Determining nitrogen deficiencies for maize using various remote sensing indices

Determining a precise nitrogen fertilizer requirement for maize in a particular field and year has proven to be a challenge due to the complexity of the nitrogen inputs, transformations and outputs in the nitrogen cycle. Remote sensing of maize nitrogen deficiency may be one way to move nitrogen fertilizer applications closer to the specific nitrogen requirement. Six vegetation indices [normalized difference vegetation index (NDVI), green normalized difference vegetation index (GNDVI), red-edge normalized difference vegetation index (RENDVI), triangle greenness index (TGI), normalized area vegetation index (NAVI) and chlorophyll index-green (CIgreen)] were evaluated for their ability to detect nitrogen deficiency and predict grain maize grain yield. Strip trials were established at two locations in Arkansas, USA, with nitrogen rate as the primary treatment. Remote sensing data was collected weekly with an unmanned aerial system (UAS) equipped with a multispectral and thermal sensor. Relationships among index value, nitrogen fertilizer rate and maize growth stage were evaluated. Green NDVI, RENDVI and CIgreen had the strongest relationship with nitrogen fertilizer treatment. Chlorophyll Index-green and GNDVI were the best predictors of maize grain yield early in the growing season when the application of additional nitrogen was still agronomically feasible. However, the logistics of late season nitrogen application must be considered.


