IRRIGATION AND DRAINAGE

Irrig. and Drain. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/ird.1751

NEW EQUATIONS FOR THE DETERMINATION OF SOIL SATURATED HYDRAULIC CONDUCTIVITY USING THE VAN GENUCHTEN MODEL PARAMETERS AND EFFECTIVE POROSITY† VASSILIS G. ASCHONITIS AND VASSILIS Z. ANTONOPOULOS* Aristotle University, School of Agriculture, Department of Hydraulics, Soil Science and Agricultural Engineering, Thessaloniki, Greece

ABSTRACT B

Modifications of the Kozeny–Carman approach (Ks = AΦ ) for the determination of saturated hydraulic conductivity Ks using the van Genuchten model parameters and the effective porosity Φe are presented in this study. Two models {a two-parametric Ks(a, Φe) and a three-parametric Ks(a, Si, Φe)} were developed for Ks determination. In the two-parametric model the power constant was replaced by the f factor (f = aΦe). The factor f includes the parameter a of the van Genuchten model, in order to describe its effect on the part of the pore size distribution which participates in the effective porosity Φe. The three-parametric model was improved by inclusion of the water retention curve slope Si at the inflection point. The models were calibrated and validated using two published data sets which cover the 12 USDA soil texture classes. The proposed models were also compared with other published models of Ks, which are based on the van Genuchten parameters and the Kozeny–Carman approach. The results indicated an adequate predictive accuracy of the models through a calibration and validation procedure using data sets from different sources and better performance compared to other models, setting a new approach for the indirect determination of Ks using only data from the water retention curve. Copyright © 2013 John Wiley & Sons, Ltd. key words: water retention curve; inflection point; saturated hydraulic conductivity; effective porosity; Kozeny–Carman equation Received 8 November 2011; Revised 19 February 2013; Accepted 19 February 2013

RÉSUMÉ Nous présentons ici les modifications de l’approche de Kozeny–Carman (Ks = AΦB) pour la détermination de la conductivité hydraulique saturée Ks en utilisant les paramètres du modèle de van Genuchten et la porosité efficace Φe. Deux modèles {un biparamétrique Ks(a, Φe) et un tri-paramétrique Ks(a, Si, Φe) fonction} ont été développés pour la détermination de la conductivité hydraulique saturée Ks. Dans l’équation bi-paramétrique Ks(a, Φe), l’exposant constant a été remplacé par le facteur f (f = aΦe). Le facteur f inclut le paramètre a du modèle de Van Genuchten, afin de décrire ses effets sur la partie de la répartition volumétrique des pores qui participe à Φe. Une amélioration supplémentaire de la détermination Ks a été l’inclusion de la pente Si au point d’inflexion de la courbe de rétention de l’eau à la tri-paramétrique Ks(a, Si, Φe). Les modèles ont été calibrés et validés en utilisant deux jeux de données publiées qui couvrent les 12 classes USDA de texture de sol. Les modèles proposés ont également été comparés avec d’autres modèles publiés de Ks, qui sont basés sur les paramètres de van Genuchten et l’approche de Kozeny–Carman. Les résultats ont indiqué que les modèles ont montré une précision prédictive suffisante grâce à la procédure de l’étalonnage et de validation en utilisant des ensembles de données provenant de différentes sources; une meilleure performance par rapport à d’autres modèles a été obtenue en mettant en place une nouvelle approche pour la détermination indirecte de Ks par la seule utilisation des données de la courbe de rétention de l’eau. Copyright © 2013 John Wiley & Sons, Ltd. mots clés: courbe de rétention de l’eau; point d’inflexion; conductivité hydraulique saturée; porosité efficace; équation de Kozeny–Carman

* Correspondence to: Prof V.Z. Antonopoulos, Aristotle University, School of Agriculture, Department of Hydraulics, Soil Science and Agricultural Engineering, 54124, Thessaloniki, Greece. E-mail: [email protected] † De nouvelles équations pour la détermination de la conductivité hydraulique saturée du sol en utilisant les paramètres du modèle de van Genuchten et la porosité efficace.

Copyright © 2013 John Wiley & Sons, Ltd.

