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Methodology for Selecting Stable UAV-Based Vegetation Indices for Prediction of Agronomic Variables in Maize Using a Multispectral Sensor

Prometheus Redaktion

Abstract Plant phenotyping based on unmanned aerial vehicles still faces challenges regarding the direct correlation between spectral information with field-collected variables, due to the influence of environmental factors and the considerable variation among maize phenological stages. Therefore, the objectives of this research were: I) to evaluate the interaction of nitrogen doses and evaluation environments (phenological stages and growing seasons) and variance components for field variables and vegetation indices; II) to identify the most suitable indices according to the evaluation environments; and III) to predict field variables based on relevant vegetation indices identified through the proposed methodology. The study was conducted using a randomized complete block design with four repetitions, in which treatments consisted of six nitrogen (N) topdressing doses (0, 50, 100, 200, 300, and 400 kg ha −1) during the 2022/2023 and 2023/2024 growing seasons. Evaluations of agronomic variables and image acquisition were performed in five distinct phenological stages throughout the maize crop cycle. The data were analyzed using deviance analysis and variance components, principal component analysis (PCA), and multivariate linear modeling for the prediction of field variables. Our results demonstrated that all indices were affected by the interaction between N doses and evaluation environments (phenological stages and growing seasons). Additionally, the most reliable were EXGRaw, TGI, GNDVI, NDRE, CIRE, GVI, CVI, BNDVI, PanNDVI, SRNIRRe, SFDVI, RGBindex, NDVI, SAVI, MSAVI, and OSAVI, which showed clustering patterns according to growing season condition and phenological stage. Finally, the variables predicted using the proposed methodology achieved coefficients of determination above 0.80, except for shoot biomass and 100-grain weight. Therefore, it can be concluded that vegetation indices are influenced by the evaluated environment; however, the proposed framework based on the deduction of fixed and random effects enables the prediction of field variables with high accuracy using relatively simple models. 1. Introduction Using multispectral or hyperspectral sensors, it has become possible to capture the electromagnetic energy reflected after interacting with the plant surface at wavelengths in the visible (400 to 700 nm) and infrared regions (750 to 2000 nm). This enables the early detection of physiological changes in vegetation caused by nutritional deficiencies, water shortage, or genotypic differences through spectral information [ 7, 8, 9]. Additionally, after obtaining the digital number for each wavelength from the images, different vegetation indices can be calculated and accurately correlated with plant growth, leaf area index, and chlorophyll content (r 2 > 0.70) [ 10, 11]. In this context, Zhou et al. [ 12] reported that spectral bands in the visible and near-infrared regions showed strong correlation with plant nitrogen concentration (r 2 > 0.80), highlighting the potential use of lower-cost multispectral sensors for predicting the nutritional status of several grain crops. Recently, plant phenomics has advanced toward high-throughput phenotyping, through the use of multispectral sensors embedded in unmanned aerial vehicles (UAVs) with greater spatial, spectral, radiometric, and temporal resolution. This approach allows faster data collection and higher image definition due to the smaller pixel size [ 13]. Furthermore, research has been conducted to adapt UAV-based field data collection for plant counting, inflorescence detection, characterization of crop growth curves, and assessment of genotype tolerance to stresses, enabling rapid evaluations throughout the entire crop cycle [ 14, 15, 16]. However, UAV-based phenotyping can be influenced by air temperature, light conditions, flight altitude above ground level, crop biomass accumulation, and treatment variability, which