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The normalized difference vegetation index (NDVI) is the most widely used vegetation index for retrieval of vegetation canopy biophysical properties. Several studies have investigated the spatial scale dependencies of NDVI and the relationship between NDVI and fractional vegetation cover, but without any consensus on the two issues. The objectives of this paper are to analyze the spatial scale dependencies of NDVI and to analyze the relationship between NDVI and fractional vegetation cover at different resolutions based on linear spectral mixing models. Our results show strong spatial scale dependencies of NDVI over heterogeneous surfaces, indicating that NDVI values at different resolutions may not be comparable. The nonlinearity of NDVI over partially vegetated surfaces becomes prominent with darker soil backgrounds and with presence of shadow. Thus, the NDVI may not be suitable to infer vegetation fraction because of its nonlinearity and scale effects. We found that the scaled difference vegetation index (SDVI), a scale-invariant index based on linear spectral mixing of red and near-infrared reflectances, is a more suitable and robust approach for retrieval of vegetation fraction with remote sensing data, particularly over heterogeneous surfaces. The proposed method was validated with experimental field data, but further validation at the satellite level would be needed.
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Analysis of NDVI and scaled difference vegetation index
retrievals of vegetation fraction
Zhangyan Jiang
a
, Alfredo R. Huete
b
, Jin Chen
a
, Yunhao Chen
a,
,
Jing Li
a
, Guangjian Yan
c
, Xiaoyu Zhang
c
a
Key Laboratory of Environmental Change and Natural Disaster Research of Education Ministry of China, College of Resources Science and Technology,
Beijing Normal University, Beijing 100875, China
b
Department of Soil, Water, and Environmental Science, University of Arizona, Tucson, AZ 85721, United States
c
Center for Remote Sensing and GIS, Beijing Normal University, Beijing 100875, China
Received 24 May 2005; received in revised form 1 January 2006; accepted 8 January 2006
Abstract
The normalized difference vegetation index (NDVI) is the most widely used vegetation index for retrieval of vegetation canopy biophysical
properties. Several studies have investigated the spatial scale dependencies of NDVI and the relationship between NDVI and fractional vegetation
cover, but without any consensus on the two issues. The objectives of this paper are to analyze the spatial scale dependencies of NDVI and to
analyze the relationship between NDVI and fractional vegetation cover at different resolutions based on linear spectral mixing models. Our results
show strong spatial scale dependencies of NDVI over heterogeneous surfaces, indicating that NDVI values at different resolutions may not be
comparable. The nonlinearity of NDVI over partially vegetated surfaces becomes prominent with darker soil backgrounds and with presence of
shadow. Thus, the NDVI may not be suitable to infer vegetation fraction because of its nonlinearity and scale effects. We found that the scaled
difference vegetation index (SDVI), a scale-invariant index based on linear spectral mixing of red and near-infrared reflectances, is a more suitable
and robust approach for retrieval of vegetation fraction with remote sensing data, particularly over heterogeneous surfaces. The proposed method
was validated with experimental field data, but further validation at the satellite level would be needed.
© 2006 Elsevier Inc. All rights reserved.
Keywords: NDVI; SDVI; Scale effect of NDVI; Vegetation fraction retrieval
1. Introduction
Vegetation is an important component of global ecosystems
and knowledge of the Earth's vegetation cover is important to
understand land-atmosphere interactions and their effects on
climate. Changes in vegetation cover directly impact surface
water and energy budgets through plant transpiration, surface
albedo, emissivity, and roughness (Aman et al., 1992). Vege-
tation amount is usually parameterized through the fractional
area of the vegetation occupying each grid cell (horizontal
density) and the leaf area index (LAI), i.e., the number of leaf
layers of the vegetated part (vertical density). Both evapotrans-
piration and photosynthesis are controlled by these two para-
meters (Gutman & Ignatov, 1998). Satellite data provide a
spatially and periodic, comprehensive view of land vegetation
cover. Several spectral vegetation indices have been developed
over the last few decades which have been used to estimate
vegetation canopy biophysical properties such as LAI, biomass
and percent vegetation cover (Huete, 1988; Kaufman & Tanré,
1992; Liu & Huete, 1995; Richardson & Wiegand, 1977; Rouse
et al., 1973; Tucker, 1979; Ünsalan & Boyer, 2004). Compa-
risons of the various vegetation indices can be found in Huete
and Liu (1994),Elvidge and Chen (1995),Huete et al. (1997),
McDonald et al. (1998) and Díaz and Blackburn (2003). Many
remote sensing studies utilize vegetation indices to study vege-
tation, assuming that the properties of the background are
constant or that soil variations are normalized by the particular
vegetation index used (Hanan et al., 1991).
Remote Sensing of Environment 101 (2006) 366378
www.elsevier.com/locate/rse
Corresponding author. Tel.: +86 10 58806098; fax: +86 10 58807163.
E-mail addresses: Jzy@ires.cn (Z. Jiang),
ahuete@ag.arizona.edu (A. Huete), Chenjin@ires.cn (J. Chen),
cyh@ires.cn (Y. Chen),
0034-4257/$ - see front matter © 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.rse.2006.01.003
The normalized difference vegetation index (NDVI) is one of
the most widely used vegetation indexes and its utility in
satellite assessment and monitoring of global vegetation cover
has been well demonstrated over the past two decades (Huete &
Liu, 1994; Leprieur et al., 2000). It is defined as
NDVI ¼NR
NþRð1Þ
where Rand Nrepresent surface reflectances averaged over
visible (λ0.6 μm) and near infrared (NIR) (λ0.8 μm) regions
of the spectrum, respectively. The NDVI is correlated with cer-
tain biophysical properties of the vegetation canopy, such as leaf
area index (LAI), fractional vegetation cover, vegetation condi-
tion, and biomass. NDVI increases near-linearly with increasing
LAI and then enters an asymptotic phase in which NDVI in-
creases very slowly with increasing LAI. Several studies have
found this asymptotic region pertains to a surface almost com-
pletely covered by leaves (Carlson & Ripley, 1997; Curran,
1983; Huete et al., 1985). Over densely vegetated surfaces, the
NDVI responds primarily to red reflectances and is relatively
insensitive to NIR variations, and hence unable to depict LAI
variations (Huete et al., 1997). According to experimental mea-
surements with different soil backgrounds (Huete et al., 1985),
NDVI approach their maximum values at fractional vegetation
covers between 80% and 90%. Similar experiments conducted
by Díaz and Blackburn (2003) showed NDVI reaching asymp-
totic values at fractional vegetation covers of only 60%.
