556

PEDOTRANSFER FUNCTIONSPEDOTRANSFER FUNCTIONS
Yakov Pachepsky1, Martinus Th. van Genuchten2
1
Environmental Microbial and Food Safety Laboratory,
Animal and Natural Resource Institute, Beltsville
Agricultural Research Center, USDA-ARS, Beltsville,
MD, USA
2
Department of Mechanical Engineering, COPPE/LTTC,
Federal University of Rio de Janeiro, UFRJ, Rio deJaneiro, Brazil

Definition
Pedotransfer functions. Equations or algorithms expressing
relationships between soil properties different in difficultyof their measurement or their availability.
Introduction
Parameters governing the retention and movement ofwater and chemicals in soils are notorious for the difficulties and high labor costs involved in measuring them.
Often, there is a need to resort to estimating these parameters from other, more readily available data. Following
Briggs and Shantz (1912), who were the pioneers in thefield, generations of researchers quantified and interpreted
relationships between soil properties. Such terms as “prediction of ” or “predicting” soil properties, “estimation of ”
or “estimating” soil properties, “correlation of ” or “correlating” soil properties, were used interchangeably to namethe contents, procedures, and results of these type of studies (Carter and Bentley, 1991; Rawls et al., 1991; van
Genuchten and Leij, 1992; Timlin et al., 1996; McBratney
et al., 2002). Relatively recently, equations expressing
relationships between soil properties were proposed tobe called “transfer functions” (Bouma and van Lanen,
1987) and later “pedotransfer functions” or PTFs (Bouma,1989). Large international databases, such as UNSODA(Leij et al., 1996), HYPRES (Lilly,1997; Wösten et al.,1999), WISE (Batjes, 1996), the NRCS pedon database(NRCS, 2007), as well as national databases such as theSoil Profiles Bank of Polish Mineral Soils (Gliňski et al.,1991) were established and used for the purpose of PTF
development. Recently the number of PTF applications
increased significantly due to development of geographic
information system based regional modeling.
Pedotransfer functions to predict soil hydraulic properties are most numerous. Such PTFs have many potentialuser groups in agrophysics. For example, soil water retention and hydraulic conductivity data are needed to partition precipitation into runoff and infiltration, to assess
evapotranspiration, to schedule management practices,
especially irrigation and chemical applications, to establish components of the heat balance, and to predict contaminant transport.
For soil water retention, one approach (using point
PTFs) consists of estimating soil water contents at several
soil water pressure heads using a separate predictive

equation for each pressure head. Another approach (usingparametric PTFs) involves estimating coefficients in equations that express the dependence of the water content on
the soil water potential. The equations that are most often
used for this purpose are the Brooks–Corey equation(Brooks and Corey, 1964) ly  yrhb¼(1)
ys  yrhand the van Genuchten equation (van Genuchten, 1980)y  yr1¼
ys  yr ð1 þ jahjn Þm(2)where y is the volumetric water content, ys is the saturated
water content, yr is the residual water content, h is the soil
water pressure head, hb is the soil water pressure headcorresponding to the soil bubbling pressure or air entry
value. The parameters yr , hb, and l in Equation 1, and yr ,a, m, and n in Equation 2 are empirical coefficients.
Pedotransfer functions have been constructed to estimate
these coefficients using many local and regional data sets.
For the saturated hydraulic conductivity, Ksat, one
approach is to estimate this coefficient from basic soil
parameters without employing soil water retention data
(e.g., Bloemen, 1980). Another approach benefits fromthe use of soil pore space models to derive Ksat equations
in which the coefficients must be estimated from basic soil
properties (e.g., Han et al., 2006). Estimates of the unsaturated hydraulic conductivity are based predominantly
on pore size distribution models that relate the unsaturated
hydraulic conductivity to Ksat as well as several geometricparameters of the pore space inferred from water retention
data. A general form of such a model was proposed byAlexander and Skaggs (1987):
8S
9d
R
>
g >
>
>
>
< ½hðyÞ dy>=b 0kðhÞ ¼ Ksat ½SðyÞ
(3)
>
R1
>
>
g >
>
>
: ½hðyÞ dy;
0where S is effective saturation give by S = (yyr)/(ysyr),
and b, g, and d are parameters. Pedotransfer functions
must be used to estimate both Ksat and h(y) in Equation 3
to evaluate the integral and calculate the unsaturated
hydraulic conductivity (Pachepsky et al., 2000).
Soil erosion prediction models frequently rely upona variety of soil pedotransfer functions that most often
estimate soil erodibility and soil infiltration parameters(Flanagan, 2004). Existing long-term historical erosion
plot data (e.g., the USLE database) provide sufficient
information to create pedotransfer equations for soil erosion models.
Solute and gas retention and transport parameters canbe predicted reasonably well also from basic soil properties, although caution should be exercised because of

