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2.1 2 Definition of the Chlorophyll Absorption in Reflectance (CAR) 
Utilizing the properties of the 550 nm and 700 nm bands in conjunction with the 670 nm chlorophyll a absorption 
maximum band led to the definition of the chlorophyll absorption in reflectance (CAR). The line (a) in Fig. 3 
(II) which was drawn from the 700 nm to 550 nm band forms the base line to measure the depth of the chlorophyll 
absorption. The slopes of this 550 nm-700 nm lines for the 50 soybean leaf level reflectance spectra are a constant. 
The distance (b) in Fig. 3 (II) from the 670 nm band perpendicular to the 550-700 nm line (absorption minima) 
can be quantified and defined as CAR. Thus, CAR is the shortest distance from the 670 nm band to the 550 nm- 
700 nm line. 
The calculation of the CAR utilizes an orthogonal projection on a 2-dimensional x-y plane using 
wavelength as x and the percent reflectance as y coordinates, respectively. By definition, the orthogonal projection 
p from a point to a vector spanned from the origin is given by 
P = 
Jh 
-°a, 
where a T (x^^ 
-550mm ^700n*-550>wi)’ 
a=\ 
X 100mm-550mm 
y 100mm-550mm 
H 
■*670™-530m. 
y 610mm-550mm 
Note that the wavelength and the reflectance coordinates are linearly transformed so that * 550nm and y 550nm 
become the origin of the x-y plane. Thus, the 550 nm-700 nm line is the vector spanned from the origin. The 
distance (CAR) of the projection from the point (670 nm) to the p is quantified as 
CAR 2 = 
I b-^f = then< 
a T a (a T a) 
CAR = 
(b T b)°(a T a)-(a T b) 2 
\ (a T a) 
CAR calculated on the reflectance spectra of 50 soybean leaves plotted against the chlorophyll a 
concentrations are shown in figure 4. There is a strong inverse-linear relationship with a regression r 2 of 0.964 
demonstrating the values of CAR 
as an accurate measurement of 
leaf level chlorophyll absorption. 
12 Characteristics of CAR in 
canopy reflectance 
Soybean canopy reflectance 
spectra, leaf area index (LAI) of 
1.0, were simulated using the 
SAIL model for dark, yellow, and 
soil high in iron contents as 
background materials. Since the 
LAI for the canopy is 1.0, the 
simulated spectra contain 
identical green biomass and the 
only differences among the 
spectra are the effects of 
reflectance characteristics of the 
soils. Figure 5 illustrates the 
resulting spectral variabilities in 
the canopy reflectance due to the 
different background reflectances, 
and that the slopes of 550 nm- 
700 nm lines of CAR vary as a 
result of the effects of the 
reflectance of nonphotosynthetic 
materials. The variations in 
canopy reflectance are recognized 
in the differences between the 700 nm to 550 nm band ratios which are 1.35, 1.44, and 1.70 for the dark, yellow, 
and iron soil, respectively. 
Chlorophyll Absorption in Reflectance (CAR) 
Figure 4 
CAR of 50 soybean leaf reflectance vs chlorophyll a 
concentration of the same leaves