Advection-Diffusion Model water column

Bruland (1980) has measured Ni concentrations (ngkg - ) and depth (z in meters) in the water column from the eastern Pacific (Table 5.11). Find the best set of coefficients for the advection -diffusion model of Craig (1969) to fit these data. 

Figure 5.10 Adjustment of Ni concentrations in the water column (data from Bruland, 1980) with the advection-diffusion model of Craig (1969).

Figure 8.24 The advection-diffusion model (Craig, 1974) in a water column of depth Z, mixing length lm, and scavenging length /s. Concentrations [left, equation (8.8.8)] and fluxes [right, equation (8.8.9)] in the water column for the IJZ values labeled on the curves.

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

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... 

In water and sediments, the time to chemical steady-states is controlled by the magnitude of transport mechanisms (diffusion, advection), transport distances, and reaction rates of chemical species. When advection (water flow, rate of sedimentation) is weak, diffusion controls the solute dispersal and, hence, the time to steady-state. Models of transient and stationary states include transport of conservative chemical species in two- and three-layer lakes, transport of salt between brine layers in the Dead Sea, oxygen and radium-226 in the oceanic water column, and reacting and conservative species in sediment. 

The distribution of a number of dissolved species (02, C-14, Ra-226, salinity) in the Central Pacific water column, at depths between 1 and 4 km, has been shown (11) to be consistent with a steady-state model of the water column in which the concentration-depth profiles are stationary and the concentrations at the boundaries 1 and 4 km are stipulated at their present values. The physical model of the water column is based on two transport mechanisms vertical eddy diffusion (eddy diffusion coefficient K — 1.3 cm2 sec"1) and upwelling of deep water (advection velocity U = 1.4 X 10 5 cm sec"1, or approximately 1 cm per day) (11). 

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. 

The tube models consider the oceanic mass of water as subdivided into columns. Mass transfer between columns takes place by advection and diffusion. Examples of tube models may be found in Munk (1966) and Bieri et al. (1966), to whom we refer readers for further clarification. 

Of the 41 listed in Table 4.1 the 16 most common mass transport processes representing the air, water, and soil and sediment media appear in Table 4.2. The media of prime concern often dictate the most convenient phase concentration used in the flux equation. For example, water quality models usually have Cw as the state variable and therefore the flux expression must have the appropriate MTC group based on Cw and these appear in the center column of Table 4.2. Aquatic bed sediment models usually have Cs, the chemical loading on the bed solids, as the state variable. The MTC groups in the right eolumn are used. All the MTC groups in Table 4.2 contain a basic transport parameter that reflects molecule, element, or particle mobility. Both diffusive and advective types appear in the table. These are termed the individual phase MTCs with SI units of m/s. Examples of each type in Table 4.2 include for water solute transport and Vg for sediment particle deposition (i.e., setting). 

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