1. 1 1 2 Infiltration into a soil profile: 1. Flux and pressure boundary conditions. Nobuo TORIDE 1 Kunio WATANABE 1 Masaru SAKAI 2 1. 1991 1984 Green-Ampt 2000 Green-Ampt Hillel, 2001; Jury and Horton, 2006 Green and Ampt 105 2007 Philip 1957a e Warrick 2003 Philip Jury and Horton, 2006 HYDRUS-1D Šimůnek et al., 2008 1 Graduate School of Bioresources, Mie University, 1577 Kurima- Machiya, Tsu, Mie 514-8507, Japan. Corresponding author: 2 Utah State University, Dep. Plants, Soils, and Climate 2009 10 23 2009 11 13 113, 31 41 (2009) Philip Green-Ampt 2. q w L T 1 q w = K(h) h K(h) (1) z K(h) L T 1 h Lz L 1 2 θ t = z [ ( )] h K(h) + K(h) z z θ L 3 L 3 t T (2) C w (h) h t = [ ( )] h K(h) + K(h) z z z (3)
32 113 (2009) Table 1 van Genuchten θ r θ s α n K s h i θ(h i ) K(h i ) Soil type (cm 3 cm 3 ) (cm 3 cm 3 ) (cm 1 ) ( ) (cm d 1 ) (cm) (cm 3 cm 3 ) (cm d 1 ) Sandy loam 0.065 0.41 0.075 1.89 106.1 500 0.079 5.5 10 6 Silt 0.034 0.46 0.016 1.37 6 500 0.228 9.5 10 4 C w (h) = θ h θ(h) Jury and Horton, 20061 θ q w = K(θ) h θ θ z K(θ) = D w(θ) θ z D w (θ) = K(θ) h θ = K(θ) C w (θ) (4) K(θ) (5) h θ K(h) C w (h) θ Jury and Horton, 2006 θ t = z [ ( )] θ D w (θ) + K(θ) z z 3 7 h θ (6) (7) 8 9 ( 1) h K (h) z z=0 + = q 0 (8) h(0,t) = h 0 (9) q 0 L T 1 h 0 10 h i z = L 11 2006 h(z,0) = h i (10) h z = 0 (11) z= L 11 3. van Genuchten 2007 2009 θ θ r θ s θ r = S e = (1 + αh n ) m (12) [ ( ) m ] 2 K (S e ) = K s Se l 1 1 S 1 /m e (13) θ r L 3 L 3 θ s L 3 L 3 S e α L 1 n m = 1 1/n K s L T 1 l Table 1 Carsel and Parrish 1988 2 l = 0.5 2009 Fig. 1 θ(h) K(h) h = 31 cm K h = 31 cm 12 van Genuchten h 4 C w Jury and Horton, 2006 C w (h) = αn (θ s θ r )(n 1)( h) n 1 [1 + α( h) n ] 2 1/n (14) Fig. 2 C w (h) C w h = 7.4 cm h = 66 cm C w
1. 33 Fig. 1 van Genuchten a θ(h) b K(h) C w h = 66 cm 4. K s 1991; 2000 q 0 t q 0 t supply-controlled flux-controlled nonponding infiltration Hillel, 2001 2006 Hillel 2001 transmission zone wetting zone wetting front 4 Hillel 2001 Fig. 3 Fig. 2 van Genuchten C w (h) Fig. 3
34 113 (2009) Fig. 4 3 q 0 = 3 0.5 0.2 cm d 1 h 0 Table 2 h θ(h ) Soil type q 0 (cm d 1 ) h (cm) θ(h ) (cm 3 cm 3 ) 3 18.2 0.278 Sandy loam 0.5 30.7 0.215 0.2 39.2 0.188 3 2.3 0.458 Silt 0.5 30.7 0.425 0.2 55.1 0.395 100 cm h i = 500 cm Table 1 h i = 500 cm θ(h i ) K(h i ) Fig. 4 3 q 0 = 3 0.5 0.2 cm d 1 h 0 Fig. 5 K s = 106.1 cm d 1 K s = 6 cm d 1 Table 1 3 cm d 1 3 6 9 cm q q 0 q 0 h 0 h Fig. 41 h 0 K(h 0 ) dh/dz h 0 q 0 h dh/dz = 01 q 0 = K(h ) h θ(h ) Table 2 Fig. 4 h h 0 6 Fig. 5 a c h i = 500 cm h = 100 cm h
1. 35 Fig. 5 3 q 0 = 3 0.5 0.2 cm d 1 (a) (b) (c) h(z) (d) (e) (f) K(z) (g) (h) (i) θ(z)
36 113 (2009) Jury and Horton, 2006 q 0 q 0 = 0.2 cm d 1 q 0 = 0.2 cm d 1 Fig. 5 d f h K(h ) = q 0 K i h i = 500 cm K i = 5.5 10 6 cm d 1 K i = 9.5 10 4 cm d 1 Table 1 K 2 K i 10 cm 5 6 K K(h ) K Fig. 5 g i Fig. 5 a c Fig. 1 a θ(h) q 0 t Table 1 θ(h i ) Table 2 θ(h ) q 0 q 0 θ(h ) Fig. 5 a c 4 C w (h) Jury and Horton, 2006 C w Fig. 2 C w Fig. 2 θ(h ) q 0 = 0.2 cm d 1 5. Rassam et al., 2004; 2006 0 cm Philip 1957a profilecontrolled Hillel, 2001 0 cm 100 cm h i = 500 cm Table 1 Fig. 6 3 h 0 = 1 31 55 cm q 0 Fig. 7 Fig. 5 20 cm 2 3 q 0 Table 3 h 0 θ(h 0 ) K(h 0 ) h 0 = 0 cm h 0 = 1 cm h = 0 cm Rassam et al., 2004 Table 3 θ(h 0 ) K(h 0 ) Soil type h 0 (cm) θ(h 0 ) (cm 3 cm 3 ) K(h 0 ) (cm d 1 ) 1 0.410 85.9 Sandy loam 31 0.215 0.51 55 0.161 0.06 1 0.460 3.69 Silt 31 0.424 0.50 55 0.396 0.21
