The Copula Application for Analysis of the Flood Threat at the River Confluences in the Danube River Basin in Slovakia

Abstract

In hydrological practice, individual elements of the hydrological cycle are most often estimated and evaluated separately. Uncertainty in the size estimation of extrema discharges and their return period can affect the statistical assessment of the significance of floods. One example is the simultaneous occurrence and joining of extremes at the confluence of rivers. The paper dealt with the statistical evaluation of the occurrence of two independent variables and their joint probabilities of occurrence. Bivariate joint analysis is a statistical approach for the assessment of flood threats at the confluence of rivers. In our study, the annual maximum discharges monitored on four selected Slovak rivers and their tributaries represent the analyzed variables. The Archimedean class of copula functions was used as a set of mathematical tools for the determination and evaluation of the joint probability of annual maximal discharges at river confluences. The results of such analysis can contribute to a more reliable assessment of flood threats, especially in cases where extreme discharges occur simultaneously, increasing the risk of devastating effects. Finally, the designed discharges of the different return periods calculated by using the univariate approach and the bivariate approach for the gauging station below the confluence of the rivers was evaluated and compared.