Fraction of Vegetation Cover_NDVI

7/30/2019 Fraction of Vegetation Cover_NDVI

1/15

Evaluating the fraction of vegetation cover based on NDVI spatial scale

correction model

X. ZHANG{, G. YAN*{, Q. LI{, Z.-L. LI{{, H. WAN{ and Z. GUO{

{State Key Laboratory of Remote Sensing Science, Beijing Key Laboratory for Remote

Sensing of Environment and Digital Cities, School of Geography, Beijing Normal

University, Beijing 100875, Peoples Republic of China

{TRIO/LSIIT (UMR7005 CNRS), Parc dInnovation, BP10413, 67412 Illkirch, France

Institute of Geographical Sciences and Natural Resources Research, Peoples Republic

of China

(Received 27 January 2005; in final form 23 February 2006)

Vegetation index (VI) is an important variable for retrieving the vegetation

biophysical parameters. With different kinds of remote sensing data sets, it is

easy to get the VI at different spatial and temporal resolutions. However, the

main concern is whether the relationship existing at some scale between the VI

and biophysical parameters is still applicable to other scales. This paper first

presents a method to correct the spatial scaling effect of NDVI by mathematic

analysis, and then analyses NDVI scale sensitivity with data from a spectral

database. The result shows that the NDVI obtained by reflectance up-scaling is

larger than the up-scaled NDVI from NDVI itself in most situations. The NDVI

scaling effect is more significant when water exists in a pixel, and increases with

the increase in the difference of the sum of visible reflectance and near-infrared

(NIR) reflectance between the vegetation and soil. Finally, a method is proposed

to estimate the fraction of vegetation cover (FVC) on the basis of the NDVI

spatial scaling correction model. The method is accurate enough to assess the

FVC taking into account the scaling effect.

1. Introduction

The fraction of vegetation cover (FVC) is an important variable for many land-

surface biophysical and biogeochemical models and serves as a useful measure of

land cover change. It can be obtained from ground measurements (Zhang et al.

2003) or remote sensing methods (Tian et al. 2004). Estimating FVC with remote

sensing technique has become the primary means due to rapid spatial and temporal

changes of vegetation cover.

Conventionally, FVC is defined as the vertical projection of the crown or shoot

area of vegetation to the ground surface expressed as fraction or percentage of the

reference area. However, taking into consideration supplementary requirements of

remote sensing techniques, FVC may be defined as the green vegetated area which is

directly detectable by the sensor from any view direction (Purevdor et al. 1998). In

this study, FVC is defined as the second meaning. FVC can be determined mainly by

International Journal of Remote Sensing

Vol. 27, No. 24, 20 December 2006, 53595372


2/15

the linear mixture method, which deconvolves proportional cover based on spectral

reflectance of endmembers or pure pixels (Jasinski 1996, Gilabert et al. 2000) or

NDVI method (Duncan et al. 1993, Zhang 1996). FVC is also attained with

physically based methods (Rosema et al. 1992), which are limited in use because of

the time-consuming need for many parameters to be input, especially for a global

image. In general, linear mixture modelling techniques have been mainly applied atlocal or regional scales over limited areas (Zhu and Tateishi 2002). As a result, the

NDVI method has been widely used since the 1990s owing to its convenience and

global scale utility. Gutman and Ignatov (1997) proposed the relationship model

between NDVI and FVC (f) as:

f~ NDVI{NDVIs = NDVIv{NDVIs , 1

where NDVIv, NDVIs are the NDVI of the dense vegetation canopy and bare soil,

respectively. However, is the mixed NDVI the sum of the NDVI of each component

in a pixel? Under what conditions can NDVI be expressed as a linear combination of

the NDVI of each component in a pixel?

