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WATER RESOURCES RESEARCH, VOL. 46, W01501, doi:10.1029/2009WR007939, 2010

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ArticleCan texture-based classification optimally classify
soils with respect to soil hydraulics?
Navin K. C. Twarakavi,1 Jirka Šimůnek,2 and M. G. Schaap3
Received 3 March 2009; revised 18 August 2009; accepted 31 August 2009; published 1 January 2010.

[1] In the past, texture-based classification of soils has been used for grouping soils invariably saturated water flow and solute transport studies. Classification of soils becomes
especially important for large-scale studies where the spatial and temporal variability inthe hydraulic properties of soils exceeds the field sampling capabilities. Although soiltexture-based classification has been widely used, questions remain about the validity of
its use from a hydraulic perspective. In this study, we attempt to answer the following
questions: (1) what is the optimal number of (soil hydraulic) classes that can adequately
classify the soils from a hydraulic standpoint, and (2) how does such a classificationcompare to the soil texture classification currently used? To investigate these questions,the commonly used k-means clustering algorithm was integrated with the ROSETTA
pedotransfer functions to predict the so-called soil hydraulic classes. The optimal soil
hydraulic classifications and the associated uncertainty were estimated for numbers ofsoil hydraulic classes varying from 2 to 30. It was concluded that the optimal number of soil
hydraulic classes is 12. The optimal soil hydraulic classes were represented in a ternary
diagram called the soil hydraulic triangle. While there exist some surprising similarities inclassification between the soil texture triangle and the soil hydraulic triangle for soils withhigh sand percentages (sand >60%), the opposite is true for soils with low sand contents.
From a hydraulic standpoint, the texture-based classification does not classify soils wellwhen there is a considerable impact of capillary forces. The soil texture and hydraulic classes
were analyzed for accuracy using two databases. Compared to the soil texture classes, it
was found that the soil hydraulic classes marginally improve the accuracy of classification.
Even though the improvement is only marginal, it was observed that the optimality ofsoil texture triangle for hydraulic studies cannot be assured because of the nonuniform
distribution of data across various textural possibilities in the two databases. As an extensionof this research, we have also estimated the average soil hydraulic parameters for thedifferent optimal soil hydraulic classes.
Citation: Twarakavi, N. K. C., J. Šimůnek, and M. G. Schaap (2010), Can texture-based classification optimally classify soils
with respect to soil hydraulics?, Water Resour. Res., 46, W01501, doi:10.1029/2009WR007939.

1. Introduction[2] Understanding hydrological processes, especially atlarger scales, requires grouping soils on the basis of somerelevant criteria. One of the most common approaches forcharacterizing soils is based on their textural properties. Soil
texture describes the relative proportion of different grain size
particles in a soil and is commonly represented by relative
proportions of sand, silt, and clay contents. Soil texture
classification has been addressed frequently, with the earliest
research dating back to the beginning of the 20th century[e.g., Atterberg, 1905, 1912]. One of the major reasons forthe popularity of texture-based classification of soil is that1
Department of Agronomy and Soils, Auburn University, Auburn,
Alabama, USA.
2
Department of Environmental Sciences, University of California,
Riverside, California, USA.
3
Department of Soil, Water and Environmental Sciences, University of
Arizona, Tucson, Arizona, USA.

Copyright 2010 by the American Geophysical Union.
0043-1397/10/2009WR007939$09.00

textural characteristics are among the most easily measured
soil properties. Skilled practitioners can determine the textural class manually. Texture-based classification categorizes
soils into so-called soil texture classes. Although several
texture-based classifications are used currently (U.S. Department of Agriculture (USDA) and International Soil Science
Society (ISSS)), the soil texture classification system proposed by the USDA is perhaps the most widely recognized.
The USDA system classifies soils into 12 soil texture classes.
This soil texture classification is conveniently represented
using the ternary diagram as proposed by Davis and Bennett[1927]. Figure 1 shows a ternary diagram of the soil texture
triangle with the USDA-based soil texture classes. A ternary
diagram represents the different soil texture classes as afunction of sand, silt, and clay percentages, in which the size
boundaries are set at 2 mm for clay/silt, at 50 mm for silt/sand,and at 2000 mm for sand/gravel.

