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Effect of Soil Properties and Landscape Features
on a Michigan Corn and Soybean Cropping System

presented by

PINGPIN G JIAN G

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6/01 cJCIRC/DateDuo.p65-p.15

EFFECTS OF SOIL PROPERTIES AND LANDSCAPE
FEATURES ON A MICHIGAN CORN AND SOYBEAN
CROPPING SYSTEM

By

Pingping Jiang

A THESIS

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

MASTER OF SCIENCE
Department of Crop and Soil Sciences

2002

ABSTRACT

EFFECTS OF SOIL PROPERTIES AND LANDSCAPE FEATURES
ON A MICHIGAN CORN AND SOYBEAN CROPPIN G SYSTEM

By

Pingping Jiang

Field scale crop yield variability is partly caused by soil and topographic variation
of the ﬁeld. A 50 hectare com-soybean ﬁeld in Michigan was sampled. Two topographic
features (elevation and slope) and twenty-three soil properties from the top two horizons
were examined. Yield data were collected from 1996 through 2001. Correlation
coefﬁcients showed that topographic data were more frequently related to soil texture.
The relationship of soil properties and ﬁeld topography to crop yield varied by year and
ﬁeld. Elevation had no signiﬁcant correlation with crop yield. The cumulative effect of
both soil and topography explained approximately 30-60% of yield variability during the
study period. However, a considerable amount of yield variability remained unexplained.

A sampling scheme that can ensure the desired accuracy in mapping soil
properties at efficient cost is always of interests. A total number of 220 samples were
taken, including 123 grid and 97 off-grid samples. A test data set of 31 samples was
randomly selected for validation and the rest of the samples were used to design four
sampling schemes. Geostatistical analysis was used to characterize spatial structure of
soil P and K and to predict values to the test data locations. Sampling schemes with
closely spaced samples performed better than the schemes with only grid samples. Less
samples would be needed without compromising the prediction accuracy if a combination

of grid samples and closely spaced off-grid samples was used.

ACKNOWLEDGEMTS

I would like to thank Dr. Fran Pierce for giving me this great and new opportunity
of education and career at MSU. I sincerely appreciate Dr. Kurt Thelen, my major
advisor, for his unreserved support and trust, which was a great help in ease of
completing the degree. My appreciation is also sent to my committee members, Dr.
Donald Christensen, Dr. Jiaguo Qi, for being like friends who always give sincere
suggestions and encouragements, and Dr. Sasha Kravchenko, for her critical review on
the Chapter 2 of this thesis.

I would like to thank Brian Long and Cal Bricker for their assistance in ﬁeld.

My appreciation always ﬂies to my parents, Jiang Lizheng and Li Jian, from the
deepest comer of my heart, for their understanding of my pursuit, for being healthy and

happy, and for being an endless source of strength and inspiration.

iii

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................... vi
LIST OF FIGURES ...................................................................................................... vii
Chapter 1

VARIABILITY OF SOIL AND LANDSCAPE PROPERTIES
AND THEIR RELATIONSHIP TO CROP YIELD IN A
MICHIGAN CORN-SOYBEAN FIELDl

ABSTRACT ................................................................................... 1
INTRODUCTION .......................................................................... 2
MATERIALS AND NIETHODS ...................................................... 5
Study site description ............................................................... 5

Field sample collection and laboratory analyses .............................. 10

Data retrieved in GIS environment ............................................. 11

Yield data .................................................................. 1 1

Slope derivation .......................................................... 11

Data analysis procedures ......................................................... 12
RESULTS AND DISCUSSIONS .................................................... 13
Soil variation and important soil variables .................................... 13

The relationship between soil properties and topographic features. . . . . . ...19
The relationship of soil properties and topographic data to crop yield. . .. 23

REFERENCES ............................................................................. 29

Chapter 2

THE EFFECT OF SAMPLING SIZE AND CONFIGURATION

ON THE SPATIAL STRUCTURE AND ACCURACY OF

PREDICTION OF SOIL P AND K 31

ABSTRACT ................................................................................. 31
INTRODUCTION ........................................................................ 32
THEORY BACKGROUND ....................................................... 35
Semivariogram .................................................................... 35
Ordinary Kriging .................................................................. 37
MATERIALS AND METHODS .................................................... 38
Study site description ............................................................. 38
Field data collection and laboratory analyses ................................. 39
Sampling scheme design ......................................................... 39
Data analysis ....................................................................... 44
RESULTS AND DISCUSION ........................................................ 46

iv

CONCLUSION ............................................................................. 61
REFERENCES .............................................................................. 62

Appendices ..................................................................................................................... 64

LIST OF TABLES

CHAPTER 1
Table 1.1. Selected variables analyzed by PCA and their summary statistics .............. 14
Table 1.2. PCA results of the ﬁrst ﬁve PCs with variable loadings. ........................ 17
Table 1.3. Importance of ﬁrst ﬁve PCs of A and B Horizons ................................ 18
Table 1.4. Summary statistics of elevation and slope at sample locations .................. 20
Table 1.5. Signiﬁcant correlation coefﬁcients (r) between topographic data (elevation,
slope) and soil properties (P _<_ 0.1) ................................................... 21
Table 1.6. Summary statistics of available soybean and corn grain yield during
1996-2001 ............................................................................... 24

Table 1.7. Correlation coefﬁcients (r) between soil properties of A and B horizons,
topographic data and yield, and the coefﬁcients of determination (R2) of
multiple regression between yield and soil properties and topographic data at

signiﬁcant level of 0.05 ................................................................ 26
CHAPTER 2
Table 2.1. Summary statistics of soil P, and K of four sampling schemes .................. 17
Table 2.2. The parameters of semivariogram models ﬁtted for soil P and K at each
sampling schemes ..................................................................... 18
Table 2.3. The G-value, RSME, and correlation of coefﬁcient between predicted and
actual values ............................................................................. 24
APPENDICES .............................................................................................................. 64
Appendix 1. Appendix 1. Summary statistics of monitor yield data from
1996 - 2001 .................................................................................................... 65
Appendix 2. Summary statistics of the selected soil properties from the A and B
horizons ......................................................................................................... 66

vi

LIST OF FIGURES

CHAPTER 1

Figure 1.1 Sample locations. Seventeen soil pedons from Field 1 and 16 from Field 2
were taken ............................................................................... 7

Figure 1.2 Topography of the study site ......................................................... 8

Figure 1.3a. Growing season precipitation during 1996-2001 ................................ 9

Figure 1.3b. Departure from normal growing season precipitation during 1996-2001.....9

CHAPTER 2
Figure 2.1a. Scheme 1. All data points used. N1=189 ..................................................... 41
Figure 2.1b. Scheme II. All one-acre-grid samples, with 42 randomly selected
off-grid samples. N2=148 ............................................................ 42
Figure 2.1c. Scheme III. One-acre-grid samples only. N3=106 ............................... 43
Figure 2.1d. Scheme IV. 59 one-acre-grid samples, with 50 randomly selected
off-grid samples. N4=109 ............................................................ 44
Figure 2.2. Example sample histograms of P and K aﬁer outliers were removed
(Scheme 1) .............................................................................. 46
Figure 2.3a. Empirical semivariograms of soil P with the semivariogram models ﬁtted.
Scheme I ................................................................................ 50
Figure 2.3b. Empirical semivariograms of soil P with the semivariogram models ﬁtted.
Scheme 11 .............................................................................. 50
Figure 2.3c. Empirical semivariograms of soil P with the semivariogram models ﬁtted.
Scheme III .............................................................................. 51
Figure 2.3d. Empirical semivariograms of soil P with the semivariogram models ﬁtted.
Scheme IV ............................................................................. 51
Figure 2.4a. Empirical semivariograms of soil K with the semivariogram models ﬁtted.
Scheme I ................................................................................ 52
Figure 2.4b. Empirical semivariograms of soil K with the semivariogram models ﬁtted.
Scheme 11 .............................................................................. 52
Figure 2.40. Empirical semivariograms of soil K with the semivariogram models ﬁtted.
Scheme III .............................................................................. 53
Figure 2.4d. Empirical semivariograms of soil K with the semivariogram models ﬁtted.
Scheme IV ............................................................................. 53
Figure 2.5a. Predicted values vs. observed values of soil P of four sampling schemes.
Scheme I ............................................................................... 57
Figure 2.5b. Predicted values vs. observed values of soil P of four sampling schemes.
Scheme 11 .............................................................................. 57
Figure 2.5c. Predicted values vs. observed values of soil P of four sampling schemes.
Scheme III ........................................................................... .58
Figure 2.5d. Predicted values vs. observed values of soil P of four sampling schemes.
Scheme IV ............................................................................. 58

vii

Figure 2.6a. Predicted values vs. observed values of soil K of four sampling schemes.

Scheme I .............................................................................. 59
Figure 2.6b. Predicted values vs. observed values of soil K of four sampling schemes.
Scheme II ............................................................................. 59
Figure 2.6c. Predicted values vs. observed values of soil K of four sampling schemes.
Scheme III ............................................................................ 60
Figure 2.6d. Predicted values vs. observed values of soil K of four sampling schemes.
Scheme IV ............................................................................ 60

viii

CHAPTER 1

VARIABILITY OF SOIL AND LANDSCAPE PROPERTIES
AND THEIR RELATIONSHIP TO CROP YIELD IN A
MICHIGAN CORN-SOYBEAN FIELD

Abstract

Field scale crop yield variability ispartly caused b_y__soil and topographic

 

variation. In certain years, soil properties and topographic features can explain as much
as 60% of yield variability. The objectives of this study were to identify soil properties
that cause most soil variation and investigate the complex interactions among crop yield,
soil properties and ﬁeld topography. A 50 hectare com-soybean ﬁeld in Michigan was
sampled, and 23 soil properties from the top two horizons up to 50 cm deep were tested.
Corn and soybean yield data were collected from 1996 through 2001 using a yield
monitor mounted on the tractor. A multivariate statistical model, principle component
analysis (PCA), was used to identify important soil properties. Eleven soil properties
returned by PCA and two topographic variables, elevation and slope derived from
elevation, were used to investigate their effect on crop yield. Correlation coefficients
showed that topographic data were more frequently related to the textual components
clay, silt and coarse sand contents. The relationship of soil properties and ﬁeld
topography to crop yield varied by year and ﬁeld. Only clay content (B horizon), K (A
and B horizons), NH4-acetate base saturation (B horizon), pH (B horizon) had a
signiﬁcant and mostly consistent correlation with yield. Elevation had no signiﬁcant

correlation with yield. The cumulative effect of both soil and topography explained

approximately 30-60% of the yield variability during the study period. However, a
considerable amount of yield variability remained unexplained.
Introduction

In agricultural ﬁelds, yield variability is partly caused by soil variability and
varying topographic features of the ﬁeld. Although yield is a ﬁmction of a host of factors
including climate, biological factors, soil properties, topography and management, in
certain years as much as 60% or even more of the yield variability can be explained by a
combination of EEBEOBG-mﬁi and topographic features (Yang, et al., 1998; Kravchenko
and Bullock, 2000). Soil properties affecting cropyiﬁeﬂlﬁdgi’nclude physical and chemical
properties such as soil available water, texture, bulk density, clay content (Stone, 1985,
Wright et a1, 1990), organic carbon (Ciha, 1984; Stone, 1985; Wright et al., 1990), pH
(Kreznor et al., 1989; Moore et al., 1993), subsoil acidity (Wright et al., 1990), fertility
and soil thickness (Kreznor et al., 1989).

