Three-region Campbell Model for Unsaturated Hydraulic Conductivity
in Undisturbed Soils
T. G. Poulsen,* P. Moldrup, B. V. Iversen, and O. H. Jacobsen
ABSTRACT region is often better described using multimodal-distri-
A three-region Campbell (TRC) type model for predicting undis- bution functions.
turbed soil unsaturated hydraulic conductivity from water retention A limited number of models for predicting the unsatu-
is presented. The model assumes that hydraulic conductivity follows rated hydraulic conductivity (K) in soils with multimodal
separate Campbell functions within the macropore (matric head pore-size distributions have been presented. Keng and
10 cm H2O), the mesopore ( 10 350 cm H2O), and the Lin (1982) presented a two-region model for predicting
micropore ( 350 cm H2O) regions, and that soil water retention K as a function of matric head ( ). This model can be
and two reference-point values of hydraulic conductivity are known. used for between 0 and 120 cm H2O. The model is
Conductivity and retention data for 100 undisturbed soils from the
based on two exponential expressions using five input
UNSODA database and 68 soils from a Danish database were used for
model development. Conductivity for both highly structured (three-
parameters. A similar approach was used by Jarvis and
region) and weakly structured (two-region) soils mostly followed a Messing (1995) and Jarvis et al. (1999) who presented a
piecewise linear function (with slope ) in a Log(conductivity) Log two-region model for predicting K in the near saturated
(water content) plot, supporting the TRC model concept. A unique region for between 0 and 20 cm H2O also using five
relationship between the Campbell soil-water retention parameter, input parameters. A three-region model for predicting
b, and the unsaturated conductivity parameter, , was found valid K as a function of based on the Mualem (1976) conduc-
for both meso- and micropore regions. It was shown that the values tivity model was presented by Wilson et al. (1992). This
of b in the mesopore and micropore regions are not correlated, making model uses 16 input parameters, most of which are fitted
the use of single-region expressions (e.g., the Mualem–van Genuchten from the soil-water retention curve. Durner (1992) and
type models) questionable and suggests that a multiregion model with
Ross and Smettem (1993) presented multiregion models
noncorrelated retention parameters between pore regions, such as
the TRC model, may provide a conceptually more correct description
based on the Van Genuchten (1980) and Brooks and
of hydraulic conductivity. The TRC model yielded improved conduc- Corey (1966) relationships. The model by Durner (1992)
tivity predictions in loamy and clayey soils whereas predictions for was later used in solving a two-region solute transport
sandy soils were comparable to the single-region Campbell and van problem by Gerke and Van Genuchten (1993). If ap-
Genuchten models. TRC model predictions compared well with inde- plied to a three-region system both these models use
pendent data for three differently textured soil profiles. 12 input parameters.
The multiregion models developed for predicting hy-
draulic conductivity throughout the entire water-con-
U nsaturated hydraulic conductivity is difficult
and time-consuming to measure. Especially, this
is the case at low soil-water matric heads where water
tent range, i.e., the models by Durner (1992), Wilson
et al. (1992), and Ross and Smettem (1993), require a
significant number of input parameters (from 12–16 if
movement is very slow. Models for predicting unsatu- a three-region problem is considered). These models
rated conductivity from parameters that are simpler and are therefore less applicable in cases where retention
faster to measure are therefore valuable. Unsaturated and conductivity measurements are limited or in cases
hydraulic conductivity is strongly dependent upon the where the models are to be used in stochastic calcula-
distribution of pore sizes in the soil and is often pre- tions where low-parameter models generally are de-
dicted assuming that the pore-size distribution is uni- sired. Models requiring fewer input parameters are fur-
modal, i.e., that it can be described by a single-distribu- ther useful in geographical information systems (GIS)
tion function. However, in undisturbed natural soils and for characterizing soils on a regional scale.
especially in structured soils pore-size distributions are The objective of this paper is therefore to present a
often multimodal requiring two or more distribution low-parameter three-region model for predicting unsat-
functions for adequate description of the entire pore- urated hydraulic conductivity in undisturbed soils from
size distribution. These soils often have a network of soil-water retention properties. The model is applicable
large interaggregate pores or cracks that are signifi- in the water content range from saturation to the wilting
cantly larger than the pores within the aggregates or point ( 15 000 cm H2O) and is developed using
soil matrix. Also the distribution of pores in the matrix measured conductivity data available in the literature.