2. Hydraulic Validity of Soil Texture Classes[3] Studies related to the hydraulic behavior of soils havetypically used soil-texture-based information. Several

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W01501Figure 1. A ternary diagram of the soil texture triangle showing the different USDA-based soil texture
classifications.
approaches are possible. For example, Carsel and Parrish[1988], Rawls et al. [1982], Wösten et al. [1995], and Schaapand Leij [1998] estimated the average soil hydraulic parameters for different textural classes, whereas other studies (forreviews, see Wösten et al. [2001] and Pachepsky and Rawls[2004]) developed pedotransfer functions (PTFs) that provided estimated hydraulic parameters as a function of continuous texture and other soil variables. In the latter case, theperformance of each PTF was quantified on a textural classbasis [e.g., Schaap and Leij, 1998]. In most or all of thesestudies, it was assumed that soil texture is the dominant soil
variable in determining hydraulic properties, while other soil
variables, such as bulk density or organic matter content, have
only a secondary effect. However, a basic (but unproven)premise of these studies is that the traditional soil texture
classification is optimal from a soil hydraulic standpoint.
The hidden assumption behind using the soil-texture-basedclasses in variably saturated flow studies is that these classes
provide the best possible grouping of soils. In other words, it
is assumed that the soils within each soil texture class are as
similar as possible to each other from the perspective of
hydraulic behavior. Also, it is assumed that the number ofclasses used (that is, the 12 textural classes) is the optimal
number of classes. Because of the wide use of soil texture
classes in soil physics and hydrology, an investigation of the
optimality of soil texture classes becomes important. Even
though the National Resources Conservation Service (NRCS)[1975] discusses soil taxonomy classification, the following
quotes [NRCS, 1975, p. 7] still hold true for soil texture
classification and its relevance for hydrological purposes.
For the different purposes of the soil survey, classes are needed thatcan be grouped or subdivided and regrouped to permit the largest

number and the most precise predictions possible about responses tomanagement and manipulation.
Classifications are contrivances made by humans to suit their purposes. They are not themselves truths that can be discovered. A
perfect classification would have no drawbacks when used for the
purpose intended. Each distinctly different purpose, to be served best,
demands a different classification.
As knowledge expands, new facts or closer approximations of truths
not only make improvements in classification possible but also makesome changes imperative. Thus, classifications are not static but
require change as knowledge expands.

[4] To understand the motive and objectives of soil texture
classification, we conducted an extensive literature review
but were unable to gather precise references. One of theearliest references discussing the soil texture triangle was the
USDA Soil Survey Manual [Soil Survey Staff, 1951], whichstates that soil texture classes in present use are definedin terms of size distribution as determined by mechanicalanalysis in the laboratory. The report also mentions thatdefinitions and boundaries for the soil texture classes resulted
from long experience and special research for maximum
general use for soil definitions and interpretations. It is also
acknowledged that the standards are not yet perfect. Soil
Survey Staff [1951] goes on to stress that textural classes must
be used exclusively to express the differences in particle size
distribution and that any other use (such as for soil structureor hydrology) will result in the loss of their fundamental
significance. It is clear that the hydraulic validity of theclassification of soils based on the soil texture triangle needs
to be scrutinized. In this study, we strive to provide answers to
the following two questions. (1) Is an optimal classificationof soils based on hydraulic characteristics (hereafter calledsoil hydraulic classes) different from soil-texture-based

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W01501classification? (2) With respect to the hydraulic characteristics, what is the optimal number of soil hydraulic classes?
[5] In this study, we do not question the optimality of the
USDA particle size boundaries (2, 50, and 2000 mm) or the
optimal number of such particle sizes. Skaggs et al. [2001]
seem to suggest that four instead of three particle size fractions are needed to adequately characterize a particle size
distribution. This would mean that the relationship between
texture and hydraulic parameters could be improved but thatthe current ternary diagrams can no longer be used.
[6] Here, we summarize the methodology of this research.
The objective of this research is achieved using the following
steps: (1) obtaining soil data sets with relevant hydraulicproperties that adequately represent the different soil texture
possibilities (that is, all possible combinations of sand, silt,
and clay percentages); (2) using appropriate techniques,grouping the soils in the data set into an optimal number ofclasses based on soil hydraulic properties; and (3) comparing
the resulting classification of soils into soil hydraulic classes
with the soil texture classes as described by the USDA
system.

3. Materials and Methods
3.1. Soil Hydraulic Properties[7] We consider the soil hydraulic parameters as describedby the van Genuchten – Mualem model [van Genuchten,
1980]:

qðhÞ ¼

8
<

qr þ

:

qs

qs  qrm½1 þ jahjn Se ðhÞ ¼

h<0

ð1aÞ

h  0;

qðhÞ  qr;
qs  qrð1bÞhi2KðhÞ ¼ Ks Sel 1  ð1  Se1=m Þm ;ð1cÞm ¼ 1  1=n;

ð1dÞn > 1;

where q(h) is the volumetric water content (L3 L3) as afunction of the pressure head h (L); qs and qr are the saturated
and residual volumetric water contents, respectively; Se(h) is
the soil water saturation (dimensionless) expressed at thepressure head h; a (L1) and n (dimensionless) are van
Genuchten shape parameters; K(Se) is the unsaturated
hydraulic conductivity (L T1) as a function of the soil water
saturation; Ks is the saturated hydraulic conductivity (L T1);and l is an empirical parameter commonly assumed to be 0.5.
3.2. The k-Means Clustering Algorithm[8] The k-means clustering algorithm [MacQueen, 1967]
is one of the simplest unsupervised clustering algorithms forsolving the well-known clustering problem. The procedure
follows a simple method for classifying a given data set ofsize N into a specific, predefined number of clusters (assumed
as k clusters). If one considers a data set that contains N data
points, each having p attributes, the objective of the k-meansclustering algorithm is to group the data set into k clusters

