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Relationship Between Coefficient of Variation Measured by Spectral Reflectance and Plant Density at Early Growth Stages


D.B. Arnall,1 W.R. Raun,1 J.B. Solie,2 M.L. Stone,2 G.V. Johnson,1 K. Desta,1 K.W. Freeman,1 R.K. Teal,1 K.L. Martin1

 1Department of Plant and Soil Sciences, 2Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078. Contribution from the Oklahoma Agricultural Experiment Station.


The use of by-plot coefficient of variation (CV) has not been evaluated in precision agricultural work.  An area of wheat with good stand establishment yet nutrient deficient can have the same average NDVI as an area with a poor stand of nutrient enriched wheat.    This study evaluated the relationship of CVs determined from normalized difference vegetative index (NDVI) sensor readings collected from 1 m2 areas and plant population, and sensing direction in relation to the crop row direction on NDVI values and the CV from spectral radiance measurements.  From 2003 to 2004, 7 site years with randomly selected plots, measuring 1m by 1m (2003) and 3 m by 1 m (2004), were established for this study.  The 3m by 1m plots were divided into three 1 m2 sub-plots with nitrogen (N) treatments; 0, 120 kg ha-1 fall applied, and 80 kg ha-1 top-dress.  Sub-plots were sensed at Feekes 5 and Feekes 7 using the Green Seekerô hand held sensor.  Results showed that CV from NDVI readings was a good predictor of early season plant stand. The relationship between vegetative RI (RINDVI) and harvest RI (RIHarvest) was shown to improve with increasing CV values.  The prediction of RIHarvest was improved when CV was integrated into the RINDVI calculation.  Seed row direction had no affect on NDVI readings using the Greek Seeker sensor.  RIHarvest can be better predicted with RINDVI when the CV of spectral radiance measurements is used in the RINDVI equation. 



The world applied approximately 82 million metric tons of nitrogenous fertilizers in 2001 (FAO, 2002).   Cereal grains accounted for 60% of the total N fertilizer applied in 1994 (FAO, 1995).  Only 33% of the fertilizer N used for cereal grain crops is removed in the grain (Raun and Johnson, 1999).

 Plant N losses in winter wheat have accounted for between 21% (Harper et al., 1987) and 41% (Daigger et al., 1976) of the total N lost using N15.  Loss of gaseous N due to denitrification is reported to range from 10% (conventional tillage) to 22% (no-till) in corn (Hilton et al., 1994).  In addition, fertilizer N losses in surface runoff range between 1% (Blevins et al., 1996) and 13% (Chichester and Richardson, 1992) of the total N applied.  Lower levels of losses due to run-off are usually associated with no-till conditions.  An additional pathway for N loss is through leaching of NO3-  when applied in excess of crop need.  In cooler temperate climates, NO3-N losses through tile drainage have approached 26 kg N ha-1 yr-1 under conventional tillage corn when only 115 kg N ha-1 was applied (Drury et al., 1996). 

While plant loss accounts for a very large portion of N loss, loss from the soil environment still accounts for a high percentage.  If any one of the pathways can be restricted and loss reduced, the benefit is significant.  Johnson and Raun (2003) calculated that a 1% global increase in cereal NUE would have a value of $235 million in N fertilizer savings if yields were maintained. Raun et al. (2002) reported an improvement in NUE of >15% when N fertilization was based on optically sensed in-season estimated yield (INSEY).

The GreenSeeker Hand Held Optical Sensor (NTech Industries, Inc. Ukiah CA.), developed by Oklahoma State University, senses a 0.6 x 0.01 m area when held at a distance approximately 0.6 to 1.0 m from the illuminated surface.  The sensed dimensions remain approximately constant over the height range of the sensor.  The sensor unit has self-contained illumination in both red (660 Ī 10 nm) and NIR (767 Ī 15 nm) bands.  The device measures the fraction of emitted light in the sensed area that is returned to the sensor (reflectance).  The algorithm currently used by N-Tech Industries, "WheatN1.0", includes several distinct components.  Raun et al.(2005a) identified three specific components: 1) mid-season prediction of grain yield, determined by dividing NDVI by the number of days from planting to sensing (estimate of biomass produced per day from planting to the specific date when sensor readings are collected); 2) estimating temporally dependent responsiveness to applied N by placing non-N-limiting strips in production fields each year, and comparing these to the farmer practice (fertilizer response index); 3) determining the spatial variability within each 0.4 m2 area using the CV from NDVI readings.

