Stratified lake

Assume sediment oxygen consumption at a rate of 60 mg/(m2 hr) is the major sink for 02 in a small lake 10 m deep. For simplicity, assume that the lake basin is in the shape of a rectangular box. When the lake stratifies in late spring, with a thermocline at 4-m depth, the water contains 10.8 mg/liter of oxygen. Assume the hypolimnion is fairly well mixed. 

Aeration of the hypolimnion (lower, colder layer of water in a stratified lake) without disruption of stratification has been used in deep lakes. This has the advantage of not increasing the temperature of the hypolimnion and prevents the advection of nutrient-rich water into the epilimnion (upper, warmer layer of water in a stratified lake). Oxygen injection is preferred in order to prevent the build up of nitrogen super-saturation which is toxic to fish. "... 

Molot LA, Dillon PJ, Clark BJ, Neary BP (1992) Predicting end of summer oxygen profiles in stratified lakes. Can J Fish Aquat Sci 49 2363-2372... 

Hurley JP, Watras CJ, Bloom NS. 1994. Distribution and flux of particulate mercury in four stratified seepage lakes. In Watras CJ, and Huckabee J, editors. Mercury as a global pollutant integration and synthesis. Chelsea (MI) Lewis, p. 69-82. 

Danz NP, Regal RR, Niemi GJ, Brady VJ, Hollenhorst T, Johnson LB, Host GE, Hanowski JM, Johnston CA, Brown T, Kingston J, Kelly JR. 2005. Environmentally stratified sampling design for the development of Great Lakes environmental indicators. Environ Monitor Assess 102 41-65. 

Konopka A, Bercot T, Nakatsu C (1999) Bacterioplankton community diversity in a serious of thermally stratified lakes. Microbial Ecol 38 126-135... 

Jones, J.G. Gardener, S. Simon, B.M. (1983) Bacterial reduction of ferric iron in a stratified eutrophic lake. J. Gen. Microbiology 129 131-139... 

There are many real-life situations resulting in a tracer pulse or front with a long tail, where the pulse or front does not decay nearly as quickly as it rises. The fit of the tanks-in-series to the tracer pulse in Example 6.7 is typical of the trailing edge problem. These can be solved by employing a leaky dead-zone model. There are physical arrangements of transport problems where the need of a leaky dead zone seems apparent, such as a side embayment on a lake or river, or a stratified lake where a well-mixed reactor will be used to model the lake. These are illustrated in... 

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. 

In the fall of 1993, the serum levels of BB-167 (2,2, 4,4, 5,5 -hexaBB) in 32 subjects, approximately 10 of whom consumed sport fish from the Great Lakes, were measured (Anderson et al. 1998). When the data were stratified by lake, on average, the Lake Huron fish consumers had the highest levels of PBBs (0.6 ppb) and Lake Erie fish consumers had the lowest (0.2 ppb). When the data were then stratified by state of residence, on average. Great Lake sport fish consumers who live in Michigan had the highest PBB level (0.7 ppb) and residents ofWisconsin had the lowest level (0.05 ppb). 

In natural systems (lakes, oceans, atmosphere) turbulent diffusion is usually anisotropic (i.e., much larger in the horizontal than vertical direction). There are two main reasons for that observation (1) the extension of natural systems in the horizontal is usually much larger than in the vertical. Thus, the turbulent structures (often called eddies) that correspond to the mean free paths of random motions often look like pancakes that is, they are flat along the vertical axis and mainly extended along the horizontal axes. (2) Often the atmosphere or the water body in a lake or ocean is density stratified (i.e., the density increases with depth). This compresses the eddies even further in the vertical. Gravitational forces keep the water parcels from moving too far away from the depth where they are neutrally buoyant, that is, where they have the same density as their environment. Thus, the anisotropic shape of the eddies results in turbulent diffusivities which differ in size along different spatial directions. 

Lakes and oceans are often vertically stratified. That is, two or more fairly homogeneous water layers are separated by zones of strong concentration and density gradients. In Chapter 21, two- and multibox models will be developed to describe the distribution of chemicals in such systems. In these models, volume fluxes, Qex, are introduced to describe the exchange of water and solutes between adjacent boxes (Fig. 19.5). Qex has the same dimension as, for instance, the discharge of a river, [L3TT ]. The net mass flux, LFnet, from box 1 into box 2 is given by ... 

Linear Two-Box Model with One Variable Linear Two-Box Model of a Stratified Lake Box 21.7 Linear Two-Box Model for Stratified Lake Illustrative Example 21.5 Tetrachloroethene (PCE) in Greifensee From the One-Box to the Two-Box Model Linear Two-Box Models with Two and More Variables Nonlinear Two-Box Models... 

As a second example of a two-box model we discuss the case of a stratified lake which is divided into the surface layer (epilimnion E, box 1) and the deep-water layer (hypolimnion H, box 2). The model and its parameters are shown in Fig. 21.10. It includes the following processes (numbers as in the figure) ... 

Figure21.10 Two-box model for stratified lake. The numbered processes are (1) input by inlets (rj is relative fraction of input going to the hypolimnion), (2) air-water exchange, (3) loss at the outlet, (4) loss by in situ chemical transformation (chemical, photochemical, biological), (5) flux on settling solid matter, (6) exchange across the thermocline. See text for definition of parameters. Note that the substance subscript i is omitted for brevity.

