modeling of soil water retention curve using soil solid phase parameters

7
Modeling of soil water retention curve using soil solid phase parameters R.T. Walczak a , F. Moreno b , C. Slawin´ski a, * , E. Fernandez b , J.L. Arrue c a Institute of Agrophysics Polish Academy of Sciences, Department of Hydrothermophysics, Doswiadczalna 4, 20-290 Lublin, P.O. Box 201, Poland b Instituto de Recursos Naturales y Agrobiologı ´a de Sevilla IRNAS-CSIC, P.O. Box 1052, 41080-Seville, Spain c Estacio ´n Experimental Aula Dei (EEAD-CSIC), Zaragoza, Spain Received 14 March 2005; received in revised form 2 March 2006; accepted 8 March 2006 Summary This paper presents the statistical–physical model (pedotransfer function) relating soil water content at defined values of soil water potential to selected parameters of soil solid phase, developed for eight arable soils representative for south-west Spain. The model contains two equations for which independent variables include the content of soil granulometric frac- tions 2.0–0.2 mm and 0.2–0.02 mm, and bulk density or total porosity. Similar correlation coefficients between measured and predicted water contents were found for both equations: 0.89 < R < 0.96 for the first and 0.88 < R < 0.96 for the second one. The model was validated for 46 Polish soils of a wide range of textures, yielding also good correlations of measured and predicted data (R values over 0.9 in both cases). That the model elaborated on the base of soil samples from mediterranean climate (Spain) was applicable for soil samples from temperate climate (Poland), proves its general usefulness for soil moisture content estimation from basic physical parameters of soil solid phase. The pre- sented model is simpler than the other commonly used ones described in the literature. c 2006 Elsevier B.V. All rights reserved. KEYWORDS Pedotransfer function; Water retention; Porosity; Bulk density; Particle size distribution Introduction Water retention is a basic hydrophysical characteristic of soil, that can be described by the dependence between soil water content and soil water potential. The knowledge of soil water retention characteristics is necessary for the study of many processes in the soil such as infiltration, drainage, solute movement and water availability for plants. The spa- tial distribution of water characteristics in the soil is also an important factor in the investigations of plant cover and hydrological changes caused by climate change (Kern, 1995; Romano and Chirico, 2004; Ronsyn, 1999; Van Genuch- ten et al., 1991; Wosten, 1997). Estimation of soil water retention curve by pedotransfer functions is very important for hydrological models describing water movement and 0022-1694/$ - see front matter c 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2006.03.005 * Corresponding author. Tel.: +48 81 7445061. E-mail address: [email protected] (C. Slawin ´ski). Journal of Hydrology (2006) 329, 527533 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol

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Page 1: Modeling of soil water retention curve using soil solid phase parameters

Journal of Hydrology (2006) 329, 527–533

ava i lab le a t www.sc iencedi rec t . com

journal homepage: www.elsevier .com/ locate / jhydrol

Modeling of soil water retention curve using soilsolid phase parameters

R.T. Walczak a, F. Moreno b, C. Sławinski a,*, E. Fernandez b, J.L. Arrue c

a Institute of Agrophysics Polish Academy of Sciences, Department of Hydrothermophysics, Doswiadczalna 4,20-290 Lublin, P.O. Box 201, Polandb Instituto de Recursos Naturales y Agrobiologıa de Sevilla IRNAS-CSIC, P.O. Box 1052, 41080-Seville, Spainc Estacion Experimental Aula Dei (EEAD-CSIC), Zaragoza, Spain

Received 14 March 2005; received in revised form 2 March 2006; accepted 8 March 2006

Summary This paper presents the statistical–physical model (pedotransfer function) relatingsoil water content at defined values of soil water potential to selected parameters of soil solidphase, developed for eight arable soils representative for south-west Spain. The model containstwo equations for which independent variables include the content of soil granulometric frac-tions 2.0–0.2 mm and 0.2–0.02 mm, and bulk density or total porosity. Similar correlationcoefficients between measured and predicted water contents were found for both equations:0.89 < R < 0.96 for the first and 0.88 < R < 0.96 for the second one. The model was validatedfor 46 Polish soils of a wide range of textures, yielding also good correlations of measuredand predicted data (R values over 0.9 in both cases).

