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Published online 11 April 2006
Published in Agron J 98:554-561 (2006)
DOI: 10.2134/agronj2005.0164
© 2006 American Society of Agronomy
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Site-Specific Analysis and Management

Univariate Distribution Analysis to Evaluate Variable Rate Fertilization

E. M. Pena-Yewtukhiwa, Gregory J. Schwabb,* and L. W. Murdockc

a Division of Plant and Soil Sciences, West Virginia Univ., P.O. Box 6108, Morgantown, WV 26506
b Dep. of Agronomy, Univ. of Kentucky, N-122 Agric. Sci. North, Lexington, KY 40546
c Univ. of Kentucky Research & Education Center, 1205 Hopkinsville Street, P.O. Box 469, Princeton, KY 42445-0469

* Corresponding author (gjschw2{at}uky.edu)

Received for publication May 30, 2005.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 CONCLUSIONS
 REFERENCES
 
Technological advances in precision fertilization such as yield monitors and remote sensing are increasing the density of samples collected and decreasing the scale inputs can be managed in the field. A compounding problem is that fertilizer applications can often be made at a much smaller scale than yield data can be collected. Analytical tools such as ANOVA and geostatistics can be used on high-density data sets; however, these analytical tools do not provide all the information required to test research ideas. An alternative to solve this problem is the use of statistics not traditionally applied to precision agricultural experiments. The objective of this study was to determine if univariate distribution (population statistics) analysis is useful in the study of wheat (Triticum aestivum L.) yield response to variable-rate N fertilization strategies using active optical sensors in red and near-infrared bands (NDVI [normalized difference vegetative index] sensors). Measurements of NDVI and fertilizer applications were on a 0.56-m2 basis, while wheat yield data were collected at a 2-m2 scale. Classical ANOVA was conducted to compare treatment effects. Analysis of univariate distributions for NDVI and wheat yield monitor data sets was used to further evaluate the effect of the treatments. In addition to a significant effect on the mean NDVI and yield, fetilizer staregies affected the normality, median, mode, skewness, and kurtosis of the resulting NDVI and yield distributions. Unlike ANOVA, the analyses of univariate distributions provided an insight on those portions of the NDVI and yield populations responsible for changes in the mean.

Abbreviations: NDVI, normalized difference vegetative index


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 CONCLUSIONS
 REFERENCES
 
NEW TECHNOLOGIES developed for precision farming provide an innovative way of collecting spatial data via the use of sensors. Sensors have the inherent capability of acquiring a large number of observations in a short time. Electrical conductivity sensors, yield monitors, and other precision agriculture sensors produce high-density geo-referenced data. This particular characteristic of these data sets imposes both restrictions and advantages on the information obtained and on analysis of these data. Restrictions are imposed by the large number of data points that need to be analyzed, but the advantage is the volume of information that the equipment can collect in a short time. There are two phases in precision agriculture data analysis that need specific consideration. These are: (i) the research phase, and (ii) the application (the farmer's control) phase. In the research phase, it is necessary to use sophisticated scientifically accepted experimental design and data analysis methods (ANOVA). For the application phase, growers require data analysis methods that are easy to use, often executed by "canned" programs for simple yield monitor statistical analysis and mapping.

It has been necessary to develop new analytical methods for such data sets. Researchers such as Whelan et al. (2001) proposed the use of "local kriging" as an alternative for spatial analysis of the yield monitor data. This method deals with highly dense spatial data sets and requires increased computation time. Diker et al. (2004) used frequency analysis to separate yield-response-based management zones. They separated the yield into classes, studied both spatial and temporal stability, and concluded that frequency analysis could be used to study yield class variability.

Recently, there have been technological improvements in the detection of N nutritional stress using spectral reflectance from the crop canopy, which is then used to adjust the N fertilization rate "on the go." The possibility of adjusting N fertilization "on the go" allows varying N input rates in space, which results in a VRN (variable-rate nitrogen application). The technology is based on active sensors that measure the reflectance of light emitted from the sensor. Coupled with the NDVI sensors is a VRN system called the GreenSeeker system (Beck and Vyse, 1995). The system was developed at Oklahoma State University and is now commercially available through Ntech Industries (Ukiah, CA). This system applies urea–NH4NO3 solution through a set of three adjacent nozzles that can be turned on and off in any combination to deliver from zero to seven times the base fertilizer rate. Each set of nozzles has an active NDVI sensor on the leading side of the tool bar to control the N application rate. The NDVI is an indicator of the greenness of the crop canopy. Using this applicator, the fertilizer N rate is determined by a mathematical algorithm that estimates N requirement based on the predicted yield potential of each 0.56-m2 area, seasonally adjusted for the crop's responsiveness to applied N (Raun et al., 2005, 2001; Lukina et al., 2001).