W01501such that the objective function, x(k), described inequation (2), is minimized:xðkÞ ¼

nk
k X
Xk xij  mi k2 ;ð2Þi¼1 j¼1

where k is the number of clusters determined a priori, nk is thenumber of points belonging to the cluster i, xij is the vector of
attributes of the jth data point of the cluster i (a vector ofhydraulic parameter values), mi is the mean value of theattributes for the data points in the cluster i (also called cluster
centers), and k k describes the Euclidean distance (a squared
distance) between two data points.
[9] The algorithm for the k-means clustering consists ofthe following steps: (1) for a predefined number of k clusters,
initialize them by placing the k cluster centers randomly in theattribute space; (2) assign each data point to the nearest
cluster center on the basis of the Euclidean distance measure;(3) for each cluster, recalculate the new centers as the mean ofthe data points assigned to it; (4) repeat steps 2 and 3 until thecluster centers no longer move. One may note that the kmeans algorithm does not necessarily find the most optimalclustering result and is significantly sensitive to the positionof the random cluster centers that are selected initially.
Several variations of the k-means clustering algorithm thatemphasize obtaining the global minimum of the objectivefunction have been proposed. In this study, we use Hartigan
and Wong’s [1979] algorithm because it performs better inobtaining the global minimum. In order to make the clusteringresults more robust, the k-means algorithm was run multiple
times (here 1000 times) with different initial cluster centers,
and the average clustering was used.
[10] As an unsupervised learning technique, the k-meansclustering algorithm requires a predefined number of clusters.
One may estimate an optimal number of clusters in the kmeans clustering algorithm using the elbow criterion. We
would like to point out that there are a number of otherapproaches for finding optimal clustering and that we chosethe elbow criterion because of its popularity and simplicity ofuse. The elbow criterion suggests that one should choose an
optimal number of clusters such that adding one additional
cluster does not add sufficient information. One may note thatthe value of the objective function of the k-means clustering
algorithm decreases as the number of required clusters
increases. However, the rate of decrease in the objectivefunction is less and less dramatic as the number of clusters
increases. The elbow criterion suggests an intuitive selectionof the optimal number of clusters such that the decrease in thevalue of the objective function is not significant enough. In
this study, we use the elbow criterion to select the optimal
number of soil hydraulic classes.
3.3. Methodology[11] A major hurdle in our research was obtaining acomprehensive soil data set with hydraulic properties thatcover the various textural combinations. A number of the soil
data sets tend to be clustered in the sand-loam-silt categories(the lower half of the soil texture triangle), with minimal data
points in the clay-dominated classes.
[12] In this study, we used the following procedure forclassifying soils from a hydraulic standpoint. First, weestimated the five soil hydraulic parameters (qr, qs, a, n,

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and Ks) throughout the entire soil texture triangle using the
ROSETTA PTFs such that the various soil texture possibilities (i.e., combinations of sand, silt, and clay percentages)
were considered. The data set was created by varying thesand, silt, and clay percentages by 1%, leading to a total of
5151 data points. The sand, silt, and clay percentages wereused as inputs to ROSETTA. We used only these percentages
as input to ROSETTA so that the results of the clustering
process could be shown in a ternary diagram as a function ofsand, silt, and clay contents.
[13] The ROSETTA PTFs use artificial neural networks
and can predict the necessary soil hydraulic parameters (aswell as their uncertainties) as a function of the soil texture(sand, silt, and clay fractions). One may note that a number of
PTFs are currently available and might also be used. However, we used ROSETTA because it is one of the more widely
accepted PTFs. Although we based our study on generated
data, we should emphasize that this does not implicitly
include the USDA textural classes as only sand, silt, andclay percentages were entered into ROSETTA and soil
texture classification was not.
[14] ROSETTA predicted the mean value and the associated uncertainties of these soil hydraulic parameters for eachof the 5151 soil data points. Once the mean and standard
deviation (uncertainty) values of the five soil hydraulicparameters at each of the 5151 soil data points were available,
they were used to develop 100 data sets of soil hydraulicparameter estimates using the Monte Carlo sampling approach.
For the 100 data sets (each having 5151 data points with theestimated soil hydraulic parameters), we estimated thefollowing hydraulic properties: (1) field capacity (qfc),(2) time needed to reach field capacity from saturated
condition (called drainability, tfc), and (3) capillary pressure
at which field capacity is attained (hfc). Appendix A discusses
the simulation approach in HYDRUS used to estimate theaforementioned hydraulic properties. It took about 800 hof run time on a 3 GHz, 3.25 GB RAM Intel Quad Core
Windows XP personal computer to carry out the required
515,100 simulations in HYDRUS. Using the soil hydraulicparameters, we also estimated the permanent wilting point(qpwp) as the water content in the soil at a capillary pressureof 15 bars. Along with estimated qfc, tfc, hfc, and qpwp, weused the saturated water content (qs) and the saturated
hydraulic conductivity (Ks) as properties to group the soils.
While qfc, hfc, qpwp, and qs represented the retention characteristics of each soil, Ks and tfc represented the dynamics ofvariably saturated water flow. At this point, we would like tomention that we purposefully avoided classification of soils
by directly using van Genuchten – Mualem soil hydraulicparameters. This is because such an approach would resultin the usability of the resulting soil hydraulic classification
being much more contingent on the interrelationships between
the parameters of the van Genuchten– Mualem model.
[15] For each of the 100 data sets, we grouped the soils
using the following properties: qfc, qpwp, qs, log10(Ks),
log10(hfc), and log10(tfc) for various possible numbers of soil
hydraulic classes (k, equation (2)). Prior to the application of
the k-means clustering algorithm on each of the 100 data sets,
the data were standardized such that each of the soil-hydraulicproperties imparted an equal influence on the clustering
process. A logarithmic transformation of Ks, hfc, and tfc