Carlson and Ripley (1997) distinguished between local
LAI, as measured in closed canopies and global LAIas
would be measured without regard to the presence of breaks
between the canopies. A local LAI would always equal or
exceed the global LAI, and in partially vegetated, open can-
opies, the difference between global and local LAI may be
considerable. It seems plausible that the variation of NDVI with
respect to the global LAI in partially vegetated areas would be
mostly controlled by the variation in the fraction of vegetated
surface area illuminated by the sun and visible to the radiometer
(Carlson & Ripley, 1997). Verstraete and Pinty (1991) discussed
the nature and extent of NDVI variations in semi-arid lands, and
argued that NDVI is more strongly controlled by changes in
vegetation cover than by changes in the optical thickness of
canopies. For partially vegetated landscapes, especially semi-
arid areas, therefore, it is more direct and reasonable to derive
vegetation fraction rather then LAI from NDVI.
Many researchers have investigated the relationship between
NDVI and vegetation fraction and the retrieval of green
vegetation fraction from NDVI. However, difficulties and
uncertainties arise by the fact that one NDVI measurement does
not allow simultaneous derivation of green vegetation fraction
and local LAI. Gutman and Ignatov (1998) resolved this
problem by prescribing local LAI equal to infinity and derived
green vegetation cover from a scaled NDVI taken between bare
soil NDVI and dense vegetation NDVI. Wittich and Hansing
(1995) studied the relationship between NDVI and vegetation
fraction at five test areas in Germany, and showed that, to a first
approximation, the vegetation cover fraction was adequately
described by the linear expression of NDVI over a wide
distributed range of heterogeneous vegetation densities. Several
other studies also showed a strong linear relation between
fractional vegetation cover and NDVI (e.g. Kustas et al., 1993;
Ormsby et al., 1987; Phulpin et al., 1990).
However, some investigations found the relationship be-
tween NDVI and vegetation fraction to be nonlinear with NDVI
yielding distinct curves with vegetation cover changes corre-
sponding to different soil types (e.g. Colwell, 1974; Huete et al.,
1985). Using a linear mixture reflectance model, Hanan et al.
(1991) found the NDVI of a mixed pixel to be dependent not
only on the NDVI of pixel components and their proportions, but
also on the brightness of the components. Dymond et al. (1992)
found a nonlinear relationship between SPOT Haute Résolution
Visible (HRV) derived NDVI and percent vegetation cover at a
rangeland site in New Zealand. Choudhury et al. (1994) and
Gillies and Carlson (1995) independently obtained identical
square root relationships between the scaled NDVI and frac-
tional vegetation cover. Carlson and Ripley (1997) used a simple
radiative transfer model with vegetation, soil, and atmospheric
components to illustrate the relation between NDVI, fractional
vegetation cover, and LAI, and confirmed the square root
relation. However, the reflectances of bare soil were fixed for all
simulations in this model. So, the variations of soil background
were not taken into account in examining the relationship
between NDVI and vegetation cover. Using simulated AVHRR
data derived from in situ spectral reflectance data which were
collected from grasslands in Mongolia and Japan, Purevdorj
et al. (1998) found a second-order polynomial best related
NDVI to percent vegetation cover. Leprieur et al. (2000) found a
curvilinear regression between the fractional vegetation cover
and NDVI for a vegetation gradient in the south Sahel.
As the spatial resolution of satellite sensors varies from a few
meters to several kilometers, and some models need input
parameters from various data sources with different spatial
resolutions, properly dealing with the spatial scale problem of
satellite data is inevitable. In quantitative analysis of remote
sensing, the relationship between surface property measure-
ments at different spatial resolutions often causes concern
(Chen, 1999). In order to compare NDVI at different spatial
resolutions over the same surface, it is desirable to evaluate the
impact of spatial resolution on the NDVI measurement. Since
vegetation cover can be highly heterogeneous spatially,
subpixel variability is likely to introduce uncertainties in the
NDVI values at different resolutions.
Several studies have investigated the impact of spatial
resolution on NDVI, but with conflicting results. Aman et al.
(1992) analyzed the correspondence between NDVI calculated
from average reflectances and NDVI integrated from individual
NDVIs by simulating AVHRR data from high spatial resolution
SPOT 1 HRV radiometer and Landsat Thematic Mapper (TM)
data. For the study sites located in tropical West Africa and
temperate France, a strong correlation was found between the
two types of NDVI computed and they concluded that NDVI
derived from the coarse spatial resolution sensor data can be
used in lieu of NDVI integrated from fine spatial resolution
without introducing significant errors. Wood and Lakshmi
367Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
(1993) showed the NDVI as scale invariant at the FIFE
experiment site in Kansas, however, the relative homogeneity of
the FIFE site prevented the generalization of this conclusion
(Hu & Islam, 1997). On the other hand, Price (1992) noted that
for a region consisting of a mixture of totally vegetated area and
non-vegetated area, prominent discrepancies occur between
NDVI derived from high resolution measurements and NDVI
derived from low resolution measurements, with the relative
difference approaching 30%. Hu and Islam (1997) agreed with
Price, and they successfully parameterized subpixel scale
heterogeneity effects on NDVI using simulated land and vege-
tation scenarios and by modeling the variances and covariance
terms with the pixel scale values. The effects of scaling on the
retrieval of LAI from NDVI based on NDVILAI relationships
were investigated using mixed water-vegetation pixels, and
large biases were found when pixels contain interfaces between
two or more contrasting surfaces (Chen, 1999).
As the literature review above indicates, there exist many
perspectives and discrepancies on the two related issues of the
relationship between NDVI and fractional vegetation cover and
the scale effect of NDVI. The principle behind derivation of
fractional vegetation cover from NDVI is to relate NDVI of mixed
pixels to reference NDVI values, such as the NDVIs of dense
vegetation and bare soil, assuming the individual component
NDVIs in mixed pixels can be represented by these reference
NDVIs. However, even if component NDVIs can be estimated as
the reference NDVI without error, there are still sources of un-
certainty caused by the scale effect of NDVI in retrieving
vegetation fraction from NDVI. NDVI of mixed pixels and that of
the components in mixed pixels are not at the same spatial scale,
as the former is at pixel scale, while the latter is at subpixel scale. It
remains unclear the extent to which the pixel scale NDVI
corresponds to the subpixel scale NDVI and what possible
relationships exist between them. The relationship between
NDVI and fractional vegetation cover appears to be directly
influenced by the scale effect of NDVI and an understanding of
this effect is essential to understanding the relationship between
NDVI and fractional vegetation cover, and for accurate retrievals
of vegetation fraction. There are few studies that have examined
the relationship between NDVI and fractional vegetation cover
taking into account of the scale effect of NDVI.
This paper has two objectives. The first is to analyze the
difference between NDVI calculated from average reflectances,
which represents NDVI derived from coarse spatial resolution data,
and NDVI integrated from individual component NDVIs, which
represents NDVI derived from fine spatial resolution data, over
heterogeneous surfaces. The second is to examine the relationship
between NDVI and fractional vegetation cover taking into account
scaling effects and then propose a scale invariant method to derive
fractional vegetation cover from red and NIR reflectances.
