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Subsurface Water Distribution from Drip Irrigation Described by Moment Analyses

N. Lazarovitch^a,*, A. W. Warrick^b, A. Furman^c and J. imnek^d

^a Wyler Dep. of Dryland Agriculture, Jacob Blaustein Inst. for Desert Research, Ben-Gurion Univ. of the Negev, Beer-Sheva 84990, Israel
^b Soil Water and Environmental Science, Univ. of Arizona, Tucson, AZ 85721
^c Soil, Water and Environmental Sciences, Agricultural Research Organization, Volcani Center, Bet Dagan, 50250 Israel
^d Dep. of Environmental Science, Univ. of California, Riverside, CA 92521

View larger version (15K): [in this window] [in a new window]   Fig. 1. (A) The vertical center of gravity, zC, for a surface point source in a two-dimensional plane as a function of time, t, for three representative soils; (B) spatial variance in the x direction, x, as a function of t; and (C) spatial variance in the z direction, z, as a function of t.

View larger version (22K): [in this window] [in a new window]   Fig. 2. Wetting patterns and ellipses for one (solid line) and two (dashed line) standard deviations about the vertical center of gravity (small filled circle), for three representative soils under a surface line source.

View larger version (14K): [in this window] [in a new window]   Fig. 3. (A) The vertical center of gravity, zC, for a surface point source in a three-dimensional plane as a function of time, t, for three representative soils; (B) spatial variance in the x direction, x, as a function of t; and (C) spatial variance in the z direction, z, as a function of t.

View larger version (21K): [in this window] [in a new window]   Fig. 4. Cross-sections of the wetting patterns and the spheroids for one (solid line) and two (dashed line) standard deviations about the vertical center of gravity (small filled circle), for three representative soils under a surface point source.

View larger version (24K): [in this window] [in a new window]   Fig. 5. Wetting patterns and ellipses for one (solid line) and two (dashed line) standard deviations about the vertical center of gravity, zC (small full circle), for a subsurface cavity source in two dimensions (2D) and the analogous results for a three-dimensional (3D) cavity for a loamy sand soil.

View larger version (17K): [in this window] [in a new window]   Fig. 6. Cumulative probability as a function of the number of standard deviations, k, for various soils, times, source locations, and two (2D) or three dimensions (3D).

View larger version (20K): [in this window] [in a new window]   Fig. 7. The vertical center of gravity, zC, for the surface point source as a function of time, t, for the sandy soil with three initial saturations (Se).

View larger version (16K): [in this window] [in a new window]   Fig. 8. Cross-sections of the spheroids (dashed lines) about the vertical center of gravity for (A) 6, (B) 9, and (C) 16 observation points (triangles) compared with the "exact" results (solid lines) under a surface point source. The associated Thiessen polygons are showed as dashed lines.

View larger version (29K): [in this window] [in a new window]   Fig. 9. The sum of squared errors, , as a function of the fitting parameters n and (m–1) for the hypothetical case of the loamy soil.