SOIL FERTILITY MAP QUALITY: CASE STUDIES IN KENTUCKY
T.G. Mueller, K.L. Wells, G.W. Thomas, R.I. Barnhisel, N.J. Hartsock
Department of Agronomy
University of Kentucky
Lexington, Kentucky
S.A. Shearer,
Department of Biosystems and Agricultural Engineering
University of Kentucky
Lexington, Kentucky
A. Kumar
Department of Computer Science
University of Kentucky
Lexington, Kentucky
C.R. Dillon
Department of Agricultural Economics
University of Kentucky
Lexington, Kentucky
ABSTRACT
The adequacy of soil fertility maps created for variable rate fertilization
depends on the variability of the soil properties, sampling design and intensity,
interpolation techniques, and mapping protocols. The objectives of this study
were to examine the impact of grid sampling intensity and interpolation
techniques on the accuracy of soil fertility maps for several fields in Kentucky.
The fields were sampled on a 30-m grid and the samples were analyzed for pH,
BpH, P, and K. From this data set, 61 and 91-m grids were created. The data
were interpolated with kriging (30-m grid) and inverse distance squared (30,
61, and 91-m grids). The root mean squared errors (rmse) were calculated
using an independent check data set. Although the data were spatially
structured, most predictions were poor at the 30-m grid scale. Soil P at the
Shelby Co location was an exception. It performed well at the 30-m grid scale
(rmse=6.8), fair at the 61-m grid (rmse=8.9), and marginal at the 91-m grid
(rmse=10.7). Generally the differences in rmse for kriging and inverse distance
weighted interpolation with a distance exponent of 2 were not large.
Keywords:
site-specific fertility management, kriging, inverse distance
INTRODUCTION
Site-specific fertility management (SSFM) is based on the premise that the
quantity of fertilizer and lime that produces the maximum economic crop
response varies spatially in a way that can be adequately predicted and managed
(Sawyer, 1994; Pierce and Nowak, 1997; Mueller, 1998). While many factors
influence economic crop responses (e.g. soil fertility levels, other factors that limit
yield, crop rotation, commodity values, and costs associated with crop
production), traditional lime, P, and K recommendations are sensitive primarily to
soil test values. Because most SSFM recommendations are based primarily on
whole-field traditional fertility recommendations, the quality of soil fertility maps
is fundamental to SSFM. Map quality is defined as the sum of a maps precision
and accuracy and is quantified as the mean square error of the residuals (predicted
– measured) obtained with a validation data set.
A number of factors affect map quality including the nature of the soil
variability (Flatman and Yfantis, 1996; Sadler et al., 1998), intensity of sampling,
and method of interpolation. In some studies, inverse distance weighted (IDW)
interpolation has performed superior to kriging (Weber and Englund, 1992;
Wollenhaupt et al., 1994; Gotway et al., 1996) while in other studies, kriging
performed superior to IDW (Creutin and Obled 1992; Tabios and Salas, 1995;
Laslett et al., 1997; Kravchenko and Bullock, 1999). Kriging requires the
preliminary step of modeling a variance-distance relationship. The IDW
procedure does not require this step and is very simply and quick. For a field in
south central Michigan, map quality was adequate for soil P (range of spatial
correlation of 125-m and 81% of the variability was spatially structured)
measured at 30.5-m or greater but was substantially poorer for other soil variables
(pH, K, Mg, Ca, and Mg). In addition, map quality decreased rapidly for all
variables as the intensity of sampling decreased to 61.5 and 100-m grids, and was
not greatly impacted by the method of interpolation (i.e. inverse distance
weighted and ordinary kriging; Mueller, 1998)
The objective of this study was to assess the impact of spatial structure,
sampling intensity, and interpolation method on map quality for Kentucky soils.
Three fields were chosen to represent several of the agriculturally important soilphysiographic regions of Kentucky. Grid and validation soil samples were
collected and analyzed. The gridded fertility values at various scales were
interpolated with inverse distance and ordinary kriging. The validation data sets
were used to assess map quality.
