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–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) the uncertainty of SDMF curves caused by input data is much bigger than the 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.