Agronomy Journal Grow Your Career With ASA
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published in Agron J 100:454-462 (2008)
DOI: 10.2134/agrojnl2007.0063
© 2008 American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Agricola
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Related Collections
Right arrow Nitrogen
Right arrow Geostatistics
Right arrow Spatial Variability
Right arrow Remote Sensing

REMOTE SENSING

Spatial Analysis of Early Wheat Canopy Normalized Difference Vegetative Index: Determining Appropriate Observation Scale

E. M. Pena-Yewtukhiwa,*, G. J. Schwabb, J. H. Groveb, L. W. Murdockc and J. T. Johnsond

a Division of Plant and Soil Sciences, West Virginia Univ., P.O. Box 6108, Morgantown, WV, 26506-6108
b N-122 ASCN, Dep. of Plant and Soil Sciences, Univ. of Kentucky, Lexington, KY, 40546-0091
c Dep. of Plant and Soil Sciences, Univ. of Kentucky, West Kentucky Research and Education Center, Princeton, KY, 42445
d Clark County Cooperative Extension Center, 4400 Gateway Blvd, Suite 104, Springfield, OH, 45502. COA-Agricultural Experiment Station No. 05-06-029

* Corresponding author (Eugenia.Pena-Yewtukhiw{at}mail.wvu.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Efficient use of real-time canopy sensors requires knowledge of the scale (resolution) of variation in the measured canopy property. Knowing the amount of needed optical data requires estimation of the optimal combination of physical sensor density (number of sensors along the applicator boom) and sensor output density (sensor readings per unit distance along the travel path). The objective of this study was to determine the sampling grid size that would adequately describe field variation in canopy normalized difference vegetative index (NDVI) by varying either physical sensor density or sensor output density. Wheat (Triticum aestivum L.) canopy NDVI data were collected at Feekes growth stage 3 in five fields in central and western Kentucky in February of 2004 or 2005. Spatial structure of NDVI was characterized by variogram analysis across grid sizes ranging from 0.56 (high-density) to 5.1 m2 and both semivariance and spatial structure parameters for high-density data sets were compared to those obtained with decreasing numbers of sampling points (greater grid size). Nugget, range, and sill values were maintained across evaluated grid sizes in four of five site-years. Correlations between each field's high-density semivariance values and those for the "low-density" data sets were generally high (1.0 < R2 < 0.8) for all site-years, but there were many cases where intercepts deviated significantly from 0.0 and slopes deviated significantly from 1.0. Observed differences in individual sensor performance did not influence the pattern of NDVI spatial structure. Grid size could be increased from 0.56 to 5.1 m2 without significantly affecting the measured spatial structure of canopy NDVI in most fields. Wheat growers might achieve spatially optimal N applications with lower data resolution and less capital intense machinery.

Abbreviations: AIC, Akaike Information Criterion • GPS, global positioning system • NDVI, normalized difference vegetative index • NIR, near infrared • VESPER, Variogram Estimation and Spatial Prediction and Error


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

1 The mention of trade or manufacturer names is for information only and does not imply an endorsement or recommendation by the authors. Back

Received for publication February 14, 2007.
   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
SENSOR TECHNOLOGIES developed for precision farming provide an innovative way of collecting spatial data. Sensors often have the capability of acquiring a large number of observations in a short time and the limitation of small data sets to the definition of spatial structure and spatial correlation is not an issue. However, the greater number of sensors and data analysis requirements can both increase sampling costs and complicate analysis.

Normalized difference vegetative index canopy reflectance sensors exhibit the previously described characteristics. These sensors measure differential absorption and reflection from surface cover (e.g., leaves, soil, residues) at different wavelengths. For a canopy reflectance sensor, the NDVI is calculated as follows:

Formula
where NIR and R are the near infrared (NIR) and red reflectance, respectively, captured by the sensor. This technology has been used, in conjunction with a calibrated N application rate algorithm, to spatially change fertilizer N rates "on the go" (Raun et al., 2002).