Crop growth and yield are also affected by ﬁeld landscape features such as
elevation, slope steepness and aspect, and surface curvature (Ciha, 1984; Daniels et al.,
1985; Stone et al., 1985; Simmons etal., 1989; Yang et al., 1998; Kravchenko and
Bullock, 2000). Field topography can have a direct effect on crop growth and yield by
redirecting and changing soil water availability, and an indirect effect through its
inﬂuence on certain soil chemical and physical properties such as organic matter content,
base saturation, soil temperature, and particle size distribution (Franzmeier et al., 1969;
Bennett et al., 1972; Stone, 1985). Walker et al. (1968) investigated a series of soil '
properties such as A horizon thickness, distance from surface to mottles, and to carbonate

and manganese segregations. They concluded that slope positions were most strongly

related to these soil properties. In addition, the authors reported that different erosion
classes caused by different slope positions could affect the speed of development and
change of certain soil properties such as clay content and organic matter. Ovalles and
Collins (1986) conducted a study on a broad selection of soil chemical and structural
properties including pH, organic carbon, total P, coarse sand, medium sand, ﬁne sand,
very ﬁne sand, total sand, silt and clay content ﬁom three topographic positions of
summit, shoulder and backslope in north central Florida. They demonstrated that all these
selected soil properties had a signiﬁcant dependence on the topographic positions of the
ﬁeld. Daniels et a1. (1985) reported a close relationship between topographic position and
erosion classes, which both have been shown to inﬂuence soil properties, and hence soil
productivity (Sinai, 1981; Ciha, 1984; Stone et al., 1985).

Field-scale yield variability is affected by these soil properties and the speciﬁc
topography of the ﬁeld. Previous studies have shown that soil properties and topographic
features effect yield differently across locations and years. F iez et al. (1994) pointed out
that due to the inconsistent effect of topographic features on crop yield, research was
needed to determine and investigate the soil factors that vary with ﬁeld topography. This
would result in a better understanding of yield variability under varying soil conditions
and ﬁeld topography. Wright et a1. (1990) found that soil properties like texture, fertility,
organic matter, and available water have a signiﬁcant effect on corn yield. A study by
Yang et a1. (1998) showed that topographic features (elevation, slope and aspect) alone
can explain 15-35% of wheat yield variability at the whole-ﬁeld scale. In addition, they
reported that topographic features account for 49-84% of the yield variability in some

areas of the ﬁeld. Higher wheat yields were generally found at lower elevation and gentle

slope positions. Lower wheat yields were associated with higher elevation level and steep
slope positions. Miller et a1. (1988) found that although sand and clay content vary with
slope position, percent sand had no correlation with yield, whereas percent clay was
negatively correlated with total above ground biomass and positively correlated with
harvest index ratio (ratio of grain wt/total above ground biomass x 100). They also found
that the total above ground biomass increased from the knolls to the swales. It also has
been reported that topographic inﬂuence on yield can be enhanced by extreme weather
conditions. For example, severe early season drought could stress the effect of elevation
on the yield (Simmons, 1989). Kravchenko and Bullock (2000) also found that in general,
the greatest effect of topography was observed during extremely dry or wet years and at
locations with extreme topography. For average weather conditions and moderate
topographic position, this effect was relatively small.

Soil information allows one to investigate part (sometimes, a large part) of the
yield variability. Due to the complex nature of soil and complicated interactions between
soil components, a multivariate analysis model is necessary to unbiasedly assess
variability within soils covariance structure. Principle component analysis (PCA) is one
of the multivariate analyses models that has been employed to investigate the covariance
structures of soil and identify important and differentiating soil variables. PCA uses
linear combinations of soil variables to explain the covariance structure of a data set with
a large number of soil variables. It reduces the dimension of the original data set without
losing substantial information and often reveals relationships that were not previously
suspected and thereby allows new interpretations or ﬁirther analysis (Johnson and

Wichem, 2000). Richardson and Bigler (1984) used this model and found that soil

electrical conductivity (EC) and soluble Mg and Na were the most important variables in
explaining observable differences in wetland soils among clay content, pH, organic
carbon, CaCO3 equivalent (CCE), EC and Mg, Ca and Na. In another soil study using
PCA, Ovalles and Collins (1988) found that the ﬁrst ﬁve principle components explained
more than 73% of the total variance. Total sand, ﬁne sand, clay and 0C contents were
selected by the PCA as important properties.
The objectives of this study were to:
1) Determine the important soil properties in explaining the variation of a wide
selection of soil properties;
2) examine the correlation between these important soil properties and ﬁeld
topographic data;
3) Investigate the relationship between crop yield variability and these soil properties

under the speciﬁc ﬁeld topography.

Materials and Methods

Study Site Description

The study site was a corn (Zea mays L.) — soybean [Glycine max (L.) Merr.] ﬁeld
located in Kalamazoo County, Michigan (42.22 N, 86.36 W). The entire study site is
approximately 50 hectare in size and was divided into two sub-ﬁelds — Field 1(east side)
and Field 2 (west side). The two sub-ﬁelds were planted to corn and soybean in an
alternate year rotation (Fig. l .1). The elevation of the study site ranges from
approximately 288 to 303 m with near level (0-2%), gentle (2-6%), and moderate (6-

12%) slopes (Fig. 1.2). The soil texture class of the study site is predominately

Kalamazoo (ﬁne-loamy, mixed, mesic Typic hapludalfs) with Oshtemo (coarse-loamy,
mixed, mesic typic Hapludalfs) at the south-west comer of the study site (Soil Survey of
Kalamazoo County, Michigan, 1979). The site was non-irrigated and a minimum tillage
system was employed. During the study period, Field 1 was planted with soybean in odd
numbered years (1997, and 1999), and with corn in even numbered years (1996, 1998,
and 2000). This sequence was rotated in Field 2 except corn was planted in both sub-
ﬁelds in 2001. Weather data were acquired from an adjacent weather station. Figure 1.3a
shows the monthly precipitation during the1996-2001 growing seasons and Figure 1.3b

depicts the departure of precipitation from normal levels.

Figure 1.1. Sample locations. Seventeen soil pedons from Field 1 and 16 from Field 2

were taken.

 

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0 ° 0
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Figure 1.2. Topography of the study site.

     

  
 
  

  
 

  
  
 

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7
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Mar. Apr May Jun Jul Aug Sep

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if 4_ .199
E 8
o 3. .199
z 200
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.8
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-3

Mar Apr May Jun Jul Aug Sep

Figure 1.3a. Growing season precipitation during 1996-2001; Figure 1.3b, Departure
from normal'i growing season precipitation during 1996-2001.

1' Average of 1971-2000.

Field Sample Collection and Laboratory Analyses

Thirty-three soil pedons were taken on May 1, 2001. In Field 1(east), 16 samples
and in Field 2 (west) 17 samples were taken. The soil cores were 1.2 m long and 4 cm in
diameter. Horizon designation was done as the soil sample cores were taken. The number
of horizons of soil pedons ranged from 3 to 6. The depth of each horizon was recorded. A
5 to 10 cm undisturbed section from the middle of each horizon was saved for bulk
density analysis. Elevation was measured using a GPS receiver mounted on a tractor. The
speed of the tractor was 12.8-19.2 km/h and transect spacing was 9 m. Elevation data
were collected at one second intervals. Since the majority of soybean roots are found in
the upper 30 cm of soil, with a dominantly large proportion of the root mass in the
topmost 16 cm, and corn roots are found in the upper 35-40 cm, only the top two
horizons were analyzed (the top two horizons are referred to as A and B horizon for
convenience, although sometimes the second horizon was designated as A2 or
transitional BE soil taxonomy horizons). The depth to the lower border of the B horizon
ranged from 35 to 85 cm with the average depth of 51 cm.

Laboratory analyses were conducted by the Soil Testing Lab at the University of
Missouri. The parameters analyzed included soil texture by the pipette method; cations
(KI, Mg”, Ca2+, Na+) by ammonium acetate extraction methods; CBC by base
summation + H ion; pH by soil solution ratio of 1:1; total C and organic C by emission
method. More than 30 soil properties were determined. Since some of the properties
represented different measures of the same parameter, only 23 soil variables were

selected for analysis (Table 1.1).

10

Data Retrieved in GIS Environment
Yield Data

Six year yield data (from 1996 through 2001) were recorded using a commercial
yield monitor mounted on a combine. Yield data were recorded every second as the
combine proceeded along the transects with the swath width being the transect spacing.
Latitude and longitude were recorded simultaneously by a GPS receiver for each yield
data point. Yield data were thus incorporated as an information layer with other soil and
topographic information, which enabled quantitative correlation between yield and ﬁeld
parameters in a GIS environment. Questionable and unrealistic yield data points possibly
caused by signiﬁcant positional errors, operating errors such as abrupt changes of speed,
partial swath entering the combine, combine stops and starts, were removed from the
dataset before any statistical analyses. In GIS Arcview (ESRI, 1996), the yield values for
the sample locations were calculated by averaging the yield points that were contained in
the circle area around each sample location with a diameter of 6.7 m. Due to the
malfunction of the yield monitor or unstable GPS signals during the harvest, only corn
yield data from 1996, 1998, 2000 and 2001, and soybean data from 1997 and 1999 were
available in Field 1, and corn yield data from 1997,1999 and 2001 were available and no

soybean data available in Field 2 during the study period.

Slope Derivation

Slope is the ﬁrst order derivative of elevation and was derived using the Spatial

Analyst of Arcview GIS. This process uses a 3 x 3 cell neighborhood around the

11

processing or center cell and the average maximum technique to calculate slope values. It
identiﬁes the maximum rate of change in value from each cell to its neighbors (Manual of

Spatial Analyst, 1996). The slopes were measured in degrees.

Data Analysis Procedures
Principle component analysis (PCA) was employed to investigate soil variance
and identify important soil variables to be used as inputs for further analysis. Calculated
PCs were in the following form:
Y1= aux, + aux) + + alep,
Where Y; is the ith principle component (PC), X1, , Xp are the original variables, and

any”, aip are the coefﬁcients of the ith PC and also an index of relative importance of the

variable to that PC. The greater the absolute values of a, are, the greater the importance of

that soil variable to the PC. We termed this value as variable loading, as referred to by the
statistical software package used (S-PLUS; Mathsoﬁ, 1999). A sample correlation matrix
was used instead of a covariance matrix in the PC calculation due to the differences of the
order of magnitude between soil variables measured. The PCs that cumulatively
explained more than 85% of the sample variance and individually explained more than
5% of the total variance were empirically retained for further processing. Variable
loadings > 0.4 were considered to be important in the given PC and were hypothesized to
have greater potential to explain yield variability. These variables were then used in
further statistical analyses. Pearson correlation coefficients (r) were calculated between
the important soil variables identiﬁed by PCA and topographic data, and yield data, and

between topographic data and yield data. Multiple linear regression was employed to

12

analyze the combined effect of both soil properties and topographic data on crop yield. A
forward stepwise regression procedure was used. All statistical analyses were conducted

using S-PLUS statistical package (Mathsoft Inc., 1999).

