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Pedotransfer functions to predict Atterberg limits for SouthAfrican soils using measured and morphological properties
J. J. VAN TOL1, A. R. DZENE
2, P. A. L. LE ROUX1 & R. SCHALL
3
1Department of Soil, Crop and Climate Sciences, University of the Free State, Nelson Mandela Dr., Bloemfontein, 9300, South
Africa, 2Department of Agronomy, University of Fort Hare, King Williamstown Rd, Alice, 5700, South Africa, and 3Department of
Mathematical Statistics and Actuarial Science, University of the Free State, Nelson Mandela Dr., Bloemfontein, 9300, South
Africa
Abstract
Atterberg limits and indices, for example liquid limit (LL), plastic limit (PL), linear shrinkage (LS)
and plasticity index (PI), are important soil properties in engineering and land evaluation for
predicting soil mechanical behaviour. This study was conducted to develop and evaluate pedotransfer
functions (PTFs) to predict Atterberg limits using measured and morphological soil properties from a
large data set in South Africa covering a vast range of soils, geologies and climates. Five PTFs were
developed; the first four using measured properties from 2330 soil horizons including extractable Fe,
Al, Mn, Na, K, Mg and Ca; organic carbon (OC); pH (H2O); cation exchange capacity (CEC); and
sand, silt and clay fractions to predict LL, PL, LS and PI. Morphological descriptors such as colour,
structure (grade, size and type), consistency, occurrence of slickensides and cutans and abundance of
roots were included in the second PTF using data from 717 horizons to predict PI. For all PTFs,
two-thirds of the data were randomly selected and used for model development and the remainder for
validation. Prediction accuracies of R2 between 0.49 and 0.77 comparable to other studies on large
data sets but underperformed when compared to localized data sets. For engineering purposes, site-
specific PTFs for prediction of Atterberg limits should be developed.
Keywords: Engineering soil properties, linear shrinkage, liquid limit, plastic limit, plasticity index,
soil mechanics, soil morphology
Introduction
In 1911, Albert Atterberg qualitatively defined seven limits
that determine the mechanical behaviour of soils at
different water contents (Atterberg, 1911 in Haigh et al.,
2013). Three of these, namely liquid limit (LL), plastic limit
(PL) and linear shrinkage (LS), are frequently used to
quantify the physical activity of soils for engineering
purposes and for the estimation of other test indices such
as shear strength, bearing capacity, compressibility, swelling
potential and specific surface area (De Jong et al., 1990;
Fanourakis, 2012; Moradi, 2013). The LL is the water
content where a soil will begin to flow (become a viscous
fluid) under its own weight, the PL is the water content at
which a soil will crumble when rolled to a diameter of
3 mm (starts to behave like a semi-solid) and the LS is the
decrease in length of a soil sample when oven-dried,
starting with a moisture content of the sample at the liquid
limit (Atterberg, 1911; De Jong et al., 1990; SCWG, 1991).
The plasticity index (PI) is the numerical difference between
the LL and PL and is an indication of the workability of
the soil. In the South African Soil Classification System
(Soil Classification Working Group (SCGW), 1991), PI is a
diagnostic criterion to classify the diagnostic vertic topsoil
horizon.