Introduction
Intensive maize production often necessitates external nitrogen inputs. Approximately 5.5 Mt of nitrogen was applied to maize (Zea mays L.) in the United States in 2018 (USDA-ERS, 2019). Despite high N-demand, determining precise nitrogen fertilizer requirements for maize has proven to be a challenge due to the complexity of the nitrogen cycle (Morris 1 3 et al., 2018). In Arkansas, as well as many other states, N-rates are established using two factors: maize grain yield goal and soil texture. For example, maize grown on silty or sandy loam soils with a grain yield goal of 11 t ha −1 will require 247 kg N ha −1 (Espinoza & Ross, 2012;Morris et al., 2018). However, it is well documented that no-tillage and winter cover crops can significantly alter nitrogen dynamics within an agroecosystem (Doran, 1987;Kaspar et al., 2012;Kuo et al., 2001;Mahal et al., 2018;Tonitto et al., 2006). As a result, N-recommendations based on conventional systems may not be applicable under the agricultural practices of no-or minimal tillage, winter cover crops and/or diverse crop rotations.
Unmanned aerial systems (UAS), which have demonstrated a wide range of capabilities, may be a valuable management asset. Gautam and Pagay (2020) found that UAS-derived data were not as impacted by cloud cover and had higher spatial and temporal resolution than satellite-based imagery. Although UAS are limited in terms of sensor size and range, they are also simpler, more cost effective and have fewer safety constraints than manned systems. Unlike ground-based sensors, aerial platforms facilitate rapid, whole-field assessments with a greater number of observations.
The broad agronomic capabilities of UAS can be summarized into three basic categories: scouting areas where issues are suspected, in-season crop monitoring and nutrient management (Hunt & Daughtry, 2018). Although the selective scouting of problem areas is feasible, farm-scale crop monitoring remains economically and logistically constrained by costs associated with data processing and management (Hunt & Daughtry, 2018). Nevertheless, the ability to quickly detect and geo-reference maize N-deficiencies during critical growth stages through optical-sensors has significant management implications (Dhital & Raun, 2016;Gabriel et al., 2016).
Using remote sensing technology, nitrogen, phosphorus, potassium and sulfur deficiencies have been successfully identified in wheat (Mahajan et al., 2014), and the association of various vegetation indices with nitrogen supply and plant chlorophyll content is well documented (Dellinger et al., 2008;Hunt, et al., 2013;Maresma et al., 2018;Preza Fontes et al., 2019). Furthermore, remote sensing-based nitrogen recommendations for maize have been suggested in prior studies (Clay et al., 2006;Dellinger et al., 2008;Schmidt et al., 2009). Although nutrient management through remote sensing has proved promising, there are a multitude of possible indices that could be used to assess nitrogen stress.
Of the following indices assessed, normalized difference vegetation index (NDVI) is one of the oldest and has been used extensively for a myriad of applications (Rouse et al., 1974). Because NDVI is associated with plant health, it has a significant relationship with early-season N 2 O emissions when low crop demand exacerbates N losses (Preza Fontes et al., 2019). Due to its relationship with leaf area index (LAI), NDVI may lose predictive power once the canopy has closed around V9 (9 true, collared leaves; Teal et al., 2006). Loss of sensitivity after canopy closure can reduce the usefulness of NDVI later in the season. However, NDVI can remain sensitive until reproductive stages if LAI remains less than 4 (Hatfield & Prueger, 2010).
Triangle greenness index (TGI) was developed by Hunt et al. (2013) as a novel chlorophyll index and potential tool for N-management. The index was found to be insensitive to LAI above 2.0 while retaining a high correlation with plant chlorophyll concentration (Hunt et al., 2013). However, TGI based N-sufficiency classification was not found to be superior to manual color (i.e., chart based) classification (Friedman et al., 2016).
Chlorophyll index green (Cl green ) and chlorophyll index red edge (CI red-edge ) were also developed to model canopy chlorophyll concentration via remote sensing . At high chlorophyll concentrations, simple reflectance becomes saturated and increasing chlorophyll concentration has little effect on simple reflectance. However, algorithms based on more sensitive wavelengths (e.g., green and red), and stable wavelengths (e.g., near infrared (NIR)) can overcome this limitation (Gitelson & Merzlyak, 1994, 1997Gitelson et al., 2003). Chlorophyll index green and CI red-edge operate on these premises with the explicit goal of sensing chlorophyll concentration.
In a midwestern soybean (Glycine max)-maize rotation, CI green and CI red-edge were found to have strong, linear relationships with canopy chlorophyll concentration . Reese et al. (2010) found that CI green was positively correlated with yield loss due to nitrogen stress in hard red spring wheat (Triticum aestivum) In the same study, CI green was negatively correlated with water stress, suggesting that chlorophyll indices could be used to differentiate between N-stress and water-stress (Reese et al., 2010). Chlorophyll index green and GNDVI were both found to have higher R 2 values and higher saturation points than NDVI at the V12 growth stage in maize. Vegetation indices that use green bands tend to have an improved potential for determining optimum N-rates for grain yield relative to indices that are dependent on red bands (Maresma et al., 2018). Hatfield and Prueger (2010) suggest that CI green could be used during early stages of crop development.
By combining stable and dynamic wavelengths, GNDVI operates on the same principles as the preceding indices. What distinguishes GNDVI from CI green and CI red-edge is that GNDVI is normalized; its values are constrained to a set range of possible values. Gitelson and Merzlyak, (1997) also noted that GNDVI is compatible with a large range of leaf pigmentations. Green NDVI has also been found to have a stronger relationship with maize grain yield than NDVI (Shanahan et al., 2001). In maize, GNDVI can be a good predictor of the economic optimum nitrogen rate (EONR) given a reference plot and the absence of pre-plant N-fertilization at the V6 to V7 growth stage (Dellinger et al., 2008). Using an active light, on-the-go sensor, GNDVI can predict maize EONRs with precision similar to traditional N-recommendation methods (soil or plant analysis, pre-sidedress nitrate test, corn stalk nitrate test; Schmidt et al., 2009).
Red-edge NDVI is computationally similar to GNDVI except it uses reflectance in the red-edge rather than the green band. Red-edge NDVI was found to have a stronger relationship with maize grain yield than NDVI, particularly when reflectance data were collected later in the season (Preza Fontes et al., 2019;Sharma et al., 2015). Additionally, RENDVI is more sensitive to chlorophyll concentration than traditional NDVI because NDVI is determined by the ratio of exposed leaf to soil surface (Sharma et al., 2015). Interestingly, NDVI was found to have a stronger relationship with maize biomass and nitrogen uptake than RENDVI, but maize grain yield had a stronger relationship with RENDVI than NDVI (Preza Fontes et al., 2019).

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Cumulatively, remote sensing apparatuses coupled with an appropriate index have demonstrated an acute ability to quickly assess plant growth and development. Evaluating crop N-demand through remote sensing indices is by no means a novel proposition (Clay et al., 2006;Sharma et al., 2015). However, considerable ambiguity remains concerning index selection and practical constraints. Although general adoption may currently be unrealistic, rapidly developing UAS, sensor and data processing technology attests to a quickly developing potential (Hunt & Daughtry, 2018). This potential is especially high in conservation systems where farmers wish to evaluate in-season changes to soil-N supply (Dhital & Raun, 2016;Gabriel et al., 2016).
The goal of this study was to determine the relationships among nitrogen fertilizer rates, maize grain yield, maize growth stage and an assortment of vegetation indices (TGI, NAVI, CI green , GNDVI, RENDVI and NDVI; Table 1). The specific objectives of this study were to determine: (i) the strengths and weaknesses of vegetation indices in detecting nitrogen fertilizer treatments, (ii) the effect of maize growth stage on the relationship between vegetation index and nitrogen treatment, and (iii) the power of vegetation indices for predicting maize grain yield during vegetative and reproductive growth stages.

