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Analytical Solutions to Evaluate the Stream Tube Approach for Field-Scale Modeling of Evaporation

^a Dep. of Civil Engineering, California State Univ., Long Beach, CA 90840
^b Dep. of Agronomy & Soils, Auburn Univ., Auburn, AL 36849

View larger version (89K): [in this window] [in a new window]   Fig. 1. Definition sketch for mathematical conditions of the evaporation problem.

View larger version (28K): [in this window] [in a new window]   Fig. 2. Normalized hydraulic conductivity, K/Ks, as a function of pressure head, h, for exponential conductivity model with = 0.5, 1, 2.5, and 10 m–1.

View larger version (15K): [in this window] [in a new window]   Fig. 3. One-dimensional profiles of: (a) normalized matric flux potential, , and (b) pressure head, h.

View larger version (60K): [in this window] [in a new window]   Fig. 4. Distribution of normalized matric flux potential, , and pressure head, h, for the three soil combinations assuming surface pressure head he = –10 m and water table depth L = 2 m.

View larger version (23K): [in this window] [in a new window]   Fig. 5. Lateral normalized matric flux potential (y) and pressure head h(y) profiles at depth z = 1 and 1.8 m assuming surface pressure head he = –10 m and water table depth L = 2 m.

View larger version (39K): [in this window] [in a new window]   Fig. 6. Distribution of horizontal flux, qy, for the three soil combinations assuming surface pressure head he = –10 m and water table depth L = 2 m.

View larger version (37K): [in this window] [in a new window]   Fig. 7. Distribution of lateral with respect to one-dimensional upward flux, |qy/qz|, for the AB medium assuming: (a) surface pressure head he = –3 m and water table depth L = 2 m, (b) he = –10 m and L = 2 m, and (c) he = –10 m and L = 5 m.

View larger version (14K): [in this window] [in a new window]   Fig. 8. Upward flux, |qz|, as a function of depth in the AB medium at y = –0.25 m (Soil A) and y = 0.25 m (Soil B) from numerical approximation of Eq. [18] (two-dimensional case) and Eq. [19] (one-dimensional case): (a) surface pressure head he = –3 m and water table depth L = 2 m, (b) he = –10 m and L = 2 m, and (c) he = –10 m and L = 5 m.

View larger version (21K): [in this window] [in a new window]   Fig. 9. Absolute value of error e for neglecting terms with vertical gradients in given by Eq. [B15] as a function of depth at y = 0.01 m for five scenarios of soils and boundary conditions.