A Modified Soil Adjusted Vegetation Index

7/26/2019 A Modified Soil Adjusted Vegetation Index

1/8

R E M O T E S E N S . E N V I R O N . 4 8 : 1 1 9 - 1 2 6 ( 1 9 9 4 )

M odified So il djus ted V egetat ion Index

J . Q i , A . Ch ehbou n i , A . R . H ue te, Y . H . K er r , an d S. Soroosh i an

T h e r e is currently a great deal of interest in the quanti-

tative characterization o f temporal a nd spatial vegetation

patterns with remotely sensed data fo r the study o f earth

system science and global change. Spectral models and

indices are being developed to improve vegetation sensitiv-

i ty b y accounting fo r atmosphere an d s oil ef fects. The

soil-adjusted vegetation index (SA VI) wa s developed to

minimize soil influences on canopy spectra by incorporat-

ing a soil adjustment facto r L intb the denominator of

the norm alized d ifference vegetation index (N DV I) equa-

tion. For optimal adjustmen t o f the soil effect, howeve r,

the L factor should vary inversely with the amount of

vegetation presen t. A modified SA VI (M SA VI) that re-

places the constant L in the SA VI equation w ith a variable

L function is presented in this article. The L function

ma y be derived by induction or by using the product o f the

ND VI an d weighted difference vegetation index (W DVI).

Results based on ground and aircraft-measured cotton

canopies are presented. The M SA VI is shown to increase

the dyna mic range of the vegetation signal while furth er

minimizing the soil background influences, resulting in

greater vegetation sensitivity as defined by a =vegetation

signal to soil noise r atio.

I N T R O D U C T I O N

T h e r e i s c u r r e n t l y a n i n c r e a s i n g i n t e r e s t i n v e g e t a t i o n

c h a r a c t e r i z a ti o n s w i t h r e m o t e s e n s i n g te c h n i q u e s . S i n c e

in fo rma t ion co n ta in ed in a s ing le spec t ra l band i s usua l ly

insuf f i c i en t t o charac te r i ze vege ta t ion s t a tus , vege ta t ion

D e p a r t m e n t o f S o il a n d W a t e r S c i e n c e , U n i v e r si t y o f A r iz o n a ,

Tucson

t Laboratoire d Etudes et de Recherches en Tflfdftection Spati-

ale (LERTS), Toulouse, France

CHydrology and Water Resources Department, University of

Arizona, Tucson

A d d r e s s c o r r e s p o n d e n c e t o J i a g u o Q i , S o u t h w e s t W a t e r s h e d

Research C tr . , USDA-ARS, 2000 E . Al len Rd . , Tucson , AZ 85719 .

R e c e i v e d 3 M a r c h 1 9 9 3 ; r e v is e d 1 8 S e p t e m b e r 1 9 9 3 .

0 0 3 4 - 4 2 5 7 / 9 4 / 7 . 0 0

Elsev ier Sc ience Inc . , 1994

6 5 5 A v e n u e o f th e A m e r ic a s , N e w Y o r k , N Y 1 0 0 1 0

i n d ic e s a r e u s u a ll y d e v e l o p e d b y c o m b i n in g t w o o r m o r e

s p e c t r a l b a n d s . T h e r e a r e t w o g e n e r a l c a t e g o r i e s in

c o mb i n i n g t w o o r mo r e s p e c t r a l b a n d s : s l o p e - b a s e d a n d

d i s t a n c e - b a s e d v e g e t a t i o n i n d i c e s ( J a c k s o n a n d H u e t e ,

1 9 9 1 ). T w o o f t h e m o s t c o m mo n l y u s e d v e g e t a t i o n i n d i -

c e s ( V I) o f t h e s e t w o c a t e g o r i e s a r e t h e n o r ma l i z e d

d i f f e r e n c e v e g e t a t i o n i n d e x ( N D V I ) ,

N DV I = PN,n- Pr~a., (1 )

Psi~ + Pred

a n d p e r p e n d i c u l a r v e g e t a t i o n i n d e x ( PV I ) ,

P V I

= ap~i. - tffp~,

(2)

w h e r e p i s r e f l e c t a n c e s i n n e a r - i n f r a r e d ( N I R) o r r e d

b a n d . T h e a a n d f l a r e s o il l i n e p a r a me t e r s . T h e c o n c e p t

o f t h e s e t w o i n d i c e s is d e p i c t e d i n F i g u r e s l a a n d l b ,

w h e r e t h e N D V I i s o l i n e s a r e s h o w n t o c o n v e r g e a t

t h e o r ig i n w h i l e t h o s e o f t h e PV I a r e p a r a ll e l. T h e s e

v e g e t a t i o n i n d i c e s a r e p r i ma r i l y r e l a t e d t o v e g e t a t i o n

b iophys ica l parameters (Asrar e t a l . , 1984 ; Wiegand e t

a l. , 1 9 9 1 ) . P r o b l e m s e x i s t b e c a u s e o f e x te r n a l f a c t o r

ef fec t s , such as so i l background var i a t ions (Huete e t a l . ,

1 9 8 5 ; H u e t e , 1 9 8 9 ) . T o r e d u c e t h e s o i l b a c k g r o u n d

e f f e c t , H u e t e ( 1 9 8 8 ) p r o p o s e d u s i n g a s o i l - a d j u s t me n t

f a c t o r L t o a c c o u n t f o r f i r s t- o r d e r s o i l b a c k g r o u n d v a r ia -

t i o n s a n d o b t a i n e d a s o i l - a d j u s t e d v e g e t a t i o n i n d e x

(SAVI):

SAVI = P N,R- - P r ed 1 + L) ,

PN~ + Pr~a+ L

3)

where L i s a so i l ad jus tmen t fac to r (F ig . l c ) . A l though

H u e t e ( 1 9 8 8 ) f o u n d t h e o p t i ma l a d j u s t me n t f a c t o r t o

vary wi th veg e ta t ion d ens i ty , he u sed a co ns tan t L -- 0 .5 ,

s i n c e t h i s r e d u c e d s o i l n o i s e c o n s i d e r a b l y t h r o u g h o u t a

w i d e r a n g e o f v e g e t a t i o n a mo u n t s . Fu r t h e r mo r e , o p t im i -

z a t i o n o f t h e L f a c t o r w o u l d r e q u i r e p r i o r k n o w l e d g e

o f v e g e t a t i o n a m o u n t s u n l e s s o n e d e v e l o p e d a n i te r a t i v e

func t ion . Al so , t he use o f a cons tan t L -- 0 .5 resu l t s i n a

l o s s i n t h e v e g e t a t i o n d y n a mi c r e s p o n s e s , s i n c e t h e L

o f 0 .5 i s u s u a l l y l a r g e r t h a n r e d r e f l e c t a n c e v a l u e s a n d ,

t h e r e f o r e , w o u l d b u f f e r r e f l e c t a n c e v a r ia t io n s .

