Flood predictions downstream of a river confluence by bivariate analysis of incoming flows

Flood predictions downstream of a river confluence by bivariate analysis of incoming flows Antonio Boccafoschi Department of Civil and Environmental Engineering, University of Catania, Catania, Italy. E-mail: boccafos@dica.unict.it, Tel: +39 095 7382725; fax +39 095 7382748 Bartolomeo Rejtano Department of Civil and Environmental Engineering, University of Catania, Catania, Italy. E-mail: breitano@dica.unict.it, Tel: +39 095 7382703; fax +39 095 7382748 The paper deals with the statistical prediction of flood flows downstream of the confluence of two sub-basins. The research refers in particular to the circumstance which occurs when significant series of annual maxima of flows are available for both the converging branches, whereas data are inadequate to cover the reach downstream of the confluence. Provided that the contributions of the sub-basins are someway correlated, a common approach to predict the peak flow downstream of the confluence for the desired return period is to sum the predicted peaks of the converging branches. This implies the conservative hypotheses that each year the return periods of annual maxima of the two sub-basins are the same, i.e. the two series are correlated perfectly, and also that the annual maxima of the converging branches occur at the same time. These hypotheses don't hold necessarily, and might result to be too conservative, thus leading to overestimate the predicted downstream flow. The research aims to remove the first one of the two hypotheses, thus reducing the overestimation effect. The proposed approach assumes that the annual maxima in the converging branches are mutually dependent, with a specific imperfect degree of correlation. The approach aims to obtain the frequency distribution of the peak flow downstream of the confluence from the frequency distributions of the converging streams and from the correlation coefficient of annual maxima. The hydrological problem implies the statistical problem of obtaining the frequency distribution of the sum of two correlated variables X e Y when their marginal distributions and the correlation coefficient are known. The distribution of the sum is obtained by numerical integration from the joint distribution of X and Y, assumed that it has been obtained previously from the marginal distributions of X and Y and from the correlation coefficient. The numerical algorithm which was developed is presented as it has been specified for the case of a joint bivariate distribution expressed by the logistic Gumbel model, with standard Gumbel marginal distributions. The sense of the proposed approach is in the possibility of evaluating the correlation on the basis of short sub-series of contemporary data for both branches, while the marginal distributions may be obtained from the complete series. An other case for appropriate use of the methodology is when the number of common years with flow data is too small, while the correlation degree can be estimated indirectly, for example on the basis of rainfall data. The validation of the procedure is obtained from an example where data are available in contemporary years for the converging branches and for the downstream reach. The results show that the proposed procedure leads to lower values than the gross sum of the branch predictions. The resulting values are still overestimated, but they are much closer to the values obtained from the plain analysis of downstream data.