In view of the details of the entire context and the methodology proposed and applied in the study, the results section presents the main highlights achieved. The results of the field variables and the different models presented, as well as the results of the UAV and Senitnel-2A/MSI, are accompanied by a series of statistical analyses, from classical to multivariate approaches.
3.2. Prediction of Productive Components
As shown in
Table 3, the IVs were better correlated with plant height in R9, where all were followed (
p-value < 0.01), the highest skill coordinators, and the lowest RMSE.
The TGI was the only parameter to show a strong correlation (r = 0.73) in R9, with a lower RMSE (7.4 cm), as expressed in the linear regression model, Equation (11). Except for SIPI2, which had the lowest fit and negative correlation (r = −47 and RMSE = 9.7 cm), the other IVs expressed moderate positive correlation (0.59 < r < 0.65; 8.3 < RMSE < 8.8 cm), indicating the viability of IVs in predicting plant height.
where x = TGI value.
Only SIPI2 was significant in V4 and VARI was the only one in R5, with correlations in both phenological stages classified as weak (−0.40 < r < 0.40). The VARI and GNDVI IVs were significant at 1% in R6 and NDRE and LCI at 5%, with r values between 0.41 and 0.57 and RMSE between 9 and 10 cm. The MCARI was the only significant IV (
p < 0.05) in R8 but with a correlation coefficient of 0.40. The VARI index had the best performance of the others in the phenological stages evaluated preceding the last one, but in R9 it had a lower performance than NDVI, MCARI, and TGI, the latter being the most prominent. Linear regression models for predicting this variable using MCARI, NDVI, and VARI are described by Equations (12), (13) and (14), respectively.
where x = MCARI value.
where x = NDVI value.
where x = VARI value.
As shown in
Table 4, for the number of pods per plant, there were no strong correlations (r > 0.7) with the vegetation indices at any phenological stage, with r values above 0.5 only in R9. There were moderate and significant correlations at 1% in this stage and at 5% in the other stages, except for R5.
Correlation coefficients above 0.6 were found in R9 for the GNDVI, NDVI, LCI, NDRE, and MCARI indices. The respective linear regression models for predicting this variable are described by Equations (15), (16), (17), (18), and (19), respectively.
where x = GNDVI value.
where x = NDVI value.
where x = LCI value.
where x = NDRE value.
where x = MCARI value.
The vegetation index that best described this variable was the GNDVI, which was significant in V4, R6, and R9, in addition to having the highest correlation coefficient value (r) and the lowest RMSE for the others in R6 and R9. In addition to GNDVI, SIPI2 was significant in V4 and R6, and MCARI in R8. In the stages preceding R9, when the pods had already formed, the correlations were weak or moderate.
Like what was observed in the remaining variables, SIPI2 was the only index with a negative correlation coefficient, and to a lesser extent in R9, being non-significant and classified as weak in predicting the number of variables. The normalized difference indices of the multispectral bands showed better performance, except for SIPI2. The GNDVI, NDVI, NDRE, LCI, and MCARI exhibited correlation coefficients greater than 0.60 and a RMSE between 4 and 4.1, while the VARI and TGI had correlation coefficients below 0.54 and RMSE between 4.3 and 4.5.
There was no strong correlation between the number of grains per pod at any phenological stage (
Table 5). Among the significant variables, the correlation was moderate, with r values between 0.36 and 0.68, which indicates little efficiency of the models in predicting this variable under the conditions studied.
The best fits were obtained for SIPI2 and VARI at R5 (RMSE = 0.7 and r = 0.68 and 0.66, respectively), as shown in Equations (20) and (21) corresponding to the respective linear regression models. The MCARI was the only vegetation index that exhibited a moderate and significant correlation in R8 (r = 0.44), while it was also significant in R5, R6, and R9, with r values between 0.56 and 0.58 and RMSE = 0.8. It can be observed that in the phenological stages V4 and R8, the adjustments were lower than in the others.
where x = SIPI2 value.
where x = VARI value.
The LCI in Stage V4, and the NDVI and SIPI2 in Stage R8, were significant at a 5% probability level (p < 0.05) for the linear regressions corresponding to the mass of a thousand grains, with correlation coefficients of −0.42, 0.39, and 0.35, and a RMSE of 18.6, 18.9, and 19.2 g, respectively. Overall, this variable showed only weak correlations across all the estimates. The NDRE showed a significant correlation at 5% for the number of branches per plant, at Stage R5 (r = −0.37). Similarly, to the mass of a thousand grains, this variable did not show significant correlations in most samples, all of which were classified as weak (r < 0.40).
The best correlations and efficiency of the regression models were found for productivity (kg ha
−1), for which there was statistical significance for at least one of the indices in all the phenological stages considered (
Table 6), in addition to all the significant indices being at 1% significance level in R9.