Results and Discussions

Soil Variation and Important Soil Variables

Principle component analysis was performed for the ﬁrst (A) and second (B)
horizons respectively. Table 1.1 shows the summary statistics of the 23 soil variables of
each of the top two horizons which were evaluated by PCA. These soil variables included
soil texture variables (total clay, ﬁne silt, coarse silt, very ﬁnd sand, medium sand, coarse
sand, very coarse sand); soil chemistry/fertility (CEC, base saturation of NH4-Acetate,
exchangeable Ca2+, Mg2+, KI, sum of basis, pH (0.01 M CaClz), acidity, organic carbon
and total N); and soil physical variables including electrical conductivity (EC), bulk

density and horizon thickness.

13

Table 1.1. Selected variables analyzed by PCA and their summary statistics.
HT‘j’ Bulk Total Total Total Fine Coarse VFI Fine Med VC§ Coarse

Density Clay Silt Sand Silt Silt

 

cm g/cm3

Sand Sand Sand Sand Sand

 

%

 

A Horizon

Mean 24.0 1.4 13.6 47.7 38.6 29.2

SD. 3.8 0.15 3.93 12.56 15.86 9.56 4.70

B Horizon

Mean 27.3 1.5 18.2 40.1 41.7 24.0

SD. 10.2 0.16 5.87 15.66 18.23 12.67 4.94

Table 1.1 (cont’d).

18.6 10.0 17.6 7.0 2.9 1.2

2.40 11.41 3.26 1.11 1.15

16.1 10.3 20.2 7.4 2.9 1.0

3.00 13.15 4.01 1.76 1.09

 

Ca Mg K Sum Acidity CEC Base 0C1] Total pH# EC
Basis Sat. N
-------------- meq/100g % mmho/cm

 

 

 

A Horizon

 

Mean 5.9 1.2 0.4 7.5 8.0 10.8 68.8 1.3 0.1 5.4 0.4
SD. 2.33 0.45 0.22 2.69 3.05 3.24 14.84 0.39 0.05 0.54 0.15
B Horizon
Mean 5.7 1.2 0.3 7.2 8.1 12.0 61.7 0.6 0.1 4.9 0.5
SD. 1.99 0.52 0.18 2.41 3.34 3.71 14.72 0.47 0.04 0.54 0.52
1' Horizon thickness

1 Very ﬁne sand

§ Very coarse sand
1| Organic carbon
# pH in 0.01M CaClz

14

The PCA results are presented in Table 1.2. In the A horizon, the ﬁrst ﬁve
principle components (PCs) accumulatively explained 86.2% of the total sample
variance, and each of them explained more than 5% of the total sample variance (Table
1.3). PC1 explained 44.3% of the total sample variance of that horizon with most of the
soil variables linearly combined except for horizon thickness, very coarse sand content,
extractable Mg, base saturation, pH and soil EC. Variable loading was established at 0.4
to be considered signiﬁcant. The results showed that the variable loadings were generally
all less than 0.4 indicating that none of these soil variables were of absolute importance,
or dominant in the PC. However, soil texture variables such as total sand (-0.304), total
silt (0.295), medium sand (-0.287), ﬁne silt (0.283) suggest that soil texture variables
were relatively more important in this PC than soil variables from other categories. A
distinct contrast was observed between the coarse materials of various sized sands and
the ﬁne materials such as clay and silts. This contrast was differentiated by the opposite
sign of the loadings (Table 1.2). In PC1 of the B horizon, a very similar situation can be
seen in terms of the relative importance of variable loadings (Tables 1.2 and 1.3). Again,
most of the soil variables were linearly combined, except for extractable Mg, base
saturation and pH. Similar soil texture variables (sand, ﬁne sand, ﬁne silt) were relatively
high in the loadings. The contrasting relationship once again appeared between coarse
materials and ﬁne materials, and only the signs were opposite with those in the A
horizon. Therefore, PC1 of both A and B horizons can be referred to as a “texture
component”. In PC2, both the A and B horizons had fewer soil variables linearly
combined than in PC1. Again, all the variable loadings were below 0.4 with the only

exception of base saturation (-0.424) in the B horizon. In PC2, higher loadings were

15

represented by chemistry/fertility variables as opposed to primarily soil texture variables
in PC1. For example, base saturation (0.389), sum of bases (0.370), extractable Ca
(0.357), and pH (0.341) were carrying the highest loadings in the A horizon, and base
saturation (0.424), Mg (0.393), sum of bases (0.366), pH (0.333) were the highest in the
B horizon. In PC2, both the A and B horizons had very similar soil chemistry/fertility
variables that appeared in ﬁrst positions. Additionally, these fertility/chemistry variables
all had a positive relationship in the PC. Therefore, we can refer to this PC as the
“fertility component”. The “fertility component” of the A horizon explained 23% of the
total sample variance and that of the B horizon explained 16 % of the total sample
variance. In sum, PC1 - “Texture component” and PC2 - “fertility component” have
accumulatively accounted for 67% and 60% of the total sample variance of the A and B
horizons, respectively. This implied that up to a depth of 50 cm (average depth of A and
B horizons), 60% or more of the total sample variance can be explained by the ﬁrst two
PCs represented primarily by soil texture and fertility variables. Richardson and Bigler
(1984) in their wetland soil study using PCA reported that PC1 was “chemical
potentiality” dominated by EC and soluble Na and Mg, PC2 was dominated by organic
carbon and PC3 was dominated by soil texture. The difference between theirs and this
study showed that results of PC analysis on soil properties are data dependent and related

to soil forming processes and ﬁeld management history.

16

Table 1.2. PCA results of the ﬁrst ﬁve PCs with variable loadings.

 

 

 

 

PC1 902 903 904 PC5

A Horizon
art -0.199 -0.155 -0.675
Bulk Density —0.220 -0.482
Total Clay 0.252 -0.376
Total Silt 0.295 -0.180
Total Sand -0.304 0.137
Fine Silt 0.283 -0.129 0.142
Coarse Silt 0.142 0.192 -0.469 -0.151
VF Sandi -0.198 0.156 -0.263 -0.301 0.255
Fine Sand -0.285 0.163 0.174
Mbd.Sand -0.287 0.194
Coarse Sand -0.152 0.222 0.222 -0.213 0.136
VC Sand§ 0.297 0.262 -0.109 -0.166
Ca 0.156 0.357 0.109 -0.118
Mg 0.315 0.190 -0.300
K 0.157 0.519 -0.133
Sun Bases 0.154 0.370 -0.111
Acidity 0.237 -0.226 0.172 0.145
CEC 0.297 -0.114
Base Sat. 0.389 0.150
ocq 0.276 0.113 0.325
pH# 0.341 -0.193 0.225 -0.134
Total N 0.266 0.218 0.182
EC 0.184 0.521 0.333

8 Horizon
art 0.126 -0.201 -0.141 -0.340
Bulk Density 0.199 0.171 -0.200 0.279
Total Clay -0.150 -0.481
Total Silt -0.287 0.184
Total Sand 0.307
Fine Silt -0.263 —0.143 0.241
Coarse Silt -0.225 0.159 -0.222 0.369
vs Sandi 0.109 0.250 -0.216 -0.361 0.146
Fine Sand 0.290 -0.231
Med.8and 0.284 0.204
Coarse Sand 0.196 0.448 0.262
vc Sand§ 0.141 0.410 0.397
Ca -0.203 0.315 -0.119 0.137
Mg 0.393 0.240 -0.315
K -0.155 0.165 -0.607
1' Horizon thickness
1 Very ﬁne sand
§ Very coarse sand
‘ﬂChgankwmubon
# pH in 0.01M CaClz

17

Table 1.2 (cont’d).

 

 

 

 

Sun Bases -0.198 0.366 -0.107
Acidity -0.226 -0.268 -0.174 0.211
CEC -0.261 -0.274 0.152
Base Sat. 0.424 0.253 -0.136
oc1l -0.239 0.305 0.116
pH# 0 .333 0.405 --0 . 122
Total N -0.249 0.280
EC 0.188 —0.133 0.133 -0.148 -0.152
Table 1.3. Importance of ﬁrst ﬁve PCs of A and B Horizons.
PC1 PC2 PC3 PC4 PCS
A Horizon
Standard deviation 3.19 2.30 1.38 1.13 1.09
proportion of Variance'j' 0. 44 0. 23 0.08 0. 06 0 . 05
Cumulative Proportion: 0.44 0.67 0.76 0.81 0.86
B Horizon
Standard deviation 3.17 1.91 1.74 1.33 1.04
Proportion of variancel 0.44 0.16 0.13 0.08 0.05
Cumulative ProportionI 0. 44 0. 60 0.73 0. 81 0.85

 

1' Proportion of variance explained by each PC.
1: Cumulative proportion of variance explained.

18

The subsequent PCs were more difﬁcult to characterize than the ﬁrst two PCs. In
PC3 of the A horizon, K had the highest loading (0.519), and the loading of coarse silt
was the second highest of -0.469. These two loadings were both above 0.4, which, by our
established criteria, were considered important. In addition, they were considerably
higher than the variables following them, such as very ﬁne sand (—0.263). Therefore K
and coarse silt were considered the two dominant variables in the PC3 of the A horizon.
In PC3 of the B horizon, clay content, and pH were the two variables with the highest
loadings, -0.481 and 0.405, respectively. In PC4 of the A horizon, soil BC was the only
important variable with a loading of 0.521. In PC4 of B horizon, two soil texture
variables, coarse sand (0.448) and very coarse sand (0.410) were important. In the last
PCs investigated, two soil physical properties, horizon thickness (-0.675) and bulk
density (-0.482) were important in the A horizon and K (-0.607) was the only important
variable in PCS of the B horizon. In sum, most of the variables that were important in
PC3, 4 and 5 were representative of soil texture and fertility, although some soil physical
properties were also important in some cases. From PC3, however, soil variables with
higher loadings in the A and B horizons began to differ. Although only a small portion of
the total sample variance was explained in the lower PCs (the portion of total sample
variance explained by PC3, PC4, PC5 was 8.3%, 5.5% and 5.1%, for A horizon and
13.2%, 7.7% and 4.7%, for B horizon, respectively), they provided insight on identifying
important soil variables and changes of soil variable covariance structure at different
depths of the soil proﬁle. In characterizing soil variability, attention has been focused on

the ﬁrst couple of PCs that generally bear most of the total variance (Ovalles and Collins,

19

1988). In this study, however, the subsequent PCs provided more information in

determining important soil properties.

