Development of pedotransfer functions for a profile cone...

Ž .Geoderma 100 2001 25–47www.elsevier.nlrlocatergeoderma

Development of pedotransfer functions for a profilecone penetrometer

S. Grunwald), D.J. Rooney, K. McSweeney, B. Lowery 1

Department of Soil Science, UniÕersity of Wisconsin-Madison, 1525 ObserÕatory DriÕe, Madison,WI 53706-1299, USA

Received 21 September 1999; received in revised form11 April 2000; received in revised form 11 July 2000; accepted 18 July 2000

Abstract

Ž .In this study, we illustrate how profile cone penetrometers PCP , can be used to measureŽ .penetration resistance rapidly to define zones similar in cone index CI , which can be related to

Ž .soil physical properties. The objective of this study was i to develop pedopedotransfer functions,Ž .which describe the relationship between CI and soil texture, bulk density r and water contentb

Ž . Ž .u , and ii to evaluate the sensitivity of parameters used in these functions. The data setrepresented soils formed in reworked silty loess overlying glacial till andror lacustrine sediments.The global data set were grouped into subsets in terms of similar CIs. A horizontal hierarchicalcluster analysis and a vertical point inflection method were used to derive cone index layer

Ž .profiles CILP1 to CILP5 . Variability of CI within CILPs was small and variability of CI amongCILPs was large. Within each group, CI was regressed with soil physical properties to develop

Ž 2.pedopedotransfer functions. These were evaluated using the coefficient of determination R . Asensitivity analysis was executed to evaluate the relative importance of different parameters in theregression models. For the total data set, R2 ranged from 0.35 to 0.48. Pedotransfer functions forthe CILPs showed largest R2 with 0.62 for CILP1, 0.76 for CILP2, 0.70 for CILP3, 0.63 forCILP4 and 0.98 for CILP5. Depth, r , clay content and u were variables with large predictiveb

power. Textural variables had strong predictive power in the top layers, CILP1 and CILP2. InCILP4, clay contents along with r and u were variables with large predictive power. In contrast,b

the predictive power of r and u was strong in layers CILP3 and CILP5, whereas soil texturalb

) Corresponding author. Current address: Earth Information Technologies Corporation, P.O.Box 14716, Madison, WI 53714, USA. Tel.: q1-877-230-1430; fax: q1-877-230-1429.

Ž .E-mail addresses: [email protected] S. Grunwald , [email protected]Ž .B. Lowery .

1 Tel.: q1-608-263-5691; fax: q1-608-265-2595.

0016-7061r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0016-7061 00 00079-3

( )S. Grunwald et al.rGeoderma 100 2001 25–4726

characteristics showed weak predictability of CI. Pedotransfer functions using the global data setshowed large sensitivities for r and u . Similar results were obtained for all other CILPs, exceptb

CILP4 where clay content showed a large sensitivity. Our results show that pedotransferpenetrometer data can improve our understanding of the spatial distribution of CI and soil physicalproperties at fine scale. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: functions; soil properties; sensitivity; soil

1. Introduction

Data provided in soil databases often do not meet the need for environmentalstudies designed to assess soil and water quality, farm management and preci-sion agriculture. To do these studies, researchers require knowledge about the

Žspatial distribution of soil physical properties at fine scale i.e. large scale,.covering small areas, e.g. fields to describe the spatial and temporal variation of

soil properties within fields. There is urgent need for such data, however, it iscostly and time consuming to obtain.

In the US, soil data are stored in information systems covering differentŽ . Ž . Ž .scales: i National Soil Geographic Database NATSGO 1:750,000, ii State

Ž . Ž .Soil Geographic Database STATSGO 1:250,000, iii Soil Survey GeographicŽ . Ž .Database SSURGO 1:15,840 to 1:31,680 and iv National Soil Characteriza-

Ž .tion Database NSSC , which currently contains analytical data for more than24,000 pedons of US soils and about 1100 pedons from other countries. UsingSTATSGO, the minimum area that can be delineated is 625 ha. A STATGOmap contains up to 21 components for which there are attribute data, but there isno visible distinction as to the location of these components within the delin-eation. Briefly, for each soil polygon, the percentages of the map units thatmakes up the polygon are given, however, no information about the location ofpolygons within the map unit is given. In STATSGO, soil properties such as

Ž . Žtexture USDA particle-size classification , flood duration classes four cate-. Ž . Žgories , hydrologic groups seven categories and drainage classes seven cate-.gories ranging from excessively to well drained are available. Bulk density

information can be derived only indirectly from taxonomic classes. Most ofthese representative soil property data are categorical, which are difficult toquantify. In a SSURGO soil map, each map unit usually corresponds to a singlesoil component, typically a soil series phase. SSURGO provides the mostdetailed level of information with representative data for each major soil layer of

Žtexture, categorical drainage class e.g. well drained, moderately well drained,.etc. , descriptive information about the impedance for root growth and structure.