W01501was used for normalization purposes. For a given numberof clusters (k), the cluster boundaries from each of the
100 data sets were collected, and the average boundary waschosen for the final classification. The cluster boundary fromthe 100 data sets was also used to define the uncertainty of the
final soil hydraulic classification. All the points with at least
one boundary line in the 100 data sets were considered to be aregion of uncertainty in the hydraulic classification.
3.4. Validation Data Sets
[16] In order to understand how well the soil hydraulictriangle classifies soils when compared to the soil texture
triangle, we analyzed their performance on different realworld databases. The first database was the one used to train
and test the ROSETTA PTFs. The database contained 2134
soil samples, with parameters describing the water retention
data. Saturated hydraulic conductivity data was available for1306 soil samples. The second database was used to develop
PTFs by Minasny et al. [2004]. This data set had 320 soil
samples with water retention data, of which 219 samples had
estimates of the saturated hydraulic conductivity. Readers arereferred to Schaap et al. [2001] and Minasny et al. [2004] fora detailed description of the databases.

4. Results and Discussion[17] As described in section 3.3, 100 data sets with theproperties qfc, qpwp, qs, log10(Ks), log10(hfc), and log10(tfc)
as a function of soil texture were developed. Each data set
consisted of 5151 data points that uniformly cover the different textural combinations. Figure 2 shows the mean estimates of these properties from the 100 data sets in a ternary
diagram. As mentioned earlier, the k-means clustering algorithm was used to classify the soils for a different, predefined
number of soil hydraulic classes, k, ranging from 2 to 30.
Figure 3 shows the value of the objective function for the
k-means clustering (described in equation (2)) as a functionof the number of soil hydraulic classes. Note that the plotshows the mean and standard deviations of the objectivefunction from the 100 data sets as a function of the numberof soil hydraulic classes. This plot is also referred to as theelbow criterion, which can be used to intuitively judge theoptimal number of soil hydraulic classes. Figure 3 also
shows the incremental improvement in classification with anincrease in the number of hydraulic classes. It was observedthat the optimal number of classes for classifying soils withrespect to soil hydraulic properties was 12. We chose theoptimal number of soil hydraulic classes to be 12 on the basisof (1) the elbow criterion and (2) consistency with the numberof soil texture classes used in the USDA classification (which
is 12).
[18] It is of interest to analyze how various soil texture
possibilities (sand, silt, and clay percentages) group fordifferent numbers of soil hydraulic classes. Figure 4 shows
the location of the soil hydraulic classes generated using the
k-means clustering approach for different predefined numberof classes. As the number of soil hydraulic classes increases(from 2 (Figure 4a) to 14 (Figure 4f)), one may note a nearlyhierarchical and consistent development of the spatial location of the hydraulic classes in the ternary diagram. Even for alower number of soil hydraulic classes (Figure 4b), a clear
distinction is observed between the sand-dominated soils