may affect the relationship between spectral information and field variables, often reducing prediction accuracy to coefficients of determination below 60% [ 8, 17, 18, 19, 20]. Moreover, the most effective vegetation indices for predicting field variables may vary depending on the evaluation environment, including genotype, phenological stage, and growing season [ 21]. Temporal analyses of vegetation indices can reveal patterns of plant growth and development, contributing to a better understanding of vegetation responses to environmental changes [ 22]. In this context, the methodology of mixed models enables the analysis of fixed and random effects that may influence data collection in experiments involving different genotypes, phenological stages, and growing seasons (years), based on restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) approaches [ 23]. This framework makes it possible to isolate specific effects, to determine parameter repeatability, and to estimate the error coefficient for each vegetation index in multiple scenarios [ 24, 25]. Additionally, the interaction between flight timing (phenological stage) and years (growing season) is crucial to assess the reliability of spectral data for plant characterization and to select the best vegetation indices [ 21], aiming to identify stable indices for predicting agronomic variables. Therefore, the objectives of the present study were: (I) to evaluate the interaction of nitrogen doses and different evaluation environments (phenological stages and growing seasons), as well as the variance components associated with agronomic variables and vegetation indices, (II) to identify the best vegetation indices according to the evaluated environment, and (III) to predict agronomic variables in maize based on the relevant vegetation indices selected using the methodology proposed in our study. 2.1. Field Experiments and Experimental Design A randomized complete block design was used, with four replications. Treatments consisting of six nitrogen (N) topdressing doses (0, 50, 100, 200, 300, and 400 kg ha −1) applied at the phenological stage of four fully developed leaves (growth stage V4) ( Figure 1C). In both growing seasons, the previous crop was oat ( Avena sativa), which was terminated at flowering using Glyphosate (3 L ha −1) and Atrazine (4 L ha −1). Subsequently, the maize hybrid P3016 VYHR was sown under a no-tillage system at a density of 8 plants per m 2 in the second half of October in both years. Each experimental plot consisted of five rows, five meters long each, with a row spacing of 0.50 m. At sowing, 20 kg ha −1 of N, 120 kg ha −1 of P 2O 5, and 60 kg ha −1 of K 2O were applied in the sowing furrow. All other agronomic practices were carried out according to the technical recommendations for maize cultivation in southern Brazil. 2.2. Agronomic Variables Evaluated Field evaluations were conducted at phenological stages V8 (eight fully developed leaves), V11, V18, R2 (onset of grain filling), and R5 (full dent stage) during the 2022/2023 season, and at V6, V8, V13, R2, and R5 during the 2023/2024 season. At each evaluation, plant height was measured in 10 plants per plot, from the soil surface to the last fully expanded leaf, using a graduated ruler, and expressed in meters. In addition, three plants per plot were cut, dried in a forced-air oven at 60 °C for determination of plant shoot dry biomass, expressed in kilograms of dry matter per hectare. Afterwards, the plant material was ground, and plant nitrogen concentration (PNC) was determined by the Kjeldahl method. 