However, no information about confidence intervals of soil properties andstandard deviations are available, which limit applications of these data. Infor-mation about gradual and continuous variation of soil properties within fieldsand soil map units is not available. Effective site-specific farming requires

( )S. Grunwald et al.rGeoderma 100 2001 25–47 27

information about the spatial and temporal variation of soil properties, whichŽ .impact crop growth and yield. Wilding et al. 1994 classified soil physical

properties in terms of their spatial variability within landscape mapping units.More permanent soil properties such as texture, r and color are less variableb

than temporal or more dynamic properties such as water content, hydraulicconductivity, or soil thickness. However, the short-range variability of perma-nent soil properties might range from few centimeters to hundreds of meters

Ž .depending on landscape characteristics Buol et al., 1997 .Direct measurement of the spatial distribution of soil physical properties at

fine scale is time consuming and expensive. Alternatively, soil physical proper-ties can be inferred rapidly using penetrometers. These tools are used to measure

Ž .penetration resistance expressed as cone index CI , which can be related to soilcharacteristics. Generally, penetration resistance increases with compactionŽ . Ž .Lowery and Schuler, 1994 , decreasing Faure and Da Mata, 1994 , and coarse

Ž .soil texture Robertson, 1990; Puppala et al., 1995 . Among the soil character-istics that influence measured penetration resistance are compaction, porosity,

Žtexture, structure, cementing agents e.g. by carbonate, silica, hydrous silicate.and hydrous iron oxide , organic matter and u . Since penetration resistance is

influenced by many variables, most cone penetration studies have focused onhomogeneous materials with disturbed soils under controlled boundary condi-

Ž .tions Kurup et al., 1994 . For example, cone penetration studies on sandyŽ . Ž .material were conducted by Kasim et al. 1986 and Puppala et al. 1995 and on

Ž . Ž .fine clays by Levadoux and Baligh 1986 , Sully and Campanella 1991 andŽ .Kurup et al. 1994 . There are two standards for the design of penetrometers

Ž Ž .American Society of Agricultural Engineers ASAE , 1983; American SocietyŽ . .for Testing and Materials ASTM , 1995 , which differ in their basal area, tip

angle and sleeve stress measurement.The relationship between CI and soil physical properties can be expressed by

pedotransfer functions. Pedotransfer functions are mathematical equations thatdescribe the relationship between the input and the output of a system in termsof the transfer characteristics. These functions do not necessarily imply topredict difficult-to-measure properties from easy-to-measure ones. For example,pedotransfer functions are widely used for estimating soil hydraulic propertiesŽRawls et al., 1982; Bouma and van Lanen, 1987; Vereecken et al., 1989; vanGenuchten and Leij, 1992; Tietje and Tapkenhinrichs, 1993; Scheinost et al.,

.1997; Schaap et al., 1998 . A pedotransfer function is a function that uses basicŽdata describing the soil e.g. particle-size distribution, r , and organic Cb

.content and yields as a result the water retention function or unsaturated andsaturated hydraulic conductivity. Other soil properties derived by pedotransfer

Ž . Ž .functions are phosphorus saturation Kleinman, 1999 and structure Kay, 1997 .The vast majority of pedotransfer functions are empirically based on linear

Ž .regression equations e.g. Rawls et al., 1982; Vereecken et al., 1989 with a fewŽbeing physical model methods Haverkamp and Parlange, 1986; Tietje and


. ŽTapkenhinrichs, 1993 and neural network models Pachepsky et al., 1996;.Schaap et al., 1998 .

Ž . Ž .Results from profile cone penetrometer PCP studies were presented as iŽ . Ž . Ž .pedotransfer functions regression equations Kasim et al., 1986 and ii CI

Žprofiles for specific soils or environmental conditions Vepraskas, 1984; Ander-son et al., 1989; Lowery and Schuler, 1991, 1994; Faure and Da Mata, 1994;

.Kurup et al., 1994; Puppala et al., 1995 . The most common use of penetrome-ters has been to determine the effect of tillage on soil compaction using methodŽ .ii . Since penetrometers were introduced in soil science, very few pedotransferfunctions have been developed.

In this study, we used a PCP to investigate the relationship between CI and avariety of different combinations of soil physical properties. These properties arerepresentative of a landscape, where soils are formed in reworked loess material

Ž .overlying glacial till andror lacustrine sediments. Our objective was i todevelop pedotransfer functions for such a landscape describing the relationshipbetween penetration resistance and the following soil physical properties: tex-

Ž .ture, r and u , and ii to evaluate the sensitivity of parameters used in theseb

functions.

2. Study areas

Two sites were selected for this study and data collected for each site wascombined to develop a global data set. Both sites consisted of glacial till androrlacustrine sediments with loess covering. One site was a 2.73-ha field located onthe University of Wisconsin-Madison Agricultural Research Station West Madi-

Ž . Ž Ž .son ARS-WM Universal Transverse Mercator UTM coordinates: lower left.corner: E 293,422; N 4,771,230; upper right corner: E 293,732; N 4,771,443

and the other was a field on the University of Wisconsin-Madison ArlingtonŽ .Agricultural Research Station A-ARS in southern Wisconsin, where we inves-

Žtigated three locations UTM coordinates: location a1 E 306,566; N 4,796,530;.location a2 E 306,698; N 4,796,590; location a3 E 306,632; N 4,796,470 .

Climate for the study sites is temperate humid and soil moisture regime rangesfrom udic to aquic.

Ž .A three-dimensional 3-D soil layer model portrays the study area at theŽ . Ž .ARS-WM Fig. 1 Grunwald et al., 2000 . Shallow reworked loess cover was

found on the eroded soils on shoulder and backslope positions, whereas thickreworked loess deposits were found on footslope and toeslope positions. Soilsalong the catena are classified as fine-loamy, mixed, mesic Typic Argiudolls.The reworked loess is underlain by sandy loam glacial till. Land use at both sites

Ž . Ž .was a corn Zea mays –alfalfa Medicago satiÕa rotation.The second site was mapped as fine-silty, mixed, mesic Typic Argiudolls on

the upland and fine-silty, mixed, mesic Typic Argiaquolls in the depressions.


Fig. 1. Three-dimensional soil layer model of the 2.73-ha study site at the ARS-WM.

