A multivariate probabilistic framework for estimating control flood hydrographs for reservoir safety re-evaluation in Slovakia

The changing climate and evolving watershed conditions pose significant challenges to the safety of flood control structures. Assessing the current safety of these structures, originally designed using limited hydrological records from the pre-climate change era, may result in inaccurate risk assessments and mitigation strategies. Additionally, traditional design methods often relied on classical frequency analysis, examining flood characteristics from a univariate perspective. This approach overlooks the multivariate nature of floods, where mutually correlated characteristics such as peak flow, volume, duration, and shape play crucial roles. Therefore, multivariate frequency analysis and the examination of joint distribution probabilities are essential to accurately reassess the risks associated with reservoir safety.

This study presents a framework that has recently been proposed in Slovakia to design new and re-evaluate safety of old reservoirs. The framework respects and describes the dependence structures among the flood peaks, volumes, and durations of observed and synthetic control flood hydrographs. The probabilistic nature of the framework lies in the fact that rather than examining the safety based on a single control flood wave, it allows to generate a set of control flood waves with associated probabilistic parameters. The seasonality of flood generation is respected by separate analyses of floods in the summer and winter seasons for which a representative dimensionless shape of the flood hydrograph is derived from a set of flood hydrographs separated from the historical records. The framework consists of five key steps: (1) separation of observed hydrographs, (2) analysis of flood characteristics and their dependencies, (3) modelling marginal distributions, (4) applying a copula-based approach for joint distribution modelling of flood peaks, volumes, and durations, and (5) constructing synthetic flood hydrographs. This offers a diverse range of control waves for assessing the safety of water structures under extreme conditions, utilizing a probabilistic and process-based framework in typical failure risk scenarios.

This multivariate probabilistic framework was tested on a case study of the Liptovská Mara reservoir in the watershed of the Váh river in Slovakia, revealing significant seasonal differences. Winter floods exhibited longer durations and larger volumes, whereas summer floods were characterized by shorter durations, smaller volumes, and higher peak flows.

Acknowledgements

This work was supported by the Slovak Research and Development Agency, under the contract No. APVV-23-0332; APVV-20-0374, and the VEGA grant agency under contract No. VEGA 1/0577/23; VEGA 1/0657/25.