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W01501Figure 2. Mean estimates of (a) qpwp, (b) qs, (c) qfc, (d) log10(Ks), (e) log10(hfc), and (f) log10(tfc) as afunction of sand, silt, and clay percentages.
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W01501Figure 3. Plot showing the mean and standard deviation of the objective function (x(k)) as a function of
the number of soil hydraulic classes (k). The plot also shows the incremental improvement in the objectivefunction, [x(k + 1)  x(k)], with a unit increase in the number of hydraulic classes.
(sand >60%) and the rest. It is safe to say that soils with higher
sand content are clearly differentiated from other soils interms of hydraulic behavior.
[19] Figure 5 shows the soil hydraulic classification for the
optimal number of soil hydraulic classes as determined by theelbow criterion. We refer to this ternary diagram as the soil
hydraulic triangle because it shows the optimal classificationof soils from a hydraulic perspective. We have named thehydraulic classes using an alphanumeric nomenclature. The
sand-dominated soils are represented by the letter A, with anumber that increases as the sand fraction decreases (A1 –A4). Similarly, silt-dominated soils are represented by theletter B, with a number ranging from 1 to 4, and claydominated soils are represented by the letter C, with a number
ranging from 1 to 4. As mentioned earlier, the optimal soil
hydraulic classification is very similar to the soil texture
classification (Figure 1) for soils where the sand percentage
dominates the silt and clay contents. This is especially true forsoils in which the proportion of sand exceeds 60% (A1– A4).
Another interesting observation relates to the relatively
similar positions of C4 in the soil hydraulic triangle and‘‘clay loam’’ in the soil texture triangle. However, thesimilarities between the soil texture triangle and the soil
hydraulic triangle are less pronounced for soils where capillary forces have a considerable impact on the water flow. To
further analyze the similarities between the soil texture
triangle and the soil hydraulic triangle, we compared therelationship of the spatial location of the textural classes andof the optimal hydraulic classes. Table 1 shows the distribution of the ternary space among the soil texture classes andthe optimal soil hydraulic classes. In soils where capillary
forces are significant, there exists a weaker correlation
between the location of the corresponding soil hydraulicand textural classes.
[20] Figure 6 shows the uncertainty in the boundaries ofthe soil hydraulic triangle shown in Figure 5. The uncertainty

in this classification is a testament to the uncertainties of the
ROSETTA pedotransfer functions used to develop the data
sets. An interesting observation in the uncertainty diagramis that the soil textures that are classified as loam in thesoil texture triangle constitute a region of uncertainty for thehydraulic classification.
[21] Schaap et al. [2001] estimated the average soil
hydraulic parameters for the different soil texture classes using
the ROSETTA training database. The average soil hydraulicparameters for different soil texture classes were estimated byaveraging of the hydraulic parameters for soils falling underthat particular textural class. A similar procedure was applied
to the data set used by Schaap et al. [2001] to estimate theaverage soil hydraulic parameters for the different soil
hydraulic classes. Table 2 lists the resulting average soil
hydraulic parameters for the optimal soil hydraulic classes.
[22] In order to understand how well the soil hydraulictriangle classifies soils compared to the soil texture triangle,
we analyzed their performance on the databases of Schaap
et al. [2001] and Minasny et al. [2004]. The soil samples inthe two databases were assigned textural classes and hydraulic classes on the basis of the sand, silt, and clay percentages,
using the USDA soil texture and the newly developed soil
hydraulic triangle. For each soil hydraulic parameter in thetwo databases, we estimated the cumulative variance of theclassifications (CUV) asCUVðpÞ ¼

k 
X

g ip  g ip

2

;

ð3Þ

i¼1

where k is the number of hydraulic or textural classes (here,12), g ip denotes values of the pth soil hydraulic parameter ofthe soil samples that fall in the ith hydraulic or textural class,and g ip is the mean value of the pth soil hydraulic parameterof the soil samples in the ith hydraulic or textural class. The

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W01501Figure 4. A ternary diagram showing the classification of soils into (a) 2, (b) 4, (c) 8, (d) 10, (e) 12, and(f) 14 classes using the k-means clustering algorithm. The boundary was selected as the average boundaryfrom the k-means clustering on the 100 data sets.
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W01501Figure 5. A ternary diagram showing the optimal soil hydraulic triangle with its 12 soil hydraulic classes.
CUV index is very similar to the objective function of the kmeans clustering algorithm. A lower value for the objectivefunction indicates better classification. Table 3 lists the valueof the CUV index for the different soil hydraulic parametersin the two data sets. It was observed that the soil hydraulictriangle performs marginally better than the soil texture
triangle in grouping the soil hydraulic parameters for bothdata sets. It is important to mention that the two databases
have data that do not adequately represent the various textural
possibilities. The data tend to represent the sand-loam-silt
textures more than the clay textures. Given that the soil
texture triangle and soil hydraulic triangle are very similarin the sand- and loam-dominated soils, it is not surprising toobserve insignificant differences. However, we are not awareof any soil hydraulic databases that represent the various
textural possibilities of soils. On the basis of our research, we
recognize the lack of a comprehensive soil hydraulic databaseas a major limitation for the progress of soil sciences,
especially in the development of soil classification systems.
[23] For the Schaap et al. [2001] data set, the optimal
hydraulic and textural classes were also used to group the(1) soil water contents (q(h)) and (2) soil unsaturated hydraulic conductivity (log10K(h)) for five pressure head classes (incm) of (0 to 10), (10 to 100), (100 to 1000), (1000
to 10,000), and (10,000 to 1). For each capillarypressure class, we grouped the q(h) and log10K(h)) values
by hydraulic or textural class, and the cumulative variance(CUV(V(H))) was estimated as described in equation (4). As

Table 1. Distribution of Textural Possibilities in the Ternary Diagram Among the Soil Hydraulic and Textural Classesa
Sand
A1
A2
A3
A4
B1
B2
B3
B4
C1
C2
C3
C4
Textural class

