1740 SSSAJ: Volume 71: Number 6 • November–December 2007

SOIL

& W

ATE

R M

AN

AG

EMEN

T &

CO

NSE

RVA

TIO

N

Soil Sci. Soc. Am. J. 71:1740–1747doi:10.2136/sssaj2006.0177Received 3 May 2006. *Corresponding author (ulrich.weller@ufz.de).© Soil Science Society of America677 S. Segoe Rd. Madison WI 53711 USAAll rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Until recently, soil mapping has been based mostly on point information from soil profi les. Compared with the spatial

variation of soil, sampling has been sparse and interpolation has had to be based either on expert knowledge or on geostatistics. This approach often does not provide information on soil het-erogeneity as precisely and as cost effectively as needed, for exam-ple, for catchment management (Lathrop et al., 2000; Zhu and Mackay, 2001), land use planning, or precision farming (Moran et al., 1997; Stafford, 2000). This motivated the testing of sev-eral noninvasive methods that promise to overcome these prob-lems associated with high-resolution mapping of soil properties (McBratney et al., 2003; Sommer et al., 2003).

Measurement of the soil’s ECa offers a fast and fairly cheap way to obtain dense soil information (McNeill, 1992). The mag-nitude of the ECa signal is determined by several soil properties, including clay content and cation exchange capacity, as well as soil moisture, temperature, and salinity (Corwin and Lesch, 2005a; Durlesser, 1999; Rhoades et al., 1999; Auerswald et al., 2001).

The spatial variation in the ECa signal is controlled by clay content and mineralogy for soils in a humid climate, if they con-tain negligible amounts of salts and are not infl uenced by ground-water (Lesch et al., 2005; Durlesser, 1999; Auerswald et al., 2001). This is due to the electrical double layer on the surfaces of clay minerals that dominates the soil’s electrical conductivity (Rhoades et al., 1976; Auerswald et al., 2001).

Several researchers have described the use of ECa for esti-mating the clay content of soil; Corwin and Lesch (2005a) gave a compilation of several studies. In individual fi elds, mapping clay content with ECa gave promising results (Durlesser, 1999;

U. Weller*Helmholtz Centre for Environ. Research-UFZDep. of Soil PhysicsTheodor Lieser Str. 406120 Halle (Saale)Germany

M. ZipprichM. SommerZALF-Leibniz Centre for Agric. Landscape Res.Institute of Soil Landscape ResearchEberswalder Str. 8415374 MünchebergGermanyandUniv. of PotsdamInstitute of GeoecologyPO Box 601553D-14415 PotsdamGermany

W. Zu CastellGSF-National Res. Centre for Environment and HealthInstitute of Biomathematics and BiometryIngolstädter Landstrasse 185764 NeuherbergGermany

M. WehrhanZALF-Leibniz Centre for Agric. Landscape Res.Institute of Soil Landscape ResearchEberswalder Str. 8415374 MünchebergGermany

Abbreviations: Corg, organic carbon content; ECa, apparent electrical conductivity; EMv, electromagnetic induction.

Detailed information on soil textural heterogeneity is essential for land management and conservation. It is well known that in individual fi elds, measurement of the soil’s apparent electrical conductivity (ECa) offers an opportunity to map the clay content of soils with free drainage under a humid climate. At the catchment scale, however, units of different land management and differing sampling dates add variation to ECa and constrain the map-ping across fi eld boundaries. We analyzed their infl uence and compared three approaches for applying electromagnetic induction (EMv) to clay-content mapping at the landscape scale across the boundaries of individual fi elds and different sampling dates. In the study region, a separate calibration of the relation between clay and ECa for each fi eld and sampling date (fi eldwise calibration) yielded satisfactory clay-content predictions only if the costly precon-dition of suffi cient calibration points for each fi eld was fulfi lled. We propose a method (near-est-neighbors ECa correction) for unifying ECa across boundaries based only on the ECa data themselves, and the assumption of continuity of textural properties at fi eld boundaries, which was fulfi lled in the landscape studied. Prediction is calibrated once for the entire land-scape, which allows a reduced set of calibration points. The coeffi cient of determination for predicting clay content (here, including silt <4 μm) was improved from R2 = 0.66 (no correc-tion for land use and sampling date) to R2 = 0.85 (n = 46). With the method developed, ECa offers a powerful and cheap method of clay-content mapping in agricultural landscapes.

Mapping Clay Content across Boundaries at the Landscape Scale with Electromagnetic Induction

SSSAJ: Volume 71: Number 6 • November–December 2007 1741

Dalgaard and Have, 2001). In this setting, the spatial variation of other factors infl uencing ECa—such as ionic composition of soil solutes, topsoil structure, bulk density, and organic carbon content (Corg)—is either reduced by the homogeneous cultivation inside the fi eld boundaries or correlated to clay content.

