11.3 Simple Constituents

As described in Section 11.1, reactive contaminants may be treated as simple constituents. That is, all reactions are simple first order reactions with user specified kinetic rates (K). There is no limit on the number of simple constituents that can be simulated at one time.

11.3.1 Overland Flow Plane

For the overland flow plane kinetic rates and other inputs are specified in the MAPPING_TABLE_FILE. For each contaminant a single value of rainfall concentration (mg L^-1) is specified. All other input values are distributed both by constituent and location on the overland flow plane with the index map and mapping table values. The following table inputs are required.

Dispersion coefficient (m² s^-1)
Decay coefficient K (d^-1)
Uptake coefficient K_u (m d^-1)
Initial loading (Kg) or (mg Kg^-1)
Groundwater concentration (g m^-3)
Initial concentration (g m^-3)
Soil water distribution coefficients K_d (L Kg^-1)
Solubility C_max (g m^-3)

See Section 13 for details on the MAPPING_TABLE inputs.

Three types of reactions can take place on the overland flow plane:

uptake from land surface,
uptake from soil,
decay.

1) The uptake coefficient controls movement of contaminants into the overland flow based on the concentration deficit (solubility of the constituent and the concentration in solution). The mass flux (F) (g s^-1) is computed as:

F=K_u A(C_max -C)/86400.0

Where C is the concentration of contaminant in the ponded surface water, and A is the area of the computational grid cell (m²). The value 86400.0 converts the reaction rate into (m s^-1).

2) If SOIL_CONTAM is included in the project file K_u is the transfer rate between the soil pore water and the water ponded on the land surface. In this case the mass flux (F) (g s^-1) is calculated as:

F=K_u A(C_ponded-C_soil)/86400.0

Where: C_ponded is the concentration in the water ponded on the soil surface, C_soil is the concentration in the soil pore water. The value 86400.0 changes the reaction rate from per day to per second. As can be seen in the equation, the direction of the flux is dependent on the relationship between the concentration of the surface water to the soil pore water volume.

While the uptake coefficient is generally considered a calibration coefficient, for contaminants in the soil column the uptake coefficient can be estimated from Thibodeaux, Environmental Chemodynamics 2nd Ed., Wiley, New York, 1996, pp. 276-277 using the relation:

K_u = D n^4/3/(0.5 d_ml)

where D is the diffusion coefficient of the chemical in water (m² s^-d), n is the porosity, d_ml is the mixing layer depth (m).

Thibodeaux list a diffusion coefficient for nitrates of 0.000164 m² d^-1. For a typical soil with porosity of 0.4 and a mixing layer depth of 0.1 m, the uptake coefficient for nitrate would be 0.001 m d^-1. Lerman, Geophysical Processes, Wiley, New York, 1979, pp. 73-121, lists diffusion coefficients for common ions. It should be noted that effective values for of uptake coefficients for nitrate used in previous modeling efforts, for example Pradhan et al. (2014), have been much lower, on the order of 10^-5 m d^{-1^.}

Pradhan, N. R., C. W. Downer, and B. E. Johnson, 2014. A Physics Based Hydrologic Modeling Approach to Simulate Non-point Source Pollution for the Purposes of Calculating TMDLs and Designing Abatement Measures, Chapter 9 in Practical Aspects of Computational Chemistry-III, DOI 10.1007/978-1-4899-7445-7_1, J. Leszczynski and M. K. Shukla, eds. Springer Science+Business Media, New York.

3) Contaminants dissolved in surface water decay at the rate:

F=KCV/86400.0

where V is the volume (m³), A times the depth.

11.3.2 Channels

For channels, the only reaction is decay, calculated as above. The decay coefficient can be set as a uniform value for every stream node by specifying the value (d^-1) with the CHAN_DECAY card. In addition to setting the rate, the dispersion coefficient (m²s^-1) can be defined with the CHAN_DISP_COEF card. Inital values (g m^-3) can be specified with the INIT_CHAN_CONC card. The default value for each of these is zero.

11.3.3 Soil Column

When transport in the soil is specified with the SOIL_CONTAM card, exchange between the top soil layer and the surface water occurs, as well as decay in the soil pore water. The reactions are the same as described above for overland flow. The soil water distribution coefficient controls the pore water concentration. The fraction of the total that is dissolved is:

where theta is the soil moisture (fraction) and rho_s is the dry soil density (Kg m^-3). So that the concentration dissolved is:

C_d=f_dM/V

where: M is the total mass in the layer (g) and V is the volume of the pore water in the soil layer (m³).

The same reaction rates specified in the MAPPING_TABLE_FILE are used for both the soils and the overland flow.

During simulations uptake, decay, and movement between layers will change the concentration in the top layer, which can be specified as the MIXING_LAYER_DEPTH, or if using INF_REDIST is the top layer depth, either TOP_LAYER_DEPTH or SOIL_MOIST_DEPTH depending on whether one or two soil infiltration layers are specified, or if using INF_LAYERED_SOIL will be the MIXING_LAYER_DEPTH or the top infiltration layer in the soil profile. In any case the concentration of materials in the surface soil layer can be held static by using the SOIL_STATIC_CONC card in the project file. This might be desirable when either the concentration in the soil is expected to held constant by addition of more constituent, such as N and P addition due to fertilizer. Furthermore, fluxes between soil layers can be halted by using the SOIL_NOFLUX card. This might be desirable to include if the material in the top layer is being flushed out at an excessive rate and reducing the surface soil layer concentration too rapidly. This option may also be desirable to use if exfiltration is occurring and an excessive amount of constituent is being added to the overland flow plane.