An assessment of the uncertainty of the extremity of flood waves with vine copulas

Flood hazard connected with the failure of hydraulic structures and flood risk associated with areas subject to flooding need to be estimated using flood hydrographs. Multivariate statistics of flood wave parameters enable quantitative conclusions about such flood hazards and risks. This study focuses on uncertainties in their estimates using unbounded and bounded marginal distributions of flood durations in the joint modelling of flood peaks, volumes, and durations with vine copulas. We have respected the seasonality of floods by distinguishing between the durations of summer and winter floods. We propose to use the bounded Johnson’s SB distribution to represent the hydrological constraints associated with flood durations. The practical consequences of selecting various unbounded and bounded distributions for modelling flood durations for the joint overall and conditional probabilities of the exceedance of flood peaks, volumes, and durations were demonstrated on data from the Parná River in Slovakia. Differences in modelling joint probabilities due to the tail behaviours of the marginal distributions tested were found. Although these are not critical for practical applications, accepting upper and lower bounds as hydrological constraints improves the quality of the statistical models.