However, efficient use of real-time canopy sensors requires knowledge of the scale (resolution) of variation in the measured property. The ideal resolution has been called the "optimum field element size," defined as the optimum area that provides the most precise measure of available nutrient where the supply of that nutrient changes with distance (Solie et al., 1996). This element has been calculated using field areas where "cause and effect" relationships can be measured (LaRuffa et al., 2001), though cause and effect relationships are not stable across fields and seasons (LaRuffa et al., 2001; Solie et al., 1999).

The "optimum field element size" can be estimated using the spatial structure of the crop canopy characteristic being measured to determine N input rates. In this approach, the "optimum field element size" is calculated from sensor NDVI readings, but this begs the question as to the best geometric distribution for the sensors. Knowing the density of optical data needed to capture canopy status allows estimation of the most efficient combination of physical sensor density (number of sensors along the applicator toolbar) and sensor output density (sensor readings per unit distance along the travel path). Engineers have defined this resolution in accord with the "expected" scale at which significant biological differences exist in agricultural fields. Solie et al. (1999) found that such data should be taken at submeter scale for full description of the variation of soil and plant stand properties in bermudagrass (Cynodon dactylon L.) sods. Solie et al. (1996), working with hard red winter wheat (Triticum aestivum L.) grown in the southern Great Plains, determined that optical sensor data should be taken at a grid-size resolution of about 2.25 m2. There is a need to understand the optimal scale of NDVI characterization for wheat canopies in other landscapes, and other cropping systems.

The objective of this study was to find the minimum number of sensors and sensor readings (combined to give the largest sample grid size) that would adequately describe field variation in the canopy NDVI of soft red winter wheat fields located in the humid eastern region of the United States.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Wheat canopy NDVI data were collected in five fields at the Feekes 3 growth stage in February of 2004 or 2005. The 2004 and 2005 Woodford fields (cv. Declaration) were located at the University of Kentucky's Animal Research Center in Woodford County (central Kentucky). The 2004 and 2005 McAtee fields (cv. Allegiance) were located at McAtee Farms in Trigg County (western Kentucky). The 2004-Princeton field (cv. Pioneer 25R37) was located at the University of Kentucky's West Kentucky Research and Education Center in Caldwell County. Population statistics for NDVI observations from each field were calculated using SAS (1999).

Instrumentation
Wheat canopy NDVI readings were taken with a field scale GreenSeeker (N Tech Industries Inc., Ukiah, CA) 1 sensor/variable N rate applicator (U.S. Patent No. 5389781) with eight individual canopy reflectance (GreenSeeker) sensors mounted at 0.75 m intervals along a 6.0 m boom, and also equipped with a global positioning system (GPS) receiver. At an average operating speed of 2.7 km/h, and set to give a scan width of 0.75 m, each sensor generated an average NDVI reading every 0.75 m along the path of travel, giving a square/rectangular scan area of 0.56 m2.

Leaves are "bright" in the red (600–700 nm) and blue (450–510 nm) components of the spectrum because leaf pigments preferentially absorb these wavelengths (Curran, 1983). The GreenSeeker active lighting optical sensor emits light at 660 nm (R) and 780 nm (NIR). The optical sensor units pulse at high frequency, the reflected light is filtered, and the magnitude of the filtered signal is measured. The individual sensors had seen <100 h of service and were factory calibrated using a "two-point" calibration technique (D. Smith, personal communication, 2007). No additional calibration of sensors was performed during the conduct of this research. The NDVI was determined from the R and NIR reflectance.

Data Analysis
Mean, mode, median, standard deviation, and skewness of the NDVI data for each site-year and for individual sensors within each site-year were calculated using PROC UNIVARIATE from SAS (1999). Sample data histograms and goodness of fit for normality (Shapiro-Wilke statistic) were also calculated. Comparisons of the NDVI means for individual sensors were performed with PROC MEANS from SAS (1996), using the least significant difference (LSD) test at the 95% level of confidence.

