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

**Experimental Site and Treatments**

A field study was carried out during the winter growing season of 2003 in Campinas, São Paulo State, Brazil (22º51'47" S; 47º04'42" W). The experiment was set up at a 4 x 5 factorial scheme, randomized, complete-block design (n = 4), and data were submitted to regression analysis to estimate biophysical variables; treatment effects were not analyzed. Treatments were applied to plots with four wheat (*Triticum aestivum*, L) cultivars (IAC-362, IAC-364, IAC-370 and IAC-373), and five levels of nitrogen fertilizer (0, 30, 60, 90 and 120 kg of N ha^{-1}). Plots were 3 m long, 1.2 m wide and 0.8 m apart. Wheat was sown in June 2003 in rows spaced 0.15 m apart, with approximately 80 seeds per linear meter of row. Phosphorus and potassium were applied at a rate of 40 and 90 kg ha^{-1}, respectively, while boron and zinc were applied at rates of 0.5 and 1.0 kg ha^{-1}, respectively. All fertilizers were applied at seeding except for nitrogen, which was applied 50% at seeding and 50% was topdressed 30 days after plant emergence, according to the nitrogen fertilizer protocol. Irrigation was applied several times during the wheat growing season to supplement seasonal rainfall.

**Plant Characteristics**

Final grain yield and plant height were measured at maturity. To eliminate 'edge-effects' a central area of 1.36 m^{2} was harvested in each plot. Wheat grains were oven-dried at 80ºC until 13% humidity was reached (Carneiro et al., 2005). Five plants per plot were used to estimate average final plant height.

**Reflectance Measurements**

Field reflectance measurements were performed over 80 wheat plots with the FieldSpec Pro FR spectroradiometer (Analytical Spectral Device Inc., 2003), at six different growth stages, from early vegetative growth until maturation (Table 1). The radiometric measurements were collected under clear-sky conditions between 10h00 and 11h00, at 1.2 m above crop canopy, with the 25º lens allowing 0.22 m^{2} field of view areas. One spectral reflectance measurement from the most central part of each plot was taken with the FieldSpec Pro FR over the spectral range 400 — 2,500 nm. These measurements were then used to simulate the narrow-bands and broad-bands from the spectral bands of the Hyperion (Earth Observation-1, 2003), and Thematic Mapper (Earth Observation Satellite Company, 1985) sensors, respectively. Due to atmospheric radiation absorption, some bands in the spectral ranges 1,350-1,440 nm; 1,790-1,990 nm; and 2,360-2,500 nm were disconsidered.

**Vegetation Indices and Regression Models**

The most widely broad band VI used in this work were:

• Simple Ratio (SR; Jordan, 1969)

• Normalized Difference Vegetation Index (NDVI; Rouse et al., 1974)

• and Soil-Adjusted Vegetation Index (SAVI; Huete, 1988)

where: B3 (630-690 nm) and B4 (760-900 nm) are simulated spectral bands from the Enhanced Thematic Mapper Plus (ETM+) sensor on board of Landsat-7 remote sensing satellite, and L is a constant value equal to 0.5 applied to minimize soil background effects (Huete, 1988).

The regression models used were:

where B is the biophysical dependent variable (wheat grain or plant height); VI is the Vegetation Index independent variable (SR, NDVI or SAVI); *a*_{0} and *a*_{1} are the regression parameters; and *m* is the degree of the model. Polynomial and exponential models were both used to improve estimates of biophysical variables from spectral variables (Turner et al., 1999; Xavier & Vettorazzi, 2004).

Reflectance data were analyzed using several methods described in the literature: *o*ptimum *m*ultiple *n*arrow-*b*and *r*eflectivity (OMNBR, Thenkabail et al., 2000; 2004); narrow-band NDVI (NB_NDVI; Thenkabail et al., 2000); best first- and second-order derivative of reflectance (Demetriades-Shah et al., 1990); and green vegetation indices based on derivatives (Chen et al., 1998; Elvidge & Chen, 1995). The OMNBR was defined using the MAXR procedure of Statistical Analysis System (SAS) version 6.12 (SAS Institute, 1997) to find the combination of narrow spectral bands that best predicted model biophysical variable (maximized the R^{2}) at each wheat growth stage

where B is the biophysical variable; NB is the narrow-band reflectance of band *j* (*j* = 1,..., *n*); *n* is the number of Hyperion bands; and *a* is the regression parameter. For 1, 2, 3 and 4 narrow-bands we have, respectively:

The narrow-band NDVI (NB_NDVI) (Thenkabail et al., 2000) is defined as:

where *i* and *j* are band numbers from 1 to 242 allowing 242 x 242=58,564 combinations of NB_NDVI for each biophysical variable. Regression coefficients R^{2} between all possible narrow-bands and biophysical variables were determinate using a routine developed with MatLab (MatLab-MathWorks, 2002), that verified for each growth stage the two narrow-bands combination that provided highest R^{2} values.

The best first- and second-order derivatives of reflectance (1_Der and 2_Der) were used to reduce background reflectance influence (Demetriades-Shah et al., 1990) and were computed as:

where NB'(l* _{i}*) and NB''(l

To generate the derivative green vegetation indices (1DL_DGVI, 1DZ_DGVI, 1DL_MDGVI and 2DZ_DGVI), the first- and second-order derivatives of reflectance were integrated to calculate the area between the wavelengths of 630 nm and 793 nm (Elvidge & Chen, 1995; Chen et al., 1998):

where NB'(l_{i}) - NB'(l_{1})>0;

where l* _{1}* and l

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