Measurements of Atterberg limits are, however, time-
consuming and expensive and, despite the fact that they are
basic soil mechanical properties, are seldom recorded in soil
survey data (Ahmadi et al., 2012). Many researchers
consequently investigated relationships between other, more
available, easily and routinely measured properties and
Atterberg limits. These include inter alia the clay content (De
Jong et al., 1990; Schmitz et al., 2004; Fanourakis, 2012),
organic carbon (OC) and organic matter (OM) (Mbagwu &
Abeh, 1998; Zhang et al., 2005; Ahmadi et al., 2012;
Zolfaghari et al., 2015), cation exchange capacity (CEC)
(Mbagwu & Abeh, 1998; Yilmaz, 2004; Yukselen & Kaya,Correspondence: J. J. van Tol. E-mail: vantoljj@ufs.ac.za
Received July 2015; accepted after revision September 2016
© 2016 British Society of Soil Science 1
Soil Use and Management doi: 10.1111/sum.12303
SoilUseandManagement
2006; Moradi, 2013), calcium carbonate (Smith et al., 1985;
Zolfaghari et al., 2015), Mg contents (Fanourakis, 2012) and
bulk density (Seybold et al., 2008). These relationships are
also termed pedotransfer functions (PTFs), which were
defined by Bouma (1989) as ‘translating data that we have
into what we need’. PTFs are generally developed for
inference of soil hydraulic properties from easily measured
properties and often make use of regression equations
(Vereecken & Herbst, 2004). Most of the previously
published PTFs on Atterberg limits made use of multiple
linear regression (e.g. De Jong et al., 1990; Seybold et al.,
2008; Fanourakis, 2012; Moradi, 2013).
PTFs are, however, often only applicable and reliable for
the areas or soils where they were developed (Wagner et al.,
2001), with limited extrapolation value for other
environments, that is different climates, geologies and soils.
In South Africa, Fanourakis (2012) produced PTFs for five
soil forms occurring on approximately 4200 km2 in the
North West Province using Mg and the clay size fraction as
predictors of Atterberg limits. In this study, we aimed to
build on the work of Fanourakis (2012) and to develop
PTFs for estimating LL, PL, LS and PI from a large data
set covering most of South Africa. As South Africa is diverse
in terms of climate, geology and soils, it is hypothesized that
such PTFs can be useable internationally as well. Specific
objectives of this study were then (i) to explore relationships
between readily available soil properties and selected
Atterberg limits, (ii) to develop PTFs to estimate selected
Atterberg limits from readily measured soil properties and
(iii) to develop a PTF to assist soil surveyors to estimate PI
in the field.
Methodology
Land Type data set and data selection
Modal profiles from the Land Type database of South
Africa (Land Type Survey Staff, 1972–2002) were utilized. A
total of 3160 horizons with measured liquid limit (LL),
plastic limit (PL), linear shrinkage (LS) and plasticity index
(PI) values were identified, representing a large spatial
distribution (Figure 1). The horizons were broadly regrouped
into 10 diagnostic entities; for the topsoils, there were
distinguished between vertic, melanic, humic and orthic
horizons and for the subsoils between apedal, gleyed,
eluviated, plinthic, structured and saprolitic horizons. The
0 125 250 500 750 1 000Kilometers N
Figure 1 Location of soil profiles (and horizons) with measured Atterberg limits (Land Type Survey Staff, 1972–2002). [Colour figure can be
viewed at wileyonlinelibrary.com].
© 2016 British Society of Soil Science, Soil Use and Management
2 J. J. van Tol et al.
diagnostic horizons were only used to determine the
intercept terms. Data with obvious errors were eliminated
(e.g. negative or zero values of measured Atterberg limits
and abnormally high LL values, i.e. >100), as well as
horizons without geographical coordinates.
For quantitative analysis, the following explanatory
variables were considered: citrate–bicarbonate–dithionate(CBD) extractable Fe (%), Al (%) and Mn (%), percentage
organic carbon (OC) measured with the Walkley–Blackmethod, pH (H2O), extractable Na, K, Mg and Ca
(cmolc kg/soil), cation exchange capacity (CEC, cmolc kg/
soil), and particle size distribution (%) for three classes, that
is sand, silt and clay (initially measured with the pipette
method for five or seven classes but converted to the
aforementioned three classes). Any abnormal or spurious
values in explanatory variables were also identified, and the
specific variable was omitted from the data set. These
included horizons where the sum of the texture classes was
below and above 95 and 105%, respectively, CEC (cmolc kg/
soil) smaller than the sum of extractable Na, Mg, K and Ca
(cmolc kg/soil) any negative values and visually obvious
outliers. A total of 2230 horizons were included in the
quantitative analysis.
