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