The VI is an algebraic combination of remotely sensed spectral bands which can

provide useful information about vegetation (Liang 2004), such as FVC (Graetz

et al. 1988, Dymond et al. 1992, Purevdor et al. 1998) and LAI (North 2002). NDVI

is one of the most commonly used VIs because: (1) there exists a good relationship

between NDVI and kinds of biophysical parameters such as LAI, FAPAR and FVC

(Huete et al. 1992, 1997, Zhang 1996); (2) NDVI can eliminate or minimize the

influences of sun angle, view angle, atmospheric effects, etc., and the effect of error

of sensor calibration reduces from 1030% on single spectra to 06% on NDVI due

to normalization of NDVI (Zhao 2003); (3) NDVI is very sensitive to the presence of

vegetation as well as the state of vegetation.Scale often refers to spatial and time interval in remote sensing (Zhou et al. 2001).

More and more satellite platforms have been launched with sensors at different

spatial resolutions ranging from less than 1 m to a few kilometers, and at different

spectral resolutions varying from single-spectral to multi-spectral, and even to

hyperspectral bands. Thus, it is difficult to select suitable sensed data for different

applications from the large variety of data types, and both the spatial and the

spectral scaling factors become more and more important while the remotely sensed

data is used to investigate some issues (Woodcock and Strahler 1987). Similarly,

because of the scaling effect, while VI can be obtained easily from remotely sensed

data, especially for large areas, it is not clear whether the VI obtained at one scalecan be used at other scales or whether the relationships existing between the VI and

biophysical parameters at one scale are applicable at other scales.

Scaling problems on the relationships between the VI and the biophysical

parameters have been studied for many years (Justice et al. 1991, Chen 1999). Three

methods have been proposed to solve these problems: the first is to downscale the

model at large scale with a generalized parameter set and then disaggregate the

results into the smaller scale using interpolating transfer functions, which are

statistical relationships between large-area and site-specific surface parameters

(Wilby and Wigley 1997); the second supposes that the parameters are invariant

from one scale to another, these parameters are used for the up-scaling or down-scaling models (Buchter et al. 1994); the third is to transform the parameters

between the different scales by establishing the transformation function (Zhang et al

5360 X. Zhang et al.


3/15

Hu and Islam (1997) quantitatively demonstrated the NDVI scaling effect with

mathematical calculations. This paper first presents an analytical NDVI spatial

scaling correction model based on the linear mixture model, and then gives a scale-

invariant method based on the NDVI scaling correction model to retrieve the FVC.

Finally, this scale-invariant method is validated with both the simulated data and

actual satellite data such as MODIS images, with resolutions of 250 m and 1 km,respectively.

2. NDVI spatial scaling correction model and analysis

2.1 NDVI spatial scaling model

Hu and Islam (1997) discussed the NDVI scaling problem with the relative

difference of up-scaled NDVI calculated using two methods. The first is to calculate

the NDVI small scale, then upscale it to large scale, denoted NDVIL; the second is

to upscale the reflectance first, then calculate the NDVI with the up-scaledreflectance at large scale, denoted NDVID. By expanding the Taylor series to the

second order, Hu and Islam (1997) derived the relative difference of NDVI as [see

formula (14) in their paper]:

NDVIL{NDVID

NDVID~

2r2

r2zr1 2r2{r1

1

m

Xmk~1

rk1{r1 2

{2r1

r2zr1 2r2{r1

1

m

Xmk~1

rk2{r2 2

z2

r2zr1 2

1

m

Xmk~1

rk1{r1

rk2{r2

,

2

where r1, r2 are the visible and near-infrared (VNIR) reflectances of a mixed pixel,

respectively, rk1 , rk2 are the VNIR reflectances of pure pixel k (component, k),

respectively, m is the total number of pure pixels (component k in a mixed pixel),

where m52 if the pixel is composed of two components.

