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Analytical Advection–Dispersion Model for Transport and Plant Uptake of Contaminants in the Root Zone

^a USDA-ARS, U.S. Salinity Lab., 450 W. Big Springs Rd., Riverside, CA 92507
^b Swedish Univ. of Agricultural Sciences, Uppsala, Sweden
^c Brazilian Nuclear Energy Commission, Rio de Janeiro, Brazil
^d Federal Univ. of Rio de Janeiro, Rio de Janeiro, Brazil

View larger version (15K): [in this window] [in a new window]   FIG. 1. Plot of h as a function of for various values of the leaching fraction, LF ( = Gardner conductivity parameter [L–1]; = Raats uptake distribution parameter [L]; and h = change in pressure head between top and bottom of root zone [L]).

View larger version (20K): [in this window] [in a new window]   FIG. 2. The change in pressure head between the top and bottom of the root zone (h) plotted as a function of rooting depth. Plots are shown for two soil types ( = Gardner conductivity parameter [L–1]) and various values of the leaching fraction (LF).

View larger version (22K): [in this window] [in a new window]   FIG. 3. Changes in soil water saturation between the top and bottom of the root zone (S) plotted as a function of the soil surface pressure head for two soil types. Plots are shown for a low-leaching, deep-rooting scenario and a high-leaching, shallow-rooting scenario. ( = Gardner conductivity parameter; LF = leaching fraction; RD = maximum rooting depth; h = difference in pressure head between the top and bottom of root zone; h = pressure head; and z = depth.)

View larger version (14K): [in this window] [in a new window]   FIG. 4. Illustration of the Michaelis–Menten and two-line uptake models. Also shown is a dilute solution approximation of the Michaelis–Menten model.

View larger version (20K): [in this window] [in a new window]   FIG. 5. Plots of solute concentration vs. depth computed for successive times with the advection–dispersion transport model. The concentration profiles were computed using the following parameter values: R = 1, = 20 cm, v0 = 1 cm d–1, vT = 0.75 cm d–1, = 0.1, L = 10 cm, CI = 0.25 C0, L = 1000 cm, and M = 80. Dashed lines are steady-state results computed for D = 0. (R = retardation factor; = root distribution parameter; q0 = water flux at soil surface; T = transpiration rate; = volumetric water content; v0 q0/; vT T/; = first-order solute uptake coefficient; L = dispersivity; D = dispersion coefficient; CI = initial soil solution concentration; C0 = infiltrating solution concentration; L = depth of computational domain; M = number of terms summed in analytical solution.)

View larger version (19K): [in this window] [in a new window]   FIG. 6. Plots of solute concentration vs. depth computed for various values of the transport parameters and L. Except where indicated otherwise, the concentration profiles were computed using the following parameter values: t = 1000 d, R = 1, = 20 cm, v0 = 1 cm d–1, vT = 0.75 cm d–1, = 0.1, L = 10 cm, CI = 0.25 C0, L = 1000 cm, and M = 80. Dashed lines are steady-state results computed for D = 0. (t = time; R = retardation factor; = root distribution parameter; q0 = water flux at soil surface; T = transpiration rate; = volumetric water content; v0 q0/; vT T/; = first-order solute uptake coefficient; L = dispersivity; D = dispersion coefficient; CI = initial soil solution concentration; C0 = infiltrating solution concentration; L = depth of computational domain; M = number of terms summed in analytical solution.)

View larger version (13K): [in this window] [in a new window]   FIG. 7. A comparison of predictions of the analytical advection-dispersion and one-compartment models for cadmium uptake into wheat grain using the following parameter values: q0 = 0.7 m yr–1, T = 0.5 m yr–1, = 0.05, Bp = 0.5 kg m–2 yr–1, = 0.4 m3 m–3, R = 376, D = 0.015 m2 yr–1, CI = 1 mg m–3 and C0 = 2.286 mg m–3, equivalent to a cadmium loading of 1.6 mg m–2 yr–1. The root depth, RD, in the advection–dispersion equation model was set to 1 m, and two values of RD are shown for the one-compartment model (0.25 and 1 m). (q0 = water flux at soil surface; T = transpiration rate; = first-order solute uptake coefficient; Bp = harvested biomass yield; = volumetric water content; R = retardation factor; D = dispersion coefficient; CI = initial soil solution concentration; C0 = infiltrating solution concentration; RD = maximum rooting depth.)