2.3. UAV-Based Image Acquisition and Vegetation Indices Calculation The collection of images for spectral evaluation of plots subjected to different N doses was carried out on the same day as the assessment of field variables, using a Phantom 4 Multispectral RTK drone (DJI, Shenzhen, China) ( Figure 1D) and a pre-programmed flight plan with autonomous control via the GS Pro Mobile application ( Figure 3). The multispectral sensor enabled the acquisition of plant reflectance in the red (R: 660 nm ± 16 nm), green (G: 550 nm ± 16 nm), blue (B: 450 nm ± 16 nm), red-Edge (RE: 730 nm ± 16 nm), and near-infrared (NIR: 840 nm ± 26 nm) bands ( Figure 3). In addition, the sensor has a focal length of 5.74 mm, a pixel pitch of 6.1 μm and a ground sample distance (GSD) that varies according to flight altitude. Flight configurations consisted of 75% frontal and lateral overlap, a flight height of 30 m above ground level, and a nadir camera angle (90°). This configuration resulted in a spatial resolution of the orthomosaics of 3.2 cm pixel −1. All flights were conducted between 11:00 a.m. and 2:00 p.m. to ensure consistent illumination conditions. An onboard irradiance sensor (“sunshine sensor”) mounted on the upper surface of the drone was used to record solar irradiance for each spectral band during image acquisition. These measurements were subsequently used for radiometric correction and reflectance calibration of the images. Flights were conducted in “hover and capture at point” mode, in which the drone remains stationary during the acquisition of each image, eliminating motion blur and maximizing image sharpness, thereby ensuring higher image quality. Image processing was performed using the software Agisoft Metashape (version 2.0.2) to generate the orthomosaics, which were georeferenced using seven ground control points measured with GNSS-RTK for accurate geometric correction. Subsequently, spectral information was extracted from the orthomosaics using the raster calculator tool in the software QGIS (version 3.40) to separate the spectral bands of each image. For each plot, the three central rows (4 m in length each) were delineated using a shapefile vector layer, and digital numbers were extracted for the red (R), green (G), blue (B), red-edge (RE), and near-infrared (NIR) bands. Finally, different vegetation indices were calculated using both visible (RGB) and multispectral bands (NIR-based) ( Figure 3, Table 1). 2.4. Statistical Analysis To evaluate the effects of N doses, evaluation environments (phenological stages × growing seasons), and their interaction, a restricted maximum likelihood (REML) approach was used to estimate variance components and obtain adjusted values for each agronomic variable. The significance of the interaction between factors was assessed through deviance analysis ( p 50%) and intermediate residual coefficients of variation (≤10%). In contrast, the indices RGBindex, NDVI, SAVI, MSAVI, and OSAVI showed lower Rp values ( 50%. Consequently, these indices were not considered in subsequent analyses. RCC, plant height, and plant nitrogen concentration showed high Rp values and low residual coefficient, 60% and 5%, respectively ( Table 3). Additionally, NDVI Greenseeker, NGE, W100G, and grain yield exhibited intermediate Rp values (40–50%), with a greater contribution from the error variation coefficient compared to the previously mentioned variables. In contrast, plant biomass presented a lower Rp (43%) and higher contribution from the residual factor (18%), due to variation in the evaluation environments tested in the experiment. Furthermore, the accuracy of all analyzed variables remained above 70% ( Table 3). However, it is noted that the indices with higher Rp and lower residual variation coefficient achieved accuracy values above 95%. These results suggest that the experimental control was adequate, with a minor contribution of experimental error to the dataset. Similar to the behavior previously observed, differences among indices regarding phenological stages were also identified during the second growing season. Consequently, the indices grouped in 2023/2024 differed entirely from those observed in 2022/23. In this context, the PCA showed that the indices EXRM and EXR exhibited behavior similar to the variance observed exclusively at the V6 growth stage. On the other hand, NDB, TGI, EXGRaw, RGBindex, EXG, and VEG were grouped at the V8, V13, R2, and R5 phenological stages, regardless of the nitrogen dose applied ( Figure 4). These results indicate that the specificity of the spectral parameters varies according to phenological stage and growing season, which may increase the complexity associated