V. G. ASCHONITIS AND V. Z. ANTONOPOULOS

INTRODUCTION Many methods are available for the direct measurement of the saturated hydraulic conductivity Ks in field or laboratory conditions, but they remain expensive and time-consuming procedures (Aimrum and Amin, 2009). For this reason indirect methods have been developed, where Ks is expressed as a function of other soil parameters. The most popular of these equations concern regression models (pedotransfer functions, PTFs), where their basic independent variables are based on particle size distribution (Saxton et al., 1986; Wösten et al., 1995). Improvements on these models were successful with further inclusion of organic matter and bulk density (Vereecken et al., 1990; Wösten et al., 1995, 1999; Aimrum and Amin, 2009). Physically based equations were also developed based on the Kozeny-Carman approach using porosity attributes such as the total porosity Φ. The initial permeability–porosity relation of Kozeny–Carman is described by: Ks ¼

Φ3 c ð1  Φ Þ2 S 2

(1)

where Φ is the total porosity (L3 L-3), c is the Kozeny constant (L T) and S is the specific surface area per unit volume of solid volume (L-1). Equation (1) was further simplified into two basic forms (Ahuja et al., 1984; Flint and Selker, 2003; Aimrum et al., 2004; Regalado and Muñoz-Carpena, 2004; Henderson et al., 2010): Ks ¼ AΦB and Ks ¼ AΦBe

(2a; b)

where A (L T-1) and B (dimensionless) are empirical constants that vary considerably with soil type and Φe is the effective porosity. Φe was introduced by Ahuja et al. (1984) and it was defined as the total porosity minus the water content at 330 cm H2O (33 kPa) (pores with equivalent diameter > 9 mm). Another group of saturated hydraulic conductivity equations considers parameters obtained by models that describe the water retention curve, such as those of van Genuchten and Brooks-Corey (Mishra and Parker, 1990; Timlin et al., 1999; Guarracino, 2007; Han et al., 2008). Timlin et al. (1999) and Han et al. (2008) modified the Kozeny-Carman equation using the l parameter of Brooks–Corey equation as exponent of Φe. The l inclusion improved the regression results compared to other models, indicating that the exponent should not be a constant but a function, which is related to the pore size distribution. Another approach, such as the use of the van Genuchten model parameters, was followed by Mishra and Parker (1990) and Guarracino (2007). The objective of this study is to propose new models of Ks using the van Genuchten parameters and Φe based on the Copyright © 2013 John Wiley & Sons, Ltd.

Kozeny–Carman approach. The calibration and validation procedure of the models was performed using the data sets of Carsel and Parrish (1988) and Schaap et al. (1998), respectively. Both data sets consist of van Genuchten model parameters and Ks values that describe the 12 USDA soil texture classes. The same calibration and validation procedure was also performed in the published models of Mishra and Parker (1990) and Guarracino (2007) in order to make comparisons with the proposed models.

MATERIALS AND METHODS Model development The van Genuchten (1980) model of water retention curve y(h) is described by: y ¼ yr þ

ys  yr m ½1 þ ðajhjÞn 

(3)

where y is the water content (cm3 cm-3) at a given pressure head h (cm), ys is the saturated water content (cm3 cm-3), yr is the residual water content (cm3 cm-3), and a (cm-1), n and m (dimensionless) are empirical curve shape parameters. Startsev and McNabb (2001) and Aschonitis et al. (2012) showed that the changes in soil physical properties can easily be detected by the most sensitive parameters of the van Genuchten model and porosity attributes. These are: the a parameter, the slope Si of the water retention curve at the inflection point and the effective porosity Φe. The effective porosity Φe is the responsible part of porosity which contributes to the main flow (Ahuja et al., 1984) and the a parameter is related to the air entry pressure head and strongly affects the pore size distribution in the part of macroporosity. At the inflection point (yi, hi) where the curvature of Equation (3) is zero {d2yi/d(hi)2 = 0}, the y(h) function presents the maximum slope {Si = dyi/d(hi)}, which corresponds to the maximum value of specific water capacity. The absolute value of Si has been considered a significant indicator of soil physical conditions concerning the degree of soil compaction (Dexter, 2004; Han et al., 2008; Guimarães Santos et al., 2011). The slope Si (cm-1) of y(h) at the inflection point is given by (Aschonitis et al., 2012): Si ¼ m1þm naðys  yr Þð1 þ mÞm1