Assuming the pixel is a mixture of vegetation and bare soil with the area fraction f

for vegetation and (1f ) for bare soil, on the basis of the linear mixed principle, the

mixed pixel reflectance at some spectral regions can be considered to be

approximately the linear combination of the reflectance of all components. Then

the VNIR reflectance of the mixed pixel is written as follows:

r1~frv1z 1{f r

s1 3

r2~frv2z 1{f r

s2, 4

where v stands for vegetation, and s for bare soil.

IfDr2 and Dr1 denote the VNIR reflectance difference between vegetation and

soil respectively,

Dr1~rv1{rs1 5

Evaluating the fraction of vegetation cover 5361


4/15

Then according to the definition of NDVI, one can write

NDVIs~ rs2{rs1

rs2zr

s1

7

NDVIv~ rv2{rv1 rv2zrv1 8

NDVID~ r2{r1 = r2zr1 , 9

and following the works of Angora et al. (1992) and Gutman and Ignatov (1997),

the integrated value of NDVI (NDVIL) on the basis of the lumping approach can be

written as

NDVIL~ 1{f NDVIszfNDVIv: 10

By simple mathematical manipulation of equations (3)(10), the relative difference

of up-scaled NDVI can be derived:

NDVIL{NDVID

NDVID~

f 1{f Dr2zDr1

r2{r1

r2Dr1{r1Dr2

rv2zrv1

rs2zr

s1

~

f 1{f Dr2zDr1

r2{r1NDVIs{NDVIv :

11

2.2 Analysis of model sensitivity

Generally, for a mixed pixel consisting of vegetation and bare soil, near-infrared(NIR) reflectance r2 is larger than the visible (VIS) reflectance r1, namely r1,r2. At

the same time, NDVIs is smaller than NDVIv. Although the NIR reflectance for

vegetation is larger than that for soil, and contrarily reflectance in VIS for

vegetation is less than that for soil, that is to say Dr2.0 and Dr1,0, generally,

Dr2 +Dr1.0, therefore, the right-hand side of formula (11) is negative, which means

that NDVIL,NDVID in most conditions.

If water is used to substitute for soil in a mixed pixel, as discussed above, since

NDVIw for water is less than zero and the reflectance in the VIS and NIR for the

water surface is much lower than that for bare soil, the absolute value of ( NDVIw

NDVIv

) and Dr2+Dr1 are both increased, but r22r1 is decreased for this case,leading to the fact that the spatial scaling effect is more significant for a mixture of

vegetation and water than for a mixture of vegetation and soil. On the basis of the

above remarks, the spatial scaling effect of NDVI should be more evident if soil is

wetter. Let us assume that every symbol in equation (11) is for dry soil, and the

decrease in VNIR reflectance for wet soil is Dx1 and Dx2 corresponding to rs1 and r

s2,

respectively, then, for the same vegetation cover, the relative difference of up-scaled

NDVI can be expressed as:

NDVIL{NDVID

NDVID

~f 1{f Dr2zDr1 zf 1{f Dx1zDx2

r2{r

1 z 1{f

Dx

1{Dx

2 rs2{r

s1

{ Dx2{Dx1

{NDVI v

! 12



5/15

Because the NIR reflectance for water surface is lower than its reflectance in the

VIS, in most conditions, Dx2.Dx1; the right-hand side of equation (12) is therefore

larger than that of equation (11). As a result, the scaling effect of wet soil is more

obvious than that of dry soil with the same vegetation cover.

Based on equations (3)(6), formula (11) can also be rewritten as

NDVIL{NDVID

NDVID~

f 1{f Dr2zDr1

f Dr2{Dr1 zrs2{r

s1

NDVIs{NDVIv : 13

For a given soil and vegetation, the FVC (f) corresponding to the maximum of the

relative difference of up-scaled NDVI can be obtained by

LNDVIL{NDVID

NDVID

Lf> 0 14

leading to

f~

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirs2{r

s1

2z rs2{r

s1

Dr2{Dr1

q{ rs2{r

s1

Dr2{Dr1

: 15

In order to show the scaling effect of NDVI under different conditions, 12 typical

soil and vegetation samples (table 1) were selected from the spectral database

supported by national high-technology developing research projects (http://

spl.bnu.edu.cn) to make up a mixture of winter wheat and non-vegetated samples.