with the generalized use of phenotypic indices. Agronomic variables subjected to BLUP analysis showed that biometric parameters also differed according to nitrogen doses and evaluation environments ( Supplementary Table S1). From the V12-V13 stage onwards, treatments receiving higher N doses (200, 300, and 400 kg ha −1) exhibited greater plant height, shoot biomass, relative chlorophyll content, and plant nitrogen concentration. A similar response was observed for grain yield components, achieving 475 grains per year in 2022/23 and 392 grains per year in 2023/24 at nitrogen doses of 300 and 200 kg ha −1, respectively. In addition, the highest grain yields were also obtained at these N doses, with values of 13,700 kg ha −1 and 8540 kg ha −1, respectively ( Figure 5). These findings support the higher repeatability coefficients and lower residual coefficients observed in the variance component analysis for these parameters ( Table 3), a pattern that was not clearly observed for NDVI Greenseeker and shoot biomass ( Supplementary Table S1). Due to the specific sampling period (phenological stage) or growing season variability, some data showed CVr values > 10% or low Rp values, resulting in lower characterization efficiency of the evaluation environments. The weight of one hundred grains was not affected by the interaction between phenological stage and growing season, with variations associated only with nitrogen dose, reaching greater grain weight when plants received 400 kg N ha −1 ( Supplementary Table S1). Based on the responses observed for the different vegetation indices and agronomic variables, an attempt was made to establish prediction models for field variables using relevant spectral information through stepwise regression analysis. The models included the intercept of the multivariate linear regression and the angular coefficient of each vegetation index ( Table 4). The adopted methodology enabled highly accurate predictions for most field variables (R 2 > 0.80), except for shoot biomass and W100G, which exhibited lower coefficients of determination of 0.71 and 0.65, respectively. Furthermore, NDVI Greenseeker, relative chlorophyll content, plant height, shoot biomass, plant nitrogen concentration, and number of grains ear −1 required, on average, 15 vegetation indices within the prediction models ( Table 4 and Figure 6). In contrast, W100G and grain yield required up to 10 predictors, highlighting the inherent complexity of each field variable and the need to identify relevant spectral vegetation indices under different evaluation environments. From the synthesis of the different indices used in the prediction models ( Figure 6), CIG, GLI, NDB, and RGBindex were able to predict 6 out of the 8 field variables evaluated. In addition, the indices BNDVI, CVI, EVI2, EXR, EXRM, MGRVI, NDVIRe, PanNDVI, RBI, RVI, and VEG were necessary to predict up to 5 field variables. Conversely, CIRE, CIVE, DVI, EVI, EXB, EXRRaw, GNDVI, GVI, NDRE, NDVI, OSAVI, RVI, SAVI, SFDVI, SRNIRRe, TGI, and VARI were associated with the prediction of 3 or fewer field variables. These findings demonstrate the existence of more generalist vegetation indices, whereas others exhibited a higher degree of specificity, depending on the variable considered. 4. Discussion Restricted maximum likelihood (RELM) analysis is a method for estimating variance components in a dataset, enabling the identification of significant variables with high repeatability, reduced influence of experimental error, and greater reliability in prediction models [ 23, 24]. In this context, repeatability coefficient analysis allows the identification of vegetation indices with greater stability and lower residual variation across nitrogen doses and evaluation environments. In addition, variables exhibiting higher repeatability and lower residual coefficients of variation demonstrate greater consistency and reliability for subsequent predictive modeling, particularly when they present Rp > 50% and low experimental error (CVr 0.80) from the V14 stage (fourteen fully developed leaves) onward. The highest predictive accuracy was achieved when data