The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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To validate this method, we used double logistic model to 
describe the temporal LAI profile of agriculture crops, and 
Kuusk model are coupled with the empirical statistical model to 
simulate the surface reflectance. The experimental results show 
that the use of multi-temporal remote sensing data can 
significantly improve estimation of canopy biophysical 
variables. 
2. DATA 
posteriori information in the model space is given by the 
marginal probability density 
cr M( m /. y )= (2) 
Suppose the prior information of observation variables and 
model parameters is independent, equation (2) is then 
Retrieval of leaf area index from MODIS surface reflectance 
data (MOD09) at the Bondville site was performed to validate 
this method. The Bondville site, located at (40.0061000, - 
88.291867), is an agricultural site in the Mid-western part of the 
United States, near Champaign, Illinois. The site is part of the 
network of eddy covariance flux towers associated with 
AmeriFlux and the network of Core Validation Sites associated 
with the MODIS Land Team. It was established in 1996, with 
the long-term goal of obtaining the necessary in situ 
information to test and improve the representation of land- 
surface processes in soil-vegetative-atmosphere transfer (SVAT) 
models. The field was continuous no-till with alternating years 
of soybean and maize crops (Meyers, 2004). In 2001, the crop 
was maize with the maximum leaf area of 4.38 and an 
associated height of 2.4m. And there are time series of field 
measurements of LAI, which can be used to compare with the 
retrieved LAI. 
, , , , , fjJ PdWijWij l™,.,) 
<7 M (m„. ) = kp M (m ,, ) J D dd (J ) 
(3) 
Further assume that model parameters, observation variables 
and the a priori information on the model parameters are 
Gaussian, then we can get the cost function shown in equation 
(4) that has been widely used in the parameter retrieval from 
remote sensing data. 
5(m f 
(g(m„)-<r) r Cl'(g(m,,)-d£) + 
c i K-cr) 
(4) 
To test the new methods, the input data include multi-year 
MODIS LAI product (MOD15A2) and time series of MODIS 
reflectance product (MOD09A1) in 2001. All these products are 
from Collection 4. And a 49km 2 region around the tower or 
field site is extracted, so there are 7X7 subsets from MODIS 
LAI product with the spatial resolution of 1km, 14 X 14 subsets 
from MODIS reflectance product with the spatial resolution of 
500m. 
3. METHOD 
where g( m ) is the forward model, C D is the covariance 
matrix representing the measurement uncertainties and model 
uncertainties, c M is the covariance matrix representing the 
uncertainties of a priori information on the model parameters. 
The retrieval of canopy biophysical variables from remote 
sensing date is to minimize the equation (4) to find the model 
parameters m , which possess the maximum a posterior 
probability. However, the equation is constructed just using the 
individual pixel measurement and a priori information on the 
model parameters. 
3.1 Retrieval method using multi-temporal data 
The problem of parameter estimation from remote sensing data 
is underestimated, and Tarantola gives the theory to resolve it 
(Tarantola, 2004). LetM be the model space, and D the data 
space. Tarantola defined the posterior probability density in the 
space of D x M as follows. 
a(d IJ ,m iJ ) = k 
P(dj j,m i j)@(d j j,m i j) 
P(d,j,m IJ ) 
(1) 
where k is a normalization constant, m and d, are vectors 
in model space and data space respectively, p(d m ( . .) is the 
prior probability density in the space of DxM , which 
represents the prior information of observation variables and 
model parameters, @(d ; ,m (/ ) is the theoretical probability 
density which constructs the physical correlations between the 
observation variables and model parameters, and 
0(d,,,m,,) = 0(d. y |m, y )// M (m iy .) given the model parameter 
m ( , ^(d ,m fy ) is the homogeneous probability density of 
observation variables and model parameters. Then, the 
Noted that most of the biophysical variables, such as LAI, are 
time-dependent and possess inherent change rules along with 
time which are often represented by process models such as 
crop growth models, we made an attempt to retrieve canopy 
biophysical variables using the multi-temporal remote sensing 
data by introducing the inherent change rules of biophysical 
variables into the retrieval methods. 
The observational information of pixel 
(i,j) at times /+1 and t can be integrated to estimate canopy 
biophysical variables of pixel (i,j) at time t. Thus, the data 
space is extended as D = D' ( x D'^ 1 , in which each vector 
isd = (d' y ,d) +1 ) • Therefore, the posterior probability density 
in the model space can be expressed as follow. 
, , , , , , , r A>(d)0(d|m; J 
a M (m,. ) = kp M (m,j) j D dd —— 
(5) 
Assume the observational data of pixel (/, j) at times f+1 and t 
are independent each other. Then, equation (5) can be extended 
as