1. 37 Fig. 6 3 h 0 = 1 31 55 cm q 0 h 0 h Fig. 4 h 0 q 0 Fig. 6 q 0 q 0 h 0 = 1 cm h 0 = 31 cm h 0 = 55 cm h 0 = 1cm h 0 = 1 cm 1 h 0 = 31 cm q 0 dh/dz = 01 q = K(h 0 ) 2006 Fig. 4 q = K(h 0 ) Table 3 Fig. 1 b h = 31 cm K h 0 = 31 cm q 0 = 0.5 cm d 1 h h 0 = 55 cm q 0 = 0.2 cm d 1 h Table 2 Table 3 3 Fig. 7 a c h 0 h i = 500 cm h = h 0 h i Fig. 6 dh/dz q 0 K(h 0 ) 1 dh/dz q 0 Fig. 5 a c q = K(h 0 ) Fig. 5 a c h 0 h 0 = 1 cm h 0 = 55 cm h 0 K(h 0 ) K i Fig. 7 d f K(h 0 ) Fig. 6 q Table 3 h 0 = 1 cm
38 113 (2009) Fig. 7 3 h 0 = 1 31 55 cm (a) (b) (c) h(z) (d) (e) (f) K(z) (g) (h) (i) θ(z)
1. 39 Fig. 8 q w (z) a q 0 = 3 cm d 1 b q 0 = 0.2 cm d 1 c q 0 = 0.2 cm d 1 K i = 5.5 10 6 cm d 1 K(h 0 ) = 85.9 cm d 1 h 0 = 55 cm K Fig. 7 g i θ(h i ) Fig. 5 Table 1 θ(h 0 ) Table 3 θ(h i ) θ(h 0 ) h 0 = 1 cm h 0 = 55 cm h 0 = 55 cm Fig. 6 Fig. 5 g i q 0 = 0.5 cm d 1 Fig. 5 h h 0 = 31 cm Fig. 7 hq 0 = 0.2 cm d 1 Fig. 5 i h 0 = 55 cm Fig. 7 i h h 0 = 1 cm Hillel, 2001h 0 h 0 6. 1 1 2 2 Hillel, 2001 Fig. 8 afig. 4 q 0 = 3 cm d 1 3d Fig. 5 d K Fig. 5 d Fig. 8 40 cm 3 cm d 1
40 113 (2009) dh/dz = 0 20 cm 5 cm 45 cm 1.54 cm d 1 1 K(h) Warrick, 2003 K 1988 Jury and Horton, 2006 q 0 = 3 cm d 1 2 d Fig. 5 d K 3 cm d 1 K i = 5.5 10 6 cm d 1 K dh/dz K K dh/dz q 0 = 3 cm d 1 40 cm Fig. 5 a Fig. 5 g 3 d 40 cm K Fig. 8 a Fig. 8 b q 0 = 0.2 cm d 1 30 d q 0 = 3 cm d 1 q 0 K q 0 = 3 cm d 1 q 0 = 0.2 cm d 1 Fig. 8 c q 0 = 0.2 cm d 1 30 d K i = 9.5 10 4 cm d 1 K i = 5.5 10 6 cm d 1 Table 1 Fig. 5 c Fig. 5 i 30d HYDRUS-1D Fig. 8 7.
1. 41 HYDRUS-1D http://www.bio.mieu.ac.jp/junkan/sec1/lab5/model/index.html Philip 1957e Philip 1957e Carsel, R. F. and Parrish, R. S. (1988): Developing joint probability distributions of soil water retention characteristics, Water Resour. Res., 24: 755 769. 2007 : W. H. Green and G. A. Ampt 1 105: 111 115. Hillel, D. (2001) II 10 pp. 1 51 Jury, W. A. and Horton, R. (2006): : pp.36 159 2007 Y. Mualem M. Th. van Genuchten 106: 105 112 1991 2 pp. 15 44 198450: 56 62 2000 2 pp. 22 38 Philip, J. R. (1957a): The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci., 83: 345 357. Philip, J. R. (1957b): The theory of infiltration: 2. The profile at infinity. Soil Sci., 83: 435 448. Philip, J. R. (1957c): The theory of infiltration: 3. Moisture profiles and relation to experiment. Soil Sci., 84: 163 178. Philip, J. R. (1957d): The theory of infiltration: 4. Sorptivity and algebraic infiltration equations. Soil Sci., 84: 257 264. Philip, J. R. (1957e): The theory of infiltration: 5. Influence of initial moisture content. Soil Sci., 84: 329 339. Rassam, D., Šimůnek, J. and van Genuchten, M. Th. (2004) HYDRUS-2D pp. 1.1 1.52 HYDRUS Šimůnek, J., Šejna, M., Saito, H., Sakai, M., and van Genuchten, M. Th. (2008): The HYDRUS-1D software package for simulating the movement of water, heat, and multiple solutes in variably saturated media, Version 4.0, HYDRUS Software Series 3, Dep. of Environmental Sciences, Univ. of California Riverside, Riverside, CA, USA.,, 1988 2 56: 61 67 J. Šimůnek2006 104: 63 73., 2009 111: 61 73. Warrick, A. W. (2003): Soil water dynamics, pp. 167 184, Oxford university press, New York. 2