Each soil pit profile at the A-ARS was described using field morphologicalŽ .criteria Schoeneberger et al., 1998 . A 3-D representation of the pit locations is

Ž .shown in Fig. 2. The Ap horizon on the upland a2 was 0–22-cm thick and inŽ .the depression a1 0–26-cm thick with silt loam texture. The transitionŽ .horizons ArB or BrA on the upland were 22–38-cm thick. They showed a

Ž .silty clay loam texture. Only on the upland, a Bt horizon 36–77 cm was foundwith silt loam texture. This horizon was underlain by glacial till parent materialŽ .horizon 2C , which loamy sand; unweathered and weathered stones were found.

Ž .In the depression, a Btg 92–196 cm was found overlying a layer of lacustrineŽ . Ž .sediment 2BC; 196–207 cm and glacial till 3C; 207 cm . The Btg had silty

Fig. 2. Three-dimensional representation of soil layers at the AARS.


clay loam texture with common prominent coarse redoximorphic features. The2BC layer was sand and silty loam. The underlying 3C was gravely sandy loam.

3. Material and methods

3.1. Cone penetrometer

We used a constant-rate PCP with a 608 cone angle, 2-cm diameter, andsurface area of 3.14 cm2. The PCP system components included the PCP probe,

Ž .2a hydraulic truck mounted push system Gidding a9HD; Fort Collins, CO , aŽ .load cell 1360-kg capacity; Omegadyne LC 101; Sunbury, OH , a depthŽ .transducer Unimeasure HX-EP; Corvallis, OR , and a data acquisition system

Ž .datalogger, Campbell Scientific 21X; Logan, UT . A detailed description of theŽ .PCP system is given in Rooney and Lowery 2000 .

3.2. Data set

While penetrating the soil profile, continuous CI profiles for depths up to 1.30m were collected. Adjacent to each penetration soil cores with a diameter of 4.3cm were collected and analyzed for texture, r , and u . Texture was analyzed byb

the UW Soil and Plant Analyses Laboratory, Madison, WI, based on theŽ .hydrometer method Gee and Bauder, 1986 . Soil u was derived by cutting soil

cores to 10-cm samples and oven drying to obtain volumetric values. Bulkdensity was determined by oven drying a known volume of soil and calculated

Ž .on dry weight basis. The total data set contained 296 data records n consistingŽ .of i measured average CI for 5-cm depth increments in kPa, and corresponding

Ž . 3 Ž . y3 Ž . 3 y3 Ž .ii percent sand, silt and clay , iii r in Mg m , iv u in m m and vb

measurement depth in cm.

3.3. Statistical analyses

While measured CI was heterogeneous along profiles, we classified CI intohomogeneous groups, which are defined here as CILPs. To identify homoge-neous CILPs, we used a horizontal hierarchical cluster analysis and a verticalinflection point method. To apply the cluster analysis, the criterion ‘average

Žlinkage within groups’ was used to combine clusters SPSS Professional Statis-.tics, 1994 . This method combines clusters so that the average distance between

all cases in the resulting cluster is as small as possible. Thus, the distancebetween two clusters is taken to be the average of the distances between all

2 Mention of company or trade name does not constitute endorsement by the University ofWisconsin-Madison or the authors.

3 Ž .Classification of sand, silt and clay based on USDA classification Soil Survey Staff, 1995 .


possible pairs of cases in the resulting cluster. Similarity between variables wasŽ .tested using the Pearson correlation coefficient r . Clusters were tested by

Ž .analyses of variance ANOVA to determine if CI profile shapes were signifi-cantly different, i.e. showed significant different CI values at specific depths.Before running the cluster analysis, it was necessary to remove noise from thedataset, which occurred in some penetrations because stone-rich material wasencountered, which caused abrupt inflections in resistance.

First, the global data set was subdivided using a hierarchical cluster analysisŽ .provided by the SPSSWIN software SPSS Professional Statistics, 1994 . The

data were formatted and denoted by the following: k corresponds to CI at aw xspecific depth, where index x of k runs from 0, 1, 2, . . . m ; k denoting CI atx 0

the bottom layer of a CI profile and k representing CI at the top layer of a CIm

profile. Different locations in space are represented by i, where index x of i xw xruns from 0, 1, 2, . . . m ; i corresponding to the first CI profile in the global0

data set and i corresponding to the last CI profile in the global data set. It wasmŽ .assumed that the spacing between locations e.g. i to i has no impact on the0 1

statistical analysis; it is simply used to identify different locations of CI profiles.Mathematically, the matrix used for the hierarchical cluster analysis can bewritten as:

top layer k i , k i , k i , . . . k i ;m 0 m 1 m 2 m m

. . .k i , k i , k i , . . . k i ;2 0 2 1 2 2 0 m

k i , k i , k i , . . . k i ;1 0 1 1 1 2 1 m

bottom layer k i , k i , k i , . . . .k i0 0 0 1 0 2 0 m.

For each layer, k i values were compared to each other using the Pearsonx x

correlation coefficient to test similarity.Second, a vertical comparison between CIs at specific depths were executed

to further homogenize the data sets in terms of similar CIs. Mathematically, thiscan be expressed as:

CI profile CI profile CI profile CI profilecluster A cluster B cluster C cluster D

top layer k i k i k i k im A m B m C m D

Dkm

. . . . . . . . . . . .Dk2

k i k i k i k i2 A 2 B 2 C 0 D

Dk1

k i k i k i k i1 A 1 B 1 C 1 D

Dk0

bottom layer k i k i k i k i0 A 0 B 0 C 0 Dw xDk with x 0, 1, 2, . . . mx


where k i denotes CI at a specific depth for cluster A starting with k at thex A 0

bottom layer and ending with k at the top layer; denotions k i , k i , k im x B x C x D

are used accordingly.Increments were calculated for cluster A between k and k starting withx xq1

k i until k i was reached. These are denoted with Dk where index x runs0 A m A xw xfrom 0, 1, 2, . . . m ; starting with Dk at the bottom layer until the top layer0

Dk is reached. Each increment Dk was compared with its preceding incre-m x

ment while tested for positive, negative or non-changing values. If valueschanged more than "10 kPa cmy1, an inflection point was set. These thresholdvalues were chosen considering that the resolution of the PCP was 4.7 kPa.Various CILP were identified based on these inflection points. This procedurewas applied for each of the clusters.