1 1 9


2/8

1 2 0 p i et a l

0 6 0

0,40

n

Z

0 , 2 0

I

- 0 , 1 0 0

- 0 , 2 0

0 , 6 0

_ _ . 0 , 4 0

o.2

~ , - 0 , 2 0 , ~ : ~ I

y r

. o 1 - 0 r

a

b

; , , . . .

0,60

I

e o

. . . . Soil

l ine

# o I o o S

o o o S Z

# s

, . - - 0 , 2 0

e t o o o I | - -

o

0 , 2 0 0 , 4 0 - 0 , 1 0 0

R e d

- 0 , 2 0

~ PVI

0,20 0,40

R e d

c d

S ~ i l line ~ ' ,, ' , , , , - ' Soilline

z [ . / .

4

VI i

4 , I

T S A V I

0 , 2 0 0 , 4 0 . ~~ . . , , , . , , ~ . ,. . .

. : . : . v . -

R e J o .2 o o . o

E'

R e d

Figure 1. Concepts of vegetation isolines for various vegetation indices.

In this s tudy, we deve lop a func t iona l L fac tor , r e -

q u i r in g n o p r i o r k n o w l e d g e o f v e g e ta t i o n a m o u n t s , t o

r e p l a c e t he c ons t a n t L = 0 .5 , i n t he SAVI e qua t ion . T h e

objec t iv e of this a r t ic le is to f ind a se l f -adjus table L so

a s t o i n c r e a se t h e SAVI ve ge t a t i on se ns i ti v i ty by i nc r e a s -

i n g t h e d y n a m i c r a n g e a n d f u r t h e r r e d u c i n g t h e s o i l

b a c k g r o u n d e f fe c ts . T h e r e s u lt w o u l d b e a n i m p r o v e d ,

mo dif ied SAVI (MSAVI) wi th a hig he r vege ta t ion s ig-

nal to soil nois e rat io.

M E T H O D S

I n o r de r t o s t ud y t he c ha r a c t e r i s t ic s o f t he soi l a d jus t -

m e n t f a c to r L , two da t a se t s we r e ob t a ine d . T he f i r st da t a

s e t c o n s i s te d o f g r o u n d - b a s e d s p e c t ra l m e a s u r e m e n t s o f

a c o t t o n c a n o p y Gossypium hirsutum L. var . DPL-70)

f o r a f u l l s e a son ( 0 - 100% gr e e n c ove r ) unde r va r y ing

soi l ba c k gr oun d c ond i t i ons ( Hue te e t a l . , 1985). A t e a c h

c o t ton de ns i t y , t he so i l ba c kgr ound wa s va r i e d by i n -

se r t i ng d i f f e r e n t so i l s unde r ne a th t he c o t t on c a nopy .

T he soi l c o lo r r a nge d f r om v e r y da r k t o ve r y b r igh t , a nd

the soi l m o i s tu r e va r i e d fr om we t t o d r y . T he r a d iom e t r i c

m e a s u r e m e n t s w e r e m a d e o v e r th e c o t t o n w i t h a m u l ti -

m o d u l a r r a d i o m e t e r ( M M R ) w h i c h h a d a s p e c t r a l b a n d

i n t h e r e d r e g i o n ( 6 3 0 - 6 9 0 n m ) a n d N I R r e g i o n ( 7 6 0 -

900 nm ) . T h i s da t a se t e na b l e d us t o s t udy t he so i l

ba c kgr ound e f f e c t s on ve ge t a t i on i nd i c e s . T he se c ond

da t a se t wa s c o l l e c t e d ove r a c o t t on Gossypium hirsu.

turn L . va r. DPL - 70) f i e ld a t M a r i c opa Agr i c u l t u r al Ce n-

te r (MAC) , Mar icopa , Ar izona , USA. The re f lec tance

f a ct o rs w e r e o b t a i n e d w i t h a r a d i o m e t e r e q u i p p e d w i t h

SPOT f i l t e r s a nd m ounte d on a n a i r c r a f t . T he SPOT

spe c t r a l wa ve l e ng th i n t e r va l s we r e 610- 690 nm f or t he

r e d b a n d a n d 7 9 0 - 8 9 0 n m f o r t h e n e a r - i n f ra r e d ( N IR )

ba nd . T he a i r c ra f t wa s f lown a t 150 m a bove g r o und

a long a t r a nse c t i n a 400 m x 1600 m r e c t a ngu la r c o t t on

f i e ld dur ing t h e g r ow ing se a son o f 1989 . T h e spa ti a l

t r a nse c t m a d e on 10 Apri l 1989 , c on t a ine d a 5 - 10 %

c ot ton c ove r ove r spa t i a l l y va r i a b l e so i l ba c kgr ounds

wh ic h i nc lud e d 1 ) a d r y sa ndy c la y l oa m r e g ion ( 0 - 480

m ) , 2 ) a d r y sa ndy loa m ( 480- 65 0 m ) , 3 ) a d r y sa ndy

c l a y l oa m ( 650- 10 00 m ) , a nd 4 ) a we t s a ndy c l a y l oa m

( 1 0 0 0 - 1 6 0 0 m ) . T h r o u g h o u t t h e r e s t o f t h e y e a r , th e

so il c ha nge d on ly i n we tne ss du e t o i r ri ga t ion a n d r a in f a ll

e ve n t s . T h i s da t a se t a l l owe d us t o e xa m ine bo th dy-

na m ic r e sponse s o f ve ge t a t i on i nd i c e s t o c o t t on g r ow th

a nd the so i l ba c kgr ound e f f e c t s .

