2.1. Lint Yield and Fertilizer N Data
Lint yield and fertilizer N application rate data for the farmer practice (FP) and OS-based VRN management were from 21 study locations (
Table 1). Farmers participating in the trials were eligible to receive payments to adopt VRN through USDA NRCS EQIP [
8]. Stefanini et al. [
24] previously reported differences in field-level fertilizer N use, lint yields, and profitability. The on-farm field trials were conducted between 2011 and 2014 at six locations in Tennessee, four locations in Mississippi, five locations in Louisiana, and six locations in Missouri. Most locations had only one year of data. However, several locations had two to three years of trials. Within each of the locations with multiyear trials, different fields were used for each year. A total of 29 site-years of data were collected in the study.
The field trial experimental design for each site-year was a randomized complete block design with three fertilizer N treatments and three replications. A strip-plot running the entire field length was used as the plot for each treatment in each replicate. Each strip-plot was further divided into sub-plots. The sub-plots were used to implement the two VRN treatments evaluated in this study. Cotton was planted on the nine strip-plots at each site, each with 8 to 10 sub-plots, that measured approximately 30.5 by 11.6 m. A different field on each participating farm was used for each site-year. While researchers attempted to choose similar field sizes in each year of the study, variation in field sizes resulted in different numbers of sub-plots within the strip-plots among the site-years (
Table 1). However, the same number of sub-plots for each strip-plot within each site-year was maintained during the study.
The trials evaluated FP N management versus two OS-based VRN management regimes. The FP treatment was N application based on the farmer’s current practice. Cotton farmers and their crop consultants often formulate their fertilizer N rate for the field using University recommendations, their experience, and agronomic and soil considerations [
6]. Optical sensing-based VRN treatment 1 (VRN 1) was VRN management calculated using the normalized difference vegetation index (NDVI) readings collected with the GreenSeeker™ Crop Sensing System (Trimble, Sunnyvale, CA, USA) or Yara™ N-Sensor (Yara North America, Tampa, FL, USA) canopy optical-sensing. The configurations of sensor arrays were different in each state where the field trials took place. In Tennessee, a GreenSeeker™ RT200 system with six sensors (1.93 m apart and 0.76 m above the cotton canopy) covering 12 rows of cotton (11.58 m wide) was used to collect about two scans s
−1 at a field speed of about 7.64 km h
−1. The second OS-based VRN treatment (VRN 2) was VRN management based on NDVI readings but augmented with additional information.
Two split applications of fertilizer N were made for the three fertilizer N management regimes. Starter fertilizer was applied at or before the planting of cotton and was determined by each farmer participating in the study. A uniform blanket rate of fertilizer N was applied to the entire field (covering all three treatment areas) with rates ranging from 33.6 to 78.4 kg N ha−1, depending on the farm field location. A second side dress application of fertilizer N for the FP was made at approximately the early bloom stage. For the two VRN treatments, crop N status was determined using canopy optical-sensing at about the early bloom stage for each site-year of the trial and fertilizer N was side dressed variably on the sub-plots, thereafter based on the NDVI readings for the VRN 1 treatment and NDVI readings and either digital yield maps (Mississippi and Tennessee), soil productivity zones (Louisiana), or soil zones (Missouri) for VRN 2. Each state used different algorithms for the VRN 1 and VRN 2 treatments because each state has different soils, climates, and management practices for cotton. The unpublished algorithms were developed based on multiple-year and multiple-location data from previous research in each state.
The other production practices used to grow cotton on each field trial site were determined by the farmer cooperators in the study. Data collected for each sub-plot (strip-plot in Missouri) included harvested seed cotton yield, lint yields, applied fertilizer N rates, and latitude and longitudes for every field site, except in Missouri, where yield data were collected at the strip-plot level rather than by sub-plot (
Table 2). In Louisiana, Mississippi, and Tennessee, cotton pickers with yield monitors were used to harvest cotton and determine sub-plot seed cotton and lint yields. Yield monitors were not available on cotton pickers at the Missouri sites so strip-plot yields rather than sub-plot yields were measured using a weigh wagon. A measure of nitrogen use efficiency (NEFF), defined as lint yield divided by fertilizer N rate, was also calculated for each N management regime (
Table 2) [
24].