Spatial Analysis
The question of the minimum data set needed to characterize a variate's spatial structure depends on the spatial "context" of the measured parameter. Characterization of spatial structure (spatial correlation) was done with geostatistical technique, the variogram. The variogram describes spatial characteristics of a measured parameter by revealing its spatial continuity (spatial correlation). The variogram can also reveal changes in spatial continuity with direction. In this study, each experimental variogram was calculated for a single realization of z (NDVI) expressed as z(xi) in Eq. [1], for regular distance intervals [hj, hj + {delta}] expressed as xi and xi-h in Eq. [1], using the following equation:

Formula 1[1]
where N = number of pairs and Formula 1j = average of all Njh's.

In this work, the aim of variogram analysis was not a prediction of NDVI values at unsampled locations, but characterization of spatial structure in each field's Feekes 3 wheat canopy NDVI. Both spatial trend and anisotropy were evaluated. Anisotropy was evaluated in two directions: (a) the direction of machine travel and (b) the direction perpendicular to the direction of machine travel; using GSTAT (2001). Anisotropy was not detected. The program Variogram Estimation and Spatial Prediction with Error (VESPER), developed by the Australian Center for Precision Agriculture, was used to calculate omnidirectional NDVI variograms (Whelan et al., 2001).

To evaluate the impact of reduced sensor readings (increased sampling grid size), the numbers of sensors (maximum of eight) and/or the number of readings along the machine's travel path were decreased. Each sensor position was identified by one number (1 through 8), and was not changed across fields and years. In the spatial analysis, the number of sensors was reduced from eight to four to three, and the distance between individual NDVI readings was increased (from 0.75 m to 1.5 and 2.25 m) by dropping out one of every two, or two of every three, NDVI readings. In all cases, the area/geostatistical support (0.56 m2) for each individual NDVI reading was kept constant. The resulting grid sizes were 0.56, 1.1, 1.7, 2.3, 3.4, and 5.1 m2, for which the possible combinations of sensors and sensing distances generated 1, 4, 5, 4, 10, and 6 variograms, respectively.

Two different methods were used to evaluate changes in the spatial structure of early wheat canopy NDVI with changes in sensor data intensity: (a) first, important diagnostic parameters from fitted variogram models were compared; (b) second, correlation was used to compare semivariance values at pre-established lags. For the first method, the same general model was fitted to the calculated semivariograms, and semivariogram parameters were compared. The sample variograms were initially fitted with both exponential and Gaussian variogram models, defined by Eq. [2] and Eq. [3] (Deutsch and Journel, 1998), respectively,

Formula 2[2]
and

Formula 3[3]
for any h ≥ 0, where a is the variogram range, c0 is the variogram nugget component, and c1 is the positive variance contribution (sill). The variogram range defines the distance beyond which spatial correlation ceases to exist. Additionally, to characterize the relative importance of nugget randomness to maximal variance, the ratio of nugget (c0) to nugget plus sill (c0+c1) was determined for each site-year. Variogram models were fitted using a weighted nonlinear least-square method, and goodness of fit was assessed by the lowest Akaike Information Criterion (AIC), which was also used to select between Gaussian or exponential models (Whelan et al., 2001). As each of the larger grid sizes was represented by more than one combination of sensor number and sensor measurement density, each combination was used to generate a variogram. Little or no difference in the spatial structure parameters for a particular grid size was found across the several combinations, so only average nugget, sill, range and nugget to total sill ratios, for each grid size, were used in the analysis. To compare variogram parameters among grid sizes for a site-year, the best fitting model (exponential or Gaussian) for the 0.56 m2 grid was considered the theoretically complete, "true," variogram model. To facilitate comparison, if fitting parameters (AIC) permitted, all variograms were fitted to one model, exponential or Gaussian. For each grid size variogram, the nugget variance, range and sill variance was compared to the "true" variogram. For each site-year, the ratios between variogram parameters calculated for other NDVI grid sizes and those for the high-density data set were calculated. A difference of 10% (ratio between 0.90 and 1.10) was considered negligible.