from the tasseling, full flowering, milk grain, and dough grain stages were combined (r 2 > 0.93). The analyzed environments also influenced the type of indices grouped together. Environments characterized by lower shoot biomass, plant height, relative chlorophyll content, number of grains per ear, and grain yield ( Supplementary Table S1 and Figure 5) were associated with indices derived exclusively from the visible spectrum (CIVE, EXB, EXRM, EXR, NDB, TGI, EXGRaw, RGBindex, EXG, and VEG). This pattern was particularly evident during the 2023/24 growing season, which was marked by high rainfall volumes and a greater number of cloudy days, resulting in lower grain yields ( 14,000 kg ha −1), likely due to a more favorable rainfall distribution, temperatures close to 30 °C, and fewer cloudy days ( Figure 2). Among the predicted variables, W100G presented the lowest coefficient of determination (R 2 = 0.65), despite exhibiting high stability across the evaluated environments. This comparatively lower prediction accuracy may be associated with the reduced phenotypic plasticity and limited variability of this trait among treatments, which can constrain the ability of vegetation indices to detect subtle differences through canopy reflectance. Consequently, even under stable experimental conditions, the spectral sensitivity for predicting W100G may remain relatively low, resulting in reduced predictive performance compared with other agronomic traits. Although the proposed models demonstrated high coefficients of determination for most agronomic variables, the absence of independent validation datasets and cross-validation procedures warrants caution when interpreting their predictive performance and generalizability. Recent studies on UAV-based sensing and predictive modeling have emphasized the importance of external validation approaches to ensure model robustness, reliability, and transferability across diverse environmental conditions and independent datasets [ 56]. Various predictive modeling approaches have been evaluated over time, differing in both their mathematical structure (linear or nonlinear) and computational complexity. Among these approaches, Random Forest and Support Vector Machine algorithms have been widely validated as effective tools for predicting grain yield, nutrient concentration, and plant biomass, often achieving high predictive accuracies (R 2 > 0.70) [ 57, 58]. However, the performance and practical applicability of these models may be compromised when trained on datasets characterized by multicollinearity, substantial residual variation, and low data reliability. In addition, their greater computational complexity and reduced interpretability may limit their adoption in plant phenotyping applications. 5. Conclusions This study aimed to evaluate the effects of fixed factors and environmental conditions on the dynamics of vegetation indices used for predicting agronomic variables in maize, emphasizing the importance of considering these factors for the appropriate selection of predictor indices in modeling approaches. The main conclusions were as follows: all vegetation indices were influenced by nitrogen doses and evaluation environments (phenological stages and growing seasons), with higher repeatability coefficients and lower coefficients of error variation observed for EXGRaw, TGI, GNDVI, NDRE, CIRE, GVI, CVI, BNDVI, PanNDVI, SRNIRRe, and SFDVI. Furthermore, a clear specificity was observed between vegetation indices and phenological stages, with multispectral indices predominantly associated with conditions of greater plant height, shoot biomass (e.g., V12, V13, V18, R2, and R5), and grain yield. In contrast, RGB-based indices were mainly grouped in environments characterized by lower shoot biomass at early growth stages (e.g., V6 and V8) and in growing seasons with lower grain yield potential. Finally, the proposed methodology enabled the identification of the most suitable indices for estimating maize agronomic variables with high accuracy using a multivariate linear modeling approach. Author Contributions C.d.S.L.: Conceptualization, methodology, validation, visualization, writing—original