Quantifying uncertainty in multivariate quantile estimation of hydrometeorological extremes via copula: A comparison between bootstrapping and Markov chain Monte Carlo

Abstract The performance of uncertainty estimation methods, namely bootstrapping and Markov chain Monte Carlo (MCMC), in univariate frequency analysis of hydrometeorological extremes has been well tested in the literature. However, the two methods have not been thoroughly compared for multivariate frequency analysis of such events. In this study, we compare the performance of bootstrapping and MCMC in estimating the uncertainty of bivariate quantiles of extremes as defined by the return period quantiles of hydrologic drought duration and severity, and concurrent meteorological drought and heat wave. Using a copula framework, we analyse the accuracy and size of confidence intervals of the bivariate quantiles, and bias in point estimates of them. We also investigate the performance of the two methods in estimating the uncertainty of univariate quantiles of the marginal distributions of the resulting bivariate copulas. This is to evaluate if any advantage of one method over the other is consistent, whether in estimating the univariate or bivariate quantiles. We conduct this study with synthetic datasets of various sample sizes and predefined distributions derived from a set of empirical data. The results show MCMC to be superior when estimating the uncertainty of bivariate quantiles where the sample size is small (~50). Where the sample size is large (~100 and ~200), the results show bootstrapping to be the better option for estimating uncertainties of bivariate quantiles. For estimating uncertainties of univariate quantiles, bootstrapping is performing better under all investigated sample sizes. Results and conclusions in this study will be beneficial for hydrometeorological risk assessment, hydrologic infrastructure design, and water resources assessment.