1.32
0.45

Loamy
Sand
2.31
0.58

Sandy
Loam

9.24
1.59

Sandy Clay
Loam

6.6

Loam

Silt

1.77

2.89

11.51

0.14
4.33
0.04

0.85
7.45

Silty Clay
Loam

Clay

0.54
0.82

1.34
7.21

Sandy
Clay

Silty
Clay

Clay
Loam

1.53
3.26

0.68

Silt
Loam

0.12

3.38

a

0.52
7.16
7.05
2.27

17

0.02
5.28

5.3

0.43
11.82
7.07
8.08
2.02
29.42

1.63
2
2.45
0.16
3.69

4.08

Values are in percent, representing the percentage of the surface area of the ternary diagram belonging to a particular soil class.

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0.19
1.98

4.14
6.31

Hydraulic
Class
1.32
2.76
10.36
10.54
3.78
7.98
11.59
11.75
11.82
9.07
10.53
8.51

TWARAKAVI ET AL.: SOIL HYDRAULIC CLASSIFICATION

W01501

W01501Figure 6. A ternary diagram showing the uncertainty in the optimal soil hydraulic classification shown in
Figure 5.
with the objective function of the k-means clustering algorithm, a lower value indicates improved clustering:CUVðVðHÞÞ ¼

k 
X

2
V i ðHÞ  V i ðHÞ :

ð4Þ

i¼1

[24] In (4), H (in cm) is one of the pressure head classes,
V i(H) denotes the q(h) (or log10 K(h)) values of the ith soil
hydraulic or textural class for the pressure head class H, V i ðHÞ
is the mean of V i(H), and k is the number of soil hydraulic or
textural classes. Table 4 shows the values of the objectivefunction for the different water content and unsaturated

hydraulic conductivity groups. Again, the soil hydraulicclasses showed a marginal improvement over the texturalclasses in the classification of soils. Since most of the soils inthe database belong to the sand- and loam-dominated textures
and texture and hydraulic triangles are very similar in theseregions, the observed similarity in the performance of the
texture and hydraulic triangles is only applicable to thesetextures.

5. Summary and Conclusions[25] Soil classification for hydraulic purposes is an important, but often ignored, topic of interest. In the past, the soil
texture triangle has been considered to be the definitive way

Table 2. Mean and Standard Deviation of Soil Hydraulic Parameters for Different Soil Hydraulic Classes Estimated from the Schaap
et al. [2001] Databasea
Soil Hydraulic
Class

qr

qS

log10(a) in log10 (cm1)

log10(n)log10(Ks) in log10 (cm/d)

A1
A2
A3
A4
B1
B2
B3
B4
C1
C2
C3
C4

0.055 (0.002)
0.053 (0.002)
0.051 (0.002)
0.055 (0.003)
0.057 (0.011)
0.053 (0.003)
0.056 (0.007)
0.073 (0.015)
0.072 (0.012)
0.091 (0.013)
0.069 (0.016)
0.064 (0.005)

0.374 (0.008)
0.386 (0.007)
0.382 (0.01)
0.387 (0.009)
0.487 (0.031)
0.425 (0.03)
0.413 (0.026)
0.47 (0.026)
0.475 (0.013)
0.436 (0.025)
0.5 (0.037)
0.421 (0.012)

1.479 (0.036)
1.474 (0.076)
1.54 (0.176)
1.672 (0.183)
2.034 (0.045)
2.278 (0.124)
2.234 (0.193)
2.016 (0.141)
1.94 (0.07)
1.444 (0.174)
1.888 (0.057)
1.83 (0.068)

0.511 (0.06)
0.276 (0.055)
0.171 (0.015)
0.14 (0.019)
0.208 (0.009)
0.206 (0.024)
0.186 (0.021)
0.16 (0.024)
0.135 (0.01)
0.106 (0.008)
0.124 (0.01)
0.137 (0.017)

2.853 (0.544)
2.093 (0.696)
1.641 (0.659)
1.242 (0.764)
1.641 (0.273)
1.714 (0.594)
1.197 (0.757)
1.115 (0.805)
1.206 (0.11)
1.263 (0.649)
1.324 (0.972)
0.642 (1.09)

aStandard deviations are given in parentheses.