VARI and SIPI2 indices evolved significantly, with the latter being inversely proportional to the analyzed variable (r = −0.60). The other indices showed strong positive correlation coefficients. The MCARI and NDVI exhibited the best performance with r = 0.82 and a RMSE below 331 kg ha
−1. Equations (22) and (23) represent the linear regression models of these indices for predicting productivity in this stage. Following that, the GNDVI, LCI, NDRE, and TGI stood out with r values between 0.74 and 0.78 and a RMSE between 355 and 385 kg ha
−1. These models are expressed by Equations (24), (25), (26), and (27), respectively.
where x = MCARI value.
where x = NDVI value.
where x = GNDVI value.
where x = LCI value.
where x = NDRE value.
where x = TGI value.
The indices exhibited negative correlation coefficients at stage V4, indicating an inverse proportion between them and the dependent variable, with only the MCARI showing a significant correlation (r = −0.37). Significant correlations were observed for the GNDVI, NDRE, MCARI, and VARI at Stages R5, R6, and R8, all of which were moderate or weak, ranging between 0.36 and 0.58. During these stages, all plots displayed high vegetative vigor and canopy coverage, leading to peak values for the indices. Several authors have reported the saturation of certain VIs, especially NDVI [
70], when they reach higher values.
Overall, MCARI exhibited the highest efficiency in predicting yield, being significant at 5% in treatments V4, R6, and R8, and were significant at 1% in R9. The GNDVI and NDRE were significant at 1% in treatments R6 and R9. With moderate correlations, VARI was significant at R5, R6, and R9.
Figure 8 displays heat maps with Pearson’s dynamics matrix depicting all possible combinations of vegetation indices and productive components for each phenological stage.
Stage V4 presented the weakest correlations, many of which were inverse, between the vegetation indices and other variables, probably due to the strong interference of the soil in the reflectance. The adjustments had a certain progression up to the R6 stage, observed in R8, which can be explained by the uniformity of the vegetative canopy, decrease in the variance between plots, and saturation of some VIs, presenting the maximum values in the entire cycle at this stage.
The best period for predicting the analyzed parameters was at the beginning of R9, when the plants started the process of senescence and grain control, allowing the identification of the best adjustments, with strong automatic coordinators, both between the IVs themselves and between these and other variables (
Figure 8e). SIPI2 was the only index with negative r values for all other variables.
Productivity was the variable with the best prediction based on vegetation indices, followed by plant height. The number of pods per plant and grains per pod presents moderate correlations, however with lower comprehension coefficients. At the models’ best performance stage (R9), these variables showed strong or moderate correlations, with a lower RMSE and proximity of observed data to those predicted by linear regression (
Figure 9). The models for predicting the mass of a thousand grains and the number of branches per plant have not presented a significant correlation.
As depicted in
Figure 9, the correlations between IVs with greater statistical significance and r values closer to 1.0 (0.93 < r < 0.99) were observed among vegetation indices derived from multispectral bands, except for SIPI2, which displayed an inverse relationship to the others and coefficients of influence smaller than 0.64. IVs derived from RGB images exhibited a strong correlation with each other (r = 0.87) and with the NDVI, GNDVI, NDRE, MCARI, and LCI indices (0.77 < r < 0.92), with the VARI showing better correlation with these indices than the TGI.
3.3. Prediction of Chlorophyll Content
In
Table 7, it can be observed that the VIs did not exhibit a significant difference (
p < 0.05) concerning chlorophyll content in Stages V4, R6, and R8. However, for Stage R5, there was a moderate and significant correlation at 5% with the MCARI (r = 0.60), VARI (r = 0.61), and TGI (r = 0.57) indices. Among these, the VARI demonstrated the lowest RMSE (16.76), the highest correlation coefficient, and, consequently, the model with the best fit.
Figure 10 illustrates the dispersion of the data, the RMSE, the equation, and the coefficient of determination of the line (R
2) for the IVs.
The RMSE values can only be compared within the same column of
Table 7 since they are influenced by the magnitude of the values of the variable they describe, and the general averages of the chlorophyll contents were different in the different stages of development of the crop, increasing until reaching the peak at R6 and then declining. This explains the low values for RMSE in V4, for example, even though the correlation coefficient was close to zero for all vegetation indices.
Most of the IVs achieved R
2 values above 0.6 (
Figure 11), considering the assessment made at the beginning of the plant senescence period and grain maturation (R9), thus demonstrating good fits of the regression models and, consequently, the high potential of these indices to estimate the chlorophyll content in the common bean crop under the conditions of the present study.