In using the NDVI approach, the study of the outcome of treatments imposed on the field is only a part of the research associated with the VRN. Another part is the establishment of the algorithms to be recommended to growers. Because of the dense data sets that NDVI sensor technology generates, definition of spatial structure and spatial correlation is not an issue; however, the large numbers of sensors and data analysis requirements increase sampling costs and might complicate the analysis. In this study, we proposed the use of univariate distribution analysis to study field-scale fertility experiments using NDVI and VRN technology.

Analysis of variance has commonly been used to study the effects of imposed treatments on determined response variables. Analysis of variance is defined as the process of dividing the total variability of experimental observations into portions attributable to recognized sources of variation (Lentner and Bishop, 1986). This method has been used to study the effect of fertilization treatments on yields of numerous species (Li et al., 2001); however, this method is limited. It assumes that all the measured yields come from the same population, but the characteristics of that population are not examined (Snedecor and Cochran, 1974). In other words, the conclusion is to reject or not reject the hypothesis, but the way in which a fertilizer treatment might affect the yield population is unknown. Li et al. (2001) reported that N treatment did not explain differences in cotton (Gossypium hirsutum L.) canopy NDVI readings and cotton lint yield in 1998, but did in 1999. Since NDVI readings are a very dense data set, composed of results from small areas, an examination of univariate population statistics between treatments might provide additional information.

Univariate distribution analysis has been used in many disciplines to study the characteristics of the population or data set. Distributions have certain characteristics, known as parameters. The parameters describe the population of data: the midpoint (mean, mode, median), spread (standard deviation, variance) and symmetry (skewness, kurtosis) of the distribution (Davis, 1986). The distribution of the data is represented by a histogram. The histogram gives visual information about the midpoint, spread, and symmetry of the data population. When a process is studied and functional characteristics are known, the histogram enables one to perceive subtleties regarding the functioning of the physical process that is generating the data population. Based on the objective of the study and prior knowledge, the histogram can suggest both the nature of, and possible changes in, the physical mechanisms at work in the process. This is an important difference from ANOVA of population means.

Population statistics or univariate distribution analysis has been used for quality control in manufacturing. In the social sciences, univariate statistics have been used to characterize the frequency of behavioral patterns in a specific social group such as women in dual-career–wage-earner families (Reeves and Darville, 1994). The characterization of rain events and subsequent water flux, used to construct dams, are based on univariate analysis of both the flux and rain events during a given period of time (Serrano, 1997). In the environmental sciences, principal component analysis and univariate statistics were used to determine the zooplankton group (cladocerans) that showed the highest sensitivity to the pesticide azinphos-methyl [S-(3,4-dihydro-4-oxobenzo[d]-[1,2,3]-triazin-3-ylmethyl) O,O-dimethyl phosphordithioate; Sierszen and Lozano, 1998].

Univariate distributions of continuous variables ignore the temporal and spatial context of the data. In the histograms, continuous data are discretized into classes, generally of equal width, and the proportions of individuals in each class are recorded. The relative proportions are the class frequencies (Goovaerts, 1997; Isaaks and Srivastava, 1989).

The rational for using univariate distribution analysis in variable fertilizer rate evaluations is that the different fertilization algorithms divide the population of NDVI values into classes, and then treat each class with a particular rate of fertilizer N. Plotting the yield histogram indicates the most common system response, the distribution of the data, the presence of outliers, and the symmetry in the response data.

The objective of this study was to determine if univariate distribution analysis can characterize the changes (shift responses) in wheat NDVI and yield data population histograms due to the use of different flat- and variable-rate N fertilization strategies implemented with spray nozzles controlled by active NDVI sensors.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 CONCLUSIONS
 REFERENCES
 
Data were collected from an ongoing study evaluating NDVI-based algorithms for wheat N management. The study site is located in Woodford County near Lexington, KY, USA. The study tested four different N requirement prediction algorithms. The four algorithms were: (i) the current best management practice (Flat 1) used by Kentucky growers, consisting of flat rates of 45 and 84 kg N ha–1 in split applications at Feekes 3 (F3) and Feekes 6 (F6), respectively; (ii) a flat rate of 45 kg N ha–1 at F3 followed by a variable rate (Variable 1) applied at F6 (Raun et al., 2005); (iii) variable rates applied at F3 and F6 (Variable 2); and (iv) flat rates at F3 and F6 consisting of the average applied N rate at each of these growth stages in Treatment 3 (Flat 2). The total N applied in each treatment, at each growth stage, is given in Table 1.