T.G. Poulsen* and P. Moldrup, Dept. of Environmental Engineering,
Institute of Life Sciences, Aalborg University, Sohngaardsholmsvej Several one-region models for predicting unsaturated
57, DK-9000 Aalborg, Denmark; B.V. Iversen and O.H. Jacobsen, hydraulic conductivity as a function of soil-water con-
Danish Institute of Agricultural Sciences, Dept. of Crop Physiology tent ( ) are available. Some of the most widely used
and Soil Science, Research Centre Foulum, P.O. Box 50, DK-8830
Tjele, Denmark. Received 22 March 2001. *Corresponding author are the Campbell (1974) and the Van Genuchten (1980)
Abbreviations: K, hydraulic conductivity; RMSE, root mean squared
Published in Soil Sci. Soc. Am. J. 66:744–752 (2002). error; TRC, three-region Campbell; , water content; , matric head.
POULSEN ET AL.: CAMPBELL MODEL FOR UNSATURATED HYDRAULIC CONDUCTIVITY IN SOILS 745
type relationships given by Table 1. Testure distribution of 100 soils from UNSODA (Leji
et al., 1996) and 68 Danish soils (Jacobsen, 1989) used in model
development: Sandy (sand), Loamy (loamy sand, sandy loam,
K KS  loam, silt loam, and silt), and clayey (sandy clay loam, silty
s clay loam, clay loam, sandy clay, silty clay, and clay) soils. Clay
0.002 mm, silt 0.002 to 0.02 mm, and sand 0.02 mm.
1 1/n 2
r r r 1 1/n Data Sandy soils Loamy soils Clayey soils
K KS 1 1 
s r s r UNSODA, 100 soils 43 46 11
Jacobsen, 68 soils 14 43 11
where KS is saturated hydraulic conductivity, s and r
are saturated and residual soil water contents, respec- soils (Lindhardt et al., 2002) not used in model develop-
tively, n is the Van Genuchten water-retention parame- ment were used for independently testing the model.
ter, b is the Campbell water-retention parameter (equal
to the slope of the soil-water retention curve in a Log Model Development
vs. Log system) and A, B and are constants related
A close examination of the conductivity measure-
to the pore-size distribution of the soil. The parameter
ments for the 168 soils revealed that the relationship
in Eq.  equals 0.5 if the Mualem (1976) hydraulic
between hydraulic conductivity and soil-water content
conductivity model is assumed. Campbell (1974) sug-
for 0 15 000 cm of H2O generally could be
gested A 2 and B 3 based on a derivation from
approximated by a function that was piecewise linear
pore-size distribution and adding a pore-connectivity
in a Log LogK system and consisted of three linear
term (increasing the B-value from 2 to 3). Poulsen et
parts each of the same form as the Campbell (1974)
al. (1999) suggested A 2 and B 10/3 based on
relationship (Eq. ). The two intercepts were generally
measurements from 191 undisturbed soils from the UN-
between 5 and 15 cm H2O and 200 and 500 cm
SODA database (Leji et al. 1996). The Campbell (1974)
model (Eq. ) is identical to the model presented by
The Campbell hydraulic conductivity model is appeal-
Brooks and Corey (1966) if r equals zero. The parame-
ing because of its simplicity and limited input parameter
ter r is in essence a fitting parameter in both the Van
requirements especially in connection with multipore-
Genuchten and the Brooks-Corey models.
region models compared with more complex models
such as the Van Genuchten (1980) or Brooks-Corey
Datasets Used (1966) relationships. The Campbell model has also been
Measurements of soil water retention and unsatu- shown to perform well in case of nonstructured soils
rated hydraulic conductivity for a selected set of undis- (Poulsen et al., 1999). This model was therefore selected
turbed soils were used in the model development. This as basis for the development of a predictive three-region
set consisted of 100 undisturbed soils (Table 1) selected model for unsaturated hydraulic conductivity in undis-
from the UNSODA database (Leji et al., 1996) and 68 turbed soils. The Campbell model is assumed valid in
soils from Jacobsen (1989). The 168 soils were selected each of the three pore-size regions, with different b-val-
based on the following criteria: (i) soil-water retention ues for the three regions.