The relative differences of up-scaled NDVI calculated using formula (11) with

different FVC for all combinations are displayed in figure 1. At the same time, the

FVC (f ) corresponding to the maximum differences of up-scaled NDVI calculatedwith formula (15) are shown in table 2.

As shown in figure 1, NDVI calculated using the up-scaled reflectance (NDVID) is

generally larger than that obtained with up-scaled NDVI (NDVIL), and if the pixel

is mixed with vegetation and water, the spatial scaling effect of NDVI is more

obvious (maximum relative difference of up-scaled NDVI is more than 10) than that

for a mixture of vegetation and soil. As a result, the spatial scaling effect of NDVI is

more pronounced if the soil is wetter.

The spatial scaling effect of NDVI is more noticeable with the increase in the sum

of the reflectance difference in VIS and NIR between vegetation and soil. As seen in

Table 1. Component reflectance for typical soil and vegetation samples from the spectraldatabase.a

Vegetationcomponents

VISreflectance,

696 nm

NIRreflectance,

896 nmBackgroundcomponents

VISreflectance,

696nm

NIRreflectance,

896 nm

Winter wheat 0.03 0.44 Bare soil 1 0.2 0.27Cotton 0.05 0.61 Bare soil 2 0.20 0.25Rice 0.04 0.31 Water 0.08 0.03Corn 0.06 0.3 Algallimestone 0.31 0.33Orange 0.05 0.7 Joseite 0.13 0.12Pine 0.05 0.6 Sandstone 0.165 0.17



6/15figure 1 and table 2, NDVI shows the most obvious spatial scaling effect at FVCranging from 10 to 30% for our study cases. The scaling effect of NDVI decreases

when FVC is far from the value at which the relative difference of up-scaled NDVI

Figure 1. Relative differences of up-scaled NDVI with the change of vegetation fractioncover for different mixed components. NDVIL: up-scaled NDVI values using the NDVIscalculated at small scale; NDVID: calculated NDVI values using the up-scaled reflectances;Dr1 and Dr2 denote the reflectance difference between vegetation and soil in red and near-infrared bands, respectively. A, mixing of winter wheat and different soils; B, same as A butfor the mixing of winter wheat and water.



7/15

3. Evaluating FVC based on NDVI scaling correction model

3.1 Scale-invariant model

It is shown through the sensitivity analysis of an NDVI scaling correction model

that the spatial scaling effect of NDVI is noticeable for some FVCs. Therefore,FVCs retrieved from NDVI also show the spatial scaling effect. In order to reduce

this effect, in the following we propose a scale-invariant model to retrieve FVCs

based on an NDVI spatial scaling correction model.

Inserting formulae (3) and (4) into (9), the FVC (f ) can be derived from

f~rs2{r

s1{NDVID r

s2zr

s1

NDVID Dr2zDr1 { Dr2{Dr1

: 16

From this equation, one can see that the FVC can be determined when the VIS

and NIR reflectances of both vegetation and soil are known. It is difficult to obtain

the pure vegetation and soil reflectances from coarse resolution image. However, ifthere exists only one type of vegetation in the studied region, it is possible to get the

pure vegetation and soil reflectance by ground measurements or a prioriknowledge,

or from remote sensing data at finer spatial scale. Therefore, the FVC can be

estimated using equation (16) with NDVI measured at coarse scale (NDVID)

provided that the pure vegetation and soil reflectance can be known.

