evaluation of soil water retention models based on basic soil physical properties

8
Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties Jeffrey S. Kern* ABSTRACT Algorithms to model soil water retention are needed to study the response of vegetation and hydrologic systems to climate change. The objective of this study was to evaluate some soil water retention models to identify minimum input data requirements. Six models that function with various combinations of particle-size distribution, bulk density (pb), and soil organic matter data were tested using data for nearly 6000 pedons. The Rawls model, which requires particle-size distribution and organic matter data, had the lowest overall absolute value of the mean error (ME) with 0.020, 0.001, and 0.007 m 3 H 2 O m~ 3 soil for matric soil water pressures of -10, - 33, and - 1500 kPa, respectively. The Saxton model, which requires particle-size distribution data, had small MEs (0.018 and 0.007 m 3 H 2 O m~ 3 soil) for -10 and -1500 kPa matric soil water pressures, and a moderately small ME (0.017 m 3 H 2 O m~ 3 soil) at - 33 kPa. The Vereecken model, which requires pb, particle-size distribution, and organic matter data, had small MEs (0.016 and 0.009 m 3 H 2 O m~ 3 soil) at matric soil water pressures of -10 and -33 kPa, with a larger ME (0.020 m 3 H 2 O m~ 3 soil) at -1500 kPa. The remaining three models had relatively large MEs for at least two of the three matric soil water pressures. For estimating water-holding capacity only, the Saxton model is adequate. The Rawls model is recommended for characterizing the relationship of water content to matric soil water pressure. S OIL WATER RETENTION is a basic soil property that is needed for the study of plant-available water, infiltration, drainage, hydraulic conductivity, irrigation, water stress on plants, and solute movement. The spatial patterns of soil hydraulic properties are important factors for studying the response of vegetation (Neilsen et al., 1989; Neilsen, 1991) and hydrologic systems to climate change (Vorosmarty etal., 1989; Dolphetal., 1992). Soil particle-size distribution strongly affects water content at matric soil water pressures < —100 kPa and, to a lesser extent, at greater matric soil water pressures where soil structure is also important (Hillel, 1982). Soil organic matter affects water retention because of its hydrophilic character and its influence on soil structure (Klute, 1986) and Pb (Rawls, 1983). There may be no change or actually an increase in plant-available water-holding capacity with changes in soil organic matter because of complex changes in water retention at both —33 and —1500 kPa and changes in p b (Bauer and Black, 1992; Stevenson, 1974). Many studies have sought to equate water retention with other commonly measured soil properties such as particle-size distribution, p b , and organic matter because water retention is difficult and expensive to measure. J.S. Kern, ManTech Environmental Research Technology Inc., U.S. Environmental Protection Agency Research Lab., 200 SW 35th Street, Corvallis, OR 97333. The information in this document has been wholly funded by the U.S. Environmental Protection Agency (EPA) under Con- tract 68-C8-006 to ManTech Environmental Technology, Inc. It has been subjected to the agency's peer and administrative review and it has been approved as an EPA document. Received 27 May 1993. *Corresponding author ([email protected]). Published in Soil Sci. Soc. Am. J. 59:1134-1141 (1995). Despite the large number of such studies, few studies have compared the various models (Williams et al., 1992) and even fewer studies have compared models that use only particle-size distribution data or particle-size distribution data in conjunction with organic matter and Pb data. The advantages of using analytical equations in soil water studies include easy comparison of hydraulic properties of different soils and horizons, characteriza- tion of the spatial variability of soil hydraulic properties, interpolation of missing data, and appropriateness to application in unsaturated flow models (van Genuchten et al., 1991). Many models have been developed to estimate soil water retention from other soil properties including parti- cle-size distribution, particle density, pore-size distribu- tion, p b , mineralogy, and soil morphology (Rawls et al., 1991; van Genuchten and Leij, 1992). Some models have used measured water retention data to predict the entire soil moisture curve, such as the RETC (RETention Curve) model by van Genuchten et al. (1991). Other approaches have used one (Gregson et al., 1987) or two (Ahuja et al., 1985) measurements of water retention to estimate the entire soil moisture curve. Saturated water content and particle-size distribution data were used by Carsel and Fairish (1988) to develop probability distribu- tions of soil water retention. The use of measured water retention data with soil physical property data has been shown to increase model effectiveness (Rawls et al., 1982; Williams et al., 1992). Models that are based on particle-size distribution, soil oranic matter, and Pb include those by Gupta and Larson (1979), Rawls et al. (1982), and Vereecken et al. (1989). De long et al. (1983) and Rawls et al. (1982), for certain matric soil water pressures, developed water retention equations from particle-size distribution and soil organic matter. Cosby et al. (1984) and Saxton et al. (1986) developed models based on particle-size distribution only. Arya and Paris (1981) predicted soil water tension curves from particle-size distribution, p b , and particle density data. Williams et al. (1983) studied the influence of particle- size distribution, structure, and clay mineralogy on water retention. A more complete discussion of many of these models and others can be found in van Genuchten et al. (1992) and Rawls et al. (1991). The purpose of this study was to evaluate some water retention models that are based on particle-size distribu- tion, soil organic matter, and Pb, which are generally available data, to determine minimal input data require- ments. METHODS AND MATERIALS Soil Water Retention Models Six models that have relatively simple formulations and require some combination of particle-size distribution, organic Abbreviations: pb, bulk density; ME, mean error; SCS, Soil Conservation Service; 6», volumetric water content. 1134