draft, writing—review and editing. A.J.T.S.: Data collection and investigation. B.d.S.N.: Data collection and investigation. A.L.V.: Conceptualization, review and supervision. I.R.C.: editing, software, formal analysis and methodology. C.B.: Supervisor, review, writing, funding acquisition and project administration. All authors have read and agreed to the published version of the manuscript. Data Availability Statement The data supporting the study findings are available on request from the corresponding authors. The data are not publicly available due to the authors’ plan to conduct a series of follow-up studies based on this dataset. Figure 1. Localization of the experimental area ( A, B), experimental design ( C) and remote sensing platforms used ( D). Figure 1. Localization of the experimental area ( A, B), experimental design ( C) and remote sensing platforms used ( D). Figure 2. Temperature and precipitation data during the 2022/23 ( A) and 2023/24 ( B) growing seasons. Figure 2. Temperature and precipitation data during the 2022/23 ( A) and 2023/24 ( B) growing seasons. Figure 3. Workflow for data acquisition and analysis during the maize growing season of 2022/2023 (S1) and 2023/2024 (S2) in different phenological stages. Figure 3. Workflow for data acquisition and analysis during the maize growing season of 2022/2023 (S1) and 2023/2024 (S2) in different phenological stages. Figure 4. Principal components analysis of the BLUP values for each vegetation index. Variance explained by PC1 and PC2 was 72% and 18,3%, respectively. Figure 4. Principal components analysis of the BLUP values for each vegetation index. Variance explained by PC1 and PC2 was 72% and 18,3%, respectively. Figure 5. BLUP estimates of maize grain yield under different nitrogen doses during the 2022/2023 ( A) and 2023/2024 ( B) growing seasons. Figure 5. BLUP estimates of maize grain yield under different nitrogen doses during the 2022/2023 ( A) and 2023/2024 ( B) growing seasons. Figure 6. Map showing the frequency and number of predictor vegetation indices for each field variable in maize. Yellow and green rectangles represent the absence or presence, respectively, of each vegetation index in the prediction model for each variable. Figure 6. Map showing the frequency and number of predictor vegetation indices for each field variable in maize. Yellow and green rectangles represent the absence or presence, respectively, of each vegetation index in the prediction model for each variable. Table 1. List of spectral vegetation indices calculated in this study. Table 1. List of spectral vegetation indices calculated in this study. Type Vegetation Indices Equation RGB Excess of green (EXG) 2 ∗ [G/(R + G + B)] − [R/(R + G + B)] − [B/(R + G + B)] Excess of green raw (EXGRaw) 2 ∗ G − R − B Excess of red (EXR) (1.4 ∗ R − G)/(R + G + B) Excess of red raw (ExRRaw) 1.4 ∗ R − G Vegetation extraction color index (CIVE) (0.44 ∗ R−0.81 ∗ G + 0.39 ∗ B)/(R + G + B)+ 18.79 Normalized green-red index (GRVI) (G − R)/(G + R) Modified excess of red (ExRM) (2 ∗ R − G − B)/(R + G + B) Vegetative index (VEG) G/(r 0.667 ୍ଠ ଭ 0.333) r = R/(R + G + B), g = G/(G + R + B), b = B/(R + G + B) Excess of blue (ExB) (1.4 ∗ B − G)/(R + G + B) Normalized difference of blue (NDB) (G − B)/(G + B) Atmospheric resistant index in the visible (VARI) (G − R)/(G + R - B) Green leaf index GLI ((G - R) + (G - B))/(2 ∗ G + R + B) Triangular green index (TGI) TGI = −0.5 × [190 (R − G) − 120(R − B)] Red-Blue index (RBI) (R − B)/(R + B) Modified green-red index (MGRVI) (G 2 − R 2)/(G 2 + R 2) RGB index RGBindex (G 2−B ∗ R)/ (G 2 + B ∗ R) MULTIESPECTRAL Normalized Difference (NDVI) (NIR – R)/(NIR + R) Red Edge (NDRE) (NIR – RE)/(NIR + RE) Soil Adjusted Index (SAVI) (1 + 0.5) ∗ [(NIR – R)/(NIR + R + 0.5)] Modified Soil Adjusted Index (MSAVI) 2 ∗ NIR + 1 − √(2 ∗ NIR + 1) 2 − 8(NIR − R)]/2 Optimized Soil Adjusted Index (OSAVI) 1.16 ∗ ((NIR−R)/(NIR + R + 0.16)) Enhanced Vegetation Index (EVI) 2.5 ∗ (NIR-R)/(NIR + 6 ∗ R −7.5 ∗ B + 1) Normalized Difference of Green (GNDVI) ((NIR−G)/(NIR + G)) Green Chlorophyll Index (CIG) (NIR/G) − 