T H E O R Y

a c k g r o u n d o n V e g e t a t i o n I n d i c e s

Dif f e r e n t ve ge t a t ion i nd i c e s ( VIs ) ha ve be e n de ve lope d

to e n ha n c e ve ge t a t i on s ignal s f r om r e m o te se ns ing m e a -


3/8

A Mo dified Soil Adjusted Vegetation Index 2

surements . The NDVI [Eq . (1 ) and Fig . l a ] i s a ra t io -

based VI whi le the PVI [Eq . (2 ) and Fig . lb ] i s a

r ep re s en t a t i v e o f t h e l i n ea r co mb i n a t i o n ca t eg o ry . T h e

PV I i s fu n c t i o n a ll y eq u i v a l en t t o t h e w e i g h t ed d i f f e r en ce

v eg e t a t i o n i n d ex (W D V I) ( see R i ch a rd s o n an d W i eg an d ,

1977; Clevers , 1988) s ince one i s read i ly der ived f rom

the o ther :

W D V I = p,,,,, - ~ffred, (4)

w h e re 7 i s t h e s l o p e o f t h e s o il l in e . T h es e t h r ee V I s

w e re d ev e l o p ed o n t h e b a s i s t h a t a ll v eg e t a t i o n i s o li n e s

( s ame v eg e t a t i o n d en s i t y w i t h d i f f e r en t s o i l b ack -

grounds) converge e i ther a t the o r ig in (Fig . l a ) o r a t

infini ty (Fig. lb) .

T h e co t t o n g ro u n d d a t a (F i g . 2 a ) s h o w t h e i s o l i n e s

t o h av e n o co mm o n co n v e rg i n g p o i n t . A s a f ir s t ap p ro x i-

ma t i o n , H u e t e (1 9 8 8 ) a s s u med t h a t t h e co n v e rg i n g p o i n t

w as a d i s t an ce

OE)

f ro m t h e o r i g i n , an d d ev e l o p ed t h e

SAVI [Eq . (3 ) and Fig . 1@ By add ing a cons ta n t so i l

ad ju s tm ent fac to r L = 11 + /2 , the SAVI m odel s the f i r st

o rd er o f so i l -ve geta t io n in terac t ions , and s ign i f i can tly

r ed u ces s o i l b ack g ro u n d e f f ec t s a c ro s s a w i d e r an g e o f

vegeta t ion cond i t ions (Huete , 1988 ; Qi e t a l . , 1993) . In

co n t r a s t t o o t h e r V I s , t h e SA V I i s o li n e s n e i t h e r co n v e rg e

a t t h e o r ig i n a s a s s u m ed b y t h e N D V I n o r a r e t h ey

p a ra l le l t o t h e s o il l i n e a s a s s u m ed b y th e PV I o r W D V I .

T h e (1 + L ) t e rm i n SA V I eq u a t i o n (3) is mean t t o r e s t o r e

t h e l o ss i n d y n ami c r an g e o f t h e SA V I r e s u l t in g f ro m

t h e ad d i t io n o f th e L f ac t o r t o t h e d e n o m i n a t o r a s w e l l

as to boun d th e SAVI wi th in the range o f 5 : 1 .

Ba re t e t a l . ( 1 9 8 9 ) an d Ba re t an d G u y o t ( 1 9 9 1 )

d ev e l o p e d a t r an s fo rm ed SA V I (T SA V I) b y t ak i n g i n to

account the so i l l i ne s lope 0 ' ) and in tercep t ( i ) :

T SA V I

=

Y(P~x, - yPr~d i)

? P ~,,, + P r . - - r i + X ( 1 + ~ ) ' ( 5 )

where X i s a fac to r (0 .08 in the i r case) ad jus ted so as

t o mi n i mi ze t h e s o i l b ack g ro u n d e f f ec t . T h e co n cep t o f

t h e T SA V I i s g r ap h i ca l l y p r e s en t ed i n F i g u re l d , w h e re

t h e co n v e rg en ce p o i n t i s c l o s e r t o t h e o r i g i n t h an t h a t

o f t h e S A VI . T h e i m p r o v e m e n t o f t h e T S A V I o v e r t h e

SAVI was to t ake th e so i l l i ne s lope (X) and in ter cep t

( i ) i n t o acco u n t , w h e rea s t h e SA V I a s s u med t h em t o b e

1 and 0 , respec t ive ly .

Ma j o r e t a l . ( 1 9 9 0 ) mo d e l ed t h e v eg e t a t i o n i s o l i n e

b eh av i o r b y u s i n g t h e r a t io b / a a s t h e s o il ad j u s t men t

f ac t o r, w i t h b a s t h e i n t e r c ep t an d a a s s lo p e o f e ach

i s ol in e . T h ey o b t a i n ed a s eco n d v e r s i o n o f t h e SA V I,

SAVI~:

SAVI~ PNIla

p,~a + b / a (6)

T h e SA V I2 d o es n o t h av e an em p i r i c a l ad j u s t me n t

f ac t o r f o r e ach i so l in e , b u t i t co n t a i n s t h e L A I p a r a m e t e r

in the a and b model ing . S ince the LAI i s usua l ly

t h e t a r g e t p a r a m e t e r b e i n g r e t r i e v e d i n r e m o t e s e n si n g

s tud ies , the SAV I2 wi l l no t b e d i sc ussed l a t e r in th i s

0.80

0.60

0 . 4 0

O

-

~ 0 . 2 0

11=

1 0 0 %

i n e

tl:tr .00y

Z o z o

-0.4 .00. -0 .30 -0 .20 -0 .10 0 .00 0 ,10

R e d R e f l e c ta n c e s

1 , 0

0 . 2 0 0 . 3 0 0 . 4 0

09

~

o 8

0

-.

c

0 0 .6

-$

O'I

0.4

0 . 2

0 0

b

, ~ , / . . ~ . f

- - - - - O k o . s o s

o -'- . - . ~ . . . . . . . Br ig h t o r d ry s oil s

I I 1 1 I

0 2 0 4 0 6 0 8 0 1 0 0

G r e e n C o v e r

Figure 2. a) Scatter plot of ground-based data in the red-

NIR space w ith regression (iso-) l ines, and b) demonstration

of dark or w et soi l effect on N DV I, SAVI, and WD VI.

a r t i c l e . T h e T SA V I w i l l n o t b e d i s cu s s ed fu r t h e r h e r e

e i ther s ince i t i s s imi lar to the SAVI.

