Pedotransfer functions for the United States

437

Chapter 23 PEDOTRANSFER FUNCTIONS FOR THE UNITED STATES W.J. Rawls USDA-ARS Hydrology & Remote Sensing Lab, Bldg. 007, Rm. 104, BARC-W, Beltsville, MD 20705-2350, USA Tel.: þ 1-301-504-8745

1. INTRODUCTION Numerous pedotransfer functions have been developed in the United States; however, most have been developed using data sets that are representative of a region or smaller area. The pedotransfer functions presented in this chapter have been developed from national databases (Rawls et al., 1982; USDA, 1997; Rawls et al., 1998). The pedotransfer functions presented are for water retention and saturated hydraulic conductivity.

2. SOIL WATER RETENTION Pedotransfer functions for water retention take one of two forms. First, pedotransfer functions that predict water retention at specific matric potentials; and second pedotransfer functions that predict the parameters of water retention models. 2.1. Pedotransfer functions for specific water potentials on the soil water retention curve

The two most frequently estimated water contents are those corresponding to soil water potentials of 233 and 21500 kPa, primarily because they are commonly measured and have commonly been referred to as field capacity and wilting point, respectively. Table 1 summarizes the soil water held at 233 and 21500 kPa for the USDA soil texture classes. Ahuja et al. (1985) showed that using a linear extrapolation between the water contents held at 233 and 21500 kPa on a log – log graph other water contents for specific water potentials could be adequately determined. Table 2 summarizes equations developed from regression analysis that estimate soil water retention at specific water potentials using: (1) soil properties; (2) soil properties and water retained at 21500 kPa; and (3) soil properties and water retained at 233 and 21500 kPa (Rawls et al., 1982). As seen in Table 2, the accuracy of the regression equations increased when the water content held at 2 1500 kPa or both 233 and 21500 kPa were included with physical soil properties. Adding the water content held at 233 and 21500 kPa is more costly and time consuming to acquire; however, they increased the explained variation from 76 to 95%. In general, the water content held at 2 33 kPa was a more significant variable for estimating water retention at matric potentials DEVELOPMENTS IN SOIL SCIENCE VOLUME 30 ISSN 0166–2481/DOI 10.1016/S0166-2481(04)30023-1

q 2004 Elsevier B.V. All rights reserved.

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Table 1 Water retention properties classified by soil texture (Rawls et al., 1982) Texture class

Sample size

Brooks– Corey parameters Total porosity (w) (cm3 cm23)

Sand

762

Loamy sand Sandy loam Loam

338

Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay a

666 383 1206 498

366 689

45 127 291

b

Residual water content (ur) (cm3 cm23)

Bubbling pressure (hb)

Water retained at Pore-size distribution (l)

Arithmetic (cm)

Geometrica (cm)

Arithmetic

Geometrica

21500 kPa (cm3 cm23)

0.437 (0.374 –0.500) 0.437 (0.368 –0.506) 0.453 (0.351 –0.555) 0.463 (0.375 –0.551) 0.501 (0.420 –0.582) 0.398 (0.332 –0.464)

0.020 (0.001 –0.039) 0.035 (0.003 –0.067) 0.041 (2 0.024 –0.106) 0.027 (2 0.020 –0.074) 0.015 (2 0.028 –0.058) 0.068 (2 0.001 –0.137)

15.98 (0.24 – 31.72) 20.58 (2 4.04 –45.20) 30.20 (2 3.61 –64.01) 40.12 (2 20.07 –100.3) 50.87 (2 7.68 –109.4) 59.41 (2 4.62 –123.4)

7.26 (1.36 – 38.74) 8.69 (1.80 – 41.85) 14.66 (3.45 – 62.24) 11.15 (1.63 – 76.40) 20.76 (3.58 – 120.4) 28.08 (5.57 – 141.5)

0.694 (0.298 –1.090) 0.553 (0.234 –0.872) 0.378 (0.140 –0.616) 0.252 (0.086 –0.418) 0.234 (0.105 –0.363) 0.319 (0.079 –0.559)

0.592 (0.334 –1.051) 0.474 (0.271 –0.827) 0.322 (0.186 –0.558) 0.220 (0.137 –0.355) 0.211 (0.136 –0.326) 0.250 (0.125 –0.502)

0.091 (0.018 –0.164) 0.125 (0.060 –0.190) 0.207 (0.126 –0.288) 0.270 (0.195 –0.345) 0.330 (0.258 –0.402) 0.255 (0.186 –0.324)

0.033 (0.007 –0.059) 0.055 (0.019 –0.091) 0.095 (0.031 –0.159) 0.117 (0.069 –0.165) 0.133 (0.078 –0.188) 0.148 (0.085 –0.211)