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Page 1: Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties

Evaluation of Soil Water Retention Models Based on Basic Soil Physical PropertiesJeffrey S. Kern*

ABSTRACTAlgorithms to model soil water retention are needed to study the

response of vegetation and hydrologic systems to climate change. Theobjective of this study was to evaluate some soil water retention modelsto identify minimum input data requirements. Six models that functionwith various combinations of particle-size distribution, bulk density(pb), and soil organic matter data were tested using data for nearly 6000pedons. The Rawls model, which requires particle-size distribution andorganic matter data, had the lowest overall absolute value of the meanerror (ME) with 0.020, 0.001, and 0.007 m3 H2O m~3 soil for matricsoil water pressures of -10, - 33, and - 1500 kPa, respectively.The Saxton model, which requires particle-size distribution data, hadsmall MEs (0.018 and 0.007 m3 H2O m~3 soil) for -10 and -1500kPa matric soil water pressures, and a moderately small ME (0.017m3 H2O m~3 soil) at - 33 kPa. The Vereecken model, which requirespb, particle-size distribution, and organic matter data, had small MEs(0.016 and 0.009 m3 H2O m~3 soil) at matric soil water pressures of-10 and -33 kPa, with a larger ME (0.020 m3 H2O m~3 soil) at-1500 kPa. The remaining three models had relatively large MEsfor at least two of the three matric soil water pressures. For estimatingwater-holding capacity only, the Saxton model is adequate. The Rawlsmodel is recommended for characterizing the relationship of watercontent to matric soil water pressure.

SOIL WATER RETENTION is a basic soil property thatis needed for the study of plant-available water,

infiltration, drainage, hydraulic conductivity, irrigation,water stress on plants, and solute movement. The spatialpatterns of soil hydraulic properties are important factorsfor studying the response of vegetation (Neilsen et al.,1989; Neilsen, 1991) and hydrologic systems to climatechange (Vorosmarty etal., 1989; Dolphetal., 1992). Soilparticle-size distribution strongly affects water content atmatric soil water pressures < —100 kPa and, to a lesserextent, at greater matric soil water pressures where soilstructure is also important (Hillel, 1982). Soil organicmatter affects water retention because of its hydrophiliccharacter and its influence on soil structure (Klute, 1986)and Pb (Rawls, 1983). There may be no change or actuallyan increase in plant-available water-holding capacity withchanges in soil organic matter because of complexchanges in water retention at both —33 and —1500 kPaand changes in pb (Bauer and Black, 1992; Stevenson,1974).

Many studies have sought to equate water retentionwith other commonly measured soil properties such asparticle-size distribution, pb, and organic matter becausewater retention is difficult and expensive to measure.

