0038-075C/96/16112-832-845$03.00/0
Soil Science

TECHNICAL ARTICLESESTIMATION OF WATER-RETENTION CHARACTERISTICS
FROM THE BULK DENSITY AND PARTICLE-SIZE
DISTRIBUTION OF SWEDISH SOILS
KLlmin Rajkai’, SBndor Kdbos’, M. Th. Van G enuchter?, and Per-Erik Jarwon
A Swedish soils database containing soil-water retention data, particlesize fractions, dry bulk density, and organic matter content, was analyzed
in order to find a relatively simple predictor of the soil-water retention
curve (SWRC). As a SWRC model we chose a three-parameter function
selected from nine van Genuchten-type retention models that were fitted
to the measured retention data by nonlinear parameter optimization. Cumulative particle-size (CP) data were described by a logistic distribution
model. Additionally, the mean and standard deviation of the CP distribution were estimated directly from the measured particle-size data. Regression equations were subsequently used to estimate the parameters inthe selected SWRC model from available soil properties, particle-size
data, and CP distribution parameters. Four alternative pedotransfer models were formulated to estimate the SWRC curve from the basic soil
properties. These models predicted the SWRC curves from either theoriginal soil data or from the CP distribution parameters. A mean estimation error of less than 2.5% was used to indicate a good estimation.
The highest ratio (67%) of good estimations and the lowest ratio (12%)
of poor estimations were obtained when both the original soil properties
and the CP model parameters were used. Our study shows that the resulting simple SWRC model gives a good description and a usable prediction of the retention properties of Swedish soils for a wide range ofsoil textures.

estimates of the water-retention
curve of soils are needed in order to model
unsaturated flow accurately. Representative databases of soil hydraulic functions are unavailable
in most countries. Direct sampling plus laboratory or field measurement of the hydraulic properties is generally too costly and time consuming and, therefore, impractical for mostapplications. Hence, methods are required forpredicting the soil-water retention characteristic

R

ELIABLE’ Research Institute for Soil Science and Agricultural Chemistry of the Hungarian
Academy of Sciences, Budapest.
2 Salinity Laboratory, USDA, ARS, Riverside, California.
3 Department of Soil Science, Swedish University of Agricultural Sciences, Uppsala
Address correspondence to K&n&n Rajkai Research Institute for Soil Science andAgricultural Chemistry of the Hungarian Academy of Sciences. 1025 Budapest,
P. 0. Box 35, Hungary.
Received May 6. 1993; accepted July 25, 1996.

8 3 2from more easily and routinely measured soil
properties.
Many attempts have been made to quantify
possible relationships between the water retention curve and other soil properties such as particle size distribution, organic matter content,bulk density, and, sometimes, cation exchange
capacity and clay mineralogy. These efforts include studies by Gupta and Larson (1979). Bloemen (1980). Urakcnsiek et al. (1981). Rajkai et
a l . (1981). Rawls a n d Brakensiek (l982). De
Jong (1983), Kritz (l983),William et al. (1983),
Wollenhaupt (l984), and Puckett ct al. (1985).
Some of these studies related specific retention
values with available soil properties, whereas
others estimated the retention curve by relating
the unknown parameters in a specific retentionfunction to the available data. Several empiricalretention functions are available for this purpose

V O L. 161 ~No. 1 2

E STIMATION OF WATER RETENTION C U R V E S(e.g., Brooks and Corey 1964; King 1965; Brutsaert 1966; Visser 1968; Laliberte 1969; Rogowski 1971; Ahuja and Swartzendruber 1972;
van Genuchten 1980). Different retention models were tested for Belgian soil by Vereeken et al.
(1989). McCuen et al. (1981) related parametersin the Brooks and Corey function in this manner to different textural classes. Madankumar(1985) correlated the parameters in the exponential function by Campbell (1974) with bulk
density and sand, silt, and clay fractions. Rawls
and Brakensiek (1989), and Vereecken et al.
(1989) similarly correlated soil water retention
parameters to soil properties. The applicability ofthese methods was tested by Tietje and Tapkenhinrichs (1993). W&ten et al (1995) derived
class and continuous pedotransfer functions forgenerating soil hydraulic characteristics.
In a different approach, Arya and Paris (1981)
predicted the soil water retention curve from particle-size distribution data, dry bulk density andparticle density. Their model was modified later
by Haverkamp and Parlange (1986), who applied
the concept of shape similarly between the retention curve and the cumulative particle-size distribution for sandy soils without organic matter.
Mishra et al. (1989), in addition, evaluated the uncertainty of the retention parameters obtained
from particle-size data.
Sweden, like several other countries, has a history of analyzing available soil water retention
data. For example, Andersson (1988) used a tangent function, Jonasson (199 1) employed different van Genuchten type functions, and Jansson(1992) applied a composite model built aroundthe Brooks and Corey function.
In this paper we test the applicability of different functions for describing the water retention prop&ties of Swedish soils. A logistic distribution function is used for describing the
cumulative particle-size fraction data of thesesoils. The selected soil water retention curve(SWRC) and cumulative particle size (CP)model parameters are then correlated to study
possible interrelationships between the water-retention and particle-size distribution curves. Empirical methods are used to derive a number ofmean and variance estimators from the particlesize data. Regression equations for the fitted
SWRC and CP models, and empirical mean andvariance estimators of the CP distribution, will
also be formulated.
THE SWEDISH SOILS DATABASEThe Swedish soil physical database contains