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  		Table 1. Total N application rate used at F3 (Feekes 3) and F6 (Feekes 6) growth stages, and total used for each treatment.

 
Each treatment consisted of four replications of a 6.1- by 250-m strip plot, laid out in randomized blocks in a 2.6-ha block (Fig. 1 ). A 6.1-m plot sprayer manufactured by Ntech Industries (Ukiah, CA) and equipped with eight red NDVI sensors was used for this study. Each sensor electronically controlled three stacked nozzles capable of delivering from zero to seven times the base rate of liquid N fertilizer. The N fertilizer rate was adjusted approximately every 0.1 s.


Figure 1
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  		Fig. 1. Treatments and allocation of replications: gray = Flat 1; stripes = Variable 1; dots = Flat 2; black = Variable 2.

 
For all of the variable-rate treatments, at either growth stage, NDVI values <0.26 were assumed to cover bare soil, so no N was applied. The Variable 1 algorithm consisted of a flat rate of 45 kg N ha–1 at F3 followed by a variable rate at F6, applying the highest rate of N to the lowest NDVI areas of the field. The fertilizer N rate decreased to zero when the canopy NDVI was equal to the NDVI of a high-N reference strip (Fig. 2 ) placed in the center of the study field.


Figure 2
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  		Fig. 2. Nitrogen application rate at (A) Feekes 3 wheat growth stage and (B) Feekes 6 for Treatment 2 (Variable 1).

 
In soft red winter wheat production, tillering and tiller survival can be enhanced by an early N application at F3 (Scharf and Alley, 1993; Weisz et al., 2001). For the Variable 2 algorithm, the F3 N application rate was based on tiller density. Tiller density was determined in several areas within the study and a hand-held sensor was used to determine NDVI at each location (Phillips et al., 2004). The field-scale application was then programmed so that areas with very thin stands (<540 tillers m–2) received 65 kg N ha–1, areas where tiller density was between 540 and 1080 tillers m–2 received 35 kg N ha–1, and areas where tiller density was >1080 tillers m–2 received no N at F3. At F6, the Variable 2 algorithm called for relatively low N applications where NDVI was low, with increasing amounts of N up to the average NDVI, and then decreasing N incrementally to zero when the NDVI equaled the NDVI of the non-N-limited strip (Fig. 3 ). The field-averaged rates of N used in executing the Variable 2 algorithm were 37 kg N ha–1 at F3 and 44 kg N ha–1 at F6, and were applied uniformly in the fourth treatment (Flat 2).


Figure 3
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  		Fig. 3. Nitrogen application rate at (A) Feekes 3 wheat growth stage and (B) Feekes 6 for Treatment 3 (Variable 2).

 
Strip-plot yields were determined by harvesting the center 4 m of each strip plot using a 2-m-wide plot combine equipped with a yield monitor that recorded yield approximately every linear meter (approximate area of 2 m2). Two passes were made in each strip plot, and whole-strip-plot yields were verified by placing harvested grain from each strip plot in a weigh wagon.

Analysis of variance was performed on whole-strip-plot mean yields as measured by weighing. For each N fertilizer treatment, Pearson correlation analysis was used to correlate NDVI values for both F3 and F6 growth stages. Population analysis for yield monitor and NDVI data sets (at both F3 and F6) was performed with PROC UNIVARIATE SAS (SAS Institute, 1996). Mean, mode, median, standard deviation, and skewness were the population parameters calculated. Data histograms and goodness of fit for normality (Shapiro–Wilk statistic) were also calculated. Comparisons of population parameters, goodness of fit, and frequency histograms for each treatment were performed. Histograms of the univariate distribution were performed by creating 10 classes of the same width for both yield and NDVI data.