Rearranging equation (16), we get our scale invariant model for FVC:

f~NDVID{NDVI

s

NDVIv{NDVIszrv

2zrv

1

rs2zrs

1

{1

NDVIv{NDVID

: 17

From this model, one can see that equation (17) is identical to equation (1) if

rv2zrv1

rs2zrs1

{1

NDVIv{NDVID

in the denominator is zero or can be neglected with respect to the quantity NDVIv

NDVIs. Since NDVIvNDVID is generally greater than zero, equation (17) turns to

be equation (1) only if

rv2zrv1

rs2zrs1

~1

which means that if the sum of vegetation reflectance in VIS and NIR is nearly equalto the sum of soil reflectance in VIS and NIR, formula (1) can be substituted for

formula (17) otherwise the difference between FVC derived from these two

Table 2. Maximum difference of up-scaled NDVI and corresponding vegetation fractioncover.

ComponentsMaximum relative difference

of up-scaled NDVICorresponding vegetation

fraction cover (%)

Winter wheat and bare soil 1 20.005 29Winter wheat and bare soil 2 20.03 27Winter wheat and algallimestone 20.22 18Winter wheat and joseite 20.34 14Winter wheat and water 210 10



8/15

3.2 Validation and sensitivity analysis

In the following, we will compare the vegetation fraction cover estimated using

equations (1), (3) and (17) with simulated and actual satellite data such as MODIS,

which has a spatial resolution of 250 m and 1 km.

3.2.1 Data. To simulate linear mixed pixels, we select six types of vegetation

canopy and six kinds of non-vegetated backgrounds listed in table 1, and then the

reflectance images in the VIS and NIR are simulated by mixing vegetation canopy

with non-vegetated backgrounds under different FVC ranging from 0 to 100% with

a step of 5%.

Two MODIS images with 250 m and 1 km spatial resolution were used to

demonstrate the superiority of equation (17) in estimating the vegetation fraction

cover. The images were taken over a region mainly covered by vegetation and water

on 19 April 2004. FVC calculated from both 250 m and 1 km images are compared.

3.2.2 Results. For the simulated image, we compared the FVC calculated usingour scale invariant model [formula (17), formulae (1) and (3)] with the known

component reflectance. The results are shown in figure 2. From this figure, we can

see that, if the component reflectances are known exactly, the FVC obtained with

formula (1) may produce very large errors depending on the different types of soil

Figure 2 Comparison of the actual FVC with that derived using different formulae with



9/15

and vegetation in a mixed pixel. In contrast, the FVC can be exactly retrieved from

formulae (17) and (3), whatever the mixture type of soils and vegetation.

In general, the component reflectances assessed using the available field data or

derived from image itself are not accurate enough and will lead to errors in the

retrieved FVC. In order to show the retrieved errors of the FVC produced by the

errors of component reflectance, we calculated the errors of the FVC derived using

different models (formulae) for two mixing pixels. One is the mixing pixel of winter

wheat and water, which exhibits the maximum spatial scale difference of NDVI, as

shown in figure 1(b), and the other is the mixing pixel of winter wheat and bare soil,

which has the minimum spatial scale difference of NDVI, as seen in figure 1(a).

First, 10% Gaussian random errors are introduced in the estimation of vegetation

and non-vegetation reflectances. Then, we compare the errors between actual FVC

and the FVC estimated using formulae (17), (1) and (3). The mean value and

standard deviation of errors in the FVC are shown in figure 3. In figure 3, the

vertical lines centered on the average value denote the standard deviation from three

models. It is clear that mean errors and the standard deviations of the FVC derivedusing formula (1) are the largest.

In contrast, the errors of FVC derived from formula (17) are the smallest when

winter wheat and water are mixed. Mean errors and the standard deviations in the

FVC derived using different formulae are all smaller when the spatial scale effect of

NDVI is not prominent.