The results of previous work have shown that stand density and uniformity have an affect on grain yield.  Weisz et al. (2001) reported that as plant stand or tiller density increased, grain yield tended to increase, and the variation within the field decreased.  Nielsen (2001) showed that in corn for every 2.56 cm standard deviation of plant-to-plant spacing there was a decrease in yield of 1567 kg ha-1 from the average yield of 9800 kg ha-1.  This indicates the need to make fertilization recommendations with stand density as a factor.  Flowers et al. (2003) validated the use of aerial photography for determining winter wheat tiller density.  Using the density estimates, he determined that basing N application on a critical density threshold had an 85.5% success rate.  Lukina et al. (2000) observed that as the vegetation coverage increased, the CV of NDVI values decreased. Raun et al. (2001) showed that NDVI values from mid-season sensor readings could be used to predict yield.  Combining NDVI and CV independently may result in improved prediction of yield potential. 

CV is defined as the standard deviation divided by the mean (Tippett, 1952; Senders, 1958; Steel et al., 1997; Lewis, 1963).  Steel et al. (1997) describe CV as a quantity of use to the experimenter in evaluating results from different experiments of the same unit of measure, that are possibly conducted by different persons.  Little and Hills (1978) suggested that CV can be used to compare experiments involving different units of measurements and/or plot sizes.  The CV is a relative measure of variation and varies with every comparison on what is considered large or small, and only experience with similar data can determine its meaning (Steel et al., 1997). 

In an evaluation of sixty-two, wheat field research projects, Taylor et al. (1997) observed that mean yield and CV were negatively correlated.  The work by Taylor et al. also showed that CVs decreased with corresponding decreases in plot size. Washmon et al. (2002) suggested that if within field CVs could be predicted, the potential response to added nutrients may also be established, and in-season nutrient additions adjusted accordingly. They further stated that the mid-season CV of a field could be equated to the response index, which is currently used by various researchers to determine topdress fertilizer rates. 

Raun et al. (2005a) predicted that when CV was low, a responsive field element should be capable of greater yield than when a similarly responsive field element CV was large.  In testing this concept, they observed that YPN-CV (predicted yield with added N using INSEY and the CV at the time of sensing), values more closely followed observed yield than did YPN (predicted yield using the INSEY equation) values.  Morris (2005) noted that when plot CVs of NDVI readings were >18, maximum yields could not be achieved when N fertilizer was delayed until mid-season.  When plot CVs were < 18, delaying all N fertilization until mid-season resulted in maximum yields and increased NUE.  

The current GreenSeeker sensor collects more than 10 readings within each 0.4 m2 traveling at 10 mph (Raun et al., 2005a).  Raun et al. (2005a) states that the 10 readings collected from each 0.4 m2 are considered to be sufficient to obtain a composite sample to reliably estimate the average, from such a small area, understanding that the 10 sensor readings were representative of the variability from the same 0.4 m2 surface area. 

            The variable rate method is a vast improvement on the use of 15 soil samples to represent a unit area that could range from a few acres to several hundred acres (Johnson et al., 2000).   If the goal is to maximize crop NUE, the use of averaged normalized difference vegetative index (NDVI) values, obtained from spectral reflectance measurements, presents a problem.  Currently, two 0.4 m2 areas with similar NDVIs would receive the same treatment, but could need two different rates.  A good stand of nutrient deficient wheat may have the same average NDVI as a poor stand of nutrient enriched wheat.  The ability to index plant stand density on-the-go may provide the needed solution.  The effect of plant population and tiller density on the GreenSeeker sensorís ability to correctly determine yield potential has not yet been assessed.

            The objectives of this work were to determine the relationship between the CV of measurements of NDVI and plant population at early growth stages. Sensing direction in relation to the crop row direction on the CV from spectral radiance measurements were also evaluated, in addition to the change in CV over time.


Experimental sites were established at EFAW Research farm in Stillwater, the Hajek farm in Hennessey, the Lake Carl Blackwell Research Station near Stillwater, and the Perkins Research Station near Perkins in the spring of 2003. The same sites were used in 2004 excluding the Hajek farm.  The soil classification for the sites is listed in Table 1.  All planting and management dates are reported in Table 2.  

In 2003, thirty plots were randomly selected at the Hajek farm and the EFAW farm.   Forty-five plots were randomly selected at the Perkins station and Lake Carl Blackwell farm.  Plots were established after germination at Feekes 1 (emergence).    The plots were established at this stage so that the plots would be oriented with seed rows.  Plot size measured 1.48 by 1.48 m, with each plot containing eight rows spaced 15 cm apart.  A total of 150 plots were used. 