Qualitative data were selected based on pedogenetic
knowledge of variables possibly influencing Atterberg limits.
These included colour, field estimated texture class, terrain
morphological unit, soil structure (grade, size and type), field
estimated consistency, occurrence of slickensides and cutans,
abundance of roots and a description of the topography of
transition between horizons. To reduce the number of colour
classes, the Munsel colour value was translated into
descriptive colours.
Derivation of PTFs
Measured (quantitative) functions. Derivation of the PTFs
started with an analysis of data transformations with two
objectives, namely (i) to determine the optimal power
transformation of the dependent variables (the Atterberg
limits LL, PL, LS and PI) to normality and (ii) to
explore the functional relationship between the
(transformed) dependent variables and the 13 explanatory
variables.
Cubic spline transformations of the explanatory variables
were fitted to the dependent variables; the splines had three
degrees of freedom and allowed for two knots. At the same
time, the dependent variable was transformed by a power
transformation (Box & Cox, 1964) which, as a limiting case,
includes the logarithmic transformation. For each dependent
variable, the optimal power parameter for transformation of
the dependent variable to normality and the optimal spline
transformation of the explanatory variables were determined.
The analysis was carried out using the SAS procedure
TRANSREG (SAS, 2013).
The optimal power parameter k for transformation to
normality of the four dependent variables was as follows:
k = 0.5 (square root transformation) for LL, k = 0.75 for
LS, k = 0.5 for PI and k = 0 (logarithmic transformation)
for PL.
Furthermore, the results of the transformation analysis
suggested that a polynomial of degree 3 (or lower)
approximated the optimal spline transformation of all
explanatory variables well. Thus, for all dependent variables,
a cubic polynomial regression model was chosen as a basis
for stepwise variable selection. Specifically, regression
variables available for selection were the following: the 13
explanatory variables as linear, quadratic and cubic terms
(3 9 13 = 39 variables); the 78 cross-terms between the 13
linear terms; and the intercept terms for the 10 horizons
(nine degrees of freedom).
Using the collection of independent variables described
above, stepwise model selection was performed as follows:
starting with the intercept, at each selection step that variable
was chosen whose inclusion in the model achieved the largest
decrease in the Schwarz Bayesian information criterion (SBC);
similarly, a variable already in the model could be chosen for
exclusion if the exclusion led to a decrease in the SBC. Among
various criteria for model selection, the SBC was chosen
because it generally led to the most parsimonious model
(model with fewest variables). At all stages during the stepwise
selection process, model hierarchy was observed, namely a
higher order polynomial term (quadratic, cubic or cross-term)
could enter the model only if all lower order terms contained
in the higher order term were already present in the model.
Similarly, a lower order term could leave the model only if
there were no higher order terms in the model which contained
the lower order term. In all cases, 75% of the data were
randomly chosen as a training sample, while the remaining
25% of the data were used for validation of the selected
model. The model selection was carried out using SAS
procedure GLMSELECT (SAS, 2013).
The final model identified by the model selection
procedure was fitted twice as follows: (i) if Y is the original
dependent variable, the model was fitted to the transformed
dependent variable Yk, where k is the parameter of the
optimal Box–Cox power transformation (k = 0.5, 0.75, 0.5
respectively, for the variables LL, LS and PI, and In(Y) for
the variable PL). The resulting regression coefficients are
reported, as well as the goodness-of-fit statistics R2 and root-
mean-square error (RMSE) of prediction. (ii) The final
model was also fitted to the transformed dependent
variableðYk � 1=ðk � Y ðk�1ÞÞ, where, as before, k is the
parameter of the power transformation, and Y is the
geometric mean of the dependent variable on the original,
untransformed, scale [for the variable PL, where k = 0, the
transformed variable is Y � lnðYÞ]. We carried out the second
fit because for this form of the dependent variable, the
RMSE values can usefully be compared to RMSE values
© 2016 British Society of Soil Science, Soil Use and Management
PTFs for Atterberg limits of SA soils 3
obtained from a fit of the untransformed variable Y. Thus,
we report the RMSE values for the second fit to facilitate
comparison with RMSE values reported in the literature
which are often based on the fit of untransformed dependent
variables (Atterberg limits).