J.S. Kern, ManTech Environmental Research Technology Inc., U.S.Environmental Protection Agency Research Lab., 200 SW 35th Street,Corvallis, OR 97333. The information in this document has been whollyfunded by the U.S. Environmental Protection Agency (EPA) under Con-tract 68-C8-006 to ManTech Environmental Technology, Inc. It has beensubjected to the agency's peer and administrative review and it has beenapproved as an EPA document. Received 27 May 1993. *Correspondingauthor ([email protected]).

Published in Soil Sci. Soc. Am. J. 59:1134-1141 (1995).

Despite the large number of such studies, few studieshave compared the various models (Williams et al.,1992) and even fewer studies have compared modelsthat use only particle-size distribution data or particle-sizedistribution data in conjunction with organic matter andPb data. The advantages of using analytical equations insoil water studies include easy comparison of hydraulicproperties of different soils and horizons, characteriza-tion of the spatial variability of soil hydraulic properties,interpolation of missing data, and appropriateness toapplication in unsaturated flow models (van Genuchtenet al., 1991).

Many models have been developed to estimate soilwater retention from other soil properties including parti-cle-size distribution, particle density, pore-size distribu-tion, pb, mineralogy, and soil morphology (Rawls et al.,1991; van Genuchten and Leij, 1992). Some modelshave used measured water retention data to predict theentire soil moisture curve, such as the RETC (RETentionCurve) model by van Genuchten et al. (1991). Otherapproaches have used one (Gregson et al., 1987) or two(Ahuja et al., 1985) measurements of water retention toestimate the entire soil moisture curve. Saturated watercontent and particle-size distribution data were used byCarsel and Fairish (1988) to develop probability distribu-tions of soil water retention. The use of measured waterretention data with soil physical property data has beenshown to increase model effectiveness (Rawls et al.,1982; Williams et al., 1992). Models that are basedon particle-size distribution, soil oranic matter, and Pbinclude those by Gupta and Larson (1979), Rawls et al.(1982), and Vereecken et al. (1989). De long et al.(1983) and Rawls et al. (1982), for certain matric soilwater pressures, developed water retention equationsfrom particle-size distribution and soil organic matter.Cosby et al. (1984) and Saxton et al. (1986) developedmodels based on particle-size distribution only. Aryaand Paris (1981) predicted soil water tension curves fromparticle-size distribution, pb, and particle density data.Williams et al. (1983) studied the influence of particle-size distribution, structure, and clay mineralogy on waterretention. A more complete discussion of many of thesemodels and others can be found in van Genuchten et al.(1992) and Rawls et al. (1991).

The purpose of this study was to evaluate some waterretention models that are based on particle-size distribu-tion, soil organic matter, and Pb, which are generallyavailable data, to determine minimal input data require-ments.

METHODS AND MATERIALSSoil Water Retention Models

Six models that have relatively simple formulations andrequire some combination of particle-size distribution, organic

Abbreviations: pb, bulk density; ME, mean error; SCS, Soil ConservationService; 6», volumetric water content.

1134

Page 2: Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties

KERN: SOIL WATER RETENTION MODELS BASED ON PHYSICAL PROPERTIES 1135

Table 1. The basic algorithms for the six soil water retentionmodels.

Model AlgorithmfCosbyDe Jong

Gupta-Larson

Rawls

Saxton

Vereecken

y =

9. = [a + [6, Oog S - 01)10, for S < 10'9W = [a + [fc (log S - 01)10, for S > W9, = (a x sand) + (fr x silt) + (c x clay) + (d x

soil organic matter) + (e pb)9, = a + (b x sand) + (c x sat) + (d x clay) +

(e x soil organic matter) + (/ pt,)

S, =exp[(2.302 - lnA)/B]d + (ahrr

S, = (9, - e,)/(9, - 9r)t V = matric potential (units are cm H2O for Cosby et al., 1984; kPa for

Saxton et al., 1986), y, = y at saturation, 9, = volumetric water content(m3 H2O m"3 soil), 9, = 9, at saturation, 9, = gravimetric water content(g H2O kg-' soU), S = y (bars, 1 bar = kPa/102), soil organic matter (%wt.), pb = bulk density (g soil cm'3), 9io = 9, at -10 kPa y, 9, =residual 9,, a through /are constants that are listed in Table 2.