In 2004, the experiment was modified to include three N treatments (0, 120 kg ha-1 fall applied, and 80 kg ha-1 topdress) each applied to a plot of 1.48 m by 4.44 m.  The treatment structure was the same for all plots. Each plot was randomly selected within each location. Twenty-five plots were established at EFAW, Lake Carl Blackwell, and Perkins at Feekes 1. 

Plant stand density was estimated for each plot at Feekes 1 by counting all plants within four rows randomly selected in each plot. This count was preformed prior to tillering; therefore, each shoot was recorded as a plant. The 120 kg ha-1 N was applied at plot establishment in fall and the 80 kg ha-1 N was topdressed at Feekes 6 (first node visible) using urea (46-0-0, N-P-K).

 Spectral radiance measurements were taken using the GreenSeeker Hand Held Optical Sensor Unit.  The device used a technique to measure crop reflectance and to calculate NDVI.   The equation for NDVI is shown below.


Where     ρNIR   - Fraction of emitted NIR radiation returned from the sensed area (reflectance)

  ρRed  - Fraction of emitted Red radiation returned from the sensed area (reflectance)

              In the 2003 season at the EFAW research station and Lake Carl Blackwell farm locations, sensing was performed once a week until maturity.  Readings were taken from Feekes 5 (leaf sheaths strongly erect) through Feekes 8 (flag leaf visible) at the Hajek farm and Perkins Research Station. A total of four sensor passes were made on each plot, holding the sensor approximately 75 to 100 cm above the crop canopy. The sensor path was parallel to the seed rows; two passes were made midway between the second and third rows, then sixth and seventh rows.  Two sensor passes were taken perpendicular to the seed rows with the passes made parallel to the plot borders and offset approximately 30 cm from the plot borders.  Time for each pass was three seconds.  Approximately thirty NDVI readings were collected with each pass.  In 2004, sensing began at all locations in January at or near Feekes 3 (tillers formed) and continued until physiological maturity.  Also in 2004, a fifth pass was added to the sensing plan, directed at a 45-degree angle to the planting direction on each subplot, for the purpose of complete evaluation of sensing direction.

  For the 2003 season, wheat head counts were taken at maturity by counting the number of heads in the rows, which had been used to estimate plant population.  In both seasons, a 1 m2 section from the center of each plot or sub-plot was harvested at maturity using a hand sickle and cutting slightly above the crown.  The harvested samples were dried, weighed and threshed using a mechanized thresher.  Sample grain was then weighed to determine yield of each plot.  Total grain N content was determined using the Carlo Erba NA 1500 Series 2 nitrogen analyzer, in the 2004 samples.  From this measurement and grain yield data.  

Two response Indices (RI) i.e. harvest RI (RIHarvest) and vegetative RI (RINDVI) were calculated using the following equations (Raun et al., 2002).


Where      YieldN-Rich = Yield of the N-Rich plot

              YieldCheck = Yield NDVI of the Check plot


Where      NDVIN-Rich = Average NDVI of the N-Rich plot

              NDVICheck = Average NDVI of the Check plot

Several equations were evaluated to improve the ability of the RINDVI to predict final yield with inclusion of CVs. The data was subjected to statistical analysis using SAS (SAS Institute, 2002).  Simple regression was the primary form of trend analysis for both measured and calculated response variables but Cate-Nelson, linear-linear and linear-plateau models were also investigated.


Using the Cate-Nelson model across all site-year combinations, a critical CV range of 17 to 20 was determined (Figure 1).  Figure 2 illustrates the change in CV of treatments over time, from January until physiological maturity; this trend was similar at all three locations in the 2004 crop year.  The maximum CV occurred near growth stage Feekes 6, (stem elongation) at all locations.  Also, CV was affected by N-treatments, but the trend of CV over time was generally the same across treatments (Figure 2).

The linear relationship (R2 = 0.17) between RIHarvest and RINDVI over all three locations is shown in Figure 3.  When this data was separated by CV values, it can be seen that with increasing CV there was an improvement in the relationship between RIHarvest and RINDVI.  When the CV of the fertilized plot was 10 or less there was no linear relationship between RIHarvest and RINDVI (R2 = 0.002), Figure 4.  Figure 5 shows the linear relationship of the two RIís when CV is between 10 and 25 (R2 = .19).  Figure 6 shows the relationship of the two when CV is greater than 25 (R2 = .30).  