The NDVI values and the resulting execution of the variable-rate N fertilization algorithm have a spatial component that is not considered when a univariate distribution analysis (population analysis) is performed; however, each NDVI value represents a specific area where a specific rate of N fertilizer is to be applied. The NDVI and yield were measured at different resolutions: 0.56 and 2 m2, respectively; however, we created a new NDVI population that better related to wheat harvest sampling areas. Each wheat yield datum had a specific position and area in the field. We averaged the F3 and F6 NDVI values so as to arrive at an NDVI data population that represents each 2-m2 harvest area. Population comparisons between the 0.56-m2 NDVI values and the 2-m2 averaged NDVI values at F6 were performed by comparing the frequencies of values observed in each NDVI class. The effects of the fertilization treatment and algorithm on F3 and F6 NDVIs and wheat yield were analyzed using a population–histogram approach.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
CONCLUSIONS
 REFERENCES
 
Four sets of data emanating from the four treatments were used to test the use of the population statistics and frequency histograms method. The use of data obtained according to the four different fertilization algorithms permits the use of different scenarios to test the proposed analysis.

Analysis of Variance
An ANOVA indicated that imposed fertilization treatments resulted in significant differences among average wheat yields (Table 2). The higher fertilization rate treatments, Flat 1 and Variable 1, resulted in higher average wheat yields and the average lower fertilization rates, Variable 2 and Flat 2, had lower average yields (Table 3). The Flat 2 treatment was significantly lower yielding than either Flat 1 or Variable 1, but Variable 2 yield was not significantly different than that observed with Variable 1.


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  		Table 2. Summary of ANOVA for winter wheat yield.

 

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  		Table 3. Mean grain yields for N fertilization treatments–algorithms ({alpha} = 0.05).

 
The ANOVA found that the fertilization treatments affected average yields, and that the location (blocking) of the strips in the field did not significantly influence mean yield variation; however, ANOVA did not give any information about how the site-specific N fertilization treatments affected the population distribution of the 2-m2 wheat yields.

Univariate Distributions Analysis of Normalized Difference Vegetative Index and Wheat Yield
Three of the N fertilization algorithms had uniform applications at F3: Flat 1 (Treatment 1), Variable 1 (Treatment 2), and the Flat 2 algorithm (Treatment 4). It was expected that, with plant development and greater canopy cover, NDVI values would increase between F3 and F6; however, changes in the shape of the distribution of NDVI values was not expected because the whole field is uniformly managed. We assumed for each treatment that changes in the NDVI value population between F3 and F6 were the result of the fertilization at F3.

Effects of Nitrogen Treatments on Normalized Difference Vegetative Index Values
Before N fertilization at F3, the NDVI data populations were normally distributed, with a negative skew for all treatments, and with small differences in the mean and coefficient of variation (Table 4). After N fertilizer application at F3, normality was lost in the Flat 1 and Variable 1 treatments. Both treatments received 45 kg N ha–1 at F3, and exhibited greater negative skewness in NDVI values measured at F6. The Flat 2 and Variable 2 treatments received only 37 kg N ha–1 at F3 and maintained a normal distribution in NDVI values measured at F6 (Table 5, Fig. 4a and 5a .).


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  		Table 4. Population statistics for normalized difference vegetative index values calculated at the Feekes 3 wheat growth stage.

 

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  		Table 5. Population statistics for normalized difference vegetative index values calculated at Feekes 6 wheat growth stage.

 

Figure 4
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  		Fig. 4. Frequency of (a) normalized difference vegetative index (NDVI) values calculated at the Feekes 6 wheat growth stage and (b) wheat yields for the Flat 1 treatment.

 

Figure 5
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  		Fig. 5. Frequency of (a) normalized difference vegetative index (NDVI) values calculated at the Feekes 6 wheat growth stage and (b) wheat yields for the Variable 1 treatment.

 
The Flat 1 treatment did increase wheat biomass and, as a consequence, the average NDVI increased, too; however, it also increased the frequency of high NDVI values compared with low NDVI values, creating a high negative skewness (Fig. 4a, Tables 5 and 6). The Variable 1 treatment area was subjected to the same F3 N application treatment, and changes in the population of F6 NDVI values were similar to those observed for Flat 1 (Tables 4 and 5, Fig. 5a). The application of a lower flat N rate (Flat 2) did somewhat change the NDVI distribution from that measured at F3, but the skewness averaged only one-half that resulting from the application of a high N rate (Tables 4 and 5, Fig. 7a). This indicates that the greater N rate did result in either greener plants or a higher tiller density.


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  		Table 6. Population statistics for normalized difference vegetative index values calculated at the Feekes 6 wheat growth stage and composite to give a single value for each 2 m2.