measurements were available down to at least 100 cm The concept of the TRC model for predicting hydrau-
H2O soil-water matric head, (ii) hydraulic-conductivity lic conductivity from soil water content is illustrated in
measurements were available down to at least 100 cm Fig. 1 using data for Soil 4032 from UNSODA. The
H2O, and (iii) there would be at least five conductivity soil water content range is divided into three separate
measurements available for each soil. In addition, reten- regions corresponding to 10 cm H2O (Region I),
tion and conductivity measurements for three Danish 10 350 cm H2O (Region II), and 350
Fig. 1. Three-region Campbell (TRC) model concept, (a) soil water retention and (b) hydraulic conductivity as a function of soil-water content.
Data from UNSODA (Leij et al., 1996) Soil 4032.
746 SOIL SCI. SOC. AM. J., VOL. 66, MAY–JUNE 2002
cm H2O (Region III). The slopes of the retention curve ( 2 and 3 ). In the macropore region, however, there
in a Log vs. Log coordinate system for the three was no correlation between the slope of the retention
regions are denoted b1, b2, and b3, respectively. Simi- curve (b1 ) and the hydraulic conductivity curve ( 1 ),
larly, the slopes of the hydraulic conductivity curve in likely because soil water retention and hydraulic con-
a Log vs. LogK coordinate system are denoted 1, ductivity are affected very differently by soil structure
2, and 3. Region I represents the macropores with in this region. We therefore suggest that the hydraulic
equivalent pore diameter, d 300 m, Region II repre- conductivity in the macropore region must be estimated
sents the mesopores, 300 d 10 m and Region III based upon direct measurements of hydraulic conduc-
represents the micropores, d 10 m. The 10 cm tivity and soil water content at saturation (KS, S ) and
H2O soil-water matric head was also proposed as the at 10 cm H2O (K2, 2 ) assuming a linear relation-
lower limit of the macropore region by Wilson et al. ship in a LogK vs. Log coordinate system as illustrated
(1992). Wilson et al. (1992) further proposed 250 in Fig. 1b, i.e., for Region I:
cm H2O as the lower bound for the mesopore region Log (K) Log(KS) (log( S) Log ( )),
whereas Addiscott and Whitmore (1992) suggested
350 cm H2O as the lower limit for the region of signifi- 2 S 
cant water flow in soils. Here 350 cm H2O is used
as it corresponded well with the matric potentials found Log(KS) Log(K2)
for the 168 soils used in the model development. The Log( S) Log( 2)
fitted values of b1, b2, and b3, for Soil 4032 in Fig. 1 are
Similarly, hydraulic conductivity in the mesopore region
51.1, 17.1, and 5.2, respectively, and 1, 2, and 3 equal
113.7, 31.6, and 5.9. The corresponding slopes of the is estimated using the known (measured) values of K2
and 2, and the slope of the hydraulic conductivity curve
Campbell (1974) model (2b 3) are 105.1, 37.3, and
2, i.e., for Region II:
13.4, respectively. This already implies that very differ-
ent values of Campbell b in the three pore-size regions Log(K) Log(K2) 2 (Log( 2) Log( )),
may be needed to realistically describe the hydraulic
3 2 
parameters throughout the whole range of soil-water
matric potentials. Values of b2 and 2 for the 168 soils determined from
Concerning very dry soil conditions measurements the ( ) and the K( ) data within Region II were used
of soil-water retention for 15 000 cm of H2O to establish a relationship between the two parameters.
