wiegand et al. 1991
TRANSCRIPT
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REMOTE SENS. ENVIRON. 35:105-119 (1991)
V egetat ion Ind ices in Crop ssessm ents
C. L . W iegand A . J . R i cha r dson D . E . E scoba r an d A .
R e mo te S e n s in g R e se a rc h Un i t ,
US DA A g r i c u l tu ra l R e se a rc h S e rv i ce , We s la c o , Te x a s
H . Ge r b erm ann
V e g e t a t i o n i n d ic e s ( V I ), s u c h as g r e e n n e s s ( G V I ) ,
p e rp e n d ic u la r ( P V I ) , t ra n s fo rme d so i l a d ju s t e d
( T S A V I ) , a n d n o r m a l i z e d d i f f e r e n c e ( N D V I ) , m e a -
su re t h e p h o to sy n th e t i c s i z e o f p la n t c a n o p ie s a n d
p o r t e n d y i e ld s . A se t o f e q u a t io n s , c a l l e d sp e c t ra l
c o m p o n e n t s a n a ly s i s ( S CA ), t h a t i n te r re la t e s V I o r
c u m u la t i v e se a so n a l V I ( Y '.V I) , l e a f a re a i n d e x ( L ),
f r a c t i o n a l p h o t o s y n t h e t i c a l l y a c t i v e r a d i a t i o n
( F P A R , d ime n s io n l e s s ) , c u mu la t i v e d a i l y P A R e n -
e r g y a b s o rb e d (E A P A R , M J / m 2 ) , a b o v e- g ro u n d
d r y ph o t om a s s ( D M , g / m 2 ) , a n d e c o n om i c y ie l d
( Y, g / m 2) a r e p r e s e n t e d a n d u s e d t o a n a l y z e d a t a
f r o m t w o s t u d i e s c o n d u c t e d i n 1 9 8 9 . I n o n e s t u d y
w e m a d e b o l l c o u n t s a n d p e r c e n t p l a n t c o v e r m e a -
su re m e n t s i n a sa l t - a f fe c t e d c o t to n f i e l d o n 6 0 m
g r id i n t e rv a l s a n d c a l c u la t e d GV I , P V I , TS A V I ,
a n d N D V I a t th e g r i d in t e r se c t io n s f o r S P O T - 1
H R V a n d v i d e o g r a p hy s c en e s. T h e f o u r V I f r o m
S P O T a c c o u n t e d f o r m o r e o f th e v a r i a ti o n i n t h e
l i nt y ie l d e s ti m a t e d f r o m t h e b o l l c o u n t s ( 7 5 - 7 6 )
t h a n t h o se f r o m v i d e o g r a p h y ( 6 1 - 6 3 ) , b u t V I
f r o m t h e d if f e r e n t s y s t e m s e a c h a c c o u n t ed f o r 6 7
o f th e v a r ia t i o n i n p la n t c o v er . A l l r e la ti o n s w e re
Address correspondence to C. L. Wiegand Remote Sensing
Research Unit USDA/ARS 2413 E. Highway 83 Weslaco TX
78596-8344.
Received June 1990: revised 12 November 1990.
0034-42,57/91 / 3.50
©Elsevier Science Publishing Co. Inc., 1991
6.55 Avenue of the Americas, New York, NY 10010
l in e a r. I n t h e o th e r s tu d y , r e f l e c ta n c e f a c to r s a n d
F P A R w e r e m e a s u r e d p e r i o d i c a l l y d u r i n g t h e s e a -
so n in c o rn p la n t e d a t t h re e d e n s i t i e s ( 7. 7 , 5 .4 , a n d
3 .1 p l a n t s ~ m 2 ) . F P A R c o u l d b e e s t im a t e d f r o m
N D V I a n d P V I , r e s p e c ti v e ly , b y F P A R = - 0 .3 4 4
+ 0 .2 2 9 e x p ( 1 . 9 5 N D V I ) ( r 2 = 0 .9 7 3) a n d F P A R =
0.015 + O.036(PVI) ( r 2 = 0 .956) . M etho ds o f ob-
ta in in g F P A R a n d th e i r e f f e c t o n t h e e f f i c i e n c y o f
c o n v e r s io n o f A P A R t o D M a r e il l u st r a te d a n d
d i sc u sse d . Th e d a ta d e mo n s t ra t e h o w S CA u n i f i e s
a n d s t re n g th e n s t h e sc i e n ti f ic b a s i s o f V I i n t e rp re -
tations.
INTRODUCTION
Var ious spec t r a l vege ta t ion ind ices Rou se e t al .,
1973 ; Kau th and Thomas , 1976 ; Richa rdson and
Wiegand , 1977 ; Tucker e t a l . , 1979 ; Pe r ry and
L a u t e n s e h l a g e r , 1 9 8 4 ) h a v e b e e n d e v e l o p e d t h a t
r e d u c e m u l t i b a n d o b s e r v a ti o n s t o a s i n gl e n u m e r i -
ca l i ndex . The index i s t yp ica l ly a sum, d i f f e r ence ,
r a tio , o r o the r l i nea r com bina t ion o f re f l ec t ance
fac to r o r r ad i ance obse rva t ions f rom two o r more
w a v e l e n g t h i n t e rv a l s. H i g h a b s o r p ti o n o f in c i d e n t
s u n l i g h t i n t h e v i s ib l e r e d R E D , 6 0 0 - 7 0 0 n m )
por t ion and s t r ong r e f l ec t ance in t he nea r - in f r a r ed
NIR,
7 5 0 - 1 3 5 0 n m ) p o r t i o n o f t h e e l e c t r o m a g -
1 0 5
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10 6 Wiega nd e t a l.
n e t i c s p e c t r u m b y p h o t o s y n t h e t ic a l l y a c ti v e t i ss u e
in p l an t s i s d i s t i nc t ive f rom tha t o f soi l and wa te r ,
t h e o t h e r t w o p r e d o m i n a n t l a n d s c a p e f e a t u r e s .
T h u s , v e g e t a t i o n i n d i c e s d e v e l o p e d f r o m s p e c t r a l
o b s e r v at i on s i n t h e s e t w o w a v e l e n g t h s h a v e c o r r e-
l a t e d h i g h ly w i t h t h e p l a n t s t a n d p a r a m e t e r s g r e e n
lea f a r ea index L) , ch lo rophy l l con ten t , f r e sh and
d r y a b o v e - g r o u n d p h y t o m a s s F M , D M ) , p l a n t
h e i g h t , p e r c e n t g r o u n d c o v e r b y v e g e t a t i o n , p l a n t
popu la t ion , and g r a in o r f o r age y i e ld Rous e e t al .,
1973; Wiegand e t a l . , 1973; Richardson e t a l . ,
1974 ; Pea r son e t a l . , 1976 ; Thomas and Gausman ,
1977 ; Tucker , 1977 ; W iega nd e t a l ., 1979 ; Cur r an ,
1980; Ho lbe n e t a l . , 1980; Kim es e t a l ., 19 81; Aase
and S iddoway , 1981 ; Walburg e t a l . , 1982 ;
Richa rdson e t a l ., 1 982 ; and ma ny o the r s subse -
quen t ly ) .
M ore spec i f ica l ly , vege ta t ion ind ices hav e bee n
c o n s i d e r e d a m e a s u r e o f v e g e t a t i o n d e n s i t y o r
cover W iegan d e t a l. , 1973); pho tosy n the t i ca l ly
ac t ive b iomass Tuck er , 1979 ; W iega nd and
Richardson , 1984); l ea f a r ea index W iegan d e t a l.,
1979); gree n leaf den si ty Tu cke r e t a l. , 1985);
pho tosyn thesis ra te Sel lers , 1985; 1987); am ou nt
o f pho tos yn the t i ca l ly ac t ive t is sue W iega nd e t a l. ,
1986b ; Wiegand and Richardson , 1987) ; and pho-
tosyn the t i c s ize o f canop ies W iegan d e t a l. , 1989;
Wiegand and Richardson , 1990) .
T h e c i t e d e m p i r i c a l st u d ie s h a v e b e e n c o m p l e -
m en ted by mode l ing e ffor ts . Goe l 1988) has sum-
m a r i z e d t h e e s s e n c e o f a l a rg e n u m b e r o f ca n o p y
b i d i r e c t i o n a l r e f l e c t a n c e m o d e l s a m o n g w h i c h
SAIL Verhoef , 1984) i s t he mo s t w id e ly used , and
d e s c r i b e d t h e i r i n v e r s i o n t o e s t i m a t e c a n o p y b i o -
phys ical var iables . Sel lers 1985; 1987) has pre-
s e n t e d t h e o r e t i c a l a r g u m e n t s a n d u s e d a tw o - s t e a m
r a d i a t i v e t r a n s f e r m o d e l t o s h o w h o w v e g e t a t i o n
ind ices r e l a t e t o canopy r es i s t ance and r a t e o f
p h o t o s y n th e s i s . G o e l a n d T h o m p s o n 1 9 8 4) d e v e l -
oped a genera l t echn ique fo r t he sens i t i v i ty ana ly -
s is o f c a n o p y r e f l e c ta n c e m o d e l s a n d C h o u d h u r y
1 9 8 7 ) e x a m i n e d t h e r e l a t i o n s h i p s a m o n g v e g e t a -
t i on ind ices , FPAR, and ne t pho tosyn thes i s u s ing
sensi t iv i ty analysis .