(4)

Taking into account the parameters a, Si and Φe, a twoparametric Ks(a, Φe) and a three-parametric Ks(a, Si, Φe) model were developed after modifications of Equation (2b), which are respectively the following: Ks ¼ C1 f

ðC2 f Þ

ðmodel 1Þ

Ks ¼ C1 jSi jðC2 f ÞðC3 f Þ ðmodel 2Þ

(5) (6) Irrig. and Drain. (2013)

SATURATED HYDRAULIC CONDUCTIVITY MODELS

where Ks is the saturated hydraulic conductivity (cm d-1), f = aΦe where Φe is the effective porosity (cm3 cm-3) and a is the shape parameter of the van Genuchten model (cm-1), |Si| is the absolute slope value of the water retention curve at the inflection point (cm-1), C1 (cm2 d-1), C2 (cm) and C3 (cm) are calibration constants. The f factor was considered to be the best selection as the exponent in Equations (5) and (6) following the approach of Timlin et al. (1999), which suggests the use of an exponent related to pore size distribution. The factor f describes the differences in the pore size distribution, where lower a values reduce the mean equivalent diameter of pores which participate in Φe. The increase of the f factor expresses the increase of water velocity due to the increase of the equivalent diameter of pores that participate in the main flow, which is attributed to the reduction of capillary rise and the reduction of frictional resistance effects. The parameter Si was also introduced in the three-parametric model (Equation 6) in order to express the specific water capacity changes at the inflection point, and consequently the changes of pores’ volume that make up the larger portion of porosity. Another two published models of Ks based on the van Genuchten model parameters were selected to be compared with the proposed models. These models were given by Guarracino (2007) and Mishra and Parker (1990) and they are respectively the following: Ks ¼ C1 ys a ðmodel 3Þ 2

model 4 of Mishra and Parker (1990) was determined equal to 2.5 via analytical procedure. The model was calibrated using data from clay, silty clay and clay loam soils. In this study C2 was considered as a fitting parameter aiming to improve the fitting ability of model 4 for a wider range of soil types.

Calibration and validation data sets The four models (Equations 5–8) were calibrated and validated using the data set of Carsel and Parrish (1988) (Table I) and the data set of Schaap et al. (1998) (Table II), respectively. These two data sets were considered the most appropriate for the procedure, because they cover the 12 USDA soil texture classes, giving the advantage of testing the models in a wide range of soils with different hydraulic properties. The accuracy of the models was evaluated using the coefficient of determination (R2) and the root mean square error (RMSE), which are described by the following equations (Antonopoulos and Wyseure, 1998): 2

Ks ¼ C1 ðys  yr Þ a ðmodel 4Þ



32

X i  X Oi  O 6 7 6 7 i¼1 6 R ¼ 6sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi7 7 N N 2 X  2 5 4 X Xi  X  Oi  O i¼1

-1

(9)

i¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X ðX i  O i Þ2 RMSE ¼ t N i¼1

(8)

where Ks is the saturated hydraulic conductivity (cm d ), ys is the volumetric water content at saturation (cm3 cm-3), yr is the residual water content (cm3 cm-3), a the shape parameter of the van Genuchten model (cm-1), and C1 (cm3 d-1) and C2 (dimensionless) are calibration constants. The constant C2 in



2

(7)

C2 2

N  X

(10)

where X is the predicted value from the model, Ο is the observed value, Ν is the number of observations and i is the subscript referred to each observation.

Table I. Van Genuchten model parameters, effective porosity and saturated hydraulic conductivity of the Carsel and Parrish (1988) calibration data set Soil texture Sand Loamy sand Sandy loam Loam Silt Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay

Number of samples

ys (cm3 cm-3)

yr (cm3 cm-3)

a (cm-1)

n –

ISil (cm-1)

Φe (cm3 cm-3)

Ks (cm day-1)