Based on the fact that there are different kinds of objects in an image, we first

classified the MODIS 250 m reflectance image into three classes using the supervised

method. Then, we obtained the component spectrum of vegetation and non-

vegetation for each class by the maximum and minimum NDVIs in the MODIS

250 m reflectance image, and calculated FVC using formulae (1), (3), (4) and (17)throughout the image. Finally, we estimated the true FVC at a scale of 1 km by

aggregating the FVC values obtained from MODIS 250 m reflectance image. The

scale effects of formulae (1), (3), (4) and (17) are compared based on the true FVC

and that obtained using MODIS 1 km reflectance image. The result is shown in

figure 4. The scale effect is obvious for formula (1). Formula (17) is robust to the

change of scale from 250 m to 1 km. Formula (1) is sensitive to scale when the FVC

is around 0.2.

Denoting the true FVC of pixel i as ftrui , the estimated FVC as fest

i , for total n

pixels, the relative root mean square (RMS) isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni~1

festi {ftru

i

ftrui

n o2,n

vuut :It is expected that the relative RMS for formula (1) is as high as 10%, while the

relative RMS for formula (17) is 5%, which is the lowest of all of these FVC

estimation formulae.

3.3 Discussion

From figures 2 and 4, we found that FVC derived from different models are quitedifferent for mixed pixels. For simulated image, our scale-invariant model [formula

(17)] can obtain actual fraction cover when no errors are introduced in the



10/15

Figure 3. The mean value and standard deviation of errors in the FVC derived usingformulae (1), (3), (4) and (18) with the component reflectances added errors by 10% ofGaussian random distribution. (a), mixing of winter wheat and water; (b), mixing of winterwheat and bare soil, where symbol denotes the standard deviation of errors in the FVCderived using formula (18), denotes the same but for formula (1) and denotes thesame but for formulae (3) and (4).



11/15

the mixing pixel is composed of vegetation and water where the maximum relative

error can reach 400%.

Furthermore, as shown in figure 1, the spatial scaling effect of NDVI is more and

more noticeable when the non-vegetated components have lower NIR reflectance

compared with that of the red band. Water is the component that has the mostsignificant scaling effect. Consequently, formula (1) gives the maximum estimation

error of FVC when water is mixed in a pixel. So, if the scaling effect of NDVI is

obvious, calculating the FVC with our scale-invariant model is much better, because

large errors will be generated using formula (1). Of course, if vegetation is very dense

or very sparse, the scaling effect of NDVI is not significant, and then our model will

give a result similar to that calculated with formula (1).

From formula (17), it can be concluded that the error between actual FVC and

the FVC from formula (1) is zero if the sum of vegetations red and NIR reflectance

is equal to that of the soil, namely,

rv2{rs2

z rv1{rs1

~0 : 18

Inserting formulae (5) and (6) into (19), we can get

Dr2zDr1~0 : 19

Since the error between actual FVC and the FVC from formula (1) is mainly

caused by the scaling effect of NDVI, when the scaling effect of NDVI is negligible,

our scale-invariant model is the same as formula (1). As a result, our model is an

extension of Gutman and Ignatovs expression by considering the scaling effect.

If we can obtain an accurate reflectance of each component, the FVC estimated

using formula (17) and linear mixing method is accurate, as shown in figure 2, andcan be proved by mathematical manipulation. However, in fact, the reflectance of

the component assessed with the available field or derived from an image usually

Figure 4. Comparison between the FVC values obtained from 250 m and 1 km MODISreflectance images using formulae (1), (3) and (18), respectively.



12/15

estimated reflectance of the component has some errors, the estimated FVC also has

error, especially when the pixel of winter wheat is mixed with water. However, if the

spatial scale effect of NDVI is not obvious, i.e. the sum of vegetations red and NIR

reflectances is nearly equal to that of the background, the errors of the FVC

estimated using three formulae are all small. As a result, the errors of the FVC

derived from formula (17) are the smallest, whatever the mixing pixel is. Therefore,formula (17) can overcome the spatial scale effect in most cases.