833

data from 2025 soil layers representing about 300
soil profiles. The data have been published by the
Swedish University of Agricultural Sciences in
Uppsala (Andersson and Wiklert 1967, 1972,
1977a, 1977b, 1977c;Wiklert et al. 1983) and areavailable in IBM PC compatible format together
with a utility program for plotting and carryingout calculations (Jansson 1992).
Water retention data in the Swedish databasewere determined on 1 O-cm-long undisturbed
soil cores having a diameter of 7 cm.The saturated water content was considered equal to total
porosity as calculated from the dry bulk density
and the particle density.Water contents at suctionsof 5, SO, and 100 cm were obtained by means ofa hanging water column. A v a c u u m pump connected to a pressure control system was used forretention measurements at 300 cm.
For the purposes of this study, we excluded
organic soils having a porosity greater than 73%
and a loss of ignition value exceeding 10%. Of
the remaining 1604 soil samples, 1 106 had six ormore measured SWRC data. Whereas the maximum number of measured SWRC values was
14, relatively few, 184 soils, had water contents
measured at the same pressure head. A subset of
the 184 samples was used for deriving an appropriate SWRC model as discussed later.This
subset involved soils having retention values atpressure heads of 1, 5, 50, 100, 300 and 15,000
cm. Once the SWRC model was selected, soils
having relatively unusual properties (e.g., thosehaving 80-cm-thick organic material a c c u m u l a tion, soils formed on glacial moraine material, or
soils having a high swelling clay content) were
excluded from the 184-sample database. The
unusual nature of the SWRC curve for thesesoils resulted in relatively high fitting errors. As
samples were excluded in the above manner, a
few soils with relatively small SWRC fitting errors were also removed.The remaining database
contained data of 156 soils. Table 1 lists themean of several soil properties for the 156 Samples as arranged in three textural groups(TK l-TK3).
Particle-size distributions in the databasewere determined using conventional methods(Ljung 1987) based o n H 2O2 pretreatment t oeliminate organic matter. Size fractions up to 60[tm were determined by pipette sampling,whereas the coarse fractions (60-200, 200-600
and 600-2000 FtIl) were obtained by wet sieving. Swedish particle-size limits differ from the
USDA standard and involve the loss of ignition
percentage. For comparability, particle-size per-

RAJKAI, KABOS,VAN GE N U C H T E N , A N D J A N S S O N

834

S O I L SCIENCETABLE 1
Average of soil properties of the data set used
Pressure head ( c m )
Case

Sand

Silt

Clay

OM

P

%

Mg/m’

3.0
2.5
2.9
3.5

1.42
1.44
1.43
1.40

%

All
TKl
TK2
TK3

6.0
10.8
5.3
2.8

65.0
80.8
67.8
46.0

29.1
8.4
27.0
51.2

1

300

15000

N

15.6
6.6
14.1
26.2

156
40
72
44

I3 (111’/111’)
46.9
45.8
46.5
48.5

36.2
28.4
37.2
41.5

TKl - TK3 are textural groups: for TK1 clay 2 15%; for TK2 clay > 15% and clay <40%; for TK3 clay I 40%.

Sample No.

Profile name

Sample No.

Profile name

l-10
20-29
40-49
62-71

Nordvik 1
Vassbo 1
Uddeholm 1
Nuntorp 1
Ryholm 2

11-19
30-39
50-61
72-81

Nordvik 2
Alvgarden 1
Apertin 1

Kungsangen

89-102109-l 18

Thorsatra 3
Tonnersa 1
Aby 1

125-129132-138
147-156

Marsta 1
Thorsatra 2
Thorsatra 5
Tonnersa 2
Ingelstorp 1

82-88
103-108
119-124130-131139-146

centages were recalculated by excluding the lossof ignition.The used particle-size limits were 2 ,6, 20,60,200,600, and 2000 pm.
The 156-element subset of Swedish soils represents a wide range of soil textures, organic matter contents, and geological origins. Clay content

Nuntorp 2

varied between 3 and 70.8%, and sand content
between 0.1 and 47.5%. Organic matter content
was calculated from the loss of ignition values asgiven in Ljung (1987).The highest organic matter content was 9.9%, and dry bulk density
ranged between 0.92 and 1.76 Mg/m’.

1.1
60

50

s
2 40
.E
z
d 30
f
e
.5
= 20
s

10
-0.1

o-

0

0.7

1.7 2.0

2.3

4.2

::
0.3

0.8

1.3

1.8

2.3

2.8 3.3

Particle-size log(pm)h log(cm)Fig. 1. Water retention characteristic curves of three soil
texture groups as described by the M8 SWRC model.
x MeankSD
a MeanZSE
I Mean‘\ TKl\ TK2. . . TK3

Fig. 2 Cumulative particle-size distribution curves ofthree texture groups as described by a logistic distribution function.
1 MeankSD
0 MeankSE,n Mean’ TK1\ TK2... TK3

E STIMATION

VOL. 161~ No.12

OF

W ATER R ETENTION C U R V E S

835

TABLE 2Models fitted to the water retention data of soils
Model
name

Numberof parameters

Ml
M2
M3

e,, e,, a, n and m
8,. Q, n and 111
e,, 8,. o and me = e,+(e,-e,)/[l+(ah)“]”8 = e,/[l+(ah)n]me = e,+(e,-er)/[l+(atl)~]~~II = 1/(1-m)
e = e,+(e, -e,)/[l+(ah)n]m” = 2/(1-m)
8 = es/[i+(ah)n]mn = 1/(1-m)
8 = es/[l+(ah)n]mn = 2/(1-m)
e = e.+(e,-e,)/[l+(ah)n]m“I= 1
8 = e,/[l+(atl)n]m
111 = 1e = l/[l+(ah)“]”“I = 1

M4
M5

M6
M7
M8
M9

Figure 1 shows the mean, standard error, andstandard deviation of the mean of the six measured retention data points of the 156 Swedish
soils. This figure also shows the fitted SWRC
curves of the separate TK1-TK3 textural groups,
and Fig. 2 illustrates the fitted CP curves for thesetextural groups.