Management practices
Winter cover crop mixes, N-fertilizer types and application timings, planting and harvesting dates, maize hybrid and crop rotation sequences were all provided by cooperating farmers (Table 2). Weather for the 2019 growing season was obtained from NOAA (Table 3). Sites were managed following conservation agriculture practices common to eastern Arkansas. Furrow irrigation was applied using lay-flat plastic tubing (Delta Plastics, Little Rock, AR, USA). Water stress was not observed at any site and, therefore, was not considered in these analyses.

Remote sensing and data extraction
Remote sensing data were collected with a 7-day temporal resolution at Cotton Plant, Arkansas, and a 30-day temporal resolution at Helena, Arkansas. The Cotton Plant site was the focus of this study with high temporal resolution, while the Helena site was used as a secondary site with less temporal resolution. Furthermore, some of the remote sensing data from the Helena site was compromised due to stitching errors. Maize growth stage Table 1 Remote sensing vegetation indices used in the analysis a Reflectance (ρ) is measured at the wavelength denoted by the subscript: red (r), green (g), blue (b) and near infrared (NIR)

Abbreviation Equation a
References Normalized difference vegetation index Hatfield and Prueger (2010), Sharma et al. (2015) and Tucker (1979) Chlorophyll index green Gitelson et al. (2003) and Hatfield and Prueger (2010) Red-edge normalized difference vegetation index Gitelson and Merzlyak (1997) and Hatfield and Prueger (2010) Green normalized difference vegetation index Gitelson and Merzlyak (1997) and Hatfield and Prueger (2010) Normalized area vegetation index Carmona et al. (2015) Triangle greenness index Hunt et al. (2011Hunt et al. ( , 2013 1 3 (Table 4) was determined from randomly selected samples near the time of each flight to determine the effect of maize growth stage on vegetation index value and model uncertainty. A UAS (Matrice 210 V-2 quadcopter, DJI, Shenzhen, China) was equipped with an Altum multispectral/thermal sensor (MicaSense, Seattle, WA, USA) to collect near infrared (NIR, 840 nm), red edge (RE, 717 nm), red (R, 668 nm), green (G, 560 nm) and blue (B, 475 nm) reflectance data (MicaSense, 2020). Data collection occurred within two hours of solar noon. Prior to each flight, calibration images were collected with a calibrated reflectance panel and downwelling light sensor (MicaSense, Seattle, WA, USA).
To maintain a 75% front/side overlap, flight plans were developed using the Atlas Flight application (MicaSense, Seattle, WA, USA). The UAS collected imagery at 120 m above ground level (AGL) while traveling at a horizontal velocity of 10 m s −1 . Flight-design parameters were determined using the MicaSense flight calculator. Pix4D Mapper (Pix4D Inc., Prilly, Switzerland) and (Agisoft LLC, St. Petersburg, Russia) were used to stitch images together and create a geo-tiff file.
Multiple stitching programs were used to convert raw images into geo-tiff files for two reasons. First, geo-tiff files created by Pix-4D are substantially larger than geo-tiff files obtained through Agisoft. Although the higher resolution from Pix-4D was beneficial in some instances, it generally did not justify the substantially larger file sizes. Whenever possible, Agisoft was used to conserve data storage space. Second, when one method failed to stitch images, a geo-tiff file could often still be obtained through the other program. By using both stitching programs, file size was controlled and the number of stitching errors was reduced.
Whole-plot yield (t ha −1 ) was compared with the mean index value for each plot. The research design consisted of randomized blocks ( Fig. 1), which allowed each flight to be evaluated separately. The relationship among index, grain yield, N-rate and timing (crop   . 2). Extraction shapefiles constructed for this process included a buffer at the top and bottom of the field to avoid turn rows (Fig. 1). Calibrated reflectance bands were used to calculate the NDVI, CI green , RENDVI, GNDVI, NAVI and TGI (Table 1).