PEDOTRANSFER FUNCTIONS

possible scale effects (i.e., the effect of the scale of solutetransport on solute dispersion and retardation). Unified
diffusivity models can use existing PTFs to estimate soluteand gas diffusivities as a function of soil water content(Minasny and Perfect, 2004). Based on current knowledge, the pore size distribution appears to be an acceptabledispersivity predictor, with water retention PTFs being
helpful in developing PTFs for the dispersivity.
Soil water retention has been related to soil rheology bydefining several characteristic points on the water retention curve that separate segments of the retention curve
where the forces causing water retention have a distinctly
different physical nature (Voronin, 1990; Shein et al.,2004). Water contents at the characteristic points in thisapproach are termed key water contents and are related
to the soil pressure head. The key water contents can be
estimated from the liquid limit, the plastic limit, and dataon evaporation from soil. As soon as they are estimated,their relationships with the soil matric potential provide
several points on the water retention curve.

PTF inputs
Soil water retention and the soil hydraulic conductivity are
essential hydraulic properties that can be estimated using
PTFs. The particle size distribution and its parameters
are used in almost all pedotransfer functions. Differencesin the particle size classes of various national and international classifications have to be factored in when PTFs
are used. It is very important to use the correct boundariesof the sand and silt textural classes from the classification
used during PTF development, rather than from a specificnational classification.
Water retention PTFs generally become more accurate
when some experimental information about water retention is used as the PTF input (Ahuja et al., 1985). Soilorganic carbon content and composition both affect soil
structure and the adsorption properties, which imply thatsoil bulk density, water retention, and hydraulic conductivity may be affected by soil organic carbon. The effectof soil organic carbon on the soil hydraulic properties
exhibits a complex dependence on proportions of texturalcomponents and amount of organic carbon (Rawls et al.,2003).
Using soil morphological attributes and soil structure inpedotransfer functions is extremely important because of
the dominant role of soil structure in soil hydrology.
Unfortunately, effectively using soil morphological attributes is also very difficult because of the semiqualitative
nature of soil morphology and related soil structure
descriptors. It is possible to develop pedotransfer relationships to predict soil hydraulic properties and soil hydrological functioning from soil morphology data, including
soil structure (Lin et al., 1999). These relationships canbe expressed as either pedotransfer functions or
semiqualitative pedotransfer rules. A considerable volume
of soil morphological data residing in national andregional databases can be of great use in providing

557

information on soil hydrology. However, future progress
may require the acceptance of standardized methodologies to describe and quantify soil morphological attributes,
as well as to measure soil hydraulic properties in the field.
Soil aggregate composition is often assumed to berelated to soil structure and as such has been expected toaffect soil water retention. That has indeed been the casewhen the quantiles of soil aggregate size distributions
have been used, instead of contents of individual aggregate fractions (Guber et al., 2003).
Soil mineralogical and chemical properties are conceptually important factors of the ability of a soil to retain andtransmit water. This may be one of the reasons why a preliminary genetic grouping of soils appears to be a usefulway to improve PTF performance (Pachepsky and Rawls,
1999). Much can be gained in understanding and estimating soil hydraulic properties when mineralogical andchemical data are coupled with soil physical information(Bruand, 2004). Such coupling is especially beneficial
for regions where soil salinity and alkalinity constituteenvironmental and management problems.

