies on the joint analysis of the underlined hydrologic variable at several sites in the region under consideration as the key point to investigate regional droughts (Yevjevich 1972;Bayazit 1981;Sen 1998;Javier and Gomez 1999;Bayazit and Onoz 2005;Paulo et al 2005). In this study, the second approach is considered to investigate regional droughts in Central Jordan.…”