The Relationship Between Soil Properties and Topographic Data

Eleven soil properties had loading > 0.4 from the ﬁrst 5 PCs of both A and B
horizons and were continuously used in the further analyses. These soil variables
included coarse silt, extractable K, soil EC, horizon thickness, bulk density from the A
horizon and NIL-acetate base saturation, clay, pH, coarse sand content, very coarse sand

content and extractable K ﬁ'om the B horizon.

Table 1.4. Summary statistics of elevation and slope at sample locations.

 

 

Field Mean Max. Min. S.D. Range
1 Elevation (m) 296.3 303.1 292.4 3.1 10.7
1 Slope (Degree) 0.97 2.04 0.29 0.47 1.75
2 Elevation (m) 297.7 302.2 292.4 3.1 9.8
2 Slope (Degree) 1.1 l 4.25 0.16 1.18 4.09

 

Table 1.4 shows the summary statistics of elevation and slope at the sample
locations in both sub-ﬁelds. The Pearson coefﬁcient of correlation (r) was calculated
between important soil variables identiﬁed by PCA and ﬁeld elevation and slope. The

results of signiﬁcant r values (P _<. 0.1) are listed in Table 1.5.

20

Table 1.5. Signiﬁcant correlation coefficients (r) between topographic data (elevation,
slope) and soil properties (P S 0.1)

 

 

 

 

Base 3qu Coarse vc# Coarse Total
K K PH§ Sat H'I‘Il Dens EC Silt Sand Sand Clay
(AT) (BI) (B) (B) (A) (A) (A) (A) (B) (B) (B)
A Horizon
Elevation -0.48 -0.43
Slope -0.47 -0.50 0.70 0.60
B Horizon
Elevation -0.69 -0.71 -0.47 -0.59 -0.63
Slope 0.56 0.59
TA horizon.
IB horizon.
§ pH in 0.01M CaClz.
1] Horizon Thickness.

# Very coarse sand.

21

Elevation had a consistently negative correlation with all K measurements except
for the B horizon in Field 1. Kravchenko and Bullock (2000) also reported a negative
correlation between elevation and K. This was likely due to greater K leaching due to
higher sand content observed at the higher elevation in both Field 1 and 2. Also, elevation
was negatively correlated with the coarse silt content of the A horizon in both ﬁelds and
clay of the B horizon in Field 2. Slope was positively correlated with very coarse sand
and coarse sand contents of the B horizon in Field 1. The correlation coefﬁcients were
0.70 and 0.60, respectively. Similarly, slope was also positively correlated with the
coarse sand content (F059) of the B horizon in Field 2. In the study by Moore et a1.
(1993), slope was also found to be positively correlated with the sand content of the
surface soil (top 0.1 m), and this study extended this depth up to 0.5 m from the surface.
K of the B horizon and A horizon thickness of Field 1 were negatively correlated to

slope, and base saturation of the B horizon in Field 2 was positively correlated to slope.

In general, elevation and Slope are the two topographic data that are most strongly
related to soil properties (Walker et al., 1967). In this study, we found that elevation and
slope were more frequently correlated to soil texture variables, such as percent clay,
coarse silt, different sized sand contents, and A horizon thickness. In addition to the
difference of parent material, this relationship was also related to the erosion class and
severity. Elevation and slope positions can alter the distribution of soil particles through
erosion, which can be increased by cultivation practices (Ciha, 1984). Both Stone et a1.
(1985) and Kreznor et al. (1989) reported that clay content increased as soil erosion class

became more severe. This was also supported by our results, as indicated by the negative

22

correlation between slope and A horizon thickness, which has been used as an indicator

of erosion severity (Deniels et al., 1985; White et al., 1985).
The Relationship of Soil Properties and Topographic Data to Crop Yield

Table 1.6 shows the summary statistics of corn and soybean yield from1996 to
2001. Dense data collected by the yield monitor allowed for the calculation of population
statistics. The numbers in the parentheses in Table 1.6 are the sample statistics. Contents
of coarse sand and very coarse sand of B horizon were summed to represent the total
amount of coarse material, and to avoid high correlation between the two in the multiple
regression analysis. Two topographic parameters, elevation and Slope, were also included
in the analyses.

Correlation coefficients between yield and soil properties, and topographic data
are shown in Table 1.7. The clay content of the B horizon seemed to be the most frequent
soil property that consistently had a negative correlation to crop yield. A negative
correlation between clay content in both A and B horizons and crop yield was also
observed in previous studies ( Stone, 1985; Wright et al., 1990). High water holding
capacity and decreased drainage rate associated with high clay content. This may cause
prolonged high moisture content in the rooting zone, and consequently has a negative

inﬂuence on root respiration. Base saturation was signiﬁcant in 3 site-years

23

Table 1.6. Summary statistics of available soybean and corn grain yield during 1996-

 

 

 

 

2001.
Field Year Crop Mean'l' S. D. 'l'
Bu/acre

1 1996 Corn 105.6 (106.5) 16.7 (11.9)
1 1997 Soybean 39.0 (38.0) 6.4 (6.8)
l 1998 Corn 161.1 (160.2) 15.1 (8.7)
l 1999 Soybean 33.9 (34.6) 4.9 (3.5)
1 2000 Corn 152.5 (150.7) 15.1 (15.0)
1 2001 Corn 123.5 (124.1) 15.1 (9.9)
2 1997 Corn 147.3 (152.2) 27.2 (20.1)
2 1999 Corn 145.0 (155.9) 27.5 (30.2)
2 2001 Corn 120.9 (125.5) 20.3 (20.3)

 

T Calculated ﬁom all yield points and yield points at sample locations

(in parentheses).

24

out of 9 studied, but both positive and negative correlations were observed. The relatively
high base saturation indicated adequate exchangeable nutrient availability and this may
not be a limiting factor of yield in general. The K of both A and B horizons had
consistent positive inﬂuence on corn yield in two consecutive years in Field 2, but was
not signiﬁcant in Field 1. Although the generally high soil testing level of K suggests that
K level is less likely a yield limiting factor, our results showed that crop yield can beneﬁt
from the excessive K levels up to the B horizon in certain years. The pH (CaClz) of the B
horizon and the coarse silt content of the A horizon had only one incidence of signiﬁcant
correlation to the corn yield in 1998 and 2000, respectively. The A horizon properties of
thickness, bulk density, and EC were not signiﬁcantly correlated to crop yield throughout
the study period.

Between the two topographic variables, slope showed consistently negative
correlation to crop yield in 3 site-years out of 9 studied. A negative relationship between
slope and yield has been reported in many other previous studies (Ciha, 1984;
Fahnestock, 1996; Changere and Lal, 1997; McConkay et al., 1997; Yang et al., 1998;
Kravchenko and Bullock, 2000). Steep slope positions tend to associate with more severe
erosion class which is characterized by thinner surface horizon, higher clay content,
lower inﬁltration rate, and greater runoff resulting in poorer productivity of soil (Wright
et al., 1990). Besides, the high coarse material content observed at steep slope positions
(Table 1.5) indicated that lower water retention and fertility at these areas. Elevation had
no signiﬁcant correlation with either corn or soybean yield through the period of study.

Kravchenko and Bullock (2000) found that elevation was the most contributing

25

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topographic factor in their study and a fairly consistent negative correlation between
elevation and crop yield was frequently observed in most of the ﬁelds studied. In most
cases, the inﬂuence of elevation on yield is reﬂected through water availability and its
effect is more readily observed in extreme weather conditions with extreme topography
(Kravchenko and Bullock, 2000). The lack of correlation between elevation and yield in
this study can be partly explained by greater inﬂuence of some other soil properties on
the yield variability, less extended extreme precipitation during growing seasons, and
bio-factors such as weeds, disease and insect injuries.

Coefﬁcients of determination (R2) are also shown in Table 1.7. All 11 soil
properties and 2 topographic variables were included in the initial analysis, and only
those that were signiﬁcant (0.05) after stepwise regression were retained in the ﬁnal
equations. Clay content of the B horizon was the only signiﬁcant soil property that
explained approximately 30% of the corn yield variability in 1996 (Field 1) and the same
amount of the soybean yield variability in 1999 (Field 1). Also in the year of 1999, the
largest portion, 64%, of corn yield variability was explained by three soil and topographic
variables, clay content of the B horizon, elevation and slope in Field 2. In Field 1, there
was no signiﬁcant terms remained in the multiple regression analysis in year 2000 and

2001.

Conclusion

PCA returned 5 PCS for each horizon investigated, which cumulatively explained
more than 85% of the total sample variance of each horizon. The ﬁrst PCs of both

horizons were represented primarily by soil texture variables and the second PCS by

27

chemistry/fertility variables. These ﬁrst two PCs explained up to 60% or more of the total
sample variance in their corresponding horizons. Subsequent PCs explained individually
a relatively small portion of the total variance, but started to Show a difference in the

variance structure of the A and B horizon.

Pearson’s coefficients of correlation showed that topographic data (elevation and
slope) were more frequently correlated with soil texture properties such as clay content,
silt content, and coarse materials. This suggested that ﬁeld topography had an indirect

effect on crop yield by inﬂuencing certain soil properties.

The relationship of soil properties and topographic data to crop yield varied by
year and ﬁeld. Both soil and topographic information were useful in explaining yield,
however, there was no explicit pattern or consistency. Only clay content (B horizon), K
(A and B horizon), NH4-acetate base saturation (B horizon), pH (B horizon) had a
signiﬁcant and mostly consistent correlation with yield. B horizon soil properties seemed
to be more informative in explaining yield variability by having more incidence of
Signiﬁcance. The combined effect of soil properties and topographic data explained
approximately 30-60% of the com/soybean yield variability during the study period. A
considerable amount of yield variability remained unexplained, and this suggested that
yield limiting factors other than soil and topography such as climate and bio-factors can

dominantly control yield variability.

28

References:

Ciha, A. J .1984. Slope Position and Grain Yield of Soft White Winter Wheat. Agron. J.
76: 193-1 96.

Bennett, O.L., E.L. Mathias, and RR. Henderlong. 1972. Effects of North and South
Facing Slopes on Yield of Kentucky Bluegrass (Poa pratensis L.) with variable rate and
time of nitrogen Application. Agron. J. 64:630-635.

Daniels, R. B., J .W. Gilliam, D. K. Cassel, and L. A. Nelson. 1985 . Soil Erosion Class
and Landscape Position in the North Carolina Piedmont. Soil Sci. Soc. Am. J ., Vol. 49:
991-995.

Environmental Systems Research Institute. 1996. ArcView Spatial Analyst. ESRI,
Redlands, CA.

F ahnestock, P., R. Lal, and GE Hall. 1996. Land Use and Erosion Effects on Two Ohio
Soils: II. Crop yields. J. Sustain. Agric. 7285-100.

Fiez, T. E., B. C. Miller, and W. L. Pan. 1994. Winter Wheat Yield and Grain Protein
across Varied Landscape Positions. Agron. J. 86:1026-1032.

Franzrneier, D.P., E.J. Pedersen, T.J. Longwell, J .G. Byme, and C. Losche. 1969.
Properties of Some Soils in the Cumberland Plateau as Related to Slope Aspect and
Position. Soil Sci. Soc. Am. Proc. 33:755-761.