2. Review of methods to retrieve vegetation fraction from
NDVI
There are three semi-empirical relationships used to derive
vegetation fraction from NDVI. Baret et al. (1995) developed a
generic semi-empirical relationship between the vertical gap
fraction and vegetation index and proposed a method to derive
vegetation fraction (f) from NDVI:
f¼1NDVIlNDVI
NDVIlNDVIS

0:6175
ð2Þ
where NDVI
and NDVI
S
are the NDVI for vegetation with
infinite LAI and bare soil, respectively. Based on a simple
radiative transfer model, Carlson and Ripley (1997) proposed a
semi-empirical relationship as follows:
f¼NDVINDVIS
NDVIlNDVIS

2
ð3Þ
Using a dense vegetation mosaic-pixel model, Gutman and
Ignatov (1998) assumed the NDVI of a mixed pixel can be
represented as,
NDVI ¼fNDVIlþð1fÞNDVISð4Þ
and the vegetation fraction derived by the scaled NDVI as,
f¼NDVINDVIS
NDVIlNDVIS
ð5Þ
3. Comparison of NDVI at different resolutions
3.1. Case I: A two-component scene model
When landscape components form large spatially coherent
patches and the vertical dimension of the vegetation is small,
spectral interactions between soil and vegetation components
are negligible (Hanan et al., 1991), and the influence of the
individual components on the observed reflectance can be
described by their spectral properties and fractional area using a
linear spectral mixing model (Adams et al., 1986; Gutman &
Ignatov, 1998; Hanan et al., 1991; Small, 2001; Smith et al.,
1990; Wittich & Hansing, 1995). Nonlinearity is introduced
when multiple scattering of radiation occurs among the different
target materials, a second-order effect that becomes dominant in
the case of intimate mixtures (Clark & Lucey, 1984). In case I,
we treat the landscape as composed of mixed pixels consisting
of homogeneous vegetation patches and soil background,
similar to the dense vegetation mosaic-pixel model proposed
by Gutman and Ignatov (1998) (Fig. 1). Shadow components
are assumed insignificant and negligible in this model. The red
(R) and near infrared (N) reflectances of the mixed pixel are the
area averaged reflectances of vegetation and soil (Manzi &
Planton, 1994; Wittich & Hansing, 1995).
R¼fRVþð1fÞRSð6Þ
N¼fNVþð1fÞNSð7Þ
where fis vegetation fraction, and R
V
and N
V
are vegetation
reflectances in red and NIR bands, respectively, and R
S
and N
S
are bare soil reflectances in red and NIR bands, respectively.
368 Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
The NDVI of the mixed pixel or coarse resolution NDVI
(NDVI
C
)is
NDVIC¼NR
NþRð8Þ
If a hypothetical, finer resolution sensor were to measure the
same landscape such that the NDVI of the two components
could be resolved, then
NDVIV¼NVRV
NVþRV
ð9Þ
NDVIS¼NSRS
NSþRS
ð10Þ
The average NDVI of the coarse mixed pixel, as measured
by the finer resolution NDVI
F
values is
NDVIF¼fNDVIVþð1fÞNDVISð11Þ
The NDVI
F
is a theoretical value which can be derived by
infinite fine resolution data. The finer the resolution of a sensor,
the lower the proportion of mixed pixels in the landscape, and
the closer the average NDVI is to the theoretical value, NDVI
F
.
The definitions of fine and coarse resolution NDVI can be
understood by comparing the resolution of sensors with the size
of the elements in a landscape. Strahler et al. (1986) noted two
discrete scene model possibilities, H- and L-resolution. In the
H-resolution case, the resolution cells of the image are smaller
than the elements, and the elements are individually resolved
with NDVI
F
values. In the L-resolution case, the resolution cells
are larger than the elements and they cannot be resolved
(Strahler et al., 1986) with the coarse resolution, NDVI
C
values.
Differences between NDVI
C
and NDVI
F
are caused by the
spatial scale of observations and the heterogeneity of the
landscape. NDVI
C
is derived from the average reflectances of
the entire pixel while NDVI
F
is an area weighted average of
component NDVIs resolved by finer resolution sensors. If A
denotes a weighted average function defined by Eqs. (6) and
(7), Vdenotes the NDVI function defined by Eq. (1), and Xis
the vector of reflectances (R,N), then we can express NDVI as,
NDVIC¼V½AðXÞ ð12Þ
NDVIF¼A½VðXÞ ð13Þ
Thus, NDVI
C
and NDVI
F
are compounded by the same two
functions, Aand V, but with reversed sequences. Because Vis a
nonlinear function of reflectances and Ais a linear function in
terms of f, the inversion of the sequence of the two functions
results in the difference between NDVI
C
and NDVI
F
. If the
equation of a vegetation index is a linear function of
reflectances, it is scale invariant in accordance with Eqs. (12)
and (13). Thus, the perpendicular vegetation index (PVI)
(Richardson & Wiegand, 1977), the Tasseled cap green
vegetation index (GVI) (Kauth & Thomas, 1976), the difference
vegetation index (DVI) (Tucker, 1979) and weighted difference
vegetation index (WDVI) (Clevers, 1989) are scale invariant if
the linear mixture model holds true.
Finer resolution sensors can observe subpixel variations in
a landscape, which are indistinguishable with coarser re-
solution sensors. In order to express NDVI
F
as the function of
coarse resolution reflectances, Nand R, the differences of red
and NIR reflectances between vegetation and soil must be
introduced,
DN¼NVNSð14Þ
DR¼RVRSð15Þ
In substituting ΔN,ΔR,N, and Rfor N
V
,R
V
,N
S
, and R
S
in
Eq. (11), NDVI
F
can then be written as,
NDVIF¼N2R2þA
ðNþRÞ2þBð16Þ
A¼ð12fÞðNRÞðDNþDRÞfð1fÞðDN2DR2Þð16 1Þ
B¼ð12fÞðNþRÞðDNþDRÞfð1fÞðDNþDRÞ2
ð16 2Þ
and NDVI
C
can be expressed similar to Eq. (16) as,
NDVIC¼N2R2
ðNþRÞ2ð17Þ
Unlike the coarse resolution NDVI
C
, the finer resolution
NDVI
F
is determined not only by the average reflectances, but
also by the subpixel variations (i.e. f,ΔNand ΔR). The
difference between NDVI
C
and NDVI
F
is expressed by the two
correction terms Aand B, which cannot be obtained from the
coarse resolution sensors and are thus neglected in NDVI
C
.
Fig. 1. Representation of mixed pixels in a landscape composed of homogeneous
vegetation patches and soil background.
369Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
It should be noted that the first terms of Aand B(A
1
and B
1
)
do not contribute to the difference between NDVI
C
and NDVI
F
,
because
ð12fÞðNRÞðDNþDRÞ
ð12fÞðNþRÞðDNþDRÞ¼NR
NþRð18Þ
The ratio of the latter terms of Aand B(A
2
and B
2
),
fð1fÞðDN2DR2Þ
fð1fÞðDNþDRÞ2¼DNDR
DNþDR
pNR
NþRð19Þ
however, explain the primary differences between NDVI
C
and
NDVI
F
.