matter, and pb data were chosen for testing with laboratorymeasurements to evaluate their effectiveness. Models that alsouse measured soil water retention have enhanced performance(Williams et al., 1992) but measured water retention data arenot generally available in soil surveys. The six models are notall of the models that use these input parameters but they aresome of the most commonly cited, as in Rawls et al. (1991,1992). The basic algorithms of the models chosen for testingare listed in Table 1 with equations or constants for the parame-ters in the algorithms in Table 2. The models selected thatare based on particle-size distribution, organic C, and pb formatric soil water pressures of —10, —33, and —1500 kPawere developed by Gupta and Larson (1979) and Vereeckenet al. (1989). The models developed by De Jong et al. (1983)and Rawls et al. (1982), which use particle-size distributionand organic matter data for these three matric soil waterpressures, were also chosen for testing. The models testedthat require only particle-size distribution as input data are theSaxton et al. (1986) model and the Cosby et al. (1984) models.

Gupta and Larson (1979) used regression analyses of datafrom 43 samples from dredged sediments and pedons from 10

locations in the eastern and central USA to derive an algorithmbased on particle-size distribution, soil organic matter, and Pband will be referred to here as the Gupta-Larson model.

The Vereecken model was formulated using stepwise multi-ple linear regression with pb, organic C, and particle-sizedistribution data from 182 horizons of 40 Belgian soil series tosolve for the parameters of the van Genuchten (1980) equation(Vereecken et al., 1989).

The De Jong model characterizes the soil moisture curvebased on particle-size distribution and organic matter data for64 samples from 32 pedons in the Canadian prairies. The DeJong algorithms describe two regression lines that intersect atthe matric soil water pressure at which it becomes more difficultto extract water with increased suction (De Jong et al., 1983).

The Rawls model was developed with a database of 5320horizons from 1323 sites in 32 states of the USA to developalgorithms based on linear regression to describe water reten-tion at 12 matric soil water pressures using particle-size distri-bution, organic matter, and pb data (Rawls et al., 1982). Sandat -1500 kPa matric soil water pressure, as well as silt andpb at -10, -33, and -1500 kPa matric soil water pressureswere not statistically significant for the Rawls model and wereleft blank in Table 2. Some of the algorithms of the Rawlsmodel were developed by adding water retention measured at—33 and/or —1500 kPa, which resulted in larger correlationcoefficients, but these algorithms were not used in this study.

Analysis of variance and multiple linear regression methodswere used for the Cosby model to derive equations of soilwater retention based on a power curve from data for 1448horizons from 35 sites in 23 states of the USA (Cosby et al.,1984). The results of the linear regression analyses for theCosby model were used in this study because the correlationcoefficients were nearly equal to the univariate regressionanalyses and linear regression was used in the developmentof three of the other five models chosen for testing.

The Saxton model was formulated using the regressionequations from the Rawls model assuming 0.66% organicmatter content to calculate water retention at 10 matric soilwater pressures for a range of soil particle size distributions(Saxton et al., 1986). The Saxton model was developed usingstepwise multiple nonlinear regression to solve for the parame-

Table 2. Parameter equations and constants for the soil water retention models basic algorithms

Model

Cosby

Waterpressure

kPaParameter equations or constants!

b = (clay x 0.157) + 3.10 (log)y, = (sand x -0.0095) + 1.540, = (sand x -0.142) + 50.5

De Jong

Gupta-Larson

Rawls

Saxton

-10-33

-1500

-10-33

-1500

a = 6.40 + (2fc = - 1.56 -

a x 103

5.0183.075

-0.059a

0.41180.25760.0260

.78 x OC) + (0.24 x clay)[0.028 (silt + clay) - (0.24 OC)]

b x 103

8.5485.8861.142b

-0.0030-0.0020

t

c x 103

8.8338.0395.766cttt

A = exp[a + (fr x clay) + (c x sand2) + (d x sand2

a-4.396

B = e + (/x6

-0.0715

clay2) + (g x sand2

c X 10-4

-4.880

x clay)d x 10-5

-4.285

6, = -42.90t = -1.12 +a x io3

4.9662.2082.228

d0.00230.00360.0050

x clay)]100

e-3.140

+ (0.55 x clay)(0.029 clay)