Johnson, R. A., and D. W. Wichem. 2002. Applied Multivariate Statistical Analysis.
Fiﬁh Edition. P.426-427 Prentice Hall.

Kravchenko, A. N., and D. G. Bullock. 2000. Correlation of Corn and Soybean Grain
Yield with Topography and Soil Properties. Agron. J. 92:75-83

Kreznor, W. R., K. R. Olson, W. L. Banwart, and D. L. Johnson. 1989. Soil, Landscape,
and Erosion Relationships in a Northwest Illinois Watershed. Soil Sci. Soc. Am. J.
53:1763-1771 (1989).

Miller, M. P., M. J. Singer, and D. R. Nielsen. 1988. Spatial Variability of Wheat Yield
and Soil Properties on Complex Hill. Soil Sci. Soc. Am. J. 52:1133-1141 (1988).

Moore, 1. D., P. E. Gessler, G. A. Nielsen, and G. A. Peterson. 1993. Soil Attribute
Prediction Using Terrain Analysis. Soil Sci. Soc. Am. J. 57:443-452 (1993).

Ovalles, F. A., and M. E. Collins. 1986. Soil-landscape Relationships and Soil Variability
in North Central Florida. Soil Sci. Soc. Am. J. 50:401-408

29

Ovalles, F. A., and M. E. Collins. 1988. Variability of Northwest Florida Soils by
Principal Component Analysis. Soil Sci. Soc. Am. J. 52:1430-1435 (1988).

Richardson, J. L., and R. J. Bigler. 1984. Principal Component Analysis of Prairie
Pothole Soils in North Dakota Soil Sci. Soc. Am. J. 48:1350—1355.

Walker, P. H., G. F. Hall, and R. Protz. 1968. Relation Between Landforrn Parameters
and Soil Properties. Soil Sci. Soc. Amer. Proc., Vol. 32, 101-104.

Walker, P. H., G. F. Hall, R. Protz. 1968. Soil Trends and Variability Across Selected
Landscapes in Iowa. Soil Sci. Soc. Amer. Proc., Vol. 32, 97-101.

Wright, R. J ., D. G. Boyer, W. M. Winant, and H. D. Perry. 1990. The Inﬂuence of Soil
Factors on Yield Differences Among Landscape Positions in an Appalachian Cornﬁeld.
Soil Sci. Vol. 149, No. 6.

Simmons, F. W., D. K. Cassel, and R. B. Daniels. 1989. Landscape and Soil Property
Effects on Corn Grain Yield Response to Tillage. Soil Sci. Soc. Am. J. 53:534-539.

Sinai, G., D. Zaslavsky, and P. Golany. 1981. The Effect of Soil Surface Curvature on
Moisture and Yield — Beer Sheba Observations. Soil Sci. 131:367-375.

Stone, J. R., J. W. Gilliam, D. K. Cassel, R. B. Daniels, L. A. Nelson, And H. J. Kleiss.
1985. Effect of Erosion and Landscape Position on the Productivity of Piedmont Soils.
Soil Sci. Soc. Am. J. 49:987-991.

Yang, Q, C. L. Peterson, G. J. Shropshire, and T. Otawa. Spatial Variability of Field

Topography and Wheat Yield in the Palouse Region of the Paciﬁc Northwest.
Transactions of the ASAE. Vol. 41(1):]7—27.

30

CHAPTER 2

THE EFFECTS OF SAMPLE SIZE AND CONFIGURATION
ON THE SPATIAL STRUCTURE AND ACCURACY OF
PREDICTION OF SOIL P AND K

Abstract

Precise soil fertility map is an important component of successful site-speciﬁc
management. Hence, a sampling scheme that can ensure the desired accuracy in mapping
soil properties at efﬁcient cost is always of interest. The objectives of this study were (i)
to evaluate effect of sample sizes and conﬁgurations on accurate description of spatial
correlation structure for soil P and K concentrations, and (ii) to determine optimal
sampling scheme for accurate and cost efficient mapping of soil P and K concentrations.
A total number of 220 samples were taken, including 123 grid and 97 off-grid samples. A
test data set of 31 samples was randomly selected for validation and the rest of the
samples were used to design four sampling schemes. Scheme 1 had all data points
(N 1=189), Scheme 11 had all grid samples and 42 randomly selected off-grid samples
(N2=148), Scheme 111 had grid samples only (N3=106), and Scheme IV had 59 grid
samples and 50 randomly selected off-grid samples (N4=109). Geostatistical analysis was
used to characterize spatial structure of the data and to predict values of the test data
locations. Criteria used to compare the performance of the four sampling schemes
included goodness of prediction (G), root mean square error (RMSE), and correlation
coefﬁcient (r). The sample semivariograms of soil P of different sampling schemes varied
considerably, whereas those of K were fairly consistent. Scheme I of both soil P and K

performed the best. Scheme IV performed as well as Scheme 11 with approximately 40

31

samples less, and Scheme III performed noticeably less accurate than Scheme IV, with

approximately the same number of samples.

Introduction

Spatial variability of soil properties has been studied intensively. In agricultural
studies, especially in site-speciﬁc management, researchers wish to have the knowledge
on the pattern that one or more soil properties change over ﬁeld and manage the ﬁeld
more efﬁciently. Many soil properties have been studied for spatial dependency,
including soil pH, P, K, N, C (Cambardella et al., 1994; Cahn et al., 1994; Sutherland et
al., 1991; Campbell, 1978; Webster and Cuanalo, 1975), soil water properties (Harnlett et
al., 1986), pesticide residuals (Rao and Wagenet, 1985), soil inﬁltration rate (V ieira et al.,
1983), soil respiration (Rochett, et al., 1991), soil bulk density (Cambardella, et al.,
1994), and soil texture (Webster and Cuanalo, 1975; Campbell, 197 8). Once the spatial
correlation is determined, predictions can be made to unsampled locations and a soil
property map can be created. Geostatistical techniques, originating from the mining
industry, have been widely used in soil spatial studies. The main motivation for using
geostatistical tools in soil science is the design of optimal sampling schemes and the
spatial prediction of soil properties (McBratmey and Webster, 1986). Semivariogram and
kriging are two central components of geostatistics. A semivariogram describes the
structure of spatially dependent soil properties, and kriging is the best linear unbiased
estimator based on the spatial structure described by semivariograms computed from

samples (Trangrnar et al., 1985). The advantage of geostatistics is that it takes into

32

account spatial structures of the data and hence improves the precision of prediction
(McBratney and Webster, 1983).

Different prediction methods have been compared in previous studies. Laslett et
a1. (1987) compared 8 prediction techniques to predict soil pH. These 8 techniques were
classiﬁed as global or local, interpolating or non-interpolating, and smooth or non-
smooth. They found that kriging and Laplacian smoothing splines, both as non-
interpolating methods, generally performed best. In a following study, Laslett and
McBratney (1990) reported universal kriging method performed consistently the best
among four methods compared. Weber and Englund (1994) reported that the choice
between kriging and inverse-distance for mapping soil properties remained unclear, since
the prediction accuracy of different methods were dependent on data characteristics, such
as variance, skewness, kurtosis, etc. Gotway et al. (1996) reported that compared to
inverse-distance method, predictions made by kriging were unaffected by sample
coefﬁcient of variation, and were relatively high for all of the sampling conﬁgurations
considered in the study. Kravchenko and Bullock (1999) also showed that ordinary
kriging performed better than inverse distance methods with different power in the
majority of the 30 data sets used in the study.

Grid sampling is the most widely used sampling scheme in soil spatial analysis
due to maximum coverage of the ﬁeld area with a minimum number of samples.
Semivariograms computed ﬁom small samples usually appear erratic and have wide
conﬁdence intervals (Webster and Oliver, 1992). Consequently a large amount of
uncertainty can be introduced into predictions. The sample size and the minimum spacing

between sample points are most important factors in designing a sampling scheme. Short

33

spaced samples can provide important information on the spatial behavior of a variable at
short distance. The difference of spacing of grids can lead to different prediction results
(Kravchenko and Bullock, 1999). Sample size and conﬁguration have greater effect on
the accuracy of prediction than the methods of prediction method used (Wollenhaupt et
al., 1994; Mohamed etal., 1996). Wollenhaupt et al. (1994) compared predictions using
samples taken from grid points and from grid cells, and found that at a 318ft grid set,
samples from grid points gave a substantial improvement in prediction accuracy over
samples from grid cells. The prediction map sampled from grid-points at 212 ft and 106 ft
further increased map accuracy. Wibawa et a1. (1993) concluded that a 50 ft grid
sampling could effectively evaluate the variability of soil fertility in the ﬁeld. The larger
and denser the sample set is, the more accurate will be the senrivariogram estimates and
subsequent prediction. However, due to the cost and time issues associated with soil
sampling and lab analysis, the optimlnn sample size and conﬁguration have been always
of interest. Ferguson et al. (1996) suggested that additional selective samples taken
several years aﬁer initial grid sampling can provide useful information on the variation of
nitrogen management. Mulla (1993) suggested an optimum sampling interval of 50-100
m would be adequate for the mapping of most soil properties. This was similar to the
results obtained by Mohamed et al. (1996). According to Webster and Oliver (1992), for
a normally distributed isotropic soil variable, 150 samples might often be satisfactory and
225 samples will usually be reliable over a study region. In summary, the sampling
scheme should vary based on the purpose of the study, scale of the ﬁeld, and the
prediction accuracy desired.

The objectives of this study were:

34

1) to examine the effect of different sample sizes and conﬁgurations on the spatial
behavior of soil P and K.
2) to evaluate the effect of different sampling schemes on the accuracy of prediction at

unsampled locations.

Theory Background
Semivariogram
Semivariogram is the essential tool to evaluate and describe the spatial
dependence of soil properties over a study region. A semivariogram represents the semi-
variance, whose numerical value equals half the expected squared difference between
sample values separated by a given distance (Trangmar et al., 1985). This process
assumes intrinsic stationarity over the study region, which is deﬁned through a constant
mean and a constant variance in the difference between values at locations separated by a
given distance and direction (Bailey and Gatrell, 1995). That is,
E (Y (5+1!) - Y(S)) = 0 (l)

VAR (Y (34"!) - Y(S)) = 270!) (2)
Where Y(s) and Y(s+h) are the observed values at location 3 and the location separated
by h from s; the 701) is the semivariogram function. The semivariance 7depends on the
separation vector 11. Three parameters, namely nugget, sill and range are used to describe
the shape of sample semivariograms. If the soil process is spatially correlated, the
semivariogram value (7) is minimal at h = 0, and increases as It increases. The level
where the senrivariogram starts to be more or less constant, is referred to as sill.