For the total data set and each homogeneous CILP, CI was regressed withpercent sand, silt and clay, r , u and depth of measurements to developb

pedotransfer functions. Multiple regression models were evaluated using theŽ 2.coefficient of determination R .

A sensitivity analysis was executed to evaluate the relative importance ofdifferent parameters in the regression models. Sensitivity here is defined as the

Ž .rate of change of a factor the value of the object function with respect toŽ .another factor one of the parameters . To eliminate scale effects, the relative

Ž .sensitivity is introduced Vereecken et al., 1989 :

SREL sOR rPr 1Ž .i i i

with< <OR s O yO rO 2Ž .i i iy1 o

and< <PR s P yP rP 3Ž .i i iy1 o

where SREL is the relative sensitivity, P is the parameter of interest, P is thei o

optimum parameter value, P is the parameter value at i times P from thei

optimum, O is the objective function or output, O is the value of the optimaloŽ .objective function so-called base value , and O is the value of the objectivei

function at a distance i times P from the optimum. The parameters with thelargest SREL have the greatest impact on model output. This provides a basisi

for comparing various parameters and focusing on sensitive parameters.

4. Results and discussion

4.1. Global and local data sets

The global data set comprised 296 data records. These data are representativefor a glaciated landscape covered with reworked loess material. The statisti-cal parameters of soil physical properties for the global data set are listed in


Table 1. Soil texture varied from silt loam, loam, silty clay loam, clay loam,sandy clay loam, sandy loam, loamy sand to sand; minimum r was 1.1 Mgb

my3 and reached a maximum of 1.8 Mg my3 while u varied between 0.059 and0.235 m3 my3; measured CI ranged from )0 to 7500 kPa.

We subdivided the global data set into subsets to develop pedotransferfunctions for groups of homogeneous CI layers. First, the global data set wassubdivided using a hierarchical cluster analysis provided by the SPSSWIN

Ž .software SPSS Professional Statistics, 1994 . While running the analysis foreach layer k i , values were compared to each other using the Pearsonx x

correlation coefficient to test for similarity. The analysis resulted in fourŽ .different clusters A to D illustrated in Fig. 3 where mean CI profiles for each

cluster are shown.

Table 1Mean, standard deviation, minimum and maximum values for soil properties of different datagroups

Data set Soil physical property Mean S.D. Minimum Maximum

Ž .G ns296 Sand% 16.9 6.9 2.0 92.0Silt% 60.0 14.9 2.0 75.0Clay% 22.6 7.2 3.0 37.0

y3Ž .Bulk density Mg m 1.40 0.09 1.10 1.803 y3Ž .Water content m m 0.192 0.023 0.059 0.235

Ž .CILP1 ns48 Sand% 21.1 8.0 12.0 48.0Silt% 64.8 7.4 37.0 71.0Clay% 14.1 3.6 10.0 24.0











Fig. 3. Homogeneous CILP.

Fig. 4. Spatial distribution of CILP for study site at the ARS-WM.


For each identified cluster, the vertical inflection point method was applied togroup homogeneous CI within profiles of clusters. This method compares CIalong profiles using the increments between each observed value along a profile.This procedure was applied for each of the clusters. The identified inflectionpoints are shown in Fig. 3. Five different layers of CILPs were distinguishedbased on the vertical inflection point method. For example, CILP1 was distin-guished from CILP2 because increments in CILP1 were positive, in contrast tonegative increments in CILP2. Cluster D showed large positive increments of upto 80 kPa cmy1 in CILP1 and large negative increments of up to 122 kPa cmy1

in CILP2. These increments were larger when compared to increments in clusterA, B and C. However, no further CILP was distinguished because otherwise thesampling size for CILP1 and CILP2 would have been too small for a subsequentregression analysis. Increments for CILP3 were smaller than 10 kPa cmy1 andtreated as insensitive. In CILP4, increments were )32 kPa cmy1 but -91 kPacmy1 and in CILP5, )35 kPa cmy1 with maximum of 333 kPa cmy1. Thespatial distribution of CILPs for the study site at the ARS-WM is illustrated inFig. 4.

After homogenizing CI profiles, correlations, scatterplots and regressionŽmodels were executed using the SPSSWIN software package SPSS Professional

.Statistics, 1994 . The stepwise regression models selected the variables, whichsignificantly improved prediction of CI based on threshold values. Variableswere selected at a 0.05 significance level for entry in the regression model,while a 0.10 significance level was applied to retain the variables in the model.Maximum predictions of CI were calculated based on the regression modelswith method enter.

