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Abstract. Although the consequences of floods are strongly related to their peak discharges, a statistical classification of flood events that only depends on these peaks may not be sufficient for flood risk assessments. In many cases, the flood risk depends on a number of event characteristics. In case of an extreme flood, the whole river basin may be affected instead of a single watershed, and there will be superposition of peak discharges from adjoining catchments. These peaks differ in size and timing according to the spatial distribution of precipitation and watershed-specific processes of flood formation. Thus, the spatial characteristics of flood events should be considered as stochastic processes. Hence, there is a need for a multivariate statistical approach that represents the spatial interdependencies between floods from different watersheds and their coincidences. This paper addresses the question how these spatial interdependencies can be quantified. Each flood event is not only assessed with regard to its local conditions but also according to its spatio-temporal pattern within the river basin. In this paper we characterise the coincidence of floods by trivariate Joe-copula and pair-copulas. Their ability to link the marginal distributions of the variates while maintaining their dependence structure characterizes them as an adequate method. The results indicate that the trivariate copula model is able to represent the multivariate probabilities of the occurrence of simultaneous flood peaks well. It is suggested that the approach of this paper is very useful for the risk-based design of retention basins as it accounts for the complex spatio-temporal interactions of floods.

Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs; however, where a self-excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.

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.