Propagation of Errors
Map quality must be considered in the context of the errors associated with
SSFM (Shearer et al, 2000). There are three basic sources: errors associated with
map production, the generation of fertilizer recommendations maps, and variable
rate application.
If the soil property of interest is not spatially structured (i.e. large nugget
variance or small range of spatial correlation), then the property cannot be
accurately predicted spatially. For spatially structured variables, errors may be
introduced by the soil sampling procedure (i.e. sampling depth, core diameter,
number and orientation of sub-samples in each composite sample), method of
sampling (grid sampling or directed/zone sampling), and intensity of sampling
(i.e. grid size, zone size). Errors associated with uncertainty of position (i.e. GPS
errors), sample preparation, and laboratory analyses may be small compared to
errors associated with prediction. The method used to generate spatial predictions
at unsampled locations (e.g. nearest neighbor, inverse distance, and kriging)
introduces error. Methods used to summarize spatial predictions with contours or
application grids cells further degrade map quality.
Errors are introduced when fertilizer recommendations are used to transform
soil property maps into application map. This may occur because not all of the
factors that contribute to an economic crop response are included in
recommendation and because recommendations were based on the hybrids, soils,
and cropping practiced used in their development. Hergert et al. (1997) provide
additional explanations: the economic environment of crop production has
changed substantially since the development of recommendations, soil variability
has increased over time with management, and spatial variability is already
compensated for in many whole field recommendations.
Variable rate technologies errors include GPS errors, errors due to
heterogeneity of fertilizer composition, errors due to application overlaps and
gaps (Fulton et al., 1999), errors due to topographic relief, and errors associated
with the response lags when changing application rates.
The errors associated with map production, the generation of recommendation
maps, and variable rate application are not independent. Errors associated with
map production will be magnified by application errors. Further, these errors may
propagate non-additively. A model that explains how each source of error affects
the economics of SSFM will allow research to be targeted at the most significant
factors. Further, SSFM methods can be adjusted by practitioners to minimize
theses errors. Approaching SSM research in this way will require an
interdisciplinary effort because of the complex nature of the problem.
METHODS
Site Description
This study was conducted on three fields in Kentucky: a 15.0 ha field in
Calloway Co., 9.6 ha field in Hardin Co. and a 53.0 ha field in Shelby Co. (Fig.
1). The Calloway field is located in the Purchase region of Kentucky where soils
are derived from loess. The principal soils in this field are the Grenada
(moderately-well drained; Fine-silty, mixed active, thermic Glossic Fragiudalfs),
Calloway (somewhat poorly drained; Fine-silty, mixed active, thermic Glossaquic
Fragiudalfs) and Henry (poorly drained; Coarse-silty, mixed, active, thermic
Typic Fragiaqualfs) series which differ in both drainage and depth of fragipan.
The Hardin field is located in the karstic Pennyroyal region, where the soils are
derived from Mississippian-age limestone residuum and a loessial cap with
variable thickness. Principal soils in this field are the Crider (Fine-silty, mixed,
active, mesic Typic Hapludalfs), Vertrees (Fine, mixed, mesic mesicTypic
Paleudalfs) and Nolin (Fine-silty, mixed, mesic Dystric Fluventic Eutrochrepts)
series, with Crider making up most of the field and the Nolin representing all the
sinkhole depressional. The Shelby field is located in the Outer Bluegrass region,
where the soils are formed in Ordovician-age limestone-shale residuum capped
with loess of variable depth. Principal soil series are Lowell (Fine, mixed, active,
mesic Typic Hapludalfs) and Nicholson (Fine-silty, mixed, semiactive, mesic
Oxyaquic Fragiudalfs). The Nicholson series has a deeper loess cap than the
Lowell and also has a fragipan.
