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A Set of Analytical Benchmarks to Test Numerical Models of Flow and Transport in Soils

^a Agrosphere Institute, ICG-IV, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
^b Department of Environmental Sciences and Land Use Planning, Université Catholique de Louvain (UCL), Croix du Sud, 2 Bte 2, B-1348 Louvain-la-Neuve, Belgium
^c Bureau de Recherches Geologiques et Minieres, BRGM, Avenue Claude Guillemin, F 45060 Orléans Cedex 02, France

View larger version (24K): [in a new window]   Fig. 1. (a) Precipitation and potential evaporation and (b) initial pressure head, , depth profile used as input in the scenario with climatic boundary conditions.

View larger version (14K): [in a new window]   Fig. 2. Pressure head, , depth profiles in layered soils for a constant downward flow rate of 0.5 cm d–1: (a) loam–sand, (b) sand–loam, and (c) clay–sand profiles. (Black line is analytical benchmark, Eq. [14]; similarity in output may overlap in the graph.)

View larger version (23K): [in a new window]   Fig. 3. Pressure head, , depth profile in a loamy soil with a water table at the 54-cm depth and a constant evaporation rate of 0.5 cm d–1. (Black line is analytical benchmark, Eq. [14]; similarity in output may overlap in the graph.)

View larger version (23K): [in a new window]   Fig. 4. (a, b, c) Volumetric water content, , depth profiles during infiltration in an initially uniform dry soil and (d, e, f) corresponding profiles against the transformed depth coordinate for a sandy (a and d), loamy (b and e), and clayey (c and f) soil profile. (Black line is the analytical benchmark, Eq. [60]; similarity in output may overlap in the graph.)

View larger version (27K): [in a new window]   Fig. 5. Evaporation rate, Eact, from initially wet (a) sandy, (b, c) loamy, and (d) clayey soil profiles. Dashed lines are simulated Eact using a spatial discretization of 1 cm, full lines using a discretization of 0.25 cm. (Black line is analytical benchmark Eq. [46] and [47]; similarity in output may overlap in the graph; R2 is calculated for simulations with a discretization of 0.25 cm.)

View larger version (19K): [in a new window]   Fig. 6. Simulated cumulative drainage at the 2-m depth (full lines) and cumulative net infiltration (precipitation – actual evaporation) (dashed lines) in (a) sandy, (b) loamy, and (c) clayey soil profiles. (Full black line is the cumulative precipitation; similarity in output may overlap in the graph.)

View larger version (27K): [in a new window]   Fig. 7. (a, b, c) Simulated resident concentration, Cr, depth profiles and (d, e, f) flux concentration, Cf, breakthrough curves at the 2-m depth for different dispersivities, . (Black lines are analytical benchmarks: Eq. [19] for depth profiles and Eq. [21] for breakthrough curves; similarity in output may overlap in the graph.)

View larger version (17K): [in a new window]   Fig. 8. (a) Simulated concentration depth profiles of a nonlinearly sorbing substance, which is continuously applied at the soil surface and (b) concentration depth profile against the transformed depth coordinate Eq. [52]. (Full black line is the analytical benchmark Eq. [55]; similarity in output may overlap in the graph.)

View larger version (18K): [in a new window]   Fig. 9. (a) Depth profiles at 200 h after tracer pulse injection of concentration in the soil solution Cr (full line), and sorbed concentration, Sr (dashed line), (Black lines are analytical benchmarks Eq. [23] and [24].) (b) Breakthrough of flux concentrations before and after a flow interruption at 200 h or 20 pore volumes T. (Black symbols are analytical benchmark Eq. [23] before flow interruption and Eq. [25] after interruption.) Similarity in output may overlap in the graph.

View larger version (26K): [in a new window]   Fig. 10. Time series of resident concentrations in the macropore (full line) and matrix region (dashed line) of a dual-velocity medium with (a) slow and (b) fast exchange of solutes between both flow domains. Time series at 100 cm downstream of the initial concentration pulse are shown. (Black symbols are analytical benchmark for the macropore Eq. [29] and for the matrix region Eq. [30]; similarity in output may overlap in the graph.)

View larger version (17K): [in a new window]   Fig. 11. Simulated solute fluxes at 2-m depth in (a) sandy, (b) loamy, and (c) clayey soil profiles for climatic boundary conditions.

View larger version (26K): [in a new window]   Fig. 12. Time series of concentrations at the soil surface (full line) and at the 100-cm depth (dashed lines) simulated for climatic boundary conditions in (a) sandy, (b) loamy, and (c) clayey soil profiles.