e x IO2

-24.230- 14.340

2.671e f

0.0317 f0.0299 J0.0158 t

/x IO-3 g x 10-'-2.22 -3.484

Vereecken 9, = 0.810 - (0.283 pb) + (0.001 clay)6, = 0.015 + (0.005 clay) + (0.014 OC)log(o) = -2.486 + (0.025 x sand) - (0.351 x clay)logOO = 0.053 - (0.009 x sand) - (0.013 x clay) + (0.00015 x sand2)

t y, = matric potential at saturation (cm H2O), 9, = volumetric water content at saturation (m3 H2O m~3 soil), 9, = residual soil water content (m3 H2Om-3 soil), Pb = bulk density, OC = soil organic C (% wt.).

t Blank values because parameter not significant at specified matric potential.

Page 3: Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties

1136 SOIL SCI. SOC. AM. J., VOL. 59, JULY-AUGUST 1995

ters in Table 2. The soil moisture curve was assumed to belinear for air-entry matric soil water pressure to -10 kPa anda separate algorithm was developed for water content for thematric soil water pressure range of -10 to -1500 kPa.

Testing of Soil Water Retention ModelsEstimated soil water content at matric soil water pressures

of —10, — 33, and —1500 kPa from the models were validatedagainst measured water content data from the USDA-SCSNational Soil Survey Laboratory Pedon Database. This data-base contains laboratory measurements for pedons sampledthroughout the USA. The SCS maintains this database ofanalyses from their laboratories at Lincoln, NE, and Riverside,CA, as well as samples from the USDA Agricultural ResearchService in Beltsville, MD. The measurements from the pedondatabase used in this study were particle-size distribution, soilorganic C, and pb with accompanying water content measuredat matric soil water pressures of -10, -33, and -1500 kPa.At the time that it was obtained (February 1991), the databasecontained data for 23874 samples from 5890 pedons withwater retention measurements for water content for at leastone matric soil water pressure of -10, -33, and -1500 kPa,particle-size distribution, organic matter, and pb data. Thetextural classes and their accompanying means and standarddeviations for organic C and pb and sample size for the data usedin this study are listed in Table 3. There were measurements ofwater content at —10 kPa matric soil water pressure for 3666samples (1028 pedons) with particle-size distribution, pb, andsoil organic C data. Measurements of water retention at —33kPa matric soil water pressure were included in the database for23642 samples (5854 pedons) with particle-size distribution,pb, and organic C data. The number of samples of measuredwater content at -1500 kPa matric soil water pressure withparticle-size distribution, pb, and organic C data was 23333(5793 pedons).

Laboratory methods used to measure the soil properties aredescribed in full by the Soil Survey Staff (1984). The pipettemethod was used to determine particle-size distribution. Bulkdensity measurements at -33 kPa water pressure were usedbecause they more closely represent field-moist conditionsthan those measured at oven dryness. Oven-dry pb tends to

overestimate pb because of sample shrinkage. In the case of425 horizons for which only oven-dry pb data were available,the pb data were adjusted using the following regression equa-tion developed from the pedon database:

Pbss = (O.SSOpboo) + 0.046(r2 = 0.89, n = 30 035 horizons)

where pb33 is pb measured water content equilibrated to —33kPa matric soil water pressure, and Phoo is pb measured afteroven drying.

The Gupta-Larson model was developed with pb measuredwith air-dried soil packed into cores and the Vereecken modelwas developed with pb measured on oven-dried cores. Neitherpb measured on air-dried cores nor pb measured on oven-driedcores were available, so pb data measured at —33 kPa wereused in this study and this inconsistency may have introducedsome error in the model evaluations.

Soil organic C on a weight basis was determined by wetcombustion with dichromate (Cr2O7~) and was converted toorganic matter content assuming that organic matter is 56%C by weight. Soil water retention values at matric soil waterpressures —10 and — 33 kPa were determined using clods ona pressure-membrane apparatus. Water retention at -1500kPa matric soil water pressure was determined on a pressure-membrane apparatus. Data quality was enhanced by the useof uniform methods among the laboratories and standardizedsampling procedures, but no quantitative statement can bemade about the data quality in terms of precision and accuracy.