Ques t ions r emain , however , abou t t he in t e r -
p r e t a t ion o f vege ta t ion ind ices i n t e rms o f t he
cu r r en t cond i t i on and l i ke ly p roduc t iv i ty o f c rop ,
r a n g e , a n d f o r e s t p l a n t c o m m u n i t i e s . T h e p u r p o s e
o f t h is pa per i s t o p rov ide exam ples f rom s tud ies
c o n d u c t e d i n 1 98 9 o f th e r e l a t i o n b e t w e e n v e g e t a -
t i on ind ices and c rop pe r fo rmance and to d i scuss
t h e m i n t e r m s o f a g r o n o m i c a n d p l a n t p h y s i o lo g i -
c a l p r i n c i p l e s e m b o d i e d i n s p e c t r a l c o m p o n e n t s
ana lys is SCA) W iegan d and Richardson , 1984 ;
1987; 1990; W ieg an d e t a l . , 1989).
M E T H O S
F i e l d M e a s u r em e n t s
Cotton
A sal t -af fected f ie ld of cot ton Gossyp ium h irsu tum
L. ) 15 km N E o f W es laco , Texas , t ha t mea su re d
3 8 8 m a c ro s s a n d h a d r o w s o r ie n t e d E - W 3 8 4 m
long spaced 1 .02 m apar t 14 .9 ha ac tua l p l an ted
a rea ) was se l ec t ed a f t e r t he c rop was e s t ab l i shed .
The so i l i n t he f i e ld r anged f rom nonsa l ine to so
s a li n e th a t p l a nt s d i d n o t e m e r g e . T h e p a t t e r n a n d
sever i ty was ve ry i r r egu la r P l a t e I ) a s is t yp ica l o f
th is s t re ss Ca r t e r and W iegan d , 1965). A square
g r id o f 36 sam ple s i t es a t 60 m in t e rva l s was
pos i t i oned wi th in the f i e ld so tha t no s i t e was
wi th in 30 m o f t he f i e ld boundary .
S P O T - 1 H R V d a t a w a v e l e n g t h s : g r e e n G R ) ,
5 0 0 - 5 9 0 n m ; R E D ) , 6 1 0 - 6 8 0 rim ; N I R , 7 9 0 - 8 9 0
nm) we re a cqu i r ed on 4 Jun e 1989 f rom 13 ° eas t ,
w h i l e n a r r o w b a n d m u l t i s p e c t r a l v i d e o g r a p h y
w a v e l e n g t h s : y e l l o w - g r e e n Y G ), 5 4 3 - 5 5 2 n m ;
R E D , 6 4 4 - 6 5 6 n m ; a n d N I R , 8 1 5 - 8 2 7 n m ) u s i n g
the h igh r e so lu t ion mul t i spec t r a l v ideo sys t em de -
sc r ibed by Ever i t t e t a l. 1991) was ob ta in ed on 19
June and 14 Ju ly 1989 f rom 1400 m a l t i t ude . P l an t
h e i g h t P H , m ) a n d p e r e e n t p l a n t c o v e r P C ) w e r e
m e a s u r e d o n 5 J u l y o n a v e r a g e s i z e d p la n t s w i t h i n
10 m o f t he g r id i n t e r sec t ions . P l an t he igh t mea-
s u r e m e n t s w e r e m a d e l o o k i n g h o r i z o n t a l l y a e r o s s
the tops o f p l an t s t o a me te r s t i ck and p l an t cover
w a s d e t e r m i n e d f r om m e a s u r e d w i d t h o f p l a n ts i n
t h e r o w d i v i d e d b y r o w s p a c i n g t i m e s 1 0 0 . T h e
n u m b e r o f b o ll s la r g e e n o u g h t o m a t u r e w e r e
cou n ted on 2 m o f r ow 2 .04 m 2 ) nea r t he g r id
in t e r sec t ion on 12 and 13 Ju ly . Bo l l eoun t s were
c o n v e r t e d t o k g l i n t / h a b a s e d o n 6 0 0 b o l l s / k g l i n t
L . N . N a m k e n , p e r s o n a l c o m m u n i e a t i o n ) a n d e x-
p a n d e d f ro m t h e s i ze o f t h e s a m p l e t o h e c t a re s .
orn
T h e c o r n
Z e a m a y s
L . ) e x p e r i m e n t , c o n d u c t e d a t
the ARS No r th Fa rm, Wes laeo , Texas 26 .2°N,
98.0°W), con sis ted of thre e populat ion s 7 .7 , 5 .4 ,
and 3 .1 p l an t s /m 2 ) o f fi e ld co rn , eu l t i va r Con lee
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Vegetation lndices in Crop ssessments
1 0 7
202, replicated 6 times in plots of 8 rows spaced
0.75 m apart and 15.2 m long. The crop
w a s
planted on 13 March and emerged on 18 March. It
reached the 10-leaf stage on 19 April and began
tasseling 8 May. The various plots reached the silk
stage between 14 May and 19 May, and physiolog-
ical maturity of the grain, as indicated by black
layer formation, from 23 to 30 June.
Plots that had reached physiological maturity
by then were harvested 28 June and the remain-
der on 1 July. Harvest consisted of cutting all
plants off just above the ground in 1 m 2 areas
(1.33 m long row segments) in each plot, removing
and putting the husked ears in one bag and all
other harvested plant material in another. After
about 2 weeks of drying in an unventilated, un-
cooled glass greenhouse, the grain was shelled
from the ears and the cobs were added to the
other stover. The grain yield (g /m 2) consisted of
the shelled grain that averaged 5.4% moisture
while the grain plus all the other aboveground
plant parts constituted the dry phytomass (DM,
g/m2).
The experimental area was fertilized twice with
liquid nitrogen at the rate of 55 kg/h a, once on 28
March and again on 17 April. The experimental
area was irrigated prior to planting and on 4 April,
10 May, and 7 June.
Spectral radiance measurements were taken
near solar noon from 2.8 m above the ground
using a Mark II radiometer (Tucker et al., 1981)
mounted on an aluminum pole on 11 dates begin-
ning on 31 March and ending 26 June. The spec-
tral bands of the Mark II are 630-690 nm and
760-900 nm and its field of view was 15 °. Two
observations per plot were taken centered over the
corn row and two centered over the furrow (each
at different places) and the measurements were
averaged. Each end of approximately a 2 m long
segment on the third row in from the north side of
the plots was flagged and we returned to this row
segment for all Mark II measurements.
Photosynthetically active radiation (PAR) inci-
dent on (Io), transmitted through (T), reflected
from the composite canopy-soil backgrounds (R),
and reflected from the bare soil (R~.) provided the
data for fractional absorbed PAR (FPAR) defined
(Hipps and Kanemasu, 1983; Gallo et al., 1985) as
FPAR = I o - T - R + T R ~ ) / I o. (1)
LI-COR l line quantum sensors (LI-191SB) were
used to measure T, R, and R,, and I 0 was mea-
sured using a quantum sensor (LI-190SB). 1 For
the T measurements the line quantum sensor
(LQS) was inserted below the canopies obliquely
middle-to-middle. For measurements of R (canopy
plus soil) the LQS was inverted 0.3 m above the
canopies and parallel to the sensor below the
canopies. The R~. term was measured by an LQS
inverted 0.3 m above a small area in the plots
where the plants had been removed soon after
emergence and weeds were controlled by hoeing
frequently. The T and R sensors were moved to
new canopy sites for each of four measurements in
each plot. The quantum sensor was mounted on a
2-m-tall stand that was moved from plot to plot
and leveled at each stop. Sensors had been inter-
calibrated before the season began. The sensor
outputs for
T , R ,
and I o and the time of observa-
tions were electronically logged simultaneously.
Care was taken to keep all sensors level and to
avoid shading the sensor measuring T by the one
measuring R. The PAR measurements described
were made on seven dates beginning 29 March
and ending 16 June. These measurements were
also made on the third row from the north in each
plot but at sites different from the reflectance
factor observations to avoid trampling.
a t a P r e p r o c e s s i n g
S P O T . Digital counts for a 51 × 81 pixel area sur-
rounding the test cotton field were extracted from
the SPOT scene digital tapes using a PCI
EASI/PACE 512 ×512 image analysis system in-
terfaced to a COMPAQ 386/25 microcomputer.
Line printer listings were generated, the bound-
aries of the test and surrounding fields were iden-
tified in these gray maps, and the pixels closest
to the grid intersections were manually selected
using the pattern of plant growth visible in the
gray maps and reference aerial photographs as
guides.
Reflectance at the top of the atmosphere R t i )
was computed from the equation (Moran et al.,
IMention of trade names does not infer preferential
treatment nor endorsement by the U S Departmen t of
Agriculture over similar products available from other sources
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1 0 8 W i e g a n d e t a l.
