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Soil Physics with HYDRUS: Chapter 3 Equations, Tables, and Figures 3.1 – 3.5 R 4 w g H Q 8 L Q H K s A L Jw Ks H L dH J w K s dz J w K s H z 3.6 – 3.9 H 2 H1 bL J w Ks Ks L L J w Ks H 2 H1 hz Ks L z h z bL Ks Ks z L b h z L Ks k l g 3.10 – 3.13 N K eff L j 1 N Lj K j 1 J w K eff j j H L N K eff L K j 1 N j L j 1 J x Ks j dz dx j 3.14 – 3.17 zmax J w K ( h) Rs 2 z02 Ks H (h z ) h z K (h) K (h) z z z z h K ( h) 1 z K (h) Ks e h K ( ) K s s m 3.18 – 3.20 K ( h) Ks h 1 a N Se K ( Se ) K s S el dSe h 2 ( Se ) 0 1 dSe h 2 ( Se ) 0 2 dSe h ( Se ) 0 l K ( Se ) K s Se 2 1 dSe h ( Se ) 0 Se 3.21 – 3.25 K (Se ) Ks Se1l 2/ K ( Se ) K s Sel 1 (1 Se1/ m )m m 1 1/ n, K ( Se ) K s ( w1Se1 w2 Se2 ) w11 1 (1 S l n 1 ) w2 2 1 (1 S ( w11 w2 2 )2 1/ m1 m1 e1 h0 c 2 K (h)dh hi K (h0 ) K (hi ) ) 1/ m2 m2 e2 2 3.26 – 3.30 c 1 x a y( x)dx 3 y1 4 y2 2 y3 4 y4 2 y5 ... 2 yn2 4 yn1 yn b K (h) K s h ha 2 3 ha K (h) K s h J w K h h2 dh z1 z2 h Jw 1 1 K ( h) h ha 3.31 – 3.34 Ks ha 1 tanh i is J w 1 i / Ks i / Ks a z 0 4c K (h0 ) 1 r 2 H c H 2 Qs K s r G G H c H2 is K s 1 2 2 G r G r ( L z) 3.35 – 3.39 2 3 1 H H H G A1 A2 A3 A4 2 r r r JwL Ks H1 H 2 Jw H H1 db Ks 2 dt L L b0 L K s ln t1 b1 L H2 is K s GG r 2 3.40 2 r H r sinh 1 H r H GG 2 1 TABLE 3.1 Brooks and Corey (1964) soil hydraulic parameters (Ks, θr, θs, ha, and λ) for 11 textural classes (Rawls et al., 1982). Macroscopic capillary length (λc) calculated using Equation 3.21 and Equation 3.25. Ks (cm d-1) θr (cm3 cm-3) θs (cm3 cm-3) Sand 504.0 0.020 0.417 -7.26 0.592 9.88 Loamy sand 146.6 0.035 0.401 -8.69 0.474 12.28 loam 62.16 0.041 0.412 -14.7 0.322 22.18 Loam 31.68 0.027 0.434 -11.1 0.220 17.79 Silt loam 16.32 0.015 0.486 -20.7 0.211 33.38 Sandy clay loam 10.32 0.068 0.330 -28.1 0.250 44.16 Clay loam 5.52 0.075 0.390 -25.9 0.194 42.27 Silty clay loam 3.60 0.040 0.432 -32.6 0.151 55.03 clay 2.88 0.109 0.321 -29.2 0.168 48.61 Silty clay 2.16 0.056 0.423 -34.2 0.127 58.96 Clay 1.44 0.090 0.385 -37.3 0.131 64.07 Textural class ha (cm) λ (-) λc (cm) TABLE 3.2 Soil properties (texture, sand, silt, clay, structure, and Ks) for the Cecil loamy sand (plot 4 from Bruce et al., 1983). Horizon Texture Clay % Silt % Sand % Structure Ks cm h-1 Weak, medium granular Weak, medium, subangular blocky Strong, medium, subangular blocky Strong, medium, subangular blocky Weak, medium, subangular blocky Massive 19.19 7.69 Ap BA Loamy sand Clay loam 7 37 15 20 78 43 Bt1 Clay 50 20 30 Bt2 Clay 41 25 34 BC Clay loam 36 27 37 C Sandy clay loam 24 24 52 10.73 0.206 0.035 0.467 TABLE 3.3 Soil texture/structure categories for estimation of macroscopic capillary length (λc), adapted from Elrick and Reynolds (1992). Soil texture/structure category Coarse and gravelly sands; may also include some highly structured soils with large cracks and/or macropores λc (cm) 2.8 Most structured soils from clays through loams; also includes unstructured medium and fine sands 8.3 Soils which are both fine textured (clayey) and unstructured Compacted, structureless, clayey materials such as landfill caps and liners, lacustrine or marine sediments, etc 25 100 TABLE 3.4 Dimensionless coefficients for the polynomial (Equation 3.35) describing the geometric factor G, valid for H/r < 10 (Bosch and West, 1998) Soil texture/structure Sand Structured loams and clays Unstructured clays A1 0.079 0.083 0.094 A2 0.516 0.514 0.489 A3 -0.048 -0.053 -0.053 A4 0.002 0.002 0.002 Figure 3.1 A vertical column of soil 40.0 cm in length with 5.0 cm of water ponded on the surface and water allowed to drip from the bottom. The soil saturated hydraulic conductivity is 10.0 cm h-1 Figure 3.2 A vertical soil column of length L and saturated hydraulic conductivity Ks. Water is ponded to a depth b at the top of the column and water discharges freely from the bottom at atmospheric pressure. Figure 3.3 A vertical soil column with an arbitrary point at height z inside the column, instead of the top of the column. Saturated Hydraulic Conductivity (cm/d) 100000 10000 1000 100 10 1 0.1 0.01 0.001 0.01 0.1 Clay Fraction (g/g) Figure 3.4 Saturated hydraulic conductivity as a function of clay fraction for 324 soils from the UNSODA database (Nemes et al., 2001). 