The error associated with the estimation models was calcu-lated by the ME and the mean relative error of each methodat —10, —33, and —1500 kPa matric soil water pressures.The ME was calculated as the mean of the measured valuesminus the estimated values. The mean relative error was calcu-lated by the mean of the measured minus estimated valuesdivided by the measured values. The standard deviation ofeach of these measures of error was also calculated as anindication of the precision of the models. Evaluation of modelsfor this study was based on the absolute values of the meanerrors, as well as the graphical results of the measured vs.estimated values. The results for the mean relative errors are

Table 3. Textural classes with their accompanying means and standard deviations for organic C and bulk density measured or estimatedat — 33 kPa water pressure, and sample size for the data used in testing of the water retention models.

Textural class

clayclay loamcoarse sandcoarse sandy loamfine sandfine sandy loamloamloamy coarse sandloamy fine sandloamy sandloamy very fine sandsandsandy claysandy clay loamsiltsilty claysilty clay loamsilt loamsandy loamvery fine sandvery fine sandy loamTotal

Mean

0.0640.0700.0370.0770.0350.0720.0950.0590.0410.0580.0270.0380.0280.0390.0800.0780.0790.0930.0720.0340.059

Organic C

Standard deviation Mean

— g C kg-1 soil ——————— —————0.0670.0880.0600.1070.0680.0990.1140.0830.0500.0950.0310.0450.027

.32

.41

.49

.41

.53

.45

.40

.41

.53

.53

.42

.57

.530.055 1.520.095 1.360.085 1.380.089 1.400.107 1.370.106 1.480.052 1.350.066 1.43

Bulk density

Standard deviation

——— g cm"3 ————————0.170.190.240.250.150.230.220.260.140.200.130.150.170.180.170.160.150.200.240.130.16

Samplesize

25292213

117770166

21123431

30528236917

183130

1417215

166424604033

87513

57323874

Page 4: Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties

KERN: SOIL WATER RETENTION MODELS BASED ON PHYSICAL PROPERTIES 1137

Table 4. Mean error (ME), mean relative error (MRE), and their standard deviations (in parentheses) associated with water retentionestimation models.

Model-10 kPa -33kPa -1500 kPa

ME

t n = number of samples.

MRE nt ME MRE ME MRE

Cosby

De Jong

Gupta-Larson

Rawls

Saxton

Vereecken

0.042(0.162)0.001

(0.198)-0.027(0.163)

-0.020(0.173)0.018

(0.162)0.016

(0.165)

0.028(0.342)

-0.065(0.431)

-0.162(0.444)

-0.138(0.410)

-0.031(0.338)

-0.060(0.404)

3666

3666

3666

3666

3666

3666

0.029(0.065)0.065

(0.102)-0.030(0.067)

-0.001(0.078)0.017

(0.067)0.009

(0.072)

0.051(0.250)0.186

(0.326)-0.127

(0.295)-0.033(0.298)0.017

(0.260)-0.003

(0.282)

23642

23642

23642

23642

23642

23642

-0.003(0.039)0.038

(0.046)-0.064(0.045)

-0.008(0.044)0.007(0.041)

-0.020(0.050)

-0.077(0.360)0.180

(0.380)-0.507

(0.551)-0.111

(0.379)-0.014

(0.370)-0.152

(0.384)

23333

23333

23333

23333

23333

23333

presented but not discussed because they are conservativeindicators at low water contents.

RESULTS AND DISCUSSIONEvaluation of Soil Water Retention ModelsThe ME and mean relative error for each of the models

are presented in Table 4. The measured vs. estimatedwater retention data are plotted in Fig. 1,2, and 3 formatric soil water pressures of -10, -33, and -1500kPa, respectively. In this discussion the absolute valuesfor the MEs are used for comparison because the signindicates whether the models overestimated (negative)or underestimated (positive) water retention.