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Table 3. Cumulative Variance Estimate for Five Soil Hydraulic Parameters From the Schaap et al. [2001] Database and Minasny et al.
[2004] Database Classified Using the Soil Hydraulic Classification and the USDA Soil Texture Classificationa
Schaap et al. [2001]

Minasny et al. [2004]

Parameter

Soil Hydraulic Classification

Soil Textural Classification

Soil Hydraulic Classification

Soil Textural Classificationqr
qs
log10(a)log10(n)log10(Ks)

2.052
2.401
18.7894.656
26.272

2.083
2.445
18.79
4.714
26.988

1.463
0.532
4.509
2.034
11.897

1.5
0.536
4.698
2.099
11.927aA lower cumulative variance (CUV) estimate indicates better classification.

of classifying soils, even from a hydraulic standpoint. In thisresearch, we have developed a new soil classification that
accounts for the hydraulic characteristics of soils. The resulting soil hydraulic triangle has been shown to improve theclassification of soils with respect to soil hydraulic characteristics. It was observed that the soil texture triangle isqualitatively very similar to the soil hydraulic triangle,
especially for soils where gravity-driven flow dominates
capillary forces (such as sands). However, the similarities
do not exist for soils where capillary forces dominate the flow
through soils. When compared to the soil texture classification, a performance analysis of the classification by soil
hydraulic classes on two real-world databases indicated amarginal improvement. Also, the average soil hydraulicparameters for each soil hydraulic class were estimated. We
do not consider soil structural effects on soil hydraulicbehavior. The results of this research pertain to uniform soils
and do not consider other soil structures. The results of thisresearch are therefore conditional on the aforementioned
important assumption. From a philosophical perspective,
the research further stresses the need to revisit and reevaluate
the results from the past in order to successfully move ahead
into the future of soil physics. Also, we recognize the lack of acomprehensive soil hydraulic database as a major limitation
for the progress of soil sciences, especially in the development of proper soil classification systems.

Appendix A[26] According to its definition, field capacity (qfc) is theamount of soil moisture or water content held in soil after
excess water has drained away and the rate of downward
movement has materially decreased. Several authors [e.g.,
Richards and Weaver, 1944] have suggested suction heads at
which soil attains qfc. However, ambiguity exists as to theaccuracy of these suggestions. In this study, we attempt toestimate qfc using a model that is based on the traditional
definition. For the purpose of our analysis, we defined qfc as
the water content at which the drainage from a profile ceases
under natural conditions. Since drainage from a soil profile ina simulation never becomes zero, we assume that drainage
ceases when the bottom flux from the soil reaches a valuethat is equivalent to the minimum amount of precipitation that
could be recorded. Dirksen and Matula [1994] observed thatthe smallest amount of rainfall measured in meteorologicalstations was 0.01 cm/d. We used 0.01 cm/d as the value of thebottom flux at which one may assume that qfc is attained.
[27] The HYDRUS-1D software [Šimůnek et al., 2005]
was used to estimate the qfc and the drainability (time needed
to reach qfc from saturated conditions) under conditions of noevaporation. The HYDRUS-1D employs the classical
Richards equation [Richards, 1931]. For a one-dimensional
scenario, the Richards equation is described mathematically
as


@q
@
@h
¼
KðhÞ  KðhÞ  S;
@t @z
@z

ðA1Þ

where q is the volumetric water content (dimensionless),
h is the soil water pressure head (L), t is time (T), z is the
distance from reference datum (L), and K(h) is the unsaturated
hydraulic conductivity (L T1) as a function of h or q.
[28] Given estimates of soil hydraulic parameters (a, n, Ks,
qs, and qr), qfc, hfc, and tfc were estimated using HYDRUS1D. In a model setup, a 1 cm long one-dimensional profile
was considered. The profile was initially considered to besaturated. A no-flux boundary condition was used at the topof the profile. A free-drainage boundary condition at thebottom of the profile was used throughout the simulation.
Under these conditions, HYDRUS-1D was used to simulate
the changes in the water content in the profile until the flux atthe bottom of the profile reached a value of 0.01 cm/d. The

Table 4. CUV Estimate for Water Contents and Unsaturated Hydraulic Conductivities as a Function of Capillary Pressure From the
Schaap et al. [2001] Database Classified Using Soil Hydraulic Classification and USDA Soil Texture Classificationa
Water Content (cm3/cm3)

Unsaturated Hydraulic Conductivity log10 (cm/d)
Capillary Pressure Head
log10 (h) log10 (cm)NumberSoil HydraulicClassification

Soil Textural
Classification

NumberSoil HydraulicClassification

Soil Textural
Classification

<1
1–2
2–3
3–4
4

335
1286
1969
434
38

1.66
10.35
12.12
2.07
0.08

1.75
10.57
12.40
2.16
0.08

1326
6782
7329
3330
1860

1271.636834.904558.64938.39368.281271.907037.68
4571.83
991.34380.00a

A lower CUV estimate indicates better classification.

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W01501

TWARAKAVI ET AL.: SOIL HYDRAULIC CLASSIFICATION

water content when the bottom flux reached 0.01 cm/d wasassumed to be qfc. The associated time needed to attain thefield capacity from saturation was considered the drainability(tfc), and the pressure head at which the field capacity wasestimated was hfc. Twarakavi et al. [2009] give a detailed
analysis of this approach, and readers are referred to theirstudy for further details.

