The testing of a multivariate probabilistic framework for reservoir safety evaluation and flood risks assessment in Slovakia: A study on the Parná and Belá Rivers

Abstract Intense floods represent a challenge to risk management. While they are multivariate in their nature, they are often studied in practice from univariate perspectives. Classical frequency analyses, which establish a relation between the peak flow or volume and the frequency of exceedance, may lead to improper risk estimations and mitigations. Therefore, it is necessary to study floods as multivariate stochastic events having mutually correlated characteristics, such as peak flood flow, corresponding volume and duration. The joint distribution properties of these characteristics play an important role in the assessment of flood risk and reservoir safety evaluation. In addition, the study of flood hydrographs is useful because of the inherent dependencies among their practice-relevant characteristics present on-site and in the regional records. This study aims to provide risk analysts with a consistent multivariate probabilistic framework using a copula-based approach. The framework respects and describes the dependence structures among the flood peaks, volumes, and durations of observed and synthetic control flood hydrographs. The seasonality of flood generation is respected by separate analyses of floods in the summer and winter seasons. A control flood hydrograph is understood as a theoretical/synthetic discharge hydrograph, which is determined by the flood peak with the chosen probability of exceedance, the corresponding volume, and the time duration with the corresponding probability. The framework comprises five steps: 1. Separation of the observed hydrographs, 2. Analysis of the flood characteristics and their dependence, 3. Modelling the marginal distributions, 4. A copula-based approach for modelling joint distributions of the flood peaks, volumes and durations, 5. Construction of synthetic flood hydrographs. The flood risk assessment and reservoir safety evaluation are described by hydrograph analyses and the conditional joint probabilities of the exceedance of the flood volume and duration conditioned on flood peak. The proposed multivariate probabilistic framework was tested and demonstrated based on data from two contrasting catchments in Slovakia. Based on the findings, the study affirms that the trivariate copula-based approach is a practical option for assessing flood risks and for reservoir safety.