When correction terms A
2
and B
2
become zero simultaneously,
the difference between NDVI
C
and NDVI
F
become zero. There
are three cases in which A
2
and B
2
are close to zero resulting in no
scale influence on NDVI. First, when fis close to zero or one,
which means that a mixed pixel is nearly homogenous spatially;
second, when ΔNand ΔRare close to zero, which means that a
mixed pixel is nearly homogeneous with respect to their spectral
reflectances; and third, when ΔN+ΔRis close to zero (i.e. N
V
+
R
V
close to N
S
+R
S
), the difference between NDVI
C
and NDVI
F
become zero. Thus, for spatially and spectrally heterogeneous
surfaces, NDVI is scale invariant only when the brightness of
vegetation (brightness defined as the sum of red and NIR reflec-
tances here) is equal to that of soil background. The brightness
contrast between vegetation and soil background and vegetation
fraction are two key factors that determine the scale effect of NDVI.
3.2. Case II: A three-component scene model
Shadows cast by vegetation canopies can be an important
component of the total pixel reflectance, particularly when the
ratio of canopy height to width is high. Shadows change not only
with the position of the sun and the amount of diffuse solar
radiation, but also with the density and geometric characteristics
of vegetation canopies (Jasinski & Eagleson, 1989; Huemmrich,
2001). Li and Strahler (1986) and Jasinski (1996) described four-
component geometrical models to estimate sunlit and shadowed
canopy and soil areas of forest canopies. Huemmrich (2001)
combined the SAIL model (Alexander, 1983; Verhoef, 1984)with
the Jasinski geometric model (Jasinski, 1990a; Jasinski &
Eagleson, 1989) to simulate canopy spectral reflectance and ab-
sorption of photosynthetically active radiation for discontinuous
canopies. Their model was a three-component geometric model
(sunlit canopy, sunlit soil, and shadowed soil), and was shown
adequate to describe forest reflectances (Huemmrich (2001).
In case II, shadows cast by plants on soil were added as a
component into the scene model of case I. This model assumes
that canopies do not shadow and overlap each other; the size of
the canopy elements is small relative to the size of pixels, and
surface is observed from nadir. The fractional area of shadowed
soil, g
sh
, can be estimated as (Jasinski, 1990a):
gsh ¼1fð1fÞgþ1ð20Þ
where ηis a nondimensional solar-geometric similarity para-
meter defined as the ratio of the mean shadow area cast by
a single plant to the mean projected canopy area (Jasinski,
1996). Analytical expressions for several geometrical shapes
have been developed by Jasinski (1990b).Thefractional
area of illuminated soil background, g
l
, can then be cal-
culated by
gl¼1fgsh ¼ð1fÞgþ1ð21Þ
The red and NIR reflectances of the scene are the area
weighted reflectances of the three components (illuminated
canopy, sunlit soil and shadowed soil,)
R¼fRVþglRSþgshRSh ð22Þ
N¼fNVþglNSþgshNSh ð23Þ
where R
Sh
and N
Sh
are the red and NIR reflectances of
shadowed soil, respectively. When sun zenith angle is 0 (i.e.
η=0), the three-component scene model reduces to the two-
component scene model.
The NDVI
F
of mixed pixels is
NDVIF¼fNDVIVþglNDVISþgshNDVISh ð24Þ
where NDVI
Sh
is the NDVI of shadowed soil component. By
defining B
V
,B
S
,B
Sh
as the brightness of vegetation canopy,
illuminated soil, and shadowed soil components (e.g. B
V
=N
V
+
R
V
), the NDVI
C
can be expressed as:
NDVIC¼fBVNDVIVþglBSNDVISþgshBSh NDVISh
fBVþglBSþgshBSh
ð25Þ
Eqs. (24) and (25) describe the relationship between pixel
scale NDVIs and subpixel scale component NDVIs. The
contribution of an individual component NDVI to the NDVI
F
is only determined by its fractional cover. However, the
contribution of an individual component NDVI to the NDVI
C
is determined not only by its fractional cover, but also by its
brightness. Eq. (25) also indicates that the NDVI
C
will not
change linearly with changing of component fractional cover
except when the brightness of all the components is equal.
Bright components will have relatively greater influence on
the NDVI
C
. At low vegetation fractions, dark soil back-
ground will increase the contribution of the NDVI
V
to the
NDVI
C
and result in overestimation of vegetation amounts.
At high vegetation fractions, shadow dominating canopy
background will bring the NDVI
C
close to the NDVI
V
even
though the scene is not fully covered by the vegetation
canopy.
Pixel scale NDVI cannot be calculated from subpixel scale
NDVI without knowledge of the component brightness values
of the mixed pixel. Uncertainty exists in Eq. (4) because of the
scale effect of NDVI which is responsible for the difference
between NDVI
C
and NDVI
F
. Consequently, for heterogeneous
surfaces, vegetation fraction cannot be accurately estimated
from NDVI because of its spatial scale effect and nonlinear
relationship with vegetation fraction.
370 Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
4. Derivation of vegetation fraction from red and NIR
reflectances
The most distinct spectral characteristic of green vegetation,
different from that of bare soil, is the strong contrast between
NIR and red reflectances, with very low red reflectance and high
NIR reflectance. The difference between NIR and red reflec-
tances of a mixed pixel can be obtained by combining Eqs. (22)
and (23)
NR¼fðNVRVÞþglðNSRSÞþgShðNSh RShÞð26Þ
Generally, the NIR reflectance of bare soil is slightly larger
than red reflectance. The reflectance of shadowed soil is very
low, but its NIR reflectance is slightly larger than red reflectance
because of higher canopy transmittance in the NIR band than in
red band. Fitzgerald et al. (2005) measured several spectra of
dry soil shadowed by one leaf layer and found their NIR
reflectances were about 0.06 and their red reflectance was about
0.02. By assuming that the difference between NIR and red
reflectances of illuminated soil and that of shadowed soil are
equal, Eq. (26) can be reduced to
NR¼fðNVRVÞþð1fÞðNSRSÞð27Þ
Thus vegetation fraction can be derived from the red and
NIR reflectances according to
f¼NRðNSRSÞ
NmRmðNSRSÞð28Þ
Since the difference vegetation index (DVI) is defined as the
difference between the NIR and red reflectances (NR), Eq. (28)
can be considered as a scaled difference vegetation index (SDVI)
between bare soil DVI, (DVI
S
) and dense vegetation DVI
(DVI
V
),
SDVI ¼DVIDVIS
DVIVDVIS
ð29Þ
In this case, SDVI is equal to fin value and thus can be used
directly as a vegetation fraction index. Fig. 2 shows the isolines
of SDVI. Adjacent isolines are parallel and equidistant, and the
slope of the soil line is assumed as 1 by SDVI. SDVI is 0 on the
soil line and SDVI becomes 1 for dense vegetation. For a mixed
pixel, SDVI and f are calculated according to the distance
between a point corresponding to the pixel and the soil line in
red-NIR space.