246 315 1183 735 82 1093 214 364 641 46 374 400

0.43 0.41 0.41 0.43 0.46 0.45 0.39 0.41 0.43 0.38 0.36 0.38

0.045 0.057 0.065 0.078 0.034 0.067 0.100 0.095 0.089 0.100 0.070 0.068

0.145 0.124 0.075 0.036 0.016 0.020 0.059 0.019 0.010 0.027 0.005 0.008

2.68 2.28 1.89 1.56 1.37 1.41 1.48 1.31 1.23 1.23 1.09 1.09

3.17E-02 2.02E-02 9.16E-03 3.24E-03 1.31E-03 1.58E-03 3.93E-03 1.01E-03 4.68E-04 1.04E-03 9.75E-05 1.68E-04

0.384 0.350 0.325 0.265 0.202 0.210 0.221 0.140 0.092 0.113 0.023 0.033

712.80 350.16 106.08 24.96 6.00 10.80 31.44 6.24 1.68 2.88 0.48 4.80

Copyright © 2013 John Wiley & Sons, Ltd.

Irrig. and Drain. (2013)

V. G. ASCHONITIS AND V. Z. ANTONOPOULOS

Table II. Van Genuchten model parameters, effective porosity and saturated hydraulic conductivity of the Schaap et al. (1998) validation data set Soil texture

Number of samples

ys (cm3 cm-3)

yr (cm3 cm-3)

a (cm-1)

n –

ISil (cm-1)

Φe (cm3 cm-3)

Ks (cm day-1)

308 201 476 242 6 330 87 140 172 11 28 84

0.375 0.390 0.387 0.399 0.489 0.439 0.384 0.442 0.482 0.385 0.481 0.459

0.053 0.049 0.039 0.061 0.050 0.065 0.063 0.079 0.090 0.117 0.111 0.098

0.0379 0.0448 0.0383 0.0205 0.0073 0.0074 0.0377 0.0274 0.0125 0.0486 0.0260 0.0255

3.3 1.8 1.47 1.5 1.71 1.7 1.35 1.44 1.55 1.21 1.34 1.26

8.90E-03 5.01E-03 3.02E-03 1.64E-03 9.66E-04 8.26E-04 2.23E-03 2.15E-03 1.24E-03 1.67E-03 1.74E-03 1.38E-03

0.321 0.302 0.243 0.210 0.223 0.189 0.189 0.227 0.219 0.119 0.194 0.156

24.48 24.31 15.48 3.70 3.34 1.75 6.94 4.99 2.23 4.34 3.17 2.98

Sand Loamy sand Sandy loam Loam Silt Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay

RESULTS AND DISCUSSION

The results of the validation procedure for the four models using the Ks values of Schaap et al. (1998) (Table II) are given in Table III. According to the statistical tests, lower prediction accuracy is observed in all models in comparison to those of the calibration procedure. The comparison among the four models showed that model 1 led to lower RMSE values and higher R2 values, while Models 1 and 2 showed higher prediction accuracy in comparison to those of Mishra and Parker (1990) and Guarracino (2007). Considering the validation results for the two proposed models (Models 1 and 2), Model 2 showed lower prediction accuracy in comparison to Model 1,

The parameters of the four Ks models (Equations 5–8) were calibrated using the first data set of Table I based on the nonlinear regression method of Statgraphics Centurion XV software. The models were fitted satisfactorily on the Ks values and the results together with the statistical tests are given in Table III. The comparison between the twoparametric models (1 and 3) and the three-parametric models (2 and 4) showed that the use of effective porosity instead of total porosity or (ys-yr), and the inclusion of Si and f function as an exponent led to higher fitting ability.

Table III. Estimated Ks (cm d-1) using the four models in the calibration and validation procedure Data set Model C1 C2 C3 Sand Loamy sand Sandy loam Loam Silt Silt loam Sandy clay loam Clay loam Silty clay loam Sandy clay Silty clay Clay R2 RMSE

Calibration set

Validation set

1

2

3

4

1

2

3

4

6.98 28.78 – 715.7 350.8 94.5 25.0 11.9 13.5 35.5 11.0 8.4 11.6 7.2 7.4 0.99 5.74

5 349 0.197 5.71 713.3 351.9 103.0 24.4 8.0 10.0 32.7 6.1 2.6 6.3 0.5 0.9 0.99 1.98