Soil Sampling and Laboratory Analysis
Soil samples were obtained from the fields using a 30.5-m regular grid (G30;
Fig. 1.; Calloway, n = 163; Hardin, n = 104; Shelby, n = 588). An additional
validation data set (GVAL) was obtained with a two-staged sampling design
(GVAL). Samples were chosen randomly with in each grid cell of a regular grid
(Fig. 1.; Calloway, n = 60; Hardin, n = 58; Shelby, n = 70). At each grid point, 5
soil sub-samples (1 at the grid point and 4 within a 7-m radius) were obtained
using a 2.1-cm diameter core to a depth of 20-cm and these samples were
combined to form a composite. Soils were air dried at 25º C and ground to pass a
2-mm sieve. Standard soil analyses were conducted by the Department of
Regulatory Services at the University of Kentucky. Analyses included pH (1:1
soil:water mixture), BpH (SMP buffer), P (Mehlich III extractable P), and K
(Mehlich III extractable K). Additional data sets were derived from the original
sampled data sets including four 61-m grids (G61) and four 91-m grids (G91). The
FULL data set consisted of the G61 and the VAL data sets.
Data Analysis
Normal probability plots were used to assess normality. Contour maps of
semivariogram surfaces were used to assess the direction and severity of
anisotropy. For the FULL and G30 data sets semivariograms were modeled with
Variowin (Pannatier, 1996) and omnidirectional and directional (for soil P)
semivariograms were fit to the empirical semivariograms. Grids (4 by 4-m) were
calculated with ordinary kriging (Surfer®, Golden Software, Golden, CO) for
each of the G30 data sets. Bilinear interpolation was used to calculate the kriged
estimate at each VAL data point. The G30, four G61 and G91 data sets were used to
calculate an interpolated value at each VAL data point with inverse distance
squared (Surfer®).
Cross-validation with an independent data set, i.e., jackknife analysis in the
sense of Deutsch and Journel (1998), were applied to the interpolations and the
mean squared error (MSE) was used as a measure of map quality. The MSE is the
sum of accuracy (bias2) and precision, being defined as
1 nv 2
MSE  Bias  precision 
 vi
n v  1 i 1
2
where vi is the difference between the predicted value and observed value at each
validation data point si, i = 1, …, nv, and nv is the number of values in the check
data sets. The root mean squared error (rmse) is the square root of the MSE and is
considered a scaled measure of precision and accuracy.
RESULTS AND DISCUSSION
Several variables were clearly normally distributed (pH at the Hardin and
Shelby fields; BpH at the Calloway and Shelby fields) according to the normal
probability plots (data not shown). Others were nearly normal but most were
clearly neither normally nor log-normally distributed. This has implications for
kriging which is guaranteed to be the best linear unbiased estimator when the data
are Gaussian (Cressie, 1993). Non parametric kriging approaches (Deutsch and
Journel, 1998; Gooovaerts, 1997) were not considered in this analysis.
Based on the field average pH and BpH values (Table 1), the Calloway field
would not require lime and the Hardin and Shelby fields would each require
(2.24 Mg ha-1) of lime to raise the pH to 6.4 according to the University of
Kentucky Cooperative Extension Service Lime and Fertilizer Recommendations
(2000). Average soil P and K values were below critical levels, the value at which
a crop response would be expected (30 mg kg-1 Mehlich III extractable P; 150 mg
kg-1 Mehlich III extractable K), for P at the Hardin field and K at the Hardin and
Shelby fields. Based on field average fertility values and if fertilizing for corn, the
Calloway field would not require P2O5 or K2O, the Hardin location would require
78 kg ha-1 of P2O5 and 45 kg ha-1 of K2O, and the Shelby location would require 0
kg ha-1 of P2O5 and 56 kg ha-1 of K2O. If the fertility values were calculated for
Table 1. Basic statistics.
mean median
min
max

CV
(%)
—————————————Calloway——————————
0.21
pH
7.0
7.0
6.2
7.7
3
BpH
7.3
7.3
7.1
7.4 0.072
1
-1
33
P (mg kg )
82
74
35
216
41
66
K (mg kg-1)
310
316
158
522
21
—————————————Hardin———————————
0.40
pH
6.1
6.2
5.6
7.0
6
0.21
BpH
6.9
6.8
6.6
7.5
3
9.1
P (mg kg-1)
15
13
7
40
60
30.3
K (mg kg-1)
105
94
82
187
29
—————————————Shelby———————————
0.36
pH
6.3
6.4
5.2
7.5
6
0.17
BpH
6.7
6.7
6.2
7.4
3
19
P (mg kg-1)
31
28
3
118
61
34
K (mg kg-1)
112
105
21
283
30
each 30-m grid sample, the Calloway field would not require P2O5 or K2O, the
Hardin location would require 79 kg ha-1 of P2O5 and 60 kg ha-1 of K2O, and the
Shelby location would require 36 kg ha-1 of P2O5 and 57 kg ha-1 of K2O. This data
suggests that there would not be savings in fertilizer costs if whole field fertility
recommendations were used site specifically.