It is well known that the errors of the estimated component reflectances will

influence the results derived from spectral mixture analysis (SMA). As shown in

figure 3, when errors are added to the component reflectances, the FVC derived

from SMA shows large error. At the same time, the FVC retrieved from our model

is more resistant to errors due to Gaussian random distribution. Of course, it is very

difficult to find a pixel which is only a mixture of two classes, especially on a large

scale, but similar analysis can be done for a mixed pixel with more classes.

4. Conclusions

This paper presents the NDVI spatial scaling correction model by mathematical

formulation. Because the expression of NDVI is non-linear and the surface is

heterogeneous, NDVI shows more spatial scaling effect. If water is mixed into a

pixel, the scaling effect of NDVI is the most significant. It is expected that the spatial

scaling effect of NDVI is more obvious when a mixed pixel is made up of vegetation

and wet soil than vegetation and dry soil. It was also proved that, when the sum of

vegetations red and NIR reflectances nearly equals that of soil, the spatial scaling

effect of NDVI can be neglected. Finally, the NDVI calculated by up-scaled

reflectance (NDVID) is more than that of up-scaled NDVI (NDVIL) because theabsolute value of the reflectance difference between vegetation and soil in the NIR

band is more than that in the red band under most circumstances.

To overcome the large error in the FVC estimation caused by the scaling effect,

we proposed a method to calculate FVC based on NDVI scaling correction model.

Our scale-invariant model takes into account the scaling effect, and is expected to

give the actual FVC of a linear mixed pixel as the model is a combination of the

NDVI method and the linear mixing method. That is to say, the model that we

propose keeps both the merit of NDVI method, which is simple and time-saving,

and scale-invariant advantage of the linear mixing method. At the same time, this

model is robust to the errors by Gaussian random distribution.The actual mixed pixel may be more complex, as it contains more components

and may even exhibit non-linear mixing properties. At the same time, it is difficult to

find out single species at coarse scale. Further study is needed on how to accurately

attain the component reflectance at coarse scale. FVC anisotropy is caused by

reflectance and NDVI anisotropy, and the scale effect at different angles needs to be

studied further. However, we expect our model to show good results for most of the

coarse resolution images.

Acknowledgements

This work is funded partially by the National Natural Science Foundation of China(grant no. 40471095), Special Funds for Major State Basic Research Project (grant

no G2000077900) and the Excellent Young Teachers Program of Ministry of



13/15

and Jindi Wang for fruitful discussions. We would also like to thank reviewers and

the editor for valuable suggestions.

ReferencesANGORA, A., RANDRIANMANANTENA, H . , PODAIRE, A. and FROUIN, R., 1992, Upscale

integration of normalized difference vegetation index: the problem of spatialheterogeneity. IEEE Transactions on Geoscience and Remote Sensing, 30, pp. 326337.

BUCHTER, B., HINZ, C. and FUHLER, H., 1994, Sample size for the determination of coarse

fragment content in a stony soil. Geoderma, 63, pp. 265275.

CHEN, J.M., 1999, Spatial scaling of a remotely sensed surface parameter by contexture.

Remote Sensing of Environment, 69, pp. 3042.

DUNCAN, J.S., FRANKLIN, D.J. and HOPE, A., 1993, Assessing the relationship between

spectral vegetation indices and shrub cover in the Jornada Basin New Mexico.

International Journal of Remote Sensing, 14, pp. 33953416.

DYMOND, J.R., STEPHENS, P.R., NEWSOME, P.F. and WILDE, R.H., 1992, Percent vegetation

cover of a degrading rangeland from SPOT. International Journal of Remote Sensing,

13, pp. 19992007.GILABERT, M.A., GARCIA-HARO, F.J. and MELIA, J., 2000, A mixture modeling approach to

estimate vegetation parameters for heterogeneous canopies in remote sensing. Remote

Sensing of Environment, 72, pp. 328345.

GRAETZ, R.D., PECH, R.R. and DAVIS, A.W., 1988, The assessment and monitoring of

sparsely vegetated rangelands using calibrated Landsat data. International Journal of

Remote Sensing, 9, pp. 12011222.