That the model elaborated on the base of soil samples from mediterranean climate (Spain)was applicable for soil samples from temperate climate (Poland), proves its general usefulnessfor soil moisture content estimation from basic physical parameters of soil solid phase. The pre-sented model is simpler than the other commonly used ones described in the literature.

�c 2006 Elsevier B.V. All rights reserved.

KEYWORDSPedotransfer function;Water retention;Porosity;Bulk density;Particle size distribution

0d

Introduction

Water retention is a basic hydrophysical characteristic ofsoil, that can be described by the dependence between soilwater content and soil water potential. The knowledge ofsoil water retention characteristics is necessary for the study

022-1694/$ - see front matter �c 2006 Elsevier B.V. All rights reservedoi:10.1016/j.jhydrol.2006.03.005

* Corresponding author. Tel.: +48 81 7445061.E-mail address: [email protected] (C. Sławinski).

of many processes in the soil such as infiltration, drainage,solute movement and water availability for plants. The spa-tial distribution of water characteristics in the soil is also animportant factor in the investigations of plant cover andhydrological changes caused by climate change (Kern,1995; Romano and Chirico, 2004; Ronsyn, 1999; Van Genuch-ten et al., 1991; Wosten, 1997). Estimation of soil waterretention curve by pedotransfer functions is very importantfor hydrological models describing water movement and

.

Page 2: Modeling of soil water retention curve using soil solid phase parameters

528 R.T. Walczak et al.

balance in soil profiles, agricultural fields, watersheds aswell as in the geographical regions (Henric et al., 1996; Hut-son and Cass, 1987). Pedotransfer functions available in theliterature mostly refer to the soils from regions of temperateclimate and these do not work properly for tropical soils(Tomasella and Hodnett, 2004; Wosten and Nemes, 2004).

The determination of soil water retention curves is timeand work consuming. Therefore, the important efforts arebeing undertaken to develop models describing the relation-ship between water potential and soil water content fromthe soil properties routinely measured in the laboratory(Assouline et al., 1998; Campbell and Shiozawa, 1994; Rajkaiet al., 2004; Williams et al., 1992). In these models most fre-quently used are particle size distribution, bulk density andorganic matter content (De Jong et al., 1983; Gupta and Lar-son, 1979; Rawls and Brakensiek, 1982; Rawls et al., 1991;Vereecken et al., 1989). At times, granulometric composi-tion is used alone (Ahuja et al., 1985; Cosby et al., 1984;Gregson et al., 1987; Haverkamp and Parlange, 1986) oradditionally soil particles density (Arya and Paris, 1981), soilstructure and mineralogical composition of clays (Williamset al., 1983). There are few cases in which soil structureparameters such as bulk density and pore size distributionare used in the models. Some experimental values of watercharacteristics are also used for the estimation of soil waterretention curves. They include the water content under com-plete saturation, water content at selected soil water poten-tial values and amount of water available for plants (Carseland Parrish, 1988; Reeve et al., 1973; Rivers and Shipp,1978). More recently, fractals are used in modeling (Birdand Dexter, 1997; Bird et al., 1996; Comegna et al., 1998;Kravchenko and Zhang, 1998; Perfect et al., 1996) and artifi-cial neural networks (Pachepsky et al., 1996; Pachepsky andSchaap, 2004; Schaap et al., 1998; Tamari et al., 1996).

During the last 20 years many pedotransfer functionshave been developed (Gupta and Larson, 1979; Rawls andBrakensiek, 1985; Vereecken et al., 1989; Walczak, 1984;Walczak et al., 2002). Many of them were tested with inde-pendent field and laboratory data sets (Cornelis et al., 2001;Hennings et al., 1996; Kern, 1995; Rajkai et al., 2004; Ron-syn, 1999; Wagner et al., 1998, 2001; Walczak et al., 2002;Williams et al., 1992). Hennings et al. (1996) assumed thatthese functions must be tested on the basis of data mea-sured for local soils to avoid repetition and find the bestestimation. The compendium of knowledge about pedo-transfer function developed up to now is presented by Pac-hepsky and Rawls (2004) in their book ‘‘Development ofPedotransfer Functions in Soil Hydrology’’.