Upon crossing the boundaries between individual fi elds, the application of ECa to map clay content is constrained. Each unit is characterized by unique land use (history) and agricultural man-agement, both of which affect soil properties. At the landscape scale, this increases the variance of the ECa signal considerably. At boundaries between meadows and arable land, discontinuities in soil structure, water content at fi eld capacity, and ionic com-position are expected to be even larger. Furthermore, different measurement dates for different landscape units are likely to occur in large and diversely cultivated areas, adding variation to ECa (Durlesser, 1999; Sudduth et al., 2001). Some researchers have found that the ECa can be used for guiding further prospection but that there is no direct connection to specifi c soil properties on the regional level (Carroll and Oliver, 2005).

In this study, we investigated the mapping of clay given a spatial and temporal mosaic of several ECa measurements in an agricultural landscape. The methods applied were based only on the measurements themselves and on textural data at calibration points. All approaches were evaluated with respect to their accu-racy of clay-content prediction at the landscape scale.

MATERIALS AND METHODSResearch Area

The region investigated, the Klostergut Scheyern of the joint research project FAM (Schröder et al., 2002), is a farm in Bavaria at 11°26′ E, 48°29.5′ N. The soils are formed on Molasse, that is, Tertiary fl uvial sediments of varied texture from clay to gravel with abrupt changes, which are partly covered by Pleistocene loess or Holocene col-luvial deposits. The region is strongly undulating. There are no consoli-dated sediments in the area.

The soil temperature regime is mesic, with an udic moisture regime. The soil epipeda are predominantly ochric, and Eutrochrept is the predominant soil taxonomic suborder. Hapludalfs are common on gentle slopes with Pleistocene loess accumulation. Udorthents and Udipsamments occur on eroded hilltops and steeper slopes and are devel-oped on Molasse. Areas with gleyic soils, that is, soils showing aquic con-ditions due to endosaturation, were not included in the study. They are present in low-lying areas, and can be easily mapped.

The development and comparison of the clay prediction meth-ods took place in eight fi elds: fi ve fi elds are in a cereal–potato (Solanum tuberosum L.)–grass rotation (A2, A3, A4, A5, and A7). Two fi elds, W2 and W3, are mead-ows, and F5 is fallow land taken out of use 10 yr ago (Fig. 1).

Apparent Electrical Conductivity Measurement

The ECa was measured using a Geonics EM38 device (McNeill, 1980) in vertical mode. The resulting signal is referred to here as EMv. Location was determined by differential global positioning system with a mean error

of <1 m and a maximal error up to 3 m (Ehrl et al., 2002). Measurements were taken by different people at various dates (Table 1). Soil moisture was near fi eld capacity on all dates, to minimize the within-fi eld spatial variance of soil water content not related to soil texture. Measurement between the end of October and April also guaranteed relatively small within-fi eld varia-tions of soil temperature and fertilizer residues.

The density of observation points varied from <1 to 3 m in the track direction and from 3 to 15 m in between the tracks (Fig. 1). The measure-ments were made in the vertical mode. For computations based on indi-vidual fi elds only, we normalized raw EMv data to 25°C using the formula derived by Sheets and Hendrickx (1995):

25

0.447 1.4034EC EC

exp26.815

T T

⎡ ⎤+⎢ ⎥⎢ ⎥= ⎛ ⎞⎟⎜⎢ ⎥− ⎟⎜ ⎟⎜⎢ ⎥⎝ ⎠⎣ ⎦

[1]

Table 1. Correlation between electrical conductivity normalized to 25°C (EC25) and weighted clay content for homogeneous landscape units.

Field and crop Date R2 n Signifi cance Prediction of clay content—————— % ——————

A2, winter rye October 1999 0.70 9 99.9 −17.0 + 0.88EC25A3, clover and grass April 2001 0.79 7 99 3.1 + 0.35EC25A4, winter wheat April 2001 0.97 7 >99.9 −5.4 + 0.64EC25A5, clover and grass October 1999 0.50 4 70 8.2 + 0.34EC25A7, winter wheat April 2001 ND† 3 <70 NDW2, meadow April 2001 (I) ND 3 <70 ND

December 2001 (II) ND 3 <70 NDW3, meadow October 1999 0.95 6 >99.9 3.0 + 0.67EC25F5, fallow land April 2001 (I) 0.91 8 >99.9 0.6 + 0.70EC25

December 2001 (II) 0.91 9 >99.9 8.1 + 0.45EC25

† ND = not determined.

Fig. 1. Apparent electrical conductivity (EC) measurement points and fi elds investigated for method comparison.

1742 SSSAJ: Volume 71: Number 6 • November –December 2007

where ECT is the EMv at soil temperature T (°C). Soil temperature was measured at a depth of 50 cm. Temperature correction is not a precondi-tion for the nearest neighbors EMv correction method (see below) and was therefore not applied to this. We used ordinary kriging to interpolate EMv between the tracks and for the prediction at the locations of the analyzed soil profi les. A spherical variogram model with nugget was used. Variogram calculations, fi tting of a spherical variogram model, and pre-dictions were accomplished with the geoR package for the statistic soft-ware R (Ribeiro and Diggle, 2001), while maps were generated with the aid of the software package ArcGIS 8.1 by ESRI (Redlands, CA).