In the second approach, using Pearson simple correlation modeling, each low-density data set variogram was related to the high-density data set (0.56 m2 grid) variogram, for a given site-year. Comparison of variograms was facilitated by calculating spatial variance at the same lag distances in all variograms. It was assumed that the "true" spatial structure or theoretically complete model of a site-year's Feekes 3 wheat canopy NDVI (the reference variogram) was contained within the high-density (0.56 m2 grid) data set. Intercepts and slopes for linear correlations between low-density variograms and the reference variogram were determined for each site-year and deviations (intercept != 0.0; slope != 1.0) were statistically evaluated using a two-sided t test at the 99% level of confidence using PROC REG in SAS (1999).


   RESULTS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Descriptive statistics were calculated for the NDVI data populations generated at all grid sizes, for all site-years (not shown). Within a site-year, the NDVI data populations were not statistically different with regard to mean, mode, median, and standard deviation and all data sets exhibited a normal distribution, though with different degrees of skewness (not shown). The high-density NDVI data populations for the different site-years did exhibit differences (Table 1 ). In 2004, average NDVI values were greatest for the Woodford field and smallest for the Princeton field. In 2005, the difference in field-average NDVI was much smaller, and that for the Woodford field was slightly lower (Table 1).


View this table:
[in this window]
[in a new window]

  		Table 1. Descriptive statistics for the high-density normalized difference vegetative index data sets taken in the Woodford, McAtee, and Princeton wheat fields in 2004 and 2005.

 
Each sensor's NDVI readings were individually evaluated. In 2004, univariate statistical analysis (Pena-Yewtukhiw et al., 2006) found seven significantly different sensor groups (Table 2 ), with sensor 8 consistently giving the highest NDVI readings and sensor 5 the smallest. The origin and consistency of the observed difference in sensor output in 2004 was not clear. In 2005, the Woodford field exhibited a similar trend, but the McAtee field did not. In 2005, an electrical problem caused one of the sensors to burn out while working in the Woodford field. The sensor was replaced, so both sensors and sensor rankings for the 2005-McAtee field were different from those used in the other site-years.


View this table:
[in this window]
[in a new window]

  		Table 2. Univariate statistical evaluation of individual sensor normalized difference vegetative index (NDVI) values taken in the Woodford, McAtee, and Princeton wheat fields in 2004 and 2005.

 
Assessment of anisotropy involved comparing high-density NDVI variograms in the directions of greatest and least continuity. Visual inspection of variograms, and a comparison of the spatial structure parameters (nugget, sill, and range) for the two different directions, found only slight differences in any site-year (not shown). In conclusion, no anisotropy was observed in the Woodford, McAtee, and Princeton fields in 2004 or 2005.

High-density NDVI variograms for the five site-years suggested that there were considerable differences in early wheat canopy NDVI spatial context among fields and years (Table 3 ). In the 2004 and 2005 Woodford fields, early wheat canopy NDVI values were spatially correlated over shorter distances (less spatially uniform) than in the McAtee and Princeton fields (Table 3). The 2004 McAtee wheat field exhibited the longest correlation distance (range), but this distance was shorter in the 2005 McAtee field, which also exhibited the largest total sill variance (Table 3).


View this table:
[in this window]
[in a new window]

  		Table 3. Spatial structure parameters for variograms derived from the high-density normalized difference vegetative index data sets for the Woodford, McAtee, and Princeton wheat fields in 2004 and 2005.

 
For a site-year, variograms for NDVI values taken at different grid sizes were initially compared (ex. variograms for 0.5, 1.1, 1.7, and 3.4 m2 grid sizes in the 2004 McAtee field– Fig. 1 ). Generally, there were few evident differences in variogram shape and semivariance magnitude among grid sizes. However, when sensors 2, 5, and 8 were separated from other sensors, a cyclical pattern in semivariance was observed at lag distances below the range for all the fields in 2004 and for the 2005 Woodford field. The NDVI variograms for these sensors, operating in the 2004 Woodford and 2004 McAtee fields, are shown in Fig. 2 .


