3. Green and Ampt. Infiltration into a soil profile: 3. Green-Ampt model. Hillel 2001; Jury and Horton 2006 G & A G & A. Philip S G & A G & A

Transcription

1 3. Green and Ampt Infiltration into a soil profile: 3. Green-Ampt model. Nobuo TORIDE 1 Kunio WATANABE 1 Yudai HISAYUKI 1 and Masaru SAKAI Philip S A 21 2 Hillel Philip Green and Ampt G & A Green and Ampt 1911 G & A 17 Hillel Green and Ampt G & A 27 G & A G & A G & A 1 Graduate School of Bioresources, Mie University, 1577 Kurima- Machiya, Tsu, Mie , Japan. Corresponding author: 2 Utah State University, Dep. Plants, Soils, and Climate , 51 6 (21) Hillel 21; Jury and Horton 26 G & A G & A G & A G & A G & A G & A G & A Fig. 3 2 Table 1 HYDRUS-1D Šimůnek et al. 28 Fig. 1 a b G & A Jury and Horton 26

2 (21) Fig. 2 a b h i = 5 cm h = 1 1, 17, 31, 55, 8 cm I t 1/2 2. h i θ i h θ Green and Ampt Fig. 1 a Fig. 1 b G & A Jury and Horton 26 L h θ K effective pressure head at the front h F Hillel 21; Warrick 23 h F h i θ i h θ L i 1 i = q = K h F h L = K h L h = h h F > i (1) I = L θ I I = t 1/2 2 θk h (4) Philip 1957 θ i θ 8 I Jury and Horton I = St 1/2 (5) S sorptivity G & A 4 Philip 5 I L t 1/2 Atkins 1993 Philip 5 S Green and Ampt Philip S 4 5 G & A h F i = d dt [(θ θ i )L] = θ dl dt (2) S = 2 θk h = 2 θk (h h F ) (6) θ = θ θ i > 1 2 L Jury and Horton 26 L 2 2 = K h θ t (3) 1 i q i = q S h F h F = h S2 2 θk (7) G & A

3 3. Green and Ampt 53 Fig. 3 h i = 5 cm 2 h = 1 31 cm a b c d h(x). 1 2 θ = [ ( )] h K(h) t x x x L h 2 4 h i Fig. 2 6 h I t 1/2 h i = 5 cm 4 I θ K h h F 5 I S h = cm θ i 2 Fig. 7 a Fig. 8 a (8) h = 1 cm h 1 Fig. 1 K h i = 5 cm h = 17 cm I I t 1/2 K 1 Fig. 1 I h h = 31 cm K h = 17 cm K h i = 5 cm h = 1 31 cm Fig. 3 Fig. 4 3 L G & A h F h F θ(h F ) Table 1 Fig. 3 h = 1 cm

4 (21) Fig. 4 h i = 5 cm 2 h = 1 31cm a b c d θ(x). Table 1 h i = 5 cm, h = 1 31 cm h F. Soil type Sandy loam Silt h h F h θ(h F ) (cm) (cm) (cm) (cm 3 cm 3 ) cm 2 d h i = 5 cm h = 1 cm K(h ) = 85.9 cm d 1 K(h i ) = cm d 1 1 Fig. 7 d K K(h i ) = cm d 1 G & A 1 G & A L h Fig. 3 a b G & A L L I = L θ C w θ 1 Fig. 2 G & A L h L h F h = 1 cm h F = 5.8 cm h = 31 cm h F = 41.1 cm h = h h F Table 1 1 K h Fig. 3 c d G & A L h F h Table 1 Fig. 4 a b G & A L G & A

5 3. Green and Ampt 55 Fig. 5 a b h h F θ i Fig. 4 h F θ(h F ) Table 1 G & A L Fig. 4 c d Fig. 2 i h = 17 cm h = 31 cm Fig. 5 h θ h F θ i h F h θ i h F h θ i h = h h F h Fig. 3 θ i h F θ i G & A h F h F θ i 2 Fig. 6 V F Fig. 7 Fig. 8 Philip 3. G & A 1 z = z = L i = q = K ( h + L) (9) L θ i i 2 i G & A 2 9 Jury and Horton 26 ( L hln 1 + L ) = K t h θ I(t) = L θ (1) ( I(t) h θ ln 1 + I(t) ) = K t (11) h θ I 11 ( ln 1 + I(t) ) I(t) h θ h θ 1 ( ) I(t) 2 (12) 2 h θ 11 I I t 1/2 4 4 L L = t 1/2 2K h θ V F V F = dl dt = K h t 1/2 2 θ (13) (14) 11 2 K