Soil Calibration DataDescriptive and analytical soil profi le information for calibration was

available for 46 points on a 50- by 50-m grid (Sinowski, 1995). Laboratory determinations of texture, organic C, and soil bulk density were made for each horizon. Soil bulk density was measured on 100-cm3 cylinders and corrected for stones >2 cm. It seemed adequate to integrate the fi ne silt fraction (2–4 μm) into the “clay fraction,” since clay minerals form part of the mineral spectrum in this particle-size class (Allen and Hajek, 1989). To correlate the EMv signal with a soil quantity, q, a weighted sum Q was calculated from the density of the measuring signal (z) (McNeill, 1980):

( ) ( )

( ) ( )

1.2m

0

11

d

= N

h h hh

Q z q z z

R d R d q−=

= Φ

⎡ ⎤−⎣ ⎦

∫

∑ [2]

where R(dh) is the proportion of the signal measured below the lower boundary, d, of the hth horizon (d0 = 0, dN = 1.2 m), and qh is the con-sidered soil quantity in the hth horizon. Only those calibration points that are inside the fi eld boundaries and at a distance of <5 m from the nearest EMv measurement point were included in regression calcula-tions. For correlating soil properties, Q, with interpolated EMv mea-surements, we assume a linear relationship:

0 1ECQ =α +α [3]

where α0 and α1 are the axis intercept and the slope, respectively.

Elimination of Land Use and Time Infl uences on Electromagnetic Induction Measurement

Method a: No CorrectionFirst, we regarded the EC25 measurements, corrected for the infl u-

ence of soil temperature only, as stable with respect to time and changes in cultivation. The fi rst step in data analysis (Fig. 2a) was then the spatial union of all different EC25 data sets, measured at different dates and on

fi elds under different cultivation. Subsequently, we approximated EC25 values, at the locations of analyzed soil samples, by ordinary kriging. Finally, we performed regression analysis using the weighted clay con-tents. This approach provides a reference by which to evaluate the quality of the methods to correct EMv for land use and time.

Method b: Fieldwise CalibrationAssuming a linear infl uence of land use and time on ECa means that

the coeffi cients α0 and α1 of Eq. [3] depend on land use and sampling date. Denoting each unique combination of management and sampling date (in practice, each fi eld and measurement campaign) by an arbitrary indicator variable, n (n = 1, 2, ..., r), we rewrite Eq. [3] as

0 1ECn nQ =α +α [4]

The fi eldwise calibration method, which pays attention to the infl u-ence of land use and sampling date on EMv, treats every EMv data set individually. Regression equations between weighted clay content and EMv were then calculated separately for each realization of the set of all unique space–time combinations, n (Fig. 2b). We then evaluated the quality of prediction at the landscape scale by comparing the predicted and the measured clay contents. We have also tested a simplifi ed version of Eq. [4], where we assumed αn1 to be fi xed to evaluate the type of infl u-ence that date and management has on ECa.

Method c: Nearest Neighbors Electromagnetic Induction Measurement Correction

To diminish the infl uence that different land management and dif-ferent measurement dates have on the correlation between clay content and EMv, we have developed a two-step approach. In the fi rst step, we tried to eliminate the differences between adjacent fi elds to form a fi t-ted, more continuous signal that we call EMvadj. This step is based only on the EMv data and its location; no additional information on soil tex-ture is included. In the second step, we then correlated this fi tted signal against clay content of the reference data points (Fig. 2c). The fi rst step is based on the assumption of continuity of clay content at fi eld boundar-ies. Therefore, we assume the existence of a spatially autocorrelated vari-able, EMvadj, which is linearly correlated to the time- and fi eld-dependent EC(x) values at position x. We can then write

,

vadj 0 1

0 1 0 1

EM EC( )

EC( ) EC( )n j mi

n n

n n nj m m mi x x

x

x x

= β +β

β +β = β +β + ε [5]

where the measurement at location xnj belongs to data set index n, and xmi to m, and ε is a random variable whose variance depends on the sampling distance ||xmi − xnj|| with mean 0. We assumed that ε is small if two points are in close proximity. We defi ned a set of points that are suffi ciently close together and belonging to different fi elds. To minimize the numerical problems, we wanted to keep this data set small; therefore, we selected only those points that are the closest to each other. Thus, given two realizations of the EMv measurements, we have the set of coordinates Xm and Xn with corresponding EMv mea-surements EC(Xm) and EC(Xn) of Nm and Nn elements, respectively.

