Determination of univariate, bivariate and conditional return periods of hydrological droughts using two-dimensional multivariate functions

Abstract

Hydrological drought is frequently considered as the most intricate type of drought because of its long-term impacts, interactions with human activities and slow response of water systems to climatic fluctuations. Drought severity and duration are key parameters to characterize the drought. This research models the conditional probabilities, univariate, bivariate and conditional return periods of drought severity and duration using two-dimensional multivariate copulas functions. The analyses use streamflow drought index (SDI) and mean monthly streamflow records of 24 stations in Ye & scedil;il & imath;rmak Basin, Turkey for a 3-month time scale. Drought characteristics are derived from Yevjevic's Run Theory. The dependence between drought characteristics is examined with non-parametric Kendall's tau. The best marginal distributions of drought characteristics are selected among six types of distributions based on goodness of fit tests. The best copulas which have been utilized for the modelling of conditional probabilities, univariate, bivariate and conditional return periods are defined across 10 types of copula functions based on tail dependence and goodness of fit tests. Results have indicated a strong correlation between drought severity and duration. Marginal distributions of drought characteristics are modelled by Lognormal and Weibull distribution mostly. In most of the stations Gumbel copula has been detected as the best copula. Results have put forth that, many parts of the basin have the risk of hydrological drought under different conditions. Therefore, the basin needs an effective drought management plan.