Objectives

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Objectives

• The objectives of the workshop are to stimulate
  discussions around the use of 3D (and probably 4D
  3Dtime) realistic modeling of canopy structure
  to be used in remote sensing applications.
• On what basis is it possible to derive simpler RT
  representations for operational applications?

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Stochastic Radiative Transfer for Remote Sensing
of Vegetation
Y. Knyazikhin1, D. Huang1, N. Shabanov1, W.
Yang1, M. Rautiainen2, R.B. Myneni1
1Department of Geography, Boston
University 2Department of Forest Ecology,
University of Helsinki jknjazi_at_bu.edu
WORKSHOP ON THE USE OF 3D REALISTIC CANOPY
ARCHITECTURE MODELING FOR REMOTE SENSING
APPLICATIONS Avignon, France, March-9, 2005
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INTERPRETATION OF SATELLITE DATA

• Satellite-borne sensors measure mean intensities
  of canopy-leaving radiance averaged over the
  three-dimensional canopy radiation field
• Three-dimensional radiation models can simulate
  3D radiation field. However, they require 3D
  input and are time consuming
• Operational data processing requires fast
  retrieval algorithms. One dimensional model is
  the desirable option.

• Problem To develop a radiative transfer approach
  for modeling the radiation regime of natural
  vegetation which is
• as realistic as 3D model
• as simple as 1D model

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3D TRANSPORT EQUATION AS A BASIS FOR REMOTE
SENSING OF VEGETATION
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MEAN CHARACTERISTICS OF 3D FIELD

• 3D APPROACH
• one first solves the 3D radiative transfer
  equation for each realization of canopy structure
  and then averages the solutions over all possible
  realizations
• 1D APPROACH
• one first averages the extinction coefficient and
  scattering phase function over space and then
  solves the 1D radiative transfer equation with
  average characteristics

• STOCHASTIC APPROACH
• to obtain closed 1D equations whose solutions are
  mean characteristics of the 3D radiation field

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HISTORY
The problem of obtaining closed equations for
probabilistic characteristics of the radiation
field was first formulated and solved by G.M.
Vainikko (1973) where the equations for the mean
radiance were derived through spatial averaging
of the stochastic transfer equation in the model
of broken cloudiness, sampling realization of
which cannot be constructed. The method of G.M.
Vainikko has limited efficiency. . These
disadvantages were avoided in later papers .
(Titov, G., Statistical description of radiation
transfer in clouds, J. Atmos. Sci., 47, p.29,
1990)
Pomraning, G.C. (1991). Linear kinetic theory and
particle transport in stochastic mixtures. World
Scientific Publishing Co. Pte. Ltd., Singapore.
Shabanov, N. V., Y. Knyazikhin, F. Baret, and R.
B. Myneni, Stochastic modeling of radiation
regime in discontinuous vegetation canopy, Remote
Sens. Environ, 74, 125-144, 2000.
George Titov and Jerry Pomraning. From A.
Marshak and A.Davis (Eds), Three-Dimensional
Radiative Transfer in Cloudy Atmospheres.
Springer Verlag.
Vainikko, G. (1973). Transfer approach to the
mean intensity of radiation in noncontinuous
clouds. Trudy MGK SSSR, Meteorological
Investigations, 21, 2837.
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PARAMETERIZATION
Horizontal plane at depth z
g(z) the probability of finding foliage elements
at depth z. GROUND COVER max g(z)
q(z,?,?) the probability of finding
simultaneously vegetation elements on horizontal
planes at depths z and ? along the direction ?.
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CORRELATION OF FOLIAGE ELEMENTS AT TWO LEVELS
CONDITIONAL PROBABILITY K(z,?,?)q(z,?,?)/g(z)
Clustering (clumping) of foliage elements arises
naturally in the framework of the stochastic
approach DETECTING A LEAF MAKES IT MORE LIKELY
THAT THE NEXT LEAF WILL BE DETECTED NEARBY
1D approach Kg(?)
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3D EFFECTS
Stochastic approach reproduces 3D effects
reported in literature
Ignoring 3D effects can result in reflectance
saturation at low LAI
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CANOPY SPECTRAL INVARIANT - 1
i(w) mean number of photon interactions with
leaves before either being absorbed or exiting
the canopy (measurable)
w leaf albedo (measurable)
p recollision probability - the probability
that a photon scattered from a leaf in the canopy
will interact within the canopy again
qi portion of shaded area
i(w)1???pw ??qi0
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CONCLUSIONS

• On what basis is it possible to derive simpler RT
  representations for operational applications?
• Stochastic Transfer Equation because
• Its solution coincides exactly with what
  satellite-borne sensors measure that is, the
  mean field emanating from the smallest area to be
  resolved, from a pixel
• It reproduces 3D effects
• It provides a powerful tool to parameterize 3D
  effects
• It is as simple as 1D Radiative Transfer Equation

• The objectives of the workshop are to stimulate
  discussions around the use of 3D (and probably 4D
  3Dtime) realistic modeling of canopy structure
  to be used in remote sensing applications.
• Realistic models of canopy structure are required
  to derive and parameterize the q-function which
  describes the correlation of foliage elements in
  vegetation canopies