On the Use of Copulas in Hydrology: Theory and Practice

Abstract

The use of copulas in hydrology is quite recent, and many important results still are to be discovered and/or derived. In this work we present some recent advances in hydrological modeling that exploit copulas. These include: (1) the calculation of conditional probabilities and their use in bivariate simulation; (2) the calculation of the level curves of joint distributions; (3) the calculation of the return periods of bivariate events, both in the conditional and unconditional cases; (4) the definition and calculation of the secondary return period; (5) a trivariate model for the temporal structure of the sequence of storms; (6) the statistical calculation of the storm depth; and (7) the calculation of the convolution variance. Several applications to hydrological data are shown. The models presented here may have important implications in many areas of water resources and hydrologic systems.