1 9 9 0 )
R t i = [ T r ( D C , / c ~ ) d Z ] / [ E s , (c o s S Z A )] , ( 2 )
w h e r e i n c i a r e g a i n - d e p e n d e n t c a l i b r a t i o n c o e ff i-
c i e n t s f o r e a c h b a n d ( S P O T D a t a U s e r s H a n d -
b o o k , F i g . 3 - 1 1 ) t h a t c o n v e r t d i g i t a l c o u n t s ( D C i )
t o r a d i a n c e a t t h e s e n s o r ( g a i n s fo r d e t e r m i n i n g C i
w e r e 6 , 7 a n d 5 f o r H R V b a n d s 1 , 2 a n d 3 ,
r e s p e c t i v e l y ) , d i s t h e e a r t h / s u n d i s t a n c e i n a s tr o -
n a u t i c a l u n i t s , Es~ i s t h e e x o a t m o s p h e r i c s o l a r
i r r a d ia n c e ( W i n - 2 s r - 1 / z m - 1) i n b a n d i , a n d S Z A
i s t h e s o l a r z e n i t h a n g l e a t t h e t i m e t h e s c e n e w a s
a c q u i r e d . F o r t h e 4 J u n e s c e n e t h e f a c t o r s t h a t
c o n v e r t e d d i g i t a l c o u n t s t o r e f l e c t a n c e w e r e 0 . 1 8 2 ,
0 . 2 2 1 , a n d 0 . 3 4 7 f o r b a n d s 1 , 2 , a n d 3 , r e s p e c -
t iv e l y . W e u s e d t h e r e f l e c t a n c e a t t h e t o p o f t h e
a t m o s p h e r e t o r e p r e s e n t g r o u n d l ev e l co n d i ti o n s .
B a r e s o i l a r e a s i n t h e 4 1 3 1 p i x e l s u b s c e n e p r o -
v i d e d d a t a f o r d e t e r m i n i n g t h e s o i l l i n e .
Multispectral Videography
D a t a f r o m e a c h c a m e r a o f t h e a i r b o r n e v i d e o
s y s t e m ( E v e r i t t e t al ., 1 9 9 1 ) w e r e r e c o r d e d o n
1 •
7 - m . f o rm a t S u p e r V H S P a n a s o n i c M o d e l A G - 7 4 0 0
p o r t a b l e v i d e o c a s s e t t e r e c o r d e r s . T h e b l a c k - an d -
w h i t e c a m e r a s ( C O H U M o d e l 4 8 10 s er ie s ) w e r e
e q u i p p e d w i t h s y n c h r o n i z e d g e n e r a t o r lo c k c o n -
n e c t i o n s s o t h a t c o n t i n u o u s l y s y n c h r o n i z e d c om -
p o s i t e i m a g e r y a n d i t s b l a c k - a n d - w h i t e c o m p o -
n e n t s w e r e a c q u i r e d .
A M a t ro x M V P d i g i ti z in g b o a r d a n d I M A G E R
s o f tw a r e w e r e u s e d t o d ig i t iz e t h e i n d i v i d u a l b a n d s
s c e n e s f o r s to r a g e o n t h e h a r d d i s k o f a m i c r o c o m -
p u t e r i n t e r f a c e d to a n E R D A S i m a g e a n a l y si s s ys -
t e m . E R D A S s o f tw a r e w a s u s e d t o p o s i t io n p o ly -
g o n s 7 p i x e l s × 7 p i x e l s i n s i ze c e n t e r e d o n t h e
g r i d i n t e r s e c t i o n s , e x t r a c t t h e d i g i t a l c o u n t s , a n d
d e t e r m i n e t h e i r m e a n s a n d s t a n d a r d d e v i a t i o n s .
T h e p r o c e d u r e s w e r e s p e e d e d b y r e g i s te r i n g al l
b a n d s t o t h e N I R b a n d o n o n e d a t e , s o t h a t p ix e l
s a m p l e s c o u l d b e e x t r a c t e d f r o m t h e i n d i v i d u a l
b a n d s o n b o t h d a t e s b y o n e s e t o f p o l y g o n c o o r d i -
n a t e s . S a m p l e s o f b a r e s o il ar e a s ( t u r n r o w s , f i e ld
r o a d s , a n d b a r r e n s i te s i n fi e ld s ) w i t h i n t h e v i d e o
s c e n e s w e r e u s e d t o d e t e r m i n e t h e s o i l l i n e
(T a b l e 1 ) .
Mark
T h e M a r k I I d a t a w e r e p r o c e s s e d t o r e f l e c ta n c e
f a ct o rs u s i n g t h e p r o c e d u r e s d e s c r i b e d b y
R i c h a r d s o n ( 1 9 8 1 ) . C u r r e n t l y , a h a l o n p a n e l i s
u s e d a s t h e r e f e r e n c e s t a n d a r d a n d w h i t e - p a i n t e d
p l y w o o d a s w o r k i n g p a n e l s . T h e s a m e s m a l l a r e a s
w h e r e t h e b a r e s oi l P A R r e f l e c t a n c e ( R s ) t e r m w a s
m e a s u r e d w e r e u s e d e a c h m e a s u r e m e n t d a t e t o
o b t a i n t h e r e f l e c t a n c e f a c to r s o f w e t a n d d r y s o i l
f r o m a h e i g h t o f 1 - 1 . 2 m . W a t e r f r o m a s p r in k l e r
c a n w a s a p p l i e d t o w e t a n a p p r o x i m a t e l y 0 . 7 m 2
a r e a . T h e p e r i o d i c a l l y o b t a i n e d w e t a n d d r y s o i l
r e f l e c t a n c e f a c t o r s w e r e p o o l e d t o d e t e r m i n e a s o i l
l i n e f o r t h e e n t i r e s e a s o n .
Table 1 S oi l L i n e S L ) a n d V e g e t a t i o n I n d e x E q u a t i o n s b y S e n so r S y s t e m a n d C r o p
Se ns or Sy s t e m Sc e ne Equa t ions
A. Cotton
SPOT HRV-1 4 June
Video 19 June
17 July
B. Corn
Mark II Periodic
All
SL: RED = -8. 20+ 1.099 NIR
GVI = 0.841 NIR- 0.438 RED - 0.317 GR- 5.84
PVI = 0.740 NIR-0.67 3 RED-5 .52
TSAVI = 0.910 NIR - .910 RED - 7 .46 ) / R ED + 0.91 NIR - 6.79)
SL: RED = 1.50+ 1.032 NIR
GVI = 0.837 NIR - 0.401 RE D - 0.372 YC - 2.69
PVI = 0.718 NI R- 0.696 RE D+ 1.04
SL: RE D = - 15.5+ 1.265 NIR
GVI = 0 .863 NIR-0 .451 RED-0 .228 YG- 14.89
PVI = 0.784 NI R- 0.620 RE D- 9.61
SL: RED = -2 .0 1+0. 765 NIR)
PVI = 0.608 RIR - 0.794 RED - 1.60
NDVI = NIR- RED) / NIR + RED)
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Vegetation Indices in Crop Assessments 109
V e g e t a t i o n I n d i c e s
T h e t h r e e - b a n d g r e e n n e s s v e g e t a t io n i n d e x ( G V I)
w a s d e t e r m i n e d f o r b o t h S P O T - 1 H R V a n d t h r e e -
b a n d v i d e o d a t a u s i n g t h e n - s p a c e p r o c e d u r e o f
Ja c kson (1983) wi t h on e modi f i c a t i on : W e c a l c u-
l a t e d t h e g r e e n n e s s o f t h e s o il p l a n e u s i n g t h e
c o e f f i c i e n t s f r o m t h e n - s p a c e p r o c e d u r e a n d a d d e d
i t a l g e b r a i c a l l y t o t h e g r e e n n e s s e q u a t i o n . T h i s
m o d i f i c a t io n p e r m i t s t h e s o il p l a n e t o h a v e a n o n -
z e r o i n t e r c e p t a n d a g r e e n n e s s o f ze r o.
S i n c e t h e p e r p e n d i c u l a r v e g e t a t io n i n d e x ( P V I )
( R i c h a r d s o n a n d W i e g a n d , 1 9 7 7 ) i s t h e o r t h o g o n a l
d i s t a n c e f r o m a v e g e t a t i o n p o i n t i n N I R a n d R E D ,
o r N I R a n d G R , 2 - s p a c e , w e u s e d t h e e q u a t i o n f o r
a pe rpe ndi c u l a r t o a l i ne ( Ja c kson e t a l . , 1980) ,
i ns t e a d o f t he o r i g i na l fo rmul a , t o c a l c u l a t e i t. Fo r
N I R o n t h e a b sc is s a an d R E D o n t h e o r d i n a te t h e
e qua t i on i s
PV I NIR,RED
= [ a , ( N I R ) - R E D + ao ]
. 2 1 1 / 2
/ [ l + ( a l ) ] , ( 3 a)
w he re a 0 is t he so i l l i ne i n t e rc e p t a n d a 1 i s t he
s l ope o f t he so il li ne . Wh e n t he so il li ne i s p re -
s e n t e d w i t h N I R o n t h e o r d i n a t e a n d R E D o n t h e
a bsc i s sa , t he e qua t i on i s
P V IR ED , N m = [ N I R - a l ( R E D ) - a o ]
/ [ 1 - 4 - - - a l 2 ] 1 / 2 , 3 b )
w h e r e a o a n d a 1 a r e, a g a in , t h e i n t e r c e p t a n d
s l ope o f t he so i l li ne . In t h i s s t ud y t he so il li ne wa s
d e t e r m i n e d b y l e a st s q u a r e s ( M a r k I I d a t a ) o r
g r a p h i c a l l y ( S P O T a n d v i d e o d a t a ) . T h e t r a n s f o r -
m e d s o il a d j u s t e d v e g e t a t i o n i n d e x , T S A V I ~ E o , N m
(Ba re t e t a l. , 1989) , is def in ed by
T SA V IR ED , N m = a l [ N I R - a , ( R E D ) - a o]
/ [RED+a, (NIR) -a l ao] .
