Multivariate uncertainty analysis of severity–duration–magnitude–frequency curves using Khoudraji copula and bootstrap method

This study seeks to apply Khoudraji asymmetric copula in a trivariate analysis of drought, focusing on the uncertainty assessment of the severity-duration and magnitude-frequency (SDMF) curve. The analysis, influenced by input data and copula parameters, was conducted in the Mina Basin, Algeria. The results showed: (1) the dependence structure of SDMF of drought characteristics can be well modelled by Khoudraji copula; (2) Gumbel and Frank copulas depart more than other copula functions in estimating SDMF curves; (3) Uncertainty of SDMF curves caused by input data is much bigger than uncertainty caused by copula parameters; (4) An increase (decrease) in the conditional probability causes a decrease (increase) in the uncertainty band, which applies to both sources of uncertainty in this law. Conversely, increasing the threshold M also increases the uncertainty. These results are very useful for reducing uncertainty caused by estimating SDMF curves and preparing strategies for different levels of drought.