Improvement of the S VI

Fi g u re 2 b d ep i c t s t h e r e l a t i v e d y n ami c r an g es an d s o i l

no i se in f luence s fo r the SAVI in re l a t ion to those o f the

N D V I a n d W D V I u s i n g t h e d a t a s e t p r e s e n t e d i n F ig u r e

2 a . Fo r mo s t o f t h e r an g e o f % g ree n v e g e t a t i o n co v e r s ,

t h e N D V I ap p ea r s mo re s en s i t i v e d u e t o i t s h i g h e r ,

n o n l in ea r , an d co n v ex r e s p o n s e . T h i s s ame r e s p o n s e

fu n c t i o n a l s o s a t u r a t e s t h e N D V I s i g n a l a t b ey o n d 8 0 %

g reen co v e r . T h e W D V I , o n t h e o t h e r h an d , h a s a

n o n l i n ea r, s l ig h t ly co n cav e r e s p o n s e t o g r een v eg e t a t i o n

co v e r , r en d e r i n g i t r e la t i v e ly i n s en s it i v e t o l o w am o u n t s

of vege ta t ion . B y con t ras t , t h e SAVI has a near - l inear

r e s p o n s e , b u t o v e ra l l l o w er s i g n a l t h an t h e N D V I

t h ro u g h o u t t h e r an g e o f g r een co v e r s . T h e h i g h e r v eg e -

t a t io n s ig n a l o f t h e N D V I , h o w ev e r , mu s t b e co mp a red

wi th i t s cor responding sens i t iv i ty to so i l - induced s ignal

variat ions.

In F i g u re 3 , t h e mean V I r e s p o n s e i s p l o t t ed a l o n g

w i t h t h e s o il n o i se , d e f i n ed h e r e a s t w i ce th e s t an d a rd

dev ia t ion ( tr ) o f VI var i a t ions d ue to d i f fe re nces in so il

b ack g ro u n d , u s i n g t h e g ro u n d -b as ed co t t o n d a t a . T h e

me an s an d s t an d a rd d ev i a t i o n s o f t h e s e V I s w e re ca l cu -


4/8

22 Q i et a l

1 . 0 5

a

0 . 9 0

o o /

o.so r - / \

0.40 l- . . / \ So i l N o is e

0.1 0 = ' ' '

0 2 0 4 0 6 0 8 0

0 . 2 0 1 . 0 5

t ~

X o . 8 0

0 .15 ~ O) O

o I ' - -

u )

- ~ 0 . 6 0

0 4

4 0

0.1 0 (1) - - -

2

N 0 4o

0 I1)

Z ~

0 . 0 5 ~

o ~

0.20

or)

0 . 0 0 0 . 0 0

1 0 0 0

0 . 2 0

b

W V I

2 0 4 0 6 0 8 0

0 . 1 5 E

._m

/)

0 4

0 . 1 0

.~_

o

Z

0.05 . '=--

0

c o

0 . ~

X 0 8 0

o

t -

0 , 6 0

t -

. o _

~ _ , O A O

II)

~ 0.20

0 . 0 5 ~ /

0

S A V I

_ .

0 . 2 0 4 0

0

o . 1 5 E

n - - 3 o

cr j

~ 0 )

. _

0 4 0

0.10 (1) Z 20

.on 0

0 .=-

z

0 .05 ~ t - 10

o

o )

o~ ~3

71.05 0

1 0 0 0

b 6 o

G r e e n C o v e r

| | t

2 0 4 0 6 0 8 0

G r e e n C o v e r

1 0 0

Figure 3 Dynamic ranges and soil noise levels of a) NDVI, b) WDVI, c) SAVI, and d) VI signal to noise ratios as a function

of percentage green cotton cover.

lated for each cotton density of different soil back-

grounds. The SAVI has a soil noise level of - 0.02-0.03,

while the WDVI has a noise level of 0.01-0.06 and the

NDVI, 0.01-0.18 throughout range of vegetation covers.

At 40% green cover, the noise level of the NDVI (0.18)

is nearly 10 times tha t of the SAVI (< 0.02) and four

times the WDVI (0.04) (Fig. 3). This corresponds to a

vegetation estimate uncertainty of + 23% green cover

for the NDVI, + 7% cover for the WDVI, and + 2.5%

for the SAVI.

In Figure 3d, the vegetation signal to soil noise

(S/N) ratio is computed for each index at each level of

vegetation cover, according to the formula:

S VI

where the bar over VI indicates the mean and tr is the

standard deviation of the VI values over different soil

backgrounds. This ratio should be a better indicator of

VI sensitivity than the simple dynamic range criteria.

The SAVI has S / N values four or five times higher than

the NDVI and WDVI values. The NDVI S / N becomes

very high beyond 75% green cover due to the saturat ed

VI signal, and has almost zero soil noise. The sensitivity

of the SAVI, as measured by the S / N ratio, is consider-

ably greater than can be obtained with the NDVI signal

under conditions of spatial and temporal (drying and

wetting) variations in the soil background.

