A MCMC-based maximum entropy copula method for bivariate drought risk analysis of the Amu Darya River Basin

[Display omitted] •A MCMC-MEC method is developed for bivariate drought risk.•It has advantages in reflecting uncertainty in bivariate drought risk assessment.•MCMC-MEC is applied to the Amu Darya River Basin, Central Asia.•The study basin experienced 42 drought events during 1935–2015.•In 2005–2015, drought risk is increased due to decreasing precipitation and runoff. In this study, a MCMC-based maximum entropy copula (abbreviated as MCMC-MEC) method is developed for assessing drought risk under uncertainty. MCMC-MEC has advantages in analyzing the bivariate drought risk (i.e. duration and severity) through runs-theory, improving the fitting processes of drought variables based on maximum entropy, and reflecting the uncertainties in bivariate drought risk assessment through MCMC. Then, MCMC-MEC is applied to the Amu Darya River Basin, a typical arid and semi-arid basin in Central Asia. Results disclose that, during 1935–2015, the study basin experienced about 42 drought events, average duration of each drought was 5 months (severity 4.38), and the most severe drought event lasted for 25.3 months (severity 27.9). Results also reveal that uncertainty in parameter of copula has effects on drought risk, and duration and severity would increase with confidence level of univariate drought probability. At confidence level of 0.9, the bivariate drought risk would be 4%-6% (duration ≥ 7.0 months and severity ≥ 5.8); at confidence level of 0.95, the drought risk would be 1%-2% (duration ≥ 10.0 months and severity ≥ 10.6). During 2005–2015, drought risk for the study basin was increased due to the decreasing precipitation and runoff, and their contribution rates to the drought risk were 55.8% and 44.2%, respectively. The findings are helpful for providing decision support of drought management and disaster prevention.