SOIL-WATER RETENTION MODELSThe Swedish soils database was used to testnine different soil-water retention models, which
are listed in Table 2. The models were fitted tothe measured data using nonlinear least-squares
optimization (Marquardt 1963). The s u m ofsquared error (SSE) was calculated for each
SWRC model, with the degree of freedom (DF)calculated as M(N-p), where M is the number of8,. 8,. Q and nle,, cx and m8,. a and 111
8,. e,, CL and n8,. tY and ”
cx and nsamples, N is the number of retention data points,
and p is the number of model parameters (seealso Table 2).The overall SSE of the nine SWRC
models (Ml to M 9 in Table 2) as fitted to the six
retention data points of all soil samples are given
in Table 3. Models M2 to M9 in Table 2 may be
regarded as special forms of Ml, assuming specific restrictions (e.g., 0, = 0 for M2); therefore,
the F-test can be carried out for model M, (i = 2
to 9). Model M, was accepted if the critical valueof the F distribution having degrees of freedom(DF,-IIF,, DF,) exceeded the F-ratio:
F=(SSE, - SSE,)IlF,
SSE,(IX, - DF,)T h e fitting error of the five-parameter v a n
Genuchten model (Ml) was compared with

SSE
_____

184
184
184

184
184
184
184
184
184

993.2
999.2
2207.22984.9230 I .6

3039.81214.21459.99148.7

P

184

368
368
368
552
552
368
552
736

0.006

1.222
2.005
0.659
1.030
0.223
0.235
2.737

1 .000

0.087

0.000
1 .OOO
0.413
1 .OOO
1 .0000.000

Parameter v a l u e and standarderror of the SWRC model

Sample
group

All
TKI
T K 2
TK3

es*

*

WUII(

~~ncncSE ,riO,

SI: I1\U,,,-.--__

47.2

0.0007’~(I.47 I!,O.(,OO.OOOll3

0.022

**

48.3

0.00196

0.58310.60

0.00073

*
*
*
*
**
*
**

46.2
47.8
46.0
47.0
48.8
51.0

0.001430.006460.000290.00~158
0.00005
0.001114

0.59720.7374
0.53660.58050.39250.44731.01

0.000220.002730.000030.0001 5
0.00001
0.00004

0.021
0.047
0.046
0.027
0.025
0.046
0.030

1 .04
0.59
0.74

1 .04
1.73

N

SE wu I,(
I56
40
72
44

Parameter value and standard
error of the CP model_-.___
Au
TKl
TK2
TK3

*
**
*
**
*
**
*
**

a< 0

? ,I

SE of 0, ,sSE of II, ,I

8.45
20.92
43.32
59.67
7.35
10.65
2.00
2.49

0.71201.0715
1.1 I44
1.57100.8056(I.97040.700’)
0.7829

0.391
2.690
2.251
11.5500.289
I.180
0.1 17
0.290

0.024
0.044
0.05x
0.1 I70.0026
0.037
0.020
0.043

N
156
40
72
44

-

*Parameter values of group f i t t i n g .
**Mean of parameter values optimized for data of soil samples separately.

those of the other models (M2 to M9) by using

the above F-test.
Results of the F-test (Table 3) show that the
four-parameter M4 and the two-parameter M9models were significantly worse than the otherfunctions. Of the six functions that fitted the retention data as well as the five-parameter van
Genuchten model (the M2, M3, M5, M6, M7,
and M8), the three-parameter M8 function was

60 ,

I

Apertin 1. 10-20 cm

1

50

OM= 4.5 %selected for further study.This function will now
be referred to as the SWRC model.
In order to determine one general SWKC
curve for each soil textural group, the selected M 8
SWKC model was fitted to all retention data i neach TK group by nonlinear regression using theStatistica package (Statistica 1994).This fitting procedure, referred to as group fitting. produced the
SWRC curves shown in Fig. 1. Parameter values of

1,1 i-

I

Apertin 1. IO-20 cm
OM=4.5 %CP model

4 0
SWRC model
I
a 3 0
8
j 20.
sz

SSE= 22.6
u,,=l6.3

SSE=1.74

n&J.93as*~I es=2369 123.5
n,~pos439

t o

0:
2
4
3
0
1
h log(cm)Fig. 3a Water retention curve of a typical Swedlsh soil.
- Fitted SWRC model A Measured SWRC data

J
1

1.5

2

2.5

3

3.5

Particle-size log(pm)Fig. 3b Cumulative particle-size distribution curve of atyplcal Swedlsh soil.
- Fitted CP model A Measured CP data

V O L. 161 ~ No. 12

ESTIMATION OF W A T E R R E T E N T I O N C U R V E S

837

TABLE 5
Errors of thr SWRC and pedotransfrr models
156

Estimation errors

SE of
ME

Mean
SSE

Z SSE
i=1

6.0

931.0

75.8

11819.9

57.6

8982.372.511303.1

Fitted S WRC model

0.67
-0.56
-0.29
-0.14
0.36
-0.01

0,

ej
ei,,

e
e ,I”,eII”>

lS,YY,-0.09-1.10- 1 .09
-0.76
0.1 I

0.90

0.07
0.08
0.08
0.06
0.09
0.05
El model
0.11
0.20

0.29
0.32
0.37
0.28
E2 model

0.02
-1.34
- 1 .00
-0.70
0.15
0.47

0.10

0. IO
0.26
0.27
0.30
0.27
E3 model0.08- 1.24
-0.74
-0.42
0.36
0.12

0.16
0.21
0.28

0.30
0.30
0.36
E4 model

-0.04
-1.41
- I .03

0.11
0.19

-0.72
0.1 1

0.31

0.86

the group-fitted SWRC curves, as well as themean parameter values of the M 8 SWRC model
fitted to retention data of each soil sample separately are given in Table 4.The same technique will
be used below for t h e cumulative particle-size
curves.
Figure 3a shows a typical example of the observed and fitted retention curves. Fitted parameter values and their standard deviations obtainedby group a n d individual fitting of the M8 SWRC
model are listed in Ta ble 4. Results indicate that
the SWRC parameter a increases from clay to the73.5

11471.11

0.28
.

