One spectral components analysis 
equation (Wiegand and Richardson, 1984) 
is 
FPAR(VI) = FPAR(L) x L(VI) [1] 
read as FPAR as a function of any 
vegetation index (VI) dominated by the 
NIR reflectance of the canopy equals 
FPAR as a function of leaf area index 
(L) times L as a function of VI. The 
equation states that because there is a 
functional relation between FPAR and L 
and between L and VI it follows that 
there is also one between FPAR and VI. 
Calibration of FPAR directly in terms 
of VI avoids the tedious labor of 
determining L, but more importantly, 
makes FPAR estimates available for many 
remotely observable fields. It is now 
recognised that FPAR is a nearly linear 
function of VI (e.g. Gallo et al., 
1985; Wiegand and Richardson, 1987), 
and attempts at the biophysical 
explanation of the linearity have been 
made (Sellers, 1985, 1987; Choudhury, 
1987). 
Fig. 1 illustrates Eq. [1] 
relationships for three different 
crops: cotton (Gossypium hirsutum, L.), 
wheat (Triticum aestivum, L.), and corn 
(maise) (Zea mays, L.). The equations 
that express the 18 functional 
relations of Fig. 1 are summarized in 
Table 4 of Wiegand and Richardson 
(1990b.) 
Remote observations of the canopies, 
expressed in Fig. 1 as PVI, are the 
independent variable used to estimate L 
in the second right side term of Eq. 
[1]. That L can be estimated from 
spectral vegetation indices, and that 
the fraction of the PAR that is 
absorbed can be estimated from L are 
well accepted. The functional 
relations of the two right side terms 
are both nonlinear while the left side 
functional relation is linear (Fig. 1). 
The significance of Eq. [1] is that 
FPAR can be estimated from remote 
observations. Since APAR drives 
photosynthesis, the process by which 
plants produce the assimilates for 
growth and reproduction, VI provide a 
way to monitor plant development and 
yield. The linearity of the relation 
makes it easy to use. 
Economic Yield from One or a Few 
Observations per Season 
An equation that contains the L(VI) 
term of Eq. [1] and incorporates 
economic yield (Y) is 
Y(VI) = L(VI) x Y(L) [2] 
where Y is the salable plant part as 
appropriate for the crop (grain, root, 
fruit, fiber, or aboveground biomass), 
g/m 2 . Eq. [2] relates the 
photosynthetic capacity of the crop 
characterized by L and VI to its 
economic yield. 
Eq. [2] applies when the number of 
remote observations is limited to one 
or a few per season between late 
vegetative and mid-reproductive 
stages. Observations during this 
interval are optimal because 
measurements of VI too early in the 
season or too late into senescence are 
not representative of the canopies' 
photosynthetic size to support creation 
and growth of the plant parts that 
constitute yield. For cereals such as 
maize, sorghum, rice, and wheat, this 
optimal period lasts from late stem 
extension to about the milk stage of 
the grain. During this interval L is 
at a stable, plateau value. Other 
crops as diverse as cotton, potato, and 
various melons also reach a plateau 
value of L during reproduction because 
most of the assimilates of 
photosynthesis is translocated to and 
stored in the reproductive organs; new 
growth of foliage is slow and part of 
it replaces leaves that senesce. 
Fig. 2 illustrates Eq. [2] 
relationships for rice (Oryza sativa, 
L.) adapted from Shibayama et al. 
(1988) and Wiegand et al. (1989). The 
data are from 13 treatments that 
consisted of imcomplete combinations of 
3 cultivars, 2 transplanting dates 
three weeks apart, and 6 nitrogen 
application rates. In Fig. 2, part 'c' 
depicts the second right side term, 
part ’b' the first right side term, and 
part 'a' the left side term of Eq. [2], 
respectively. The Lh and PVIh in Fig. 
2 designate averages of these variables 
by treatment for three dates 
surrounding heading. 
As was characteristic of Eq. [1], the 
right side terms in Eq. [2] depicted in 
Fig. 2 are nonlinear whereas the left 
side term is linear. Diversity in the 
treatments pooled for part 'c' and 
experimental error in all measurements 
account for the scatter in part 'a'. 
In spite of the data limitations, 63% 
of the yield variation is attributable 
to PVIh and the relation is 
unmistakeably linear. 
Fig. 3 illustrates Eq. [2] 
relationships for grain sorghum 
(Sorghum bicolor L. Moench) after 
Wiegand and Richardson (1984). Leaf 
area index was measured periodically 
during the growing seasons of 1973, 
1975, and 1976 in farmers' fields, 
Landsat MSS digital counts acquired 
during grain filling were extracted 
from computer compatible tapes provided 
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