In Figure 4, the potential errors (e%) of different

vegetation indices, as defined below, in the estimation

of vegetation amounts are compared:

e% = VI - VIo.100 (8)

VIo

where VIo was calculated with optimal L values obtained

by regression of each isoline of the ground cotton data

used in Figure 2. The NDVI consistently overestimated

(NDVI > VIo) while WDVI consistently underestimated

(WDVI < VIo) the vegetat ion amount. In contrast, the

SAVI only slightly overestimated the VIo at low vegeta-

tion cover and underestimated VIo at higher vegetation

covers. Therefore, the SAVI is a more representa tive

vegetation indicator than the other VIs.

Although the SAVI has higher S / N ratios than other

indices, it still has some limitations. As shown in Figure

4, there exist potential errors on the vegetation estima-

tions, especially at low and high vegetation covers. Also,

the use of a constant L of 0.5 results in a loss in the

vegetation dynamic responses, because the L of 0.5 is

usually much larger than red reflectances and, conse-


5/8

A MO dified Soil Adjus ted Veg etation.Index

23

I(XJ

5O ~ N D V I

Vlo

W O V l ' . . . . . . . . . . . . * . . . . . . . . . . - . . . . . . .

- 5 0 , . . . . . .

I I

- t 0 0 2 0 4 0

Green Cover

Figure 4.

Potential errors on the estimation of green cot-

ton co ver with the use o f different vegetation indices.

60 80 100

quen t ly , bu f fe rs re f l ec t ances var i a t ions . Op t imiza t ion o f

t h e L a d j u s t me n t f a c t o r , t h e r e f o r e , c o u l d o v e r c o me

t h e s e s h o r t c o mi n g s w h i l e f u r t h e r i n c r e a s i n g t h e v a l u e

of the SAVI.

L u n c t i o n s

T h e g r o u n d - b a s e d c o t t o n , p l o t t e d i n F i g u r e 2 a , s h o w e d

t h e v e g e t a t i o n i s o l i n e s c o n v e r g i n g a t v a r y i n g d i s t a n c e s

s o me w h e r e b e t w e e n t h e o r i g i n a n d i n f i n i t y , n o t a t a

c o m m o n p o i n t as i n d i c a te d i n F i g ur e s l c a n d l d . H i g h

v e g e t a t i o n i s o l in e s t e n d t o c o n v e r g e c l o s e t o t h e o r ig i n,

w h i l e l o w v e g e t a t i o n i s o l i n e s t e n d t o i n t e r s e c t w i t h t h e

so i l l i ne fu r the r a wa y f rom the o r ig in (F ig . 2a) . Thus ,

t h e o p t i ma l L f o r t h e s o i l a d j u s t me n t v a r i e s w i t h t h e

a m o u n t o f v e g e t a t i o n p r e s e n t . A t l o w v e g e t a t i o n

a mo u n t s , a l a r g e L v a l u e w o u l d b e s t d e s c r i b e s o i l -

v e g e t a t i o n i n t e r a c ti o n s w h i l e , w i t h i n c r e a s in g v e g e t a t i o n

a mo u n t s , L s h o u l d b e c o me s ma l l e r .

A n E m pi r i c a l L F unc t ion

T h e r e a r e m a n y f u n c t i o n s f o r L t h a t w o u l d s a t is f y t h e

a b o v e c r i t e r i a o f L d e c r e a s i n g w i t h i n c r e a s i n g v e g e t a t i v e

c o v e r. A s im p l e a p p r o a c h w o u l d b e t o u s e 1 - N D V I .

H o w e v e r , b e c a u s e N D V I i s i n f l u e n c e d b y s o i l b a c k -

g r o u n d s , e s p e c i a l l y b y t h e s o il b r i g h t n e s s, t h e L w o u l d

c o n t a i n s o i l n o i s e . I n F i g u r e 2 b , w e s e e t h a t b o t h t h e

N D V I a n d W D V I v a r y w i t h t h e s o i l b r i g h t n e ss , b u t i n

a n o p p o s i t e ma n n e r , t h a t i s, d a r k e r ( o r w e t ) b a c k g r o u n d s

r e s u l t i n h i g h e r N D V I v a l u e s , b u t l o w e r W D V I v a l u e s

t h a n b r i g h t e r ( o r d r y ) b a c k g r o u n d s f o r i d e n t ic a l a m o u n t s

o f vege ta t ion . To d ecr eas e the sens i t iv i ty to so i l no i se ,

o n e a p p r o a c h f o r a n L f u n c t i o n i s t o l e t t h e L f u n c t i o n

b e t h e p r o d u c t o f t h e N D V I a n d W D V I i n o r d e r t o

c a n c e l o r m i n i mi z e t h e s o il b r i g h t n e s s e f f e c t. Co n s e -

q u e n t l y , w e p r o p o s e t h e f o l lo w i n g s e l f -a d j u s t a b le L :

L = 1 - 2 y N D V I x W D V I , ( 9)

w h e r e y i s t h e p r i ma r y s o i l l i n e p a r a me t e r ( s e t t o b e

1 . 0 6 h e r e) , a n d t h e f a c t o r 2 i s t o i n c r e a s e t h e L d y n a m i c

range . The resu l t ing modi f i ed SAVI (MSAVI) would

t h e n b e

M S A V I I =

P N - P r ~ L ( I + L ),

(10)

PNm -F

red

-I-

w he re L i s g iven in Eq . (9 ), i n s t ead o f a cons tan t , an d

the su ff ix 1 i s use d to .d i s tingu i sh th i s vers ion o f the

MSA V I f r o m t h e i n d u c t i v e M SA V I th a t w i l l b e d i s c u s s e d

l a t er . T h e l o w e r b o u n d a r y o f t h is e m p i r i c a l L f u n c ti o n

[ E q . (9 ) ] g o e s t o n e g a t iv e w h e n t h e p r o d u c t o f t h e N D V I

a n d W D V I a p p r o a c h e s 0 . 5 , w h i c h r e q u i r e s a v a l u e o f