Incorporating CV into the calculation of RI as RINDVI-CV, significantly improved the relationship with RIHarvest (R2 = 0.38, Figure 7) when compared with that of RINDVI and RIHarvest. The best equation is:


Where      NDVIN-Rich and NDVICheck  are as defined in Eq.[3]

              CVMax = Maximum Coefficient of Variation

  CVCheck = Coefficient of Variation of NDVI readings taken from the check plot

  CVCritical = Critical Coefficient of Variation


The CVMax, which is the highest observed CV, used in the calculation was 45.  A CVCritical of 17, derived from Figure 1, was employed.  These values, CVMax and CVCritical are expected to change in different production environments and for different crops.

Regression analysis of the relationship between average NDVI readings collected in the direction of the seed row vs. those collected from the same area moving perpendicular to the seed row is reported in Figure 8 for EFAW, Lake Carl Blackwell, Perkins, and Hennessey in 2003 and 2004.  The trend line fit a linear relationship with a slope of 1.0 and an intercept of 0 with an R2 of 0.97.  3660 observations, compiled from 2 years of readings over 7 locations were used in the regression. A highly significant linear relationship (R2 = 0.97) was also found for NDVI readings collected in the direction of the seed row versus those taken from the same area moving at a 45-degree angle across the seed rows.

            The relationship between the CV of NDVI readings taken with the seed row and perpendicular to the seed row was determined to be quadratic (R2 of 0.78, Figure 9).  At high CV where plant stand was poorest, the value of the CVís collected with the row and perpendicular to the row tended to converge.


            In this study, 7 site years were used to evaluate plant populationís affect on CVs of NDVI readings.  No one site-year could be used to identify a critical CV because there was little difference in population at any one site.  The critical CV value determined from this study corresponds with the results presented by Morris et al. (2005).  They observed that plots of winter wheat with a CV greater than 18 were unable to completely recover from early season N stress. This clearly indicates that in areas of a field where CV exceeds the critical level of approximately 20 it is recognized that the crop will not be able to utilize the additional N. This has potential use in variable rate application where the amount of N fertilizer applied could be reduced.

Raun et al. (2005b) observed a peak in CV in corn at the V6 stage and inferred that the peak could represent the best time to apply in-season foliar N fertilizer as this was the time when spatial variability of NDVI values were greatest.  Similar results were found in this study.  The first peak in CV occurred near the Feekes 6 growth stage.  This coincides with the time when spatial variability is the greatest.  This in turn suggests the time when variable rate technology could have the greatest benefit at least for detection of yield potential.  It is necessary to apply topdress N prior to Feekes 6, because soon after stem elongation, it is much easier to damage the crop with applicator traffic.    Commonly in Oklahoma, topdress N application timing is determined by weather and field conditions.  Often, the topdress N application takes place from December through March.  This is typically well before the crop reaches Feekes 6. 

The linear relationship found between the RIHarvest and the RINDVI was found to be poor in this small plot experiment (Figure 3). This result suggested that we were not able to reliably predict yield response to added N mid-season at this scale.  Hodgen et al. (2005) found, that the relationship between RIHarvest and RINDVI was strong with a R2 of 0.75.  In their study, location averages were used to determine the relationship while this study used each individual plot. 

The linear relationship between vegetative RI and harvest RI was improved with increasing CV (Figures 4, 5, 6).  RIHarvest and RINDVI showed the best linear relationship when the CV of the fertilized plot was greater than 25.  A linear relationship was still seen between CVís of 10 to 25, but at a lower significance level.  When the CV was less than 10 there was no relationship between RIHarvest and RINDVI. 

The data indicates when the CV is at higher levels; the calculation for RINDVI is appropriate.  However, at a CV < 10, RINDVI was unable to predict RIHarvest.  Understanding this, RINDVI-CV was introduced to incorporate CV into the RI equation.  RINDVI-CV, which is a derivative of RINDVI that includes the CV of the check plot, has a much better relationship with RIHarvest (R2 = 0.37, Figure 7).   This improvement of more than 50% indicates the ability of CV to identify the reduced yield potential in those plots with poor stands.  An improvement in RI estimation should improve variable rate N application and NUE. 