Figure 1
View larger version (16K):
[in this window]
[in a new window]

  		Fig. 1. Variograms for early wheat canopy normalized difference vegetative index (NDVI) values taken at 0.56, 1.1, 1.7, and 3.4 m2 grid sizes in the 2004 McAtee field.

 

Figure 2
View larger version (13K):
[in this window]
[in a new window]

  		Fig. 2. Variograms for early wheat canopy normalized difference vegetative index (NDVI) taken at a 1.7 m2 grid size in the Woodford and McAtee fields in 2004 using sensors 2, 5, and 8.

 
To facilitate comparison of variogram parameters among grid sizes for a site-year, an exponential model was considered the theoretically complete model, fitted to each variogram, and variogram parameters (nugget variance, range, and sill variance) were determined (Table 3). For each site-year, the ratios between variogram parameters calculated for other NDVI grid sizes and those for the high-density data set (Table 4 ) were used to evaluate changes in NDVI spatial structure due to reduction in sensor numbers and/or sensor measurement density. A difference of 10% (ratio between 0.90 and 1.10) was considered negligible. Range ratios suggested that changes in grid size most influenced this variogram parameter, especially in the Woodford field in 2005 (Table 4). The range generally rose as the grid size increased, a phenomena oft observed (Nielsen and Wendroth, 2003). Changing grid size most influenced NDVI variogram parameters in 2005, in both Woodford and McAtee fields (Table 4). In the latter field, both nugget (c0) and nugget to total sill ratios (c0/c0 + c1) were often reduced at larger grid sizes.


View this table:
[in this window]
[in a new window]

  		Table 4. Ratio of variogram parameters for each of the five grid sizes to the variogram parameters for the high-density (0.56-m2 grid size) normalized difference vegetative index (NDVI) data set for the five site-years.{dagger}

 

View this table:
[in this window]
[in a new window]

  		Table 5. Regression of semivariance for the low-density normalized difference vegetative index (NDVI) data sets against the semivariance for the high-density NDVI data set for the 2004 McAtee field.

 

Figure 3
View larger version (15K):
[in this window]
[in a new window]

  		Fig. 3. (a) High-density and low-density (5.1 m2, sensors 2-5-8; taken from Table 5) variograms for the 2004 McAtee field. (b) Correlation of the low-density semivariance against the high-density semivariance.

 

View this table:
[in this window]
[in a new window]

  		Table 6. Regression of semivariance for the low-density normalized difference vegetative index (NDVI) data sets against the semivariance for the high-density NDVI data set for the 2005 McAtee field.

 

Figure 5
View larger version (27K):
[in this window]
[in a new window]

  		Fig. 5. (a) High-density and divergent low-density (2.3 m2, sensors 1-3-5-7 and 2-4-6-8; both taken from Table 6) variograms for the 2005-McAtee field. (b) Correlation of low-density semivariance against the high-density semivariance.

 

   DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Negligible differences in descriptive statistics due to grid size for NDVI data sets (data not shown), for all site-years, indicates that the decreased sampling associated with larger grid sizes still well represented the "total NDVI population" in these wheat fields. As grid size increased, normality (Kolmogorov-Smirnov test) in NDVI data was maintained, and no transformation was necessary before geostatistical analysis. Differences in NDVI values between the 2004 and 2005 Woodford, McAtee, and Princeton wheat fields were related to their magnitude and spatial structure. The greater mean NDVI for the 2004 Woodford field (Table 1) reflected generally greater wheat growth due to cultivar choice, better soil fertility, and/or better growth conditions. Smallest mean NDVI values were observed for the 2004 Princeton field, which suffered establishment problems. The distribution of NDVI values from the Woodford fields, although normal, was slightly skewed toward smaller values (negative skew), while those for the McAtee and Princeton fields were slightly skewed toward larger values (Table 1). Statistical analysis of individual sensor NDVI readings found significant individual sensor performance, independent of the field studied (Table 2). This indicates differences in sensor quality or calibration. In 2005, this trend was broken, due to sensor malfunction, between NDVI measurement of the wheat canopies in the Woodford and McAtee fields. Nonetheless, NDVI readings from individual sensors were always significantly different.

