Although time dependencies of hydrologic processes have been statistically studied in the past decades, classical statistical analysis such as correlation or covariance often fails to capture all the dependencies between random variables due to the fact that it regresses the statistical information to a single value. In addition, multivariate distributions cannot precisely be modeled by a traditional Gaussian approach whenever large asymmetries exist. In contrast, copulas can capture more precise dependence structures of hydrological variables and allow describing the dependence structure independently from the marginal distributions.
This thesis aimed to perform the statistical analysis of the time series discharges reproduced by the rainfall-runoff modeling by applying the copula based methods. Semi-distributed HBV models were developed for the selected subcatchments located in the Upper Neckar catchment, south-west Germany. Identifications of the hydrological characteristics in the subcatchments were undertaken and the model ability in representation of the dynamical changes detected in copulas was investigated as parts of the study objectives.
Bivariate empirical copulas with varying values of time lag were constructed. Auto copula analysis results showed that the models were capable of reproducing strong dependencies of the low quantiles for small time lag values while this ability was deteriorated once time lag values increased due to systematic errors produced by the models. Catchment characteristics investigated by asymmetric properties of the simulated time series discharges indicated that the high performance models tend to react to the rainfall events in the similar way with the observed discharges. The study of distances between two copulas estimated by beta kernel density detected the structural changes in the observed discharge datasets, which possibly caused by anthropogenic impacts. However, the models could capture these changes only in some periods of the series. Conditional copula autoregressive simulations were performed and demonstrated that the conditional copula models reproduced similar structures of asymmetries for small dimensions.
Kamkaew, K. (2013). Statistical analysis of discharge and development of time series model using copulas. Master’s thesis. Institut für Wasser- und Umweltsystemmodellierung, Universität Stuttgart.