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Quantitative Analysis of Drought Uncertainties Using Copula Methods
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DOI：10.1007/s11269-026-04844-4.png)
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Abstract
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Copula distribution functions are effective tools for analyzing the multivariate and conditional frequency of drought. Nevertheless, uncertainties arising from various sources, such as the sampling variability of drought events and uncertainty in copula parameter estimation, have received limited attention. This study evaluates the uncertainty in severity–duration–magnitude–frequency (SDMF) curves of drought using the Maximum Entropy (ME), Empirical (EM), and Maximum Likelihood (MLE) copula methods. We construct a composite meteo–groundwater drought index using three derivation approaches and delineate SDMF curves under different conditional probabilities (CPs). The normal copula effectively captures the regional dependence structure of severity, duration, and magnitude. Comparing CP across methods reveals an intensity ranking of MLE > EM > ME, with ME and EM producing similar results. Both sampling variability and copula parameter uncertainty affect CP isolines, with their effects decreasing consistently across methods and scenarios as CP decreases. The uncertainty band of SDMF curves widens as drought magnitude increases. Uncertainty under MLE exceeds that of EM and ME, while ME and EM show strong agreement. The uncertainty associated with sampling variability of drought events has a greater impact than that arising from copula parameter estimation. The Maximum Entropy method, with its flexibility in combining different marginal distributions, proves effective. Considering these uncertainties, multivariate drought frequency analysis can provide valuable information for water managers and disaster preparedness programs across different drought severity levels.
Keywords:
Bootstrap technique
Tri-variate copula
Maximum entropy-copula
Severity-duration-magnitude curves
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