The aim of this work was to elaborate a statistical–phys-ical model of retention curve (pedotransfer function) basedon minimal number of soil physical parameters for soils frommediterranean climate (Spain) and to test its validity fordifferent soils from the region of temperate climate (Po-land) as well as to compare the elaborated model with theother similar models well known from the literature.

Materials and methods

The investigated eight soil profiles are located in the prov-ince of Seville, and represent a wide range of textures.These soils are classified (Soil Taxonomy) as Xerofluvent,

Rhodoxeralf, Pelloxerert, Arent and Fluvaquent (Arrue,1976). Soil samples from particular genetic horizons weresampled into 200 cm3 steel cylinders of 4 cm height, attwo water content levels – the field water capacity (in Jan-uary–February) and permanent wilting point (in August–September). Sampling was carried out at 10 cm depth fromthe soil surface down to 1 m. Four replications were used ineach soil profile and depth. Altogether the first dataset of74 samples comes from soils at permanent wilting pointand the second dataset of 61 samples, from soils at fieldwater capacity.

The following properties were determined in thelaboratory:

– Particle size distribution (sand (F1): 2.0–0.2 mm, silt(F2): 0.2–0.02 mm, clay (F3): 0.02–0.002 mm and colloi-dal fraction (F4) <0.002 mm) was determined by thechain hydrometer (De Leenheer et al., 1965).

– Bulk density from the mass:volume ratio of soil cores ofcylindrical shape (8-cm diameter and 4-cm height).

– Total soil porosity from the soil bulk density and soil par-ticle density and additionally from moisture retentioncharacteristic curves.

– Moisture retention characteristic curves by suctionmethod in fritted-glass plates (Vomocil, 1965) and byexternal pressure in ceramic plates (Richards, 1948).The moisture content was measured for the followingwater potentials: �0.1 kPa – pF 0; �0.32 kPa – pF 0.5;�1 kPa – pF 1; �1.96 kPa – pF 1.3; �3.2 kPa – pF 1.5;�9.8 kPa – pF 2; �31 kPa – pF 2.5; �490 kPa – pF 3.7;�1470 kPa – pF 4.2.

– Soil organic carbon according to Walkley and Black(1934).

– Total CaCO3 following Demolon and Leroux (1952).

Data processing

The both datasets were subjected to statistical analysis. Tocheck the possibility of combining the datasets into onedatabase it was necessary to test if, from the statisticalpoint of view, there were no differences between mean val-ues of parameters belonging to each dataset. The followingparameters were considered: total porosity obtained fromthe bulk density and particle density – P1tot (% vol.), totalporosity obtained from retention curve – P2tot (% vol.), bulkdensity – Bd (g cm�3), percentage content of fractions:2.0–0.2 mm – F1 (%); 0.2–0.02 mm – F2 (%); 0.02–0.002 mm – F3 (%); <0.002 mm (%), organic carbon content– C (%), CaCO3 content – CaCO3 (%), pH (H2O), geometricalsurface area of soil particles – Sg (cm2 g�1) and meanweight statistical diameter of soil particles – D (mm).

The first step of statistical analysis was to test if eachparameter distribution may be considered as a normal dis-tribution. The test, based on the Kolmogoroff–Smirnoffprocedure showed that each parameter distribution maybe considered as normal. The test of t-Student was per-formed for independent samples for checking if there wereno differences between mean values of investigated param-eters. At the significance level equal to 0.05 there was nobasis for rejection of the hypothesis of equality of mean

Page 3: Modeling of soil water retention curve using soil solid phase parameters

Table

1Coefficients

ofco

rrelationbetw

eenwaterco

ntentva

luesat

give

nwaterpotential

and

selected

param

eters

ofsoil

structure

(letters

inbold

markco

efficients

statisticallyva

lid)

Waterpotential

(kJm�3)

Param

eter

C(%)

CaC

O3(%)

P1 t

ot(%

vol.)

F1(%

vol.)