Initial spatial investigation found neither anisotropy nor spatial trend in the NDVI data for any of the five site-years. This indicated that omnidirectional variograms could be used to characterize NDVI spatial structure. In 2004, high-density NDVI variograms indicated that although average NDVI values were smaller for the McAtee and Princeton fields (Table 1), the McAtee field exhibited greater spatial variation (greater sill and nugget values, Table 3). The 2004 Woodford wheat field exhibited the strongest spatial structure in NDVI, with a nugget/total sill ratio <0.4 (Cambardella and Karlen, 1999). The 2004 Princeton wheat field exhibited the smallest sill variance, and the weakest spatial structure (ratio of nugget/total sill > 0.4). In 2005, the fields were less similar than those studied in 2004. The high-density NDVI variogram for the 2005 McAtee wheat field had a smaller nugget, greater sill and a much greater spatial structure than the 2005 Woodford wheat field (Table 3).

When variograms were calculated for the various grid-size data sets, a cyclical variance pattern was sometimes observed (Fig. 2). The common feature to these variograms, for all fields in 2004, and for the 2005 Woodford field, was that the data came from a three-sensor combination that always included sensors 5 and 8, which exhibited the lowest and highest average NDVI measurements, respectively. The cyclical pattern to these variograms, a cyclical increase and decrease in the semivariance, was due to the cyclical pattern of difference between NDVI data points taken with sensors 5 and 8 (increased variance) and that between NDVI data points measured with 5 or 8 and the third sensor (decreased variance). This explanation was confirmed when the NDVI data from the 2005 McAtee field were examined. The same cyclical pattern was observed whenever three sensors were used, but was not related to the use of NDVI data from sensors 5 and 8, but rather to data from sensors 1 and 7, which exhibited the greatest difference in average NDVI values at this site-year (Table 2).

Using a common model (exponential) for the variogram and the ratio of spatial structure parameters for high- and low-density data sets, the greatest grid size (5.1 m2) was adequate for early wheat canopy NDVI characterization in all three fields studied in 2004 (Table 4). In these wheat fields, early canopy NDVI variogram model nugget, range and sill values were conserved across the grid sizes evaluated. In 2005, the model nugget, sill, range and nugget/sill values were more often >10% different from those for the 0.56 m2 grid size, and the potential for decreasing sensor numbers/measurements was not as clear as in 2004. The change in sensors in 2005 likely contributed to the differences in observed variogram parameter stability across the evaluated grid sizes. The discrepancy was bigger for the 2005 Woodford wheat field, where the sensor problem occurred during NDVI data acquisition, than in the 2005 McAtee wheat field, where a new sensor was used throughout the field. The parameter ratio analysis still indicated that NDVI grid size could be >0.56 m2 in these fields (Table 4); raised to 1.1 or 1.7 m2 in the 2005 Woodford field, and to 1.7 or 5.1 m2 in the 2005 McAtee field.

Results of the analysis presented above (Table 4) are based on fitting a selected model to each field's NDVI variograms. Error, over one or more portions of the variogram, is implicit to fitted variogram models and the spatial structure parameters determined from them, and make the previous analysis subject to challenge. A more robust approach was needed.