According to the graphs in
Figure 11, in Stage R9, there was a significant interaction with 7 of the 8 vegetation indices tested, showing a strong Pearson correlation and lower RMSE values for MCARI (r = 0.81), NDVI (r = 0.81), NDRE (r = 0.79), LCI (r = 0.79), GNDVI (r = 0.78), and VARI (r = 0.78). Equations (28)–(33) represent the linear regression models of these indices for predicting chlorophyll content. The TGI and SIPI2 exhibited moderate correlation, 0.59 and −0.48, respectively, and the RMSE for both was higher compared to the others (14.03 and 15.16), with SIPI2 being the only non-significant IV.
where x = MCARI value.
where x = NDVI value.
where x = NDRE value.
where x = LCI value.
where x = GNDVI value.
where x = VARI value.
The IVs that exhibited the best performance for the analysis of chlorophyll content were the MCARI and NDVI, with R
2 values of 0.66 and 0.65, respectively. The NDRE, LCI, GNDVI, and VARI also demonstrated prediction coefficients close to these, with R
2 values ranging between 0.60 and 0.63, indicating their high potential for monitoring chlorophyll contents in the vegetative canopy. However, SIPI2 deviated from the other IVs, showing a negative correlation, lower R
2 (0.24), and higher RMSE (15.16). Tisost [
71] also obtained negative results between SIPI2 and chlorophyll content, with an R
2 of 0.25.
Regarding the chlorophyll content and productive variables, no significance was obtained in the regressions for the estimates made in V4, R5, R6, and R8. In R9, there were significative interactions with productivity (
p-value < 0.01), pods per plant, and grains per pod (
p-value < 0.05). Correlations for the number of pods per plant and grains per pod were moderate, with values of r = 0.59 and 0.61, respectively, while for productivity it was strong (r = 0.78). Javed et al. [
72] also found positive correlations between chlorophyll concentration and grain yield.
Figure 12 allows characterizing the behavior of the relationship between relative chlorophyll content, productivity, and vegetation indices in the phenological stage R9.
The UAV detection of different crop responses based on vegetation indices highlights an important complement to agricultural management and monitoring, particularly considering the challenges in experimental field conditions. Therefore, the combined results provide effective support, primarily for monitoring bean crop growth, facilitating management decisions almost in real time.
3.5. Satellite Data Analysis (Sentinel-2A/MSI)
In addition to the various analyses, multispectral data from Sentinel-2A/MSI were also applied to the study area, with a spectral resolution of 10 and 20 m, depending on the estimated indices. Thematic maps were generated to visualize the surface estimates of normalized vegetation indices (NDVI, NDMI_GAO, and NDWI_GAO), with values ranging between −1 and 1.
Figure 14 illustrates these thematic maps, which depict various aspects such as photosynthetic activity (RGB), the NDVI, NDMI_GAO, and NDWI_GAO (are presented on the map in columns). The maps correspond to specific dates, namely 19 July 2021 (V4), 3 August 2021 (R5), 16 August 2021 (R6), 30 August 2021 (R8), and 14 September 2021 (R9) (are presented on the map in lines), representing the progress of days of analysis of treatments from the field experiment. Each line of the map provides a spatial analysis highlighting the respective biophysical indices, offering insights into the vegetation dynamics and health over time during the common bean crop cycle.
The use of the infrared multispectral band is important to evaluate photosynthetic and chlorophyll activity, mainly due to the RGB combination of the near-infrared (Band 8), red (Band 4), and green (Band 3) multispectral bands, in addition to the applicability of the indices biophysical. Therefore, throughout the bean crop cycle, the indices showed a significant increase in their density, which presented healthy vegetation, important for adequate development and effective productivity (
Figure 14).
In
Figure 14, it is observed that the NDVI, NDMI_GAO, and NDWI_GAO have a similar spectral behavior pattern throughout the phenological stages of the bean crop. The vegetation indices used by default vary between −1 and 1. More specifically, the NDVI varied from 0.05 to 0.88, the NDMI_GAO between −0.16 and 0.49, and the NDWI_GAO varied from −0.80 to −0.40. Throughout the bean crop cycle (99 DAS), as it developed, an increase in indices was observed, highlighting the contribution of plant biomass.
The NDVI thematic map was sensitive, as expected, especially on 3 August 2021, 16 August 2021, and 30 August 2021 (corresponding to treatments R5 (47 DAS), R6 (60 DAS), and R8 (74 DAS), respectively), which presented the highest NDVI values, identifying the potential of vegetation green of the bean crop. It is worth highlighting that the spectral explosion in the experimental area with the bean crop occurs, mainly, after the application of the magnesium dose, at 56 days (
Figure 14).
The NDVI identified values between 0.40 and 0.50 in the crop growth stage. With the crop in a good state of vegetation, values between 0.60 and 0.70 were observed. According to the results, the bean crop expressed its maximum biomass productivity potential when values from 0.80 were observed, reaching its saturation point (
Figure 14).
