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Results and Discussion
- Hyperspectral field reflectance measurements to estimate wheat grain yield and plant height

Wheat grain yield and final plant height ranged from 1,628 kg ha-1 to 5,593 kg ha-1, and from 58 cm to 97 cm, respectively. The relatively large variation observed in these data is mainly attributed to different N treatments and to some extent to differences among genetic material. Moreira et al. (2005) studied spectral reflectance variation among 20 wheat genotypes, and registered that spectral reflectances and final biomass weight, for three of the genotypes used in the present work (IAC 364, IAC 370 and IAC 373), were quite similar. Also, significant improvements in R2 values were not observed for regressions performed by cultivar; therefore, regression analysis was performed by pooling genotypes.

Correlation coefficient between grain yield and plant height was 0.50. Figure 1 indicates that data asymmetry was not observed. 

Figure 2 shows the average spectral reflectance behavior at each growth stage for the 80 plots. Spectral variations among curves are mainly due to differences in crop growth stages. Lowest reflectance values in near infrared wavelengths (NIR; l ~ 700 - 1300 nm) were observed for the early developmental stage (Tillering I), where biomass is low and reflectance is influenced mainly by soil. Maximum reflectance in the NIR was observed for the Jointing stage, which is coincident with highest values of green leaf area index, consequently low reflectance of solar radiation in red wavelengths and high scattering of solar radiation in NIR (Moreira et al., 1999). At Heading and Maturation stages, reflectance in visible (VIS; 350 - 700 nm) and NIR regions increase and decrease, respectively, when compared to the previous growth stages, which is mainly caused by the increase of senescent leaves. 

Correlation coefficients (r) between each narrow-band and grain yield (Figure 3a) and plant height (Figure 3b) at different growth stages are presented in Figure 3. The pattern of r curves for grain yield and plant height, at distinctive growth stages, were similar; although, r in absolute values for plant height were smaller than those for grain yield. Lowest absolute r values were observed at Tillering I as a result of low crop development at this growth stage. Maximum negative values of r were observed at Heading stage for grain yield, and at Booting stage for plant height in the 680 nm wavelength, which corresponds to high solar radiation absorption by chlorophyll pigments. For the red-edge region (630-793 nm), a high increase of r values was observed, which is coincident with the reflectance increase of vegetation in this region (Figure 2). Greater positive r values were recorded between 760-880 nm wavelengths. For grain yield, the maximum positive r value observed was 0.72 at 902 nm during Booting stage. For plant height, the maximum positive r value observed was 0.62 at 813 nm during Jointing stage. Similar results were also observed by Yang & Chen (2004) for several biophysical parameters. 

Table 2 presents the regression coefficients for the relationship between biophysical variables and OMNBR, NB_NDVI, and broad band VI (SR, NDVI and SAVI) at different growth stages. In general, greater R2 values were observed at full crop development during Booting and Heading stages, for all independent variables. On the other hand, lowest R2 values were observed at Tillering I and Maturation stages, when green biomass was low.

The OMNBR presented increased R2 values as the number of narrow-bands were added to the regression model. Best regression for grain yield (R2 = 0.74) and plant height (R2 = 0.68) were obtained with four narrow-bands at Heading stage. A significant increase in R2 values was observed for each new narrow-band incorporated in the model. For instance, at Booting stage 16% of wheat grain yield variation was explained with one narrow-band and up to 46% was explained with four narrow-bands. These results are in agreement with those obtained by Thenkabail et al. (2004) and Yang & Chen (2004). The most frequent four-narrow-bands in the OMNBR model were those from NIR (l ~ 700 nm - 1,300 nm), followed by short wave infrared (SWIR; l ~ 1,300 nm - 2,400 nm) and VIS (l ~ 350 nm - 700 nm) indicating the relevance of the combined use of spectral bands from these three regions (NIR, SWIR, and VIS) for vegetation studies (Thenkabail et al., 2000; 2004).

The NB_NDVI index explained up to 67% of grain yield variation and up to 65% of plant height variation for Booting stage (Table 2). Best results were observed for bands in the NIR region for grain yield and in the VIS region for plant height.

Table 2 also presents the broad band VI and its relationship to both grain yield and plant height as well as the model type. Best overall R2 values, for grain yield and final plant height, during Jointing and Heading stages, were achieved with SR vegetation index using the linear model. Best individual result for broad band VI was obtained for both SAVI (R2 = 0.60) and SR (R2 = 0.59) to estimate grain yield during Heading and Booting stages, respectively. These results are in agreement with those reported by Tucker (1979), Turner et al. (1999), and Xavier & Vettorazzi (2004), studying several other biophysical variables.

Figure 4 shows the scatter plots for the grain yield estimates provided by the broad band VI that yielded best R2 values in Table 2. Relationships were positive, as expected (Asrar et al., 1984). In theory, plants with higher production capacity should have higher LAI values and consequently higher VI values. 

Figures 5a and 5b present the reflectance spectra, during Heading stage, for the lowest (1,629 kg ha-1) and highest (5,593 kg ha-1) wheat grain yield plots, respectively. The less developed plants from the lowest grain yielding plot reflected more VIS solar radiation and scattered (reflected and transmitted) less NIR radiation (Figure 5a). In contrast, the highest grain yielding plot (Figure 5b) presented low VIS reflectance and high NIR reflectance, and affected differently the first- and second-order derivatives for the low and high grain yielding plots, as observed in Figure 5(c-f). The area to be integrated for the low grain plot is much smaller than the one for the high grain plot for both first (Figure 5c, d; 1DZ_DGVI) and second-order derivative (Figure 5e, f; 2DZ_DGVI ).

Table 3 shows R2 values for estimates of grain yield and plant height from first-order derivative of reflectance, second-order derivative of reflectance and derivative of green vegetation indices at different wheat growth stages. Greatest R2 values were obtained with the first-order derivative, but similar results were also achieved with the second-order derivative, both with bands from the NIR region. Best growth stages to estimate biophysical variables from spectral reflectance measurements were within Jointing and Heading stages.

Regression coefficients were similar among derivative green vegetation indices (1DL_DGVI, 1DZ_DGVI, 1DL_MDGVI and 2DZ_DGVI) with lower overall performance when compared to: first-order derivative, second-order derivative (Table 3) or even with broad band VI (Table 2).

Figure 6 (a, b) shows that in most cases both grain yield and plant height were better estimated from hyperspectral indices (OMNBR, NB_NDVI, first- and second-order derivative indices) than from broad band indices. Major improvements of explained variance were observed early and late in the season. However, from Tillering II to Heading stages, when plants had a significant amount of green material, the broad band vegetation indices performed close to the narrow band VI, especially the NB_NDVI and the derivative indices. Among the hyperspectral indices, the OMNBR performed best in terms of R2 values (Figure 6).

Hyperspectral indices provided an overall better estimate of biophysical variables when compared to broad band VI. Major performance improvements with hyperspectral indices were observed early and late in the season when crop green leaf material was quite low. Among the several hyperspectral VI analyzed in this study the OMNBR with four bands presented highest R2 values to estimate both grain yield (R2 = 74% at Booting and Heading stages) and plant height (R2 = 68% at Heading stage). Best results to estimate biophysical variables, independently of narrow or broad band VI, were observed for spectral measurements acquired between Tillering II and Heading stages. Broad band VI performed almost as well as narrow band VI derived from hyperspectral bands for wheat crop with significant amount of green material.

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