We defi ne a set Pmn of EMv measurements at nearest neighbor points as

( )

( )

n

mi nj

EC( )EC( ) where

EC(x ), EC(x )

if = d ,

and = d ,

mn n

mn

mi nj mi n

mi nj nj m

P X x

P

x x x X

x x x X

⊂

⎡ ⎤ ∈⎢ ⎥⎣ ⎦−

−

[6]

Fig. 2. Workfl ow for electromagnetic induction measurement (EMv) to clay mapping: (a) no correction for infl uence of land use and time; (b) fi eldwise calibration; and (c) nearest neighbors EMv correction.

SSSAJ: Volume 71: Number 6 • November–December 2007 1743

with d(x, Xm) = min1

mNk=

||x − xmk|| being the distance between Point x and the points in Set Xm. In other words, given two points belonging to dif-ferent data sets (Point 1 to Set m and Point 2 to Set n), these two points are called nearest neighbors if, and only if, Point 1 is the closest point in Set m to Point 2, and Point 2 is the closest point in Set n to Point 1. In this study, we restricted the sets of pairs to those with a maximum separation distance of 15 m. Furthermore, if there were terrace steps between two near-est neighbor points, violating the assumption of spatial autocorrelation, we eliminated these pairs from the set of nearest neighbor points. These terrace steps violate the assumption of continuity of soil properties, and they were easy to detect in the landscape by using the digital elevation model that is available for the study area.

Given the union of all nearest neighbor sets Q = , 1 ,r

m n n mnP≠ =∪ we have to minimize the sum of residuals from Eq. [5] as given by

( )20 1 1( , )

m m mi n njymi ynj Q

y y∈

β +β −β∑ [7]

We also have the boundary condition that the overall mean should be pre-served and the trivial solution of all coeffi cients being zero should be excluded. This is achieved by adding Σ 0

ri= β0i = 0 and Σ 0

ri= β1i = r to the

system of linear equations.In matrix form, the equation system is given with

00

0( 2 1)00 01 01

10 11 1( 2 1) 10

11

0

1

0

0

0

1 0 1 00

0 1 0 1

k

k

k

k

k

−

−

⎛ ⎞β ⎟⎜ ⎛⎟⎜ ⎟⎛ ⎞ ⎜⎜αα α ⎟β ⎜⎟⎜⎜ ⎟⎟ ⎜⎜⎜ ⎟⎟ ⎜⎜ ⎟⎜ ⎟ ⎜α α α ⎜ ⎟⎜ β⎟ ⎟ ⎜⎜⎜ ⎟ ⎟ ⎜⎜⎜ ⎟ ⎟ ⎜⎜⎜ ⎟ ⎟β =⎜⎟⎜ ⎟⎟⎜⎜ ⎟⎟⎜⎜ ⎟⎟⎜ ⎟⎜ ⎟ ⎟⎜⎜ ⎟ ⎟⎜⎜ ⎟ ⎟⎜⎜ ⎟ ⎟⎜⎟⎜ β⎟⎜ ⎟⎝ ⎠⎜ ⎟⎜ ⎝⎟⎜ ⎟⎟⎜β⎝ ⎠

……

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎠ [8]

with p1i and p2i as the fi rst and second point of the ith pair, the matrix coeffi cients are given by

[ ]

[ ]

1i j

2i2( 1)

1 1i j

2i 2i2 1

1 if X

1 if

0 otherwise

EC( ) if X

EC( ) if

0 otherwise

ji j

i

ji j

p

p X

p p

p p X

−

−

⎧ ∈⎪⎪⎪⎪α = − ∈⎨⎪⎪⎪⎪⎩⎧ ∈⎪⎪⎪⎪α = − ∈⎨⎪⎪⎪⎪⎩ [9]

The least square fi t for the unknown variables β was done by a stan-dard iterative method (conjugate gradient, Fletcher and Reeves, 1964), which is implemented in the analytical software package R, Version 1.6.1 (Ribeiro and Diggle, 2001). The direct linear solution was too memory consuming for the larger data fi elds. The second step is then analogous to Method a, but based on the EMvadj values as defi ned in Eq. [5].

To analyze the correlation between the prediction error of the nearest neighbors method and the number of calibration points, k, we chose lk sub-samples randomly from the n = 46 points with lk = min[1000,( n

k )] and k = 4, 5, ..., n. For each subsample, we determined regression parameters and predicted the clay content for the n points. We then calculated the RMSE for predicted vs. measured weighted clay content and, fi nally, the median of the RMSE and the 25 and 75% quantiles for each k.

RESULTS AND DISCUSSION

To apply ECa to map clay content at the landscape scale, we had to verify the validity of two premises: fi rst, we ascertained the relation of EMv to clay content locally; second, we estab-lished the continuity of this relation at the landscape scale.

Field ScaleFigure 3a shows the variograms for Fields A2 and F5. The

differences in the local variation of the EC signal were high. None of the variograms show a signifi cant nugget effect, thus the mea-surement error can be neglected. The coeffi cients of determination between weighted clay content and the interpolated EC25 values are listed separately in Table 1 for each fi eld and sampling date. For the fi elds investigated, soil clay content controlled the spatial

Fig. 3. Semivariograms for electromagnetic induction (EMv) measure-ments: (a) variograms for two fi elds compared with regional semivariogram after electrical conductivity (EC) correction; and (b) regional semivariogram with and without EC correction.