Eq. (26) indicates that, unlike the NDVI, the DVI is
insensitive to the variation of fractional cover of shadowed soil
since the DVI value of shadowed soil is often very small.
Soil background spectra are widely variable with variations
in soil biogeochemical constituents, moisture and roughness.
The soil reflectance at one band is often functionally related to
the reflectance at another band, and the reflectances of various
soils would fall on a straight line, called a soil line, in spectral
space. Orthogonal vegetation indices, including the PVI, GVI
and DVI, were developed based on the concept that a vegetation
point would deviate from the soil line with the perpendicular
distance from the point to the soil line being a measure of the
amount of vegetation present (Jackson, 1983). Other orthogonal
vegetation indices instead of the DVI could be applied in
Eq. (29). Price (1992) proposed that the vegetation fraction of a
mixed pixel can be derived by the ratio of the PVI of the pixel to
dense vegetation PVI, which differs from SDVI only in the slope
of the soil line in that DVI assumes it equal to 1. Raffy et al.
(2003) and Raffy and Soudani (2004) reported that the
percentage of forest cover could be accurately estimated by a
scaled PVI when the local LAI of a forest varies slightly.
5. Results
5.1. NDVIs at different resolutions
Following Carlson and Ripley (1997), the red and NIR
reflectances of soil background in the mixed pixel (Fig. 1) were
set at 0.08 and 0.11, respectively, and those of vegetation
patches were set at 0.05 and 0.50, respectively. The shadow
component was included in the three-component scene model
by setting ηat 1. The two-component scene model is a special
case of the three-component scene model when ηis 0. The NIR
and red reflectances of shadowed soil were assumed 0.06 and
0.02, respectively, and the NDVI
Sh
is 0.5. When η=0, NDVI
F
varies linearly with the variation of fractional vegetation cover,
but NDVI
C
yields an upward-convex curve as the vegetation
cover changes (Fig. 3a). The difference between NDVI
C
and
NDVI
F
is significant in this case. Since they are measurements
of the same heterogeneous landscape, the resolution of measure-
ments is responsible for the difference between them. The
average ΔNDVI (NDVI
C
minus NDVI
F
) is 0.107 over the entire
range of vegetation fraction covers with a maximum ΔNDVI of
0.171 at a vegetation fraction of 0.35. When η= 1, both NDVI
C
and NDVI
F
are increased in comparison with the corresponding
NDVI
C
and NDVI
F
with η=0. The average ΔNDVI is 0.089
over the entire range of vegetation fraction covers.
If the red and NIR reflectances of soil background are set at
0.18 and 0.23, respectively, the difference between NDVI
C
and
0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
Soil line
Red Reflectance
NIR Reflectance
Dense
vegetation
SDVI=0.5
SDVI=0
SDVI=0.75
SDVI=0.25
Fig. 2. Isolines of SDVI for estimation of vegetation fraction.
371Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
NDVI
F
is insignificant (Fig. 3b). When η= 0, NDVI
C
is close to
NDVI
F
at any fractional vegetation cover. The average ΔNDVI
is 0.032 over all vegetation fractions and ΔNDVI reaches a
maximum of 0.051 at a vegetation fraction of 0.45 for this case.
When η=1, both NDVI
C
and NDVI
F
are increased, particularly
at high vegetation fractions, in comparison with the
corresponding NDVI
C
and NDVI
F
with η=0. The average
ΔNDVI is the same as that with η=0, but ΔNDVI reaches a
maximum of 0.063 at a vegetation fraction of 0.60 for this case.
Thus, the nonlinearity of NDVI
C
becomes prominent not only
with the darkening of soil background, but also with the
presence of shadow. We can conclude that the presence of
shadow in partially vegetated surfaces will result in overesti-
mation of NDVI and vegetation amounts in mixed pixels, as
well as result in saturation at high vegetation fractions.
In the case of mixed, vegetation-water landscapes, the dif-
ference between NDVI
C
and NDVI
F
is extreme (Fig. 3c). The
red and NIR reflectances of water are assumed at 0.02 and
0.015, respectively, with vegetation reflectances the same as
above. Shadow on water surfaces was negligible for very low
reflectances of water. NDVI
C
is far larger than NDVI
F
and
throughout most vegetation fractions the nonlinearity of NDVI
C
with vegetation fraction is particularly strong. When vegetation
fraction is 0.15, NDVI
C
is 0.56 even though the value of NDVI
F
is only zero. NDVI
C
cannot truly approximate the presence of
vegetation in this case. There is a large bias in NDVI values at
different resolutions in landscapes containing vegetation and
open water. Chen (1999) similarly found large biases in LAI,
which is retrieved by using a NDVILAI relationship at
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
NDVIC(η=0)
NDVIC(η=1)
NDVIF(η=0)
NDVIF(η=1)
0
0.2
0.4
0.6
0.8
Vegetation Fraction (%)
-0.2
0
0.2
0.4
0.6
0.8
NDVIF
NDVIC
a
b
c
0 20 40 60 80 100
0 20 40 60 80 100
NDVIC(η=0)
NDVIC(η=1)
NDVIF(η=0)
NDVIF(η=1)
Fig. 3. NDVI of a mixed vegetation-soil (water) landscape at fine and coarse
resolutions versus fractional vegetation cover, N
V
=0.5, R
V
=0.05, N
Sh
=0.06,
R
Sh
=0.02, (a) N
S
=0.11, R
S
=0.08. (b) N
S
=0.23, R
S
=0.18. (c) R
W
=0.02,
N
W
=0.015 (shadow was neglected).
0.1 0.2 0.3 0.4
0.2
0.3
0.4
0.5
0.6
0.7
-0.1
0
0.1
0.2
η=0
ΔNDVI
NDVIC
NDVIF
Soil red reflectance
NDVI
ΔNDVI
0.2
0.3
0.4
0.5
0.6
0.7
-0.1
0
0.1
0.2
η=1
ΔNDVI
NDVIC
NDVIF
a
b
0.1 0.2 0.3 0.4
ΔNDVI
NDVI
Soil red reflectance
Fig. 4. Relationship between soil background red reflectance and NDVIs at fine
and coarse resolutions, and the difference between them (ΔNDVI) for the case
of vegetation fraction= 0.4, vegetation reflectances as in Fig. 3, and soil line of
y=1.062× + 0.026 (Huete et al., 1985). (a) η= 0; (b) η=1.
372 Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
different resolutions in boreal forestwater mixed landscapes.
These biases are introduced by resolution-dependent differences
between NDVI
C
and NDVI
F
.
