A FAQ on Vegetation in Remote Sensing



Written by Terrill W. Ray
	   Div. of Geological and Planetary Sciences
	   California Institute of Technology

email: terrill@mars1.gps.caltech.edu

Snail Mail:  Terrill Ray
	     Division of Geological and Planetary Sciences
	     Caltech
	     Mail Code 170-25
	     Pasadena, CA  91125

THIS FAQ AVAILABLE VIA ANONYMOUS FTP AT:

     kepler.gps.caltech.edu  -  /pub/terrill/rsvegfaq.txt

Version 1.0:  10/13/1994

Acknowledgements:  Thanks to the following people for comments and 
		   suggestions (listed in no particular order)

		   A. Chehbouni - ORSTOM
		   Martin Hugh-Jones - Louisiana State University
		   Kjeld Rasmussen - 
                   Mike Stevens - University of Nottingham

Printed and electronic publications may reprint this FAQ in whole 
or in part, at no charge, if they give due credit to the author.  
It is requested that the author be informed of any publication, 
and that a copy of the publication be sent to the FAQ author.  
[No, I do not expect you to send me a copy of a book retailing 
for $70, but if you are feeling generous...]
		   
Revision History:
Version 1.0 - major revision.  Discussion of radiance vs. reflectance
	      added.  Addition of vegetation indices designed to
	      minimize atmospheric noise (GEMI, ARVI, etc.).  Addition
	      of SPOT HRV bands.  Numerous minor changes.  Cautions
	      regarding the use of SAVI, MSAVI, etc. added.
Version 0.7 - numerous minor non-substantive typos fixed. Addition
	      of question 14a.  Some stylistic and grammatical
	      problems dealt with.
Version 0.6 - major typo in TSAVI equation fixed and minor typo
	      in MSAVI2 fixed.
Version 0.5 - original version posted

Conventions:
     In most cases, reflectance, apparent reflectance and 
	  radiance can be used interchangeably in this FAQ. 
	  (But see question #5 for some important considerations 
	  about this.)
     Wavelengths are given in nanometers (nm).
     The "origin" is the point of zero red reflectance and zero 
	  near-infrared reflectance.
     The abbreviation SPOT refers to the Systeme Pour
	  l'Observation de la Terre which has five bands of
	  interest (the bandpasses may not be precisely correct
	  since the document I am looking at lists the "proposed"
	  bands)
	  SPOT1 covers 430-470 nm
	  SPOT2 covers 500-590 nm
	  SPOT3 covers 610-680 nm
	  SPOT4 covers 790-890 nm
	  SPOT5 covers 1580-1750 nm
     The abbreviation AVHRR refers to the Advanced Very High   
	  Resolution Radiometer which has two bands of    
	  interest:
	  AVHRR1 covers 550-700 nm
	  AVHRR2 covers 700-1000 nm
     The abbreviation TM refers to the Landsat Thematic 
	  Mapper which has six bands of interest:
	  TM1 covers 450-520 nm
	  TM2 covers 520-600 nm 
	  TM3 covers 630-690 nm
	  TM4 covers 760-900 nm
	  TM5 covers 1550-1750 nm
	  TM7 covers 2080-2350 nm
     The abbreviation MSS refers to the Landsat 
	  MultiSpectral Scanner.
     MSS bands are referred to by the old system:
	  MSS4 covers 500-600 nm
	  MSS5 covers 600-700 nm
	  MSS6 covers 700-800 nm
	  MSS7 covers 800-1100 nm
     NIR is used to indicate a band covering all or part of 
	  the near-infrared portion of the spectrum (800-     
	  1100 nm or a subset of these wavelengths).  
	  Examples:  MSS7, TM4, AVHRR2
     R is used to indicate a band covering all or part of 
	  the portion of the visible spectrum perceived as      
	  red by the human eye (600-700 nm).  Examples MSS5, 
	  TM3, AVHRR1


Questions:
GENERAL
1)  What are the important spectral characteristics of vegetation 
that I should know about?
2)  I have some remote sensing data, what bands will show vegetation 
best?
     2a) TM data
     2b) MSS data
3)  I want to use band ratioing to eliminate albedo effects and 
shadows.  What band ratios are best?
     3a) TM data
     3b) MSS data
4)  Why is vegetation usually shown in red by remote sensing people?
5)  What is the difference between radiance and reflectance?
VEGETATION INDEX
6)  What the &*(^ is a vegetation index?
7)  What are the basic assumptions made by the vegetation indices?
8)  What is the soil line and how do I find it?
BASIC INDICES
9)  What is RVI?
10)  What is NDVI?
11)  What is IPVI?
12)  What is DVI?
13)  What is PVI?
14)  What is WDVI?
INDICES TO MINIMIZE SOIL NOISE
15)  What is Soil Noise?
16)  What is SAVI?
16a) Why is there a (1+L) term in SAVI?
17)  What is TSAVI?
18)  What is MSAVI?
19)  What is MSAVI2?
INDICES TO MINIMIZE ATMOSPHERIC NOISE
20)  What is Atmospheric Noise?
21)  What is GEMI?
22)  What are the atmospherically resistant indices?
OTHER INDICES
23)  What is GVI?
24)  Are there vegetation indices using other algebraic functions of 
the bands?
25)  Are there vegetation indices that use bands other than the red 
and NIR bands?
26)  Plants are green, why isn't the green chlorophyll feature used 
directly?
27)  How well do these vegetation indices work in areas with low 
vegetation cover?
28)  What the ^&*(*&^ is "non-linear" mixing?
29)  Is the variation in the soil the only problem?
30)  What if I can't get a good soil line from my data?
31)  How low a plant cover is too low for these indices?
32)  I hear about people using spectral unmixing to look at 
vegetation, how does this work?
33)  Are there any indices which use high spectral resolution data?
34)  What vegetation index should I use?
References