(4)
C o n c e p t u a l l y , T S A V I i s a m e a s u r e o f t h e a n g l e
b e t w e e n t h e s o il li n e a n d t h e l i n e j o i n i n g t h e
v e g e t a t i o n p o i n t w i t h t h e s o i l l i n e i n t e r c e p t . F o r
t h e s p e c i a l c a se o f a s o il l i n e s l o p e - - 1 . 0 a n d
i n t e r c e p t = 0 , T S A V I r e d u c e s t o N D V I d e f i n e d b y
N D V I = ( N I R - R E D ) / ( N I R + R E D ) . (5 )
Th e spe c i f i c e qu a t i ons o f t he so il li ne s and
ve g e t a t i on i nd i c e s fo r t he va r i ous da t a s e t s o f t h i s
s t u d y a r e s u m m a r i z e d i n T a b l e 1 . T h e v e g e t a t i o n
i n d i c e s i n T a b l e 1 f o r S P O T d a t a a r e c a l c u l a t e d
f r o m e x o a t m o s p h e r i c r e f l e ct a n c e s ( ) , f r o m e i g h t-
b i t d i g i t a l c ount s (DC ) fo r t he v i de o da t a , a nd
f rom re f l e c t a nc e fac t o r s ( ) fo r t he M a rk I I da t a .
T h e s o il li n e e q u a t i o n s a r e p o o r f o r th e v i d e o d a t a
b e c a u s e t h e s m a l l a r e a s i n t h e s c e n e s u s u a l l y
c o n t a i n e d o n l y d r y s o i l t h a t r e p r e s e n t e d o n l y a
s h o r t s e g m e n t o f t h e s o il l in e . C o n s e q u e n t l y , t h e r e
w a s u n c e r t a i n t y i n t h e m . T h e b u i l t - i n a u t o m a t i c
g a i n c o n t r o l i n t h e v i d e o c a m e r a s a l s o m a d e t h e
DC of t he so i l un i qu e fo r e a c h ove r f l i gh t , so tha t
d a t a c o u l d n o t b e p o o l e d a c ro s s d a t e s .
ata I n terp reta t ion
O n e s p e c t r a l c o m p o n e n t s a n a ly s i s e q u a t i o n
( W i e g a n d a n d R i c h a r d s o n , 1 9 8 4 ) i s
F P A R (V I ) = F P A R ( L ) × L ( V I ) = F P A R ( L [V I I ) ,
6 )
w h i c h i s r e a d a s F P A R a s a f u n c t i o n o f a n y v e g e t a -
t i o n i n d e x ( V I ) d o m i n a t e d b y t h e N I R r e f e c t a n c e
o f t h e c a n o p y e q u a l s F P A R a s a f u n c t i o n o f l e a f
a r e a i n d e x ( L ) t i m e s L a s a fi m c t i o n o f V I . T h e
e qua t i on s t a t e s t ha t be c a use t he re i s a func t i ona l
r e la t io n b e t w e e n F P A R an d L a n d b e t w e e n L a n d
V I i t f o l l o w s t h a t t h e r e i s a l s o o n e b e t w e e n F P A R
a n d V I . C a li b r a ti o n o f F P A R d i r e c t l y i n t e r m s o f
V I a v o i d s t h e t e d i o u s l a b o r o f d e t e r m i n i n g L , b u t ,
m o r e i m p o r t a n t l y , m a k e s F P A R e s t i m a t e s a v a i l -
a b l e f o r m a n y r e m o t e l y o b s e r v a b l e f ie ld s . I t is n o w
r e c o g n i z e d t h a t F P A R i s a n e a r l y l in e a r f u n c t i o n o f
V I a n d a t t e m p t s a t t h e b i o p h y s i c a l e x p l a n a t i o n o f
t he l i ne a r i t y ha ve be e n ma de (Se l l e r s , 1985; 1987;
C h o u d h u r y , 1 98 7).
A n e q u a t i o n t h a t c o n t a i n s t h e L ( V I ) t e r m o f
E q . ( 5 ) a n d i n c o r p o r a t e s e c o n o m i c y i e ld ( Y ) i s
Y ( VI ) = L ( V I ) X ¥ ( L ) = Y ( L [ V I ] ), ( 7)
w h e r e Y is t h e s a l a b le p l a n t p a r t a s a p p r o p r i a t e f o r
t he c rop (g ra i n , roo t , f ru i t , f i be r , o r a bove -ground
b i o m a s s ) ( g / m 2 ) . E q u a t i o n ( 7 ) r e l a t e s t h e p h o t o -
s y n t h e t i c c a p a c it y o f t h e c r o p c h a r a c t e r i z e d b y L
a n d V I t o i ts e c o n o m i c y i e ld . T h e t e r m L ( V I ) l in k s
Eqs . (6 ) a nd (7 ) .
M e a s u r e m e n t s o f V I m a d e t o o e a rl y in t h e
g r o w i n g s e a s o n o r t o o l a t e i n t o s e n e s c e n c e d o n o t
r e l a t e w e l l t o y i e l d i n E q . ( 7 ) b e c a u s e t h e m e a -
s u r e m e n t s d o n o t r e p r e s e n t t h e c a n o p i e s ' p h o t o -
s y n t h e t i c s iz e. T h e v a l u e s o f V I c o r r e s p o n d i n g t o
t he p l a t e a u L va l ue s fo r t he se a son , o r t he ma xi -
m u m l e a f a r e a i n d e x ,
L m
o b s e r v e d f o r e a c h f i e l d
o r t r e a tm e n t o f in t e re s t , c a n b e u s e d t o d e t e r m i n e
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11 0 Wiega nd et al.
the Y(VI) func t iona l re la t ion . As a ru le , when L
reaches i t s p la teau va lue fo r the season , the s inks
fo r pho tosyn the t ic a ss imi la te s a re domina ted by
the p lan t pa r t s tha t cons t i tu te y ie ld .
An equa t ion tha t expresses the le f t s ides o f
Eqs . (6 ) and (7 ) as da i ly inc rem en t ed cumula t ions ,
d e s ig n a t e d b y E , a n d c o u p l e s t h e m th r o u g h g r o w th
analysis (Warren Wilson, 1981) is
Y ( E V I ) = E A P A R ( E V I ) × A D M ( ~ A P A R )
× Y ( A D M ) ( 8)
w h e r e i n
APAR = FPAR × I 0 . (9 )
Equ a t ion (8 ) p rov ides th e ra t iona le fo r expec t -
i n g y i e ld s ( Y ) t o b e e s t im a b l e f r o m c u m u la t i v e
da i ly vege ta t ion ind ices , tha t i s , f rom the a rea
under the seasona l VI ve rsus t ime cu rves . In Eq .
(8) , APAR is the p ro duc t o f da ily FPAR (un i t le ss )
f rom Eq . (6 ) and da i ly inc iden t PAR f lux ,
I 0 ( M J / m Z / d a y ) , w h i c h i n c u m u l a t i o n s h a s t h e
un i t s M J /m 2. By it s ve ry na tu re D M is in teg ra l
g rowth tha t we express a s the d ry ma t te r change ,
A D M .
Th e cum ula t ions o f a l l t e rms o f Eq . (8 ) beg in
lo g ic a ll y a t s e e d l i n g e m e r g e n c e s o t h a t t h e c u m u -
la t ions fo r a ll va r iab les be g in e i the r a t ze ro o r th e
va lue fo r ba re soi l. At seed l ing em erg enc e DM 1 i s
so smal l tha t i t i s u sua l ly ignored . I f economic
y ie ld (Y) o f nonfo rage c rops i s o f p r im e in te res t ,
e n d in g d a t e D M , D M 2 , c o r r e s p o n d s t o e i t h e r
physiological maturi ty or to harvest , forc ing a l l
o the r te rms to be eva lua ted a t th i s end t ime .
S in c e F P A R c a n b e e s t im a t e d a lm o s t a s w e l l
f rom VI as f rom L (Ga l lo e t a l . , 1985; W iegan d
and Richardson , 1987) , EAPAR and EVI mus t a l so
be c lose ly re la ted because APAR is the ene rgy
ava i lab le fo r pho tosyn thes is and VI i s a mea sure o f
the p ho tosy n the t ic s ize o f canopy . We can an t ic i-
pa te tha t ~V I w i l l r e la te func t iona l ly to and p ro -
v id e a g o o d e s t im a t e o f y ie ld i f EA P A R w o u ld . W e
h a v e t e r m e d t h e s l o pe o f t h e EA P A R( EV I ) r e la -
t i on t h e e f f i ci e nc y o f a b s o r p ti o n ( e~ , M J m - 2 /V I
un i t ) in te rms o f the ph o tosyn the t ic s ize o f the
canopy.