If the fractional vegetation cover is fixed at 0.4 and the
reflectances of vegetation are assumed as above, ΔNDVI
becomes a function of soil background reflectances. If a soil line
is assumed, as measured by Huete et al. (1985),ΔNDVI
changes with variations of soil red reflectance (Fig. 4). When
η=0, NDVI
F
changes very little with the variation of soil red
reflectance, and this small change is due to the variation of
NDVI of the soil component, which changes from 0.19 for dark
soil to 0.06 for bright soil. But NDVI
C
changes dramatically
with variations in soil red reflectance, from 0.63 for dark soil
background to 0.32 for bright soil background. ΔNDVI is large
when soil background is dark and it becomes small and negative
when soil red reflectance is larger than 0.26. In case of η=1,
ΔNDVI, NDVI
C
and NDVI
F
behave similar to those without
shadow, but NDVI
C
and NDVI
F
are increased in comparison
with those without shadow, particularly over bright soil back-
grounds. This demonstrates that the measurement spatial
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
Vegetation cover (%)
NDVI
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
0
0.2
0.4
0.6
0.8
1
NDVIC
Modeled
NDVIF
ab
cd
ef
Vegetation cover (%)
NDVI
Vegetation cover (%)
NDVI
Vegetation cover (%)
NDVI
Vegetation cover (%)
NDVI
Vegetation cover (%)
NDVI
0 20 40 60 80 100
0 20 40 60 80 100 0 20 40 60 80 100
0 20 40 60 80 100 0 20 40 60 80 100
Fig. 5. Comparison of modeled NDVI
F
with theoretical NDVI
F
. (a) Superstition sand (dry). (b) Superstition sand (wet). (c) Avondale loam (dry). (d) Avondale loam
(wet). (e) Whitehouse-B sandy clay loam (dry). (f) Whitehouse-B sandy clay loam (wet).
373Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
resolution makes a significant difference in NDVI values com-
puted over heterogeneous landscapes with and without
shadows.
The NDVI
C
and NDVI
F
are two extreme cases of NDVI over
heterogeneous surfaces. When scaling down from coarse
resolution to fine resolution, the NDVI of a heterogeneous
landscape would change monotonously from NDVI
C
to NDVI
F
,
because the heterogeneity within pixels would decrease at the
scaling-down process until no mixed pixels exist, i.e. no
heterogeneity existing within pixels.
5.2. Correcting coarse resolution NDVI to fine resolution
NDVI using experimental data
As demonstrated in Fig. 3, the NDVI of a mixed pixel does
not vary linearly with fractional vegetation cover, so it cannot
quantify the amount of vegetation accurately. However, NDVI
derived from a hypothetical fine resolution sensor, NDVI
F
, does
vary linearly with fractional vegetation cover according to the
two-component scene model. In this section, we use experi-
mental data from Huete et al. (1985) to examine the usefulness of
Eq. (16) to correct coarse resolution NDVI to fine resolution
NDVI.
Huete et al. (1985) measured the reflectances of a developing
cotton canopy in red (0.630.69 μm) and NIR (0.760.90 μm)
bands over four different soil backgrounds in dry and wet
condition and for six different green cover levels. The theo-
retical NDVI
F
of a landscape composed of two homogeneous
components is calculated by the straight line interpolation of
component NDVIs using fractional vegetation cover (Eq. (11)).
Solar zenith angle variations along with cotton canopy
development through the growing season, result in complex
shadow component variations that are difficult to quantify. For
simplicity, the shadow effects were not taken into account in the
correction. Estimates of expected NDVI
F
were calculated using
Eq. (16) with prior knowledge of fractional vegetation cover
and red and NIR reflectance differences between components
(vegetation and soil), but without knowledge of the red and
near-infrared reflectances (Fig. 5). The modeled NDVI
F
values
for various soil backgrounds corresponded fairly closely to the
theoretical NDVI
F
, suggesting that the two-component scene
model could explain the nonlinearity of NDVI in most cases.
For dry Superstition sand, which is brighter than the other soils,
modeled NDVI
F
was not as close to the theoretical NDVI
F
as
NDVI
C
(Fig. 5a). This was possibly caused by shadow effects
since shadows dominate soil background when vegetation
fraction is high and the bright soil is darkened by shadow. The
shape of the NDVI-fcurve in this case is similar to that of the
NDVI
C
-fcurve with η=1 in Fig. 3b, i.e. NDVI increases
linearly at low vegetation fractions and becomes saturated at
Table 1
Comparison of the deviations of NDVI
C
and NDVI
F
from theoretical NDVI
F
Soil Soil red
reflectance
No. of
Points
NDVI
C
mean
deviation
NDVI
F
mean
deviation
Superstition (Dry) 0.337 8 0.0574 0.0626
Avondale loam (Dry) 0.188 8 0.0793 0.0211
Superstition (Wet) 0.187 4 0.1131 0.0152
Whitehouse (Dry) 0.158 8 0.0843 0.0180
Whitehouse (Wet) 0.126 4 0.1206 0.0316
Avondale loam (Wet) 0.107 3 0.1616 0.0683
Total 35 0.0896 0.0344
Table 2
Mean errors of the four methods used to derive vegetation fraction over each soil
background
Soil Dry/
wet
No. of
points
R
S
SDVI
(%)
Gutman
and Ignatov
(%)
Carlson
and
Ripley
(%)
Baret
et al.
(%)
Superstition D 8 0.337 2.65 6.90 9.84 4.26
W 4 0.187 5.23 13.67 5.00 1.41
Avondale D 8 0.188 4.17 9.32 8.69 3.28
W 3 0.107 8.39 21.44 6.91 6.22
Whitehouse D 8 0.158 4.83 11.10 7.70 2.15
W 4 0.126 7.22 15.94 6.74 5.22
Cloversprings D 8 0.062 7.51 17.01 6.64 7.29
W 5 0.029 8.55 26.14 15.54 17.93
Total 48 5.65 13.92 8.51 5.64
R
S
is the red reflectance of soil background.
0 20 40 60 80 100
0
20
40
60
80
100
SDVI
Gutman
Carlson
Baret
1:1 line
Observed fraction (%)
Estimated fraction (%)
0
20
40
60
80
100
SDVI
Gutman
Carlson
Baret
1:1 line
a
b
Observed fraction (%)
Estimated fraction (%)
0 20 40 60 80 100
Fig. 6. Comparison of observed fractions and estimated fractions using the four
different methods over individual soil backgrounds (a) over dry Superstition
sand (bright) background. (b) Wet Cloversprings loam (dark) background.
374 Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
high vegetation fractions, indicating the shadow effects are
mostly responsible for the nonlinearity of NDVI over bright soil
backgrounds. The correction of NDVI for the mixed pixel with
Cloversprings loam background which is very dark (R
S
0.062)
was unsuccessful, which may be a result of the numerator and
denominator of NDVI
F
(Eq. (16)) being so small that slight
changes in reflectance from the linearity assumption could
cause great error in NDVI
F
estimation.