 

Figure 7
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  		Fig. 7. Frequency of (a) normalized difference vegetative index (NDVI) values calculated at the Feekes 6 wheat growth stage and (b) wheat yields for the Flat 2 treatment.

 
The Variable 2 treatment was applied to a wheat crop exhibiting a nearly normal population of NDVI values at F3, and the result of that application was a slight increase in the proportion of higher NDVI values at F6, without substantially changing the shape of the F6 NDVI distribution (Tables 4 and 5, Fig. 6a ).


Figure 6
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  		Fig. 6. Frequency of (a) normalized difference vegetative index (NDVI) values calculated at the Feekes 6 wheat growth stage and (b) wheat yields for the Variable 2 treatment.

 
Comparison between Normalized Difference Vegetative Index for Flat and Variable Nitrogen Rates
The application of variable-rate N fertilizer (Variable 2) at F3 affected NDVI differently than the same rate applied uniformly (Flat 2). Although both NDVI populations maintained normality, the difference in skewness between the NDVI populations for Flat 2 and Variable 2 was greater at F6 than at F3 (Tables 4, 5, and 6). Compared with Flat 2, the Variable 2 treatment reduced the coefficient of variation by reducing the incidence of low NDVI values, while increasing the incidence of NDVI values near the mean (Table 5, Fig. 6 and 7) .

These NDVI measurements had a spatial component, and spatial changes in NDVI between F3 and F6 depended on the N fertilization treatment. Using Pearson simple correlation analysis, it was observed that the correlation between NDVI values at F3 and F6 was significant and positive (r = 0.31) for flat-N-rate treatments (Flat 1 and Flat 2); however, for the Variable 2 treatment where higher N rates were applied to field areas exhibiting lower NDVI values, the correlation was not significant (r = 0.15). These results were expected, given that flat-rate N applications tend to reinforce existing crop color patterns, while variable N rates tend to do just the opposite.

Relating Population Normalized Difference Vegetative Index and Yield Observations
The fertilization treatments applied at F3 cannot be directly related to the resulting wheat yield; however, based on the assumptions that the NDVI is related to the health of wheat plants and that healthy plants yield more, we tried to relate wheat yield to NDVI measured at F6, the N fertilization treatment, or both. All the N treatments produced normally distributed yield populations (Table 7). Using the coefficient of variation as a dispersion indicator, we can analyze the population of yield observations resulting from each treatment. Variable 2 exhibited the most compact, least dispersed distribution (lowest standard deviation and skewness; Table 7). The most dispersed was Flat 2, followed by Flat 1 and Variable 1. The main differences between the treatment yield populations were in their values for skewness and kurtosis. The Variable 1 yield population exhibited greater data frequencies close to the mean (Table 7, Fig. 5b), while the Flat 1 yield population exhibited a longer tail toward lower yield values. Because each NDVI value represents an area, the Flat 1 treatment increased all the NDVI values on an area basis, but lower NDVI values were less responsive to this treatment (Fig. 4a and 4b). The N fertilization treatments changed not only the average yield, but also the characteristics of the population of yield observations. The population of yield observations could be related to spatial differences in yield response, as each yield measurement represents an area of the field. The population of yield observations represents all possible yield values for an area of 2 m2 in the field. The area was determined by the harvest combine characteristics. For example, although the Flat 1 treatment produced the highest average yields, the existence of lower yields—areas that did not respond equally to the N fertilizer input—was evident in the yield population histogram.


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  		Table 7. Wheat yield population statistics.

 
Variable 1 and Flat 1 received the same constant N fertilizer rate at F3, and the variable N rate was applied at F6. Using population statistics analysis, we observed that the Variable 1 treatment produced high yields, and the variable-N-rate application decreased the unresponsive areas, compared with Flat 1, while increasing the number of areas that produced yields close to the treatment average (Fig. 4b and 5b).

Conversely, Variable 2 and Flat 2 exhibited the lowest yields due to higher frequencies in the lower yield ranges. The main difference between these two treatments was that the Variable 2 treatment resulted in a higher frequency of greater yield values than did the Flat 2 treatment. Another difference was that the Flat 2 treatment exhibited the smallest range in yield values, while the Variable 2 treatment resulted in the highest range (Fig. 6b and 7b).