The ME of water content estimated at —10 kPa matricsoil water pressure for the De Jong model was the smallestof all the models but the standard deviation of the ME wasthe largest. There was considerable scatter in estimatedvalues from the De Jong model at -10 kPa matric soil

water pressure (Fig. 1), illustrating that the model isnot very accurate but it consistently underestimated andoverestimated the values. The Vereecken, Saxton, andRawls models had similar MEs and standard deviationsof the MEs at -10 kPa matric soil water pressure. Thelargest MEs for estimated water content at —10 kPawere calculated for the Gupta-Larson and Cosby models.Graphically (Fig. 1) the Gupta-Larson and Rawls modelsappeared to overestimate water content at >0.40 m3 tbOm~3 soil (9V) and the sign of the MEs for these modelswas negative. At measured water contents below 0.106V all of the models overestimated water content (Fig.1). The precision of the models, as indicated by thestandard deviation of the MEs, at a matric soil waterpressure of —10 kPa was similar for most of the modelsat 0.162 to 0.173 0V except for 0.198 6V calculated forthe De Jong model.

Considerably more measurements of water content at-33 kPa matric soil water pressure were available than

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Estimated water content (vol./ vol.)Fig. 1. Measured vs. estimated volumetric water contents corresponding to a matric soil water pressure of -10 kPa for the six water retention

models evaluated.

Page 5: Evaluation of Soil Water Retention Models Based on Basic Soil Physical Properties

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KERN: SOIL WATER RETENTION MODELS BASED ON PHYSICAL PROPERTIES 1139

of those models. The Cosby model truncated estimatesat 0.40 0V for both —10 and —33 kPa matric soil waterpressures (Fig. 1 and 2), presumably because the dataused to formulate the model (as summarized in Table 3of Cosby et al., 1984) had saturated water contents thataveraged 0.46 0V for all textural classes, which set theupper limit. The De Jong model exhibited a pronouncedbreak at 0.20 9V at -33 kPa matric soil water pressurein Fig. 2 that reflects its two-straight-line regressionorigin. Based on Fig. 2, the Saxton model seemed tooverestimate water retention at -33 kPa matric soilwater pressure in the high and low range of 9V, withsome underestimation in the midrange. Despite thedifferences in MEs of the various models for estimatedwater content at -33 kPa matric soil water pressure,the models had similar precision at 0.065 to 0.078 0Vexcept for the De Jong model.

The Cosby model had the smallest ME for estimatedwater content at a matric soil water pressure of —1500kPa, which was considerably better than its performanceat -10 and -33 kPa matric soil water pressures. TheRawls and Saxton model had nearly the same smallME at -1500 kPa matric soil water pressure, perhapsreflecting the common origin of the data used to derivethe models. Graphically in Fig. 3, the Saxton modelappeared more precise below 0.24 0V than the Rawlsmodel but above that water content it overestimatedwater retention, which may be due to the Rawls model'sconsideration of organic matter content. The Vereeckenmodel estimates of water retention at —1500 kPa matricsoil water pressure resulted in a relatively larger MEthan was observed for the model at matric soil waterpressures of —10 and —33 kPa with the tendency shownin Fig. 3 for overestimation. The ME and Fig. 3 showthat the De Jong model had a tendency to underestimatewater retention at a matric soil water pressure of -1500kPa while the Gupta-Larson had a stronger tendency tooverestimate water content at —1500 kPa. The precisionof the models was the greatest at -1500 kPa than forthe other matric soil water pressures as evidenced bythe small standard deviation of the MEs, which rangedfrom 0.039 to 0.050 0V.

The performance of the models at matric soil waterpressures of -33 kPa and -1500 kPa was deemed mostimportant because plant-available water-holding capacityis often calculated as the difference in soil water retainedat these two matric soil water pressures. At these twoimportant matric soil water pressures, the Rawls andSaxton models resulted in relatively small MEs. TheSaxton model was derived from data calculated usingthe Rawls model so the similarity is not surprising. Theadvantages of the Saxton model compared with the Rawlsmodel is that it requires only particle-size distributiondata and it has one algorithm to describe the range ofmatric soil water pressures from —10 to —1500 kPa.The Cosby model is less reliable than the Saxton modelfor estimating water-holding capacity because the Cosbymodel resulted in a larger ME at -33 kPa matric soilwater pressure. The Cosby model had a smaller ME ata matric soil water pressure of —1500 kPa than did theSaxton model but the water content is relatively small