1 Figure 3.5 Saturated hydraulic conductivity as a function of depth in a Cecil series soil from North Carolina Piedmont (Schoneberger and Amoozegar, 1990). Figure 3.6 A soil column with N layers of thickness L1...LN and saturated hydraulic conductivites K1...KN on the left side. An equivalent uniform column on the right with a saturated hydraulic conductivity Keff. Figure 3.7 A column consisting of a sand layer 30.0-cm thick overlying a loam layer 20.0-cm thick. The saturated hydraulic conductivities of the sand and loam layers are 21.0 and 1.32 cm h-1, respectively. Water is ponded at the top of the column to a depth of 5.0 cm and allowed to drip from the bottom of the column. Figure 3.8 Geometry considered for defining the drainage equation. Water height in the ditch or drain is z0 (Warrick, 2003). Figure 3.9 Examples of unsaturated hydraulic conductivity curves as a function of pressure head (top) and volumetric water content (bottom) for the sand, loam, and clay soil textural classes based on parameters in Table 3.1. Figure 3.10 Boreholes and wetting fronts in a soil with a small λc and a soil with a large λc. Figure 3.11 Excel spreadsheet with Brooks and Corey parameters for a loamy sand from Table 3.1. Figure 3.12 The sum of the Simpson terms in column C is calculated in cell C18. The integral of K(h) is calculated in cell C19 by multiplying the sum by 10/3 (h/3) (see Equation 3.27). In cell C20, λc is calculated by dividing the integral by the difference between Ks and K(-100) (see Equation 3.25). 0 -10 -20 Depth (cm) -30 -40 i = 0.5 cm/d i = 1.5 cm/d -50 -60 -70 -80 -90 -100 -40 -30 -20 -10 0 Pressure Head (cm) Figure 3.13 Distribution of h as a function of z for a steady low infiltration rate (0.5 cm d -1) and a high infiltration rate (1.5 cm d-1) based on Equation 3.31 (adapted from Jury and Horton, 2004). Figure 3.14 Steady 3-D infiltration of water from a ring of radius r at the soil surface. Figure 3.15 Steady 3-D infiltration of water from a borehole. Figure 3.16 New Project dialog window in HYDRUS-1D. Figure 3.17 Project panel in HYDRUS-1D. Figure 3.18 Geometry Information dialog window in HYDRUS-1D. Figure 3.19 Time Information dialog window in HYDRUS-1D. Figure 3.20 Soil Hydraulic Property Model dialog window in HYDRUS-1D. Figure 3.21 Water Flow Parameters dialog window in HYDRUS-1D. Figure 3.22 Rosetta Lite dialog window in HYDRUS-1D. Figure 3.23 Predicted parameters for a loamy sand textural class in the output panel. Figure 3.24 Section of capillary tube of radius R and length L filled with water flowing in response to a pressure difference P2 - P1 (Jury and Horton, 2004). 1 0.8 r/R 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 V(r)/Vmax Figure 3.25 Parabolic distribution of velocities within a cylinder. The velocity is zero at the wall where r = R and at a maximum = Vmax at the center of the cylinder where the r = 0 (Jury and Horton, 2004). Figure 3.26 Excel spreadsheet for calculating pressure head distribution under steady flow in a profile of the Cecil soil with properties from Table 2.4 and Table 3.2 . Water is ponded to a depth of 0.1 cm at the surface and there are tile drains at a depth of 250 cm (pressure head equals zero).