Morphological (qualitative) function. Morphological data
were only used to predict PI. The effect of different classes
within a variable (e.g. apedal, weak, moderate and strong for
structure grade) on PI was identified using multiple linear
regression correlations between the individual morphological
variables (with various classes) and PI. The slope (m) of the
linear function of various classes was then coded from lowest
to highest with whole numbers starting at 1. Again, two-
thirds (477) of the horizons were randomly selected and used
to develop the PTF between morphological variables and PI,
and the remaining 240 horizons were used to evaluate the
PTF using R2 and RMSE. The number of horizons used for
the morphological PTF is considerably smaller than that
used for quantitative PTFs as not all morphological
variables were described for all the horizons.
Results
PTFs based on quantitative data
The selected horizons represent a healthy range within
measured soil properties (Table 1), for example clay contents
ranged from 9.7 to 84.5%, pH between 4.3 and 10.2 and OC
between 0.03 and 5.0%. The vast range of within measured
soil properties reflects the heterogeneity of South African
soils, climate and geology (Figure 1).
Significant correlations existed between most variables and
Atterberg limits (Table 1). Large positive correlations exist
between clay content and all Atterberg limits. The same
applies to CEC. Extractable cations (Mg, Ca, K and Na) are
well correlated with most of the Atterberg limits, especially
PI. Significant negative correlations exist between sand
content and all Atterberg limits, as well as between most
variables and PL. Interestingly, there is no significant
correlation between OC and PI.
Inclusion of diagnostic horizons made only a significant
contribution to the prediction of LL (Tables 2 and 3). The
PTFs for the estimation of Atterberg limits suggested
predictions of LL from measured properties are the most
accurate (R2 = 0.77 for training data, Table 3). This
supported by the highest Pearson correlation coefficients
(Table 1). All the PTFs were, however, significant
(P < 0.0001). Fe and CEC are present in all the PTFs and
texture (sand, silt and clay) also have a significant influence on
the Atterberg limits. The R2 for prediction of LS (0.56), PL
(0.53) and PI (0.62) are relatively low when compared to LL.
PTF based on qualitative data
Despite the low correlation coefficients, the relationships
between morphological properties and PI were significant
Table 1 Summary of explanatory variables and Pearson’s correlations between individual measured variables and Atterberg limits (n = 2230)
Explanatory variable Min Max Med Std. Dev.
Pearson’s correlation
LL PL LS PI
Clay (%) 9.700 84.500 40.385 14.221 0.673** 0.3789** 0.609** 0.558**
Silt (%) 0.300 61.800 21.110 11.696 NS 0.251** 0.112** �0.109**
Sand (%) 1.600 75.600 36.902 16.922 �0.605** �0.490** �0.585** �0.387**
CEC (cmolc kg/soil) 2.120 61.000 15.079 7.549 0.614** 0.204** 0.539** 0.619**
Mg (cmolc kg/soil) 0.040 28.600 4.518 3.989 0.413** NS 0.371** 0.623**
Ca (cmolc kg/soil) 0.050 69.600 6.396 6.501 0.308** �0.116** 0.293** 0.503**
K (cmolc kg/soil) 0.020 5.140 0.421 0.487 0.078** �0.113** NS 0.144**
Na (cmolc kg/soil) 0.010 14.830 0.661 1.099 0.193** �0.116** 0.100** 0.354**
pH (H2O) 4.290 10.200 6.686 1.183 NS �0.354** NS 0.290**
OC (%) 0.030 5.000 0.949 0.878 0.219** 0.371** 0.165** NS
Mn (%) 0.000 1.127 0.041 0.071 0.120** 0.056* 0.128** 0.108**
Al (%) 0.001 3.221 0.317 0.363 0.244** 0.510** 0.166** �0.095*
Fe (%) 0.030 17.320 2.567 2.131 0.336** 0.474** 0.250** 0.050**
Min 13.000 5.000 0.070 1.000
Max 92.000 50.000 26.000 64.000
Med 38.767 18.437 6.281 20.295
Std. De. 11.566 6.548 3.302 9.156
Significance levels of a = 0.05 and 0.01 indicated by * and **, respectively.
