"Contaminant Transport in Lake Constance: Analysis of Moments and the Dilution Index"Lake Constance constitutes one of the major sources for the drinking water supply in southwestern Germany. Quick prediction tools for contaminant transport need to be developed that help the drinking water suppliers to assess the risk and consequences of contaminant releases and to take decisions, protecting the quality of drinking water. As detailed models are complex and do usually not allow for adequate real-time decision support, decisions often have to be based on simplified models. Much quicker than setting up a detailed transport model is prediction via the method of moments, where the contaminant plume is conceptualized via its center of gravity (first spatial moments) and a spread around that point (second central spatial moments). Theoretical and empirical models that predict the growth of second central moments over time exist and have been applied in preliminary studies.
These spatial moments cannot distinguish between actual dilution and irregularity of contaminant plumes. For prediction of risk, however, the dilution of the contaminant needs to be quantified. A more powerful measure is the Dilution Index, which only accounts for dilution and eliminates the influence of plume irregularity from the analysis. The underlying problem is that most mechanistic models for moment growth assume separation of scales, i.e., that there are subscale fluctuations in the velocity field that are a driving force for dilution, but that there are no plume-scale fluctuations that lead to irregularities of the plume shape. The Dilution Index will help to overcome this problem.
A second problem of moment growth models (regardless whether using moments or the Dilution Index) is the assumed absence of boundaries. In Lake Constance with its elongated shape, contaminant plumes released from any point will come into contact with the shoreline after seven days at most, as has been shown in preliminary work. Limitations of the moment growth models due to shore contact will have to be assessed and quantified in the form of maximum model validity time as a function of initial plume location. Separating between plume irregularity and dilution, we believe that an analysis based on the Dilution Index is superior in resolving the shore influence since it avoids the fuzziness induced by simultaneous presence of both problems. Hence, we expect that analyzing and quantifying the model limitations due to shore contact can be substantially improved over results of preliminary studies.