The NDMI_GAO thematic map was sensitive in identifying the pattern of change in water content in the leaves of the bean crop. It followed spectral behavior like the NDVI, mainly on 16 August 2021 and 30 August 2021. The NDMI_GAO values characterized around zero correspond to crop water stress. The highest positive values of the NDMI_GAO represent leaves without water stress, especially those close to or equal to 1. The NDMI_GAO also efficiently highlighted the moisture distribution conditions in the experimental area (
Figure 14).
The NDWI_GAO was also sensitive to the water content present in the leaves of the bean crop. And it followed the same pattern of spectral behavior as the other normalized indices, for all days of analysis and treatments. The spectral behavior of the NDWI_GAO demonstrated healthy vegetation throughout the phenological stages of the bean crop, due to the water present in the leaf canopy (
Figure 14).
3.6. Multivariate Analysis: PCA and CCC from Sentinel-2A/MSI x UAV to Treatments (V4, R5, R6, R8, and R9)—Values of the NDVI
Figure 15 highlights the multivariate statistical analysis of principal components—PC1 and PC2 (
Figure 15a) and the Pearson correlation (
Figure 15b) as a function of the UAV and Sentinel-2A/MSI. The responses are based on the average pixel of the NDVI calculation, according to the variables predicting the phenological stages of the crop (V4, R5, R6, R8, and R9), totaling 32 samples for the UAV and 32 for the Sentinel-2A/MSI. It is noteworthy that according to the criterion established by Kaiser [
66], the eigenvalues must be greater than 1 for the components to have a significant information load, which is observed in PC1 and PC2. However, it should be noted that the total variance of the sum of PC1 and PC2 is highly significant, with a total variance of around 88.08% for the experimental area with common beans (
Figure 15a).
Between treatments V4 and R9, a significant inversely proportional correlation was observed, with a negative relationship coefficient of −0.8. This response pattern is attributed to the initial phenological stage of the common bean crop (V4) being spectrally confused with the final stage of leaf senescence (R9). During R9, the crop experiences a decrease in chlorophyll pigments and defoliation, resulting in reduced photosynthetic activity, which adversely affects the NDVI values.
On the other hand, in treatments R5 and R6, it was observed a highly significant correlation, indicating a positive relationship coefficient of 0.9. This similar spectral behavior can be attributed to both stages of the common bean crop being in full formation and development, characterized by excellent photosynthetic activity and high chlorophyll content. Additionally, both R5 and R6 showed a good correlation with R8, with a positive relationship coefficient of 0.5. These phenological stages coincide with the application of MgSO4 via foliar spray at 27 and 56 DAS.
Figure 16 illustrates the optimal grouping method for the UAV and Sentinel-2A/MSI samples (four doses of magnesium sulfate—MgSO
4: 0, 250, 500, and 1000 g ha
−1), determined using the multivariate analysis of the Cophenetic Correlation Coefficient (CCC), which employed the median method. This grouping method demonstrated a satisfactory adjustment with a CCC value of 0.8776 (with a reference value of CCC > 0.70) and a
p-value of 0.001 (with a reference value of
p < 0.01), as established in [
68]. Thus, this grouping method is recommended for the joint analysis of UAV and satellite data.
Cluster analysis using the CCC confirmed the formation of two distinct groups (Cluster 1 and 2), exhibiting similar pattern responses within each group (
Figure 16). Cluster 1 comprises samples from stages R5, R6, and R8, for both the UAV and the Sentinel-2A/MSI satellite. Within this cluster, the joint correlation between R5_UAV and R5_Sentinel-2A/MSI is noteworthy, indicating no observed distinction in the phenological stage with the use of multispectral geotechnologies. Additionally, the correlation between R6_UAV and R8_UAV is notable, with analysis conducted at 60 and 74 days, respectively. Both also demonstrated a correlation with R8_Sentinel-2A/MSI and R6_Sentinel-2A/MSI (
Figure 16). It is important to highlight that UAV and orbital technologies detected more homogeneous pixel patterns in the experimental area of the common bean, especially when NDVI values were high.
Cluster 2 consists of samples from Stages V4 and R9, for both the UAV and the Sentinel-2A/MSI. Within this cluster, the similarity and correlation pattern of the V4_Sentinel-2A/MSI with R9_Sentinel-2A/MSI stands out, along with their correlation with the V4_UAV and R9_UAV. Despite being different periods representing the beginning (V4) and end (R9) of the common bean crop cycle, they exhibited conditions of low photosynthetic activity and chlorophyll content. Notably, even when the NDVI values are low, Sentinel-2A/MSI tends to homogenize the pixels, which differs from the UAV, highly sensitive in quantitatively detecting differences between V4 and R9, with V4_UAV observing the lowest NDVI values compared to the R9_UAV (
Figure 16).