© 2016 British Society of Soil Science, Soil Use and Management
4 J. J. van Tol et al.
(P < 0.01) for all the properties (Table 3). The occurrence of
slickensides and cutans, structure (grade, type and size) and
the field estimated consistency proved to be the best
predictors of PI. Although texture was a key determining
factor of PI with measured data (Pearson’s
correlation = 0.56, Table 1), the field estimated texture
classes appear inadequate to predict PI, with the lowest R2
(Table 4).
Following the stepwise selection criteria, the best model to
predict PI with morphological data is as follows:
PI ¼ �4:831þ 2:028 x Structure gradeþ 2:519
xConsistencyþ 2:459 xRootsþ 5:368 x Slickensides:ð5Þ
With a model accuracy of R2 = 0.51 and RMSE = 7.47 it
was considerably lower than obtained from measured data
(Table 3). The validation data are presented in Figure 2, and
again regression correlations are much lower than those of
measured data (Table 3) with slight overestimations of high
PI values. The relatively high RMSE (7.03) is reflected by
the scattering as shown in Figure 2.
Discussion
Measured data
Significant positive correlations existed between clay
fractions and most of the Atterberg limits studied, with
significant negative correlations between sand fractions and
all Atterberg limits (Table 1). These correlations are
expected and agree with other studies (e.g. De Jong et al.,
1990; Ahmadi et al., 2012) as clay is the major contributor
to plasticity in soils and inversely correlated to the sand plus
silt content. Large positive correlations also existed between
CEC and all Atterberg limits. The CEC is largely controlled
by the amount of swelling clay in most soils and therefore
Table 2 PTFs for estimating Atterberg limits from measured soil properties
Prediction equation for LL0.5 Prediction equation for LS0.75 Prediction equation for logPL Prediction equation for PI0.5
Parameter Estimate P-value Parameter Estimate P-value Parameter Estimate P-value Parameter Estimate P-value
Intercept 4.757 <0.001 Intercept 4.459 <0.001 Intercept 4.095 <0.001 Intercept 0.741 0.003
Humic-A*1 �0.601 <0.001 Fe 0.292 <0.001 Fe 0.198 <0.001 Fe 0.126 <0.001
Melanic-A �0.352 0 pH �1.331 <0.001 Al 0.136 <0.001 OC �0.068 <0.001
Orthic-A �0.402 <0.001 K �0.638 <0.001 OC 0.022 0.3022 Na �0.041 0.282
Apedal-B*2 �0.141 0.124 Mg 0.04 0.001 pH �0.364 <0.001 Mg 0.075 <0.001
Eluvial-B �0.495 <0.001 CEC 0.068 <0.001 CEC 0.005 0.005 CEC 0.027 <0.001
Gleyed-B 0.05 0.613 Si 0.049 <0.001 Sa �0.017 <0.001 Clay 0.134 <0.001
Plinthic-B 0.017 0.864 Cl 0.061 <0.001 (Fe)2 �0.01 <0.001 (Fe 9 Cl) �0.002 <0.001
Saprolitic B/C 0.054 0.563 (Fe 9 Cl) �0.004 <0.001 (Fe 9 OC) �0.016 <0.001 (Na 9 CEC) 0.005 0.002
Structured-B �0.102 0.227 (pH)2 0.086 <0.001 (Fe 9 pH) �0.013 <0.001 (Cl)2 �0.001 <0.001
Fe 0.411 <0.001 (K)2 0.116 0.002 (OC)2 0.018 0.002 (Cl)3 0.001 <0.001
Al 0.192 <0.001 (Si)2 �0.001 <0.001 (pH)2 0.025 <0.001
OC 0.277 <0.001 (CEC 9 Sa) 0.001 <0.001
pH �0.186 <0.001 (Sa)2 0.001 <0.001
Na �0.026 0.398 (Fe)3 0.001 0.004
Ca �0.107 <0.001
Mg 0.059 <0.001
CEC 0.062 <0.001
Sa 0.003 0.075
Cl 0.025 <0.001
(Fe 9 OC) �0.035 <0.001
(Fe 9 Sa) �0.003 <0.001
(Fe 9 Cl) �0.005 <0.001