Table 2. Correlations between electrical conductivity normalized to 25°C (EC25), weighted clay content, organic C content (Corg), and bulk density for homogeneous land units.

Field n

Coeffi cient of determination with EMv

Coeffi cient of determination with clay content

Clay content

CorgBulk

densityCorg Bulk density

A2 9 0.70 0.00 0.02 0.17 0.02A3 7 0.79 0.53 0.65 0.48 0.41A4 7 0.97 0.08 0.17 0.06 0.16A5 4 0.50 0.45 0.45 0.00 0.18W3 6 0.95 0.01 0.01 0.11 0.04F5 (I) 8 0.91 0.51 0.83 0.62 0.71F5 (II) 9 0.91 0.01 0.67 0.01 0.68

1744 SSSAJ: Volume 71: Number 6 • November –December 2007

variation of the EMv signal. The infl uence of other soil properties on EMv was weak (Table 2).

For three fi elds only (A3, A5, and F5), Corg or soil bulk density correlate with EMv. In these cases, there is usually strong interdependence between these variables and clay content. For prediction of clay content, the coeffi cients of determination, R2, ranged from 0.7 to 0.97 for fi elds with n ≥ 6 profi les with labo-ratory clay analysis (Table 1). This represents the upper limit of values reported by other researchers. Dalgaard and Have (2001)

found similar coeffi cients of determination (R2 = 0.79) for soils developed on moraine, while Schmidhalter et al. (2001) reported values of R2 from 0.31 to 0.67. In the fi elds studied, several other conditions favored the application of EMv for clay prediction. The soil water status was near fi eld capacity, and there was no infl uence of groundwater with a possibly differing ionic composition.

The F test for different statistical models showed a clear infl u-ence of the date and fi eld of measurement. The performance of a model with a fi xed slope but different intersects for the relation EMv vs. clay content performs only slightly better than the model with no correction (F = 1.5, P = 0.19). The infl uence of an adjusted slope for each date and fi eld combination has a signifi cant better correlation (F = 3.6, P = 0.005). The residual sums of squares were 0.064 for no correction, 0.052 for different intersects, and 0.024 for different intersects and slopes.

Infl uence of Time and Land UseTo unify multiple EMv measurements for clay prediction

at the landscape scale, we analyzed the infl uence of manage-ment practices and time of measurement on EMv.

First, we analyzed the reproducibility of measurements made within 1 wk, but differing by track direction (Fig. 4). Regions where absolute and relative differences of interpolated EC25 exceeded 3 mS m−1 and 10%, respectively, were concentrated (Fig. 4b) between distant tracks as well as where there was a strong gradient in EC25, where small positioning errors have the greatest impact. The coeffi -cient of determination between the two measurements with different track directions is R2 = 0.96, based on points within <1-m distance of the set in the other track direction (n = 163). Resulting EC25 pat-terns (Fig. 4a) are basically independent of track direction and can be reproduced by repeated measurement. The observed differences (RMSE = 2.6 mS m−1) are within the range reported by Sudduth et al. (2001) for short-term fl uctuations in EMv signal due to drift of the EM38. For multiple EC25 measurements, made within a few days of each other on another fi eld of Klostergut Scheyern, we do fi nd a similarly good fi t: R2 = 0.95, n = 185.

Fig. 4. Comparability of multiple electromagnetic induction (EMv) measurements: I. Reproducibility of electrical con-ductivity (EC) measurements.

Fig. 5. Comparability of multiple electromagnetic induction (EMv) measurements: II. Infl uence of time of measurement on electrical conductivity (EC) measurements.

Fig. 6. Comparability of multiple electromagnetic induction (EMv) measurements: III. Infl uence of time and cultivation on elec-trical conductivity measurements normalized to 25°C (EC25). Each symbol represents one spatial point and its EC25 signal at Date 1 (x axis) vs. the measurement at Date 2 (y axis).

SSSAJ: Volume 71: Number 6 • November–December 2007 1745

Second, we compared mea-surements of the same fi eld made at different times of the year and under different conditions in terms of land use. For all dates, the soil was near fi eld capacity. Figure 5 compares two sampling dates in a meadow, and shows that patterns of EC25 are basi-cally independent of time, but the EC25 values and their ranges differ signifi cantly. Cultivation did not alter EC25 patterns either (Fig. 6). Sudduth et al. (2001) also found a strong linear correlation between multiple EMv measure-ments made on the same fi eld in different years.

Correlation turns out to be weaker, though, if ECa values measured in summer are compared with spring measurements (Durlesser, 1999). During summer, the infl uence of spatially vari-ant water tension and solute concentrations on ECa imply that ECa cannot always be optimally used for mapping soil clay content.