(Campbell and Shiozawa 1992) and Schofeld (1935) for The relation between the two parameters in general
seven soils of different texture indicate that the re- followed a linear relationship,
tention curve in this dry region is linear in a vs. Log 1.2 b2 3.2 r2 0.90 
coordinate system and approaches zero soil water
content at a soil-water matric head of 107 cm of The hydraulic conductivity as a function of soil water
H2O (corresponding to oven-dry soil). The soil-water content in the micropore region is calculated using a
retention curve in the very dry region (could be labeled value of LogK3 LogK2 2 (Log 2 Log 3 ) in combi-
as a Region IV) therefore does not share the Campbell nation with measured or predicted values of 3 and 3,
(1974) form. This also suggests that the residual soil i.e., for Region III:
water content used in the models by Van Genuchten Log(K) Log(K3) (Log( 3) Log( )),
(1980) and Brooks and Corey (1966) should always be
equal to zero as discussed by Webb (2000). It is noted 3 
that the present TRC model does not per se assume A relation between 3 and b3 similar to Eq.  was
zero residual soil water content but merely assumes that established using retention and conductivity data in the
any residual water content will not affect the hydraulic micropore region, where available (data were available
conductivity within each of the three separate pore-size for a total of 56 out of the 168 soils). Again the relation-
regions. The likely explanation for the different shape ship was linear and very similar to the relationship be-
in the soil-water retention curve for 15 000 cm of tween b2 and 2.
H2O is that in this region most of the soil water is sorbed
to the soil particles in the form of water films (Petersen 3 1.2 b3 2.0 r2 0.85 
et al., 1996) and water retention therefore behaves dif- The two relationships, Eq.  and , are plotted to-
ferent in this region. It is likely that the shape of the gether with the measured data in Fig. 2. The relation-
hydraulic conductivity curve is also different for ships yield very similar predictions of b and in Regions
15 000 cm of H2O but as there are no data available II and III. The relationship between b and for all data
for characterizing the hydraulic conductivity in this ex- in the two regions combined is
tremely low soil-water matric head region it is not con-
sidered in the present study. 2,3 1.2 b2,3 2.75 r2 0.90 
It was observed that the slope of the soil-water reten- This relationship is also shown in Fig. 2 together with
tion curve (Log vs. Log ) in the mesopore region the 95% prediction interval. The accuracy of Eq.  is
(b2 ) and the micropore region (b3 ) in general were pro- identical to that of Eq.  and higher than Eq. . The
portional to the corresponding slopes of the hydraulic explanation is that the number of data points in Region
conductivity curve (LogK vs. Log ) in the same regions III is smaller than that in Region II and they therefore
POULSEN ET AL.: CAMPBELL MODEL FOR UNSATURATED HYDRAULIC CONDUCTIVITY IN SOILS 747
Fig. 3. Relation between soil-water retention parameters b2 and b3
for 100 soils from UNSODA. Dotted lines indicate 95% predic-
soils used in the model development. The retention data
Fig. 2. Relation between the Campbell soil-water retention parame- clearly illustrate the lack of correlation between b2 and
ters (b2, b3 ) and the TRC hydraulic conductivity parameters ( 2, b3 as soils have similar b3 but widely differing b2. The
3 ) in the mesopore and micropore regions.
very steep decrease of several orders of magnitude in
hydraulic conductivity with soil water content in the
have a minor effect on overall prediction accuracy. Be-
macropore region for the soils in Fig. 4 suggests that
cause Eq. , , and  are all very similar we suggest
they have a significant amount of macropores (likely
that in each Region (II, III) be predicted from b in
structure related cracks or pores in large soil grains).
each Region (II, III) using the general Eq. . Interest-
Predictions of hydraulic conductivity were calculated
ingly, although the value of Campbell b is typically very
using the new model (Eq. –, , and ) in combi-
different in the mesopore (II) and the micropore (III)
nation with the measured values of KS, K2, S, 2, 3. For
regions (e.g., Fig. 2), there seems to exist a unique rela-
comparison predictions by the Campbell (1974) (Eq.
tionship between the Campbell pore-size distribution
) and the Van Genuchten (1980) (Eq. ) models
(water retention) parameter, b, and unsaturated hydrau-
are also shown. Predictions by Eq.  were calculated
lic conductivity parameter, , which spans both regions.
using b b2 and predictions by Eq.  were calculated
Soil water retention and hydraulic conductivity is often
based on the Van Genuchten parameters fitted from
calculated assuming implicitly that soil-water retention
soil-water retention data across all three pore regions.