Separation distance, at which semivariogram reaches its sill is called range. At the

35

distance beyond the range, the soil process is no longer Spatially correlated (Trangmar et
al., 1985). The semivariogram value at It = 0 is called nugget variance or nugget effect,
which represents random variation and cannot be evaluated at the sampling scale. Nugget
effect is caused by soil property variation at distances shorter than the minimum distance
between the samples and by measurement errors. Most soil properties Show distinct
nugget effects (Burgess and Webster, 1980). The nugget plays an important role in
kriging, because it sets a limit to the precision of the interpolation (Burrough, 1983;
Trangrnar et al., 1985). The estimates of the semivariogram can be calculated using the

following equation:

1 n
2( Y(s.+h)—Y(sl))2 (3)
2n(h) i=1

r(h)=

 

Where n(h) is the number of samples separated by a distance of It, Y(s;) are the values of
the measured property at location s1, and Y(s,+h) are the values of the measured property
at location SrHt.

Semivariogram model is a continuous function ﬁtted to a sample semivariogram,
and is used to provide parameter estimates computed from samples at any separation
distance, which is required in kriging (Isaaks and Srivastava, 1989). Most commonly

used types of semivariogram models include, spherical model, expressed by,

= C (3h/2r — 1:729) for h s r

r (h)
= C otherwise, (4)
and exponential model, expressed by:
r(h)= C(l-e"*") (s)

where, r is the range and C is the sill (McBratney and Webster, 1986).

36

McBratney and Webster (1986) reviewed different methods of ﬁtting a model to
sample variograrns, and noted that the least squares estimation procedure requires strict
distribution assumptions on residuals; the generalized least squares with relaxed residual
distribution assumptions and the maximum likelihood estimation are generally regarded
as efficient means of estimation, but both methods involve a formidable amount of
computation. A weighted least squares estimator was found to be reliable and

computationally efﬁcient, if the weights can be determined properly.

Ordinary Kriging

Kriging combines knowledge of both observed values and the spatial correlation
between data values at sampled locations characterized by semivariogram. Kriging
estimates at unsampled locations are optimal and unbiased (Trangmar et al., 1985). Under
kriging paradigm, ordinary kriging is focused on optimal local spatial prediction. It forms
the prediction of the process at unsampled location by using a weighted linear
combination of the observed values y; at the sample sites 8]. Estimated values Y(s) are

obtained by calculating the following formula:

I]
f<s>= ions.) (6)
i=1

where Y(s) are the locations to be estimated, Y(s;) are the neighboring samples and
weights ((0) are a function of spatial structure described by semivariogram. The weights

are chosen so that the estimated value is unbiased, i.e.

EW(s)-Y(s)] =0 (7)

37

This process assumes that the mean of Y(s) and Y(s) are all u and constrains that the sum

of the n weights ((0) is unity. The expected mean square error between true values and
observed value in kriging is minimized, i.e.

:2 = VAR [Y(s)-Y(s)] = minimum (3)

The estimated value at any unsampled location is the most precise possible from
the available data and one that can be used with known conﬁdence (McBratney et al.,
1982). The estimation variance depends only on the semivariogram and the conﬁguration
of the sample locations in relation to the predicted points and not on the observed values
themselves (Burgess and Webster, 1980). The weights are determined by taking account
of the known spatial dependence expressed in the serrrivariogram and geometric
relationships among observed point locations. In general, near points carry more weight
than distant points, points that occur in clusters carry less weight than lone points, and
points lying between the point to be predicted and more distant points screen the distant

points so that they have less weight (Burgess and Webster, 1980).

Materials and Methods

Study Site Description

The study site was a corn (Zea mays L.) — soybean [Glycine max (L.) Merr.] ﬁeld
located in Kalamazoo County, Michigan (42.22 N, 86.36 W). The ﬁeld is approximately
50 hectares and was planted to corn and soybean in an alternate year rotation. The
elevation of the ﬁeld ranges from 288 to 303 m with near level (0-2%), gentle (2-6%),
and moderate (6-12%) slopes. The soil of the study site is predominately Kalamazoo

(ﬁne-loamy, mixed, mesic Typic hapludalfs) with Oshtemo (coarse-loamy, mixed, mesic

38

typic Hapludalfs) at the south-west corner of the ﬁeld (Soil Survey of Kalamazoo
County, Michigan, 1979). The ﬁeld was non-irrigated and employed a minimum tillage
system. The whole ﬁeld was divided into two sub-ﬁelds — Field 1 (east side) and Field 2

(west side) by the rotation boundary of soybean and corn.

Field Data Collection and Laboratory Analyses

Soil sampling was conducted along 9 transects in April 2000. The total number of
soil samples was 220. Two sets of grid samples, 123 one-acre samples and 25 ﬁve-acre
samples, as well as 72 off-grid samples were taken. The smallest spacing between one-
acre-grid samples was approximately 64 m. The off-grid samples were taken 7 .5 m, 15 m,
and 30 m away from three randomly selected one-acre-grid points in each of 9 transects
in one of the four possible directions. The sample (topsoil) for each location was
composited from one subsample taken from the center location and other four subsamples
taken from 1.5 m away from the center in four directions. Soil P (Bray and Kurts P1,
Knudsen and Beagle, 1988), and K (1N NILOAc at pH 7.0, Brown and Warncke, 1988)

were determined by the Michigan State University soil testing lab.

Sampling Scheme Design

A subset of 31 samples, randomly selected from the total 220 samples, was used
as a test dataset for validation purposes. The rest of the dataset (n=189) was used to
create four sampling schemes with different sample sizes and conﬁgurations that were
used for spatial analysis. These four sampling schemes were designed in the following

ways and are graphed in Figure 2.1.

39

Scheme I: All data points were used, which included 106 one-acre grid points, and 83
off-grid points. Five-acre grid points were treated as off-grid samples. The total number
of samples used in Scheme I (N 1) is equal to 189.

Scheme 11: All one-acre grid points (106) were used along with 42 randomly selected
off-grid samples. The number of the off-grid samples was equal to half of that used in
Scheme 1. N2=148. The total number of samples used in Scheme 11 (N2) is equal to 148.
Scheme 111: Used one-acre grid points only. The total number of samples used in
Scheme 111 (N3) is equal to 106.

Scheme IV: 59 one-acre grid points, obtained by removing every other one-acre grid
points, and 50 randomly selected off-grid samples. The total number of samples used in

Scheme IV (N4) is equal to 109.

40

Figure 2.1a-d. Four sampling schemesl'. a, Scheme 1. All data points used, N1=189; b,
Scheme 11. All one-acre-grid samples, with 42 randomly selected off-grid samples.
N2=l49; 0, Scheme III. One-acre-grid samples only. N3=106; (1, Scheme IV. 59 one-acre-
grid samples, with 50 randomly selected off-grid samples. N4=109.

 

a. . . .
e O 0 +001-
0. “9 ‘>
Q g 0 O O
0 O0 0 O
O O 04. +
g e e e 04.
.0 . 0 Q 0 C 0 .
e e + 0
e + .I-o O +
are 0 0 § 0
.0 . 0 . 0 0 .
Q 0
e e g e O I +
- ' t ‘ ..
64. e e 0
84s °e D 3
+ e O O 0
e e e
e we 0 O
0. 0+ ' .
O O
3 e g e
e + e O
. 0
3+ 0 °g + °
+ O 9
0 O O
+ e g e
i. a... +
O 0 g
+ O 0

 

 

 

41

Figure 2.1. (cont’d).

 

 

0.0.0.

 

 

42

Figure 2.1. (cont’d).

 

++e

 

+++e

0+.-

 

43

 

Figure 2.1. (cont’d). m

 

d.
0
+49-
. ”8 0
Q 0 O 0
eg 4» O
oer +
g I O 0
.0 .0 Q Q 0 C
Q + O
+ + +
01-0 0 +
Q C O O O
O o . i
Q +
' 8
o. O C .0
«re ° 9 d)
+ O
O
O 01- . O
00 0+ 0
O
.8
e + e O
O
'1'. 0°: + °
+ O
Q 0
+ 0 9
$ 00 ‘8 +
O O +
+ O +

 

 

 

1' The dots represent one-acre-grid samples, the diamonds represent off-grid samples, and
the crosses are the locations where predictions were to be made.

44

Data Analysis

Sample omnidirectional semivariograms were calculated for both soil P and K for
four sampling schemes using Eq.3. A semivariogram model was ﬁtted to each calculated
sample serrrivariograrn. Then, ordinary kriging (Eq.6) was performed to predict values for
the 31 locations of the test dataset. The predicted values and the actual values at these
locations were compared using goodness-of-prediction criteria, G (Gotway et al., 1996;
Kravchenko and Bullock, 1999), root mean square error (RMSE), and coefficient of
correlation (r). The goodness-of-prediction, G, was calculated using the following
equation:

G={1-Z [Z*(Xi)-Z(xl)l2/i[Zn-Z0012} x 100 [91
' i=1

[=1

where Z*(x.) are the predicted values at location i, Z(x.) are the observed values at
location i, Z... is the mean of the observed values, and n is the number of samples used
for calculation. The root mean square error (RSME) was calculated by the following

equation:

 

RMSE = (i 12*(xo- zeal” In) [10]
i=1

The statistical software package SPLUS (Mathsoﬁ, 1999) was used to perform the
statistical analyses. Ordinary kriging was performed by Gstat (Pebesma, 1999), a

geostatistical package.

45

Results and Discussion

Table 2.1 shows the summary statistics of soil P, and K concentrations calculated
based on the data from the four sampling schemes. The minima and maxima were equal
to 15.5 and 270.5 mg/kg for soil P and 75.0 and 435.0 mg/kg for K, respectively. Several
outliers in both P and K were observed and caused the histograms of the two soil
properties to be severely skewed (P>l40 mg/Kg, and K>350 mg/Kg were considered as
outliers). Since sample semivariograms are ideally calculated based on a normal
distribution (Trangmar et al., 1985; Bailey and Gatrell, 1995), and the estimator of the
semivariogram can be sensitive to departures from normality of the data (McBratney and
Webster, 1986), the outliers were removed from the training datasets before sample
semivariograms were calculated. Both skewness and kurtosis of the two soil properties
improved after the outliers were removed. (Table 2.1. The numbers in parentheses Show
the improved skewness and kurtosis). Figure 2.2 presents sample histograms of P and K

at Scheme I with outliers removed.

Figure 2.2. Example sample histograms of P and K after outliers were removed (Scheme
I .

40 so an

20

102033405060

   

0

 

 

 

i l l T T T 7% 1 r i Y t
0 20 40 60 80 100 120 140 50 100 150 200 250 300 350

P (mg/Kg) K (mg/Kg)

46

Table 2.1. Summary statistics of soil P, and K of four sampling schemes.