2.2. Landscape, Soil, and Weather Data
Landscape, soil, and weather data were collected to determine differences within and between fields for each location-year. Georeferenced landscape, soil, and weather data were assembled from the center point of each sub-plot (strip-plot for Missouri locations) using ArcGIS 10.1 (ESRI, Redlands CA, USA). Sub-plot elevations (m above sea level) were collected from the National Elevation Dataset [
29]. Soil water-holding capacity (volume fraction), soil organic matter (%), soil texture, soil depth (cm), field slope, and soil erosion factors were gathered from the Soil Survey Geographic (SSURGO) database [
30]. Soil texture data in SSURGO were used to rank textures by coarseness—clay (finest), silt, loam, and sand (coarsest)—using the USDA soil texture calculator [
31].
A soil erosion index (SEI) was created using SSURGO [
30] data, USDA Revised Universal Soil Loss Equation, version 2 (RUSLE2) data [
32], and a modified universal soil loss equation to account for the physical factors of the fields [
24]:
where
KF is an erodibility factor due to water,
LS is a soil length (
L) and slope steepness (
S) factor,
R is the rainfall and runoff factor from USDA RUSLE2 version 2.5.2.11 [
32]; and
TF is a soil tolerance factor.
Weather was measured by temperature [
33], expressed as seasonal growing degree days. To calculate seasonal growing degree days, the positive values of daily average temperature minus 15.6 °C was summed over 1 April through 31 October for each site-year.
2.3. Fertilizer N Management Net Returns
Net returns for the FP, VRN 1, and VRN 2 treatments were estimated using sub-plot lint yields, fertilizer N rates, lint and N fertilizer prices, and partial budgeting costs for OS and VRN technologies (
Table 2). Price and budget data are in real 2013 US dollars indexed using the annual Gross Domestic Product Price Deflator Index [
34]. Crop revenues were estimated by multiplying lint yields for each N management treatment by the national average marketing year cotton lint price of USD 1.86 kg
−1 received for 2011 through 2014 [
35]. EQIP cost-share payments (NRCS precision nutrient management practice code number 590) for each state for 2011 through 2014 were also added to crop revenues. Estimated payments were USD 68.21 ha
−1 in Mississippi [
36], USD 68.46 ha
−1 in Louisiana [
37], USD 65.85 ha
−1 in Tennessee [
38], and USD 32.64 ha
−1 in Missouri [
39].
Fertilizer N cost of USD 0.93 kg
−1 was multiplied by the fertilizer N rate to determine fertilizer N cost for each N management regime. The fertilizer N price is the national average marketing year fertilizer N prices received for 2011 through 2014 [
40]. Following Stefanini et al. [
24], budgeted skilled operator labor and equipment operating and ownership costs of USD 2.14 ha
−1 and USD 2.45 ha
−1, respectively, for OS of the crop canopy was assumed for GreenSeeker™ sensors retrofitted to a boom sprayer measuring 24.7 m wide. The cost of yield monitoring data identifying yield productivity zones in the field was assumed to be used to augment OS information for the VRN 2 prescription and had a budgeted cost of USD 2.73 ha
−1. In addition, the budgeted costs of a computer to manage yield monitor data of USD 0.31 ha
−1 and reported cost of technical advice for incorporating yield monitor with OS information of USD 12.63 ha
−1 [
41], respectively, were included in the total cost for VRN 2. The cost of VRN application was estimated to be USD 6.60 ha
−1 more than for the FP [
41].