F2(%

vol.)

F3(%

vol.)

F4(%

vol.)

pH(H

2O)

S g(cm

2g�

1)

Bd(g

cm�3)

D(m

m)

0.1

0.01

0.59

0.92

�0.35

�0.55

0.63

0.39

0.39

�0.44

�0.93

0.44

0.3

0.03

0.59

0.92

�0.36

�0.56

0.63

0.41

0.40

�0.45

�0.93

0.46

10.05

0.60

0.91

�0.38

�0.59

0.65

0.44

0.41

�0.47

�0.93

0.49

20.07

0.60

0.90

�0.39

�0.62

0.67

0.48

0.44

�0.49

�0.92

0.52

3.16

0.09

0.59

0.89

�0.41

�0.66

0.69

0.52

0.47

�0.52

�0.91

0.56

9.81

0.22

0.59

0.80

�0.54

�0.76

0.75

0.67

0.54

�0.66

�0.82

0.71

310.28

0.54

0.71

�0.56

�0.83

0.77

0.76

0.57

�0.69

�0.74

0.80

250

0.19

0.43

0.50

�0.51

�0.83

0.67

0.83

0.61

�0.65

�0.53

0.85

1500

0.18

0.40

0.52

�0.50

�0.84

0.66

0.83

0.62

�0.64

�0.54

0.85

Modeling of soil water retention curve using soilsolid phase parameters 529

values of parameters belonging to a particular dataset. Onthis basis, one can say that both sets of parameters areequal in the statistical sense and the values of the parame-ters were independent of the soil water content during sam-pling. A significant difference between mean values wasfound only for total porosity obtained from retention curve.Mean value of total porosity obtained from retention curvefor dry soil samples was 52 (% w/w) and for samples taken atfield capacity condition was 47.86 (% w/w). This differenceis statistically valid and it is probably due to air closing inpores for samples taken at field water capacity. Becauseof this, the total porosity value obtained from moisture–retention curve characteristics was rejected from both setof parameters. Finally, both sets of parameters weremerged into one database with 135 samples. Using this data-base the statistical analysis was carried out for the con-struction of the correlation model for the prediction ofthe retention curve.

The first step was to calculate partial correlation be-tween water content h (w/w) and the investigated soilstructure parameters. The calculated partial correlation be-tween the water content values at the analyzed values ofthe soil water potential and the chosen parameters of thesoil solid phase are presented in Table 1. To create a spe-cific statistical–physical model, a sub-set of parameterswas selected on the basis of the following criteria: thereis relatively high value of correlation coefficient betweena chosen soil solid phase parameter and the value of watercontent and no functional or statistical dependence existsbetween the physical parameters of soil solid phase chosenfor model creation. Therefore, the following two equationsof linear multiple regression were created:

h1P ¼ a0 þ a1F1þ a2F2þ a3P1tot ð1Þ

h2P ¼ b0 þ b1F1þ b2F2þ b3Bd ð2Þ

where h1P and h2

P are the predicted water content (% w/w).The parameters of both equations are presented for investi-gated values of water potential in Tables 2 and 3. In bothequations, the parameters of the soil solid phase are statis-tically valid at the significance level 0.05. The obtained cor-relation coefficients (0.88 < R < 0.96) are relatively high.

Model validation

Total number of 46 soil samples from Poland were used forvalidation of the elaborated model and for comparisonwith other models. Their basic properties are presented inTable 4. The soil samples were takenwith preservation of ori-ginal structure into cylinders of 100 cm3 volume (height5 cm). The characteristics of soil water potential–soil watercontent, i.e. soil water retention curves, were determinedduring the drying process, for soil water potentials:�0.1 kPa – pF 0; �1 kPa pF 1; �3.2 kPa – pF 1.5; �9.8 kPa– pF 2; �31 kPa – pF 2.5; �490 kPa – pF 3.7; �1470 kPa –pF 4.2 using low and high pressures (Richards, 1948).