0.37
0.29

sand texture group, whereas the opposite is true
for the parameter n. Relatively large values for o!
and n are characteristic of the coarse-textured soils,
whereas the opposite is the case for the clay category (fine-textured soils).Values for n and IX for thesilt category are in-between those of the s a n d andclay groups. These results reflect the fact that water
retention values at 3 given pressure head are lower,
and the SWRC curves are steeper, for coarse-textured compared with fine-textured soils.
Table 5 shows the mean error of the fitted
SWRC model at each pressure head. The selected

838

RAJKAI, KABOS, VAN GENUCHTEN,AND JA N S S O N

M8 SWRC model generally overestimated water
retention at saturation (h = 1 cm) and at field capacity (h = 300 cm), whereas it underestimatedretention at 5, 50, and 100 cm pressure heads.
Still, the suitability of the chosen three-parameter
function for describing Swedish SWRC data is
indicated by the relatively small values of themean SSE in Table 5.
CUMULATIVE PARTICLE-SIZE
DISTRIBUTION ANALYSIS
A two-parameter function was used to describe
the cumulative particle-size (CP) data as follows:
F(d) = 1 / (I + (%P /d)“CP(1)

where F is the cumulative particle-size fraction, dis the particle diameter (mm), and ~lcp and flcp
are fitting parameters. The parameter a in the
SWRC model (see Table 2) is marked as aswKc,
and in the CP function as c&. Similar subscripts(SWRC and CP) are used for the parameter n.
Notice that Eq. (1) can be rewritten as:
F(X) = 1 / (1 + e -((+))(2)

where x = 111((r). The function F(x) defined by
Eq. (2) is known as the logistic probability distribution function (e.g., Johnson and Kotz 1970).
The parameters in Eq. (1) and Eq. (2) are related
as follows:a = ln(a,p)

6 = l/rr,,

The above relationships suggest that parameters in Eq. (1) carry information about the particle-size distribution. This connection was previously shown to hold by Campbell (1985) andlater used by Haverkamp and Parlange (1986) intheir analysis of shape-similar SWRC and CP
distributions.
Without having to invoke a particular function, one can estimate the distribution parameters directly from the CP data. The idea stems
from previous parameter estimation methods
using the method of moments (e.g., Ledermann
1984) and is described in Appendix 1. The estimation procedure in Appendix 1 is ‘model-freesince the method depends only on the observed
distribution and not on the model used to describe the data. We also estimated the mean
(DG) and the standard deviation (KG) of theparticle-size distributions from the sand, silt, andclay fractions, as was done previously by Campbell (1985).
The logistic distribution (Eq. (1)) was previously considered suitable for about half of the

S OIL S C I E N C E

soils in the USDA triangle (Buchan 1989). Figure 2 shows the distribution function fitted toparticle-size data of the three TK groups. A typical example of the CP model fitted to soil texture data is given in Fig. 3b.The percentage ofpoor fits of the CP model to the total number of
CP data sets was found to be 12%. From this weconcluded that the logistic model is useful forthe majority of Swedish soils. An advantage ofusing the logistic distribution model is that thismodel yields estimates directly for the parameters acp, which reflects the modal particle-size,
and nCPI which gives the standard deviation of
the CP distribution. Table 4 indicates that theacp and r~,, parameter values are characteristic
for the different TK groups.The acp and )I,:, parameter values are becoming larger from clay tosand, again showing that the modal particle-sizeand the slope of the distribution are higher forcoarse-textured materials (Fig. 2). The texturedependent behavior of the SWKC model (Fig.
1) is used below for predicting SWRC parameters from selected soil properties and CP distribution parameters.
PEDOTRANSFER FUNCTIONSParameters in the M8 SWRC model werecorrelated with the original soil properties alone,
and together with the particle-size distribution
parameters, using step-wise linear regression
analysis.The log transform of the OL values werealso used in the analysis.
In the regression analysis, the M8 SWRC
model parameters were taken as the dependent
variables. The independent variables werearranged in four groups.The first set of predictor
variables (El) was formed by the original soil
properties. The second set (E2) considered theparameters in the CP model in addition to thosein El. The third set (E3) included the LTE andLTD empirical mean and variance estimators, inaddition to those of El. Finally, the fourth set(E4) contained the DG and RG parameter values
and those in El .The obtained pedotransfer functions are summarized. in Table 6.
The accuracy of the different pedotransfer,
SWRC, and CP models was tested by calculating
the SSE of the fit using the measured soil-water
retention or CP data. Absolute values of theresidual of the moisture content (denoted by IEl
and expressed in volumetric percentages) wasused for evaluating the accuracy of the different
pedotransfer models (El to E4). First, [El was calculated separately for each of the six retention
data, and next the mean was taken of the six /ElV O L. 161 ~No. 12

E S T I M A TI ON

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839

W A T E R R E T E N TI O N C U R V E STABLE 6
Pedotransfer functions for parameters in thr M8 SWRC model

p. S 1. OM
PO,:I., OM

C

p. LTE, OM
C
p, IX, OM
IS

8, = I1 1.5-4O.O*p-8.1*1+14.9*s-0.74’0M0, = 107.6 -38.5*p-O.S*OM-3.7%1(C)+o.l*cx~p0s = 106.9-39.6’p-O.68*0M+2.47*LTE+5.27%(C)8, = 111,1-38.O’p- 15.0*1+184.2*DC-0.48’OM- 16.8*SIn(u,wac:) = -7.3-3.5*p-O.8’1n(C)+lO.2*S+3.7*1h+Y ,,“,,,)=-2.27-3.s*p+o.o27’~~,~-4.9*c

0.83

El

156

0.85

E2

156

0.84

E3

156

0.85

E4

156

0.60

El

156

0.61

E2

156

0.58

E3

156

0.61

E4

156

0.41

El

156

0.66

E2

156

0.64

E3

156

0.41

E4

156

USWKC
LTLp

IX.

h+xs~~~:)=-6.4+3.03’1n(LTE)-3.2*pp.cInsw,,c=0.36+0.35*n,:r-0.002’a,:,.
-0.37’CI
p = bulk density (Mg/m’); OM = o r g a n i c matter (%); s = sand(>5O IUn).
I = silt (50-2 ptn); C = clay (<2 FL”‘); DG= mean estimator of CP by Campbell
LTE = mean estimator of CP by method of moments.
LTD = variance estimator of CP by method of moments.

