Mass conserving modelling of aquatic ecosystems with a variable tide level—Why extrapolation from point tracers is inadmissible and how to solve the problem with a semi-Lagrangian approach

In earlier Lagrangian descriptions of aquatic systems point tracers were considered for describing the pelagic part of the systems. A coupling of such a model to a benthic model is not satisfactory if the system’s water level is variable and mass conservation is needed. The article shows that a pelagic–benthic coupling is not possible by extrapolating the properties of the tracers to the total water body. In the second part a solution for this problem is given. In this concept the tracers are assumed to have a finite volume and the total volume of all tracers within a considered region at a considered time represents the actual volume of the real system. The coupling to the benthic system is realized by a semi-Lagrangian scheme defining a contact area of every tracer to the sediment. The magnitude of the contact area depends on the actual water depth. The exchange processes between the pelagic and the benthic system are calculated for every contact area.