Regression analysis
All statistical analyses were performed using SAS statistical software (SAS University Edition, SAS Institute INC, Cary, NC, USA: Release 3.8, Version 9.4M6). Analysis of vegetation indices was limited to observations obtained between the V6 (six true, collared leaves) and R4 (dough formation) growth stages. This period of crop development was selected because it captured a wide range of maize N-uptake while ignoring less active growth periods. Typically, 65% of total N-uptake occurs between V6 and vegetative tasseling (VT) (English et al., 2017). Approximately 20% of maize nitrogen demand is satisfied between VT and R3 (milk-like liquid present in kernels) with some uptake extending into later stages (English et al., 2017). Additionally, mid-to late-season analysis helps control for soil effects due to increased vegetative ground coverage and LAI. Multiple linear regression was used to determine relationships for each index and maize growth stage and N-fertilizer rate (Table 5). Polynomial terms were added to a model if they improved model fit (i.e. better met the assumptions of regression) or improved predictive power of the model. To avoid over-parameterization, only second-degree polynomials were used. The adjusted coefficient of determination (R 2 adj. ) was used to evaluate the strength of these relationships. When the remote sensing index value was treated as the dependent variable, nitrogen rate and maize growth stage were included in the model as second-degree polynomials equation (1): where Y i is the index value, x iN−rate is the nitrogen rate and x istage is the growth stage. Since the scope of this study was focused on large scale (large plot scale) analysis, the use of regression analysis was chosen, which inherently limits the analysis of temporal information and uncertainty of the model.
Simple linear regression was used to determine the six index relationships with maize grain yield (Table 6). Since the regression analysis was conducted on a plot basis, the spatial analysis was global and not site-specific. When predicting yield by remote sensing index values Eq.
(2), terms related to maize growth stage were removed due to their high correlation with the index values. Each growth stage was analyzed separately, thereby avoiding multi-collinearity. As before, R 2 was used to evaluate the strength of relationships between index values and grain yield. All yield regression analyses were performed using robust parameter estimates to (1) control for any heteroscedasticity present in the data. Heteroscedasticity consistent standard errors were calculated using the White (HC1) method (White, 1980): where y i is the maize grain yield and x iindex is the index value.

Saturation analysis
The ability of an index to distinguish among N-fertilizer rate treatments was evaluated using a general linear model (GLM). Factor level (N-rate) analysis was performed using a Dunnett's T-test. Index values for each N-rate was compared to index values obtained from the control N-rate (247 kg N ha −1 ) (Eq. 3). The relationship between maize grain yield and N-fertilizer rate was also analyzed using a GLM and Dunnett's T-test with the same control N-rate of 247 kg N ha −1 (Eq. 4). Familywise error rates were controlled at α ≤ 0.05 for both models.
where y iindex is the index value and x iN−rate is the nitrogen application rate.
(2)  where y iyield is the maize grain yield and x iN−rate is the nitrogen application rate. This factor-level analysis demonstrates the ability of each vegetation index to distinguish N-rate treatments from the 247 kg N ha −1 control. Vegetation index or crop yield saturation occurs when they become insensitive to additional N-application (Maresma et al., 2018). Ideally, a vegetation index will become saturated at the same (or greater) N-rate as yield. When a vegetation index and yield become saturated at the same N-rate, the index is determined to have a strong sensitivity to N-deficiency in maize.

Relationship among N-rate, stage and index values
At Cotton Plant, GNDVI was found to have the highest R 2 adj. value (0.88) followed by CI green (R 2 adj = 0.85) and RENDVI (R 2 adj = 0.85) when index was modeled as a quadratic function of N-rate and growth stage (growth stages ranging between V6 and R4 (Table 5). At Helena, a quadratic model with index as a function of N-rate indicated RENDVI to have the highest R 2 adj value (0.81) followed by CI green (R 2 adj = 0.79) and GNDVI (R adj 2 = 0.78). Stage was not parametrized at Helena because data was only available at the R2 growth stage (kernel blister stage). Stage and N-rate variables explained more variation in GNDVI, CI green and RENDVI than in TGI, NAVI and NDVI at both sites (Table 5).