PTFs in a spatial context
PTFs generally are constructed using data from small
point samples, but then are most often applied to large spatial units. Results of applications will depend on basic soil
data availability within those units, on soil variability
within those units, on the capability of PTFs to reproduce
this variability, and on our ability to modify PTFs
according to the scale of the application. The spatial
dependencies in PTF input may not necessarily translatecorrectly to spatial dependencies in the PTF output, inwhich case corrections of the existing PTFs are needed
to reflect the spatial dependencies (Romano, 2004).
A relatively new promising direction in PTF development is the use of spatially dense physical information
related to the soil cover. Soil properties are known tobe related to landscape position. Since geomorphic information has long been routinely used in soil mapping,geomorphometry may be a valuable data source to predict
basic soil properties. In particular, soil texture, organic
matter content, and bulk density are known to reflect bothlandscape position and land surface shape. Because thesesoil properties are most often included in pedotransfer
functions, one can hypothesize that soil hydraulic properties should have some relationship to landscape positionand land surface shape. Overall, the reported studies andrelated discussions confirm the usefulness of topographic
attributes as ancillary data to indirectly estimate soil
hydraulic properties. Geophysical techniques, such as
ground-penetrating radar, penetrometers, electric conductivity surveys, and remote sensing provide spatial coverage that shows great potential to be included in PTFs.
Methods to develop PTF
Statistical regression has been a popular tool for PTF
development for many decades (e.g., Rawls et al., 1982).

558

PEDOTRANSFER FUNCTIONS

An advantage of regression techniques is the possibility toobtain rigorous estimates of the statistics of the predictedvalues and the coefficients in the PTF equations. However, as shown by Vereecken and Herbst (2004), the blinduse of statistical computer packages without a preliminary
and a posteriori data analysis can have a deleterious effecton the regression results. Model misspecification, thepresence of outliers, multicollinearity, and other drawbacks, have to be anticipated and overcome. As such,
constructing PTFs using regression is an iterative procedure that may require many iteration steps.
Applying statistical regression to predict soil properties
that are difficult to measure requires (a) deciding which
properties are to be used as predictors and (b) which regression equation to use. Those decisions are not straightforward, especially when the databases involved containmany potential predictors and the relationships between
soil properties may be different in different parts of thedatabases. For this reason, PTF development recently has
employed data mining and exploration methods, as wellas machine learning algorithms, which automate predictor
and equation selections. Artificial neural networks havebecome a common tool for modeling complex “input–
output” dependencies in pedotransfer functions becauseof their ability to mimic the behavior of complex systems(Pachepsky et al., 1996; Schaap and Bouten, 1996).
While being powerful approximators, artificial neuralnetworks often lack a built-in methodology to remove
the less or least important input variables. PTF development for this reason benefits from methods that do notassume a certain type of dependency, while still being able
to eliminate some predictors. The most important predictors may also be different in different parts of the database.
The database then has to be quite large to permit the useof artificial neural networks. A data exploratory technique
aimed at uncovering some structure in the data can be useful in such cases. Regression tree modeling (e.g., Rawls
and Pachepsky, 2002) is such a technique that gives transparent results and can be applied not only to numerical but
also to categorical soil data. Another drawback of usingneural networks may be the inability of finding the best
approximation for the entire database. Using support vector machines in PTF development may provide a goodsolution (Lamorski et al., 2008).
PTF development presumes that similarity in input will
result in similarity in output. For large enough databases,
one can find soils with properties that are very close to
the soil for which the pedotransfer prediction is needed.
In such case, finding the closest neighbors and using their
hydraulic properties as the required PTF predictions has
been shown beneficial (Nemes et al., 2006).
PTFs have also been developed based on the additivity
hypothesis that the property of interest (e.g., water retention) is known for certain soil components (e.g., certain
particles size ranges), and that this property then can be
estimated for the entire soil by adding component values
with appropriate weights (Zeiliguer et al., 2000).