6 (21) Fig. 6 a b c d e f h i = 5 cm 3 h = cm h(z). I = K t (15) L = K t/ θ V F V F = dl dt = K θ (16) 2 7 G & A 11 G & A 9 L h/l L h/l I G & A Radcliffe and Šimůnek 21 L = θ/i 9 i Hillel 21 2 i = K θ h I + K (17) 17 G & A 17 I 1 2 i I 1 i K h F I 11 t I(t) f ( h,t) ( f ( h,t) = I(t) h θ ln 1 + I(t) ) K t (18) h θ f ( h,t) = h

7 Pressure head at the front, h F (cm) Green and Ampt 57 (a) Sandy loam Based on each time I Fitted with the overall I Time (d) (b) Silt Fig. 7 a b h i = 5 cm h = 1 cm h F I h F Table 2 h i = 5 cm, h = 1 31, 55 cm h F. Soil type h h F h θ( h F ) (cm) (cm) (cm) (cm 3 cm 3 ) Sandy loam Silt h = h h F h F I t 1/2 Fig. 2 h F h F h F Radcliffe and Šimůnek 21 I(t) h F h F I(t) G & A I(t) h F 11 I t 11 t I t(i) h F I (t(i) t) 2 h h F θ i h F 11 A6 θ i Fig. 6 1 cm h i = 5 cm 3 h = cm 1 Fig. 6 1 Fig. 7 Fig. 6 G & A I h F h F Table 2 L θ i A5 Fig. 6 Fig. 3 1 h = 1 cm h = h h F h Fig. 7 h = 1 cm I h F I 11 h F h F h F Fig. 7 t = h F Fig. 3 h = 1 cm h F Table 1 4 h F h F h F t h F 2 Philip 2 1 S A S/A h θ

8 (21) h i θ i S/A h h i Fig. 7 h = 1 cm h i = 5 cm S/A Fig. 9 h F h F h F i i i 2 Fig. 2 b h = 1 cm h i = 5 cm i G & A i Philp 2 1 h F h F h = h h F G & A h F Fig. 5 h θ h F h F θ i h F h θ i h F h = h h F h F Table 1 Table 2 h θ i Fig. 7 h = h h F h = 1 cm h i = 5 cm 1 Fig. 7 g Fig. 1 b G & A Fig. 5 h F G & A h F Fig. 7 a h F 4. G & A G & A Philip I h F h h i I t 1/2 h F h = h h F h θ i h F θ i h F I h F h F h = h h F I h F h F h θ i h F h F θ i Atkins 1993 S Philip Green and Ampt 1911 I h F G & A G & A I V F 9 G & A h F h F G & A G & A 1

9 3. Green and Ampt 59 Green and Ampt 1911 h F Neuman 1976 h F Fig. 5 c i i = θ dl dt + K i (A1) K i = K(h i ) 8 θ dl dt = K L ( h+l) K i= K { ( h + 1 K ) } i L L K η = 1 K i /K (> ) L L LdL h + ηl = 1 η 2 LdL h + ηl = K t dt = K t θ θ { ( ηl hlog 1 + ηl )} h (A2) (A3) (A4) I(t) = L θ + K i t L = I(t) K it θ A3 A4 A5 I(t) K i t η h θ η 2 ln [ 1 + η(i(t) K it) h θ (A5) ] = K t (A6) K K i η = 1 A6 11 Atkins, P.W. (1993) 4 pp Green, W.H. and Ampt, G.A.(1911): Studies on soil physics: I. The flow of air and water through soils. J. Agric. Sci., 4: W. H. Green and G. A. Ampt 1 15: Hillel, D. (21) II 1 pp Jury, W.A. and Horton, R. (26): pp Radcliffe, D.E. and Šimůnek, J. (21): Soil physics with HY- DRUS: Modeling and applications. pp , CRC Press, New York pp pp Neuman, S.P. (1976): Wetting front pressure head in the infiltration model of Green and Ampt. Water Resour. Res., 12: Philip, J.R. (1957): The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci., 83: Šimůnek, J., Šejna, M., Saito, H., Sakai., M. and van Genuchten, M.Th., (28): The HYDRUS-1D software package for simulating the movement of water, heat, and multiple solutes in variably saturated media. Version 4., HYDRUS Software Series 3, Dep. of Environmental Sciences, Univ. of California Riverside, Riverside, CA, USA. 29 : : : : Warrick, A.W. (23): Soil water dynamics. pp , Oxford university press, New York.

10 6 115 (21) Green and Ampt G & A I t 1/2 h F h F h θ i G & A I V F h F h F h F G & A Green and Ampt