GUTMAN, G. and IGNATOV, A., 1997, The derivation of the green vegetation fraction from

NOAA/AVHRR Data for use in numerical weather prediction models. International

Journal of Remote Sensing, 19, pp. 15331543.

HU, Z. and ISLAM, S., 1997, A framework for analyzing and designing scale invariant remote

sensing algorithms. IEEE Transactions on Geoscience and Remote Sensing, 35, pp. 747757.HUETE, A.R., HUA, G., QI, J., CHEHBOUNI, A. and LEEUWEN, W.J.D., 1992, Noarmalization

of multidirectional red and NIR reflectance with the SAVI. Remote Sensing of

Environment, 41, pp. 143154.

HUETE, A.R., LIU, H.Q., BATCHILY, K. and VAN LEEUWEN, W., 1997, A comparison of

vegetation indices over a global set of TM Images for EOS-MODIS. Remote Sensing

of Environment, 59, pp. 440451.

JASINSKI, M.F., 1996, Estimation of subpixel vegetation density of natural regions using

satellite multispectral imagery. IEEE Transactions on Geoscience and Remote Sensing,

34, pp. 804813.

JUSTICE, C.O., TOWNSHEND, J.R.G. and KALB, V., 1991, Representation of vegetation by

continental data set derived from NOAA-AVHRR data. International Journal ofRemote Sensing, 12, pp. 9991021.

LIANG, S.L., 2004, Quantitative remote sensing of land surfaces, pp. 200 (New York: John

Wiley & Sons).

NORTH, P.R.J., 2002, Estimation of fAPAR, LAI, and vegetation fractional cover from

ATSR-2 imagery. Remote Sensing of Environment, 80, pp. 114121.

PUREVDOR, T., TATEISHI, R., ISHIYAMA, T. and HONDA, Y., 1998, Relationships between

percent vegetation cover and vegetation indices. International Journal of Remote

Sensing, 18, pp. 35193535.

ROSEMA, A., VERHOEF, W., NOORBERGEN, H. and BORGESIUS, J.J., 1992, A new forest light

interaction model in support of forest monitoring. Remote Sensing of Environment, 42,

pp. 2441.TIAN, J., YAN, Y. and CHEN, S.B., 2004, The advances in the application of the remote sensing

technique to the estimation of vegetation fractional cover Remote Sensing for Land



14/15

WILBY, R.L. and WIGLEY, T.M.L., 1997, Down-scalling general circulation model output: a

review of methods and limitations. Progress in Physical Geography, 21, pp. 530548.

WOODCOCK, C.E. and STRAHLER, A.H., 1987, The factor of scale in remote sensing. Remote

Sensing of Environment, 21, pp. 311332.

ZHANG, R.H., 1996, Remote Sensing Experiment Model and Ground Basic (Beijing: Science

Press).ZHANG, X., DRAKE, N. and WAINWRIGHT, J., 2002, Scaling land-surface parameters for

global scale soil-erosion estimation. Water Resources Research, 38, pp. 11801189.

ZHANG, Y., LI, X.B. and CHEN, Y.H., 2003, Summarize on multi-scale remote sensing of grass

vegetation cover and method of ground measurement. Process in Earth Science, 18,

pp. 8593.

ZHAO, Y., 2003, Remote Sensing Application: Analysis and Method, pp. 374 (Beijing: Science

Press).

ZHOU, C.H., LUO, J.C. and YANG, X.M., 2001, Geographic Understanding and Analysis on

Remote Sensing Image, 2nd edn (Beijing: Science Press).

ZHU, L. and TATEISHI, R., 2002, Linear mixture modeling for quantifying vegetation cover

using time series NDVI data. Available at: www.gisdevelopment.net/aars/acrs/2002/

luc/luc006pf.htm

5372 Evaluating the fraction of vegetation cover


15/15

Documents

Fraction of Vegetation Cover_NDVI