Using soil properties dataset the elaborated model wastested and compared with well established pedotransferfunctions of Gupta and Larson, Rawls and Brakensiek,Vereeken and Walczak (Gupta and Larson, 1979; Rawls andBrakensiek, 1985; Vereecken et al., 1989; Walczak, 1984;Walczak et al., 2002). In Fig. 1, the measured values of

Page 4: Modeling of soil water retention curve using soil solid phase parameters

Table 2 Values of coefficients of Eq. (1)

Water potential (kPa) Coefficients

a0 a1 a2 a3 R

0.1 �17.18 �0.121 �0.0727 1.184 0.940.32 �16.146 �0.132 �0.08 1.159 0.941 �14.207 �0.144 �0.093 1.115 0.941.96 �11.783 �0.153 �0.109 1.057 0.943.2 �8.698 �0.161 �0.124 0.975 0.959.80 2.207 �0.312 �0.192 0.736 0.9631 10.395 �0.337 �0.265 0.543 0.96490 20.506 �0.289 �0.297 0.159 0.891470 16.849 �0.259 �0.278 0.187 0.89

Table 3 Values of coefficients of Eq. (2)

Water potential (kPa) Coefficients

b0 b1 b2 b3 R

0.1 103.04 �0.0968 �0.0578 �45.36 0.940.32 101.04 �0.0968 �0.0578 �44.4 0.941 99.01 �0.122 �0.0797 �42.73 0.951.96 95.54 �0.1323 �0.0965 �40.49 0.953.2 90.24 �0.1424 �0.113 �37.3 0.959.80 76.48 �0.3018 �0.1866 �27.83 0.9631 64.89 �0.3323 �0.2641 �20.3 0.96490 36.31 �0.2907 �0.3015 �5.83 0.881470 35.19 �0.2601 �0.2815 �6.7 0.88

530 R.T. Walczak et al.

water content are compared with the values estimated fromthese models for water potential from �1 to �1500 kPa. It isnecessary to mention that the number of points in particularmodels is different due to differences in the points (waterpotentials) at which the water content was measured andpredicted from particular equation. In the Gupta and Lar-son, and Rawls and Brakensiek models the organic matercontent is needed as independent variable therefore thiswas derived by multiplying the organic carbon content byfactor of 1.72 (Bauhus et al., 1998).

From Fig. 1 one can see that both equations estimatemoisture content, at different soil water potential values,with good accuracy. This is confirmed by high values ofdetermination coefficients: R2 = 0.86 and R2 = 0.81, respec-tively. This is seen that in the range of moisture content be-low 20% (vol./vol.) both equations overestimate the results,similarly as the Gupta–Larson, Rawls–Brakensiek andVerecken models. The Walczak model shows good predic-tion in this range, probably because it includes specific sur-face area responsible for water binding energy at smallvalues of water content. In the range between 20% and50% (vol./vol.) both elaborated equations gives comparableresults. Comparison of the determination coefficients ob-tained during the validation of the proposed model and coef-ficients gained from other models shows that the best fit isobtaining by Eq. (1) (R2 = 0.86) of the elaborated model.The accuracy of Gupta–Larson, Rawls–Brakensiek and Ver-eecken models is comparable that is pointed out by similarvalue of the coefficients of determination: 0.68; 0.75 and0.73, respectively. The coefficients of determination of

the Walczak model (R2 = 0.83) and Eq. (2) of the elaboratedmodel (R2 = 0.81) are similar and higher than Gupta–Larson,Rawls–Brakensiek and Vereecken models.

Due to that the Polish systematics distinguishes sand1–0.1 mm, silt 0.1–0.02 mm, clay 0.02–0.002 mm and col-loidal fraction <0.002 mm and the Spanish one sand 2–0.2 mm, silt 0.2–0.02, clay 0.02–0.002 mm and colloidalfraction <0.002 mm, it seems that the applied range of gran-ulometric fractions do not influence the accuracy of theelaborated model.

Some pedotransfer functions, for example Walczak’smodel (Walczak et al., 2004), include the specific surfacearea as a parameter strongly influencing the retention curvefor water potentials corresponding to pF values higher than2.7. However, the Spanish soils database did not containsurface areas. This was the reason that we replaced the spe-cific surface area values by the geometrical surface areathat was calculated assuming the spherical shape of soil par-ticles. The calculated geometrical surface area was in-cluded in the equations for water potential correspondingpF 3.7 and 4.2. But, the correlation coefficient increasedonly by 0.01.