2.4. Statistical Analysis
Two statistical models were used to evaluate OS-based VRN in-field fertilizer N rate, lint yield, and net return (NR) relationships with farm field characteristics. The first is a general linear model for the fertilizer N management mean differences. The sub-plot lint yields (YLD), fertilizer N rates (FNs), N efficiency (FNEFF), and NRs (FNRs) that are summarized in
Table 2 were used to construct the regressions’ dependent variables. The dependent variables were created using paired sub-plot observations in each strip-plot to measure differences between VRN 1 and the FP (VRN 1-FP) and VRN 2 and the FP (VRN 2-FP). For example, field 1, replication 1, and sub-plot 1 for the VRN 1 treatment versus field 1, replication 1, and sub-plot 1 for the FP treatment. This procedure resulted in 1263 observations available for each of the regressions (
Table 3). Fixed effects included in the mean difference regressions are landscape, soil, and weather characteristics georeferenced to each sub-plot. To account for potential differences in landscape and soil characteristics between paired VRN and FP sub-plot observations within each replication, observations were omitted from the regressions if soil characteristics differed between the two sub-plots. For example, if soil texture differed across field 1, replication 1, and sub-plot 1 for the VRN treatment versus sub-plot 1 for the FP treatment, then the observation was omitted from the regressions; if not, the observation was retained for the estimation. The summary statistics for the landscape, soil, and weather variables used as fixed effects in the mean difference regressions are also presented in
Table 3.
The general linear model for the fertilizer N management mean differences was:
where
i = 1 (VRN 1
FP), 2 (VRN 2
FP);
j = 1, …, 21 farm field locations;
k = 1, 2, and 3 replications on fields;
l = 1, …, 8 to 10 replication sub-plots within each strip-plot;
t = 2011, 2012, 2013, and 2014;
is defined as the mean difference in the response variable
Y (lint yields (ΔYLD, kg ha
−1), fertilizer N rates (ΔFN, kg ha
−1), YLD/FN (ΔFNEFF, index), and NR (ΔFNR, USD ha
−1)) for VRN 1 or VRN 2 compared to the FP;
is the conditional mean;
X includes sub-plot measurements on soil texture (clay, silt, loam, and sand), elevation above sea level (m), soil water-holding capacity (volume fraction), soil organic matter (%), soil depth (cm), soil erosion index, and seasonal growing degree days (degrees Celsius);
is a vector of the estimated average landscape, soil, and weather effects on
; and
is a 0–1 variable indicating the VRN 2 treatment. The parameters
and
are the farm field location random effects and the nested random effects from replications in farm field locations, with
and
. The model error is
[
42].
The models using Equation (2) were estimated using the MIXED model procedure and restricted maximum likelihood in SAS 9.2 [
43]. The sand soil texture 0–1 variable was dropped to estimate regressions and was included as the reference variable in the intercept term. The mean difference models were evaluated for multicollinearity using variance inflation factors (VIF) estimated using the REG model procedure in SAS 9.2 [
43]. VIF exceeding 10 may indicate that multicollinearity is increasing the size of the parameters’ standard errors [
44]. Models estimated using Equation (2) tested the null hypotheses that mean yields, fertilizer N rates, NRs, and N efficiency were not different between VRN and FP, holding landscape, soil, and weather factors constant.
The second statistical model is estimated as a mixed logistic regression:
where
is the probability that the response variable (lint yields (YLD, kg ha
−1), fertilizer N rates (FN, kg ha
−1), YLD/N (NEFF, index), and NRs (FNR, USD ha
−1)) for VRN falls above or below the FP value. The sub-plot data summarized in
Table 2 were used to construct the logit regressions’ dependent variables and are presented in
Table 3. The binary dependent variables using the paired sub-plot observations in each strip-plot were calculated as:
Equations (4)–(7) were estimated for each binary dependent variable with the same set of fixed effects summarized in
Table 3 and the same random effects used for the mean difference regressions described above. The logit models were estimated using the GLIMIX model procedure and restricted maximum likelihood in SAS 9.2 [
43]. Multicollinearity was also evaluated in the logit regressions with the same procedures used for the mean difference regressions [
44]. The odds ratios calculated using the estimated coefficients
of these logistic regressions are used to test the hypotheses comparing FP and OS-based VRN. Each covariate’s impact on the odds VRN < FP is
). In percent terms, the change in the log odds probability that VRN lint yields, N rates, NEFF, or NRs exceeded those of the FP is
. The null hypotheses for Equations (4)–(7) was that the N management regime does not affect the probability that yields, N rates, N efficiency, and NRs differ for VRN versus the FP, holding soil, landscape, and weather variables constant.