The total mean deviation of modeled NDVI
F
from theoretical
NDVI
F
is 0.0344, which is much smaller than the mean
deviation of NDVI
C
, 0.0896 (Table 1). The deviation of
modeled NDVI
F
is mostly caused by the shadow effects. The
relatively big deviation of NDVI
C
can be mostly explained by
the scale effect of NDVI, as dark soil backgrounds correspond
to big deviations of NDVI
C
, and except for the dry Whitehouse
loam, the darker the soil background is, the bigger the deviation
of NDVI
C
.
5.3. Validation of the SDVI as a vegetation fraction index
The experimental data measured by Huete et al. (1985) was
used to validate Eq. (28) and estimate the accuracy of SDVI as a
vegetation fraction index. Three methods reviewed above that
derive vegetation fraction from NDVI were also evaluated and
compared to the proposed method. First, the performances of
the four methods were evaluated and compared using specific
soil backgrounds. NDVI
S
and NDVI
V
were given by NDVI for
bare soil and fully covered vegetation, respectively. At 100%
green cover, only the dark Cloversprings loam and bright
Superstition sand were used as soil background since the soil
background influence is negligible in the red and very small in
the NIR (0.017) for the dense vegetation (Huete et al., 1985).
The mean errors, calculated by the mean deviations of derived
fraction from observed fraction, of the four methods are sum-
marized in Table 2. The total mean error of SDVI was the lowest
and was approximately the same as the method of Baret et al.
(1995). The method of Gutman and Ignatov (1998) produced
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
ab
cd
0 20 40 60 80 100
Observed fraction (%)
Estimated fraction (%)
0 20 40 60 80 100
Observed fraction (%)
Estimated fraction (%)
0 20 40 60 80 100
Observed fraction (%)
Estimated fraction (%)
0 20 40 60 80 100
Observed fraction (%)
Estimated fraction (%)
Fig. 7. Comparison of observed vegetation and estimated vegetation fractions using different methods over various soil backgrounds. (a) SDVI. (b) Gutman and
Ignatov's method. (c) Carlson and Ripley's method. (d) Method by Baret et al.
Table 3
Evaluation of different methods to derive vegetation fraction
Methods Mean
error (%)
RMSD
(%)
Standard
deviation (%)
Bias
(%)
SDVI 5.42 7.11 5.25 4.79
Gutman and Ignatov 12.82 16.34 11.38 11.72
Carson and Ripley 8.11 10.63 10.47 1.81
Baret et al. 6.00 8.28 7.80 2.73
375Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
the biggest error, particularly with dark soil backgrounds (Fig.
6b). The mean error of the method of Carlson and Ripley (1997)
was intermediate, but significant for the darkest soil back-
ground. The mean error of the method by Baret et al. is small
except for over the darkest soil background. All the three NDVI
based methods produced large error over dark soil background,
and by contrast the SDVI performed fairly well over all soil
backgrounds (Fig. 6).
The four methods were also evaluated over all the soil
backgrounds (Fig. 7 and Table 3). The R
S
,N
S
and NDVI
S
were
given by the average red, NIR reflectances, and NDVI of all the
bare soil backgrounds, respectively, and the R
V
,N
V
and NDVI
V
were given by the average red, NIR reflectances, and NDVI of
vegetation at 100% cover, respectively. SDVI performed best
over the four methods with the estimated fraction close to the
observed fraction over all percent vegetation covers with
various soil backgrounds (Fig. 7a). The mean error and root
mean square deviation (RMSD) of SDVI were least, 5.42% and
7.11% (Table 3), respectively. The low standard deviation
results of SDVI indicated that variation of soil backgrounds
produced the smallest influence on SDVI and that SDVI was
robust enough to derive vegetation fraction over a wide range of
soil background conditions. The bias of SDVI was 4.79%,
indicating that the method slightly underestimated vegetation
fraction. The bias can be largely explained by a nonlinear
increase in NIR reflectance beyond 90% green cover, which
was attributable to rapidly accumulating green biomass with
only gradual lateral percent cover increase (Huete et al., 1985).
Large errors were brought out by Gutman and Ignatov's
method with mean error and RMSD of 12.82% and 16.34%,
respectively. The estimated fractions were 11.72% larger than
the observed fractions on average, indicated by its bias, which
can be largely explained by the scale effect of NDVI. When soil
background is dark, the subpixel scale NDVI of the vegetation
component has more influence on the pixel scale NDVI, which
causes scaled NDVI to overestimate vegetation fraction. The
large standard deviation of this method indicated that great
uncertainty is introduced by soil background variations using
this method. The mean error and RMSE were intermediate in
Carlson and Ripley's method and were further reduced by the
method of Baret et al. Mean biases were dramatically reduced
by the latter two methods. In fact, these two methods transform
scaled NDVI through power functions, which can produce
negative modifications on scaled NDVI, and subsequently re-
duce the positive bias of the scaled NDVI. However, the
transformation process removed only small uncertainties in
NDVI caused by the variation of soil background. Thus, the
standard deviations of these two methods were relatively large.
Although the method by Baret et al. performed slightly better
than SDVI using individual soil backgrounds, SDVI out-
performed this method over the various soil backgrounds,
which demonstrated that the method by Baret et al. only per-
forms better when soil background is invariant and its re-
flectances are given. The SDVI performed better over global
soil background conditions, without knowledge of individual
soil reflectances.
6. Discussion
Based on the assumption that the reflectances of a pixel
composed of homogeneous vegetation, illuminated and
shadowed soil can be calculated by area weighted averages
of component reflectances, the difference between NDVI of a
mixed pixel calculated at pixel scale, NDVI
C
, and NDVI
integrated by component NDVIs at the subpixel scale, NDVI
F
,
was analyzed. Analytical results showed that they are different
in formulation. It is suggested that for heterogeneous surfaces,
spatial resolution has an important impact on NDVI
measurement and NDVI at different scales may not be
comparable.
The nonlinearity of NDVI
C
becomes prominent not only
with the darkening of soil background, but also with the
presence of shadow. Even if the reflectances of a mixed pixel
can be described by a linear mixing model, the NDVI of a mixed
pixel cannot be calculated by the area weighted average of
component NDVIs. Vegetation fraction should not be estimated
by the scaled NDVI taken between the bare soil NDVI and
dense vegetation NDVI, which would overestimate vegetation
fraction in most cases. The proper linear relationship between
NDVI and fractional vegetation cover is not reproduced by a
coarse resolution sensor which acquires, with a single mea-
surement, the vegetation index of an area of mixed cover, and
thus NDVI does not have a unique correlation with vegetation
cover (Price, 1990). The power function transformations of the
scaled NDVI may improve the accuracy of vegetation es-
timation to a certain extent, but they cannot reduce the un-
certainty in NDVI caused by the variation of soil backgrounds.