Th e s e c o n d r ig h t s i d e t e rm , A D M ( EA P A R ) , is
o f ten approx imate ly l inea r fo r much o f the season
fo r a g iven p lan t ing (M onte i th , 1977) and i t s s lope
is the e f f ic iency o f convers ion o f pho tosyn the t i -
ca l ly ac t ive rad ia t ion to d ry mass (e c , g D M /
MJ) , somet imes ca l led rad ia t ion use e f f ic iency
( RU E) . U n d e r l o w to m o d e r a t e s t r e s s c o n d i t i o n s
A D M ( Y A P A R) i s l i n e a r b e c a u s e a n y r e d u c t i o n i n
APAR reduc es th e supp ly o f ass imi la te s o f pho to -
s y n th e s is a n d c o n s e q u e n t l y d e c r e a s e s t h e d r y m a t -
te r ch ange (g row th) p ropor t iona l ly .
W h e n t h e f u l l g r o w in g s e a s o n , e m e r g e n c e t o
ha rves t , i s cons ide red the th i rd te rm in Eq . (8 ) ,
Y(DM2) , i s , by de f in i t ion , the ha rves t index . The
harvest index is approximately 0 .5 for s tarchy en-
dospe rm g ra in c rops (e .g ., co rn , t emp era te ce rea ls,
g ra in so rghum) when adap ted cu l t iva rs and rec -
o m m e n d e d a g r o n o m ic p ra c t ic e s a r e f o l l o w e d u n -
le ss ex t reme s t re ss t runca tes rep roduc t ion ( fo l ia r
d isease , d rough t , fo r example ) . Ev idence i s accu-
mu lat ing (e .g. , H ow ell , 1990) that the harv est in-
d e x is c l im a t e - d e p e n d e n t , h e n c e s i t e - d e p e n d e n t .
The r igh t -hand s ide te rms in Eq . (8 ) do no t
n e e d t o b e k n o w n o r o b s e r v e d t o u s e t h e l e f t - h a n d
s ide in app ly ing rem ote obse rva t ion capab i li ty ; the
r i g h t - h a n d s i d e t e r m s p r o v id e t h e a g r o n o m ic a n d
phys io log ica l exp lana t ion o f why the le f t s ide re la -
t ion ex is t s and i s mean ingfu l . We have te rmed the
s lope o f the Y(~V I) re la t ion the y ie ld e f f ic iency
( ey , g m - 2 / V I u n it ) in t e rm s o f th e p h o t o s yn t h e ti c
s ize o f the canop y (W iegan d e t a l . , 1989 ; W iegan d
and Richardson , 1990) . The numer ica l va lue o f ey
is s imilar for the indices GVI and PVI, and for
NDVI and TSAVI because those VI pa i r s have
s imi la r magn i tudes .
Eq u a t i o n s ( 6 ) a n d ( 7 ) d e s c r i b e d LA N D S A T
MSS obse rva t ions fo r g ra in so rghum Sorghum
bicolor
L. M o e n c h ) ( W ie g a n d a n d R ic h a r d s o n ,
1984) and smal l p lo t handhe ld rad iomete r s tud ies
f o r w h e a t
Triticum aestivum
L.) , cot ton, and corn
(Wiegand e t a l . , 1986a , Wiegand and Richardson ,
1987). Equations (6) , (7) , and (8) have been veri-
f ied for r ice
Oryza sativa
L.) (Wiegand e t a l . ,
1989).
Spec t ra l componen ts ana lys i s (SCA) assumes
impl ic i t ly tha t i ) p lan t s tands in teg ra te th e g row -
in g c o n d i t i o n s e x p e r i e n c e d a n d e x p r e s s t h e n e t
ass imi la t ion th rough the canop ies ach ieved , i i )
s t re sses seve re eno ugh to af fect eco nom ic y ie ld
wi l l be de tec tab le th rough the i r e f fec ts on the
d e v e lo p m e n t a n d p e r s i s t e n c e o f p h o to s y n th e t i ca l l y
ac t ive t i s sue in the canop ies , i i i ) h igh economic
y ie lds canno t be ach ieved un less p lan t canop ies
are achieved that fu l ly u t i l ize avai lable solar radia-
t ion as the p lan ts en te r the rep ro duc t ive s tage , and
iv ) vege ta t ion ind ices ca lcu la ted f rom remote ob-
se rva t ions in appropr ia te wave leng ths e f fec t ive ly
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Vegetat ion Ind ices in Crop Assessm ents 11 ]
m e a s u r e t h e p h o t o s y n t h e t i c s i z e o f t h e c a n o p ie s .
Equ a t ions 6 ), 7 ), and 8 ) a r e u sed to a id the
in t e rp r e t a t ion o f da t a f r om the s tud ies r epor t e d
h e r e i n .
R E S U L T S
C o t t o n
Figu re 1 d i sp l ays the sca t t e r i n t he bo l l coun ts ,
exp ress ed as l i n t y i e ld kg /ha ) , f o r t he 36 samples
f rom wi th in the sa l t - a f f ec t ed co t ton f i e ld ve r sus
the fou r vege ta t ion ind ices ca l cu la t ed fo r t he
SPOT-1 HRV da ta . The func t iona l r e l a t i ons a r e
those fo r t he l e f t - hand s ide o f Eq . 7 ) app l icab le t o
in t e rp r e t ing spec t r a l da t a ob ta ined du r ing ac t ive
r ep roduc t ion by the c rop . A t t he s tudy s i t e , co t ton
i s b looming and se t t i ng bo l l s by 15 May . Af t e r 1
J u n e t h e p h o t o s y n t h e t i c s i z e o f t h e c a n o p y i n -
c r eases on ly modes t ly because a ss imi l a t e s i n ex -
cess o f t hose fo r r e sp i r a t ion , w a te r an d n u t r i en t
u p t a k e , a n d s t r u c t u r a l e n l a r g e m e n t s u p p o r t b o l l
g rowth , wh ich con t inues fo r i nd iv idua l bo l l s f o r
abou t 40 days . Consequen t ly , t he pho tosyn the t i c
0
r-
O~
J¢
v
I . -
z
. J
1 8 0 0
1 6 0 0
1 4 0 0
1 2 0 0
1 0 0 0
8 O O
6 O O
4 0 O
2 0 0
0
0
Figure I
L in t yield of c otton versus fo ur vegetation indices calculated from SPOT-1 HRV observations.
6 - 0 4 - 1 9 8 9
Y I E L D , , - 110+95.6 G VI) / x
R M S E - 2 2 2 x
r * , 2 -. 7 56 x xX x y
/
x X x
x x
x X
x x x
X X X
5 l O 1 5
t
- I
.I
I
A 1
2O
1 8 0 0
1 6 0 0
1 4 0 0
1 2 0 0
l O 0 0
8 O O
6 O O
4 0 0
2 O O
. 1 0
6 - 0 4 - 1 9 8 9
Y IE L D - -6 4 9 + 4 5 3 6 . 8 ( N O M )
R M S E - 2 2 3
r * ,2 , , .75 4 x /
X X X
X X
: S
x x x
x
x
x J ' x x x
i I ~ I
0 . 3 0 0 . 5 0
GVISPOT
N D VI SPOT
o
r ,
I , -
,_i
1 8 0 0
1 6 0 0
1 4 0 0
1 2 0 0
1 0 0 0
8 O 0
8 O 0
4 0 O
2 0 0
0 0 :
I i i
6 - 0 4 - 1 9 8 9
Y I E L D - , - 3 , ~ + 104 2 PVI ) / x
/
R M S E - 2 2 2 x /
r ** 2- , 757 x xX x J
/
x x X
~Ot x
x x ~
X I* X X
~ 1 I I X
i I
5 1 0 1 5
C
1 8 0 0
1 6 0 0
1 4 0 0
1 2 0 0
1 0 0 o
8 O O
6 O O
2 O O
i
6 - 0 4 - 1 9 8 9
Y I E L D ,, - 8 9 + 3 8 6 7 8 ( T S A V I )
R M S E - 2 2 3 , / k
r * - 2 - . 7 5 6 x ~ /
x ) I x x
0 2 0 0 4 0
0
PVIspoT TSAVI
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Vegetat ion Indices in Crop Assessm ents 1 1 3
T h e l i n t y i e l d v e r s u s G V I a n d N D V I a s in t h e
l e f t s i d e t e r m o f E q . 7 ) f o r v i d e o d a t a c o l l e c t e d o n
1 9 J u n e a n d 1 4 J u l y is s h o w n i n F i g u r e 2 . T h e
c o e f f ic i e n ts o f d e t e r m i n a t i o n a r e s l i g h tl y h i g h e r f o r
1 9 J u n e t h a n f o r 1 4 J u l y , b u t l o w e r f o r b o t h d a t e s
t h a n f o r t h e S P O T - 1 H R V d a t a . B y 1 4 J u l y b o l l s
w e r e o p e n i n g a n d h a r v e s t w a s o n ly a b o u t 3 w e e k s
a w a y . I n F i g u r e 2 , t h e G V I a r e m u c h l a r g e r t h a n
i n F i g u r e 1 b e c a u s e t h e y a r e b a s e d o n d i g i ta l
c o u n t s t h a t h a d v a l u e s a b o u t f i v e t i m e s a s l a r g e a s
t h e r e f l e c t a n c e s u s e d f o r t h e H R V d a t a . T h e H R V
s e n s o r h a s a n o m i n a l g r o u n d r e s o l u ti o n o f 2 0 m
w h e r e a s t h e 4 9 v i d e o p i xe l s r e p r e s e n t e d a d i s ta n c e
7 . 2 m a c r o s s t h e r o w s a n d 9 . 3 m d o w n t h e r o w s .