4.2. Preanalysis

A preliminary analysis showed that significant correlations exist between soilŽ . Ž .physical properties and CI Table 2 . The correlation coefficient r , calculated

for the global data set between r and CI was 0.30, between silt content and CIb

was 0.28 and between depth and CI was 0.65 at the two-tailed significancelevels of -0.01. Significant correlation existed between soil physical proper-ties, which influence the regression equations in terms of which predictorvariables were included in the regression model and the multiplication factor for

Ž .each predictor variables Table 2 . For example, the correlations for sand andŽ . Ž . Ž .clay content y0.85 , sand and silt content y0.42 , u and r 0.27 , u andbŽ . Ž . Ž .clay content 0.33 , u and silt content 0.40 , u and sand content 0.30 , depth

Ž . Ž . Ž .and r 0.43 , depth and clay content 0.35 , depth and sand content y0.28bŽ .and depth and u y0.28 were significant at the 0.01 level. The observed linear

correlations are useful for determining if a model is over-defined and containstoo many parameters. Before conducting the regression analysis scatter plots of

Ž . Žthe response variable CI against several predictor variables depth; sand, silt,


Table 2Correlation coefficients for different data sets

Data set CI r Clay% Silt% Sand% u Depthb

) ) ) ) ) ) )G CI 1.0 0.300 0.290 y0.277 0.082 y0.167 0.645)) ))r 1.0 0.104 0.010 y0.104 0.274 0.427b

) ) ) ) ) )Clay% 1.0 0.002 y0.849 0.329 0.346)) ))Silt% 1.0 y0.424 y0.397 0.090

)) ))Sand% 1.0 0.298 y0.283))u 1.0 y0.276

Depth 1.0)) ))CILP1 CI 1.0 y0.405 y0.019 y0.224 0.216 y0.151 0.701

)) )) )) ))r 1.0 0.561 0.448 y0.581 y0.812 y0.162b) ) )Clay% 1.0 y0.076 y0.386 y0.430 y0.317))Silt% 1.0 y0.891 y0.097 y0.097

Sand% 1.0 y0.024 0.235u 1.0 y0.244Depth 1.0

)) ))CILP2 CI 1.0 y0.099 y0.607 y0.031 0.473 y0.056 y0.209)) )) )) )r 1.0 0.667 0.059 y0.808 y0.779 y0.367b

) ) ) )Clay% 1.0 y0.095 y0.669 y0.323 0.568)) )Silt% 1.0 y0.676 0.400 0.138

))Sand% 1.0 y0.060 y0.523)u 1.0 y0.290

Depth 1.0)) ) ))CILP3 CI 1.0 0.458 y0.128 y0.136 0.144 y0.221 0.582

)) )) )) )) ))r 1.0 y0.479 y0.674 0.652 y0.390 0.486b) ) ) ) ) ) )Clay% 1.0 0.658 y0.820 0.761 y0.235

)) ))Silt% 1.0 y0.971 0.720 y0.059))Sand% 1.0 y0.791 0.120

u 1.0 y0.139Depth 1.0

)) )) ))CILP4 CI 1.0 y0.198 0.682 0.090 y0.262 0.741 0.669r 1.0 0.074 y0.184 0.120 y0.309 0.209b

) ) )Clay% 1.0 0.461 y0.662 0.192 0.300))Silt% 1.0 y0.970 0.216 0.305

Sand% 1.0 y0.235 y0.339))u 1.0 0.858

Depth 1.0) ))CILP5 CI 1.0 0.411 y0.347 y0.127 0.214 y0.034 0.773

) )) ))r 1.0 y0.435 y0.612 0.612 y0.476 0.351b) ) ) ) ) )Clay% 1.0 0.597 y0.794 0.722 y0.320

)) ))Silt% 1.0 0.962 0.696 y0.239))Sand% 1.0 y0.774 0.290

u 1.0 y0.101Depth 1.0

Gsglobal data set.)Correlation is significant at the 0.05 level.))Correlation is significant at the 0.01 level.


.clay content; r ; u were plotted, indicating that no transformations wereb

improving normal distribution nor gave larger correlations with different soilproperties. For each regression performed, residual and partial residual plots forthe different predictor variables were analyzed to check the validity of the modelspecification, i.e. correct form of the independent variables — normal distribu-tion and to detect outliers.

4.3. Regression analysis

The performance of several multiple regression models was evaluated usingŽ 2.the coefficient of determination R listed in Table 3. Non-linear functions

were analyzed but these are not presented in this paper because they did notimprove R2 significantly.

Ž .Regression models using all data records G; n: 296 indicated that inestimating CI, the predictor variables depth, silt and clay content, r and u ,b

Ž Ž ..explained 48% of the variability Table 3; Eq. 1.5 . An increase in CIcorresponded to increasing depth, r and u and decreasing silt and clay content.b

These pedotransfer functions have to be interpreted considering relationshipsbetween predictor variables. For example, significant correlations between clay

Ž . Ž .content and sand content y0.85 and silt content and sand content 0.42 are

Table 3Ž .Coefficients for multiple linear regression equations for prediction of cone index CI in kPa

2Data M Intercept Depth Sand Silt Clay r u R Eq.by3 3 y3Ž . Ž . Ž . Ž . Ž . Ž .sets cm % % % Mg m m m

G S 818.45 13.15 0.345 1.1S y2318.77 10.39 2348.36 0.409 1.2S y1434.77 12.88 y25.61 2031.77 0.446 1.3S y3615.65 13.52 y32.74 2704.26 69.61 0.468 1.4E y3371.53 12.52 y12.54 y27.48 2614.97 101.29 0.480 1.5

CILP1 S 1029.54 14.75 0.445 1.6E 4992.29 3.75 1.16 y39.80 y1203.12 y80.87 0.621 1.7

CILP2 S 1820.82 y30.57 0.331 1.8S 1082.59 37.81 y46.14 0.422 1.9E 5853.12 48.16 86.76 15.04 y1483.21 y288.05 0.760 2.0

CILP3 S 852.58 8.53 0.510 2.1S y820.41 6.88 1284.51 0.655 2.2E y3209.55 6.49 15.82 y1.87 2410.55 y4.78 0.700 2.3