The NDVI is an ad hoc prescription with no explicit physical
relationship to vegetation measures such as LAI and vegetation
fraction (Price & Bausch, 1995), It infers the presence of
vegetation on the basis of the ratio of NIR reflectance to red
reflectance, but does not provide areal estimations of the
amount of vegetation (Small, 2001). Small (2001) found that the
NDVI obtained from Landsat TM becomes asymptotic above
intermediate vegetation fractions in much the same manner that
it saturates with increased values of LAI and overestimates the
abundance of interspersed vegetation relative to more densely
0 0.1 0.2 0.3 0.4
0
20
40
60
80
100
Soil background red reflectance
SDVI (%)
0%
20%
25%
40%
60%
75%
90%
95%
100%
Fig. 8. Relationship between the SDVI and bare soil red reflectance for various
vegetation fractions. The data is from Huete et al. (1985).
376 Z. Jiang et al. / Remote Sensing of Environment 101 (2006) 366378
vegetated areas. This phenomenon may be partly due to the
shadow effects on the NDVI.
The vegetation fraction of a mixed pixel can be estimated by
a linear function of red and NIR reflectances, SDVI, which is
scale invariant. This method of estimating vegetation fraction
was validated by the experimental data acquired by Huete et al.
(1985). Although soil and plant spectra interactively mix in a
nonadditive, partly correlated manner to produce composite
canopy spectra, the estimated vegetation fractions are fairly
close to the observed fractions, which suggest SDVI being a
robust index to derive vegetation fraction from red and NIR
reflectances.
The variation of soil background brightness introduced
relatively insignificant variation in SDVI at a constant
vegetation cover, and SDVI is almost directly proportional
to fractional vegetation cover (Fig. 8). The linearity of SDVI
ensures that it outperforms NDVI to estimate vegetation frac-
tion. Compared with other vegetation indices, Díaz and
Blackburn (2003) found the difference vegetation index
(DVI) to be the optimal vegetation index for estimating the
biophysical properties of mangroves with various soil back-
grounds because it has a robust linear relationship with LAI
and percent cover.
Many vegetation indices are used to estimate vegetation
fraction. However, a vegetation index compresses the volume of
remote sensing data by a factor equal to the number of channels
used, and significantly reduces the information contained in the
original data set (Verstraete et al., 1996). The choice among
vegetation indices to be used to infer vegetation fraction is
crucial to the accuracy of estimation. The results of this study
suggest that SDVI is an appropriate index to infer vegetation
fraction of partially vegetation surfaces to the extent that the
assumption of spectral mixture linearity holds. The extension
of this approach to more complicated vegetation canopies
(e.g. forests) remains to be analyzed. As other orthogonal
vegetation indices, SDVI does not take into account the dif-
ferential canopy transmittances in red and NIR wavelengths and
nonlinear spectral mixing of soil and vegetation components.
Both linear relationships with a biophysical parameter, e.g.
vegetation fraction or LAI, and nonlinear spectral mixtures of
landscape components should be considered and balanced in an
optimal manner in future studies to develop an ideal vegetation
index.
It should be noted that our analysis and validation were both
based on ground surface reflectances. Atmospheric effects were
not considered and evaluated in this study, and remain to be
studied. Atmospheric correction thus may be necessary before
using SDVI to derived vegetation fraction. Further validation
based on satellite data with coincident field measurements over
various landscapes would further provide meaningful results
and be beneficial to assess the general applicability of SDVI as a
vegetation fraction index.
Acknowledgements
This work was supported by the Natural Science Foundation
of China (40201036) and the Project of the Ministry of
Education on Doctoral Discipline of China (20030027014). We
thank two anonymous reviewers for their helpful comments on
the earlier version of the manuscript.
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Linear combinations of n spectral bands form physically significant indices in space. The 2-dimensional (2-D) perpendicular vegetation index (PVI) of Richardson and Wiegand and the 4-D tasseled cap of Kauth and Thomas are special cases of indices. A procedure for calculating the coefficients of indices is described. Spectra from 12 wheat and two bare soil (wet and dry) plots were multiplied point by point (at 1-nm intervals) by response functions representing five satellite sensors. Reflectance values were obtained for each band for each sensor (atmospheric effects and sensor characteristics such as noise, resolution, and calibration, were not considered). indices were calculated for various band combination for the several sensors and their dynamic range for a 0–100% change in vegetation was compared. A 6-D vegetation index (greenness) calculated using six of the thematic mapper bands had the greatest dynamic range, followed closely by two 5-D and one 4-D greenness from the same sensor. The 2-D greenness using bands 4 (near-IR) and 7 (mid-IR) of the thematic mapper had a greater dynamic range than any band combination of the other four satellite sensors. The 4-D greenness of the Landsat-4 MSS and the 3-D index of the SPOT HRV were similar. The 2-D indices from the AVHRR sensors on NOAA-6 and NOAA-7 changed less with vegetation changes than did the other three.
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Realistic parameterization of land surface processes must take into account heterogeneities in the land surface. In the case of a sparse canopy, interpretation of remotely sensed measurements is very difficult and somewhat questionable in attempts to relate the vegetation indices (VIs) to fractional vegetation cover information. This paper provides an intercomparison of satellite observations at different scales for the purpose of assessing and monitoring vegetation changes at a regional scale. It is designed (1) to evaluate the level of association that can be expected from a model relating basic tools such as spectrally derived VIs from AVHRR and green biomass data for a set of heterogeneous surfaces in a representative semi-arid region and (2) to determine the best strategy for using satellite imagery in that context. The quantitative relationships between radiation data collected in space and characteristics of land surfaces are investigated in the context of the HAPEX-Sahel study over the Niger. A north-south vegetation gradient was accurately located and documented. Corresponding SPOT data, acquired on the same day for the same test site, at 20m spatial resolution were then resampled to the plate carree projection for comparison with National Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer (NOAA AVHRR) HRPT data (1km spatial resolution). This processing helped in the description and full interpretation of the evolution of various vegetation indices derived from NOAA AVHRR data on these semi-arid regions. One outcome of the data processing is that the resulting relationship between spectral indices and the effective biomass is found to be nonlinear within our low biomass range. When this scheme is applied to NOAA AVHRR data, the Normalized Difference Vegetation Index (NDVI), the Modified Soil-Adjusted Vegetation Index (MSAVI) and the Global Environment Monitoring Index (GEMI) appear to provide detailed information about biomass evolution. However, the accuracy is somewhat different depending on the fractional vegetation cover value. Strategies to estimate information on green biomass in semi-arid regions are different depending on the vegetation index used. In order to use the NDVI or MSAVI properly at the surface level, we have no choice but to perform carefully prepared atmospheric corrections. This data preprocessing is not necessary for the GEMI, which is computed without the need for any atmospheric corrections.