(pH 9 Ca) 0.015 <0.001
(Na 9 Ca) �0.006 0.005
(Na 9 CEC) 0.007 <0.001
(CEC 9 Cl) �0.001 <0.001
(Clay)2 0 <0.001
Fe and Al: CBD iron and aluminium content (%); OC: organic carbon content (%); Na, Ca, K and Mg: pH: pH (H2O); extractable sodium,
calcium, potassium and magnesium (cmolc kg/soil); CEC: cation exchange capacity (cmolc kg/soil); Sa, Si and Cl: sand, silt and clay fractions
(%). *1-A refers to topsoil horizons and *2-B to subsoil horizons.
© 2016 British Society of Soil Science, Soil Use and Management
PTFs for Atterberg limits of SA soils 5
related to clay mineralogy (Moradi, 2013). Higher CEC
values are typically associated with soils dominated by 2:1
clay minerals which are plastic by nature. The role of
magnesium (Mg) in the structure of montmorillonitic clay
implies a link to CEC and an indirect, although strong,
correlation with PI. Fanourakis (2012) found that Mg in the
clay-sized fraction can predict LL, PI and LS sufficiently in
apedal subsoils with r values of 0.92, 0.72 and 0.82,
respectively (albeit for a much smaller, localized data set).
Positive correlations between Atterberg limits and cations
were also reported by De Jong et al. (1990), Ahmadi et al.
(2012) and Moradi (2013). The lack of impact by OC on the
indicators of PI may be due to a contribution to CEC of the
soil imitating higher physical activity but is actually
physically stabilizing the soil. Zolfaghari et al. (2015) also
reported no significant correlations between LL and PI and
OC, but Seybold et al. (2008) considered OC an important
predictor of PI.
The PTFs developed (Tables 2 and 3) have low predictive
value when compared to other studies with smaller data sets
and localized studies. For example, Ahmadi et al. (2012),
using 26 samples, obtained R2 of 0.87, 0.77 and 0.84 for LL,
PL and PI, respectively. The RMSE (%) was below 3 for all
these predictions. The modelling accuracy of Fanourakis
(2012) reported earlier was obtained on 30 samples of the
same diagnostic horizon.
Model accuracy of PTFs conducted on larger data sets is
more comparable to our results (Table 3). De Jong et al.
(1990) working with approximately 260 samples reported R2
of 0.86, 0.35 and 0.35 for LL, PL and PI, respectively. The
prediction of LL of Seybold et al. (2008) on 4332 samples
(R2 = 0.79; RMSE = 6.694) is comparable with our results
(R2 = 0.77; RMSE = 5.38). Likewise, our prediction of PI
(R2 = 0.62; RMSE = 5.19) is analogous with that of Seybold
et al. (2008) on 2797 samples (R2 = 0.69; RMSE = 5.429).
The higher R2, in comparison with De Jong et al. (1990), for
prediction of PL and PI, and lower RMSE, compared to
Seybold et al. (2008), might be attributed to a more complex
model structure (Tables 2 and 3).
Morphological data
Physical activity leaves conspicuous signatures in the soil.
The expression of these signatures could be related to the
parameters of PI. Slickensides, cracks in the dry state and
structure are commonly known as inherently part of swelling
soils and therefore used as classification criteria for
extremely swelling soils.
The relationship with terrain relates to hydrology. The
distribution of swelling clays is related to wetness.