1 Rededge Chlorophyll Index (CIRE) (NIR/RE) − 1 Simple Ratio Index (RVI) NIR/R Vegetation Difference Index (DVI) NIR−R Green Vegetation Difference Index (GDVI) NIR−G Green Ratio Vegetation Index (GVI) NIR/G Vegetation-Chlorophyll Index (CVI) (NIR ∗ R)/(G 2) Enhanced Vegetation Index 2 (EVI2) 2.5 ∗ (NIR−R)/(NIR + 2.4 ∗ R + 1) Normalized Difference of Blue (BNDVI) (NIR − B)/(NIR + B) Normalized Difference R-Re (NDVIRE) (RE − R)/(RE + R) PanNDVI (PanNDVI) (NIR − (G + R+B))/(NIR + (G + R+B)) Simple Ratio NIR/RE (SRNIRRe) NIR/RE Spectral Feature Depth (SFDVI) ((NIR + G)/2)/((R + RE)/2) Table 2. Deviance analysis using the maximum likelihood ratio test (LRT) ( p < 0.05). Table 2. Deviance analysis using the maximum likelihood ratio test (LRT) ( p < 0.05). Model EXG EXGRaw EXR EXRRaw CIVE GRVI EXRM Doses of N ୫.୨୪ ୍ଠ ୧୦ −7୨.୨୧ ୍ଠ ୧୦ −90.00253 0.00057 ୨.୪୬ ୍ଠ ୧୦ −90.00389 0.24621 Doses*Evaluation Environments ୯.୦୯ ୍ଠ ୧୦ −5୧.୭୨ ୍ଠ ୧୦ −19୨.୯ ୍ଠ ୧୦ −11୧.୬୨ ୍ଠ ୧୦ −16୫.୫୦ ୍ଠ ୧୦ −19୧.୩୧ ୍ଠ ୧୦ −14୨.୫୪ ୍ଠ ୧୦ −21Model VEG EXB NDB VARI GLI TGI RBI Doses of N ୫.୩୬ ୍ଠ ୧୦ −60.00262 0.01216 0.00969 0.06862 ୨.୪୩ ୍ଠ ୧୦ −91.00000 Doses*Evaluation Environments ୪.୬୦ ୍ଠ ୧୦ −12୬.୬୯ ୍ଠ ୧୦ −19୨.୯ ୍ଠ ୧୦ −28୩.୬୨ ୍ଠ ୧୦ −24୫.୩୫ ୍ଠ ୧୦ −16୯.୮୯ ୍ଠ ୧୦ −21୧.୭୩ ୍ଠ ୧୦ −48Model MGRVI RGBindex NDVI SAVI MSAVI OSAVI EVI Doses of N 0.00514 ୪.୧୮ ୍ଠ ୧୦ −82.3 x10 −72.19 x10 −7୯.୬୧ ୍ଠ ୧୦ −72.32 x10 −70.56113 Doses*Evaluation Environments ୪.୨୭ ୍ଠ ୧୦ −8୧.୭୧ ୍ଠ ୧୦ −5୨.୯ ୍ଠ ୧୦ −10୨.୮୩ ୍ଠ ୧୦ −10୨.୦୧ ୍ଠ ୧୦ −8୨.୯୬ ୍ଠ ୧୦ −10୩.୪୯ ୍ଠ ୧୦ −7Model GNDVI CIG NDRE CIRE RVI DVI GDVI Doses of N ୨.୩୫ ୍ଠ ୧୦ −14୩.୦୩ ୍ଠ ୧୦ −12୧.୬ ୍ଠ ୧୦ −13୮.୦୨ ୍ଠ ୧୦ −12୧.୨୦ ୍ଠ ୧୦ −10୯.୪୮ ୍ଠ ୧୦ −12୬.୬୯ ୍ଠ ୧୦ −14Doses*Evaluation Environments ୪.୮୬ ୍ଠ ୧୦ −6୩.୮୮ ୍ଠ ୧୦ −10୧.୫ ୍ଠ ୧୦ −27୫.୦୬ ୍ଠ ୧୦ −31୫.୯୯ ୍ଠ ୧୦ −6୩.୬୫ ୍ଠ ୧୦ −3୪.୩୪ ୍ଠ ୧୦ −2Model GVI CVI EVI2 BNDVI NDVIRe PanNDVI SRNIRRe Doses of N ୩.୦୩ ୍ଠ ୧୦ −12୧.୭୬ ୍ଠ ୧୦ −12୫.୮ ୍ଠ ୧୦ −8୨.୬୨ ୍ଠ ୧୦ −11୮.୪୮ ୍ଠ ୧୦ −2୧.୫୮ ୍ଠ ୧୦ −13୧.୫୮ ୍ଠ ୧୦ −12Doses*Evaluation Environments ୩.୮୮ ୍ଠ ୧୦ −10୬.୩୩ ୍ଠ ୧୦ −14୯.୪ ୍ଠ ୧୦ −11୧.୧୧ ୍ଠ ୧୦ −5୮.୦୮ ୍ଠ ୧୦ −6୨.୮୫ ୍ଠ ୧୦ −5୨.୫୦ ୍ଠ ୧୦ −19Model SFDVI NDVIG RCC Plant height Shoot biomass NGE W100G Doses of N ୩.୧୫ ୍ଠ ୧୦ −14୫.୭ ୍ଠ ୧୦ −8୧.୩ ୍ଠ ୧୦ −9୯.୪ ୍ଠ ୧୦ −11୨.୪୧ ୍ଠ ୧୦ −60.11902 0.04193 Doses*Evaluation Environments ୨.୪୩ ୍ଠ ୧୦ −3୪.୩ ୍ଠ ୧୦ −7୧.୭ ୍ଠ ୧୦ −22୩.୮ ୍ଠ ୧୦ −27୫.୨୨ ୍ଠ ୧୦ −29୧.୫ ୍ଠ ୧୦ −80.24488 Model Grain yield Plant nitrogen content (PNC) Doses of N 0.13656 ୧.୫୯ ୍ଠ ୧୦ −12Doses*Evaluation Environments ୧.୯ ୍ଠ ୧୦ −8୬.୫୦ ୍ଠ ୧୦ −13 NDVIG: NDVI Greenseeker, RCC: Relative chlorophyll content, Shoot biomass: Shoot dry biomass (kg ha −1), NGE: number of grains per ear, W100G: weight of one hundred grains, Plant nitrogen content (PNC): % of nitrogen in plant. Table 3. Estimates of variance components by restricted maximum likelihood (REML) for the vegetation indices and variables analyzed in different phenological stages and two growing seasons in maize. Table 3. Estimates of variance components by restricted maximum likelihood (REML) for the vegetation indices and variables analyzed in different phenological stages and two growing seasons in maize. Variables Phenotypic Variance Repeatability Coefficient Accuracy CVr EXG <0.01 0.30 0.96 7.73 EXGRaw 34,022.94 0.50 0.97 10.50 EXR <0.01 0.17 0.90 24.02 CIVE 5511.53 0.50 0.97 11.51 GRVI <0.01 0.17 0.89 9.50 EXRM <0.01 0.06 0.71 16.04 VEG 0.03 0.32 0.95 5.19 EXB <0.01 0.20 0.89 12.73 NDB <0.01 0.17 0.87 5.14 VARI 0.01 0.17 0.87 9.03 GLI <0.01 0.10 0.81 2.64 TGI 8538.50 0.51 0.97 10.07 MGRVI <0.01 0.14 0.88 8.40 RGBindex <0.01 0.35 0.96 5.15 NDVI <0.01 0.42 0.97 3.86 SAVI <0.01 0.37 0.96 3.87 MSAVI <0.01 0.33 0.95 2.68 OSAVI <0.01 0.42 0.97 3.86 GNDVI 0.01 0.69 0.99 5.24 CIG 1.46 0.66 0.99 13.22 NDRE <0.01 0.67 0.98 7.02 CIRE 0.05 0.62 0.98 10.11 RVI 3.13 0.46 0.98 11.96 DVI 279,301.62 0.45 0.98 9.34 GDVI 400,991.23 0.60 0.99 10.07 GVI 1.46 0.66 0.99 10.56 CVI 0.53 0.69 0.99 10.80 EVI2 0.02 0.40 0.96 5.02 BNDVI <0.01 0.58 0.98 2.44 NDVIRe <0.01 0.09 0.83 5.34 PanNDVI 0.01 0.65 0.99 12.29 SRNIRRe 0.07 0.71 0.99 4.53 SFDVI 56,236.85 0.64 0.99 9.73 NDVIG <0.01 0.46 0.97 4.62 RCC 55.00 0.62 0.98 5.88 Plant height 361.61 0.63 0.98 4.25 Shoot biomass 1,045,457,500 0.44 