properties in the mesopore region are related to those
Two sets of predictions by Eq.  are shown; (i) using
of the micropore region. Examples are the retention
values of KS, S together with the fitted Van Genuchten
and conductivity models by Mualem (1976) and Van
retention parameters, and (ii) using KS K2, and S
Genuchten (1980). These models use the same set of
2 together with the fitted retention parameters, i.e.,
parameters to predict retention and conductivity across
predicting only the hydraulic conductivity in the meso
the entire pore-size distribution. The calculated values
and micropore regions and using (K2, 2 ) as reference-
of b2 and b3 for the 56 soils were therefore compared
point in the Van Genucthen hydraulic conductivity
to investigate possible relations. The results shown in
model. The new TRC model predicts hydraulic conduc-
Fig. 3 indicate that there is no relation between the two
tivity well for all four soils whereas the Campbell (1974)
parameters for the 56 soils investigated (r 2 0.01).
model gives a fair prediction of hydraulic conductivity
Conceptually, this makes the use of closed-form expres-
curve in the macro and mesopore regions for three out
sions such as the Van Genuchten (1980) model question-
of four soils. It is, however, not able to predict conductiv-
able, although they can often near-perfectly fit the mea-
ity in the micropore region for any of the soils in Fig.
sured data because of the many fitting parameters. The
4. The Van Genuchten (1980) model using (KS, S ) as
suggested TRC model (Eq. –, , and ) is con-
reference-point has the lowest prediction accuracy for
ceptually appealing as it does not per se assume any
the four structured soils and is only able to give a fair
correlation between the soil-water characteristics in the
prediction of hydraulic conductivity for the sandiest soil
different pore-size regions.
(Soil 4650). Replacing KS and S with K2 and 2 in the
Van Genuchten model, i.e., predicting K in the meso
Model Validation and micropore regions only, greatly improves prediction
Figure 4 shows soil water retention and hydraulic accuracy especially for the more fine-textured soils. This
conductivity curves for four soils from the set of 168 indicates that soil macroporosity have a significant im-
748 SOIL SCI. SOC. AM. J., VOL. 66, MAY–JUNE 2002
Fig. 4. Soil water retention, hydraulic conductivity, and predicted hydraulic conductivity by the Campbell (1974) model with b b2, the Van
Genuchten (1980) model using (KS, S ), the Van Genuchten (1980) model using (KS K2, S 2 ), and the TRC model. Data for four
undisturbed, structured soils from UNSODA.
pact on hydraulic conductivity in the near-saturated re- Van Genuchten (1980) using K2 (the most accurate of
gion and must be taken into account to achieve accurate the existing models tested) has an average deviation of
predictions of hydraulic conductivity. Figure 4 also illus- 0.47 decades for the meso and micropore regions for
trates the problem of using a residual soil water content all soils together. It is noted that the Van Genuchten
(Soil 4650) where Log is significantly overpredicted model is not able to predict conductivity throughout the
by the Van Genuchten model for the lowest values of . micropore region for Soil 4650 as part of this region lies
The TRC model is in general able to predict LogK below the residual water content used in the model.
with an average deviation in predictions of 0.28 de- Figure 6 shows measured retention and hydraulic con-
cades for the four soils in Fig. 4. Prediction accuracy ductivity curves for two unstructured soils from UN-
is similar for all three regions (Fig. 5) with average SODA together with predictions by the Campbell
deviations of 0.23, 0.33, and 0.28 for the macro, meso, (1974), the Van Genuchten (1980) and the new TRC
and micropore regions, respectively. In comparison, the model. For these soils, showing only two-region behav-
POULSEN ET AL.: CAMPBELL MODEL FOR UNSATURATED HYDRAULIC CONDUCTIVITY IN SOILS 749
Fig. 6. Soil water retention, hydraulic conductivity, and predicted hydraulic conductivity by the Campbell (1974) model with b b2, the van
Genuchten (1980) model using (KS, S ), the Van Genuchten (1980) model using (KS K2, S 2 ), and the TRC model. Data for two
undisturbed, non-structured soils from UNSODA.
ior, all three K( ) models are able to predict hydraulic TRC model. This is because of poor prediction accuracy
conductivity equally well. The data in Fig. 4 and 6 indi- in the micropore region where both models significantly
cate that the Van Genuchten model is adequate in case under predicts the measured hydraulic conductivity val-
of nonstructured soils such as sand. In case of structured ues. In case of the sandy soils, all three models yield
soils, it is only possible to use the Van Genuchten model similar results (Table 2). The TRC model gives the best
for Region II and III, whereas including Region I re- results in terms of the RMSE. The Campbell (1974) and
quires a multiregion modeling approach. For example the Poulsen et al. (1999) models yield similar RMSE
the Van Genuchten model used for Regions II and III values as also discussed by Poulsen et al. (1999).
could be combined with the simple Campbell based
model for Region I given in Eq.  and . In this case,
however, the simple Campbell-based TRC concept with
noncorrelated model parameters in Regions I, II and
III seems more appealing.
