Lake models

Reckhow KH (1979) Empirical lake models for phosphorus development, applications, limitations and uncertainty. In Scavia D, Robertson A (eds) Perspectives on lake ecosystem modeling. Ann Arbor Science, Ann Arbor, Michigan... 

Weilenmann, U., Ch. R. O Melia, and W. Stumm (1989), "Particle Transport in Lakes Models and Measurements," Limnology Oceanography 34, 1-18. 

Simple steady-state models may be used in order to relate quantitatively the mean concentration in the lake water column and the residence time of metal ions to the removal rate by sedimentation (for a detailed treatment of lake models see Imboden and Schwarzenbach, 1985). In a simple steady-state model, the inputs to the lake equal the removal by sedimentation and by outflow the water column is considered as fully mixed mean concentrations and residence times in the water column can be derived from the measured sedimentation fluxes. The binding of metals to the particles is fast in comparison to the settling. 

Imboden, D. M., and R. P. Schwarzenbach (1985), "Spatial and Temporal Distribution of Chemical Substances in Lakes Modeling Concepts", in W. Stumm, Ed., Chemical Processes in Lakes, John Wiley and Sons, New York, 1 -30. 

The compound formaldehyde is biodegrading in several systems simultaneously (1) a lake, modeled as a complete mix reactor (2) an estuary, modeled as three complete mixed reactors in series (3) a large river, modeled as 10 complete mixed reactors in series, and a small stream, modeled as a plug flow reactor. What is the nondimensional reaction/residence time, k p, that is required for each of these systems to reach a degradation of 50%, 90%, 99%, and 99.9% ... 

Desborough, G. A. 1978. A biogenic-chemical stratified lake model for the origin of oil shale of the Green River Formation An alternative to the playa-lake model. Geological Society of America Bulletin, 89, 961-971. 

Obviously, there is not much time to organize an elaborate measurement campaign and to mn a sophisticated lake model. Thus a worst-case scenario must be sufficient for a quick decision. Based on the estimated cloud size the initial concentration of atrazine in the lake is about ... 

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

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

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

Let us demonstrate the power of the one-box lake model by analyzing the fate of two different polychlorinated biphenyl congeners (PCBs) in Lake Superior (North America). Characteristic data of the lake are given in Table 23.3. 

C. Three-phase one-box lake model (from Table 23.5) ... 

The application of the continuous lake model is illustrated by continuing the story of tetrachloroethylene (PCE) in Greifensee. Remember that PCE is a compound which is quasi-conservative in the water and is not significantly sorbed by particles. Besides flushing, exchange at the air-water interface is the only relevant process to be considered (see Box 21.2 and Illustrative Examples 21.5, 21.6)... 

As shown in Figure 23.7, the continuous lake model nicely describes the concentration maximum, which slowly moved to greater depth due to the deepening of the surface mixed layer. From the model calculation we can conclude that the processes involved in producing this maximum were the combination of riverine PCE input into the surface mixed layer and loss to the atmosphere by gas transfer. The extra input of PCE into the lake between May 6 and July 1, 1985 had to be about 360 moles. The model calculations suggest that the input had dropped to virtually zero after July 1. Part of the compound was quickly and continuously lost to the atmosphere so that the PCE content of the lake never increased much beyond 200 moles. 

As mentioned before, the 1DV lake model, although still relatively simple compared to the three-dimensional nature of real transport and reaction processes, predicts concentrations and inventories which in most cases are not matched by available field data in terms of chemical, spatial, and temporal resolution. In fact, in a time when powerful computers are ubiquitously available, it is not unusual to find publications in which highly sophisticated model outputs are compared to poor data sets for which much simpler models would have been adequate. However, this is not an... 

In Box 23.2 it is shown that the combined exchange of a chemical at the sediment-water interface due to sediment resuspension and to diffusion, respectively, can be expressed by a single exchange velocity. Explain why this result is a direct consequence of the assumption that the lake model can be formulated in terms of linear differential equations. 

In what sense is the 1DV lake model more than one-dimensional, in spite of the fact that the resulting differential equation is one-dimensional Why is this important for describing sediment-water exchange ... 

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