0 . 7 f o r b o t h N D V I a n d W D V I . Fo r a r i d a n d s e mi a r i d

r e g i o n s, n o n e o f t h e s e t w o i n d i c e s r e a c h e s 0 . 7 v a l u e

a n d , t h e r e f o r e , t h e e mp i r i c a l L f u n c t i o n u s u a l l y ra n g e s

f r o m 0 t o 1 . A t h i g h v e g e t a t i o n p e r c e n t a g e c o v e r , h o w -

e v e r , a s ma l l n e g a t iv e L v a l u e ma y b e p o s s i b l e , t h o u g h

n o t s e e n g r a p h i c a l l y i n F i g u r e 2 , b e c a u s e i n c r e a s i n g

v e g e t a t i o n d e n s i t y w o u l d r e s u l t i n a n i n c r e a s e i n t h e

N I R w h i l e t h e r e d r e ma i n s i n v a r i a n t . T h i s c o u l d r e s u l t

in an i so l ine tha t i s a lmos t para l l e l t o the NIR ax i s . As

a resu l t , t he i so l ine 'wi l l meet the so i l l i ne in the f i r s t

quar t e r , resu l t ing in a nega t ive L va lue .

A n I nduc t i v e L F unc t ion

T h e p r o p o s e d e mp i r i c a l L f u n c t i o n u t i l i z e d t h e a d v a n -

t a g es o f t h e o p p o s i t e tr e n d s o f N D V I a n d W D V I w i t h

the so i l background var i a t ions . However , t he so i l no i se

w a s n o t c o m p l e t e l y c a n c e l e d o u t b e c a u s e o f t h e d i f f e re n t

deg ree o f so i l e f fec t s as seen in F ig ure 2b . Also , due to

t h e n e g a t i v e l o w b o u n d a r y , t h e r e s u l t a n t MSA V I ma y

r e a c h a v a l u e g r e a t e r t h a n 1 , c o n s e q u e n t l y li m i t in g i t s

use fo r h igh vege ta t ion dens i ty su r faces . In th i s sec t ion ,

w e w i l l e mp l o y a n i n d u c t i o n me t h o d t o d e r i v e L o r

MSAVI, which wi l l be shown to be sa t i s fac to ry .

Us ing any see d va lue , L0 (0 - + oo), wo u ld m in imize

the soi l effects in MSAVI:

P ~ , . - P r d

(1 + L0). (11)

SAV I0 -- - - ,

P N m + P r e d + L o

D u e t o t h e u s e o f L0 , t h e MSA V I 0 w o u l d mi n i mi z e t h e

s o i l b a c k g r o u n d e f f e c t a n d c o u l d b e u s e d i n t h e s e a r c h

fo r an L func t ion to fu r ther min imize the so i l e f fec t .

N o w , s i n c e w e h a v e o b t a i n e d a n M SA V I0 t h a t m i n i mi z e s

the so i l e f fec t s , we cou ld ob ta in ano ther L func t ion LI :

L1 - 1 - MSA VI0, (12)

w h i c h w o u l d r e s u l t i n a n MSA V I 1 t h a t f u r t h e r m i n i mi z e s

the soi l effect :

MS AVI1 = PN,,

--

Pred

PNm pred

+ 1 -- MSAVIo 2 MSAVIo). (13)

Co n t i n u i n g t h i s p r o c e s s n t i me s , w e o b t a i n

L, = 1 - M SAV I,_ 1, (14)


6/8

1 2 4 Q i e t a l.

and

MSAVT, = PNIR - Pred

pN,. + Pred + 1 - MSAVI._ x 2

MSAVI,

1 .

(15)

With this processing, there exists an iteration time N

such that MSAVIN= MSAVIN_I, where soil effects can-

not be minimized further. Then we have

MSAVI~

= pN , . P r ed 2

MSAVI~).

PN,, + Prea + 1 - MSAVIN

(16)

One of the two solutions for Eq. (16) within the range

of 0 and 1 is

- b - b ~ ~ - 4c

MSAVI,, = , (17)

2

where b =

-

(2pNm + 1) and c

= 2 P N I R P r e d ) .

Therefore,

with an inductive L function of

L = 1 - MSAVI2, (18)

the resultant MSAVI by induction, MSAVI2, becomes

2 p , , ,, , + 1 - 4 ( 2 p . . , + 1 ) 2 - 8 ( p m R Pred)

MSAVI2 = (19)

2

RESULTS

In relation to the SAVI (L = 0.5), the dynamic range of

the MSAVI1 was increased (Fig. 5a) for the ground-based

cotton data. Soil noise influences are also reduced and

the VI response to percentage green cover becomes

more linear. The vegetation estimate uncertainty is re-

duced from +2.5% (SAVI) to +1.6 % (MSAVI1). In

Figure 5b, the vegetation signal to soil noise ratio is

plot ted for the SAVI and MSAVIs as a function of %

green cover. The variable L function improved vegeta-

tion sensitivity, particularly at high vegetation densities.

However, at 60 % green cover and above, the S / N ratio

(Fig. 5b) of the MSAVI1 dropped below that of the

SAVI.

The results of the MSAVI2 by induction were com-

pared wi th the previous MSAVI1 and the original SAVI

in Figure 5. The dynamic range was also increased (Fig.

5a) while the soil noise was kept minimal, resulting in

a higher S/ N ratio over the SAVI and slightly lower

ratios over the MSAVI1 at low vegetation cover and

slightly higher S/N ratios at high vegetation density.

Overall, the MSAVIx and MSAVI2 were similar in many

ways in sensitivity to vegetation and normalization of

the soil noise. As a result, the MSAVI may be derived

as in Eq. (10) or (19).

