Objectives

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. 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@bu.edu WORKSHOP ON THE USE OF 3D REALISTIC CANOPY ARCHITECTURE MODELING FOR REMOTE SENSING APPLICATIONS Avignon, France, March-9, 2005

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 • as realistic as 3D model • as simple as 1D model

4. 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 3D DISTRIBUTION OF SCATTERED RADIATION (3) incident radiation field ANGULAR DISTRIBUTION OF INCIDENT RADIATION Azimuth Solar zenith angle 3D TRANSPORT EQUATION AS A BASIS FOR REMOTE SENSING OF VEGETATION

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. 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, 28–37.

7. 0 z  1  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 .

8. 0 z  1  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: K=g()

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

10. NIR RED 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

11. 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 = 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