orn
E x p e r i m e n t a l d a t a f o r t h e l e f t si d e o f E q . 7 ),
F P A R a s a f u n c t io n o f V I , a r e p r e s e n t e d i n F i g u r e
3 f o r t w o v e g e t a t i o n i n d i c e s , P V I a n d N D V I . W e
d i d n o t e x p e r i m e n t a l l y d e t e r m i n e t h e r i g h t - h a n d
s ide t e rms beca us e E q . 7 ), it s e lf , imp l ie s tha t i t
i s n o t n e c e s s a r y t o d o s o . E x p e r i m e n t a l d a t a i n
t h e l i t e r a t u r e G a l l o e t a l. , 19 85 ; W i e g a n d a n d
R i c h a r d s o n , 1 9 8 7 ) a l s o s h o w t h a t F P A R c a n b e
e s t i m a t e d w e l l f r o m V I a s F i g u r e 3 d e m o n s t r a t e s
a g a i n r 2 = 0 .9 5 6 a n d 0 . 9 7 3 f o r P V I a n d N D V I ,
r e s p e c t i v e l y ) , d u r i n g t h e p r e t a s s e l i n g f i rs t t a ss e ls
b e c a m e v i si b le o n 8 M a y a n d t h e m a x i m u m V I
r e a d i n g s o c c u r r e d o n 9 M a y b e f o r e t h e y h a d
e m e r g e d ) o r p r e - V l m a x p e r i o d . W h e n t h e t a s s e l s
f u ll y e m e r g e d , t h e y s h a d e d t h e s e n so r s m e a s u r i n g
t r a n s m i t t a n c e T ) a n d F P A R i n c r e a s e d b y
0 . 1 0 - 0 .1 5 . T h u s P A R w a s i n t e r c e p t e d b y p h o to -
s yn th e t i ca l ly inac t iv e t i s s ue Ro s en th a l e t a l. , 1985)
w h i c h p e r v e r t s F P A R d e f i n e d b y E q . 1 ). T h e
s o l u ti o n w e h a v e s u g g e s t e d i s u s e o f V I m e a s u r e d
t h r o u g h o u t t h e s e a s o n i n t h e f u n c t i o n a l r e l a t i o n
b e t w e e n F P A R a n d V I d e v e l o p e d f r o m t h e p r e-
V l m a x p o r t i o n o f t h e s e as o n .
I n F i g u r e 3 , t h e p o s t - V l m a x r e g r e s s i o n l i n e
a n d e q u a t i o n a r e f o r t h e d a t a p o o l e d a m o n g p o p u -
l a ti o n s. H o w e v e r , i t i s k n o w n e . g. , R o s e n t h a l
e t a l., 1 9 8 5) t h a t F P A R f o r th e p o s t - V l m a x p e r i o d
i n t e r c e p t s t h e F P A R a x i s b e t w e e n 0 . 3 a n d 0 . 7 f o r a
c o m p l e t e l y s e n e s c e n t c a n o p y d e p e n d i n g u p o n
d e n s i t y o f t h e s t an d . C o n s e q u e n t l y , h a d e x p e r i-
m e n t a l F P A R o b s e r v a t i o n s c o n t i n u e d a f t e r 1 6 J u n e ,
t h e l o w p o p u l a t i o n t r e a t m e n t , a t l e a s t , w o u l d r e -
q u i r e a d i f f e r e n t f i t f r o m t h e o t h e r t w o t r e a t m e n t s
a n d w o u l d l i k e l y i n t e r c e p t b e l o w 0 . 3 .
0 . 9 0
0 . 7 0
0 . 5 0
0 . 3 0
0 . 1 0
i i
P R E I ~ q m o x P O S T
H I G H P O P • . • ~ I / D I D / / 0
i . m p o P _ , . , ¢ 0 * / I °
L o w P O p , o _ = / . I h . / o
• . r / ~
. o / ~ ,
7 - _
/ / • ~ t r - - PRE-PVlmm¢
• / . . , . , ~ , ~ F P A R - - . O 1 5 + . O ~ ( P V l )
r ~ 2 - . 9 5 6 RMSE- .O81
I~ P O - - - P ( ) S T - P V I m o x
FPAR,,.114+.037(PM)
r ~ 2 , - . 6 3 9
RMSE- .092
- - 0 . 1 0 , I , I ,
0 10 20 .30
P V l u K ,
P ~
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1 1 4 W i e g a n d e t a l
H P O P 7 . 7 ) m . . 2 ) A
] e - e M E D P O P 5 . 4 / m * . 2 )
20
i
0 | I ~ 1 1 ~ : I I I I
8 0
1 0 0 1 2 0 1 4 0
1 6 0
HIGH~ P O P ( 7 . 7 / m * . 2 ) ~ 1
--
o---o MED POP (5 .4 /m *.2) --,-- Is
. .
L o w P O P . L
0 . 8
o . 6 1
0.4
0.2
0.0
8 0 1 O 0 1 2 0 1 4 0 1 6 0
OY
Figure 4
Experimentally observed PVI and FPAR means
and standard deviations by population treatm ent versus day of
year (DOY ) for corn.
t " q
4l-
t .
E
c n
v
C3
._J
LI.J
> -
9 0 0
7
5
. . . . i . . . .
H I G H P 0 P ' 6 / 0 5 1 8 9 A
o ME{ ) POP
,, LOW POP o
O
El
o
r * . 2 = , 3 2 6 ~ Q
O
3 0 0 . . . . . . . . i . . . .
,5 10 15
PVI UK
4l.
4l-
E
C ~
v
_ J
LIJ
> -
9 0 0
700
500
• • I 1 i
O H I G H P O P W H O L E S E A S O N
o M E D P O P
A L O W P O P o
o
E l
Y I E L D = 1
/t)+.¢~ tt :wU o
o
(O)
r * , 2 = . 2 3 5 R M S E = 1 5 5 o
A
8
( Q
(~ , I , I * I , I ,
3 0 C 7 0 0 9 0 0 1 1 0 0 1 0 0
PV I MK.
Figure 5
Grain yield of corn versus PVI on one date [left
side of Eq. (7)] and cum ulative PVI for the growing season,
EPVI [left side of Eq. (8)].
h a d t o o f e w p l a n t s / m 2 t o u t i li z e t h e P A R e f f ec -
t i ve ly F ig . 4 ) and the r e was in su f f i c ien t e l a s t i c it y
in ea r s i ze t o compensa t e f o r t he de f i c i t i n p l an t
p o p u l a t i o n . T h e m e d i u m p o p u l a t i o n w a s a b o u t
t h a t r e c o m m e n d e d l o c a l l y f o r c o m m e r c i a l c o r n
p r o d u c t i o n a n d t h e r e w a s a g o o d b a l a n c e a m o n g
p lan t popu la t ion , f e r ti l it y , wa te r , and ava i l ab l e PAR
r e s o u r ce s . T h e r e w e r e t o o m a n y p l a n t s i n t h e h i g h
popu la t ion fo r t he nu t r i en t cond i t i ons tha t ex i s t ed
a n d v e r y s m a l l e a r s w e r e p r o d u c e d t h a t y i e l d e d
l es s g r a i n / m 2 t h a n d i d t h e m e d i u m p o p u la t io n .
T h e d a t a p o i n t e n c l o s e d i n p a r e n t h e s e s f o r o n e
p lo t o f each t r ea tm en t i s f r om the f ir s t t i e r o f p lo t s
o n o n e s i d e o f t h e e x p e r i m e n t a l a r e a w h e r e t h e
p lan t s w ere v i s ib ly n i t r ogen de f i c i en t due to
l each ing by excess ive i r r i ga t ion the p r ev ious c rop
season.
Th e da t a o f F igu re 5 i ll u s t r a t e t ha t i n t e rp r e t a -
t io n i s a i d e d b y a g r o n o m i c u n d e r s t a n d i n g o f l im i t -
ing f ac to rs i n c rop g row th and y i e ld o f t en re -
v e a l e d t h r o u g h t h e p a t t e r n s s e e n i n m u l t i t e m p o r a l
i m a g e r y o f t h e g r o u n d s c e n e s ). T h e a p p r o a c h i s
i n t e n d e d t o a p p ly t o c o m m e r c i a l c r o p s h u s b a n d e d
b y r e c o m m e n d e d p r a c t i c e s f o r t h e p r o d u c t i o n a r e a
w h e r e g r o w n .
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V e g e ta t io n I n d i c e s i n C r o p A s s e s s m e n t s 1 1 5
Table 2 .
Solution of Eq. (8) Term by Term for the Whole Corn Growing Season (Emergence to Physiological
Maturity of the Grain) by Population Treatment
Y i el d Y i e ld A D M ~ A P A R
P o p u la ti o n E P V I - A D M × F~APA---------R × EP~----Q--F
(p lan ts / m 2 ) (g m - 2 PVI un i t ) a (g m - e / g m - 2 ) t (g / MJ) : (MJ m - 2 PVl un i t ) a
A. PVI and APAR Summed Daily (based on Fig. 5)
7.7 0.576 0.436 2.726 0.484
5.4 0.738 0.473 3.000 0.520
3.1 0.611 0.452 2.774 0.487
B. FPAR after 9 May (tasseling) from FPAR = - 0.015 + 0.036 (PVI) of Fig. 4a
7.7 same same 3.249 0.406
5.4 same same 3.706 0.419
3.1 same same 3.251 0.416
ayield efficiency ey in terms o f cumulative perpendicular vegetation index.
t Harvest index, HI.