 

 

Scheme Mean SD. Skewness Kurtosis Mean SD. Skewness Kurtosis
(N) --Mg/Kg-- --Mg/Kg--

B E
I (189) 50.0 31.3 3.2 (1.5) l6.0(3.0) 172.3 59.1 1.3 (0.8) 2.7 (0.6)
11(148) 49.7 31.8 3.7 (1.4) 19.3(3.1) 173.9 59.6 1.4 (0.7) 3.3 (0.7)
111(106) 51.4 34.5 3.9 (1.5) l9.4(2.8) 178.4 58.9 1.5 (0.6) 3.5(O.1)
1V(109) 50.1 34.4 3.4 (1.5) 16.9(2.8) 173.7 63.3 0.7 (0.8) 0.4(0.8)

 

 

Figures 2.3 and 2.4 Show the semivariograms of soil P and K calculated at each
sampling scheme. The lags used to calculate the semivariograms were adjusted to
produce a better recognizable semivariogram and help visual ﬁtting of a semivariogram
model. This resulted in different numbers of data pairs in semi-variance estimators of the
sample semivariograms. The lag values used in semivariogram calculations ranged from
20 to 45 m. An empirical semivariogram model was ﬁtted “by eye” to each calculated
sample semivariogram. Soil P was best ﬁtted with an exponential model and soil K was
best ﬁtted with a spherical model for all four sampling schemes. The parameters of each

semivariogram model ﬁtted were summarized in Table 2.2.

47

Table 2.2. The parameters of semivariogram models ﬁtted to each sampling scheme of
soil P and K.

 

 

Scheme (N) Range'l' Sill Nugget Nugget/ Sill
-..m---
P
(Exponential)
I (189) 225 510 150 0.29
11 (148) 750 430 230 0.53
111 (106) 1110 310 200 0.65
IV (109) 240 560 240 0.43
K
(Spherical)
I (189) 280 2900 900 0.31
11 (148) 300 2600 1000 0.38
111 (106) 320 2900 1000 0.34
IV (109) 300 2400 1100 0.32

 

1' The ranges of P are actual ranges, which were obtained by multiplying by 3 the ranges
from the ﬁtted exponential models.

Among the four models ﬁtted to soil K, Scheme I (N .=1 89) had the shortest range
of 280m, and Scheme III (N2=106) had the longest range of 320 m. Scheme 11 and IV had
the same range of 300m. The shortest and longest ranges occurred at the same schemes in
case of soil P with value of 75m (Scheme 1) and 370m (Scheme 111), respectively. Nugget
effect of soil K increased slightly from 900 (Scheme 1) to 1100 (Scheme IV), whereas the
nugget effects of P varied much more noticeably from 150 (Scheme 1) to 240 (Scheme
IV). Nugget effect arises due to the combination of variation over distances smaller than
the closest sample spacing and random measurement errors (McBratney and Webster,
1986). Both P and K had appreciable nugget effect in the study site at all sampling
schemes. As expected, the shorter the sample spacing, the smaller the nugget effect

(Trangmar et a1, 1985). In both P and K, Scheme I (N 1=1 89) had the smallest nugget

48

effect, and Scheme IV (N4=109), with no short spaced samples, had the largest nugget
(Table 2.2). Commonly, the ratio of nugget to sill is used to express the relative amount
of the nugget effect. (Trangamar et al., 1985; Bailey and Gatrell, 1995). Cambardella et
a1, (1994) used this measure to examine the strength of spatial correlation of soil
properties. They determined that if the ratio is S 25%, the variable has strong spatial
dependence, if the ratio is between 25-75%, the variable has moderate spatial
dependence, and if the ratio is >75%, the variable has weak spatial dependence. By these
criteria, both soil P and K had moderate spatial dependency (Table 2.2). However, the
spatial dependency of K was reﬂected quite similarly by all sampling schemes, whereas
that of P was noticeably different at different sampling schemes. The shapes of all
semivariograms of K were fairly consistent (Fig. 2.4), and the nugget/sill ratios were low.
Schemes II and III of P showed very weak spatial structure by having a large nugget to
sill ratio and an extremely long range compared to Schemes I and 1V (Fig 2.3). This
implied that the short distance variation of soil K was rather small in the study ﬁeld, and
the sampling schemes didn’t inﬂuence the three parameters considerably. For soil P,
however, there may be appreciable noise in the samples besides the short distance
variation. Webster and Oliver (1992) noted that semivariograms depend more on the
shortest spacing of samples, and less on the number of samples. In case of P, an
insufﬁcient number of short spaced samples in Scheme III caused the loss of a

considerable amount of spatial structure (Fig 2.30).

49

Figure 2.3. Empirical semivariograms of soil P with the senrivariograrn models ﬁtted.
a. Scheme 1. b. Scheme 11. 0. Scheme 111. d. Scheme IV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a 8 _ . 0
CD 0
re 8
O
O O
O
-
GB
or .8.-
§ ‘ Range=225 m
8 Sill=510
,. ‘ Nugget=150
N/S=0.29
o -l
0 100 200 300 400 500
Distance (m)
b
O
O
o
o - 4..
st
0
9 e
o
E . *
E o
S a ‘
Range=750 m
8 ‘ Sill=430
‘- Nugget=230
N/S=0.53
o —
0 100 200 300 400 500

Distance (m)

50

Figure 2.3. (cont’d).

 

 

 

 

 

 

 

 

o
o —
('0
o
m _
N
8 _
(B N
E a
N
O) 8 .
‘- Range=1110 m
o Sill=310
*0 ‘ Nugget=200
N/S=0.65
o _.
0 100 200 300 400 500

Distance (m)

 

l

I

I

l

1002003m400500600

1

 

9

 

 

 

Range=240 m
Sill=560
NuggeF24O
N/S=0.43

 

 

 

l I

200 300
Distance (m)

51

I

400

 

 

Figure 2.4. Empirical semivariograms of soil K with the semivariogram models ﬁtted.
a. Scheme 1. b. Scheme 11. c. Scheme 111. d. Scheme IV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a 8 . . e e
8 r—.
O O Q C
O _ O
a e
O
i s -
O
E .
a g _. Range=280 m
2 Sill=2900
8 _ Nugget=900
In N/S=0.31
O -1
0 100 200 300 400 500
Distance (m)
b
8 _
IO
N
8 .
o
(B N
c
:0 8 _
U) 4°- Range=300 m
o Sill=2600
3 ‘ NuggeFl 000
N/S=0.38
o —i
0 100 200 300 400

Distance (m)

52

Figure 2.4. (cont’d).

 

l

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i.
i
:0 g1
E
7
g g Range=320 m
07 § _ Sill=2900
:- NuggeFlOOO
§ _ N/S=0.34
° ..
0 100 200 300 400 500
Distance (m)
d e .
c
o _
o
0
(0
E 8 _
E 8
10
a) Range=300 m
8 _ Sill=2400
3 Nugget=1100
N/S=O.32
o _.
0 100 200 300 400 500

Distance (m)

53

Although the serrrivariograms appear similar at different sample sizes and
conﬁgurations, they can differ greatly in conﬁdence intervals of estimates of semi-
variance for each lag. Webster and Oliver (1991) noted that the larger the sample size and
the shorter the sample spacing, the smaller the conﬁdence interval. The conﬁdence
intervals will be very important when prediction is concerned since the prediction
variance can be very sensitive to the conﬁdence intervals of sample serrrivariograms.

The goodness-of-prediction, G (Eq. 9), the root mean square error (RMSE,

Eq.10), and the correlation coefficient (r) were summarized in Table 2.3.

Table 2.3. The goodness of prediction (G), root mean square error (RSME), and
correlation coefﬁcient (r) between predicted and actual values.

 

 

Scheme (N) G RSME r G RMSE r
B E
I (189) 55.1 14.2 0.76 50.0 37.4 0.72
11 (148) 45.9 15.6 0.76 42.9 40.0 0.68
111 (106) 38.9 16.6 0.69 34.1 43.0 0.63
IV (109) 46.0 15.6 0.71 45.3 39.1 0.69

 

54

The G value is a measure that provides information on the improvement made by
the used prediction method as compared to using the sample mean as a predictor. The
greater the G value, the better the prediction method performed (Gotway, 1996). The
highest G value of P and K both occurred at Schemes I (55.1 and 50.0, respectively).
Also, the RMSE of both Schemes I was the lowest (14.2 and 37.4 for P and K,
respectively). Scheme 11 and IV of both P and K performed almost equally well in
general. Their G values and RMSE were Similar (Table 2.3), although Scheme 11
(N 2=148) had approximately twice as many as acre grids than Scheme IV (N4=109) did.
Schemes III for both P and K had the lowest G value (38.9 and 34.1, respectively) and the
highest RMSE (16.6 and 43.0, respectively). The correlation coefficients (r) between
predicted and actual values again were the highest in Schemes I (0.76 and 0.72 for P and
K, respectively), the lowest in Schemes 111 (0.69 and 0.63 for P and K). These results
indicate that a lack of short spaced samples considerably inﬂuences the accuracy of
prediction. Webster and Oliver (1992) noted that since ordinary kriging put more weight
on nearby samples and less weight on remote ones, the close-by samples are of more
importance than distant ones, and short spaced samples can provide more information
than regular grid samples at longer distances. With a similar number of short Spaced
samples, the extra one-acre-grid samples in Scheme 11 (N2=148) did not improve the
prediction accuracy compared to Scheme IV (N4=109). On the other hand, at similar
sample sizes, Scheme IV (N4=109) performed considerably better than Scheme III
(N 3=106) due to the short spaced samples.

Figure 2.5 and 2.6 plotted the predicted values versus actual values of soil P and

K, with a 1:1 line presented. Compared with the 1:1 line in the plots, it can be observed

55

that the kriging predictions at all sampling schemes tended to overestimate the low data
values and underestimate the high data values. This trend was particularly evident in P
predictions (Fig. 2.5) and less so in K predictions (Fig. 2.6). This implied that even the
largest sample size was not able to accurately predict local high and low values. If a
higher level of accuracy of prediction is desired, additional samples would be needed,
even in Scheme 1, to capture local high variation. However, if an accurate soil property
map is of interest, a sampling scheme like Scheme IV in this study can serve as a start
with relative small number of samples and reasonable prediction accuracy. The residual
map could be helpful to identify the areas where the prediction error is high. Extra
samples can be taken selectively at those areas to improve the predictions for high and

low observations.

56

Figure 2.5a-d. Predicted values vs. observed values of soil P of four sampling schemes. a.
Scheme 1. b. Scheme 11. 0. Scheme 111. d. Scheme IV.

 

   

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
a
e

o) 80 -
x
B
E_ 60 «
0- e
E
3 40 —
o
3 Scheme 1,

20 ‘ N1=189

0 l T T I
0 20 40 60 80 100
Observed P, mgIKg
100
b

80 ~
o)
X
B)
E 50 -
a:
E
3 40 —
o. 20 - Scheme 11,

N2=148
0 l T I F
0 20 40 60 80 100
Observed P, mgIKg

57

Figure 2.5. (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 00
c
o) 80 ~
X
T:
E, 60 ~
ll
3
., 40 4
‘6'
2
m _
20 Scheme III,
N3=106
O l l I l
0 20 40 60 80 1 00
Observed P, mgIKg
100
d
80 —
or
L6
o)
E 60
o.“
o
g 40
'1':
E
20 1
Scheme IV,
N4=109
0 I I I I
0 20 40 60 80 100
Observed P, mglKg

58

Figure 2.5a-d. Predicted values vs. observed values of soil K of four sampling schemes.
a. Scheme 1. b. Scheme 11. 0. Scheme 111. d. Scheme IV.

