Downstream-Directed Performance Assessment of Reservoirs in Multi-Tributary Catchments by Application of Multivariate Statistics

In the past the flood design was dominated by safety oriented concepts. A design flood was chosen with the basic assumption that it defines the limit up to which a flood can be controlled completely by technical measures. Often peak values with very small probabilities are used. Thus the risk of an event beyond the design flood seems to be very small and even negligible. Caused by the increasing risk awareness, changes of the design philosophy became necessary. The remaining danger of failure, which may result from the hydrological risk of an extreme event, but also from operational and technical risks, requires more complex assessments. For this purpose a differentiated view on hydrological risk becomes essential. In this paper the multiple aspects of risk oriented specifications of hydrological loads are discussed. In difference to other applications of multivariate statistics which are used to specify the hydrological characteristics of flood events by consideration of peak-volume relationships, we are interested in spatial interactions of discharge waves from different tributaries. Here it is not sufficient to estimate the most critical combinations by scenarios but to estimate their probabilities. It is shown how the probability of coincidences of critical hydrograph characteristics can be specified by multivariate statistics, based on copulas. We discuss the influence of upstream flood detention measures on the discharge downstream of a confluence. For that purpose the effect of a reservoir is evaluated statistically downstream of a multi-tributary catchment. This more complex approach for flood risk assessments is demonstrated with two practical examples.