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Experimental and Numerical Evaluation of Analytical Volume Balance Model for Soil Water Dynamics under Drip Irrigation

Khumoetsile Mmolawa and Dani Or^,*

Dep. of Biological and Irrigation Engineering and Dep. of Plants, Soils and Biometeorology, Utah State Univ., Logan, UT 84322-4820

View larger version (41K): [in a new window]   Fig. 1. (a) Cross-sectional view of time domain reflectometry (TDR) monitoring grid for soil water status under cropped and non-cropped situations. The surface area (A2) attributed to this cross-sectional uptake is 0.15 by 0.40 m = 0.06 m2. (b) Control soil volume for local volume balance calculation.

View larger version (15K): [in a new window]   Fig. 2. Schematic shape of the root water uptake term, S, as function of the absolute value of the soil water head, h, (Source: Feddes et al., 1978; Simunek et al., 1999).

View larger version (23K): [in a new window]   Fig. 3. Illustration of water flow parameter estimation for linearizing the Warrick (1974) analytical flow model, (a) successive approximations of and Ks by using tangents to the K(h) versus h curve, (see Table 2 for values), (b) estimated k() = dK()/d using the van Genuchten (1980) model and some estimated k() values from flow experiments with different ranges of water content.

View larger version (26K): [in a new window]   Fig. 4. Two-dimensional cross-section of the observed and fitted uptake intensity (m3 m-3 d-1) distribution around a buried dripper on crop row of a field grown corn plant 83 DAE. The discharge rate of the dripper is 1.6 L h-1. For these measurements the observed total daily water content change is 1.44 m3 d-1.

View larger version (118K): [in a new window]   Fig. 5. Illustration of the three-dimensional water uptake transformed from the two-dimensional cross-sectional uptake, see Fig. 1a and 5. This transformed uptake pattern is attributed to a wetted circular surface area (A3), r2 = 0.5 m2, for a radius of r = 0.40 m. This area is one half of the total area (A1 = 1 m2) averaged transpiration area, which is a product of the emitter spacing (1 m) and row spacing (1 m). The other marked surface area A2 = 0.15 m x 0.4 m = 0.06 m2.

View larger version (26K): [in a new window]   Fig. 6. Fitting of the two models to obtain water flow parameters. (a) Analytical model fitted to measured soil water dynamics without plants at a location r = 0.0 m, z = -0.10 m, (b) fitting of the Hydrus 2-D (H2D) model to measured soil water dynamics without plants at a location r = 0.0 m, z = -0.10 m.

View larger version (30K): [in a new window]   Fig. 7. (a) Observation of soil water dynamics by the analytical model simulation at a depth z = -0.10 m with observation points at different radial distances from the point source. (b) Observation of soil water dynamics by Hydrus 2-D (H2D) model at a depth z = -0.10 m with observation points at different radial distances from the point source.

View larger version (31K): [in a new window]   Fig. 8. Fitting of the analytical and Hydrus 2-D(H2D) models to measured data at r = 0.10 m, z = -0.10 m in presence of plants. (a) Analytical model fitted to measured soil water dynamics with plants at a location r = 0.0 m, z = -0.10 m, (b) H2D model fitting to measured soil water dynamics with plants at a location r = 0.0 m, z = -0.10 m.

View larger version (35K): [in a new window]   Fig. 9. Observation of soil water dynamics in presence of plants as the observation points shift radially away from the source at depth z = -0.10 m. The observation points vary from r = 0.10 m to r = 0.40 m at the same depth z = -0.10 m. (a) analytical model, (b) Hydrus 2-D (H2D) model.

View larger version (36K): [in a new window]   Fig. 10. Temporal soil water dynamics comparison of measured water content data at r = 0.0 m, z = 0.0 m to the two models (a) in the absence of root water uptake, (b) in the presence of root water uptake.

View larger version (32K): [in a new window]   Fig. 11. Depicts the comparison of soil water dynamics with and without plants between Hydrus 2-D (H2D) and the analytical model at a monitored location r = 0.20 m, z = 0.20 m, (a) without plants and (b) with plants.

View larger version (30K): [in a new window]   Fig. 12. Illustration of soil water distribution both measured and predicted in absence of plants in a two-dimensional space at t = 10 h since the start of irrigation. For (a) analytical model and (b) H2D model.

View larger version (30K): [in a new window]   Fig. 13. Comparison of measured and predicted soil water dynamics in the presence of plants in 2D space at t = 10 h since the start of irrigation. The irrigation interval is 4 d. (a) Comparison of the analytical model simulation to measured data, (b) H2D compared with measured data.

View larger version (29K): [in a new window]   Fig. 14. Comparison of measured and predicted soil water dynamics in the presence of plants in two-dimensional space at 5 h before the onset of irrigation (the irrigation interval is 4 d). Comparison of (a) the analytical model simulation and (b)Hydrus 2-D (H2D) compared with measured data.

View larger version (22K): [in a new window]   Fig. 15. Simulated soil water dynamics in the presence of plants in a two-dimensional space at 5 h before the start of irrigation (the irrigation interval is 1 d). Comparison of (a) the analytical model and (b) Hydrus 2-D (H2D) model.