Surface mixed sediment layer model

Now we want to apply the box model approach to a two-box system which consists of a completely mixed water body in contact with a sediment box. Although the sediment column can hardly be visualized as being completely mixed, the concept of a surface mixed sediment layer (SMSL) introduced in the previous section is an approximate view of the sediments as mixed box. In fact, for strongly sorbing chemicals the diffusive penetration into the sediment column is so slow and the storage capacity of the top 1 to 2 cm so large, that the deeper parts of the sediments can be treated as sort of a permanent sink from which no feedback to the SMSL and to the open water column is possible. 

In the last step (Part 3), the sedimentary compartment (the surface mixed sediment layer , SMSL) was treated as an independent box (Table 23.7). The steady-state solution of the combined sediment/water system explained another characteristic of the observed concentrations, which, as mentioned above, could not be resolved by the one-box model. As shown in Table 23.8, for both congeners the concentration measured on particles suspended in the lake is larger than on sediment particles. The two-box model explained this difference in terms of the different relative organic carbon content of epilimnetic and sedimentary particles. This model also gave a more realistic value for the response time of the combined lake/sediment system with respect to changes in external loading of PCBs. However, major differences between modeled and observed concentrations remained unexplained. 

The model (Fig. 23.6) consists of three compartments, (a) the surface mixed water layer (SMWL) or epilimnion, (b) the remaining open water column (OP), and (c) the surface mixed sediment layer (SMSL). SMWL and OP are assumed to be completely mixed their mass balance equations correspond to the expressions derived in Box 23.1, although the different terms are not necessarily linear. The open water column is modeled as a spatially continuous system described by a diffusion/advection/ reaction... 

Simulation modeling of the fate of DOC under different conditions emphasises these simple relationships in marine sediments. Figure 14 shows the rates at which DOC is stipulated to be produced by hydrolysis of POM at proximately 6, 36 and 60 mmol/m /day either at the surface of the sediment (TOP), or as a linear gradient from the surface down (LINEAR), or equally to all sediment layers down to 5 cm (MIX). The matrix in Figure 14 represents sediments receiving increasing quantities of POM (arrow down) at increasing frequencies (arrow across). 

In particular, horizontal advection and horizontal diffusion in the Chesapeake Bay are comparable while vertical difiiision is a fast process that acts over short distances, and a model must account for all three. In this environment, atrazine that is discharged to the surface waters could be horizontally distributed over a distance of 1 km over a period of one week, since the time scale of horizontal advection-difiusion processes is 10 -10 s (approximately 3 hours). As atrazine is distributed horizontally, it also mixes vertically down the water coluitm. With the estimates of verticd diffiisivity for the Bay that are available in the literature, for a depth of 10-20 m the time scale for vertical diffusion processes is on the order of 15 minutes, and can be as short as 3 minutes. The sidfidic vraters are in the sediment porewaters and atrazine needs to be transported to the water-sediment inter ce in order to encounter and react with reduced sulfiir species. The characteristic horizontal and vertical scales that describe the flow in the Bay indicate that it is possible for atrazine to reach the depth of the water-sediment interface before it is horizontally transported out of the system. The subsequent exchange at the water-sediment interface depends on many factors, including half-life of atrazine, the hydraulic residence time of the bottom layer, turbulent processes, and other characteristics of the water column above the sediment layer. Simple box models cannot capture the dynamics necessary to describe these exchanges that ultimately govern the te of atrazine in the Bay. 

As shown in Fig. 3, CHEMGL considers 10 major well-mixed compartments air boundary layer, free troposphere, stratosphere, surface water, surface soil, vadose soil, sediment, ground water zone, plant foliage and plant route. In each compartment, several phases are included, for example, air, water and solids (organic matter, mineral matter). A volume fraction is used to express the ratio of the phase volume to the bulk compartment volume. Furthermore, each compartment is assumed to be a completely mixed box, which means all environmental properties and the chemical concentrations are uniform in a compartment. In addition, the environmental properties are assumed to not change with time. Other assumptions made in the model include continuous emissions to the compartments, equilibrium between different phases within each compartment and first-order irreversible loss rate within each compartment [38]. 

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. 

The bed surface, in the context of this section, is considered to be nonmobile porous material made of various size solid particles. The particles typically range in diameter from a few millimeters to less than a micron. The various bed types generally reflect the fluid dynamic nature of the water column above the bed. Table 12.7 contains typical porosity values for sediment. Section 12.2.1 contains an overview description of the types of aquatic streams and currents above the beds. These aquatic systems include rivers, lakes, estuaries, shelf, and marine environments. Unlike the air-water interface, the sediment-water interface has a single fluid (i.e aqueous phase) on either side. Water, the continuous phase, exists from within the column above, through the imaginary interface plane and into the porous bed where it is termed porewater. The interface plane is not a sharp one. It can be considered a thin mixed layer of finite thickness in the context of mass-transfer modeling (DiToro, 2001). Visual and physical examination of thin-sliced (0.1mm) layers of a frozen core sample from a lake sediment bed microcosm showed the presence of a finite flocculent layer positioned between the water side and the particles on the bed surface (Formica et al 1988). Little is known about this layer from a mass-transfer perspective, it will not be considered further. Mass transport in those bed surface layers at and below the first layer of solid particles will be the subject of this section. 

Most of the models used for bioturbation are based on a diffusion analogy, which best describes mixing of materials over short distances or local mixing. These models treat mixing as diffusive and divide sediments into a surface layer, which is mixed at a uniform rate and a lower unmixed layer so as to incorporate a biodiffusion coefficient... 

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