In summary, ECa is a function of time of measurement, management practice, land use, and soil surface topography (Corwin and Lesch, 2005b). The multiple measurements are lin-early correlated with each other and most of the spatial variation of ECa is explained by soil clay content. Given the continuity of soil textural properties at fi eld boundaries, this implies that the relative ECa patterns are constant across spatial and temporal boundaries at a fi rst approximation.

Mapping at Landscape ScaleMethod a: No Correction

To map clay content at the landscape scale, we used the entire multispatial and multitemporal set of EC25 data. Let us fi rst dis-regard the infl uence of land use and sampling date (Fig. 2a). The correlation between interpolated EC25 and clay content then yields a lower coeffi cient of determination (R2 = 0.66; Fig. 7a; Table 3, Regression 1) compared with the single fi elds (Table 1).

Different levels and ranges of EC25 measured on fi elds of dif-fering land use and at different dates are shown by marked discon-tinuities of the predicted clay contents at fi eld boundaries (Fig. 8a). Thus, multiple ECa measurements cannot be evaluated jointly in terms of clay content without taking land management and time into account. Other investigators who looked at a set of fi elds, and who did not take into account the infl uence of different land use and management, also found fairly weak correlations between clay content and ECa. For measurements conducted on fi elds of the same research farm Klostergut Scheyern, Schmidhalter et al. (2001)

and Durlesser (1999) reported coeffi cients of determination for the relation between clay content and ECa of R2 = 0.45 (here, clay + fi ne silt), and R2 = 0.51, respectively. The procedure (no correction) is similar to kriging with regression (Knotters et al., 1995).

Method b: Fieldwise CalibrationOne way of accounting for the infl uence of time and cultiva-

tion on ECa is to calibrate the relationship between EMv and clay for each data set separately (Fig. 2b). This gives an apparently strong prediction of clay content with R2 = 0.90 (Fig. 7b) and a RMSE of <4% clay content (Table 3, Regression 2). The correlation is, however, highly unstable, as in our example calibration points are sparse for some landscape units (Table 1). To achieve robust results, this method requires suffi cient soil profi les for calibration in each individual fi eld. This is a serious problem for mapping soil clay

Fig. 7. Comparison of methods to correct electromagnetic induction (EMv) measurement of electri-cal conductivity normalized to 25°C (EC25) for infl uences of time and cultivation with regard to prediction of soil clay content.

Table 3. Comparison of methods to correct electromagnetic induction (EMv) fi eld values of electrical conductivity nor-malized to 25 °C (EC25) for infl uences of time and cultiva-tion with regard to prediction of clay content (n = 46).

Method for correction R2 RMSEPrediction of clay

content%

No correction 0.66 6.56 3.3 + 0.47EC25Fieldwise calibration 0.90 3.60 fi eldwise

Nearest neighbors EMv correction 0.85 4.34 −6.4 + 0.76EC25

Fig. 8. Discontinuities of soil clay content predicted by mea-surements of electrical conductivity (EC) on the boundaries between landscape units.

1746 SSSAJ: Volume 71: Number 6 • November –December 2007

content at the catchment scale, where many, often small, land units are to be recognized. Obtaining calibration data is time consuming and expensive. In addition, artifi cial discontinuities of predicted clay content at fi eld boundaries persist even for a relatively large number (n ≥ 6) of calibration points per fi eld (Fig. 8b, Table 1).

The fi eldwise calibration method represents a combination of kriging with regression and kriging with stratifi cation (Stein et al., 1988). The stratifi cation variables in this case are the fi elds and the sampling date of the data set.

Method c: Nearest Neighbors CorrectionThis method (Fig. 2c) takes into account spatial soil relation-

ships and thereby reduces the variance of EMv by >50% (Fig. 3b). Correction of the infl uence of land use and time lowered the sill of the variogram from 265 mS2 m−2 for EC25 (no correction) to 125 mS2 m−2 for EMvadj. For the prediction of weighted clay content with EMvadj, a coeffi cient of determination of R2 = 0.85 was achieved with the nearest neighbors EMv correction method (Table 3, Regression 3; Fig. 7c). In contrast to the fi eldwise calibra-tion method, the correlation is more robust. The two parameters

per fi eld (for intersect and slope correction) are estimated from the large data set of EMv measurement point pairs, and the fi nal cor-relation only costs two degrees of freedom.

The regression functions between EMv and clay content are built only once for all landscape units and sampling dates together. This is essential for the application of the method in the framework of mapping soil clay content at catchment and landscape scales. Compared with the fi eldwise method, a sig-nifi cantly smaller set of calibration points is suffi cient to achieve reliable prediction. Reducing the number of calibration points to eight, that is, only one profi le per fi eld, increases the median RMSE by <0.5% clay (Fig. 9).