Relationship between maize grain yield and vegetation indices during vegetative growth stages
At the V6 growth stage, CI green had the best relationship with yield (R 2 = 0.29) followed by GNDVI (R 2 = 0.24) and RENDVI (R 2 = 0.24; Table 6). This same ranking was preserved at the V7 growth stage, but with stronger relationships: CI green (R 2 = 0.77) > GNDVI (R 2 = 0.71) > RENDVI (R 2 = 0.68). At the V8 growth stage, the relationship between yield and index strengthened, but index rankings changed: GNDVI (R 2 = 0.89) = CI green (R 2 = 0.89) > RENDVI (R 2 = 0.84). For all indices, the relationship between maize grain yield and reflectance collected during vegetative growth strengthened as the season progressed. Even though the rankings changed slightly over time, the same three indices (CI green , GNDVI and RENDVI) remained the strongest throughout vegetative growth (Table 6).

Sensitivity/distinguishing capability of each index during vegetative growth stages
As the maize crop developed, the distinguishing capabilities and saturation points of each index increased (Table 7). At the V6 growth stage, only TGI distinguished any of the different N-fertilizer rates from the control (247 kg N ha −1 ). By the V7 growth stage, RENDVI, GNDVI and CI green were able to differentiate the 0 kg N ha −1 and 62 kg N ha −1 treatments from the control (α < 0.05). Triangle greenness index could distinguish between 62 kg N ha −1 and the control (α < 0.05). At the V8 growth stage, CI green , RENDVI and GNDVI were still only able to differentiate between the control treatment and N-rates up (4) y iyield = 0 + 1 x iN−rate + i , Table 7 Factor level analysis of vegetation indices and maize grain yield a Dunnett's t-test used for factor level analysis. b University of Arkansas recommended rate is the control nitrogen rate. *, **,*** significant at the 0.05, 0.01, 0.001 and probability levels respectively. Otherwise not significant (NS) to 62 kg N ha −1 , but with greater confidence (P < 0.01). During vegetative growth stages (Cotton Plant), no index was able to differentiate between the control and the N-fertilizer rates with the same sensitivity as grain yield. Grain yield was responsive to N-application up to 124 kg N ha −1 , but index saturation consistently occurred at 62 kg N ha −1 (V7 and V8 growth stages) for the top performing indices.

Relationship between maize grain yield and vegetation indices at the R2 growth stage
When limiting the analysis to only observations at the R2 growth stage, CI green had the strongest relationship with maize grain yield at Cotton Plant (R 2 = 0.98; Table 6). Red-edge NDVI (R 2 = 0.96) and GNDVI (R 2 = 0.95) closely followed CI green in terms of predicting grain yield. Similar results were observed at Helena at the R2 growth stage where GNDVI, CI green and NDVI all had a strong relationship with grain yield (R 2 = 0.96). The remaining indices had significant relationships with yield (R 2 ≥ 0.89; Table 6).

Sensitivity/distinguishing capability of each index during the R2 growth stage
Increased predictive power from later image acquisition allowed RENDVI, GNDVI, CI green and TGI to differentiate among N-fertilizer rate treatments and the control with a sensitivity similar to grain yield (Table 7). At Helena, all indices distinguished between the control and N-rate treatments with a precision similar to grain yield. At Cotton Plant, RENDVI, GNDVI and CI green also demonstrated a sensitivity similar to grain yield. This relationship was not replicated at Cotton Plant with NDVI, NAVI and TGI.

Discussion
The growth stage of maize had a significant effect on index values (Table 5), suggesting that models used to predict N-demand must account for growth stage at the time of data collection. Otherwise, data collection must occur at a specific maize growth stage to obtain comparable results across sites. Depending on the crop's maturity when imagery is captured, remote sensing data can be used in one of two manners: ex post facto (retrospective analysis of N-supply) and ex ante facto (concurrent analysis of N-supply).

Prediction of maize grain yield by vegetation indices
The utility of remotely sensed multispectral vegetation indices for in-season N-management (ex ante facto analysis) is dependent on their performance during the early stages of crop development. It is during these stages that fertilizer and irrigation management practices can be adjusted (Joshi et al., 2019). These results agree with Teal et al. (2006) who found that relationships with maize grain yield strengthened rapidly between V6 and V8 (Table 6). Likewise, Olson et al. (2019) found R 2 values for maize gain yield:RENDVI to increase as the season progressed. Increased predictive power may be the result of decreased soil background or a greater proportion of N-deficiency having been realized as the season progressed (Corti et al., 2019). By the V8 stage, the regression models explained 89, 88 and 83% of the maize grain yield variance for CI green , GNDVI and RENDVI respectively (Table 6). Early-season sensitivity of CI green was also observed by Hatfield and Prueger (2010), who found CI green to be more sensitive than the normalized pigment chlorophyll ratio index early in the season.