0.464 (0.409 –0.519) 0.471 (0.418 –0.524)

0.075 (2 0.024 –0.174) 0.040 (2 0.038 –0.118)

56.43 (2 11.44 –124.3) 70.33 (2 3.26 –143.9)

25.89 (5.80 – 115.7) 32.56 (6.68 – 158.7)

0.242 (0.070 –0.414) 0.177 (0.039 –0.315)

0.194 (0.100 –0.377) 0.151 (0.090 –0.253)

0.318 (0.250 –0.386) 0.366 (0.304 –0.428)

0.197 (0.115 –0.279) 0.208 (0.138 –0.278)

0.430 (0.370 –0.490) 0.479 (0.425 –0.533) 0.475 (0.427 –0.523)

0.109 (0.013 –0.205) 0.056 (2 0.024 –0.136) 0.090 (2 0.015 –0.195)

79.48 (2 20.15 –179.1) 76.54 (2 6.47 –159.6) 85.60 (2 4.92 –176.1)

29.17 (4.96 – 171.6) 34.19 (7.04 – 166.2) 37.30 (7.43 – 187.2)

0.223 (0.048 –0.398) 0.150 (0.040 –0.260) 0.165 (0.037 –0.293)

0.168 (0.078 –0.364) 0.127 (0.074 –0.219) 0.131 (0.068 –0.253)

0.339 (0.245 –0.433) 0.387 (0.332 –0.442) 0.396 (0.326 –0.466)

0.239 (0.162 –0.316) 0.250 (0.193 –0.307) 0.272 (0.208 –0.336)

Antilog of the log mean. First line is the mean value, the second line is ^ one standard deviation about the mean.

b

233 kPa (cm3 cm23)

Table 2 Linear regression equations for predicting soil water content at specific matric potentials (Rawls et al., 1982) Matric potential (kPa)

Intercept

Regression coefficients a 24 0.7899 0.6275 0.1829 27

2 10

2 20

2 33 2 60

2 100

Sand (%)

Silt (%)

Clay (%)

Organic matter (%)

Bulk density (g cm23)

233 kPa water retention (cm3 cm23)

21500 kPa water retention (cm3 cm23)

b 2 0.0037 2 0.0041

c

d

e 0.0100 0.0239 2 0.0246

f 2 0.1315

g

h

1.89

2 0.08 2 1.38

0.58 0.57 0.77

1.53

0.25 2 0.81

0.74 0.74 0.91

1.34

0.41 2 0.51

0.81 0.81 0.95

1.01

0.61 2 0.06

0.86 0.89 0.99

0.72

0.87 0.92

0.80 0.39

0.87 0.94 0.99

0.7135 0.4829 0.8888

2 0.0030 2 0.0035 2 0.0003

0.0017

0.4118 0.4103 0.0619

2 0.0030 0.0031 2 0.0002

0.0023

0.3121 0.3000 0.0319

2 0.0024 2 0.0024 2 0.0002

0.0032

0.2576 0.2391

2 0.0020 2 0.0019

0.0036

0.2065 0.1814 0.0136

2 0.0016 2 0.0015

0.0040

0.0349

2 0.0376 2 0.1693

0.0263 2 0.0107 0.0317 0.0260 2 0.0067 0.0314 0.0235 0.0299 0.0210 0.0275 0.0178 2 0.0091 0.0014

0.0055

0.0251

0.66

Correlation coefficient, R

0.87

439

440

Table 2. Continued 0.1417

2 0.0012

0.0151 0.0022

2 0.0034 2 200

2 400

2 700

2 1000

21500

0.0281 0.0986 2 0.0043 0.0238 0.0649 2 0.0038

0.0011

0.0008

0.0052

2 0.0006

0.0216 0.0429 2 0.0027

2 0.0004

0.0205 0.0309 2 0.0019

2 0.0003

0.0260

0.0054

0.0009

0.0006

0.0005

0.0050

0.0049

0.0050

0.0200 0.0116 0.0026 0.0190 0.0085 0.0026 0.0167 0.0062 0.0024 0.0154 0.0049 0.0022

0.52

0.85 0.54

0.36

0.90 0.69

0.24

0.93 0.79

0.86 0.97 0.99 0.84 0.98 0.99

0.16

0.94 0.86

0.81 0.98 0.99

0.11

0.95 0.89

0.81 0.99 0.99

0.0158

Sand (%) þ silt (%) þ clay (%) ¼ 100; Sand ¼ 2.0 –0.05 mm; Silt ¼ 0.05 –0.002 mm; Clay , 0.002 mm. ux ¼ a þ bsand (%) þ csilt (%) þ dclay (%) þ eorganic matter (%) þ fbulk density (g cm23) þ g(233 kPa moisture (cm3 cm23)) þ h(2 1500 kPa moisture (cm3 cm23)). ux ¼ predicted water retention (cm3 cm23) for a given suction. a– h ¼ regression coefficients.