References
Atterberg, A. (1905), Die rationale Klassifikation der Sande und Kiese,
Chem. Ztg., 29, 195 – 198.
Atterberg, A. (1912), Die Konsistenz und die Bindigheit der Boden, Int.
Mitt. Bodenkunde., 2, 148 – 189.
Carsel, R. F., and R. S. Parrish (1988), Developing joint probability distributions of soil water retention characteristics, Water Resour. Res., 24,755 – 769, doi:10.1029/WR024i005p00755.
Davis, R. O. E., and H. H. Bennett (1927), Grouping of soils on the basis ofmechanical analysis, Dep. Circ. 419, U.S. Dep. of Agric., Washington,
D. C.
Dirksen, C., and S. Matula (1994), Automated atomized water spray system
for soil hydraulic conductivity measurements, Soil Sci. Soc. Am. J., 58,
319 – 325.
Hartigan, J. A., and M. A. Wong (1979), A k-means clustering algorithm,
Appl. Stat., 28(1), 100 – 108, doi:10.2307/2346830.
MacQueen, J. B. (1967), Some methods for classification and analysis ofmultivariate observations, in Proceedings of 5th Berkeley Symposium on
Mathematical Statistics and Probability, vol. 1, pp. 281 – 297, Univ. of
Calif. Press, Berkeley.
Minasny, B., J. W. Hopmans, T. H. Harter, A. M. Tuli, S. O. Eching, and
D. A. Denton (2004), Neural network prediction of soil hydraulic functions for alluvial soils using multi-step outflow data, Soil Sci. Soc. Am. J.,
68, 417 – 429.
National Resources Conservation Service (NRCS) (1975), Soil Taxonomy:
A Basic System of Soil Classification for Making and Interpreting Soil
Surveys, U.S. Dep. Agric. Handb., vol. 436, 754 pp., U.S. Gov. Print.
Off., Washington, D. C.
Pachepsky, Y. A., and W. J. Rawls (2004), Development of Pedotransfer
Functions in Soil Hydrology, Dev. Soil Sci., vol. 30, Elsevier, Amsterdam.
Rawls, W. J., D. L. Brakensiek, and K. E. Saxton (1982), Estimation of soil
water properties, Trans. ASAE, 25(5), 1316 – 1320.
Richards, L. A. (1931), Capillary conduction of liquids through porous
media, Physics, 1, 318 – 333, doi:10.1063/1.1745010.

W01501

Richards, L. A., and L. R. Weaver (1944), Moisture retention by someirrigated soils as related to soil moisture tension, J. Agric. Res., 69,
215 – 235.
Schaap, M. G., and F. J. Leij (1998), Database-related accuracy and uncertainty of pedotransfer functions, Soil Sci., 163, 765 – 779, doi:10.1097/
00010694-199810000-00001.
Schaap, M. G., F. J. Leij, and M. T. van Genuchten (2001), ROSETTA:
A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions, J. Hydrol., 251(3 – 4), 163 – 176,
doi:10.1016/S0022-1694(01)00466-8.
Šimůnek, J., M. T. van Genuchten, and M. Šejna (2005), The HYDRUS-1D
software package for simulating the movement of water, heat, and multiple solutes in variably saturated media, version 3.0, HYDRUS Software
Ser. 1, Dep. of Environ. Sci., Univ. of Calif., Riverside.
Skaggs, T. H., L. M. Arya, P. J. Shouse, and B. P. Mohanty (2001), Estimating particle-size distribution from limited soil texture data, Soil Sci.
Soc. Am. J., 65, 1038 – 1044.
Soil Survey Staff (1951), Soil Survey Manual, U.S. Dep. Agric. Handb.,
vol. 18, 503 pp., U.S. Gov. Print. Off., Washington, D. C.
Twarakavi, N. K. C., M. Sakai, and J. Šimůnek (2009), An objective studyof the dynamic nature of field capacity, Water Resour. Res., 45, W10410,
doi:10.1029/2009WR007944.
van Genuchten, M. T. (1980), A closed-form equation for predicting thehydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44(5),892 – 898.
Wösten, J. H. M., P. A. Finke, and M. J. W. Jansen (1995), Comparison ofclass and continuous pedotransfer functions to generate soil hydrauliccharacteristics, Geoderma, 66, 227 – 237, doi:10.1016/0016-7061(94)00079-P.
Wösten, J. H. M., Y. A. Pachepsky, and W. J. Rawls (2001), Pedotransfer
functions: Bridging the gap between available basic soil data and missing
soil hydraulic characteristics, J. Hydrol., 251, 123 – 150, doi:10.1016/
S0022-1694(01)00464-4.



M. G. Schaap, Department of Soil, Water and Environmental Sciences,
University of Arizona, Tucson, AZ 85721, USA.
J. Šimůnek, Department of Environmental Sciences, University ofCalifornia, 2208 Geology Building, Riverside, CA 92521, USA.
N. K. C. Twarakavi, Department of Agronomy and Soils, Auburn
University, 258 Funchess Hall, Auburn, AL 36832, USA. (twarakavi@
auburn.edu)

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