Prediction accuracy for the Campbell (1974), the
Poulsen et al. (1999), and the present TRC model was
evaluated using the measured hydraulic conductivity
data for the 100 soils from UNSODA. The root mean
square error (RMSE) was used as the measure of predic-
RMSE (Xi,measured Xi,predicted)2 
N i 1
where X denotes the parameter value and N is the
number of measurements. Calculated values of the
RMSE for the 100 UNSODA soils are listed in Table
2 for all three models and measured and predicted val-
ues of LogK for the Campbell (1974) and the TRC
models are shown in Fig. 7. Also shown are the best-
fit regression lines for the data. For all soils combined Fig. 5. Relative deviation between measured and predicted LogK as
the Campbell (1974) and the Poulsen et al. (1999) mod- a function of scaled water content ( min )/( s min ) where min
els yield less accurate predictions compared with the is the smallest for which LogK is measured in Fig. 4.
750 SOIL SCI. SOC. AM. J., VOL. 66, MAY–JUNE 2002
Table 2. Hydraulic conductivity prediction accuracy for 100 soils (2504 measurements) from the UNSODA database (Leji et al., 1996)
for the Campbell (1974), the Poulsen et al. (1999), and the new three region (TRC) model in terms of the root mean square error (RMSE).
Sandy soils (43) Loamy/clayey soils (57) All soils (100)
Region Campbell Poulsen TRC Campbell Poulsen TRC Campbell Poulsen TRC
I 0.46 0.46 0.24 0.66 0.66 0.29 0.56 0.56 0.26
II 0.81 0.77 0.77 1.48 1.49 0.61 1.12 1.11 0.71
III 2.79 2.83 0.78 5.82 5.91 0.76 5.15 5.24 0.77
I II III 0.83 0.81 0.74 3.84 3.89 0.50 2.79 2.83 0.70
The best-fit lines in Fig. 7 show that the Campbell accuracy will strongly depend upon the actual soil type.
model has almost no bias in the predictions for the sandy Another source of discrepancy is the sometimes curved
soils (Fig. 7a) but significantly underestimates hydraulic shape of the LogK Log relationship in Region II
conductivity for the loamy and clayey soils (Fig. 7b). that causes overestimation of K as seen for Soil 4033 in
The TRC model has low bias for both soil texture groups Fig. 4.
(Fig. 7d,e). The apparent overestimation seen from the The TRC model was tested against retention and
data points in Fig. 7d and 7e for the TRC model is hydraulic conductivity data for three undisturbed Dan-
because in part of a few soils where Region II starts at ish soils (Lindhardt et al., 2002; see Table 3) not used
a matric head significantly below 10 cm. Measured in the model development. Hydraulic conductivity for
and predicted values of K are shown for four of these the three soils was measured down to 100 cm
soils in Fig. 8. It is seen that K is significantly overesti- H2O using an automated drip infiltrometer (van den
mated for all soils but improved predictions could be Elsen et al., 1999) that measures the unsaturated hy-
achieved if proper values for (K2, 2 ) could be found draulic conductivity at steady-state water flow condi-
for these soils. Here the locations of the break-points tions in the soil at different matric heads. An initially
(K2, 2, and K3, 3 ) were selected based on values pro- saturated soil sample is placed on a sandbox and five
posed in the literature. Alternative methods for pre- ceramic cups connected to transducers are placed in
dicting the break-points could be developed using for the sample. When steady-state water flow is reached a
instance fractal methods such as described by Nimmo measurement is conducted and the infiltration is contin-
(1997) or Hunt et al. (2001). Development of theoretical ued at a lower matric head. The infiltrometer is able to
methods for predicting the break-points, however, is measure unsaturated hydraulic conductivity in the near
beyond the scope of this work. However, the effects of saturated region very closely. Soil water retention was
choosing a different location for the break-point be- measured in triplicate and the data used for model verifi-
tween the meso and micropore regions on prediction cation are arithmetic averages of three measurements.