0.96 0.99

0.80

441

between 0 and 233 kPa and the water content held at 21500 kPa was a more significant variable for estimating water retention at water potentials between 233 and 21500 kPa. Ahuja et al. (1985) developed a method to estimate the soil water retention curve from soil bulk density, water content held at 233 kPa and a reference soil water retention curve for the soil texture class (Figure 1). The procedure is demonstrated in Figure 1 on page 73. The above procedures estimate points on the water retention curve to which water retention models such as those given in Table 3 can be fitted to describe the entire water retention curve.

Figure 1. Representative water retention curves for USDA soil texture classes (Rawls et al., 1992).

2.2. Estimation of soil water retention model parameters

Table 4 summarizes Brooks – Corey (Brooks and Corey, 1964) parameters for the USDA texture classes. The model parameters subsequently related to physical soil properties using regression analysis (Table 4). Also included in Table 4 are independent equations for estimating the Campbell water retention model parameters (Campbell, 1974).

Hydraulic soil characteristic Brooks and Corey (1964) Soil water retention,
l u 2 ur h ¼ b w 2 ur h Hydraulic conductivity,
 KðuÞ u 2 ur n ¼ ¼ ðSe Þn Ks w 2 ur Campbell (1974) Soil water retention,
1=b u Hb ¼ w h Hydraulic conductivity,


n KðuÞ u ¼ Ks w

van Genuchten (1980) Soil water retention,  m u 2 ur 1 w 2 ur 1 þ ðahÞn Hydraulic conductivity, "
 (
 #m )2 KðuÞ u 2 ur 1=2 u 2 ur 1=m ¼ 12 12 Ks w 2 ur w 2 ur

442

Table 3 Soil water retention and hydraulic conductivity relationships with parameter correspondence Parameters

Parameter correspondence

l ¼ pore-size index hb ¼ bubbling capillary pressure ur ¼ residual water content w ¼ porosity Ks ¼ fully saturated conductivity (u ¼ w) 2 n¼3þ l

l¼l hb ¼ hb ur ¼ ur w¼w Ks ¼ Ks

w ¼ porosity Hb ¼ scaling parameter (length) b ¼ constant

w¼w Hb ¼ hb 1 b¼ l

n ¼ 3 þ 2b

w ¼ porosity ur ¼ residual water content a ¼ constant n ¼ constant m ¼ constant

w¼w ur ¼ ur a ¼ (hb)21 n¼lþ1 l m¼ lþ1

u ¼ water content; h ¼ capillary suction (cm); K(u) ¼ hydraulic conductivity for a given water content (cm h21).

Table 4 Estimation equations for the Brooks – Corey and Campbell water retention model parameters Brooks –Corey parameters (Rawls and Brakensiek, 1985) hb – Brooks – Corey bubbling pressure (cm) hb ¼ e½5:340 þ 0:185ðCÞ 2 2:484ðwÞ 2 0:002ðCÞ2 2 0:044ðSÞðwÞ 2 0:617ðCÞðwÞ þ 0:001ðSÞ2 ðw2 Þ 2 0:009ðC2 Þðw2 Þ 2 0:00001ðS2 Þ £ ðCÞ þ 0:009ðC 2 ÞðwÞ 2 0:0007ðS2 ÞðwÞ þ 0:000005ðC 2 ÞðSÞ þ 0:500ðw2 ÞC l – Brooks –Corey pore size distribution index l ¼ e½20:784 þ 0:018ðSÞ 2 1:062ðwÞ 2 0:00005ðS2 Þ 2 0:003ðC 2 Þ þ 1:111ðw2 Þ 2 0:031ðSÞðwÞ þ 0:0003ðS2 Þðw2 Þ 2 0:006ðC 2 Þ £ ðw2 Þ 2 0:000002ðS2 ÞðCÞ þ 0:008ðC 2 ÞðwÞ 2 0:007Þðw2 ÞðCÞ ur – Brooks –Corey residual water content (vol. fraction) ur ¼ 20:018 þ 0:0009ðSÞ þ 0:005ðCÞ þ 0:029ðwÞ 2 0:0002ðCÞ2 2 0:001ðSÞðwÞ 2 0:0002ðC2 Þðw2 Þ þ 0:0003ðC2 ÞðwÞ 2 0:002ðw2 ÞðCÞ where: C ¼ % clay S ¼ % sand w ¼ porosity (vol. fraction) Campbell parameters (Campbell, 1985) Campbell air entry potential at standard bulk density (1.3 mg m23) meters: 1 hb ¼ ð20:5ðdg Þ2 2 Þ(BD/1.3)(0.67b); Campbell b: b ¼ 2 2hb þ 0.2sg;

