The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
m 
S j = £k,R„,+v j j = 1,2...,p 
i=l 
m 
i = £k, Ki>=o 
i=l 
(1) 
(2) 
Where m is the number of components, in this case, m is the 3 
components of C, G and T; p is the number of image bands; K 
is the fractional abundance of each component within the pixel 
and v is the residual for each band. 
In this study we unmix the MODIS pixels, so the pixel-based 
reflectance (S) is provided by the MODIS image. However, we 
now consider that the fractions (K) are known and estimated 
from the TM fractional images. Then we can calculate each 
endmember (R) by solving equation (1) simultaneously for a 
series of equations using a least squares approach (Haertel and 
Shimabukuro, 2005). The overlapping area between the MODIS 
and TM images is used for this, and subsequently the obtained 
spectral reflectance of the three components (G, C and T) being 
the MODIS endmembers is assumed to be valid for the whole 
Three Gorges region. 
3.3 Spatial Interpolation 
In areas where the Li-Strahler model inversion is infeasible, CC 
values will be obtained by a hybrid spatial interpolation 
technique, i.e. regression kriging. Regression kriging employs 
regression analysis to model the trend of a target variable with 
one or more {p) exhaustively sampled auxiliary variables and 
spatial interpolation (kriging) of observed residuals to predict 
local departures from that trend (Hengl et al., 2007). The 
method is also referred to as universal kriging (Pebesma, 1997; 
Pebesma and Wesseling, 1998) or kriging with external drift 
(Deutsch and Joumel, 1998). For CC interpolation, it can be 
expressed as: 
CC(x 0 ) = q J 0 • P GLS + '(CC-q• p GLS ) (3) 
Where CC(x 0 ) denotes the predicted CC at location x 0 ; qo is a 
vector with 1 as the first element, followed by the p auxiliary 
values at the location to be predicted; Pgls is a vector of 
regression coefficients obtained by generalized least squares 
(GLS) fitting; CC - q • Pgls are n observed residuals in the 
neighborhood of x 0 ; and A, 0 is the vector of n kriging weights. 
Estimation of the regression coefficients by GLS requires prior 
knowledge of the covariance matrix of the residuals (Cressie, 
1993): 
P G l S = (q T ■ ^ 1 ■ q) -1 ■ q T ■ ^ 1 ■ cc (4) 
Where £ is the covariance matrix of the residuals and CC is the 
vector of estimated CC by the Li-Strahler model inversion. In 
geostatistics it is common practice to derive £ from a (semi) 
variogram which describes spatial dependence as a function of 
the distance between locations (Isaacs and Srivastava, 1989). 
Typically, it suffices to approximate this function from the 
residuals of a drift model obtained by ordinary least squares 
(OLS) fitting of the target variable on the secondary variable(s), 
in a single iteration (Kitanidis, 1993). 
We adopt this approach using the Gstat software (Pebesma, 
1997; Pebesma and Wesseling, 1998), with a single secondary 
variable that is selected from the commonly used vegetation 
indices (i.e. the normalized difference vegetation index (NDVI), 
the simple ratio (SR), the reduced simple ratio (RSR) (Brown et 
al., 2000), and also a single near-infrared (NIR) band) as the 
one having the highest linear correlation with CC. The choice 
for these variables is based on their expected correlation with 
CC while they are also readily derived from the both MODIS 
images. 
4. RESULTS AND DISCUSSION 
Since the TM fractional images are re-sampled to 25 m, each 
MODIS pixel corresponds to 20 x 20 TM pixels. When 
applying the linear unmixing model in the overlapping area 
(excluding clouds) of the MODIS image and the TM fractional 
images (G, C and T) for both years, the extracted spectral 
reflectance can be used as the regional scaling-based MODIS 
endmembers. Then, the fractions of sunlit background (K g ) 
from the both MODIS images are derived for inverting the Li- 
Strahler model to estimate CC on a per-pixel basis. 
After a correlation analysis, NDVI shows the highest linear 
correlation with the model estimated CC in the Three Gorges 
region for both 2002 (R=0.61) and 2004 (R=0.57), which is 
then selected to be the secondary variable used in the regression 
kriging. The final CC maps of 2002 and 2004 (Figure 1) display 
that the percentage of pixels with feasible CC values in the 
forested areas of the Three Gorges region increases from 70% 
(without interpolation) to current 95%. Only the cloud covered 
areas can not be estimated. Based on the 25 sample sites, 
validations show that for both years this method yields similar 
accuracies (R 2 2oo2 = 0.614; RMSE 20 o2 = 0.060; R 2 200 4 = 0.631 
and RMSE 2 oo4= 0.052). 
Figure 1. Mapping results of forest crown closure for 2002 (up) 
and 2004 (down) in the Three Gorges region.