values for one retention

curve (ME). Estimation
was considered good if the absolute or the mean
absolute difference between the estimated andmeasured retention values was 52.5%. The
SWRC prediction was judged to be poor whenthe estimation error was higher than the threshold value of the upper decile of the SSE of the
M8 SWRC model fitted individually to SWRC
data of the 156 soils (SSE > 12).The fit of the CP
model was similarly considered poor wheneverSSE exceeded 1 80. The estimation efficiency, as
expressed by the ratio of good to total estimations, is shown in Fig. 4.
The El model (Table 6) for 8, used as deterministic predictors of the bulk density, and the silt
and clay fractions of the soil. The clay and silt
fractions and the soil bulk density determined thelogarithm of parameter ~.The model parameter

8, was determined within 83% and the parametera within 60% by the basic soil properties. The parameter n was defined mostly by only the silt
fraction. The coefficient of determination (R*)
was relatively low.
The E2 predictive model equations inTable 6
combined soil properties with the fitted CP parameters. In this way the information content ofparticle-size distribution parameters is potentiallybetter preserved. The regression equation for f&
includes, in addition to the clay fraction, the parameter CLc.r as a substitute for the sand and silt
fractions as used for the El model. In the regression equation for (rlw,,(:, c1,-,, substituted the silt
fraction, while keeping the clay fraction and bulk
density as predictors. The R’ of the regression
equation increased or remained almost the same
as for E 1. The li’ of the regression equations for

840

RAJKAI, KABOS, VAN GE N U C H T E N , ANDJANSSONS OIL SCIENCEh (cm)
Fig. 4. Ratio of ‘good’ water retention estimations by pressure heads.
m Fitted SWRC modelm El modelE3 modelm E4 models,,,,, was 10% smaller, and for nswnc 1% smaller,
when only the CP parameters were used as independent predictors in the regression analysis.
A modal pore diameter (ra) of a soil may beobtained by considering the a parameter of the
SWRC function as an equivalent soil water pressure value, i.e.:r, = 0.1469 /asbmc(3)

where r, is the pore diameter in cm, and q,,, isthe pressure head in 1 cm of water at roughly the
inflection point of the SWRC function. Because
the SWRC model parameter c&,~~: and the pore
diameter r, calculated by Eq. (3) differ only by aconstant, we performed a statistical analysis using
the original parameters of the SWRC and CP
models.
The significant relationship between CI,,,,and acp found in our study is consistent with therelationship between mean pore and mean particle diameter first described by Arya and Paris(1981) and later modified by Arya and Dierolf(1992). In our analysis we observed that fitted OL
values in the SWRC model showed an approximately lognormal distribution. Based on this fact
G,,,, values were transformed into logarithms in
the regression analysis with basic soil properties
and CP distribution parameters (see Table 6).
The regression equation established between
the parameters II in the SWRC and CP models
also showed a high coefficient of determination(R* = 0.60).The significant relationship between
11,,,~ and n,, experimentally verifies the shapem E2 model

similarity assumption of the SWRC and CP
curves invoked by Brooks and Corey (1964) andHaverkamp and Parlange (1986).
The E3 and E4 predictive SWRC models in
Table 6 used empirical particle-size distribution
parameters together with the original soil properties.The E3 model used the LTE and LTD distributional parameters as its predictor variables
instead of the fitted CP parameters.The results of
the regression analysis illustrate the applicabilityof the LTE and LTD empirical parameters forrepresenting the particle-size distribution of soils(see Table 6).
The E4 predictive SWRC model, using the
DG and RG empirical parameters as its predictors, has a similar R2 as the regression equation for
IX based on the original soil properties. However,the parameters DG and RG were not deterministic in the regression equation for parameter tt.
Therefore, the IZ in the E4 model was regressed
only against the silt fraction, as was done for the
El model. We believe that the statistically significant relationships found between the SWRC and
CP model parameters are useful in practice for
estimating SWRC curves via parameter estimation of the SWRC model.
Parameter estimation by regression is often
considered to give less accurate results than methods based on regression estimates of individual
SWRC data points (e.g., Thomasson and Carter1992). However, simulation models in soil hydrology generally require continuous functions
for the SWRC.To further evaluate the accuracy