0.95 18.00 Number of grains ear −110553.18 0.59 0.97 8.31 100-grain weight 16.06 0.55 0.99 8.26 Grain yield 10,186,376.14 0.57 0.97 11.43 Plant nitrogen content (PNC) 0.32 0.69 0.99 12.00 CVr: coefficient of variation in the residual. Table 4. Multivariate models for predicting agronomic variables based on vegetation indices in maize. Table 4. Multivariate models for predicting agronomic variables based on vegetation indices in maize. Predicted Variable Selected Vegetation Indices R 2Adjusted p < 0.05 NDVI Greenseeker * (Intercept: 6.38) ** (0.003) EXRRaw, (−0.03) CIVE, (−3.0) VEG, (17.36) EXB, (59.65) NDB, (−0.02) TGI, (−19.69) RBI, (3.94) MGRVI, (−24.47) RGBindex, (3730) NDVI, (−2481) SAVI, (−11.65) GNDVI, (0.0003) DVI, (−2.83) EVI2, (−3.30) NDVIRe, (9.73) PanNDVI, (−0.001) SFDVI 0.93 ୨ ୍ଠ ୧୦ −16Relative chlorophyll content (RCC) (Intercept: 1450) (5757) EXR, (−0.07) EXRRaw, (0.04) CIVE, (−4421) EXRM, (4529) NDB, (−4299) GLI, (−1189) RBI, (1473) MGRVI, (−1987) RGBindex, (−15.71) CIRE, (2.20) GVI, (84.64) EVI2, (−194) NDVIRe 0.86 ୨ ୍ଠ ୧୦ −16Plant height (Intercept: 60910) (117800) EXR, (1.68) CIVE, (74660) GRVI, (37530) NDB, (−6745) VARI, (92030) GLI, (0.97) TGI, (−26700) RGBindex, (−268.60) CIG, (2008) NDRE, (70.05) RVI, (191.60) CVI, (−3249) BNDVI, (2095) NDVIRe 0.89 ୨ ୍ଠ ୧୦ −16Shoot biomass (Intercept: −28000000) (25860000) EXR, (21930000) GRVI, (21510000) EXRM, (−503500) VEG, (19100000) NDB, (50270000) GLI, (−6657000) RBI, (1308000) MGRVI, (−15950000) RGBindex, (204500000) NDVI, (−136300000) SAVI, (−1122) EVI, (−2947) CIG, (44410) NDRE, (−285500) BNDVI, (158100) PanNDVI 0.71 ୨ ୍ଠ ୧୦ −16Plant nitrogen concentration (PNC) (Intercept: 1667) (−2975) EXR, (−1502) GRVI, (40.29) VEG, (−1683) NDB, (76.47) VARI, (−2635) GLI, (0.005) TGI, (344.10) RBI, (959) RGBindex, (28.50) OSAVI, (0.43) CIG, (−1.41) CIRE, (−17.94) EVI2, (24.63) BNDVI 0.87 ୨ ୍ଠ ୧୦ −16Number of grains ear −1(Intercept0: 95389) (−300483) EXR, (231189) EXB, (−118205) MGRVI, (50691) RGBindex, (65919) SAVI, (6727) CIG, (−2683) CIRE, (−2773) RVI, (−4105) CVI, (−101759) EVI2, (−47033) BNDVI, (−17368) NDVIRe, (142005) PanNDVI, (125000) NDB 0.80 ୪ ୍ଠ ୧୦ −10100-grain weight (Intercept: −7230) (6518) EXRM, (−280) VARI, (13488) GLI, (−1478) RGBindex, (−118) CIG, (50) RVI, (84) CVI, (609) EVI2, (168) NDVIRe, (−1238) PanNDVI 0.65 ୧ ୍ଠ ୧୦ −7Grain yield (Intercept: −4217772) (4862062) EXRM, (320572) VEG, (−1559654) NDB, (8022900) GLI, (22051) GNDVI, (14563) CIG, (307968) NDRE, (−26282) CVI, (−70675) SRNIRRe 0.85 ୧ ୍ଠ ୧୦ −14 * Intercept value of the equation for each model, ** Angular coefficient for each vegetation index within the model. Share and Cite MDPI and ACS Style Lima, C.d.S.; Soares, A.J.T.; Nogueira, B.d.S.; Vian, A.L.; Carvalho, I.R.; Bredemeier, C. Methodology for Selecting Stable UAV-Based Vegetation Indices for Prediction of Agronomic Variables in Maize Using a Multispectral Sensor. Plants 2026, 15, 1782. https://doi.org/10.3390/plants15121782 AMA Style Lima CdS, Soares AJT, Nogueira BdS, Vian AL, Carvalho IR, Bredemeier C. Methodology for Selecting Stable UAV-Based Vegetation Indices for Prediction of Agronomic Variables in Maize Using a Multispectral Sensor. Plants. 2026; 15(12):1782. https://doi.org/10.3390/plants15121782 Chicago/Turabian Style Lima, Charleston dos Santos, Ana Júlia Teixeira Soares, Bárbara da Silva Nogueira, André Luis Vian, Ivan Ricardo Carvalho, and Christian Bredemeier. 2026. "Methodology for Selecting Stable UAV-Based Vegetation Indices for Prediction of Agronomic Variables in Maize Using a Multispectral Sensor" Plants 15, no. 12: 1782. https://doi.org/10.3390/plants15121782 APA Style Lima, C. d. S., Soares, A. J. T., Nogueira, B. d. S., Vian, A. L., Carvalho, I. R., & Bredemeier, C. (2026). Methodology for Selecting Stable UAV-Based Vegetation Indices for Prediction of Agronomic Variables in Maize Using a Multispectral Sensor. Plants, 15(12), 1782. https://doi.org/10.3390/plants15121782 Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here. Article Metrics Article metric data becomes available approximately 24 hours after publication online.

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