Soil fertility values varied spatially within each field and between locations
(Fig. 2.) There were significant areas in the Hardin and Calloway fields that were
in the critical ranges for P and K. The Calloway field was above the critical levels
for all sample points for P and K. The low P values, especially for the Shelby
field, were well clustered.
The data were spatially structured (Fig. 3), although the semivariogram
parameters varied substantially (Table 2). The ranges of spatial correlation and
relative structural variability values (RSV) values were large (i.e. range > 100-m
and > 90%) for P at the Hardin and Shelbyville locations and K at the Hardin
location. Soil P exhibited intrinsic behavior (i.e. drift) which was handled by
nesting two exponential models (Table 2). The large differences in total spatial
variation (i.e. semivariance at the plateau of the semivariograms) was due to the
large differences in sampling variance (i.e. note the differences in the standard
deviations in Table 2).
Table 2. Semivariograms model parameters for the FULL data sets. Range is
the range of spatial correlation, sill is the partial sill, RSV is the
relative structural variability calculated where RSV = sill (sill +
nugget)-1, and e indicates an exponential semivariogram model. Min
indicates minimum, max indicates maximum,  indicates the
standard deviation, and CV indicates the coefficient of variation.
—————Structure 1————
———Structure 2———
model range
Sill
RSV
model range
Sill
m
%
m
———————————————Calloway——————————————
pH
0.028
E
190
0.015
35
BpH
0.0006
E
62
0.0042
88
P
0
E
34
419 100
E
1000
1075
K
2000
E
90
1920
49
———————————————Hardin———————————————
pH
0.032
E
133
0.15399
83
BpH
0
E
80
0.0316 100
P
36
E
430
450
93
K
0
E
415
4500 100
———————————————Shelbyville—————————————
pH
0.02
E
67
0.07599
79
E
600
0.046
BpH
0.0057
E
84
0.0153
73
E
600 0.0105
P
0
E
330
345 100
E
800
45
K
334
E
134
541
62
E
600
265
nugget
Fig. 2. Posted maps overlain by 1.0-m elevation contours (black contours).
0.24
0.04
BpH
0.18
0.03
0.12
0.02
0.06
0.01
0.00
0.00
P
K
(mg kg )
4000
3000
2
-2
800
2
-2
(mg kg )
Semivariance
pH
400
2000
1000
0
0
0
100
200
300
400
lag (m)
0
100
200
300
400
Calloway
Hardin
Shelby
Fig. 3. Experimental semivariograms using the FULL data sets for each
Fig. 3. Experimental
semivariograms using the FULL data sets for each location.
location.
The plots of predicted versus measured indicated that the kriged prediction for
soil P using the 30-m grid was exceptional for the Shelby field (Fig. 4).
Predictions at the Hardin field were good for soil BpH, P, and K. The
performance of P at the Hardin and Shelby fields is encouraging especially
considering its agronomic and environmental significance. However, 8 of 12
fertility variables were poor.
While in some cases ordinary kriging with isotropic models performed better
than IDW (Fig 5.), the improvement in rmse may not have been sufficient to
justify the additional time required for kriging (i.e. modeling the semivariogram).
It is important to note that we have not exhausted all the possible geostatistical
techniques in this analysis (e.g. kriging with different models, kriging with a trend
model, kriging with normal score transformations, kriging with an external drift,
co-kriging, etc.).
Most of the variables in this study did not exhibit anisotropic behavior.
However, some variables did exhibit anisotropy. For example P at the Calloway
field which was modeled and kriged with an anisotropic semivariogram model.