Conclusions

The results obtained for very different soils, from differentgeographical regions like Spain and Poland, prove that theelaborated model is very useful for estimation of moisturecontent on the basis of selected physical parameters of soil

Page 5: Modeling of soil water retention curve using soil solid phase parameters

Table 4 Basic properties of Polish soils (dataset used for testing of the models)

Soil Sample Particle size distribution (diameter inmm) (%)a

Total porosity (vol.)b Bulk density (g cm�3)c

1–0.1 0.1–0.02 <0.02

1 35 25 40 0.380 1.812 41 27 32 0.483 1.383 44 30 26 0.378 1.804 57 15 28 0.452 1.715 30 44 26 0.455 1.376 40 30 30 0.342 1.717 33 24 43 0.455 1.578 10 45 45 0.417 1.679 35 29 36 0.378 1.80

10 42 46 12 0.444 1.5311 42 43 15 0.432 1.6012 12 58 30 0.336 1.6013 50 32 18 0.325 1.7114 44 31 25 0.396 1.8015 21 42 37 0.517 1.2616 20 35 45 0.447 1.4917 61 16 23 0.465 1.5018 45 31 24 0.400 1.8219 44 37 19 0.413 1.7220 61 16 23 0.465 1.5021 53 29 18 0.354 1.7722 71 18 11 0.400 1.7423 80 14 6 0.426 1.4724 75 19 6 0.459 1.4825 3 54 43 0.400 1.6026 2 61 37 0.438 1.5127 2 61 37 0.486 1.5228 4 60 36 0.497 1.4229 5 58 37 0.486 1.2830 1 60 39 0.467 1.6131 8 58 34 0.482 1.4632 28 52 20 0.415 1.6633 8 50 42 0.494 1.4134 22 26 52 0.514 1.3935 67 22 11 0.475 1.4436 63 17 20 0.494 1.3037 4 50 46 0.487 1.3938 65 15 20 0.432 1.6039 1 67 32 0.488 1.3240 5 55 40 0.513 1.2541 1 36 63 0.503 1.2942 20 38 42 0.448 1.1243 8 35 57 0.437 1.4144 34 42 24 0.414 1.3845 33 50 17 0.419 1.5546 13 37 50 0.415 1.66a Sedimentation (areometric) method.b Mercury porosimeter.c Oven-dried soil at 105 �C.

Modeling of soil water retention curve using soilsolid phase parameters 531

solid phase. The model presented in this study is simplerthan other – commonly used – models described in theliterature.

On the basis of statistical analysis and validation proce-dure for measured and calculated water retention curvesit was found that:

Page 6: Modeling of soil water retention curve using soil solid phase parameters

Figure 1 Measured vs. predicted volumetric water contentcorresponding to a matric soil water potential of �1500 kPa forthe six water retention models.

532 R.T. Walczak et al.

– It is possible to elaborate pedotransfer model for the pre-diction of the water retention curve with acceptableaccuracy using only three easily measurable soil physicalparameters,

– The comparison of the elaborated model (Eqs. (1) and(2)) with other well known models: Gupta–Larson,Rawls–Brakensiek, Vereecken and Walczak, shows thatthe best fit between measured and predicted water con-tent is obtained by Eq. (1) (R2 = 0.86) of the proposedmodel, while the Walczak model and Eq. (2) of the pro-posed model gives comparable results (R2 = 0.83 andR2 = 0.81, respectively). The coefficients of determina-tion of Gupta–Larson, Rawls–Brakensiek and Vereeckenmodels are 0.68; 0.75 and 0.73, respectively, and theseare lower than coefficients of determination of the pro-posed model.

– The model for retention curve prediction, elaboratedwith the use of soil physical parameters of mediterraneansoils, works with acceptable accuracy also for soils oftemperate climate regions,

– The model validation shows that particle size distributionused in the Spanish and the Polish systematics can beapplied in an exchangeable manner, although soil parti-cle size fractions are different.

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