46 500 – – 420.4 293.1 107.2 25.9 5.5 8.4 63.1 6.9 2.0 12.9 0.4 1.1 0.96 86.54

2438 840 4.485 – 709.1 351.4 116.0 29.2 13.6 13.2 32.9 5.0 2.0 5.9 0.2 0.8 0.99 4.32

6.98 28.78 – 32.7 37.2 24.4 13.7 9.4 9.1 19.2 17.3 11.1 16.5 15.0 13.1 0.94 10.32

5 349 0.197 5.71 72.4 42.4 22.6 10.4 5.6 4.7 15.6 14.6 7.4 11.2 11.4 8.7 0.85 15.99

46 500 – – 25.0 36.4 26.4 7.8 1.2 1.1 25.4 15.4 3.5 42.3 15.1 13.9 0.35 14.26

2438 840 4.485 – 21.7 39.3 31.4 7.9 3.2 1.6 21.2 19.4 5.7 15.7 19.1 16.4 0.59 11.15

Copyright © 2013 John Wiley & Sons, Ltd.

Irrig. and Drain. (2013)

SATURATED HYDRAULIC CONDUCTIVITY MODELS

(a)

(b) 1000

1000

R2=0.998 RMSE=6.933

2

R =0.998 RMSE=7.503 100

Ks (cm d-1)

Ks (cm d-1)

100

10

10

1

1

0.1 0.1

0.1

1

Ks (cm

10

d-1)

100

1000

0.1

model 1

Ks (cm

(c)

10

100

d-1)

model 2

1000

(d)

1000

1000

R2=0.998 RMSE=8.006

2

R =0.996 RMSE=43.904

100

Ks (cm d-1)

100

Ks (cm d-1)

1

10

10

1

1

0.1

0.1 0.1

1

10

100

1000

Ks (cm d-1) model 3

0.1

1

10

100

1000

Ks (cm d-1) model 4

Figure 1. Observed versus estimated Ks values after the recalibration procedure for (a) model 1 (Equation 11), (b) model 2 (Equation 12), (c) model 3 (Equation 13) and (d) model 4 (Equation 14) using the pooled data of Carsel and Parrish (1988) and Schaap et al. (1998)

probably due to over-fitting. Model 2 has more parameters and this increases its fitting ability, but when the observations are few during calibration the model may describe the random error of the data instead of the underlying relationship. The calibration procedure was performed again using both data sets in order to improve the prediction ability of the four models for a wider range of soils. The final recalibrated forms of the four models are the following: Ks ¼ 5:69f ð30:08f Þ ðmodel 1Þ Ks ¼ 1632:5jSi jð3:9f Þ

ð30:9f Þ

(11) ðmodel 2Þ

(12)

Ks ¼ 79:73  103 ys a2 ðmodel 3Þ

(13)

Ks ¼ 3:65  106 ðys  yr Þ4:9 a2 ðmodel 4Þ

(14)

Ks is the saturated hydraulic conductivity (cm d-1), f = aΦe where Φe is the effective porosity (cm3 cm-3) and a is the shape parameter of the van Genuchten model (cm-1), ys is Copyright © 2013 John Wiley & Sons, Ltd.

the volumetric water content at saturation (cm3 cm-3), yr is the residual water content (cm3 cm-3). The comparison between the pooled Ks data of Carsel and Parrish (1988) and Schaap et al. (1998) versus the estimated Ks of each model and their respective statistical tests are given in Figure 1. According to the statistical tests, the fitting ability of the models followed the order: model 2 > model 1 > model 4 > model 3.

CONCLUSIONS The results of this study showed that the ability of the Kozeny–Carman equation to determine the saturated hydraulic conductivity was improved using the effective porosity Φe, the van Genuchten model parameter a, the slope Si of the water retention curve at the inflection point and the function f (f = aΦe) as exponent. The use of the proposed models indicates the need to optimize the description of macroporosity attributes through the water retention curve using the van Genuchten model parameters. The two models showed higher fitting ability and higher prediction accuracy during the calibration and validation procedure, Irrig. and Drain. (2013)

V. G. ASCHONITIS AND V. Z. ANTONOPOULOS

respectively, in comparison to the Guarracino (2007) and Mishra and Parker (1990) models, setting a new approach for the indirect determination of Ks using only data from the water retention curve. Finally, a recalibration procedure of the four models was performed using both data sets of Carsel and Parrish (1988) and Schaap et al. (1998) in order to improve the predictive ability of the models for a wider range of soil types, with the aim of being useful for future studies.