VOL. 161 ~No. 12

E STIMATION OF W ATER R ETENTION CURVES

841

of the El to E4 SWRC predictive models, calcuApertin 1. IO-20 cm
lated retention data were compared with the50measured values for the 156 soils. The errors of d?
OM= 4.5 %estimation were evaluated by calculating the SSE .?
.g 40of the different predictive models. Table 5 shows$these errors of estimation. The results in this table•I 30
indicate that the mean error of estimation at each./ 20
pressure head is less than 2% for all predictivemodels. The sign of the deviation for all predic5
tive models is mostly negative in the low pressure
head range (h 5100 cm) and positive at 300 and
15000 c m .
I
0
2
3
4
The predictive models reproduced the beh log(cm)havior of the selected SWRC model qualitatively, i.e., they generally underestimated reten- Fig. 5. Water retention curve as predicted by the differtion values in the 5 to 100-cm r a n g e a n d ent pedotransfer models.
overestimated them at the 300-cm pressureA
Measured SWRC data
- El modelhead. Of the four types of regression approaches,------E2 model-.-.- E3 modelE3 was the only one that estimated the retention
values at 15,000 cm as well as did the fitted. . . . E4 model
SWRC model (see Table 5).
The mean SSE of the prediction was inmost cases 10 to 12 times larger than the SSE of
the fitted SWRC model. The E2-model had the ciency varied from 57 to 67%. The El and E-llowest mean SSE, but it was still about 10 times models showed almost the same estimation efficiency (57 and 58%), while E3 yielded 59%.The
higher than the SSE of the fitted SWRC model.
highest estimation efficiency (67%) was obtained
We note here that the M 8 SWRC f u n c t i o n ,with the E2 model. This predictive model rewhen fitted individually by nonlinear regression
sulted in the highest number of good estimations.
to the 156 soils, used 468 free parameters,
An important advantage of using the DG andwhereas the E2 predictive model contained only
RG empirical parameters in the Ed model was its
13 free parameters for all cases.
Figure 5 illustrates one example of the types relatively high accuracy in the low pressure headof predictions obtained with the El to E4 mod- range (< 100 cm).
An evaluation of the mean SSE of the preels. Notice the very similar behaviors of models
E2 and E3, and of models E 1 and E4 in the 100 dictions, as given in Table 5 is also informative.
to 300-cm pressure head range. Also, the mod- The number of poor estimations was 22%, 12%,17%, and 19% for the E 1, E2, E3, and E4 models,els using parameters based on detailed particlerespectively. Altogether, 1 1 of 156 soils weresize distribution (E2 and E3) gave better results
qualified as poorly predictable by all four models.
than the others.
The invoked measure of having good predic- The fitting error of the SWRC model was also
tions, i.e., when the absolute difference of esti- high (SSE > 12) for six of these I 1 soils.The highmated and measured retention value was I 2.5% fitting error of the CP model also seemed to be
at a given pressure head, is shown in Fig. 4. The associated with poor estimations (6 of I I soils).
From this we conclude that poor predictions
results show that the probability of estimating as h o u l d b e expected f o r soils that have different
water retention value within 2.5% is high in the
low pressure head range (5 1-93%), lowest at field shapes of the SWRC curve as compared to thepredictive modcl.
capacity 45-54%), and intermediate at the wiltErrors in the predicted SWRC curves difing point ( 5 0 - 5 6 % ) . Also, the mean error of thepredictive models increased with increasing pres- fered in the TK groups for models E 2 and E3.
The highest mean estimation error (SSE = 7 1 .O
sure head values. This phenomenon is consistentfor E2) was found for the coarse textured, andwith known behavior of retention data, i.e., dethe lowest (SSE = 54.1 for E2) for the fine-texcreasing values with increasing pressure heads but
tured TK group. However, the same tendency waswith their absolute error increasing.
When the mean |E|l was used, i.e., as derived apparent by the mean fitting errors of the SWRC
and CP models in the TK groups.
from all six retention data, the prediction effi-

842

RAJKAI, KABOS, VAN GENUCHTEN, AND JANSSONFor one soil profile (MBrsta l), the frequencyof poor estimations was high, i.e., 10 of the 14
horizons showed poor results. Four of the 11
most poorly predicted results pertained to theMsrsta 1 soil profile. Overall, poor predictions
generally resulted from having a high organic
tnatter content (OM >5%). However, several of
the poorly estimated SWRC curves did not havea high organic matter content. In this case, thetype of organic matter or clay minerals present
on the soil structure may have caused the extraordinary results. In general, the obtained SWRC
estimation techniques seem to be acceptable formost non-site specific applications for Swedish
soils. The wider applicability of the predictive
procedure may need to be evaluated in futurestudies.
CONCLUSIONS
A three-parameter van Genuchten-typemodel was used to describe the water retention
characteristic data of Swedish soils. A logistic distribution model was proposed for the particlesize data of soils. Fitted logistic CP parameters,
and empirical mean and variance estimators (LTEand LTD), were used to represent the CP distribution of soils. SWRC model parameters were regressed with original soil properties and CP distribution parameters. A significant correlation
was found between the SWRC and CP model
parameters using linear regression.The parametercorrelation was found to be consistent with earlier assumptions about the shape similarity of the
SWRC and CP curves.The obtained regression
equations allow prediction of the SWRC curvefrom soil properties and particle-size data. The
ratio of good estimation generally increased
when using CP distribution parameters, i.e., fitted
CP model parameters, and the derived LTE andLTD empirical parameters.
The best predictions (67% of good estimations) were produced with the E2 model using
fitted CP parameters, together with the clay andsilt fractions, and the soil bulk density. Poor estimation is to be expected when the organic matter content is high (OM >5%).The mean errorof the SWRC prediction decreased from thecoarse-textured to the fine-textured soil group.
The procedure for SWRC pedotransfer parameter estimation, but not the parameter values as estimated from basic soil properties and particlesize parameters, seems to be applicable to a wider
array of soils than the Swedish soils databasealone.

SOIL SCIENCEREFERENCES
Ahuja, L. R., and D. Swartzendruber. 1972. An improved form of soil-water diffusivity function. Soil
Sci. Soc. Am. Proc. 36:9-14.

Andersson, S. 1988. O m metoder att med utgangspunkt fran bidningskurvan bcr3kna den kapilf6r
Institutionen
Iira ledningsf6rmsgan.
markvetenskap. Avdelningen fijr landbrukets hydroteknik. Rapport 157. Uppsala, Sweden (inSwedish).
Andersson, S., and P. Wiklert. 1967. Markfysilaliska undersiikningar i odlad jord. XVII. O m de vattenh%lande egenskaperna h o s rena system och blandsystem av sand, lera och torv. GrundfiirbSttring, 20.
3-27. Uppsala, Sweden (in Swedish).
Andersson, S.. and P.Wiklert. 1972. Markfysilaliska understikningar i odlad jord. XXII. Om de vattenhallande egenskaperna hos svenska jordar. GrundfdrbIttring, 25.53-243. Uppsala, Sweden (in Swedish).
Andersson, S. and P. Wilklert. l977a. Studier av
markprofiler i svenska akerjordar. En faktasammanst8llning. Del II. Norrbottens, Vasterbottens,
Visternorrlands o c h Jimtlands IZn. Lantbrukshtigskolan, Institutionen flir markvetenskap, Avdelningen fiir landbrukets hydroteknik. Stenciltryck nr
104. Uppsala, Sweden (in Swedish).
Andersson, S., and I? Wiklert. 1977b. Studier av
markprofiler i svenska akerjordar. En faktasammansdllning. Del III. Givleborgs, Kopparbergs och
VIrmlands 1Hn. Lantbrukshtigskolan, Institutionen
fiir markvetenskap, Avdelningen f6r landbrukets
hydroteknik. Stenciltryck nr 105: Uppsala, Sweden(in Swedish).
Andersson, S., and P Wiklert. 1977c. Studier av
markproliler i svenska dkerjordar. En faktasammanst&ing. Del IV. hvsborgs och Giiteborgs-och
Bohus Ij_n, LantbrukshGgskolan, Institutionen fdr
markvetenskap, Avdelningen fiir landbrukets hydroteknik. Stenciltryck nr 106. Uppsala, Sweden (inSwedish).
Arya, L. M., and J. F. Paris. 1981. A physico empiricalmodel to predict the soil moisture retention characteristic from particle size distribution and bulk
density data. Soil Sci. Soc. Am. J. 45: 1023-1030.
Arya, L. M., and T. S. Dierolf. 1992. Predicting soil
moisture characteristics from particle size distributions: An improved method to calculate pore radiifrom particle radii. In Proc. Int. workshop on indirect methods for estimating the hydraulic propertiesof unsaturated soil. M.Th. van Genuchten, F. J. Leij,and L. J. Lund (eds.). University of California,
Riverside, CA, pp. 115-l 24.
Bloemen, G. W 1980. Calculation of hydraulic conductivities of soil from texture and organic matter.
Z. Planzenernahr. Bodenkd. 143:58 1-605.
Brakensiek, D. L., R. L. Engleman, and W. J. Rawls.
1981,Variation within texture classes of soil waterparameters.Trans. ASAE 24:335-339.