For all site-years, initial visual inspection of the variograms calculated at the different grid sizes did not show clear differences (Fig. 1). Visually, there was often greater coincidence between the individual variograms than between an individual variogram and its fitted model. This suggested an alternate approach to variogram evaluation; the linear correlation of each low-density NDVI variogram to the site-year's high-density NDVI variogram. The relationship (Y = mX + b, where X = semivariance for the high-density data set and Y = semivariance for the low-density data set) was statistically evaluated for equality to the 1:1 relationship (Y = X) by determining whether the intercept (b) was equal to 0.0 and the slope (m) was equal to 1.0. For this analysis, it was necessary to calculate the semivariance for all the low- and high-density data sets at the same lag distances.

The slopes and intercept for all comparisons are presented in Tables 5 through 9. As an example, for the 2004 Woodford field (Table 7 ), the 2.3 and 3.4 m2 grids, obtained with a combination of sensors (1, 3, 5, and 7), and either one-half or two-thirds fewer measurements along the path of travel, exhibited semivariance coincident to that of the exhaustive data set. In other words, the number of sensors could be reduced from eight to four, and NDVI measurements reduced by one-half or two-thirds, and the same NDVI spatial structure was still obtained. The 2005 Woodford field (Table 8 ) also exhibited coincidence in semivariance between the high-density data set and that for the 1.7 m2 grid using all sensors, but two-thirds fewer measurements along the travel path, and also that for the 3.4 m2 grid obtained with sensor combination 1-3-5-7 and two-thirds fewer measurements along the travel path. In the 2005 McAtee field, the 1.7 m2 grid obtained with all sensors and two-thirds fewer measurements along the path of travel gave the same spatial structure as that for the field's high-density data set.


View this table:
[in this window]
[in a new window]

  		Table 7. Regression of semivariance for the low-density normalized density vegetative index (NDVI) data sets against the semivariance for the high-density NDVI data set for the 2004 Woodford field.

 

Figure 4
View larger version (18K):
[in this window]
[in a new window]

  		Fig. 4. (a) High-density and low-density (1.7 m2, sensors 2-5-8; taken from Table 7) variograms for the 2004 Woodford field. (b) Correlation of the low-density semivariance against the high-density semivariance.

 

View this table:
[in this window]
[in a new window]

  		Table 8. Regression of semivariance for the low-density normalized difference vegetative index (NDVI) data sets against the semivariance for the high-density NDVI data set for the 2005 Woodford field.

 
The results indicated that the semivariance relationships between low- and high-density data sets were "close," but statistical coincidence was not usual. This is typified by the 2004 McAtee (Table 5) and 2004-Princeton (Table 9 ) fields, where there were no grid sizes (combinations of sensor numbers and number of measurements along the path of travel) where both the intercept equalled 0.0 and the slope equalled 1.0. In these two fields, low-density data set semivariance was generally strongly related to that of the high-density data set (R2 ≥ 0.87); intercept values were often close to 0.0; but slope values were usually <1.0 (Fig. 3 ). Slope values tended to decline as the NDVI grid size was increased in these two fields, suggesting that maximal semivariance, especially at lag distances near/above the range, was lower with fewer sensors/measurements along the path of travel. This was especially evident in the 2005 Woodford field (Table 8), where both the slope and quality (R2) of semivariance relationships declined at the greatest grid sizes.


View this table:
[in this window]
[in a new window]

  		Table 9. Regression of semivariance for the low-density normalized difference vegetative index (NDVI) data sets against the semivariance for the high-density NDVI data set for the 2004 Princeton field.

 
The relationship in Fig. 3 also exhibits an intercept value significantly greater than 0.0. Though there was variation in relationship intercept values, both 2004 McAtee and 2004 Princeton fields tended to exhibit positive intercepts, indicating that most of the low-density data sets possessed greater variance at small lag distances than did the high-density data set. This was true in all but the 2005 Woodford field (Table 8), where positive and negative intercepts were nearly equal.

The relationship in Fig. 4 (from 2004 Woodford field,Table 7) is opposite that exemplified in Fig. 3. The intercept is significantly <0.0, indicating that the low-density data set possessed less variance at small lag distances. The slope was significantly > 1.0, indicating that maximal semivariance at lag distances near/above the range was lower with fewer sensors/measurements along the path of travel. Variogram shapes for different sensor combinations were very similar (Fig. 4). Semivariance relationship slopes > 1.0 were less common, and tended to be associated with particular sensor groupings in the 2005 McAtee (Table 6) and 2004 Woodford (Table 7) fields.