Figure 8 demonstrates the linearity in the relationship of NDVI readings as a direction of travel over the seed row.  This issue becomes important when considering that fertilizer applicators will be outfitted with the sensors. Unlike research where sensor direction can be carefully adjusted, the direction of the movement of sensors on an applicator is much more difficult to control in winter wheat.  Figure 8 shows a strong significant linear relationship with a slope of 1 and an intercept of 0. These results indicate that NDVI readings are independent of direction of travel.  With the determination of the relationship between with seed row CV and perpendicular to seed row CV it will also make it possible to include the use of CV into variable rate nitrogen application.


It was observed that when CVs were greater than approximately 20, the plant population was poor with <100 plants/m2.  The ability of the crop to respond to added N was evaluated using several response indices (RIHarvest, RINDVI, RINDVI-CV). It was found that RINDVI-CV Eq. [4] provided improved prediction of RIHarvest compared to the conventional RINDVI Eq. [3]. It is suggested that when this is implemented into the algorithm, variable rate applicators will apply less N over areas that have CVs greater than 20.  The reduction in N applied reduces the expense of farmers and risk of N being lost to the environment. 

            The observation that CV reached a peak at Feekes 5 to 6 suggests that current timing of application may have to be changed in order to maximize the efficiency of the technology.  As to application direction, it was beneficial to see that it does not matter what direction the sensors are traveling across the seed row and that the NDVI values will remain the same.  This is extremely important in that the applicators do not have the need to follow any rigid guidelines for the equipment to perform properly. 

            Integrating CV into N fertilization algorithms will be more challenging with the observation that across the seed row, CV is consistently higher than other directions.  CVs can be used as an estimate of variation in plant stand densities by identifying the areas where plant stand is so poor that N application is unnecessary.  The use of CV from NDVI readings could improve upon the efficiency at which variable topdress N is applied. 



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Table 1.  Soil classification for all experimental sites,  (Lake Carl Blackwell, Perkins, EFAW, and Hajek Farm) in 2003-2004.


Soil Classification

Lake Carl Blackwell

Port fine-silty, mixed, superactive, thermic Cumulic Haplustoll

Perkins Research

Konawa Teller association

Konawa fine-loamy, mixed, active, thermic Ultic Haplustalf

Teller fine-loamy, mixed, active, thermic Udic Argiustoll


Norge fine silty, mixed, active, thermic Udic Paleustoll

Hajek Farm

Shellabarger fine-loamy, mixed, superactive, mesic Udic Argiustoll


Table 2.  Planting date, variety, seeding rate, and topdress application dates for all experimental sites, (Lake Carl Blackwell, Perkins, EFAW, and Hajek Farm) in 2003-2004.


Crop Year





Rate kg ha-1



Lake Carl Blackwell






























OK 101



Hajek  Farm












Figure 1. Relationship between the CV of NDVI readings and winter wheat plant population (7 locations, 2003-2004, multiple seeding rates and 6 varieties).  The critical CV range of 17 to 20, identified as the region between the two vertical lines, was determined using the Cate-Nelson model.

Figure 2.   Change in mean CV, from NDVI readings collected from three N treatments with the row in winter wheat, over time at the EFAW Research Farm, Stillwater OK (2004). 

Figure 3.  Comparison of RIHarvest (yield of N-rich plot / yield of check) versus RINDVI     (NDVI of the N-rich plot / NDVI of the check) for all CV data.


Figure 4.  Comparison of RIHarvest ( yield of N-rich plot / yield of check) versus RINDVI     ( NDVI of the N-rich plot / NDVI of the check) when the CV of the fertilized plot was ≤10.

Figure 5.  Comparison of RIHarvest ( yield of N-rich plot / yield of check) versus RINDVI     ( NDVI of the N-rich plot / NDVI of the check) when the CV of the fertilized plot was  10 < and ≤ 25.

Figure 6.  Comparison of RIHarvest ( yield of N-rich plot / yield of check) versus RINDVI     ( NDVI of the N-rich plot / NDVI of the check) when the CV of the fertilized plot was    > 25.

Figure 7.  Comparison of RIHarvest ( yield of N-rich plot / yield of check) versus        RINDVI-CV { (NDVI of the N-rich plot / NDVI of the check) * ( Max CV - check CV / Max CV Ė Critical CV)}. 

Figure 8.  Comparison of with seed row NDVI readings versus across seed row NDVI readings. (7 locations, 2003-2004, multiple seeding rates and 6 varieties, n = 3660)

Figure 9. Relationship between with seed row CV of NDVI readings versus across seed row CV of NDVI readings.