The uncertainty associated with the use of copulas in multivariate analysis

The dependency structure between hydrological variables is of critical importance to hydrological modelling and forecasting. When a copula capturing that dependence is fitted to a sample, information on the uncertainty of the fit is needed for subsequent hydrological calculations and reasoning. A new method is proposed to report inferential uncertainty in a copula parameter. The method is based on confidence curves constructed with the use of a pseudo maximum likelihood estimator for the copula parameter. The method was tested on synthetic data and then used as a tool in two hydrological examples. The first examines the probability of major floods in two locations on the Rhine River and its tributaries in the same calendar year. In the second example, rainfall-runoff from a karst region in Tunisia was analysed to determine a confidence interval for the delay between precipitation and runoff.

Automated summary

The dependency structure between hydrological variables plays a critical role in hydrological modeling and forecasting. This study proposes a new method to report inferential uncertainty in a copula parameter, which is based on confidence curves constructed using a pseudo maximum likelihood estimator. The method was tested on synthetic data and applied to two hydrological examples to analyze the probability of major floods and determine the confidence interval for the delay between precipitation and runoff.