Abstract. Global climate change can have impacts on characteristics of rainfall-runoff events and subsequently on the hydrological regime. Meanwhile, the catchment itself changes due to anthropogenic influences. However, it is not easy to prove the link between the hydrology and the forcings. In this context, it might be meaningful to detect the temporal changes of catchments independent from climate change by investigating existing long-term discharge records. For this purpose, a new stochastic system based on copulas for time series analysis is introduced in this study.A statistical tool like copula has the advantage to scrutinize the dependence structure of the data and, thus, can be used to attribute the catchment behavior by focusing on the following aspects of the statistics defined in the copula domain: (1) copula asymmetry, which can capture the nonsymmetric property of discharge data, differs from one catchment to another due to the intrinsic nature of both runoff and catchment; and (2) copula distances can assist in identifying catchment change by revealing the variability and interdependency of dependence structures. These measures were calculated for 100 years of daily discharges for the Rhine River and these analyses detected epochs of change in the flow sequences. In a follow-up study, we compared the results of copula asymmetry and copula distance applied to two flow models: (i) antecedent precipitation index (API) and (ii) simulated discharge time series generated by a hydrological model. The results of copula-based analysis of hydrological time series seem to support the assumption that the Neckar catchment had started to change around 1976 and stayed unusual until 1990.

Abstract. Global climate change can have impacts on characteristics of rainfall-runoff events and subsequently on the hydrological regime. Meanwhile, the catchment itself changes due to anthropogenic influences. In this context, it can be meaningful to detect the temporal changes of catchments independent from climate change by investigating existing long term discharge records. For this purpose, a new stochastic system based on copulas for time series analysis is introduced. While widely used time series models are based on linear combinations of correlations assuming a Gaussian behavior of variables, a statistical tool like copula has the advantage to scrutinize the dependence structure of the data in the uniform domain independent of the marginal. Two measures in the copula domain are introduced herein: 1. Copula asymmetry is defined for copulas and calculated for discharges; this measure describes the non symmetric property of the dependence structure and differs from one catchment to another due to the intrinsic nature of both runoff and catchment. 2. Copula distance is defined as Cramér-von Mises type distance calculated between two copula densities of different time scales. This measure describes the variability and interdependency of dependence structures similar to variance and covariance, which can assist in identifying the catchment changes. These measures are calculated for 100 years of daily discharges for the Rhine rivers. Comparing the results of copula asymmetry and copula distance between an API and simulated discharge time series by a hydrological model we can show the interesting signals of systematic modifications along the Rhine rivers in the last 30 years.

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