Sensitivity of remote sensing indices
Ideally, an index will fail to incur significant differences relative to the control treatment at or above the factor level where yield becomes unresponsive to additional N-supply. In this study, all indices failed to demonstrate a sensitivity similar to yield, at or prior to, the V8 growth stage (Table 7). Although severe N-deficiencies were detected by CI green , GNDVI and RENDVI, slight N-deficiency, capable of causing yield loss, remained undetected. Therefore, remote sensing with these indices during vegetative growth stages may overlook agronomically-significant N-deficiency. However, deficiency of a large magnitude may be discernible using CI green, GNDVI or RENDVI.

Potential application
At the V8 growth stage, the three best performing indices (CI green , RENDVI and GNDVI) all had relatively wide prediction intervals of ± 2.5, 3.1 and t ha −1 grain yield, respectively. Additionally, the index's relationship with yield and the time window for sidedress N-application were inversely related. As the index's predictive power increased, the opportunity to sidedress nitrogen decreased simultaneously because of increasing maize height. The relationship between growth stage and model variability creates an optimization problem where minimizing model variability will be hindered by N-sidedress timing constraints. The combination of timing (crop stage and N-application constraints) and wide prediction intervals (variability) may hinder in-season N-adjustments based on remote sensing as described by Clay et al. (2006). In their 2006 study, they suggested that remotely sensed N-demand could be used to calculate nitrogen credits Eq. (5): They further suggested that nitrogen credits calculated via remote sensing may be an improvement on simple yield-based recommendations.
The findings suggest that, unless N-sidedress occurs late in the growing season, variability in yield by index regressions during vegetative growth may impede remote sensing-based N-credits. Nitrogen controls or "ramps" may be necessary to account for site, year and cultivar effects (Dellinger et al., 2008;Maresma et al., 2018;Olson et al., 2019;Schmidt et al., 2009). When these effects are controlled, EONRs can be predicted by GNDVI during vegetative growth stages (Dellinger et al., 2008;Schmidt et al., 2009).
Despite limitations concerning sensitivity, predictive power and significant growth stage effects, chlorophyll indices may still be a pragmatic N-management tool without requiring further adjustments. Because the index values had lower N-saturation points than yield (Table 7), yield reduction can occur without a corresponding change in index values. When index values differed among treatments, maize grain yield was significantly different. Therefore, a significant difference in index values between N-deficient and N-sufficient maize will likely correspond with grain yield loss.
(5) N ∼ demand = (0.021 × optimal yield) − (remote sensing predicted yield) These latter principles may be applied to scenarios where N-dynamics have undergone radical alteration. For instance, remote sensing after a flood may be a niche where UASbased adjustments would be beneficial (Hunt & Daughtry, 2018). In this scenario, farmers or crop consultants could detect areas where persistent saturation has increased denitrification, leaching or reduced the maize stand count. Appropriate remediation strategies, such as applying additional N-fertilizer, could then be implemented to minimize yield loss (Hunt & Daughtry, 2018).

Improving remote sensing sensitivity and decreasing variance in N-deficient maize
Several techniques are available that may assist with the detection of N-stress and reduce index variability during the vegetative growth stages. First, maize grain yield by NDVI index regressions can be improved between V7 and V9 if growing degree days are included in regression models. Prior to V8, yield potential is not fully developed, which introduces variability (Teal et al., 2006). Second, the relationship between the predictive power of chlorophyll indices and yield increases with maize growth stage progression. Therefore, remote sensing data acquisition should be performed as late as possible (i.e. late vegetative or early reproductive stages) for optimal sensitivity. Finally, adjusting index values to account for soil background can significantly improve the predictive power (Corti et al., 2019). Reese et al. (2010) came to a similar conclusion for hard red wheat. They found that waiting until later crop development stages minimized soil interference and reduced variability. However, this may not be applicable to all indices. Because some indices, like NDVI, are primarily determined by leaf to soil ratio, they may be less reliable late in the season once canopy closure has occurred (Sharma et al., 2015). This was observed by Olson et al. (2019), who found maize grain yield by NDVI regressions had R 2 values ranging from 0 to 0.69 at the R1 (silk) growth stage. Using the same growth stage and statistical model, RENDVI had R 2 values ranging from 0.74 to 0.79.