Fig. 7. Measured and predicted values of hydraulic conductivity for 100 soils from UNSODA using the Campbell (1974) model with b b2,
and the TRC model for sandy soils, loamy and clayey soils and all soils combined.
POULSEN ET AL.: CAMPBELL MODEL FOR UNSATURATED HYDRAULIC CONDUCTIVITY IN SOILS 751
Table 3. Texture and retention properties of three Danish soils (Lindhardt et al., 2002) used in testing the TRC model. Numbers in
parenthesis give the observed range. Also shown are root mean square error (RMSE) and bias values for predictions of Log (hydraulic
conductivity) by the TRC model and the Campbell (1974) model.
Soil N† Clay Silt Sand Organic C b2 TRC Campbell
Jyndevad 114 5.2 (3.0–9.6) 1.3 (0.5–3.2) 92.5 (88.3–96.4) 0.9 (0.1–3.4) 1.0–3.7 0.31 0.47
Tylstrup 100 5.7 (4.7–6.4) 4.1 (3.6–4.3) 88.4 (87.2–89.6) 2.3 (1.4–2.7) 1.5–5.2 0.35 0.39
˚ 72 16.0 (12.6–23.6) 12.7 (11.3–13.4) 67.4 (52.6–74.6) 1.0 (0.1–2.6) 7.3–26.4 0.30 2.04
†N number of data points.
Because no measurements were available for Region the macropore ( 10 cm H2O), the mesopore ( 10
III, it was only possible to test the TRC model against 350 cm H2O), and the micropore ( 350
data in Region I and II for the three soils. 15 000 cm H2O) was developed using soil water
Figure 9 shows measured conductivity data for three retention and hydraulic conductivity measurements for
selected locations one for each soil. Also shown are the 168 soils with a broad range of textures.
TRC model predictions. In all three cases, the TRC The model requires knowledge of the soil-water re-
model is able to well predict the measured data. Mea- tention curve and uses seven input parameters: hydrau-
sured and predicted values of LogK and the correspond- lic conductivity at 0 and 10 cm H2O, the soil
ing 95% prediction interval for all data from the three water contents at 0 cm H2O, 10 cm H2O and
soils are plotted in Fig. 10. The RMSE and bias calcu- 350 cm H2O, and the Campbell b values for the
lated for each soil using the TRC model is given in soil-water retention curve in the meso and micropore
Table 3. For comparison RMSE and bias for the Camp- regions.
bell (1974) model are also given. For the nonstructured Although the value of Campbell b was often very
Jyndevad and Tylstrup soils the Campbell model is only different and noncorrelated in the mesopore (II) and
slightly less accurate, whereas for the very structured the micropore (III) regions, a unique relationship be-
Fardrup soil, the Campbell model significantly overpre- tween the Campbell pore-size distribution (water reten-
dicts the measured data. This is consistent with the find- tion) parameter, b, and unsaturated hydraulic conduc-
ings in Table 2 as Fardrup has higher content of clay tivity parameter, , seems to exist spanning both regions.
and silt compared with the two other soils. The TRC Hydraulic conductivity predictions by the new TRC
model is generally able to predict hydraulic conductivity model were compared with existing models for 100 soils
to within 0.75 orders of magnitude (Fig. 10). These re- from UNSODA and improved prediction accuracy was
sults support the use of the TRC model to predict unsat- found in the case of the more structured loamy and
urated hydraulic conductivity in undisturbed soils. clayey soils. For the typically less structured sandy soils
the existing models and the TRC model yielded similar
CONCLUSIONS prediction accuracy.
A soil-type dependent, TRC model for predicting un-
saturated hydraulic conductivity in undisturbed soils in
Fig. 9. Soil water retention, hydraulic conductivity, and predicted hy-
Fig. 8. Three soils from UNSODA where Region II starts at a soil- draulic conductivity by the TRC model for three selected sampling
water matric head significantly below 10 cm H2O causing over- locations in three undisturbed Danish soils from (data from Lind-
prediction of unsaturated hydraulic conductivity by the TRC model. hardt et al., 2002).
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