CILP4 S y18,182.50 735.50 0.455 2.4S y23,509.00 574.02 482.03 0.601 2.5S y19,755.80 606.14 y2107.70 411.32 0.622 2.6E 23,395.32 56.29 527.97 y12,414.9 y1110.04 0.630 2.7

CILP5 S 532.47 33.21 0.851 2.8S y4679.62 30.32 2883.32 69.20 0.900 2.9E y5777.01 27.54 29.03 y90.66 3775.17 117.09 0.980 3.0

M: methods; S: stepwise; E: enter.Ž .Example Eq. 1.2 : CIsy2318.77q10.39)depthq2348.36) r .b


responsible for treating sand content as a redundant variable and therefore it isnot used as predictor variable. Water content showed strong correlations to r bŽ . Ž . Ž . Ž .0.27 , clay content 0.33 , silt content 0.40 and sand content 0.30 . Thestepwise regression models showed that depth and r were the most importantb

Ž . Ž .predicting variables Eqs. 1.1 and 1.2 , followed by clay content and u Eqs.Ž . Ž .1.3 and 1.4 .

Generally, R2 for the global data were small, and a close relationshipbetween CI and soil physical properties was not encountered. This findingcontrasts with other studies, which demonstrated close relationships between

Ž . ŽCIrsoil texture Kurup et al., 1994; Puppala et al., 1995 , CIrr Pidgeon andb. ŽSoane, 1977; Henderson et al., 1988 and CIru Ayers and Perumpral, 1982;

.Faure and Da Mata, 1994 . However, these studies used homogeneous soilmaterials to analyze relationships between CI and soil attributes. In our study,we used heterogeneous soil materials covering a variety of different combina-tions of soil physical properties.

We attempted to improve coefficients of determination using classified dataŽ .sets e.g. the five homogeneous CILPs . The CILP1 represents a top soil layer

corresponding to an Ap horizon strongly influenced by tillage operations,organic matter accumulation and pedological transport processes such as ero-sion, deposition and bioturbation. In CILP1, CI was estimated to a maximum

Ž Ž ..explanation level of the variance of 62% Table 3; Eq. 1.7 . Predictor variableswere depth, sand and clay content, r and u . The predictor variable sandb

Ž Ž ..content explained 45% of the variability of CI Table 3; Eq. 1.6 .Ž Ž ..In CILP2, CI was explained with maximum of 76% Table 3; Eq. 2.0 . This

layer is influenced by tillage and bioturbation, however, to lesser extent whencompared to CILP1. Depth and clay content explained 42% of the variance Eq.Ž . Ž .1.9 , while clay content explained 33% of the variance Eq. 1.8 .

Ž .The dominant textural class in the top layers was silt loam 91.3% followedŽ . Ž .by silty clay loam 6.1% and loam 2.6% of all cases in CILP1 and CILP2.

Minimum r in CILP1 and CILP2 was 1.1 Mg my3 and maximum r wasb by3 Ž .1.53 Mg m Table 1 . In CILP1 and CILP2, CI was influenced predominantly

by soil textural characteristics, which were included in the stepwise regressionequations. The influence of r on CI is negligible, which might be explained byb

tillage operations affecting the top soil layers. Tillage loosen the material andbreak down aggregates and affect r . However, it is surprising that theb

Ž Ž .coefficient for r in the regression models for CILP1 and CILP2 Eqs. 1.7 andbŽ ..2.0 was negative, which suggests that CI increased with decreasing bulkdensities. This might be explained by the strong positive correlations betweenclay content and r of 0.56 in CILP1 and 0.67 in CILP2 and between sandb

Ž .content and r of y0.58 in CILP1 and y0.81 in CILP2 Table 2 . In short, ifb

r increases so does clay content and if clay content increases, CI decreasesbŽ . Ž . Ž . Ž .according to Eqs. 1.7 , 1.8 and 1.9 Table 3 . If r increases sand contentb

Ž . Ž .decreases and if sand content decreases so does CI according to Eqs. 1.6 , 1.7


Ž . Ž . Ž .and 2.0 . Additionally, in Eqs. 1.7 and 2.0 , the multiplication factors for r b

were smaller when compared to pedotransfer functions for CILP3, CILP4 andCILP5, which illustrates the small influence of r on CI in contrast to theb

strong influence of soil textural characteristics in CILP1 and CILP2. Watercontent depends largely on soil textural characteristics and the distribution ofpores within soils. This might explain why u did not play a significant role inpredicting CI because it was treated as redundant information within thestepwise regression models of CILP1 and CILP2. The unexplained variability ofCI might be explainable using organic matter content, which generally showslarger values in the top layers when compared to underlying layers.

In CILP3, CILP4 and CILP5, the impact of tillage and bioturbation on soilcharacteristics is less when compared to CILP1 and CILP2. The CILP3 wasdefined by a large depth range between 40 and 130 cm. This explains why depthwas the most important predicting variable explaining 51% of the CI variabilityŽ Ž ..Table 3; Eq. 2.1 . Bulk density and depth were also variables with strong

Ž . Ž .predictability 65% of CI in CILP3 Eq. 2.2 . Positive coefficients for depth andr suggest that as depth and r increase so does CI. This characteristic wasb b

opposite to the influence of r on CI in CILP1 and CILP2. Regression modelsbŽ .using method enter Eq. 2.3 showed that in estimating CI, the predictor

variables depth, silt and clay content, r and u , explained 70% of the variabilitybŽ Ž .. Ž . ŽEq. 2.3 . The coefficient of determination was 0.655 for Eq. 2.2 method:

. Ž . Ž . Žstepwise and 0.700 for Eq. 2.3 method: enter . The additional variables soil. Ž .texture introduced in the multiple regression model of Eq. 2.3 indicated

Ž .limited model improvement when compared to Eq. 2.2 . The negative coeffi-Ž .cient for clay content in Eq. 2.3 suggests that CI increases while clay content

Ž .is decreasing. The positive coefficient for silt content in Eq. 2.3 indicates thatCI increases along with silt content.