at -1500 kPa matric soil water pressure. The Vereeckenmodel had a small ME at -33 kPa so it would beuseful for estimating water-holding capacity but it hadan intermediate ME at a matric soil water pressure of-1500 kPa and has the disadvantage of requiring organicmatter and pb data as well as particle-size distribution.Bulk density data are often not available and it has beenreported that Pb is difficult to reliably estimate (Manriqueand Jones, 1991). The Gupta-Larson model had the sameinput data requirements as the Vereecken model but hadconsistently large MEs, possibly due to being based on 43soil materials from only 13 pedons while the Vereeckenmodel was based on 182 horizons from 40 soil series.Both the De Jong and the Rawls models were developedusing particle-size distribution and organic C (or organicmatter) but the Rawls model had lower MEs at —33and -1500 kPa, which may be due to the much largersample size of the Rawls model database. The Rawlsmodel was formulated with data from 5350 horizons for1323 pedons from 32 states, compared with the De Jongdatabase of 64 layers from 32 pedons from the Canadianprairies. In addition to the effect of sample size, the DeJong model may have had relatively large MEs becauseit was tested in this study against data from a wide rangeof soils from throughout the USA but it was developedusing a relatively small number of soils from a singleregion in Canada.

Williams et al. (1992) tested the Rawls and Gupta-Larson models, among others, against a database of 366samples from a single soil series in Oklahoma. Theyreported that the Rawls model had very similar MEs tothis study at matric soil water pressures of -10 and-33 kPa, and a slightly smaller ME at -1500 kPa thanthis study. The MEs for water retention estimated at-10 and -33 kPa for the Gupta-Larson model werelarger than this study but the ME at -1500 kPa matricsoil water pressure was half in the Williams et al. (1992)study. The standard deviation of the MEs tended to belarger in this study than reported by Williams et al.

0.30

0.27

0.24

0.21

0.18

0.15

0.12

0.09

0.06

0.03

Organic nutter (% wt) S.4

, 3.8

..-""' / .--2.2

S = sand, LS=loamy sand, SC=sandy daySCL=sandy day loam. SL^sandy loamC=day. L l̂oam. CL=day loamSIC=silty day, SICL=sitty day loamSIL=silt loam, Si-silt

S LS SC SCL SL C L CL SIC SICL SIL SI

Textural ClassFig. 4. The interactive effects of organic matter and soil textural

classification on the water-holding capacity estimated by the differ-ence between water content at - 33 and -1500 kPa as determinedby the Rawls et al. (1982) model (dashed lines) and the Saxton etal. (1986) model (solid line).

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1140 SOIL SCI. SOC. AM. J., VOL. 59, JULY-AUGUST 1995

-1600 0.21.0 2.2 3.8 5.4 Organic matter content (% wt.)

0.1 0.2 0.3 0.4Estimated water retention (vol./vol.)

0.5

Fig. S. The interactive effects of organic matter content on the esti-mated water content of a loam soil as determined by the Rawls etal. (1982) model.

(1992), which may be caused by the much greater samplesize and wider range of soils used here.

Organic Matter Effect on Water RetentionThe effect of soil organic matter on plant-available

water-holding capacity for 12 textural classes is shownin Fig. 4, which compares estimated plant-available wa-ter-holding capacity from the Rawls model at variouslevels of organic matter with the Saxton model usingthe central values of sand, silt, and clay for the texturalclasses. Increasing soil organic matter from 1.0% to3.8% resulted in increased plant-available water-holdingcapacity of only 0.35 for the loam texture using theRawls model (Fig. 4). The reason for this small increaseis that with higher soil organic matter content, the watercontent at both —33 and —1500 kPa increased at nearlythe same rate. The effects of different organic mattercontents on a loam-textured soil as predicted by theRawls model is shown in Fig. 5. The primary differencewith different soil organic matter levels is that the matricsoil water pressure for a given water content changedconsiderably (Fig. 5). For example, the matric soil waterpressure for a loam-textured soil with 1.0% organicmatter at a water content of 0.20 6V would be —160kPa, but the same soil with organic matter content of3.8% at the same water content would have a matricsoil water pressure equal to -700 kPa. Thus, if watercontent at a given matric soil water pressure or matricsoil water pressure at a given water content is importantfor an application rather the water-holding capacity,models such as the Rawls or the Vereecken would be abetter choice than the Saxton or Cosby models becausethey consider the effects of organic matter content onwater retention.

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