There was a small reduction in the rmse; however, the improvement in the
prediction was not substantial enough to make a difference in the appearance of
the plot of predicted versus measured (Fig. 6).
Calloway
Hardin
Shelby
r2 = 0.50
r2 = 0.21
r2 = 0.31
7.0
pH
6.3
5.6
5.6
6.3
7.0
5.6
r2 = 0.22
6.3
7.0
5.6
r2 = 0.60
6.3
7.0
r2 = 0.10
7.3
BpH
Predicted
6.9
6.5
6.5
6.9
7.3
6.5
6.9
7.3
6.5
r2 = 0.55
r2 = 0.11
6.9
7.3
r2 = 0.83
120
P 60
(mg kg-1)
0
0
60
120
0
60
120
0
r2 = 0.66
r2 = 0.02
60
120
r2 = 0.21
300
K 150
(mg kg-1)
0
0
150
300
0
150
300
0
150
300
Measured
Fig. 4. Predicted vs measured for ordinary kriging using the G30 data set with
the regression line (solid line) and coefficient of determination for the
regression (r2). The first bisector is shown as a dashed line.
0.5
Calloway
Hardin
Shelby
0.4
0.3
pH
0.2
0.1
0.0
0.15
BpH 0.10
Rmse
0.05
0.00
30
20
P
(mg kg-1) 10
0
75
50
K
(mg kg-1-1)
25
G91
G61
G30
0
1 2 3 4
IDW
exponent
1 2 3 4
1 2 3 4
IDW
exponent
IDW
exponent
Fig. 5. Performance of IDW (line graphs) at distance exponents of 0.1 to 5.0
for the G30, G61, and G91 data sets and ordinary kriging (bar chart) for
the G30 data set. The locations are indicated at the top of the figure
and the variables and the units for the rmse values are indicated to
the right of the figure.
rmse=6.8
G30
35
-1
Predicted (mg P kg )
rmse=6.4
70 G30
IDW
OK
0
rmse=8.6
70 G61a
rmse=9.3
G61b
rmse=8.5
G61c
rmse=9.0
G61d
35
IDW
0
rmse=11.1
70 G91a
IDW
rmse=10.6
G91b
IDW
rmse=10.6
G91c
IDW
rmse=10.3
G91d
35
IDW
IDW
IDW
IDW
0
0
35
70 0
35
70 0
35
70 0
35
70
Measured (mg P kg-1)
Fig. 6. Predicted vs measured for ordinary kriging (OK) using the G30 data
set and for IDW with a distance exponent of 2 using each data set (i.e.
G30, G61a-d, and G91a-d). The regression lines are shown as solid lines
and the first bisector as a dashed line. The rmse of the prediction of
each prediction is given.
Map quality for soil P was also examined at the G61 and G91 scales (Fig. 6).
Map quality was fair for the G61 data sets and marginal for the G91 data set.
Whether map quality was adequate for variable rate P management depends not
only on these errors. It also depends on the appropriateness of the fertilizer
recommendations for this field and on the errors associated with P application.
The relationship between IDW and RMSE appeared to be linear (Fig. 7).
-1
RMSE (mg P kg )
12
11
10
9
8
7
6
20
40
60
80
100
Grid size (m)
Fig. 7. The RMSE of IDW interpolations with a distance exponent of 2 vs
grid size.
CONCLUSIONS
The data in each field were spatially structured. Nevertheless, spatial
predictions were poor for many of the variables at many of the locations. Spatial
predictions for soil P at the Shelby Co. were very good at the 30-m grid scale and
fair at the 91-m grid scale. Generally we found that the predictions at the 30-m
grid were fair to very good for the variables that were well spatially structured
(i.e. range > 100-m and > 90%). Ordinary kriging the G30 data set using
exponential models did not yield spatial estimates that were much better than
those generated by IDW interpolation. There are other geostatistical techniques
than may improve spatial estimates; however, these generally are more time
consuming than ordinary kriging or IDW.