443

where: BD ¼ bulk density (mg m23) w ¼ porosity (vol. fraction). If porosity (w) is not known, estimate it from bulk density (w ¼ air multiplier(1 2 BD/2.65)) where air multiplier ¼ 0.93 usually, must be (0.8, 0.98) dg ¼ geometric mean particle diameter (mm) ¼ exp[2 0.025 2 3.63silt 2 6.88clay] 1 sg ¼ geometric standard deviation ¼ exp½13:32silt þ 47:7clay 2 lnðdg Þlnðdg Þ 2

444

Table 5 Summary of soil water retention equation parameters derived by Saxton et al. (1986) Applied tension range (2kPa)

Equation

. 1500 –10

C ¼ AuB A ¼ exp½a þ bð%CÞ þ cð%SÞ2 þ dð%SÞ2 ð%CÞ100 B ¼ e þ f ð%CÞ2 þ gð%SÞ2 ð%CÞ C ¼ 10:0 2 ðu 2 u10 Þð10:0 2 Ce Þ=ðus 2 u10 Þ u10 ¼ exp½ð2:302 2 ln AÞ=B Ce ¼ 100:0½m þ nðus Þ us ¼ h þ jð%SÞ þ k log10 ð%CÞ u ¼ us K ¼ 2:778 £ 1026 {exp½p þ qð%SÞ þ½r þ tð%SÞ þ uð%CÞ þ vð%CÞ2 ð1=uÞ} Coefficients p ¼ 12.012 g ¼ 2 3.484 £ 1025 h ¼ 0.332 q ¼ 2 7.55 £ 1022 j ¼ 2 7.251 £ 1024 r ¼ 2 3.8950 k ¼ 0.1276 t ¼ 3.671 £ 1022 m ¼ 2 0.108 u ¼ 2 0.1103 n ¼ 0.341 v ¼ 8.7546 £ 1024 Definitions u10 ¼ water content at 2 10 kPa (m3 m23) K ¼ water conductivity (m s21)

10 – Ce

Ce – 0.0 . 1500 –0.0

a ¼ 2 4.396 b ¼ 2 0.0715 c ¼ 2 4.880 £ 1024 d ¼ 2 4.285 £ 1025 e ¼ 2 3.140 f ¼ 2 2.22 £ 1023

C ¼ water potential (2 kPa) Ce ¼ water potential at air entry (2 kPa) u ¼ water content (m3 m23) us ¼ water content at saturation (m3 m23)

(%S) ¼ percent sand (e.g., 40.0) (%C) ¼ percent clay (e.g., 30.0)

Table 6 Saturated hydraulic conductivity (Ks) classified by USDA soil texture classes and porosity (Rawls et al., 1998) Geometric mean Ksa (mm h21)

Porosity (m3 m23)

Water retained at at 233 kPa (m3 m23)

Water retained at 21500 kPa (m3 m23)

Sand (%)

Clay (%)

Sample size

Sand

181.9 (266.8–96.5) 91.4 (218.5–64.0) 141.3 (236.1–118.1) 100.0 (219.8–68.1) 123.0 (195.5–83.8) 41.4 (77.6–30.5) 62.2 (122.0–35.6) 12.8 (116.0–6.8) 55.8 (129.6–30.5) 12.8 (31.3–5.1) 22.4 (35.6–9.8) 8.2 (17.0–3.4) 3.9 (28.4–1.6) 6.2 (16.5–2.8) 14.4 (37.1–7.6) 3.4 (9.9–1.0) 7.7 (50.5–2.0) 2.8 (10.9–1.0) 4.2 (13.1–2.2) 0.7 (3.8–0.2) 3.7 (10.4–2.3) 4.9 (14.0–2.3) 0.9 (2.5–0.3) 1.8 (7.5–0.5) 2 (6.0– 0.9) 1.8 (6.9–0.3)

0.44 0.39 0.49 0.39 0.45 0.37 0.46 0.37 0.47 0.37 0.45 0.36 0.47 0.39 0.49 0.39 0.44 0.37 0.48 0.4 0.50 0.43 0.39 0.53 0.48 0.4

0.07 0.09 0.07 0.07 0.09 0.14 0.11 0.2 0.23 0.2 0.24 0.21 0.3 0.28 0.34 0.31 0.31 0.29 0.32 0.34 0.37 0.36 0.3 0.41 0.4 0.36