 

300
250 -
200 ~
150 1

100 —

 

Predicted K, mglKg

 

0|
0

Scheme 1,
N1=189

0 I I I I I
0 50 100 150 200 250 300

Observed K, mgIKg

 

 

 

 

 

 

 

300
250 ~
200 ~
150 1

100 ~

 

Predicted K, mglKg

 

01
0

Scheme 11,
N2=148

 

 

 

 

 

0 50 100 150 200 250 300
Observed K, mgIKg

59

Figure 2.6. (cont’d).

300

 

250 -

N
O
O

.3
0|
O

100 -

Predicted K, mgIKg

 

 

50 1 Scheme III,
N3=I 06

 

 

 

 

 

 

0 50 100 150 200 250 300
Observed K, mgIKg

300

 

250 -

200 1

150 ~

100 ~

 

Predicted K, mgIKg

 

50 4 Scheme IV,
N3=1 09

 

 

 

 

 

0 . . . m .
0 50 1 00 1 50 200 250 300

 

Observed K, mgIKg

60

Conclusion

The effects of sampling scheme on the spatial variation of soil P and K and the
accuracy of prediction were investigated by four sampling schemes designed using 189
grid and off-grid samples. Scheme I had all data points (N 1:] 89), Scheme 11 had all grid
samples and 42 randomly selected off-grid samples (N2=148), Scheme 111 had grid
samples only (N 3=106), and Scheme IV had 59 grid samples and 50 randomly selected
off-grid samples (N4=109). The sample semivariograms of soil P calculated based on the
data from the four different sampling schemes varied considerably, whereas those of K
were fairly consistent. Schemes I with the largest number of samples (N4=189) produced
the most accurate predictions for both soil P and K. Schemes IV (N4=109) performed as
accurately as Scheme 11 (N2=148) for both P and K, however with approximately 40
samples less. Scheme III (N 3=106) performed noticeably less accurate than Scheme IV
(N4=109), with approximately the same number of samples. The results indicated that the
short spaced samples provided more valuable information than regularly spaced samples
separated by long distances. All four sampling schemes tended to overestimate low
values, and underestimate high values. This indicated that even the most dense sampling
scheme (Scheme 1) in the study couldn’t predict well the local high and low values, and
they were somewhat “averaged” by the neighbor values used to predict them. If
appreciably higher prediction accuracy is desired, this problem can be improved by
checking the residual map for high error areas and taking additional samples in those

areas.

61

Reference

Bailey, T.C., and AC. Gatrell. 1995. Interactive Spatial Data Analysis. Longman Group
Limited.

Cambardella, C.A., T.B. Moorman, J .M. Novak, T.B. Parkin, D.L. Karlen, R.F. Turco,
and A.E. Konopka. 1994. Field-Scale Variability of Soil Properties in Central Iowa Soils.
Soil Sci. Soc. Am. J. 58:1501-1511.

Campbell, J .B.l978. Spatial Variation of Sand Content and pH within Single Contiguous
Delineations of Two Soil Mapping Units. Soil Sci. Soc. Am. J. 42:460-464.

Ferguson, R. B., C. A. Gotway, G. W. Hergert, and T. A. Peterson. 1996. Soil Sampling for
Site-Speciﬁc Nitrogen Management. Proceedings of 3lrd Intl. Conference, Precision
Agriculture.

Gotway, C.A., R.B. Ferguson, G.W. Hergert, and TA. Peterson. 1996. Comparison of
Kriging and Inverse-Distance Methods for Mapping Soil Parameters. Soil Sci. Soc. Am.
J. 60:1237-1247.

Hemlett, J .M., R. Horton, and N.A.C. Cressie. 1986. Resistant and Exploratory
Techniques for Use in Semivariogram Analyses. Soil Sci. Soc. Am. J. 50: 868-875.

Isaaks, E.H., and RM. Srivastava. 1989. An Introduction to Applied Geostatistics.
Oxford University Press, Inc.

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.

Laslett, G.M., and AB. McBratney. 1990. Further Comparison of Spatial Methods for
Predicting Soil pH. Soil Sci. Soc. Am. J. 54:1553-1558.

McBratney, A.B., and R. Webster. 1983. Optimal Interpolation and Isarithmic Mapping
of Soil Properties. J. Soil Sci. 34, 137-162.

McBratney, A.B., and R. Webster. 1986. Choosing Functions For Serni-variograms of
Soil Properties and Fitting Them to Sampling Estimates. J. of Soil Sci. 37, 617-639.

Mohamed, S. B., E. J. Evans, and R. S. Shiel. 1996. Mapping Techniques and Intensity of

Soil Sampling for Precision Farming. Proceedings of 3rd Intl. Conference, Precision
Agriculture.

62

Mulla, DJ. 1991. Mapping and Managing Spatial Patterns in Soil Fertility and Crop
Yield. p15-26. In P.C. Robert et al. (ed.) Soil Speciﬁc Crop Management: A workshop in
research and development issues. Proc. Workshop, Minneapolis, MN. 1992. ASA, CSSA,
and SSSA, Madison, WI.

Rao, P.S.C., and R.J. Wagenet. 1985. Spatial variability of Pesticides in Field Soils:
Methods for Data Analysis and Consequences. Weed Sci. 33 (Suppl. 2): 1 8-24

Rochette, P., R.L. Desjardins, and E. Pattey. 1991. Spatial and Temporal Variability of
Soil Respiration in Agricultural Fields. Can. J. Soil Sci. 71 :189-196.

Sutherland, R.A., C. van Kessel, and DJ. Pennock. 1991. Spatial Variability of Nitrgen-
15 Natural Abundance. Soil Sci. Soc. Am. J. 55:1339—1347.

Trangrnar, B.B., R.S. Yost, and G. Uehara 1985. Application of Geostatistics to Spatial
Studies of Soil Pr0perties. Advances in Agron. Vol.38.

Vieira, S.R., D.R. Nielsen, and J .W. Biggar. 1981. Spatial Variability of Field-Measured
Inﬁltration Rate. Soil Sci. Soc. Am. J. 45:1040-1048.

Weber, DD, and EJ. Englund. 1994. Evaluation and Comparison of Spatial
Interpolators 11. Math. Geol. 26:589-603.

Webster, R., and HE. Cuanalo DE LA C. 1975. Soil Transect Correlograms of North
Oxfordshire and Their Interpretation. J. Soil Sci. 26, 176-194.

Webster, R, and MA. Oliver.1992. Sample Adequately to Estimate Variograrns of Soil
Properties. J. of Soil Sci. 43, 177-192.

Wibawa, W.D, D.L. Dludlu, L.J. Swenson, D.G. Hopkins, and WC. Dahnke. 1993.
Variable Fertilizer Application Based on Yield Goal, Soil Fertility , and Soil Map Unit. J.
Prod. Agric. 6:255-261

Wollenhaupt, N.C., R.P. Wolkowski, and MK. Clayton. 1994. Mapping Soil Test

Phosphorus and Potassium for Variable-Rate Fertilizer Application. J. Prod. Agric.
7:441 -448.

63

APPENDICES

64

Appendix 1. Summary statistics of monitor yield data from 1996 - 2001.

 

 

 

Year Crop 1:515:38: Mean Max. Min. S.D.
Bu/acre
W
1996 Corn 35,567 105.6 176.2 32.6 16.7
1997 Soybean 27,302 39.0 65.1 15.3 6.4
1998 Corn 31,156 161.1 218.5 83.8 15.1
1999 Soybean 32,061 33.9 54.2 15.1 4.9
2000 Corn 31,379 152.5 215.1 86.2 15.1
2001 Corn 23,789 123.5 189.9 49.3 15.1
M
1997 Corn 17,636 147.3 224.6 21.7 27.2
1999 Corn 17,419 145.0 248.9 10.1 27.5
2001 Com 12,968 120.9 193.0 49.3 20.3

 

65

Appendix 2. Summary statistics of the selected soil properties from the A and B horizons.

 

Soil Properties

Horizon Thickness (cm)
Bulk Density (g/cm3)
Total Clay (%)

Total Silt (%)

Total Sand (%)

Fine Silt (%)

Coarse Silt (%)

Very Fine Sand (%)
Fine Sand (%)
Medium Sand (%)
Very Coarse Sand (%)
Coarse Sand (%)

Ca (meq/100g)

Mg (mqu 1 00g)

K (meq/100g)

Sum of Basis (meq/ 100g)
Acidity (meq/ 1 00g)
CEC (meq/100g)

Base Saturation (%)
Organic Carbon (%)
Total N (%)

pH (CaClz)

EC (mmho/cm)

Max.

32.5
1.9
19.1
66.1
83.6
46.6
24.4
14.3
56.3
15.4
5.8
5.3
12.6
2.4
1.2
14.9
14.0
18.0
100
2.2
0.3
6.7
1.1

Min.
A Horizon
17.5
1.2
3.8
12.5
17.8
7.7
4.8
4.9
5.9
2.3
1.2
0.1
1.9
0.4
0.1
2.5
2.4
3.5
37.0
0.5
0.0
4.4
0.2

Mean

24.0
1.4
13.6
47.7
38.6
29.2
18.6
10.0
17.6
7.0
2.9
1.2
5.9
1.2
0.4
7.5
8.0
10.8
68.8
1.3
0.1
5.4
0.4

SD.

3.8
0.15
3.93
12.56
15.86
9.56
4.70
2.40
11.41
3.26
1.11
1.15
2.33
0.45
0.22
2.69
3.05
3.24
14.84
0.39
0.05
0.54
0.15

 

66

Appendix 2. (cont’d)

 

Soil Properties Max. Min. Mean SD.
B Horizon

Horizon Thickness (cm) 60 12.5 27.3 10.2
Bulk Density (g/cm3) 2.1 1.2 1.5 o. 16
Total Clay (%) 28.1 3.4 18.2 5.87
Total Silt (%) 67.1 9.3 40.1 15.66
Total Sand (%) 87.3 15.3 41.7 18.23
Fine Silt (%) 54.4 5.5 24.0 12.67
Coarse Silt (%) 23.9 3.8 16.1 4.94
Very Fine Sand (%) 16.7 2.7 10.3 3.00
Fine Sand (%) 63.2 5.7 20.2 13.15
Medium Sand (%) 17.8 2.2 7.4 4.01
Very Coarse Sand (%) 8.1 0.9 2.9 1.76
Coarse Sand (%) 5.9 0.1 1.0 1.09
Ca (meq/ 100g) 8.7 0.7 5.7 1.99
Mg (meq/ 100g) 2.8 0.4 1.2 0.52
K (meq/ 100g) 1.0 0.1 0.3 0.18
Sum of Basis (meq/ 100g) 11.6 1.2 7.2 2.41
Acidity (meq/ 100g) 15.9 1.8 8.1 3.34
CEC (meq/ 100g) 18.4 2.4 12.0 3.71
Base Saturation (%) 95.0 33.0 61.7 14.72
Organic Carbon (%) 2.0 0.1 0.6 0.47
Total N (%) 0.2 0.0 0.1 0.04
pH (CaClz) . 6.2 4.0 4.9 0.54
EC (mmho/cm) 1.7 0.2 0.5 0.52

 

67