Ž .Soil physical properties of CILP3 and CILP4 were very similar Table 1 .Soil textural ranges were similar, while bulk densities were slightly larger inCILP4 with a mean value of 1.52 Mg my3 and a minimum of 1.42 Mg my3

when compared to bulk densities in CILP3 with a mean value of 1.42 Mg my3

and minimum of 1.20 Mg my3. Mean u in CILP3 was 0.208 m3 my3 and inCILP4 0.206 m3 my3. Measured CI was larger in CILP4 with a mean of 2810kPa when compared to 1505 kPa in CILP3. The CILP3 is a silt-rich layercorresponding to reworked loess material and CILP4 cannot be classified as apedologically distinct layer.

The most important soil properties controlling CI in CILP4 were clay content,Ž Ž . Ž . Ž .. 2u and r Table 3; Eqs. 2.4 , 2.5 and 2.6 where corresponding R wereb

0.455, 0.601 and 0.622, respectively. CI can be estimated to a maximumŽ . 2explanation level of the variance of 63% Eq. 2.7 . The improvement in R

Ž . Ž .between Eqs. 2.6 and 2.7 was extremely small, so we suggest that theŽ .additional variable silt content in Eq. 2.7 is redundant information. Coeffi-

Ž . Ž . Ž .cients for clay content in Eqs. 2.4 , 2.5 and 2.6 were positive, which


indicated that increasing clay content corresponded to increasing CI. Watercontent and clay content were positively correlated in CILP4, which was

Ž . Ž .indicated by a positive coefficients Eqs. 2.5 and 2.6 . The negative coefficientŽ .for r in Eq. 2.6 suggests that decreasing r was associated with increasingb b

CI in CILP4.The maximum predictability of CI in CILP5 was very large with R2 0.98

Ž Ž ..Table 3; Eq. 3.0 . The unexplained variability of CI was very small, indicat-ing that additional variables, for example, soil structure would not appreciablyimprove predictions. The stepwise regression models suggests that depth can

Ž Ž ..predict CI to 85% Table 3; Eq. 2.8 and depth, u and r can predict CI tobŽ .90% Eq. 2.9 . CI layer profile 5 differed from all other CILPs because of its

Ž .large sand content with a mean of 75% Table 1 corresponding to glacial tillmaterial. Associated with a large sand content were large bulk densities with amean of 1.61 Mg my3 and maximum of 1.8 Mg my3 and small u with a meanof 0.121 m3 my3, minimum of 0.059 m3 my3 and maximum of 0.17 m3 my3.Measured CIs were larger with a mean of 3250 kPa when compared to all otherCILPs. The stepwise regression models suggest that soil textural characteristicsare redundant information in CILP5, which did not improve R2 significantly.

4.4. SensitiÕity analysis

In order to evaluate the relative importance of the different parameters in thepedotransfer functions, a sensitivity analysis was performed for each regression

Ž Ž ..model using SREL Eq. 1 . Values P were changed by "10% to derive Pi o i

values within the range of each considered P, i.e. sand, silt and clay content,r , u and depth. Corresponding O values were calculated according to theb i

functions of each regression model.Results of the sensitivity analysis are graphically illustrated in Figs. 5–10,

where the relative sensitivity is plotted on the right y-axis and the predicted CIsfor variables used in the regression models on the left y-axis. The rhombusicons illustrate the relative sensitivity and the columns represent predicted CI.To compare predicted to measured CI box plots of measured CI were plotted foreach CILP. The top and bottom of the box plot correspond to standard deviation,the middle line corresponds to mean. The whiskers on the bottom and toprepresent minimum and maximum values, respectively. Using a sensitivityindex, it was possible to identify the variables with greatest impact on modeloutput, i.e. to predict CI. The larger relative sensitivity the greater the impact onmodel output.

From this analysis, we concluded that r is the most sensitive parameter inbŽ .predicting CI using the global data set Fig. 5 . We conclude that the relative

importance of r requires an accurate measurement of this parameter tobŽ . Ž .estimate CI based on Eqs. 1.1 – 1.5 . The relative sensitivity for r rangedb

Ž Ž .. Ž Ž .. Ž Ž .. Ž Ž ..from 1.99 Eq. 1.2 , 1.71 Eq. 1.3 , 2.30 Eq. 1.4 to 2.19 Eq. 1.5 . The


Fig. 5. Relative sensitivity and range of predicted CIs for predictor variables used in regressionŽ . Ž .models of Eqs. 1.1 – 1.5 from Table 3.

Fig. 6. Relative sensitivity and range of predicted CIs for predictor variables used in regressionŽ . Ž .models of Eqs. 1.6 and 1.7 from Table 3.


Ž Ž ..second most sensitive parameter was u with SREL of 1.16 Eq. 1.5 and 0.81iŽ Ž ..Eq. 1.4 . If SREL is smaller than 1, relative change in output exceedsi

relative change in the input parameter, whereas a SREL larger than 1 meansi

that relative change in an input parameter exceeds the relative change of output.Other predictor variable depth, clay and silt content were relatively insensitiveŽ .Eq. 1.5 . Most of the predicted minimum and maximum CI for each predictorvariable were within the standard deviation of measured CI.

