Modeling the Hydrological Regime of the Dnipro River During Flood Events Using Copula Theory

The article presents a model of the hydrological regime of the Dnipro River at the control points of the Dnipro Hydropower Cascade during flood events using copula theory. The study accounts for the existence of correlation relationships between natural and climatic factors, in particular between maximum flood discharges at various sections of the cascade. The input data used for modeling consist of time series of maximum flood discharges from 1787 to 1999. The aim of the study is to build a statistically sound model of the dependencies between hydrological parameters based on copulas. Four types of copulas most commonly used in hydrology are considered: Clayton, Frank, Gumbel, and Gaussian. Each has unique features for modeling dependencies in the lower, middle, or upper parts of the distribution. The goodness-of-fit of the models was assessed using the Copula Goodness-of-Fit test. The analysis showed that all the considered copulas are statistically acceptable for modeling dependencies between water discharges at different hydropower site pairs, although the accuracy of the modeling varies significantly. In particular, for the Vyshhorod – Kyiv pair, the Gaussian copula showed the best fit, indicating a symmetric linear dependence between discharges. A similar result was observed for the Vyshhorod – Kremenchuk pair. In contrast, for the Vyshhorod – Lozmano-Kamyanka pair, the Gumbel copula demonstrated the highest accuracy, pointing to a strong dependence in the upper tail of the distribution, which is typical for extreme flood events. The Frank and Clayton copulas showed lower accuracy and are therefore not recommended as primary models. The results highlight the necessity of selecting the copula individually for each hydropower pair. The proposed models can be used to construct joint probability distributions, generate synthetic hydrological scenarios, and assess the risk of synchronous flood events within the Dnipro Hydropower Cascade.