1. Objectives  The objectives of the workshop are to stimulate discussions around the use of 3D (and probably 4D = 3D+time) 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?

2. WORKSHOP ON THE USE OF 3D REALISTIC CANOPY ARCHITECTURE MODELING FOR REMOTE SENSING APPLICATIONS Avignon, France, March-9, 2005 Y. Knyazikhin 1, D. Huang 1, N. Shabanov 1, W. Yang 1, M. Rautiainen 2, R.B. Myneni 1 1 Department of Geography, Boston University 2 Department of Forest Ecology, University of Helsinki jknjazi@bu.edu Stochastic Radiative Transfer for Remote Sensing of Vegetation

3. 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 1.as realistic as 3D model 2.as simple as 1D model

4. 3D TRANSPORT EQUATION AS A BASIS FOR REMOTE SENSING OF VEGETATION To estimate the canopy radiation regime, three important features must be carefully formulated. (1) architecture of individual plant and the entire canopy (2) optical properties of vegetation elements and soil Solar zenith angle Azimuth ANGULAR DISTRIBUTION OF INCIDENT RADIATION (3) incident radiation field 3D DISTRIBUTION OF SCATTERED RADIATION

5. 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

6. “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) Vainikko, G. (1973). Transfer approach to the mean intensity of radiation in noncontinuous clouds. Trudy MGK SSSR, Meteorological Investigations, 21, 28–37. Pomraning, G.C. (1991). Linear kinetic theory and particle transport in stochastic mixtures. World Scientific Publishing Co. Pte. Ltd., Singapore.HISTORY 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.

7. PARAMETERIZATION g(z) the probability of finding foliage elements at depth z. GROUND COVER = max {g(z)} Horizontal plane at depth z q(z, ,  ) the probability of finding simultaneously vegetation elements on horizontal planes at depths z and  along the direction . 0 z   11

8. 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 0 z   11 1D approach: K=g(  )

9. 3D EFFECTS Stochastic approach reproduces 3D effects reported in literature saturation Ignoring 3D effects can result in reflectance saturation at low LAI

10. CANOPY SPECTRAL INVARIANT - 1 i(  ) mean number of photon interactions with leaves before either being absorbed or exiting the canopy (measurable) q i portion of shaded area  leaf albedo (measurable) i(  )[1  p  ]  =  q i0 p recollision probability - the probability that a photon scattered from a leaf in the canopy will interact within the canopy again NIR RED

11. CONCLUSIONS  The objectives of the workshop are to stimulate discussions around the use of 3D (and probably 4D = 3D+time) 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  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