Besides improving clay prediction at point support, our method enables us to map patterns of clay content across the boundaries of individual fi elds (Fig. 8c). Furthermore, additional information in the form of multiple measurements of one fi eld is incorporated into the optimization process. Other soil properties explaining ECa may easily be incorporated into the framework of the method, provided they are invariant to time and land use. Finally, the method implies no need to perform temperature correction of the ECa value explic-itly: fi rst, the formula for temperature correction strictly speaking demands local validation; and second, determination of the effective soil temperature of the measurement volume is tedious.

We need to stress, however, that the nearest neighbors EMv correction method is subject to two preconditions. First, a signifi -cant number of measurements should be placed near fi eld bound-aries, since the distance between neighboring EMv measurements should be small compared with the spatial range of correlation.

The second, more fundamental precondition is that there should be no sharp discontinuities in soil texture at the fi eld bound-aries considered. This assumption is fulfi lled in our case: the parent materials in the Bavarian Molasse region mostly are highly variable fl uvial sediments. On the one hand, this signifi es that natural dis-continuities in soil texture are unlikely to be linear, in contrast to, for example, a cuesta landscape. On the other hand, the size of single areas of the pattern is mostly small compared with the length of fi eld boundaries. In its current form, the method uses an ordinary least squares fi t. This could be generalized to take into account the dis-tance between the data pairs. One way to do this would be to weight each equation with the spatial variance for the given point distance. Another way would be the use of a more general system to predict one data point from the other data set and to use these predictions in the linear equation system. We chose the nearest neighbor method due to the computational simplicity and as it proved to be suffi cient with the given large number of data pairs.

The nearest neighbors EMv correction was applied to the entire farm Klostergut Scheyern to three contiguously mea-sured subareas. Figure 10 shows the map of predicted clay content and its pattern.

CONCLUSIONSWith our nearest neighbors EMv correction method, we can

extend the application of ECa for clay-content mapping from the fi eld to the landscape. This is possible without analyzing the signal variation due to land use, management practices, and sampling date in detail. The method developed adjusts for the unwanted infl uence of measurement conditions based merely on the signal, the spatial arrangement, and the stratifi cation of the data. This nearest neighbors EMv correction provided the best results for

Fig. 9. Dependence of RMSE for clay content prediction by mea-surements of electrical conductivity (EC) on the number of calibration points.

Fig. 10. Map of estimated clay content of the Klostergut Schey-ern using the nearest neighbors electromagnetic induction measurement (EMv) correction method.

SSSAJ: Volume 71: Number 6 • November–December 2007 1747

the detection of continuous soil structures across fi eld boundar-ies. In contrast, separately predicting clay content for each fi eld and sampling date is not applicable to heterogeneous agricultural landscapes with numerous small fi elds, because a vast number of calibration points is necessary to attain unbiased results.

The easy measurement and simple calibration promotes the combination of the ECa technique and the nearest neighbors EMv correction as a standard tool in spatial soil investigation. The nearest neighbors EMv correction method can be easily applied to simi-lar problems associated with mapping at the landscape scale, where land-use boundaries restrict the pedological interpretation of indi-rect techniques. It can be used as an independent preprocessing step for other methods, e.g., guided sampling (Lesch et al., 1995).

ACKNOWLEDGMENTSWe thank U. Schmidhalter and H. Stanjek of the Technical University of Munich-Weihenstephan (TUM) for kindly making available the EM38 measuring device. We also thank K. Heil and E. Neudecker for joint EMi measurements of the fi elds A3, A4, A7, W2, and F5, and H.-P. Durlesser and C. Sperl for making their EMi data available. We wish to also thank M. Stephan for his assistance with fi eld measurements during severe weather. This work was performed under the Research Network Agroecosystems Munich (FAM) and fi nanced by the BMBF.

REFERENCESAllen, B.L., and B.F. Hajek. 1989. Mineral occurrence in soil environments.

p. 199–278. In J.B. Dixon and S.B.Weed (ed.) Minerals in soil environments. 2nd ed. SSSA Book Ser. 1. SSSA, Madison, WI.

Auerswald, K., S. Simon, and H. Stanjek. 2001. Infl uence of soil properties on electrical conductivity under humid water regimes. Soil Sci. 166:382–390.

Carroll, Z.L., and M.A. Oliver. 2005. Exploring the spatial relations between soil physical properties and apparent electrical conductivity. Geoderma 128:354–374.

Corwin, D.L., and S.M. Lesch. 2005a. Apparent soil electrical conductivity measurements in agriculture. Comput. Electron. Agric. 46:11–43.

Corwin, D.L., and S.M. Lesch. 2005b. Characterizing soil spatial variability with apparent soil electrical conductivity: I. Survey protocols. Comput. Electron. Agric. 46:103–134.

Dalgaard, M., and H. Have. 2001. Soil clay mapping by measurement of electromagnetic conductivity. p. 367–372. In G. Grenier and S. Blackmore (ed.) European Conf. on Precision Agriculture, 3rd, Montpellier, France. 18–20 June 2001. Agro Montpellier, Montpellier, France.