GENERAL

1)  What are the important spectral characteristics of vegetation 
that I should know about?
A:  The cells in plant leaves are very effective scatterers of light 
because of the high contrast in the index of refraction between the 
water-rich cell contents and the intercellular air spaces.  
Vegetation is very dark in the visible (400-700 nm) because of the 
high absorption of pigments which occur in leaves (chlorophyll, 
protochlorophyll, xanthophyll, etc.).  There is a slight increase in 
reflectivity around 550 nm (visible green) because the pigments are 
least absorptive there.  In the spectral range 700-1300 nm plants 
are very bright because this is a spectral no-man's land between the 
electronic transitions which provide absorption in the visible and 
molecular vibrations which absorb in longer wavelengths.  There is 
no strong absorption in this spectral range, but the plant scatters 
strongly as mentioned above.
     From 1300 nm to about 2500 nm vegetation is relatively dark, 
primarily because of the absorption by leaf water.  Cellulose, 
lignin, and other plant materials also absorb in this spectral 
range.
SUMMARY:  400-700 nm = dark
	  700-1300 nm = bright
	  1300-2500 nm = dark (but brighter than 400-700 nm)

2)  I have some remote sensing data, what bands will show vegetation 
best?
A:  Basically a band covering part of the region from 700-1300 nm if 
you want the vegetation to be bright.  (Using a band covering part 
of 400-700 nm would make vegetation dark, but this isn't the way we 
generally do things.)
2A)  For TM data, either TM4 or TM5
2B)  For MSS data, either MSS6 or MSS7 (MSS7 is usually better since 
it avoids the transition near 700 nm).

3)  I want to use band ratioing to eliminate albedo effects and 
shadows.  What band ratios are best?
A:  If you want the vegetation to turn out bright (which is usually 
the most sensible approach) ratio a band covering part of the range 
700-1300 nm with a band covering either 400-700 nm or 1300-2500 nm.  
Ratioing a near-infrared band to a visible band is the traditional 
approach.  Usually a visible band covering 650 nm is preferred since 
this is near the darkest part of the vegetation spectrum usually 
covered by remote sensing instruments.  Basically you want a band 
where vegetation is bright on the top of the ratio, and a band where 
vegetation is dark on the bottom.
     Although vegetation is more highly reflective in green than in red, 
early work showed that near-infrared-red combinations were 
preferable to green-red combinations (Tucker, 1979).
3A)  TM:  The traditional ratio is TM4/TM3
	  TM5/TM7 is also good, but many clays will also be 
	       fairly bright with this combination.
	  I see no immediate reason why TM5/TM3 or TM4/TM7    
	       wouldn't work, but they usually aren't used.
3B)  MSS:  The traditional ratio is MSS7/MSS5
	   MSS6/MSS5 is also used.

4)  Why is vegetation usually shown in red by remote sensing people?
A:  This is one of the apparently silly things done in remote 
sensing.  There are three reasons for it:
The first (and rather pointless) reason is TRADITION.  People in 
remote sensing have been doing this a long time and virtually 
everyone who has spent much time working with remote sensing will 
instinctively interpret red splotches as vegetation.  Bob Crippen 
(not the astronaut) at JPL said that he spent some time trying to 
break this tradition by showing vegetation in green, but he was 
ultimately beaten into submission.  (Consider it this way:  you are 
a remote sensing professional, you usually give talks to remote 
sensing professionals.  They expect vegetation in red so you don't 
have to add an explanation that "vegetation is shown as green."  
This simplifies your life.)
     The second reason is the fact that the human eye perceives the 
longest visible wavelengths to be red and the shortest visible 
wavelengths to be blue.  This is an incentive for remote sensing 
images to be set up so that the shortest wavelength is shown as blue 
and the longest one is shown as red.  Usually a near-infrared band 
is the longest wavelength being displayed (this is especially true 
for MSS and aerial color infrared photography).  Since vegetation is 
brightest in the near-infrared, vegetation turns out red.  Using red for
vegetation in digital data makes the digital data color scheme 
similar to that for color infrared film.  This can make it easier for
a person familiar with color infrared film pictures to adjust to the
interpretation of digital remote sensing data.
     The third (and only sensible) reason is to remind the audience that 
they are not seeing real colors.  If vegetation is shown as green, 
the audience is more likely to subconsciously think that the image 
is true color, while if vegetation is red they will immediately 
realize that the image is false color.

5)  What is the difference between radiance and reflectance?
A:  Radiance is the variable directly measured by remote sensing 
instruments.  Basically, you can think of radiance as how much light
the instrument "sees" from the object being observed.  When looking
through an atmosphere, some light scattered by the atmosphere will 
be seen by the instrument and included in the observed radiance of
the target.  An atmosphere will also absorb light, which will decrease
the observed radiance.  Radiance has units of watt/steradian/square meter.
    Reflectance is the ratio of the amount of light leaving a target 
to the amount of light striking the target.  It has no units.  If all of 
the light leaving the target is intercepted for the measurement of 
reflectance, the result is called "hemispherical reflectance."
    Reflectance (or more specifically hemispherical reflectance) is a
property of the material being observed.  Radiance, on the other hand,
depends on the illumination (both its intensity and direction), the
orientation and position of the target and the path of the light 
through the atmophere.  With effort, many of the atmospheric effects 
and the solar illumination can be compensated for in digital remote 
sensing data.  This yields something which is called "apparent
reflectance," and it differs from true reflectance in that shadows
and directional effects on reflectance have not been dealt with.  Many
people refer to this (rather inaccurately) as "reflectance."
    For most of the vegetation indices in this FAQ, radiance, 
reflectance, and apparent reflectance can be used interchangibly.
However, since reflectance is a property of the target material 
itself, you will get the most reliable (and repeatable) vegetation
index values using reflectance.  Apparent reflectance is adequate in
many cases.


VEGETATION INDEX

6)  What the &*(^ is a vegetation index?
A:  A vegetation index is a number that is generated by some 
combination of remote sensing bands and may have some relationship 
to the amount of vegetation in a given image pixel.  If that sounds 
sarcastic or even insulting, it's meant to.  Jim Westphal at Caltech 
pointed out to me one day that vegetation indices seemed to be more 
numerology than science.  This may be an overly harsh assessment, 
since there is some basis for vegetation indices in terms of the 
features of the vegetation spectrum discussed above; however, the 
literature indicates that these vegetation indices are generally 
based on empirical evidence and not basic biology, chemistry or 
physics.  This should be kept in mind as you use these indices.

7)  What are the basic assumptions made by the vegetation indices?
A:  The most basic assumption made is assuming that some algebraic 
combination of remotely-sensed spectral bands can tell you something 
useful about vegetation.  There is fairly good empirical evidence 
that they can.
	A second assumption is the idea that all bare soil in an image 
will form a line in spectral space.  This is related to the concept 
of the soil line discussed in question number 7.  Nearly all of the 
commonly used vegetation indices are only concerned with red-near-
infrared space, so a red-near-infrared line for bare soil is 
assumed.  This line is considered to be the line of zero vegetation.
	At this point, there are two divergent lines of thinking about 
the orientation of lines of equal vegetation (isovegetation lines):
	1) All isovegetation lines converge at a single point.  The 
indices that use this assumption are the "ratio-based" indices, 
which measure the slope of the line between the point of convergence 
and the red-NIR point of the pixel.  Some examples are:  NDVI, SAVI, 
and RVI
	2) All isovegetation lines remain parallel to soil line.  
These indices are typically called "perpendicular" indices and 
they measure the perpendicular distance from the soil line to the 
red-NIR point of the pixel.  Examples are:  PVI, WDVI, and DVI.

8)  What is the soil line and how do I find it?
A)  The soil line is a hypothetical line in spectral space that 
describes the variation in the spectrum of bare soil in the image.  
The line can be found by locating two or more patches of bare soil 
in the image having different reflectivities and finding the best 
fit line in spectral space.  Kauth and Thomas (1976) described the 
famous "triangular, cap shaped region with a tassel" in red-NIR 
space using MSS data.  They found that the point of the cap (which 
lies at low red reflectance and high NIR reflectance) represented 
regions of high vegetation and that the flat side of the cap 
directly opposite the point represented bare soil.
	THE SIMPLE WAY OF FINDING THE RED-NIR SOIL LINE:  Make a 
scatterplot of the red and NIR values for the pixels in the image.  
I recommend putting red on the x-axis and NIR on the y-axis (the 
rest of the instructions assume this).  There should be a fairly 
linear boundary along the lower right side of the scatterplot.  The 
straight line that best matches this boundary is your soil line.  
You can either select the points that describe the boundary and do a 
least squares fit, or you can simply made a hardcopy and draw in the 
line that looks like the best fit.  (You have to make a lot of 
judgment calls either way.)

9)  What is RVI?
A)  RVI is the ratio vegetation index which was first described by 
Jordan (1969).  This is the most widely calculated vegetation index, 
although you rarely hear of it as a vegetation index.  A common 
practice in remote sensing is the use of band ratios to eliminate 
various albedo effects.  Many people use the ratio of NIR to red as 
the vegetation component of the scene, and this is in fact the RVI.  
SUMMARY:  ratio-based index
	  isovegetation lines converge at origin
	  soil line has slope of 1 and passes through origin.
	  range 0 to infinity
CALCULATING RVI:  
			 NIR
		  RVI = -------
			 red

10)  What is NDVI?
A)  NDVI is the Normalized Difference Vegetation Index which is 
ascribed to Rouse et al. (1973), but the concept of a normalized 
difference index was first presented by Kriegler et al. (1969).  
When people say vegetation index, this is the one that they are 
usually referring to.  This index has the advantage of varying 
between -1 and 1, while the RVI ranges from 0 to infinity.  RVI
and NDVI are functionally equivalent and related to each other
by the following equation:
			      RVI-1
		     NDVI = ---------
			      RVI+1

SUMMARY:  ratio-based index
	  isovegetation lines converge at origin
	  soil line has slope of 1 and passes through origin
	  range -1 to +1
CALCULATING THE NDVI:
			      NIR-red
		      NDVI = ---------
			      NIR+red

11)  What is IPVI?
A)  IPVI is the Infrared Percentage Vegetation Index which was first 
described by Crippen (1990).  Crippen found that the subtraction of 
the red in the numerator was irrelevant, and proposed this index as 
a way of improving calculation speed.  It also is restricted to 
values between 0 and 1, which eliminates the need for storing a sign 
for the vegetation index values, and it eliminates the conceptual 
strangeness of negative values for vegetation indices.  IPVI and NDVI
are functionally equivalent and related to each other by the following
equation:
			       NDVI+1
		      IPVI = ----------
				 2  
SUMMARY:  ratio-based index
	  isovegetation lines converge at origin
	  soil line has a slope of 1 and passes through origin
	  range 0 to +1
CALCULATING IPVI:
			    NIR
		   IPVI = --------
			  NIR+red

12)  What is DVI?
A)  DVI is the Difference Vegetation Index, which is ascribed in 
some recent papers to Richardson and Everitt (1992), but appears as 
VI (vegetation index) in Lillesand and Kiefer (1987).  [Lillesand 
and Kiefer refer to its common use, so it was certainly introduced 
earlier, but they do not give a specific reference.]  
SUMMARY:  perpendicular index
	  isovegetation lines parallel to soil line
	  soil line has arbitrary slope and passes through origin
	  range infinite.
CALCULATING DVI:
		  DVI=NIR-red

13)  What is PVI?
A)  PVI is the Perpendicular Vegetation Index which was first 
described by Richardson and Wiegand (1977).  This could be 
considered a generalization of the DVI which allows for soil lines 
of different slopes.  PVI is quite sensitive to atmospheric variations,
(Qi et al., 1994) so comparing PVI values for data taken at different 
dates is hazardous unless an atmospheric correction is performed on the
data.
SUMMARY:  perpendicular index
	  isovegetation lines are parallel to soil line
	  soil line has arbitrary slope and passes through origin
	  range -1 to +1
CALCULATING PVI:
		   PVI = sin(a)NIR-cos(a)red

  a is the angle between the soil line and the NIR axis.

14)  What is WDVI?
A)  WDVI is the Weighted Difference Vegetation Index which was 
introduced by Clevers (1988).  This has a relationship to PVI similar to 
the relationship IPVI has to NDVI.  WDVI is a mathematically simpler 
version of PVI, but it has an unrestricted range.  Like PVI, WDVI is
very sensitive to atmospheric variations (Qi et al., 1994).
SUMMARY:  perpendicular index
	  isovegetation lines parallel to soil line
	  soil line has arbitrary slope and passes through origin
	  range infinite
CALCULATING WDVI:
		   WDVI = NIR-g*red

    g is the slope of the soil line.

INDICES TO MINIMIZE SOIL NOISE

15)  What is Soil Noise?
A)   Not all soils are alike.  Different soils have different 
reflectance spectra.  As discussed above, all of the vegetation
indices assume that there is a soil line, where there is a single
slope in red-NIR space.  However, it is often the case that there
are soils with different red-NIR slopes in a single image.  Also,
if the assumption about the isovegetation lines (parallel or 
intercepting at the origin) is not exactly right, changes in soil
moisture (which move along isovegetation lines) will give incorrect
answers for the vegetation index.  The problem of soil noise is most
acute when vegetation cover is low.
     The following group of indices attempt to reduce soil noise
by altering the behavior of the isovegetation lines.  All of them are
ratio-based, and the way that they attempt to reduce soil noise is
by shifting the place where the isovegetation lines meet.
     WARNING:  These indices reduce soil noise at the cost of 
decreasing the dynamic range of the index.  These indices are slightly
less sensitive to changes in vegetation cover than NDVI (but more
sensitive than PVI) at low levels of vegetation cover.  These indices
are also more sensitive to atmospheric variations than NDVI (but less
so than PVI). (See Qi et al. (1994) for comparisons.)
    
16)  What is SAVI?
A)   SAVI is the Soil Adjusted Vegetation Index which was introduced 
by Huete (1988).  This index attempts to be a hybrid between the 
ratio-based indices and the perpendicular indices.  The reasoning 
behind this index acknowledges that the isovegetation lines are not 
parallel, and that they do not all converge at a single point.  The 
initial construction of this index was based on measurements of 
cotton and range grass canopies with dark and light soil 
backgrounds, and the adjustment factor L was found by trial and 
error until a factor that gave equal vegetation index results for 
the dark and light soils was found.  The result is a ratio-based 
index where the point of convergence is not the origin.  The 
convergence point ends up being in the quadrant of negative NIR and 
red values, which causes the isovegetation lines to be more parallel 
in the region of positive NIR and red values than is the case for 
RVI, NDVI, and IPVI.  
  Huete (1988) does present a theoretical basis for this index based 
on simple radiative transfer, so SAVI probably has one of the better 
theoretical backgrounds of the vegetation indices.  However, the 
theoretical development gives a significantly different correction 
factor for a leaf area index of 1 (0.5) than resulted from the 
empirical development for the same leaf area index (0.75).  The 
correction factor was found to vary between 0 for very high 
densities to 1 for very low densities.  The standard value typically 
used in most applications is 0.5 which is for intermediate 
vegetation densities.
SUMMARY:  ratio-based index
	  isovegetation lines converge in negative red, negative NIR
	       quadrant
	  soil line has slope of 1 and passes through origin.
	  range -1 to +1
CALCULATING SAVI:        
			  NIR-red
		   SAVI = ----------(1+L)
			  NIR+red+L

where L is a correction factor which ranges from 0 for very high 
vegetation cover to 1 for very low vegetation cover.  The most 
typically used value is 0.5 which is for intermediate vegetation 
cover.

16a) Why is there a (1+L) term in SAVI?
A)  This multiplicative term is present in SAVI (and MSAVI) to 
cause the range of the vegetation index to be from -1 to +1.
This is done so that both vegetation indices reduce to NDVI
when the adjustment factor L goes to zero.

17)  What is TSAVI?
A)  TSAVI is the Transformed Soil Adjusted Vegetation Index which 
was developed by Baret et al. (1989) and Baret and Guyot (1991).  
This index assumes that the soil line has arbitrary slope and 
intercept, and it makes use of these values to adjust the vegetation 
index.  This would be a nice way of escaping the arbitrariness of 
the L in SAVI if an additional adjustment parameter had not been 
included in the index.  The parameter "X" was "adjusted so as to 
minimize the soil background effect," but I have not yet been able 
to come up with an a priory, non-arbitrary way of finding the 
parameter.  The value reported in the papers is 0.08.  The 
convergence point of the isovegetation lines lies between the origin 
and the usually-used SAVI convergence point (for L = 0.5)
SUMMARY:  Ratio-based index
	  isovegetation lines converge in negative red, negative NIR 
	       quadrant
	  soil line has arbitrary slope and intercept.
	  range -1 to +1
CALCULATING TSAVI:
			       s(NIR-s*red-a)
		  TSAVI = ---------------------------
			   (a*NIR+red-a*s+X*(1+s*s))

where a is the soil line intercept, s is the soil line slope, and X 
is an adjustment factor which is set to minimize soil noise (0.08 in 
original papers).

18)  What is MSAVI?
A)  MSAVI is the Modified Soil Adjusted Vegetation Index which was 
developed by Qi et al. (1994).  As noted previously, the adjustment 
factor L for SAVI depends on the level of vegetation cover being 
observed which leads to the circular problem of needing to know the 
vegetation cover before calculating the vegetation index which is 
what gives you the vegetation cover.  The basic idea of MSAVI was to 
provide a variable correction factor L.  The correction factor used 
is based on the product of NDVI and WDVI.  This means that the 
isovegetation lines do not converge to a single point.
SUMMARY:  ratio-based index
	  isovegetation lines cross the soil line at different 
	       points
	  soil line has arbitrary slope and passes through origin
	  range -1 to +1
CALCULATING MSAVI:
			    NIR-red
		  MSAVI = ------------- (1+L)
			   NIR+red+L

where L = 1 - 2*s*NDVI*WDVI
and s is the slope of the soil line.

19)  What is MSAVI2?
A)  MSAVI2 is the second Modified Soil Adjusted Vegetation Index 
which was developed by Qi et al. (1994) as a recursion of MSAVI.  
Basically, they use an iterative process and substitute 1-MSAVI(n-1) 
as the L factor in MSAVI(n).  They then inductively solve the 
iteration where MSAVI(n)=MSAVI(n-1).  In the process, the need to 
precalculate WDVI and NDVI and the need to find the soil line are 
eliminated.
SUMMARY:  ratio-based
	  isovegetation lines cross the soil line at varying points.
	  soil line has arbitrary slope and passes through origin
	  range -1 to +1

CALCULATING MSAVI2:
	     MSAVI2 = (1/2)*(2(NIR+1)-sqrt((2*NIR+1)^2-8(NIR-red)))

where ^2 signifies the squaring of the value and sqrt() is the 
square-root operator.

INDICES TO MINIMIZE ATMOSPHERIC NOISE

20)  What is Atmospheric Noise?
A)   The atmosphere is changing all of the time and all remote sensing
instruments have to look through it.  The atmosphere both attenuates
light passing through it and scatters light from suspended aerosols.
The atmosphere can vary strongly across a single scene, especially in
areas with high relief.  This alters the light seen by the instrument
and can cause variations in the calculated values of vegetation indices.
This is particularly a problem for comparing vegetation index values
for different dates.  The following indices try to remedy this problem
without the requirement of atmospherically corrected data.  
     WARNING:  These indices achieve their reduced sensitivity to the
atmosphere by decreasing the dynamic range.  They are generally slightly
less sensitive to changes in vegetation cover than NDVI.  At low 
levels they are very sensitive to the soil background. (See Qi et 
al. (1994) for comparisons.)
     NOTE:  I seldom work with data without performing an atmospheric
correction, so I have made no significant use of any of the indices
in this section (T. Ray).

21)  What is GEMI?
A)   GEMI is the Global Environmental Monitoring Index which was 
developed by Pinty and Verstraete (1991).  They attempt to eliminate
the need for a detailed atmospheric correction by constructing a 
"stock" atmospheric correction for the vegetation index.  Pinty
and Verstraete (1991) provide no detailed reasoning for this index
other than that it meets their requirements of insensitivity to
the atmosphere empirically.  A paper by Leprieur et al. (1994) 
claims to find that GEMI is superior to other indices for satellite
measurements.  However, A. Chehbouni (who happens to be the fourth
author of Leprieur et al. (1994)) showed me some examples using real
data (the analysis in the paper was based on a model) which strongly
contradicted the Leprieur et al. (1994) conclusions.  Qi et al. (1994)
shows a violent breakdown of GEMI with respect to soil noise at low
vegetation covers.  I understand that there are several ongoing studies
to evaluate GEMI, and I think that the jury is still out.
SUMMARY:
	 Non-linear
	 Complex vegetation isolines
	 Range 0 to +1
CALCULATING GEMI:
					   red - 0.125
		 GEMI = eta*(1-0.25*eta)- -------------
					      1 - red

where :
			 2*(NIR^2-red^2)+1.5*NIR+0.5*red
		 eta = ------------------------------------
				NIR + red + 0.5

 
22)  What are the atmospherically resistant indices?
A)   The atmospherically resistant indices are a family of indices
with built-in atmospheric corrections.  The first of these was
ARVI (Atmospherically Resistant Vegetation Index) which was 
introduced by Kaufman and Tanre (1992).  They replaced the red
reflectance in NDVI with the term:

		rb = red - gamma (blue - red)

with a value of 1.0 for gamma.  Kaufman and Tanre (1994) also 
suggested making the same substitution in SAVI which yields SARVI
(Soil adjusted Atmospherically Resistant Vegetation Index).  Qi 
et al. (1994) suggested the same substitution in MSAVI2 which 
yields ASVI (Atmosphere-Soil-Vegetation Index).  Obviously the
same substitution can also be made in MSAVI or TSAVI.
     Qi et al. (1994) showed that this class of indices were very
slightly more sensitive to changes in vegetation cover than GEMI
and very slightly less sensitive to the atmosphere and the soil 
than GEMI for moderate to high vegetation cover.  The atmospheric 
insensitivity and the insensitivity to soil break down violently
for low vegetation cover.
SUMMARY:
	 ratio-based
	 isovegetation lines cross as assumed by parent index
	 soil line as assumed by parent index
	 range -1 to +1
CALCULATING ARVI:
			  NIR-rb
		 ARVI = ----------
			  NIR+rb

with rb defined as:

		  rb = red - gamma*(red - blue)

and gamma usually equal to 1.0
     The parent index of ARVI is NDVI.  The substitution of rb
for red in any of the ratio-based indices gives the atmospherically
resistant version of that index.

[NOTE:  I view these indices for reducing atmospheric noise as late-
evolving dinosaurs.  The utility of a good atmospheric correction
for remotely-sensed data is so high as to make the effort of performing
a proper atmospheric correction worthwhile.  These end runs around
this problem may serve a useful purpose at present while better 
atmospheric corrections for data collected over land are being 
developed.  However, the move towards atmospheric correction of remote
sensing data is underway, and it is almost certainly the wave of the
future. - Terrill Ray]

OTHER INDICES

23)  What is GVI?
A)  GVI stands for Green Vegetation Index.  There are several GVIs.  
The basic way these are devised is by using two or more soil points 
to define a soil line.  Then a Gram-Schmidt orthogonalization is 
performed to find the "greenness" line which passes through the 
point of 100% (or very high) vegetation cover and is perpendicular 
to the soil line.  The distance of the pixel spectrum in band space 
from the soil line along the "greenness" axis is the value of the 
vegetation index.  The PVI is the 2-band version of this, Kauth and 
Thomas (1976) developed a 4-band version for MSS, Crist and Cicone 
(1984) developed a 6-band version for TM, and Jackson (1983) 
described how to construct the n-band version.
SUMMARY:  perpendicular vegetation index using n bands
	  isovegetation lines are parallel to soil line.
	  soil line has arbitrary orientation in n-space
	  range -1 to +1
CALCULATING GVI:
     Default version for MSS
	   GVI = -0.29*MSS4 - 0.56*MSS5 +0.60*MSS6+0.49*MSS7

     Default version for TM
       GVI = -0.2848*TM1-0.2435*TM2-.5436*TM3+0.7243*TM4+0.0840*TM5-             
	      0.1800*TM7

24)  Are there vegetation indices using other algebraic functions of 
the bands?
A)  Yes.  Rouse et al. (1973, 1974) proposed using the square root 
of NDVI+0.5, Goetz et al. (1975) proposed log ratios, Wecksung and 
Breedlove (1977) proposed arctangent ratios, and Tuck (1979) 
discussed the square root of the NIR/red ratio.  These seem to have 
been generally abandoned.  They make the same assumptions about the 
isovegetation lines and the soil lines as made by RVI and NDVI, and 
they have neither the value of common use or of ease of calculation.  
You will probably never see these, and there is really no good reason 
to bother with them.

25)  Are there vegetation indices that use bands other than the red 
and NIR bands?
A)  Yes.  First, the various GVIs make use of more than just the NIR 
and red bands.  In general, the GVI for a given multispectral sensor 
system uses all of the available bands.  Secondly, there have been 
attempts to develop vegetation indices based on green and red bands 
as discussed in the next question.
	 Mike Steven at the University of Nottingham has recently 
informed me of some work on an index using NIR and mid-infrared
bands.  More on this will be included when I have received a paper
from him.

26)  Plants are green, why isn't the green chlorophyll feature used 
directly.
A)  There are several reasons for this.  First, the reason that 
plants look so green is not because they are reflecting lots of 
green light, but because they are absorbing so much of the rest of 
the visible light.  Try looking at an area of bare dry soil and 
compare that to a grassy field.  You will immediately notice that 
the grassy field is generally darker.  It is generally easier to 
detect things when they are bright against a dark background.
    Second, this was tried early in the history of satellite remote 
sensing by Kanemasu (1974) and basically abandoned after a study by 
Tucker (1979) which seemed to demonstrate that the combinations of 
NIR and red were far superior than combinations of green and red.  
The idea of using red and green with MSS data was resurrected in 
recent years by Pickup et al. (1993) who proposed a PVI-like index 
using MSS bands 4 and 5 which they called PD54 (Perpendicular 
Distance MSS band 5 MSS band 4).  They claimed a tassel cap like 
pattern in the scatterplot for these two bands, but most of the MSS 
data I have looked at doesn't show this pattern.  A significant 
point for PD54 was that it detected non-green vegetation (dry 
grass).
    Third, many soils have iron oxide absorption features in the 
visible wavelengths.  As the soil gets obscured by vegetation cover,
this feature becomes less apparent.  It is likely that a great deal  
of the variance measured by the green-red indices is due to this 
instead of the plant chlorophyll feature (which is why PD54 might 
appear to be sensitive to non-green plant material).  This is fine 
if you know that the iron oxide absorption in the soil is uniform 
across the image, but if the iron oxide absorption is highly 
variable, then this will confuse green-red indices.

PROBLEMS

27)  How well do these vegetation indices work in areas with low 
vegetation cover?
A)  Generally, very badly.  When the vegetation cover is low, the 
spectrum observed by remote sensing is dominated by the soil.  Not 
all soils have the same spectrum, even when fairly broad bands are 
being used.  Both Huete et al. (1985) and Elvidge and Lyon (1985) 
showed that the soil background can have a profound impact and 
vegetation index values with bright backgrounds producing lower 
vegetation index values than dark backgrounds.  Elvidge and Lyon 
(1985) showed that many background materials (soil, rock, plant 
litter) vary in their red-NIR slope, and these variations seriously 
impact measurements of vegetation indices.  Then there is the problem 
of non-linear mixing.

28)  What the ^&*(*&^ is "non-linear" mixing?
A)  A lot of remote sensing analysis has been based on the concept 
of the Earth as spots covered by differently-colored paint.  When 
the spots of paint get too small, they appear to blend together to 
form a new color which is a simple mixture of the old colors.  
Consider an area covered by 50% small red spots and 50% small green 
spots. When we look at the surface from far enough away that we 
can't see the individual dots, we see the surface as yellow.  
Different proportions of red and green dots will produce different 
colors, and if we know that the surface is covered by red and green 
dots we can calculate what the proportions are based on the color we 
see.  The important thing to know is that any light reaching the 
observer has only hit one of the colored dots.  That is linear 
mixing.  
    Non-linear mixing occurs when light hits more than one of the 
colored dots.  Imagine a surface with a lot of small, colored bumps 
which stick out varying distances from the surface.  We can now 
image that light could bounce from one colored bump to another and 
then to the observer.  Now some of the light coming from the green 
bump bounced off of a red bump first, and this light will have 
characteristics of both the red and green bumps.  There is also 
light coming directly from the green bump that only bounced from the 
green bump.  If we could see this individual green bump, it would not 
look as green as it should.  Now, when the light from all of the 
bumps reaches the observer, the light looks different than when the 
bumps were simple spots even through the proportion of the area 
covered by each color is unchanged.  (We are assuming that there are 
no shadows.)  
    A second way for non-linear mixing to happen is if light can 
pass through one material and then reflect off of another.  Imagine 
a piece of translucent plastic with half of the area covered by 
randomly placed translucent green spots placed on top of a red 
surface.  Now light can pass through a green spot on the plastic and 
then reflect off of the red below before returning to the observer.  
Once again, the interaction of the light with multiple spots along 
its path changes the character of the light coming from each spot.  
Once again the color looks different than the linear case, which is 
just the case when light cannot pass through green spots.
    The basic point is that non-linear mixing twists the spectra of 
the materials being observed into different spectra which do not 
resemble any of the targets.  This can magnify the apparent 
abundance of a material.  Consider the piece of translucent plastic 
with the translucent green dots.  If we put it on top of a low-
reflectivity surface, very little of the light that passes 
through the green dots will be reflected back, so all we see is the 
light directly reflected from the green dots.  Now we put a highly 
reflective surface behind it, and we see a brighter green because we 
now see both the light directly reflected from the dots and most of 
the light which has passed through the green dots (which is green) 
is reflecting back from the highly-reflective background.  If we 
didn't know better, we might think that we just had more green dots 
instead of a brighter background.