In Box 21.2 we analyzed the dynamics of PCE in Greifensee and found that the air-water exchange velocity, v/a/w, which explains the observed concentration, turned out to be unrealistically small. One reason could be that the lake is stratified during the summer and thus the surface concentration of PCE, which determines the size of both air-water exchange and loss at the outlet, is overestimated. Use the physical characteristics of Greifensee listed in Table 21.1. Total input of PCE is /,tot = 0.90 mol d-1. The PCE concentration in air is smaller than 10 8molnT3. Note that the air-water exchange velocity of PCE at u10 = lm s-1 is via/w = 4.9 x 10-6 m s 1 (Table 21.1). 

In Illustrative Example 21.5 we discussed the behavior of tetrachloroethene (PCE) in a stratified lake. As mentioned before, our conclusions suffer from the assumption that the concentrations of PCE in the lake reach a steady-state. Since in the moderate climate zones (most of Europe and North America) a lake usually oscillates between a state of stratification in the summer and of mixing in the winter, we must now address the question whether the system has enough time to reach a steady-state in either condition (mixed or stratified lake). To find an answer we need a tool like the recipe for one-dimensional models (Eq. 4, Box 12.1) to estimate the time to steady-state for multidimensional systems. 

Inhomogeneous systems. If Eq. 21-46 is an inhomogeneous system, that is, if at least one Ja is different from zero, then usually all eigenvalues are different from zero and negative, at least if the equations are built from mass balance considerations. Again, the eigenvalue with the smallest absolute size determines time to steady-state for the overall system, but some of the variables may reach steady-state earlier. In Illustrative Example 21.6 we continue the discussion on the behavior of tetrachloroethene (PCE) in a stratified lake (see also Illustrative Example 21.5). Problem 21.8 deals with a three-box model for which time to steady-state is different for each box. 

In Illustrative Example 21.5 we calculated the steady-state concentrations of tetrachloroethene (PCE) in the epilimnion and hypolimnion of Greifensee for two different input situations. In case a, all the PCE is put into the surface water (epilimnion) whereas in case b the PCE is added only to the hypolimnion. In reality, Greifensee is not stratified during the whole year. Periods of stratification during the warm season are separated by periods of complete mixing (winter). Thus, the lake switches between two distinctly different stages. It seems that the steady-state considerations made in Illustrative Example 21.5 do not adequately reflect the real behavior of Greifensee. 

In Chapter 21 the model of a stratified lake served as a prototype of a linear two-box model (Fig. 21.10). The necessary mathematics were developed in Boxes 21.6 and 21.7. In Illustrative Example 21.5 the fate of tetrachloroethene (PCE) in Greifensee was used to demonstrate that for the case of a two-box model it is still possible to carry out back-of-the-envelope calculations. Further examples are given in Problems 23.2 and 23.3, where the behavior of anthracene in a mixed as well as in a stratified lake is assessed. 

If the lake is stratified, vertical transport is commonly the time-limiting step for complete mixing. This was the reason for applying the two-box model to the case of PCE in Greifensee (Illustrative Example 21.5). Now we go one step further. We consider a vertical water column of mean depth h with a constant vertical eddy diffusion coefficient Ez. The flux Fa/VJ of PCE escaping to the atmosphere is given by Eq. 20-la ... 

With a leachate from a coal tar site, each day 2 kg of anthracene are introduced continuously into the epilimnion of a eutrophic lake. The lake is stratified between April and November. As an employee of the state water authority you are asked to monitor the anthracene concentration in the epilimnion of this lake. In order to get an idea of how sensitive your analytical technique has to be, you wonder what anthracene... 

Dissimilatory reduction by anaerobic bacteria occurs in the anoxic hy-polimnion of stratified lakes and in sediments just below the oxic-anoxic boundary. It produces H2S,... 

DOM is derived from autochthonous sources such as phytoplankton and photosynthetic bacteria (16) at Big Soda Lake near Fallon, Nevada. This lake is alkaline (pH 9.7) and chemically stratified. It contains DOC concentrations as high as 60 mg/L and dissolved salt concentrations as high as 88,000 mg/ L (17). The DOM in this lake is colorless. The fulvic acid fraction was isolated by adsorption chromatography (Amberlite XAD-8 resin) (18) and by zeo-trophic distillation of water from N,N-dimethylformamide (19). Average molecular model synthesis was achieved in a manner similar to that used for fulvic acid from the Suwannee River. The characterization data are presented in Table I and the structural model is presented in Structure 2. 

Abiotic oxidation of sulfide by oxygen cannot supply sulfate at rates comparable to rates of sulfate reduction. Unless high concentrations of sulfide develop and the zone of oxidation is much greater than 1 cm, rates of chemical oxidation of sulfide by oxygen will be much less than 1 mmol/m2 per day (calculated from rates laws found in refs. 115-118). Such conditions can exist in stratified water columns in the Black Sea water column chemical oxidation rates may be as high as 10 mmol/m2 per day (84). However, in lakes in which sulfide is undetectable in the water column and oxygen disappears within millimeters of the sediment-water interface (e.g., 113), chemical oxidation of sulfide by oxygen is unlikely to be important. 

---