One-dimensional continuous lake model

One-Dimensional Continuous Lake Models (Advanced Topic)... 

In this chapter we will keep the description of transport simpler than Fick s law, which would eventually lead to partial differential equations and thus to rather complex models. Instead of allowing the concentration of a chemical to change continuously in space, we assume that the concentration distribution exhibits some coarse structure. As an extreme, but often sufficient, approximation we go back to the example of phenanthrene in a lake and ask whether it would be adequate to describe the mass balance of phenanthrene by using just the average concentration in the lake, a value calculated by dividing the total phenanthrene mass in the lake by the lake volume. If the measured concentration in the lake at any location or depth would not deviate too much from the mean (say, less than 20%), then it may be reasonable to replace the complex three-dimensional concentration distribution of phenanthrene (which would never be adequately known anyway) by just one value, the average lake concentration. In other words, in this approach we would describe the lake as a well-mixed reactor and could then use the fairly simple mathematical equations which we have introduced in Section 12.4 (see Fig 12.7). The model which results from such an approach is called a one-box model. 

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