VOL. 161 ~No. 12

E STIMATION OF W ATER R ETENTION C URVES

Brooks, R. H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrology Paper No. 3,
Colorado State Univ., Fort Collins, CO.
Brutsaert,W. 1966. Probability laws for pore size distributions. Soil Sci. 101:85-92.
Buchan, G. D. 1989. Applicability of the simple lognormal model to particle-size distribution of soils.
Soil Sci. 147:155-161.
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. Developments in Soil Sci., 14. Elsevier,Amsterdam.
De Jong R. 1983. Soil water desorption curves estimated from limited data. Can. J. Soil Sci.
63:697-703.
Gupta, S. C., and W. E. Larson. 1979. Estimating soil
water retention characteristics from particle size
distribution, organic matter percent and bulk density.Water Resour. Res. 15:1633-1635.
Haverkamp, R., and J.Y. Parlange. 1986. Predicting thewater retention curve from particle size distribution: 1. Sandy soils without organic matter. Soil Sci.
108:149-153.
Jansson, P E. 1991. Simulation model for soil water andheat conditions. Description of the Soil model.
Swedish Univ. ofAgric. Sci., Dep. ofSoil Sci., Division ofAgric. Hydrotechnics. Report 165, p. 72.
Jansson, P. E. 1992. PLOTPF, User’s manual. Dep. of
Soil Sci., Swedish Univ. of Agric. Sci., Uppsala,Sweden.
Johnson, N. L, and Kotz, S. 1970. Distribution in statistics,Vol. 2. Continuous univariate distributions.
Wiley, NewYork.
Jonasson, S. A. 1991. Estimation of soil water retention
for natural sediments from grain size distribution
and bulk density. Publ. A62. Geologisca institutionen, Gateborg, Sweden.
King, L. G. 1965. Description of soil characteristic forpartially saturated flow. Soil Sci. Soc. Am. Proc.
29:359-362.
Kritz. G. 1983. Physical conditions in cereal seedbeds:
A sampling investigation in Swedish spring-sown
fields. Report Nr. 65. of Swedish Univ. of Agric.
Sci., Dep. of Soil Sci., Division of Soil Management, Uppsala, Sweden.
Lalibrrte, G. E. 1969. A mathematical function for describing capillary pressure-desaturation data. Le colloque ‘Transferts en Milieux t’oreux non SaturZ,
March 27-28. 1969. Grenoble, France.
Ledermann, W. (ed.). 1984. Handbook of appliedmathematics, Vol. VI. Statistics.Wiley-Intersci., NewYork.
Ljung, G. 1987. Mekanisk analys. Beskrivning av en rationell metod f o r jordart~hestlin~~~lflg. Sveriges
Lantbruksuniversitet Institutionen for markvetenskap. Avdelningen for Iantbrukets hydroteknik,
Uppsala. Sweden (in Swedish).

843

Madankumar, N. 1985. Prediction of soil moisturecharacteristics from mechanical analysis and bulk
density data. Agric. Water Manage. l0:305-312.
Marquardt, D.W 1963. An algorithm for least squares
estimation of non linear parameters. J. Soc. tndust.
Appl. Mater. 2:431-441.
McCuen, R. H., W. J. Rawls, and D. L. Brakensiek.
1981. Statistical analysis of the Brooks-Corey andGreen-Ampt parameters across soil textures. Water
Resour. Res. 17:1005-1013.
Mishra, S..J. C. Parker, and N. Singhal. 1989. Estimationof soil hydraulic properties and their uncertainty
from particle size distribution data. J. Hydrol.
108:1-18.
Puckett, W. E., J. H. Dane, and B. F. Hajek. 1985. Physical and numerological data to determine soil hydraulic properties. Soil Sci. Soc. Am. J. 49:831-836.
Rajkai, K., Gy.V&llyay, J. A. Pacsepszkij, and R. A. Scserbakov. 1981. Calculating water retention curvefrom particle-size distribution and bulk density ofsoils. Agrok&n. Talajtan. 30:409-438 (in Hungarian).
Rawls, W. J. and D. L. Brakensiek. 1982. Estimating ofsoil water retention from soil properties. ASCE J.
Irrig. Drainage. 108: 166-171.
Rawls, W. J., and D. L. Brakensirk. 1989. Estimation ofsoil water retention and hydraulic properties. I n H. J.
Morel-Seytoux (ed.). Unsaturated flow hydrologic
modeling theory and practice. Kluwer Academic
Publishers, Dordrecht, The Netherlands, pp.
275-300.
Rogowski,A. S. 1971.Watershed physics: Model ofsoil
moisture characteristic. Water Resour. Res.
7:1575-1582.
STATISTICA for the Windows Operation System,Vol.
1. 1994. Non-Linear Estimations, StatSoft Inc.
Thomasson, A. J., and A. D. Carter. 1992. Current andfuture uses of the UK soil water retention data set.
In Proc. tnt. workshop on indirect methods for estimating the hydraulic properties of unsaturated
soils. M.Th. van Genuchten, F. J. Leij, and L. J. Lund(ed.). University of California, Riverside, CA, pp.
355-358.
Tietje O., and M.Tapkenhinrichs 1093. Evaluation of
pedotransfer functions. Soil Sci. Soc. Am. J.
57:1088-1095.
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.
Vereecken, H., J, Maes, J. Feyen, and P . Darius. 1989. Estimating the soil moisture retention characteristicfrom texture, bulk density, and carbon content. Soil
Sci. l48:389-403.
Visser,W. C. 1968. An empirical expression for the description curve. I n Proc. JASH, UNESCO Symp.
on 'Water in the unsaturated zone,’ Vol. 1. Wageningen,The Netherlands, pp. 329-335.
Williams, J., R. E. Prebble, W. T. Williams, and C. T.
Hignett. 1983. The influence of texture, structureRAJKAI, KABOS,VAN GE N U C H T E N , AND JANSSON