CEfl~ciency of conversion o f absorbed PAR to dry matter, e,..
aEfficiency of absorption, e, , in terms of perpendicular vegetation index.
The so lu t ion o f Eq . ( 8 ) f o r t he who le co rn
g r o w i n g s e a s o n ( e m e r g e n c e t o p h y s i o lo g i c a l m a t u -
r i ty o f t h e g r a i n ) is p r e s e n t e d t e r m b y t e r m b y
p o p u l a t i o n t r e a t m e n t i n T a b l e 2 . A b s o r b e d P A R
was ca l cu la t ed two ways : 1 ) by mul t ip ly ing exper i -
m e n t a l F P A R o f F i g u r e 4 b b y t h e u n i q u e o b s e r v ed
da i ly i nc iden t PAR f lux (upp er pa r t o f Tab le 2 ),
and 2 ) a s i n 1 ) , above , t h rough 9 May bu t t he r e -
a f t e r by in se r t i ng o bse rve d da i ly va lues o f PVI in to
t h e p r e - P V I m a x ( p r e t a s s e l i n g ) F P A R e q u a t i o n i n
F i g u r e 3 a a n d m u l t i p l y i n g t h a t a n s w e r b y t h e
inc iden t PAR f lux fo r each day . Cumula t ive (o r
i n t e g r a l ) A P A R w a s o b t a i n e d b y s u m m i n g t h e
da i ly va lues t h rou gho u t t he season .
Th i s p rocedura l d i f f e r ence a f f ec t s t he l a s t two
r igh t s ide t e rms o f Eq . ( 8) , t he e f f ic i ency o f con -
v e r s i o n o f a b s o r b e d P A R t o d r y m a t t e r , e c a n d t h e
e f f i c iency o f abso rp t ion in t e rm s o f the vege ta t ion
index , e a . S ince Y ',APAR i s sm a l l e r w he n pho tosyn-
the t i ca l ly i nac t ive t i s sue a f f ec t ing FPAR i s min i -
miz ed, e c is 1 .19, 1 .24, and 1 .17 t im es large r for
h i g h , m e d i u m , a n d l o w p l a n t p o p u l a t i o n s , r e s p e c -
t iv e l y , i n t h e l o w e r t h a n i n t h e u p p e r p a r t o f T a b l e
2 . T h e v a l u e s i n t h e l o w e r p a r t o f T a b l e 2 a g r e e
w e l l w i t h t h e v a lu e o f 3 .4 g D M / M J P A R re c o m -
mended fo r co rn by S inc l a i r and Hor i e ( 1989) .
L ikew ise , t he e f f i c ienc i es o f abso rp t ion a r e sm a l l e r
b y a l m o s t t h e s e s a m e f a c t o r s . W e c o n c l u d e t h a t
w o r k n e e d s t o b e d o n e t o e d u c a t e u s e r s a b o u t t h e
var i ab i l i t y i n e f f i c i enc i es o f conver s ion o f PAR to
d r y m a t t e r b a s e d o n m e t h o d s o f d e t e r m i n i n g
F P A R .
I n T a b l e 2 , t h e h a r v e s t i n d i c e s - - t h e s l o p e o f
g r a in y i e ld a s a f unc t ion o f t o t a l abovegro und d ry
m a t t e r i n c l u d i n g t h e g r a i n - - r a n g e d f r o m 0 . 4 3 6 f o r
the denses t popu la t ion to 0 .473 fo r t he in t e rmed i -
a t e p l an t ing . Th i s r ange i s qu i t e na r row bu t s t i l l
impor t an t . A t ha rves t t o t a l above g round a i r -d ry
phy tomass , DM 2 , was 1645 , 1700 , and 1115 g / m 2
fo r h igh , med ium, and low popu la t ions , r e spec -
t ive ly . Fo r D M 2 = 1500 , each 0 .01 inc r ease in t he
h a r v e s t i n d e x m e a n s a 1 5 g / m 2 o r 1 5 0 k g / h a
inc r ease in g r a in y i e ld , enough to make a d i f f e r -
ence in p ro f i t o r l o ss t o t he g rower in cu r r en t
na r row p ro f i t - l o ss marg ins .
Th e y i e ld e f fi c i ency , t he l e f t s ide t e rm in Eq .
(8 ) was in t he sam e o rde r a s t he e f f i c i ency o f
a b s o rp t io n , t h e s a m e f i n d i n g r e p o r t e d b y W i e g a n d
et a l . (1989) for r ice . In that s tudy there were 13
t r e a t m e n t s c o n s i s ti n g o f i n c o m p l e t e c o m b i n a t io n s
o f two p l an t ing da t es , t h r ee cu l t iva r s , and 6N
app l i ca t ion r a te s . R e la t ive to t he m ean , va r i a t i on in
t h e ~ A P A R ( E P V I ) t e r m w a s a b o u t 1 5 c o m p a r e d
wi th 5 fo r t he o the r two righ t s ide t e rms , so tha t
i t d o m i n a t e d t h e Y ( E P V I ) t e rm . I t is n o t n e c e s s a r y
t o k n o w w h i c h o f th e r i g h t s i d e t e r m s i n E q . ( 8 )
d e t e r m i n e ~ V I f o r i t t o b e c o m e a v i a b l e r e m o t e
es t ima to r o f y i e ld . Tha t i s h igh ly des i r ab le f o r
s c ie n t if ic u n d e r s t a n d i n g a n d c a n b e e s t a b l is h e d b y
add i t i ona l i n t ens ive smal l p lo t s tud ies .
D I S C U S S I O N
The spec t r a l componen t s ana lys i s (SCA) equa t ions
r e v i e w e d a n d i l l u s t r a t e d p r o v i d e a f r a m e w o r k
w i t h i n w h i c h t o e x a m i n e a l a r g e n u m b e r o f r e la -
t i onsh ips t ha t desc r ibe the g rowth , pho tosyn the t i c
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11 6 Wiegand et al.
s i ze, and y i e ld o f c rops a s a f fec t ed by the i r env i -
ronmen t s and s t re sses . The spec t ra l t e rms ( t hose
invo lv ing VI) i n t e r re l a t e V I , L , FPAR , APAR, y i e ld ,
a n d D M i n a w a y t h a t i s c o n s i s t e n t w i t h p h y s i c a l
a n d p h y s i o l o g i c al p r i n c i p le s a n d i n a g r e e m e n t w i t h
g row th and y i e ld behav io r o f c rops i n t he f i e ld .
I n t e r n a l c o n s i s t e n c y i s e n h a n c e d b y t h e f a c t s t h a t
FPAR, VI , and y i e ld a l l app roach l im i t i ng va lues
a s y m p t o t i c a l l y a s L i n c r e a s e s ( W i e g a n d a n d
Rich ardson , 198 4; Sel lers , 1985).
T h e e q u a t i o n s w e r e d e v e l o p e d t o m a x i m i z e
the i n fo rmat ion ex t rac t ab l e f rom spec t ra l obse rva -
t i ons abou t c rop cond i t i ons and y i e lds . The l e f t
s ide t e rms o f Eqs . (6 ) , (7 ), and (8 ) a re e mp has i z ed
to take adv an tage o f rem ote obse rv a t ion capab i l i t y
whi l e t he r i gh t s i des add ress t he p l an t p rocesses
i n v o l v e d . U n t i l t h e e q u a t i o n s w e r e d e v e l o p e d ,
t h e r e w a s n o t h e o r y t o u n d e r g i r d t h e i n t e r p r e t a -
t i ons . Hopefu l ly , SCA wi l l i nc rease t he appea l o f
spec t ra l obse rva t ions t o o the r po t en t i a l u se rs o f
th i s capab i l i t y , fo r example , p l an t p rocess mode l -
e rs , eco log i s ts , hydro log i s t s , and me teo ro log i s t s .