Sensitivities of predictor variables were less for data set CILP1 whencompared to the global data set. Largest sensitivity showed u with 1.23 and r b

Ž .with 1.22 Fig. 6 . The sensitivity for sand content in Eq. 1.6 was small with0.23, i.e. if sand content changed 10% predicted CI changed 2.3%. Applying Eq.Ž .1.6 , minimum predicted CI was 1208 kPa and maximum 1738 kPa comparedto the standard deviation of measured CI ranging from 681 to 1691 kPa andmaximum of 3418 kPa.

All calculated SREL in CILP2 were smaller than 1 indicating limitediŽ .sensitivity of predictor variables Fig. 7 except for u with a sensitivity of 2.70

Ž Ž .. Ž Ž ..Eq. 2.0 . Sensitivity for the predictor variable depth was 0.86 Eq. 1.9 andŽ Ž ..r 0.83 Eq. 2.0 . Small sensitivities were shown by soil textural predictorb

Ž .variables. Predicted CI values showed a good fit with measured CI for Eq. 2.0 .Sensitivities for pedotransfer functions predicting CI for CILP1 and CILP2 werevery different, however, identifying u as the most sensitive variable in bothCILPs.

CILP3 stands out with a narrow range of measured CI values with minimumŽ .870 kPa and maximum 2193 kPa Fig. 8 . We noticed the large SREL of ri b

Ž . Ž .with 2.21 in Eq. 2.3 and 1.15 in Eq. 2.2 . All other sensitivities for predictorvariables in CILP3 were smaller than 1. The large variation of predicted CI bychanging silt content is merely due to the large variation of measured siltpercentage ranging from 25% to 68%.

Sensitivities for pedotransfer functions of CILP4 were fairly large whencompared to the other CILPs. Large SREL were calculated for clay contenti

Ž Ž .. Ž Ž .. Ž Ž .. Ž Ž ..with 8.53 Eq. 2.4 , 6.44 Eq. 2.5 , 6.71 Eq. 2.6 5.39 Eq. 2.7 , u withŽ . Ž .8.34 Eq. 2.7 and r with 6.79 Eq. 2.7 . The variation of soil physicalb

properties in CILP4 was not exceptionally large. However, sensitivities werevery large and resulted in a large range of predicted CI values.

Ž Ž .. ŽIn CILP5, sensitivities were largest for r with 1.15 Eq. 2.9 and 1.40 Eq.bŽ ..3.0 . Predictor variable depth, silt and clay content were insensitive for modeloutput.

5. Summary and conclusions

In this study, we used a PCP to collect CI data. These were grouped intoŽ .different data sets CILPs . Variability of CI within groups was small and


variability of CI between groups was large. We developed pedotransfer func-Žtions to relate CI to measured soil physical properties sand, silt and clay

.content, r and u . The data set was representative for a landscape where soilsb

are formed in reworked loess material overlying glacial tillrlacustrine sedi-ments. Because pedotransfer functions presented in this study are empirical, thetransferability to landscapes with contrasting characteristics in soils, climate andmanagement is limited. Depth, r , clay content and u showed largest pre-b

dictability for CI using the global data set. Textural variables had strongpredictive power in the top layers, CILP1 and CILP2. In CILP4, clay contentalong with r and u were variables with large predictive power. In contrast, theb

predictive power of r and u was strong in layers CILP3 and CILP5, whereasb

soil textural characteristics showed low predictability of CI.Expressions used in this paper such as ‘the predictability of CI using soil

properties as predictor variables’ or ‘CI can be estimated by clay content andbulk density’ describe the statistical relationship between CI and soil physicalproperties. For practical applications, the measurement of CI can be used inconjunction with pedotransfer functions to predict soil physical properties. CIcan be measured continuously, rapidly and in situ. For example, a dense data set

Ž .of CI profiles can be collected for a study area e.g. farms, small watershedsefficiently and with a small budget. Sampling of soil physical properties can betargeted to the ones with large predictive power and the most sensitive ones

Ž .based on location or CILPs and pedotransfer functions.The sensitivity analysis calculated the relative importance of variables using a

specific pedotransfer function to predict CI. Sensitivity values have merit forany user who might apply one of the pedotransfer functions. Parameters withlargest sensitivity have the greatest impact on model output and therefore shouldbe collectedrmeasured carefully. Pedotransfer functions using the global dataset showed large sensitivities for r and u . Similar results were calculated forb

all other CILPs, except CILP4 where clay content showed large sensitivity.Penetrometer measurements are useful to describe gradual and continuous

variation of CI and associated soil properties within fields and within soil mapunits. Besides detailed measurements of soil physical and hydraulic properties,the collection of CI facilitates to improve our knowledge of the within-fieldspatial variability of soil properties. This is the basis for effective site-specificfarming, which is environmentally sound and economical. The costs for mea-surements of texture, bulk density and water content with high precision wouldbe higher when compared with the approach presented in this paper. A draw-back of using pedotransfer functions is the uncertainty associated with estimates.

To improve the performance of the pedotransfer functions in estimating CI,we consider that additional soil information, quantifying the soil structure andorganic matter content, has to be monitored and integrated into the functions.Additionally, it would be valuable to enhance the global data set by including alarger range of soil physical factor combinations. Future investigations should


aim to improve the presented pedotransfer functions in terms of their perfor-mance.

We believe that pedotransfer functions for cone penetrometers would makethese devices widely applicable. Measurements of CI are rapid and the costs aremodest when compared to traditional soil sampling of soil physical properties.We conclude that this technique shows promise to improve fine scale samplingof soil physical properties. Considering the limited nature of this study, theseresults strongly indicate the feasibility of this approach.

Acknowledgements

The authors acknowledge Peter Almond, visiting scientist from LincolnUniversity, New Zealand, who provided soil morphological descriptions.

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