Estimation of Coinciding Flood Discharges in the Extended Area of the Sava / Danube Confluence Applying Different Approaches – Proil Model and Copula Method

The junction of two major lowland rivers, such as the confluence of the Sava and the Danube, is highly problematic for determining design flood discharges for flood protection systems. Namely, in areas where a recipient and a tributary join, the flood process tends to be complex in view of the mutual influence of flood flows as a result of asynchronous maximum discharges of the two rivers. It is generally known that the creation and development of flood waves on neighboring rivers differs as a rule, such that the highest flood waves do not occur simultaneously. As a result, the mutual influence of the two rivers needs to be taken into account in order to properly select their design discharges, which is achieved by estimating the probability of simultaneous “coupled” events, or, in other words, the coincidence of maximum annual discharges of both rivers. The outcomes of a case study applying different procedures (methods) to estimate the coincidence of flood discharges in the extended area of the Sava/ Danube confluence are presented in the paper. The estimation methods are only briefly described, given the fact that their theoretical backgrounds are explained in detail in cited references. In essence, two approaches are used: (i) estimation of exceedance probability in two-dimensional space, referred to as the PROIL model, and (ii) use of three families of so-called Archimedean copulas (COPULA): Gumbel’s, Clayton’s and Frank’s, to determine common probability distributions of different random variables in multidimensional space of probabilities. The coincidence of flood discharges of the Sava and the Danube is estimated applying the above approaches to the extended area of their confluence, from the gauging stations at Sremska Mitrovica on the Sava and at Slankamen and Smederevo on the Danube. The results are presented numerically, via marginal probabilities of the considered combinations of variables for which coincidences are defined, as well as graphically by means of parallel lines of exceedance probability for all the cases addressed applying both methods.