PTF evaluation and selection
Evaluation of PTFs is an essential element of their development and use. Pachepsky et al. (1999) broadly defined
the accuracy of a PTF as the degree of correspondence
between measured and estimated data for the data set fromwhich the PTF was developed. The reliability of a PTF
was assessed in terms of the correspondence between
measured and estimated data for the data set(s) other thanthe one used to develop the PTF. Finally, the utility ofa PTF in modeling was viewed as the degree of correspondence between measured and simulated environmental
variables.
The concept of PTF uncertainty (Schaap and Leij,
1998) encompasses the ambiguity in PTF predictions
and parameters caused by input data variability anduneven representation of soils with different properties inthe database. The uncertainty in PTF estimates may beevaluated using replicated PTF development with data
resampling by either the bootstrap (Schaap et al., 1998)
or jackknife (Pachepsky and Rawls, 1999) methods.
The reliability of a PTF is not directly related to its utility (Pachepsky et al., 1999). The latter is affected by thesensitivity of the model to PTF predictions, and also by
the uncertainty in other model inputs (Leenhardt, 1995).
The functional evaluation of PTFs considers the evaluation of PTFs on the base of their utility and uses criteria
directly related to specific applications rather than statistics to characterize the accuracy. PTF accuracy may be
not an issue since at least four factors affect the performance of a PTF in simulations. These are the accuracyof basic soil data used as inputs in the PTFs, the accuracyof the PTF itself, specific features of the simulation model,
and the output used in the functional criteria (Wösten andvan Genuchten, 1988).
Database size and measurement method are among themore important factors affecting PTF accuracy and reliability. The number of samples has to be large enough todevelop PTFs that are both accurate and reliable. Whenthe reliability of USA-wide PTFs was compared with theaccuracy of those based on several smaller databases,
and the PTFs were ranked by their reliability, the allUSA PTFs usually had one of the highest rankings (Tietje
and Tapkenhinrichs, 1993; Kern, 1995). However, PTFs
based on local information appear to be more accurate in
the area where the data were collected.
There are indications that PTFs developed fromregional databases give good results in regions with similar soil and landscape histories. For example, water
retention PTFs developed in Belgium (Vereecken et al.,1989) were the most accurate as compared with 13 PTFs
based on a database of Northern Germany (Tietje andTapkenhinrichs, 1993). Water retention PTFs developed
for the Hungarian Plain (Pachepsky et al., 1992) wereapplicable to the Caucasian Piedmont Plain (Nikolaeva
et al., 1988). The development of PTF equations adapted
for the conditions of Brazilian weathered soils allowed
much better estimates of the parameters in Equation 2, as

PEDOTRANSFER FUNCTIONS

compared to the performance of PTFs derived for soils
from temperate climates (Tomasella et al., 2000). It
remains to be seen whether this observation holds forother cases, and which soil and landscape features haveto be similar in two regions to assure the mutual reliabilityof the PTFs developed.
The use of models depends on the easiness to operatethem, and PTFs are no exception. A PTF user has to beable to make an informed choice of the PTF, and to havea convenient tool to apply the PTF technology. One example of creating a multipurpose PTF tool is the soil inference system (McBratney et al., 2002). Also, software
packages like Rosetta (Schaap et al., 2001) and k-Nearest(Nemes et al., 2008) provide graphic user interfacesthat substantially simplify PTF use and the interpretationof results.
Since pedotransfer functions are empirical regressiontype relationships, their accuracy outside of their development region is essentially unknown. Instead of attempting
to find a single best PTF, Guber et al. (2009) proposed theuse of multimodeling. The approach involves assigningweights to the simulation results obtained with different
PTFs and then using the weighted average of these results.
Improvements in the predictions have been attributed to
the fact that multimodeling provides better coverage ofpossible variations in PTF inputs.

Limits of PTF accuracy
The accuracy and reliability of a PTF is sometimes limited
by temporal variations in soil properties caused bychanges in vegetation and soil management. Incorporationof organic matter, soil erosion, and tillage practices cancause variations in hydraulic properties that are comparable with variations within regional databases (Wösten
et al., 2001). The PTFs may require a temporal component
and vegetation parameters to improve their reliability(Sharma et al., 2006). Differences in measurement techniques for the samples in the same database will definitely
affect PTF performance. Future PTF improvements willstrongly depend on advances in characterization of finescale soil physical and chemical heterogeneities that controls flow and transport in soils at PTF application scales.
Conclusions
The history and the current status of PTF development
demonstrate the need in and value of integrative studies.
Systematic coupling measurements of various soil
properties add value to all of those measurements aspedotransfer relationships can be derived for a variety
of agrophysical applications. PTF development contributes to understanding of soil functioning and enhances
the role of soil information in multiple applications.
PTFs hence are essential tools to translate data that wehave to data we need in agrophysical research and management applications.

559

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Cross-references
Agrophysical Properties and Processes
Bulk Density of Soils and Impact on their Hydraulic Properties
Databases of Soil Physical and Hydraulic Properties
Field Water Capacity
Hydraulic Properties of Unsaturated Soils
Mapping of Soil Physical Properties