One-dimensional vertical lake

Box 23.4 Numerical Approximation of Partial Differential Equations of One-Dimensional Vertical Lake Model Application of the 1DV Lake Model... 

Internal Transport versus Reaction and Boundary Fluxes One-Dimensional Vertical (1DV) Lake Model... 

In Section 23.1, this procedure will be applied to just one completely mixed water body. This control volume may represent the lake as a whole or some part of it (e.g., the mixed surface layer). Section 23.2 deals with the dynamics of particles in lakes and their influence on the behavior of organic chemicals. Particles to which chemicals are sorbed may be suspended in the water column and eventually settle to the lake bottom. In addition, particles already lying at the sediment-water interface may act as source or sink for the dissolved chemical. In Section 23.3, two-box models of lakes are discussed, particularly a model consisting of the water body as one box and the sediment bed as the other. Finally, in Section 23.4, one-dimensional vertical models of lakes and oceans are discussed. 

Concentrations of minor elements in lake water are usually determined by adsorption onto settling particles, desorption from settling particles and interaction of sediments and bottom water. Thus, one dimensional vertical model assuming laterally homogeneous concentration is useful for the analysis of distribution of minor element concentration. Imboden and Schwarzenbach (1985) calculated tetrachloroethylene concentration in Zurich lake, Switzerland based on this model. Basic equations used by them are mass balance equation concerning solutes and particles, mass balance equation concerning minor elements on particles in sedimentary column, and diffusion equation at the boundary between sediment surface and bottom water. Results of calculation based on these equations and vertical concentration profile are shown in Fig. 6.19. 

In deep lakes the vertical stratification becomes important and dius a one-dimensional modelling approach is needed. Based upon heat conservation the lake temperature satisfies ... 

In Fig. 4 (Ljungemyr, pers. comm.), the one dimensional lake model presented above is compared to the zero dimensional model discussed in Section 2.1. The lake considered is the eastern part of Lake V9nem, a large and deep lake in the central part of Sweden. From the figure we can notice that the slab model does not simulate summer temperatures correctly, but comes close during autumn and winter periods when the whole lake is vertically mixed. 

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