In multidimensional water quality modelling the spatial and temporal distributions of dissolved substances and suspended particles are simulated in order to account for inhomogeneities in the transport and reactive processes[ The exchange processes at the water surface\ e[g[ photosynthesis and oxygen transfer\ and at the waterรsediment interface\ e[g[ erosion\ deposition and oxygen transfer\ are basically multidimensional[ A homogeneous distribution can be expected only if the mixing processes generated by the hydrodynamics occur in a short time period compared with the reaction rates[ This article presents sample results of a three!dimensional water quality model that includes the lake hydrodynamics\ sedimentation and the proper representation of physical and reactive processes at the bottom and surface boundaries[ The goal is to use this insight in order to obtain a better description of water quality with lower!dimensional models using spatial averaging techniques[ For this purpose\ the program TELEMAC!2D\ which is able to calculate three!dimensional free surface ~ows and transport\ was extended to include reactive processes[ Ordinary di}erential equations remain to be solved following the solution of the non!reactive transport equations using operator!splitting techniques[ These are in turn solved using a fourth!order RungeรKutta method[ As the reaction rates are in part considerably long compared with the hydrodynamics\ a larger time!step is used for solving the transport equations[
The model was applied to a lake in Berlin\ Germany\ the Gro)er Mu ร ggelsee[ Although comparatively shallow\ it experiences extensive multidimensional hydrodynamics as a result of wind!induced currents and the Spree River\ which ~ows through it[ Numerous water quality measurements undertaken by the Institu ร t fu ร r Gewa รssero ร kologie und Binnen_scherei "IGB# demonstrate the in~uence of the hydrodynamics on the concentration distributions[ A comparison between calculations with the spatial average of the 2!D model and directly calculated 9!D model results using the same reactiveรkinetic formulations clearly demonstrates that the multidimensional e}ects\ including the current distribution\ have a signi_cant e}ect on the water quality[ Therefore\ care must be taken to correctly include multidimensional e}ects for detailed assessment of possible remedial measures to improve the water quality[ An averaging technique for including these e}ects is presented [ Copyright ร 1999