0.03 0.02 0.03 0.02 0.04 0.06 0.06 0.12 0.1 0.12 0.1 0.11 0.15 0.13 0.14 0.14 0.2 0.21 0.22 0.25 0.23 0.23 0.22 0.27 0.31 0.3

92 91 89 92 82 82 82 68 65 68 70 69 38 43 18 21 56 58 29 35 10 10 51 4 18 26

4 4 3 4 6 7 6 12 11 13 14 14 23 22 19 20 26 26 35 35 34 32 36 49 53 50

39 30 14 9 19 28 18 112 75 112 24 36 44 65 61 46 20 53 20 53 26 33 14 10 20 21

Fine sand Loamy sand Loamy fine sand Sandy loam Fine sandy loam Loam Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay a

Ks ¼ saturated hydraulic conductivity; first line is mean value; in brackets are 25 and 75% percentile values.

445

USDA Soil texture class

446

Using the correspondence between model parameters given in Table 3, the equations in Table 4 can be used to apply the Brooks and Corey (1964), Campbell (1974) and van Genuchten (1980) water retention models. Saxton et al. (1986) developed pedotransfer functions for a modified model of Campbell (1974). A summary of the parameters is given in Table 5.

3. SATURATED HYDRAULIC CONDUCTIVITY Rawls et al. (1998) assembled a national database of saturated hydraulic conductivity data from which the geometric means of the Ks, sorted according to the USDA soil texture classes and two bulk density classes, along with the 25 and 75% percentile values were developed and are given in Table 6. Ahuja and associates (1984) proposed a generalized Kozeny – Carman equation (Carman, 1956) relating the saturated hydraulic conductivity to effective porosity in the following form: Ks ¼ Cfm e

ð1Þ

where Ks is the saturated hydraulic conductivity (mm h21); fe, the effective porosity (m3 m23) (total porosity, w, minus water content at 233 kPa pressure head, u1/3) and C and m are empirically derived constants. Rawls et al. (1998) also parameterized equation 1 by redefining the exponent m equal to 3 minus the Brooks – Corey pore size distribution index (l) and C equal to 1930. The Brooks –Corey pore size distribution index (l) was obtained by fitting a log – log plot of water content vs. pressure-head using only the 233 and 21500 kPa water contents.

REFERENCES Ahuja, L.R., Naney, J.W., Green, R.E., Nielsen, D.R., 1984. Macroporosity to characterize spatial variability of hydraulic conductivity and effects of land management. Soil Sci. Soc. Am. J. 48, 699-702. Ahuja, L.R., Naney, J.W., Williams, R.D., 1985. Estimating soil water characteristics from simpler properties or limited data. Soil Sci. Soc. Am. J. 49, 1100-1105. Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Hydrology Paper No. 3, Colorado State University, Fort Collins, CO, 27 pp. Campbell, G.S., 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci. 117, 311-314. Campbell, G.S., 1985. Soil Physics with BASIC: Transport Models for Soil– Plant Systems. Elsevier, New York, 150 pp. Carman, P.C., 1956. Flow of Gases Through Porous Media. Academic Press Inc., New York. Rawls, W.J., Brakensiek, D.L., 1985. Prediction of soil water properties for hydrologic modeling. In: Jones, E.B., Ward, T.J. (Eds.), Proceedings of the Symposium of

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Watershed Management in the Eighties. April 30 –May 1, 1985, Denver, CO. Am. Soc. Civil Eng., New York, NY, pp. 293-299. Rawls, W.J., Brakensiek, D.L., Saxton, K.E., 1982. Estimation of soil water properties. Trans. ASAE 25 (5), 1316-1320, see also p. 1328. Rawls, W.J., Ahuja, L.R., Brakensiek, D.L., Shirmohammadi, A., 1992. Infiltration and soil water movement. In: Maidment, D.R. (Ed.), Handbook of Hydrology. McGraw-Hill Inc., New York, Chapter 5. Rawls, W.J., Gime`nez, D., Grossman, R., 1998. Use of soil texture, bulk density, and the slope of the water retention curve to predict saturated hydraulic conductivity. Trans. ASAE 41 (4), 983-988. Saxton, K.E., Rawls, W.J., Romberger, J.S., Papendick, R.I., 1986. Estimating generalized soil water characteristics for texture. Soil Sci. Soc. Am. J. 50, 1031-1036. USDA, 1997. National Characterization Data. Soil Survey Laboratory, National Soil Survey Center, and Natural Resources Conservation Service, Lincoln, NE. van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892-898.