To further examine its vegetation dynamic re-

sponses and soil background variations, the MSAVI was

applied to the aircraft cotton data set. In Figure 6, we

can see the dramatic impact of wetting the soil surface

in raising the NDVI values as well as the effect of the

1 . 0 0

0 . 8 0

x

ID

- - 0 . 6 0

0 . 4 0

>

0 . 2 0

SAVI - -N- Noise a

MS VIt

- -4 - - N o i u l

0 . 0 0 I ~ I

0

9 0

0 . 2 0

0 . 1 5

E

._~

0 - 1 0 ~

q

.cn

O

o . o s Z

0

6O

0 . 0 0

2 0 4 0 6 0 8 0 1 0 0

- - = - S A V= b

80 - ' O ' - - M S A V I1

~

MSAV~2

I ~ 6 0

.~_

0 50

z

~ 40

t~

e-- 30

._~

f ,D 20

10

I I I I

0 2 0 4 0 6 0 8 0 1 0 0

G r e e n C o v e r

Figure 5 . a) Dynamic ranges and soil noise levels and b) sig-

nal to noise ratios of the original SAVI and MSAVI.

brighter sandy loam substrate in decreasing the NDVI

response. In contrast, the SAVI showed a very slight

sensitivity to soil background influences while the

MSAVI and WDVI nearly eliminated these influences

completely. Over sparse or incomplete canopy covers,

the NDVI produces higher VI values than the other

indices. This is an artifact of the nonlinear convex

response pattern of the NDVI to green cover. When

ratioed by the amount of soil noise, this apparent

sensitivity disappears as the S / N becomes the lowest of

all the indices (Fig. 3d). The MSAVI is similar to the

WDVI on soil noise reduction because the WDVI is

actually MSAVI when the L approaches infinity. The L

in MSAVI approaches the maximum value of 1 only;

therefore, MSAVI resulted in higher VI values than

WDVI.

The vegetation dynamic ranges of these indices to

the cotton cover over the entire growing season are

shown in Figure 7 and summarized in Table 1 along

with the ground-based cotton experiment results. The

MSAVI had the highest dynamic ranges of 0.87' and

0.94, respectively (Table 1) for the two data sets, and

is almost linearly related to the cotton percentage cover,

while the SAVI had dynamic ranges of 0.71 and 0.69,

respectively. Therefore, the dynamic range of the

MSAVI was increased by 15% and 30% compared with


7/8

A M od i f i e d So i l Ad j us t e d Ve ge t a t i on I nde x

25

0 . 2 0

0 . 1 5

~ 0 . 1 0

D

1)

> 0 0 5

0 . 00

Ma r ic o p a A i rc ra f t D a ta

_

MSAV I

m D w ~ m m -

D r y S a n d y

D r o a C ~ Y ~ . I L o a m I q l . _ _ _ D r y C l a y

r - - i - - i a m

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0

w i w

S p a t ia l T r a n s e c t W e s t - E a s t ) m )

WDV I

W e t C l a y

L o a m

I I

1 2 0 0 1 4 0 0

Figure 6 . Dem ons t ra t ion of so il backgroun d in f luences on the MSAVI, SAVI , WD VI, and NDVI us ing MAC a i rc ra f t dat a.

t h e S A V I f o r t h e t w o d a t a s e t s. T h e M S A V I r e a c h e d

a l m o s t t h e m a x i m u m v a l u e o f 1 f o r th e M A C a i rc r a ft

d a ta , w h i l e N D V I , S A V I, an d W D V I r e a c h e d o n l y 0 .9 ,

0 . 7 8 , a n d 0 . 6 2 , r e s p e c t i v e l y . O n c e a g a i n , i n F i g u r e 7 ,

o n e c a n s e e a n a p p a r e n t g r e a t e r se n s i ti v i ty o f t h e

N D V I t o g r e e n v e g e t a t i o n , s i m i l a r t o t h a t e n c o u n t e r e d

i n F ig . 2 b . T h e s a t u r at i o n o f t h e N D V I a t h i g h e r a m o u n t s

o f v e g e t a t i o n i s a l so e v i d e n t a t d a y o f y e a r ( D O Y ) 2 0 0 ,

w h e r e a s a l l o t h e r i n d i c e s c o n t i n u e t o r i s e f o r a t l e a s t

t w o m o r e w e e k s . T h i s w a s a l s o e v i d e n t i n F i g u r e 2 b .

D I S C U S S I O N A N D C O N C L U S I O N S

I n c o n c l u s i o n , t h e a i r c r a f t a n d g r o u n d - b a s e d d a t a s e t s

c o l l e c t e d o v e r c o t t o n s h o w e d a g r e a t e r d y n a m i c r a n g e

Table 1 . Dyn amic Ranges o f Vege tat ion Indices Using

Two Cot ton Da ta Se t s

H ue t e e t a l . 1 9 8 5 ) M A C 1 9 8 9 )

C o t to n D a t a A i r c r a f t D a t a

VI s M i n M ax 6 M i n M ax 6

NDVI 0.13 0.89 0.76 0.10 0.90 0.80

SAVI 0.06 0.75 0.69 0.07 0.78 0.71

WDV I 0.03 0.63 0.60 0.03 0.62 0.59

MSAVI 0.05 0.92 0.87 0.06 0.99 0.94

ad~ = max

-

min.

r e s p o n s e b y t h e M S A V I a s w e l l as a l o w e r e d s e n s i ti v i ty

t o t h e s o il b a c k g r o u n d s p a ti a l a n d t e m p o r a l v a r ia t io n s .

B y r a i si n g t h e v e g e t a t i o n s i g na l a n d s i m u l t a n e o u s l y l o w -

e r i n g s o i l - i n d u c e d v a r i a ti o n s , t h e M S A V I c a n b e s a id t o

b e a m o r e s e n si ti v e i n d ic a t o r o f v e g e t a t io n a m o u n t o v e r

t h a t o f S A V I a s w e l l a s o t h e r i n d i c e s p r e s e n t e d h e r e .

B o t h t h e d y n a m i c r a n g e a n d n o i s e r e l a t e d e ff e c t s a r e

i m p o r t a n t t o c o n s i d e r i n t h e e v a l u a t i o n a n d i m p r o v e -

Figure 7 .

Tem pora l dynam ic re sponses of the MSAVI,

SAVI , WD VI, and NDVI to co t ton growth us ing MAC a i r-

craft data.