REFERENCES Ahuja LR, Naney JW, Green PE, Nielsen DR. 1984. Macroporosity to characterise spatial variability of hydraulic conductivity and effects of land management. Soil Science Society of America Journal 48: 699–702. Aimrum W, Amin MSM. 2009. Pedo-transfer function for saturated hydraulic conductivity of lowland paddy soils. Paddy Water Environment 7: 217–225. Aimrum W, Amin MSM, Eltaib SM. 2004. Effective porosity of paddy soils as an estimation of its saturated hydraulic conductivity. Geoderma 121: 197–203. Antonopoulos V, Wyseure G. 1998. Modeling of water and nitrogen dynamics on an undisturbed soil and a restored soil after open-cast mining. Agricultural Water Management 37: 21–40. Aschonitis VG, Kostopoulou SK, Antonopoulos VZ. 2012. Methodology to assess the effects of rice cultivation under flooded conditions on van Genuchten’s model parameters and pore size distribution. Transport in Porous Media 91: 861–876. Carsel RF, Parrish RS. 1988. Developing joint probability distributions of soil water retention characteristics. Water Resources Research 24: 755–769. Dexter AR. 2004. Soil physical quality: Part I. Theory, effects of soil texture, density, and organic matter, and effects on root growth. Geoderma 120: 201–214. Flint EL, Selker JS. 2003. Use of porosity to estimate hydraulic properties of volcanic tuffs. Advances in Water Resources 26: 561–571. van Genuchten MTh. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898.

Copyright © 2013 John Wiley & Sons, Ltd.

Guarracino L. 2007. Estimation of saturated hydraulic conductivity Ks from the van Genuchten shape parameter a. Water Resources Research 43(w11502): 1–4. Guimarães Santos G, Medrado da Silva E, Leandro Marchão R, Marques da Silveira P, Bruand A, James F, Becquer T. 2011. Analysis of physical quality of soil using the water retention curve: validity of the S-index. Comptes Rendus Geoscience 343: 295–301. Han H, Giménez D, Lilly A. 2008. Textural averages of saturated soil hydraulic conductivity predicted from water retention data. Geoderma 146l: 121–128. Henderson N, Brettas JC, Sacco WF. 2010. A three-parameter Kozeny– Carman generalized equation for fractal porous media. Chemical Engineering Science 65: 4432–4442. Mishra S, Parker JC. 1990. On the relation between saturated conductivity and capillary retention characteristics. Ground Water 28(5): 775–777. Regalado CM, Muñoz-Carpena R. 2004. Estimating the saturated hydraulic conductivity in a spatially variable soil with different permeameters: a stochastic Kozeny–Carman relation. Soil & Tillage Research 77: 189–202. Saxton KE, Rawls WJ, Romberger JS, Papendick RI. 1986. Estimating generalized soil water characteristics from texture. Soil Science Society of America Journal 50: 1031–1036. Schaap MG, Leij FL, van Genuchten MTh. 1998. Neural network analysis for hierarchical prediction of soil hydraulic properties. Soil Science Society of America Journal 62: 847–855. Startsev AD, McNabb DH. 2001. Skidder traffic effects on water retention, pore size distribution and van Genuchten parameters of boreal forest soils. Soil Science Society of America Journal 65: 224–231. Timlin DJ, Ahuja LR, Pachepsky Ya, Williams RD, Gimenez D, Rawls W. 1999. Use of Brooks-Corey parameters to improve estimates of saturated conductivity from effective porosity. Soil Science Society of America Journal 63: 1086–1092. Vereecken H, Maes J, Feyen J. 1990. Estimating unsaturated hydraulic conductivity from easily measured soil properties. Soil Science 149: 1–12. Wösten JHM, Finke PA, Jansen MJW. 1995. Comparison of class and continuous pedotransfer functions to generate soil hydraulic characteristics. Geoderma 66: 227–237. Wösten JHM, Lilly A, Nemes A, Le Bas C. 1999. Development and use of a database of hydraulic properties of European soils. Geoderma 90: 169–185.

Irrig. and Drain. (2013)