ACKNOWLEDGEMENTS
We would like to express our appreciation to Mike Ellis, Rick Murdock, and
Charlie Stuecker for allowing us access to their farms. In addition, we would like
to thank, the agricultural extension agents in each county: Gerald Claywell
(Calloway), Rod Grusy (Hardin), and Brittany Edelson (Shelby). Finally, we
would like to express our appreciation to Danna Reid, Frank Sikora, and the
University of Kentucky, Department of Regulatory Services for processing the
soil samples.
REFERENCES
Cressie, N. 1993. Statistics for spatial data, rev. ed. John Wiley & Sons, New
York.
Creutin, J.D., and C. Obled. 1982. Objective analysis and mapping techniques for
rainfall fields: An objective comparison. Water Resour. Res. 18:413-431.
Deutsch, C.V., and A.G. Journel. 1998. GSLIB: Geostatistical software library
and user’s guide, 2nd ed. Oxford University Press, New-York. New York
Flatman, G.T. and A.A. Yfantis. 1996. Geostatistical sampling designs for
hazardous waste sites. p. 779-801. In L.H. Keith. (ed) Principles of
environmental sampling. 2nd edition. American Chemical Society,
Washington, DC.
Fulton, J.P., S.A. Shearer, G. Chabra and S,G. Higgins. 1999. Field Evaluation of
a Spinner Disc Variable-Rate Fertilizer Applicator. ASAE Paper No.
991101. Annual International Meeting, Sheraton Centre, Toronto, Canada,
July 18-21.
Gotway, C.A., R.B. Ferguson, G.W. Hergert, and T.A. Peterson. 1996.
Comparisons of kriging and inverse-distance methods for mapping soil
parameters. Soil Sci. Soc. Am. J. 60:1237-1247.
Goovaerts, P. 1997. Geostatistics for natural resource evaluation. Oxford
University Press, New-York, New York
Hergert, G.W., W.L. Pan, D.R. Huggins, J.H. Grove, and T.R. Peck. 1997.
Adequacy of current fertilizer recommendations for site-specific
management. In F.J. Pierce and E.J. Sadler (ed) The state of site specific
management for agriculture. ASA special publication.
Kravchenko, A., and D.G. Bullock. 1999. A comparative study of interpolation
methods for mapping soil properties. Agron. J. 91:393-400.
Laslett, G.M., A.B. McBratney, P.J. Pahl, and M.F. Hutchinson. 1987.
Comparison of several spatial prediction methods for soil pH. J. Soil Sci.
38:325-341.
Mueller, T.G. 1998. Accuracy of soil property maps for site-specific management.
Ph.D. diss. Michigan State Univ., East Lansing (diss. Abstr. 99-22353)
(Diss. Abstr. Int. 60B:0901).
Pannatier, Y. 1996. Variowin: Software for spatial data analysis in 2D. Springer,
New York.
Pierce, F.J., and P. Nowak. 1999. Aspects of precision agriculture. Adv. in Agron.
87:1-85.
Sadler, E.J., W.J. Busscher, P.J. Bauer, and D.L. Karlen. 1998. Spatial scale
requirements for precision farming: a case study in the southeastern USA.
Agron. J. 90:191-197.
Sawyer, J.E. 1994. Concepts of variable rate technology with considerations for
fertilizer application. J. Prod. Agric., 7(2):195-201.
Shearer, S.A., T.G. Mueller, C.R. Dillon, J.P. Fulton, N. Hartsock and J. Stull.
2000. A GIS-Based simulation model for estimating the potential benefits
of variable-rate fertilizer application. ASAE Paper No. 001105. Annual
International Meeting, Milwaukee, July 9-12.
Tabios, G.Q., and J.D. Salas. 1985. A comparative analysis of techniques for
spatial interpolation of precipitation. Water Resour. Bull. 21:365-380.
Weber, D., and E. Englund. 1992. Evaluation and comparison of spatial
interpolators. Math Geol. 24:4.
Wollenhaupt, N.C., R.P. Wolkowski, and M.K. Clayton. 1994. Mapping soil test
phosphorus and potassium for variable-rate fertilizer application. J. Prod.
Agric. 7(4):441-448.