1 . 0 0

0 . 8 0

~ c O . 6 0

. ~ 0 .4 0

0 . o 0

5 0

\ M S A V I

/ \

N D V I

/ . . . . . =

/ , ' , . W D V I

, 7 ,

,i'~

] I I I

1 G o 1 5 0 2 o 0 2 5 0 3 o 0

D a y o f Y e a r . 1 9 8 9

3 5 0


8/8

1 2 6 Q i e t a l

ment of vegetation indices, particularly for large scale

and global) studies that encompass considerable soil

spatial and temporal variations unrelated to the vegeta-

tion signal.

The MSAVI is a modified version of the SAVI, which

replaces the constant soil adjustment factor, L, with a

self-adjusting L. Although the L factor does not appear

in the second version of the MSAVI, an iterative L

function was used in the derivation of the MSAVI2.

Consequently, both MSAVI and SAVI use soil-adjust-

ment factors. The dif ference is that SAVI uses a manual-

adjustment L, while the MSAVI uses a self-adjustment L.

The former requires a prior knowledge about vegetation

densities in order to use an optimal L value in SAVI

equation, while the latter automatically adjusts its L

values to optimal.

The signal to noise ratio was higher for the MSAVI

than that o f other vegetation indices including the

original version of SAVI). This suggests that the use of

the L functions not only increased the vegetation dy-

namic responses, but also further reduced the soil back-

ground variations. At higher vegetation covers, L ap-

proaches 0, and the MSAVI behaved like the NDVI,

while at low vegetation covers, the L approaches 1, and

the MSAVI behaved like PVI or WDVI. For intermedi-

ate vegetation cover, the MSAVI is similar to the SAVI.

The use of the product of NDVI and WDVI in the

empirical L expression may not be the best function

and may not work well for other canopy types. At low

vegetation covers, the WDVI is less affected by soil

background, while the NDVI is strongly affected. The

product in the L function may, therefore, inherit more

soil noise than if WDVI were used alone. At high

vegetation cover, the use of NDVI alone may be better,

since the NDVI is much less affected than the WDVI

at high vegetation density. However, the inherited noise

in L ff not canceled out by the product) would become

secondary when used as an adjustment factor in the

MSAVI. L may also be derived by induction that works

quite well over a wide range of vegetation types and

conditions.

The inductive L has boundary conditions of 0 and

1 and the resulting MSAVI is only a function of the

reflectances. The dynamic range of the inductive MSAVI

was slightly lower than that of the empirical L function

due to the difference in the L boundary conditions.

However, both versions of the MSAVI proved to be sat-

isfactory with respect to the vegetation sensitivity and

soil noise reduction.

Finally, the MSAVI was validated using ground and

aircraft-based radiometric measurements only. It needs

to be validated further with other remote sensing data,

particularly with satellite data. In addition, only soil

background effects were examined here. The sensitivi-

ties to other external factors such as sensor viewing

angles, atmospheric conditions, and solar illumination

conditions ought to be tested thoroughly in order to

evaluate the MSAVI on vegetation monitoring. Furthe r

work will be needed to ensure these effects are ac-

counted for when interpreting the results of the MSAVI.

This work w as completed in the ram e work o f an EOS interdisci-

plinary investigation. It was a join t effort of the exchange studen t

programs o f the EOS-Hydrology project. On e author ]. Q.)

was fun de d b y NA SA Project NAW G-194 9, Eos-NAWC ,-2425,

MO DIS Contract NAS5-31364, a nd LERTS, and another A. C.)

was fun ded by L ERT S and the Univers ity o f Ar izona Hydrology

an d W ater Resources Department. The authors greatly appreci-

ated Dr. Ra y Jackson fo r his encouragement an d advice and

Dr. M . S. Moran fo r h er advice and com ments. J. Q. was grateful

to LERTS and the Soi l and Water Science Department of the

University o f Arizona for the wo rking environments.

R E F E R E N E S

Asrar, G., Fuchs, M., Kanemasu, E. T., and Hatfield, J. L.

1984), Estimating absorbed photosynthetic radiation and

leaf area index from spectral reflectance in wheat, Agron.

J. 76:300-306.

Baret, F., and Guyot, G. 1991), Potentials and limits of vegeta-

tion indices for LAI and APAR assessment, Remote Sens .

Environ.

35:161-173.

Baret, F., Guyot, G., and Major, D. 1989), TSAVI: A vegeta-

tion index which minimizes soil brightness effects on LAI or

APAR estimation, in 12th Canadian Symposium on Remote

Sensing and IGARSSX30, Vancouver, Canada, 10-14 July.

Clevers, J. G. P. W. 1988), The derivation of a simplified

reflectance model for the estimation of leaf area index,

Remote Sens. Environ.

25:53-70.

Huete, A. R. 1988), A soil-adjusted vegetation index SAVI),

Remote Sens. Environ. 25:295-309.

Huete, A. R. 1989), Soil influences in remotely sensed vegeta-

tion-canopy spectra, in Theory an d Applications o f Optical

Remote Sensing G. Asrar, Ed.), pp 107-141.

Huete, A. R., Jackson, R. D., and Post, D. F. 1985), Spectral

response of a plant canopy with different soil backgrounds,


17:37-53.

Jackson, R. D., and Huete, A. R. 1991), Interpreting vegeta-

tion indices, J. Preventative Vet. Med. 11:185-200.

Major, D. J., Baret, F., and Guyot, G. 1990), A ratio vegetation

index adjusted for soil brightness, Int. J. Remote Sens. 11 5):

727-740.

Qi, J., Huete, A. R., Moran, M. S., Chehbouni, A., and Jackson,

R. D. 1993), Interpretation of vegetation indices derived

from multi-temporal SPOT images,


44:89-101.

Richardson, A. J., and Wiegand, C. L. 1977), Distinguishing

vegetation from soil background information,Photogramm.

Eng. Remote Sens . 43:1541-1552.

Wiegand, C. L., Richardson, A. J., Escobar, D. E., and Gerber-

mann, A. H. 1991), Vegetation indices in crop assessments,

Remote Sens. Environ. 35:105-119.

Documents

A Modified Soil Adjusted Vegetation Index