Treatment Effects on the Relationships between Normalized Difference Vegetative Index Values at Feekes 3 and Feekes 6 and Wheat Yield
The relationship between yield and NDVI at F6 is confounded for treatments where there is an application of N at the time of sensing (on the go); however, uniform application treatments are easier to analyze because one would not expect a change in the distribution of the population NDVI values. Assuming that the distribution in NDVI values between F6 and harvest does not change, we could expect that the yield population at high flat rates would be skewed, favoring high yields over lower ones—in other words, we are overfertilizing. This assumption was confirmed with the results of the Flat 1 treatment (Fig. 4). For low flat rates of N, the yield population is not skewed; the data are closer to a normal distribution.

The effect of a variable-N-rate treatment applied at F6 could be related to the resulting yields via NDVI analysis. We assumed that the Variable 1 treatment could be expected to increase the interquartile range because the N application algorithm decreases the applied N rate as the NDVI increases, and this treatment was applied to an initially highly negatively skewed population of F6 NDVI values. The resulting distribution of yield data supported our previous assumption (Fig. 5). The Variable 2 treatment was applied to field area exhibiting a nearly normal population of NDVI values at F6, and this algorithm favors higher N application rates at average NDVI values. As such, it was expected that the distribution of yield observations would be similar to that of the distribution in F6 NDVI values, which was observed in this trial (Fig. 6).

Each NDVI reading represented a field area of 0.5 m2; however, the harvest area for yield was different (2 m2). Repeating the analysis using average NDVI values calculated for each harvest area, the first step was to develop histograms for each treatment's set of data and compare this with that of the larger NDVI data set (from which it was extracted). If the statistical parameters describing the new distribution were different from those of the more dense NDVI population, any relationships between wheat yield and these calculated average F6 NDVI values that we established would be questionable. We did compare the frequency distributions for both sets of data, for each treatment's classes (Table 8). In all cases, these frequency distribution comparisons exhibited a high correlation (R2 > 0.97). This confirmed that the analysis previously used on the 0.5-m2 NDVI values could be applied to the smaller population of 2-m2 averaged NDVI values.


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  		Table 8. Relationships between 0.5-m2 (point) normalized difference vegetative index values (NDVI p) and averaged 2-m2 (aerial) NDVI values (NDVI a) for each treatment, including regression coefficients for frequency distributions.

 
A final observation about the variable-rate algorithms Variable 1 and Variable 2 is that both algorithms recommend decreasing N rates once NDVI exceeds 0.65 (Fig. 8 ).


Figure 8
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  		Fig. 8. Comparison between recommended N rates by Variable 1 and Variable 2 algorithms (NDVI = normalized difference vegetative index).

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 CONCLUSIONS
REFERENCES
 
While it is early to draw specific conclusions regarding the performance of the N fertilization algorithms, the results presented here demonstrate the utility of univariate analysis for large data sets. The ANOVA enabled mean comparisons among the flat and variable N rates, but univariate analysis provided insight on the mechanisms responsible for changes in the mean values. Population analysis does not use spatially referenced data, but because of the high sample density, these data fully represent the spatial population. Since each yield and NDVI reading represents an area in the field, population analysis gives a good idea of how areas within the field responded to a given N fertilization algorithm. Moreover, the fact that each sampling point can be assigned a specific location in the field permits the data user the option of a geostatistical analysis.

We observed that the Variable 2 treatment targeted specific areas in the field, reducing the frequency of low-yielding areas and causing a more consistent yield across the whole field. In contrast, the Flat 1 treatment did not target specific areas. Rather this treatment favored the best areas of the field, producing a greater frequency of high-yielding areas, but also persistence of low-yielding areas. The effect of variable and constant N fertilizer rate applications was observed in analysis of the population of NDVI values and changes in those populations between F3 and F6. Population analysis also illuminates the effects of the different N fertilization algorithms on wheat yields, and their relationship to NDVI measurements at F6.

On-the-go N fertilization technologies do not take location into account, as occurrence of a given NDVI triggers a programmed rate of N application. Univariate distribution analysis does not take into account the spatial location of NDVI or yield data, but does give insight into changes in the data population in response to a specific N fertilization treatment. In conclusion, this method is useful in the development and evaluation of new management practices that are based on site-specific technologies that generate high-density data sets.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 CONCLUSIONS
 REFERENCES
 




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E. M. Pena-Yewtukhiw, G. J. Schwab, J. H. Grove, L. W. Murdock, and J. T. Johnson
Spatial Analysis of Early Wheat Canopy Normalized Difference Vegetative Index: Determining Appropriate Observation Scale
Agron. J., February 29, 2008; 100(2): 454 - 462.
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