In the 2005 McAtee and 2004 Woodford fields, groups of sensors, created by dropping one of every two, or two of every three, sensors along the boom, tended to segregate as regards their semivariogram behavior. In the 2005 McAtee field, sensor groupings including sensors 1 and 7 result in greater NDVI semivariance, especially at greater lag distances, than sensor groupings including sensors 2 and 8 (Fig. 5 ), though variogram shape is quite similar. The influence of sensor grouping was more complicated in the 2004 Woodford field. Sensor groupings including sensor 4 exhibited a lower slope to their NDVI semivariance relationship with the high-density data set than did sensor groupings that included sensor 5.

The variograms presented in Fig. 1, 3, 4, and 5 are illustrative of the general observation that different combinations of sensors and sensing distances (different grid sizes) exhibited similar spatial structure. The true variograms were more similar to each other than to the fitted variogram model (not shown), and this similarity was generally supported by the high R2 values exhibited (Tables 5–9GoGoGoGo), even for the 2005 McAtee field (Table 6). The lone exception was the 2005 Woodford field, where the linear variogram comparisons became more dissimilar (R2 ≤ 0.8) for some sensor and sensing distance combinations giving a grid size of 3.4 m2 and for all combinations giving a grid size of 5.1 m2.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
There were spatial (field to field) and temporal (year to year) differences in the spatial structure of Feekes 3 wheat canopy NDVI values. However, these differences were of little consequence to the conclusions. The approaches we used to evaluate possible reductions in sensor numbers, and/or sensor measurements along the travel path, found that individual sensor performance, as regards the characterization of spatial variation in NDVI, was similar.

When a "common model" approach was used to characterize NDVI variograms and the ratio of spatial structure parameters for high- and low-density data sets was determined, the greatest grid size (5.1 m2) was adequate to characterize early wheat canopy NDVI in all three 2004 fields. Though there were differences in observed variogram parameter stability across the evaluated grid sizes in 2005, both the parameter ratio analysis and the linear correlations among variograms still indicated that NDVI grid size could be as great as 1.7 m2 in the 2005 Woodford field, and 5.1 m2 in the 2005 McAtee field.

Though the evidence was mixed, linear comparisons of NDVI semivariance for the low-density data sets with those of high-density data sets, for the same field, suggest that the possibility of reducing sensor numbers and/or the number of NDVI measurements should not be discarded. Although individual sensors affected the depiction of spatial variation, sensor NDVI values tended to mimic each other and the grand average NDVI. Wheat canopy NDVI grid size in these fields could be increased to 5.1 m2 with confidence. Reducing sensor density and/or their output requirement should reduce the cost of using this technology.


   ACKNOWLEDGMENTS
 
The material underlying the present study at Kentucky is based on work supported by the Cooperative State Research, Education and Extension Service, U.S. Department of Agriculture, under Agreement No. (KY0-05019). Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the U.S. Department of Agriculture.

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

1 The mention of trade or manufacturer names is for information only and does not imply an endorsement or recommendation by the authors. Back


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




This article has been cited by other articles:


Home page
 Agron. J.Home page
D. F. Roberts, V. I. Adamchuk, J. F. Shanahan, R. B. Ferguson, and J. S. Schepers
Optimization of Crop Canopy Sensor Placement for Measuring Nitrogen Status in Corn
Agron. J., January 8, 2009; 101(1): 140 - 149.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Agricola
Right arrow Articles by Pena-Yewtukhiw, E. M.
Right arrow Articles by Johnson, J. T.
Related Collections
Right arrow Nitrogen
Right arrow Geostatistics
Right arrow Spatial Variability
Right arrow Remote Sensing

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Crop Science Vadose Zone Journal
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome