VEGETATION INDEX
1) 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
2) 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
3) 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
4) What is DVI?
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
5) 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.
6) 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
7) What is Soil Noise?
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.)
8) 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.
9) 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.
10) 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).
11) 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.
12) 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
13) 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).
14) What is GEMI?
A) GEMI is the Global
Environmental Monitoring Index which was developed by Pinty and Verstraete
(1991). They attempt to eliminatethe 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
15) 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.