844
a n d clay m i n e r a l o g y o n

the soil moisture character-istic. Aust. J. Soil Res. 2 I: 15-32.
Wiklert, P., S. Andersson and B. Weidow. 1983. Studier
av markprofiler i svenska Skerjordar. En faktasamm
Del V. Skaraborgs 13n. LantbrukInstitutionen Institutionen fiir markvetenskap, Avdelningen fiir landbrukets hydroteknik. Rapport 130.
Uppsala, Sweden (in Swedish).
Wollenhaupt, M. C. 1984. A technique for estimating
plant available moisture capacity from soil texture.

chosen by minimizing the sum of absolute jumps
at the nodes.
APPENDIX 2
List of Abbreviations and Symbols

aacp

N. D . Acad. Sci. 36:53.

When, J. H. M., P . A. Finke, and M. J.W. Jansen. 1995.
Comparison of class and continuous pedotransfer
functions to generate soil hydraulic characteristics.
Geoderma 66:227-237.

APPENDIX 1
Properties of the logistic distribution used for
the CP data motivated the calculation of CP parameters using a procedure other than the usual
nonlinear least-squares methodology. The method
consists of the following steps:
Expressing moments in terms of parameters
appearing in Eq. (2). In the present case: E = a
a n d D’ = 1/3*b’*n*.where E is the mean of
the logistic distribution and D’ the variance.
l Substituting moments
by their corrected empirical equivalents (in the present case: LTE for
E and LTD for D).
l Calculating
the parameters by the moment
equations (in the present case Empiric = exp(LTE)a n d n,.,, = (1/3)“‘*n/(LTD)“*).

%w.
0

Qr

0s
:
CP
d
DF
VG

l

Empirical means (LTE) and variances (LTD’)
were calculated as the corresponding theoretical
moments of the empirical density function,
which is derived from the empirical distributionfunction. The empirical distribution function, inturn, is calculated directly from the measured particle-size data.
The lower limit (0%) of the particle-size distribution was taken to be at 0.5 pnl and denoted
by x,,.The other particle-size limits (2,6,20,. . . ,2000 pni) were associated with N nodes denoted
by XI,. . . , x,,. Let r,, be the relative frequency ofparticles with size between x,,., and x,,, 11 = l..N,and cl let the relative frequency of particles
smaller than x1. First, the density function isfound which (1) has the support [x0,x,,], (2) is linear between two consecutive nodes, and (3) has
an integral equal to r,, between two consecutive
nodes, x,,_, and x,,.

A function satisfying these requirements is
continuous except at the nodes. The function was

S OIL S C I E N C E

IEl
El
E2

E3

E4

F(d)
F(x)
F
11
I
LTD
LTE
m

parameter in the SWRC and CP models
parameter in the CP model; modal particle-size
paratneter in the selected M8 S W R C
model
soil moisture content (In3/ui3)
parameter in several SWRC models;
residual water content
parameter in the SWRC models; watercontent at saturation (rn3/n?)
dry soil bulk density (Mg/tn3)
clay content (C <2 pm) (“A)
cumulative particle-size distribution
particle-size (/hii)
degree of freedom
mean estimator of CP by Campbell(1985)
absolute value of residual calculated as
1 measured-estimated 1
S W R C predictive model using basic
soil properties
SWRC predictive model using basic
soil properties and CP model parameters
SWRC predictive model using basic
soil properties and the LTE, LTD distribution parameters
SWRC predictive model using basic
soil properties and the DG, RG distribution parameters
cumulative particle-size distributionfunction
logistic distribution function
value of F-ratio
suction head ( c m )silt content (2 ~111 51550 pm) (‘XI)
variance estimator of CP by method of
moments
mean estimator of CP by method of
moments
parameter in the SWRC models; exponentMEmean of |E|
SWRC soil water retention characteristicnparanleter in the SWRC and CP models; exponent
parameter in the CP model; variance ofnc P
C P distribution

V O L. 161 ~No. 12n,,,,,:E STIMATION OF W A T E K R E T E N T I O N CURVES

parameter in the selected SWRC
model; exponent
organic matter content (%) calculated
OM
from loss of ignition by Ljung (1987)
pore diameter calculated from &,, byraEq. (3)r0,. .,r, relative frequency of particles in particle-size classes
RG
variance estimator of CP by Campbell(1985)

845

S
SD
SE
SSE
TK
TKl
TK2

sand content (>50 pm) (%)
standard deviation
standard error
sum of squared error
textural category of soils
the sand category if C 5 15%
the silt category if C > 15% and C<40%
TK3
the clay category if C ~40%
x0, . 9 X” cutpoints of particle-size classes

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