Pedological wetness of a terrain position is dependent on
climate as locally manipulated by hydrology. A very large
area of South Africa is semi-arid with a long boundary to
the arid climate zone. Climatically the dry semi-arid climates
are too dry for the development of swelling clays either by
weathering of basic igneous rock to swelling clay or the
neoformation of clay. Hydrological redistribution of water to
valley bottoms results in the crest of the hillslope being to
dry and the valley bottom wet enough for the formation
of swelling clay. This is in agreement with the results of
Zolfaghari et al. (2015) who recorded greater plasticity at
deeper positions in the profile. A positive correlation
between swelling properties and structure, specifically coarse
angular blocky and prismatic, and slickensides confirms tacit
knowledge in every soil surveyor working with a variety of
swelling soils (Table 4). The positive correlation of physical
Table 3 Characteristics of final selected regression models for Atterberg limits (n = 2230)a
Atterberg
limit (dependent
variable) to
be predicted
Exponent of
optimal power
Transformation of
dependent variablebHighest
term selected
Intercept
terms for
horizon
selected?
Number of
model parameters
(excl overall
intercept) R2 (training data)
RMSE
(training data)cRMSE
(validation data)c
LL k = 0.5 Quadratic Yes 27 0.774 5.380 5.160
0.439 0.430
LS k = 0.75 Quadratic No 11 0.563 2.10 2.050
1.050 1.020
PL k = 0. (logarithm) Cubic No 14 0.526 4.130 4.610
0.229 0.255
PI k = 0.5 Cubic No 10 0.624 5.19 5.130
0.614 0.607
aOf the total sample (n = 2230), 75% of observations (nT = 1669) were randomly selected as training sample, and 25% (nV = 561) as validation
sample. bPower parameter k of Box–Cox transformation of dependent variable (Box & Cox, 1964). cFor each model, the first line provides
RMSE values for the transformed dependent variable scaled as ðYk � 1=ðk � Y ðk�1ÞÞ, where k is the parameter of the power transformation, and Yis the geometric mean of the dependent variable on the original scale (these RMSE values can usefully be compared to RMSE values obtained
from a fit of the untransformed variable Y); the second line (in italics) provides RMSE values for the transformed dependent variable Yk. When
k = 0, the transformed dependent variables, respectively, are given by Y � lnðYÞ and ln(Y).
© 2016 British Society of Soil Science, Soil Use and Management
6 J. J. van Tol et al.
Table
4Morphologicalsoilproperties,regressionslopes
andassociatedcodingusedin
developmentofPTF
Texture
(R2=0.014)
Class
(N)
SiLm
(41)
Sa(5)
Si(1)
SiClLm
(73)
SaLm
(84)
SaCl(225)
Lm
(100)
SaClLm
(580)
SiCl(115)
ClLm
(283)
Cl(873)
m0.000
0.011
0.018
0.045
0.052
0.080
0.099
0.111
0.176
0.181
0.273
Code
12
34
56
78
910
11
Structure
type
(R2=0.163)
Class
(N)
Mass
(981)
Crumb(76)
Granu(45)
Platy
(17)
Sanbl(1064)
Colum
(20)
Prism
(185)
Anbl(492)
m�0
.232
�0.063
�0.019
�0.011
0.000
0.008
0.107
0.236
Code
12
34
56
78
Colour
(R2=0.071)
Class
(N)
Yellow
(29)
Red
(550)
Brown(1740)
Grey(146)
Black
(129)
m0.000
0.011
0.085
0.219
0.221
Code
12
34
5
TMU
(R2=0.016)
Class
(N)
Crest
(340)
Midsl(1559)
Valbt(273)
Ftsl(829)
m�0
.095
�0.085
0.000
0.030
Code
12
34
Structure
grade
(R2=0.224)
Class
(N)
Aped
(1001)
Weak(819)
Modr(572)
Strng(501)
m�0
.087
0.000
0.271
0.415
Code
12
34
Structure
size
(R2=0.121)
Class
(N)
None(898)
Fine(519)
Med
(857)
Coar(488)
m0.000
0.206
0.301
0.338
Code
12
34
Consistency
(R2=0.150)
Class
(N)
Loose
(45)
Frbl(613)
Firm
(1026)
VFrm
(221)
m�0
.596
�0.407
�0.218
0.000
Code
12
34
Cutans
(R2=0.164)
Class
(N)
None(531)
Few
(542)
Cmn(520)
Many(283)
m0.000
0.233
0.378
0.459
Code
12
34
Roots
(R2=0.060)
Class
(N)
Many(253)
Cmn(498)
Few
(635)
None(141)
m�0
.147
�0.131
�0.120
0.000
Code
12
34
Transitiontopo
(R2=0.015)
Class
(N)
Broke(33)
Smoo(1566)
Tong(93)
Wavy(387)
m�0
.122
�0.077
�0.022
0.000
Code
12
34
Slickenside
(R2=0.361)
Class
(N)
None(554)
Few
(91)
Many(103)
m0.000
0.319
0.517
Code
12
3
SiLm,Silty
Loam;Sa,Sand;Si,Silt;SiClLm,Silty
ClayLoam;SaLm,SandyLoam;Lm,Loam;SaClLm,SandyClayLoam;SiCl,Silty
Clay;ClLm,ClayLoam;Cl,Clay;Mass,
Massive;
Granu,Granular;Sanbl,Sub-angularblocky;Colum,Columnar;Prism
,Prism
atic;
Anbl,Angularblocky;Midsl,Midslope;
Valbt,Valley
bottom;Ftsl,Footslope;
Aped,
Apedal;Modr,Moderate;Strng,Strong;Med,Medium;Coar,Coarse;
Frbl,Friable;VFrm
,Veryfirm
;Cmn,Common;Smoo,Smooth;Tong,Tongey;Topo,Topography;TMU,
Terrain
MorphologicalUnit.
© 2016 British Society of Soil Science, Soil Use and Management
PTFs for Atterberg limits of SA soils 7
activity with soil colour is also a confirmation of tacit
knowledge. The selection of data across all soil types brings
another element to the front. Black colours are commonly
associated with increased clay in a calcium-rich environment
and grey colours with water logging; yet, both are positively
correlated with the parameters of physical activity. The
positive correlation with consistence confirms the
relationship between vertic soils and gleyed subsoils. Gleyed
subsoils are generally waterlogged or at least wet, and
typical vertic morphology does not occur. It indicates an
impact of soil water regime on the development of vertic
properties often overlooked.
The negative correlation of roots and horizon transition
with parameters of physical activity is indirect (Table 4).
Stunted growth of trees on soil with extremely high physical
activity is claimed to be from root pruning related to
shrinking in the dry state.
Although the accuracy of PTF to estimate PI from
morphological data is not comparable to those developed
from measured properties (Table 3), and especially not to
those developed from measured properties on local scale
(e.g. Fanourakis, 2012), it might be able to assist pedologist
to quantify PI in the field with a degree of accuracy.
Conclusion
Atterberg limits are generally used for engineering purposes,
which by nature requires site-specific information. Although
the PTFs presented are comparable with other studies
working on large data sets, it is clear that PTFs for specific
areas are more accurate and hence more applicable in
practice. For engineering purposes, PTFs of Atterberg limits
should therefore be developed for specific areas. The
presented PTFs can, however, be valuable for reconnaissance
purposes, for example identifying areas likely to pose
structural challenges on large-scale developments.
Although the PTF developed from morphological
properties has a low prediction accuracy, it does suggest that
there is potential to use these properties in PTFs. Future
research should therefore aim to combine morphological
properties and routinely measured soil properties to improve
PTFs.
Acknowledgements
We would like to express our gratitude towards all Land
Type personnel who classified the soils and collected soil
samples as well as towards the Agricultural Research
Council of South Africa for availing the data.
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R2 = 0.485
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40
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Mea
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I
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PTFs for Atterberg limits of SA soils 9
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