Prediction of maize grain yield by vegetation indices
The relationship between index values and maize grain yield was stronger at the R2 growth stage than at V8 for all indices studied (Table 6). Even NDVI performed well at the later stages of maize growth and development. The R 2 value for maize grain yield as a function of NDVI at R2 was 0.82 and 0.96 respectively at the Cotton Plant and Helena locations. This suggests that canopy closure may have been incomplete (Hatfield & Prueger, 2010;Teal et al., 2006).
Chlorophyll indices performed well overall. At both sites, the relationship between RENDVI, GNDVI, CI green and grain yield produced R 2 values greater than 0.93. The high correlation between maize-grain yield and index values during the early reproductive stages is supported by other recent studies. For example, Olson et al., (2019) found RENDVI to best predict maize grain yield during the R1 growth stage in a study in western Minnesota. Results from other growth stages (V4 to R4) showed significantly weaker correlations compared to the R1 growth stage. Preza Fontes et al. (2019) found that the correlation between maize grain yield and NDVI increased as the season progressed, and the maize entered the R1 growth stage. Likewise, Shanahan et al. (2001) observed a strong correlation between GNDVI captured during mid-grain fill and yield (r = 0.70 and 0.92 during the 1997 and 1998 cropping seasons respectively). Like the findings at the Cotton Plant site, correlation coefficients for NDVI were significantly lower than GNDVI at the same growth stage.

Sensitivity of remote sensing indices
At R2, CI Green , RENDVI and GNDVI had saturation points similar to maize gain yield across all sites in the current study. However, at Cotton Plant, NDVI, NAVI and TGI failed to demonstrate a sensitivity similar to yield, whereas these three indices did demonstrate sensitivity to yield at Helena at R2, similar to the other indices (Table 7). Although N-application during early reproductive stages may not be practical, CI green , RENDVI and GNDVI may still be useful in ex post-facto assessments of grain yield and N-supply, possibly providing a retrospective assessment. Shanahan et al. (2001) suggested GNDVI measurements made during maize grain fill as a possible alternative to combine generated yield maps. It has been estimated that only 50% of maize farmers utilize georeferenced grain yield monitoring, which can increase profits by almost 3% (Schimmelpfennig, 2016). Small-scale (< 1 174 ha) maize farmers are less likely to adopt georeferenced grain yield monitoring than farmers with acreage greater than 1 174 ha. Ex post-facto analysis may be a critical management tool for farmers who have not invested in yield monitors, but desire yield maps for certain fields.

Potential application
Due to the high N-leaching potential of sandy soils, N-deficiency is more common on coarse-textured soils than on fine-textured soils. Ex post-facto analysis may allow interspersed sandy locations to be delineated. This would allow estimates to be made of the severity of the N-stress during the past season relative to high yielding portions of the field.

Conclusions
All six remote sensing indices evaluated had significant relationships with N-fertilizer rate and maize growth stage when analyzed using multiple linear regression models. The predictive power of the models evaluated increased when the remote sensing data were collected later in the growing season. The ability of the indices to distinguish various N-rate treatments from the N-sufficient control treatment also increased during the later stages of development. Across all study sites and stages, CI green , GNDVI and RENDVI demonstrated the greatest reliability for detecting N-deficiency in maize. Overall, CI green , RENDVI and GNDVI may prove to be valuable tools for N-management.
Any attempt to use remote sensing to predict yield differences due to N-stress in maize must account for several factors, especially maize growth stage. Additionally, site, year, cultivar, tillage system and various agronomic stresses may affect plant reflectance. These variables must be controlled either by N-sufficient control strips or additional site-specific yield modeling that incorporates remote sensing data Future studies that incorporate LAI measurements, multiple study sites in multiple locations and harvest yield monitor data are recommended in order to enhance understanding of remote sensing utilization for N management.

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Author contributions All authors contributed to the study conception and design. Field management was performed by VSG, JHM and BWB. Remote sensing data collection and analysis was performed by BWB and AAH. Statistical analysis and modeling were performed by BWB, MM and AMS, MAAA-B provided significant contribution in plant and soil nitrogen dynamics. The first draft of the manuscript was written by BWB and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This research was funded in part by a United States Department of Agriculture-NRCS Arkansas Conservation Innovations Grant (#68-7103-18-004) and United States Department of Agriculture-NIFA Grant (#2018-70001-27817) along with support from the University of Arkansas System Division of Agriculture.
Data availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflict of interest
The authors declare that they have no conflict of interest.
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