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Institut für Wasser- und Umweltsystemmodellierung - IWS



"Characterisation of tracer distribution in Upper Lake Constance using spatial moments "

Horizontal mixing in Upper Lake Constance was investigated analysing the development of the tracer distribution of conservative tracers simulated using the model ELCOM [3]. In four simulations each including ten different tracer experiments in depths around 3 metres, 30 metres and 60 metres the three-dimensional concentration distributions were calculated for a period of two weeks after release. The method of spatial moments according to Peeters et al. [1] was used to analyse the temporal development of the tracer distribution. Therefore mainly the advetive motion of a tracer cloud and the temporal development of the spreading along the principal axes and of the cloud size was considered. In addition, theoretical models for horizontal mixing were tested. It was shown that especially the upper layers - the epilimnion - are important considering horizontal mixing. For tracers injected close to the surface in a distance lager than two kilometres to the shore the method of spatial moments approximated the tracer cloud in a satisfying way during the first week after release. Afterwards and for tracers released close to the shore the approximation was not reliable. After two weeks the cloud sizes ranged in a magnitude between 10 and 32 km2. Only for tracers released in a central position of Lake Constance a similar behaviour of the growth of the cloud size could be observed during the first week of the experiments. Afterwards and for other release points boundary influences became to strong. Also effects of large scale advective motion showed up after one week. Application of theoretical approaches for horizontal mixing according to Peeters et al. [1] showed that a shear diffusion model is able to provide a satisfying description of the behaviour of the cloud for 60% of the tracers injected in central position until day seven after release. This model also accounts for the fact that the tracer clouds were not radially symmetric. The hypothesis that the cloud size grows with elapsed time to the power of 3 according to the inertial subrange model could not be approved. Considering the peak concentration as measure for dilution a concentration of around 0.1% of the initial concentration could be observed for tracers injected into the near-surface layers after two weeks.