29)  Is the variation in the soil the only problem?
A)  No.  Many of the commonly studied areas with low vegetation 
cover are arid and semi-arid areas.  Many plants which grow in such 
areas have a variety of adaptations for dealing with the lack of 
water and high temperatures.  (Even plants growing in areas with 
relatively cool air temperature have problems with heat regulation 
in dry climates since transpiration is the main way they keep cool.)  
These adaptations often decrease the amount of visible light 
absorbed by the plants and/or decrease the amount of sunlight 
striking the plants (hence the plants do not reflect as much light).  
These inherent qualities make arid and semi-arid vegetation hard to 
detect unless it is observed during periods of relatively abundant 
water when a whole new set of adaptations to maximize plant 
productivity takes effect.

30)  What if I can't get a good soil line from my data?
A)  If you're working in an area with high plant cover, this can be 
common.  This makes it virtually impossible to use the perpendicular 
indices or things like TSAVI and MSAVI1.  However, NDVI is at its 
best with high plant cover, so it is still available to you.  The 
correction factor L for SAVI should be near 0 for this sort of 
situation, which makes SAVI equivalent to NDVI.  MSAVI2 also need no 
soil line.  If you really want to use an index which requires a soil 
line, you will need to construct it with field and laboratory 
spectra, but this is not an easy task, and really not advisable.

31)  How low a plant cover is too low for these indices?
A)  These are rules of thumb, your mileage may vary:
	   RVI, NDVI, IPVI = 30%
	   SAVI, MSAVI1, MSAVI2 = 15%
	   DVI = 30%
	   PVI, WDVI, GVI = 15%

The more uniform your soil, the lower you can push this.

FUTURE DIRECTIONS

32)  I hear about people using spectral unmixing to look at 
vegetation, how does this work?
A)  See 22 for a thumbnail description of linear mixing.  Basically, 
you assume that the given spectrum is a linear combination of the 
spectra of materials which appear in the image.  You do a least 
squares fit to find weighting coefficients for each individual 
material's spectrum which gives the best fit to the original 
spectrum.  The weighting coefficients are considered to be equal to 
the abundances of the respective materials.  For detailed 
discussions of this see Adams et al. (1989), Smith et al. (1990), 
Roberts et al. (1994) and Smith et al. (1994).  There is also the 
highly sophisticated convex geometry technique discussed in Boardman 
(1994).

33)  Are there any indices which use high spectral resolution data?
A)  Yes.  Elvidge and Chen (1994) have developed indices of this 
kind.  They depend on the fact that when you take a derivative of 
the red edge in the vegetation spectrum you get a bump at about 720 
nm.  It is known that the red edge in be seen in high spectral 
resolution data down to about 5% cover (Elvidge and Mouat, 1988; 
Elvidge et al., 1993).  Three indices were developed.  The first 
used the integral of the first derivative of the reflectance 
spectrum over the range 626-795 nm.  The second took the first 
derivative of the reflectance spectrum, subtracted the value of the 
derivative at 625 nm and integrated the result over the range 626-
795 nm.  The third index used the integral of the absolute value of 
the second derivative of the reflectance spectrum integrated over 
the range from 626-795 nm.  Of these three indices, the first one 
was found to have greater predictive power than RVI or NDVI, but 
less predictive power than SAVI or PVI.  The index which used the 
second derivative has greater predictive power than SAVI and PVI.  
The index which used the difference between the first derivative and 
the value of the first derivative at 625 nm had the greatest 
predictive power.

FINAL QUESTION

34)  What vegetation index should I use?
A)  NDVI.
    Nearly everyone who does much with the remote sensing of 
vegetation knows NDVI, and its often best to stick to what people 
know and trust.  NDVI is simple.  It has the best dynamic range of
any of the indices in this FAQ and it has the best sensitivity to
changes in vegetation cover.  It is moderately sensitive to the soil
background and to the atmosphere except at low plant cover.  To just
take a quick qualitative look at the vegetation cover in an image,
you just can't beat NDVI unless you are looking at an area with low 
plant cover.
     PVI is somewhat less common in its use, but it is also widely
accepted.  It has poor dynamic range and poor sensitivity as well as
being very sensitive to the atmosphere.  It is relatively easy to use,
and finding the soil line is important for using some of the other 
indices.  It sometimes is better than NDVI at low vegetation cover.
     You really should probably use SAVI if you are looking at low 
vegetation cover, and if you use a correction factor which is not 
0.5 you had better be prepared to cite the Huete (1988) paper and 
the fact the correction factor is larger than 0.5 for very sparse 
vegetation.  MSAVI is also good, but it has seen very little use.  
If you have high spectral resolution data, you should consider the 
Elvidge and Chen (1994) indices.
     Remember that many of the indices which correct for the soil 
background can work poorly if no atmospheric correction has been 
performed.  If you are planning to seriously use vegetation indices 
for a multitemporal study, you should take a close look at the 
variability of the soil, and you should do an atmospheric correction.  
There is some concern about vegetation indices giving different values
as you look away from the nadir, but this may not be terribly serious
in your application.
SUMMARY:  In order of preference for each type of sensor:
     TM or MSS (or any broad-band sensor)
	     1:  NDVI (or IPVI)
	     2:  PVI
	     3:  SAVI (top of list for low vegetation)
	     4:  MSAVI2

     High Spectral Resolution Data (e.g. AVIRIS)
	     1: First derivative index with baseline at 625 nm.


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