Durlesser, H.P. 1999. Determination of the variation of soil physical parameters through time and space by electromagnetic induction. (In German.) FAM-Bericht 35. Shaker, Aachen, Germany.

Ehrl, M., M. Demmel, H. Auernhammer, W. Stempfhuber, and W. Mauer. 2002. Spatio-temporal quality of precision farming applications. Pap. 023084. In ASAE Annual Meeting, Chicago. Am. Soc. Agric. Eng., St. Joseph, MI.

Fletcher, R., and C.M. Reeves. 1964. Function minimization by conjugate gradients. Comput. J. 7:148–154.

Knotters, M., D.J. Brus, and J.H. Oude Voshaar. 1995. A comparison of kriging,

cokriging and kriging combined with regression for spatial interpolation of horizon depth with censored observations. Geoderma 67:227–246.

Lathrop, R.G., J.D. Aber, and J.A. Bognar. 2000. Spatial variability of digital soil maps and its impact on regional ecosystem modeling. Ecol. Modell. 82:1–10.

Lesch, S.M., D.L. Corwin, and D.A. Robinson. 2005. Apparent soil electrical conductivity mapping as an agricultural management tool in arid zone soils. Comput. Electron. Agric. 46:351–378.

Lesch, S.M., D.J. Strauss, and J.D. Rhoades. 1995. Spatial prediction of soil salinity using electromagnetic induction techniques: 2. An effi cient spatial sampling algorithm suitable for multiple linear regression model identifi cation and estimation. Water Resour. Res. 31:387–398.

McBratney, A.B., M.L. Mendoça Santos, and B. Minasny. 2003. On digital soil mapping. Geoderma 117:3–52.

McNeill, J.D. 1980. Electromagnetic terrain conductivity measurement at low induction numbers. Tech. Note 6. Geonics Ltd., Mississauga, ON, Canada.

McNeill, J.D. 1992. Rapid, accurate mapping of soil salinity by electromagnetic ground conductivity meters. p. 209–229. In G.C. Topp et al. (ed.) Advances in measurement of soil physical properties: Bringing theory into practice. SSSA Spec. Publ. 30. SSSA, Madison, WI.

Moran, M.S., Y. Inoue, and E.M. Barnes. 1997. Opportunities and limitations for image based remote sensing in precision crop management. Remote Sens. Environ. 61:319–346.

Rhoades, J.D., F. Chanduvi, and S.M. Lesch. 1999. Soil salinity assessment: Methods and interpretation of electrical conductivity measurements. FAO Irrig. Drain. Pap. 57. FAO, Rome.

Rhoades, J.D., P.A.C. Raats, and R.J. Prather. 1976. Effects of liquid-phase electrical conductivity, water content and surface conductivity on bulk soil electrical conductivity. Soil Sci. Soc. Am. J. 40:651–655.

Ribeiro, P.J., and P.Y. Diggle. 2001. geoR: A package for geostatistical analysis. Available at http://cran.r-project.org/doc/Rnews/Rnews_2001-2.pdf (verifi ed 2 June 2007). R News 1(2):15–18.

Schmidhalter, U., A. Zintel, and E. Neudecker. 2001. Calibration of electromagnetic induction measurements to survey the spatial variability of soils. p. 479–484. In G. Grenier and S. Blackmore (ed.) European Conf. on Precision Agriculture, 3rd, Montpellier, France. 18–20 June 2001. Agro Montpellier, Montpellier, France.

Schröder, P., B. Huber, U. Olazàbal, A. Kämmerer, and J.C. Munch. 2002. Land use and sustainability: FAM research network on agroecosystems. Geoderma 105:155–166.

Sheets, K.R., and J.M.H. Hendrickx. 1995. Non-invasive soil water content measurement using electromagnetic induction. Water Resour. Res. 31:2401–2409.

Sinowski, W. 1995. The three-dimensional variability of soil properties. (In German.) FAM Bericht 7. Shaker, Aachen, Germany.

Sommer, M., M. Wehrhan, M. Zipprich, U. Weller, W. zu Castell, S. Ehrich, B. Tandler, and T. Selige. 2003. Hierarchical data fusion for mapping soil units at fi eld scale. Geoderma 112:179–196.

Stafford, J.V. 2000. Implementing precision agriculture in the 21st century. J. Agric. Eng. Res. 76:267–275.

Stein, A., M. Hoogewerf, and J. Bouma. 1988. Use of soil-map delineations to improve (co)kriging of point data on moisture defi cits. Geoderma 43:163–177.

Sudduth, K.A., S.T. Drummond, and N.R. Kitchen. 2001. Accuracy issues in electromagnetic induction sensing of soil electrical conductivity for precision agriculture. Comput. Electron. Agric. 31:239–264.

Zhu, A.X., and D.S. Mackay. 2001. Effects of spatial detail on soil information on watershed modeling. J. Hydrol. 248:54–77.