Sa t e l l i t e obse rva t ion capab i l i t y shou ld pe rmi t
e s t i m a t i o n o f F P A R f o r v e g e t a t e d a r e a s e x p r e s s e d
b y
F e A R = ( 1 - R ) ( 1 - T ) , ( 10 )
w h e r e i n s u r f a c e r e f l e c t a n c e R c a n b e a p p r o x i -
m a t e d b y a b r o a d v i s i b l e b a n d s u c h a s t h e
p a n c h r o m a t i c b a n d ( 5 1 0 - 7 3 0 n m ) o f t h e S P O T - 1
HRV . One l im i t o f R i s t he re f l ec t ance o f ba re so il
( 0 . 0 5 - 0 .2 0 , d e p e n d i n g o n w a t e r c o n t e n t a n d c o l o r)
and the o the r ex t reme i s t he i n f in i t e re f l ec t ance o f
t h e c a n o p y ( 0 . 0 3 - 0 .0 5 ) . I n t e r c e p t e d P A R , ( 1 - T ,
c a n b e e s t i m a t e d b y t h e S A I L o r o t h e r c a n o p y
r e f l e c t a n c e m o d e l f r o m o b s e r v e d N I R a n d R E D
ban d re f l ec t ances . I f capab i li t y t o execu te t he SA IL
mode l i s l ack ing , t he func t iona l re l a t i on be tween
( 1 - T ) a n d V I m a y b e f o u n d i n t h e l it e r at u r e o r
c a n b e e x p e r i m e n t a l l y d e v e l o p e d f o r t h e c r o p ( s ) o f
in t e res t . S ince [ Io (1 - R)] i s a l so phys i ca l ly t he ne t
d o w n w a r d f l u x , A P A R ( M J / m 2 / d a y ) i s t h e p r o d -
u c t [ I o ( 1 - R ) ] ( 1 - T ) . F o r b a r e s oil T = 1 .0 s o
tha t APA R = 0 , and fo r a ve ry d ense canopy T
approa ches 0 , so t ha t APAR = (0 .95 -0 .97 ) /0 . Pe r i -
o d i c r e m o t e o b s e r v a t i o n s o f R a n d m o d e l e s t i -
m a t e s o f T n e a r s o l a r n o o n p e r m i t g r a p h s o f
1 - R ) a n d ( 1 - T ) v e r s u s D O Y ( l i k e F i g . 4 ) f r o m
wh ich es t ima tes fo r al l days o f i n t e res t ca n be
m a d e . C h o u d h u r y ( 1 9 8 7 ) h a s u s e d a r a d i a t i v e
t r a n s f e r e q u a t i o n t o e s t i m a t e F P A R a n d B a r e t a n d
co-workers (e .g . , Baret and Ol ioso , 1989) have
u s e d t h e S A I L m o d e l i n c o n j u n c t i o n w i t h e s t i -
ma tes o f l i gh t abso rp t ion by c anop ies bu t no t i n
con tex t o f Eq . (10 ). Adv ances mu s t be m ade in
s t andard i z ing the e s t ima t ion o f PAR abso rp t ion by
canop ies , l e s t t he e f f i c i enc i es o f convers ion o f
APAR to DM wi l l remain va r i ab l e . In t h i s s t udy
t h e t w o m e t h o d s o f c a l c u la t io n u s e d g a v e v a l u es
tha t d if fe red by abou t 20 .
I t i s ev iden t t ha t ~VI i s s imi l a r i n some re -
s p e c ts t o l e a f a re a d u r a t i o n ( L A D ) p r o p o s e d b y
W a t s o n (1 95 2) , w h i c h h a s l a r g e ly b e e n a b a n d o n e d
b e c a u s e i t d id n o t h o l d a c r o ss e n v i r o n m e n t s ( E v a n s
and Ward law, 1976) . (LAD used he re i s no t t o be
confu sed wi th l ea f ang le d i s t r i bu t ion as u sed in
c a n o p y r a d i a t i v e t r a n sf e r m o d e l i n g .) L e a f a r e a d u -
ra t i on had the un i t s , days , and made no d i s t i nc t ion
b e t w e e n , f o r e x a m p l e , c o o l , l o w i r r a d i a n c e w i n t e r
a n d w a r m , h i g h i r r a d i a n c e s u m m e r d a y s . I n c o n -
t ra s t , t he VI measu re t he pho tosyn the t i c s i ze o f
the canop ies a s a f fec t ed by env i ronmen ta l va r i -
ab l es . The va r i ab l es t ha t con t ro l t he po t en t i a l VI
a re s t ab l e fo r a g iven p roduc t ion a rea f rom yea r t o
yea r (day leng th o r i n so l a t i on , i nhe ren t so i l p roper -
t i e s , cu l t i va rs , managemen t p rac t i ces ) wh i l e t he
st ress variables (precip i ta t ion , d iseases , toxic pest i -
c i d e r e s i d u e s , w e a t h e r e v e n t s , e t c . ) a r e g r o w i n g -
s e a s o n - d e p e n d e n t . T h e r e f o r e , c a l ib r a ti o n s o f y i e l d
ve rsus VI ac ross good and poor g rowing cond i t i ons
w i t h i n p r o d u c t i o n a r e a s c a n d e s c r i b e t h e r e s u l ts o f
pas t and fu tu re g rowing seasons accep tab ly .
T h e c a l i b r a t i o n s a r e n e e d e d p r e s e n t l y b e c a u s e
two o f t he t h ree r i gh t s i de te rms in Eq . (8 ) a re
s i t e - d e p e n d e n t . W e s p e c u l a t e t h a t t h e d o m i n a n t
env i ronmen ta l va r i ab l e caus ing va r i ab i l i t y i n t he
dxDM(EAPAR) func t iona l re l a t i on i s ambien t
t empera tu re ; i n p r inc ip l e , any s t re ss such as l ow
t e m p e r a t u r e t o w h i c h c e l l e x p a n s i o n a n d p h o t o -
syn thes i s d i f fe r i n sens i t i v i t y , o r above op t imum
t e m p e r a t u r e w i t h i n t h e p l a n t t o l e r a n c e r a n g e t o
which re sp i ra t i on and pho tosyn thes i s d i f fe r i n sen -
s i t i v i t y , can cause dev ia t i on f rom cons t ancy in t he
e f f i c iency o f convers ion .
The ha rves t i ndex i s h ighes t fo r a g iven c rop
where i t i s bes t adap ted and dec reases a s i t i s
g r o w n u n d e r l e s s i d e a l c o n d i t i o n s . W e s p e c u l a t e
that s a tura t ion defic i t s of the a i r , insola t ion , and a i r
and so i l t empera tu res t ha t a re pa r t l y con t ro l l ed by
l a t i t u d e a n d e l e v a t i o n a r e p r o b a b l y t h e i m p o r t a n t
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8/18/2019 Wiegand et al. 1991
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V e g e t a t i o n I n d i c e s in C r o p A s s e s s m e n t s
7
f a c t o r s . U n f o r t u n a t e l y , t h e f a c t o r s t h a t c a u s e t h e
e f f ic i e n c y o f c o n v e r s i o n a n d t h e h a r v e s t i n d e x t o
v a r y g e o g r a p h i c a l l y a r e p o o r l y r e s e a r c h e d .
I n te r m s o f a p p l y i n g E q s . 7 ) a n d 8 ) , w e c a n
s a y th a t t h e l e f t s id e t e r m s w o u l d n o t b e s i t e -
d e p e n d e n t i f t h e r i g h t s id e t e r m s w e r e n o t . L i k e -
w i s e , if t h e r i g h t s i d e s it e d e p e n d e n c i e s w e r e
k n o w n , t h e l e f t s i d e s it e d e p e n d e n c i e s w o u l d b e
p r e d i c t a b l e a n d t h e l e f t s i d e f u n c t i o n a l r e l a t i o n s
w o u l d n o t h a v e t o b e c a l i b r a t e d b y p r o d u c t i o n
a r e a s . O n t h e o t h e r h a n d , i f t h e l e f t s i d e t e r m
f u n c t io n a l r e l a ti o n s a r e c a r e f u l l y d e t e r m i n e d , t h e y
c a n h e l p e l u c i d a t e t h e r i g h t s i d e f u n c t i o n a l r e l a -
t i o n s .
I n s u m m a r y , o b s e r v e d y i e l d d i f f e r en c e s a m o n g
f i el d s a r e a s s o c i a t e d w i t h d i f f e r e n c e s in L , D M ,
a n d p e r c e n t c o v e r th a t s t ar t b e c o m i n g e v i d e n t i n
t h e v e g e t a t i o n i n d i ce s e a r l y i n v e g e t a t i v e d e v e l o p -
m e n t e . g . , R i c h a r d s o n e t a l. , 1 9 8 2 ) . T h e d i f fe r -
e n c e s i n g r o w t h h a v e m a n y p o s s i b l e c au s e s
m a n a g e m e n t p r a c ti c e s , w e a t h e r , i n h e r e n t s o il
p r o p e r t i e s , b i o t i c s t r e s s e s , e t c . ) . D i r e c t o b s e r v a t i o n
o f t h e p h o t o s y n t h e t i c s i z e o f t h e c a n o p i e s a n d t h e
i n t e r p r e t a t i o n o f t h o s e o b s e r v a t i o n s w i t h in t h e
f r a m e w o r k o f s p e c t r al c o m p o n e n t s a n a ly s is p e r -
m i t s i n f e r e n c e s a b o u t t h e d e v e l o p m e n t , g r o w t h ,
a n d y i e l d o f t h e p l a n t c o m m u n i t i e s t h a t c o n s t it u t e
t h e c a n o p i e s o b s e r v e d . Y i e ld w a s e m p h a s i z e d i n
t h e p a p e r b e c a u s e o f i ts e c o n o m i c i m p o r t a n c e t o
p r o d u c e r s a n d i n w o r l d t r a d e .
W e thank Dr. M elba C rawfi~rd, University of Texas, Austin,
f i ) r providing the SPOT-1 scene; Dr . S tepha n Maas for des ign-
ing the corn exper iment and get t ing i t in i t ia ted; Edgar Smi th
for a l lowing us to use h i s cot ton fi e lc~ Ren e D avis for p i lo t ing
the plane to acquire the v ideo data an d fo r pr int ing Plate I ;
Noe l Garcia f i )r processing data on the im age analysis systems;
Rom e o Rodr i gue z and A l v i n G e r be r m ann f o r a s si st anc e w i t h
f ield work, d ata reduction, statistical analysis, an d fo r f igur e
preparation; and Carol Harvil le and S aida Cardoza fo r
manuscript preparation.
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