1. Modeling the radiance field
within 3D crop canopies
Michaël Chelle, Bruno Andrieu
UMR Environnement et Grandes Cultures
INRA Thiverval-Grignon - France

2. Modeling 3D light transfer
Light-leaf interaction
incident
reflection
Sanz et al, 1997
Maize leaf BRDF
absorption
transmission

3. Modeling 3D light transfer
Light-leaves interactions
interception
scattering
The radiance equation
L(y,yx)
Complexity of solving this equation depends on the number of surfaces Sy
=> Not working on a whole canopy, but on a significant pattern ∞ duplicated

4. First order of scattering
Projection (Z-buffer)
Efficient treatment of periodic infinite canopy
Canopy gap fraction => single Z-buffer : Monogap
Canopy BRDF => double Z-buffer : Bvis (B. Andrieu, 1999)

5. Example of application
First order of scattering
Example of application
Estimation of the clumping parameter

6. Monte Carlo ray tracing Our Monte Carlo ray tracing : PARCINOPY
Multiple scattering
Monte Carlo ray tracing
Ross & Marshak (1988); ART (Dauzat, 1991) Raytran (Govaerts, 1994), North(1996), BPMS (Lewis, 1999),…
Following stochastically the propagation of light rays within a 3D canopy
Our Monte Carlo ray tracing : PARCINOPY
Polygons set, various leaf BRDF
Multispectral: work in progress
* Classic CG algorithms
* Numerous output variables
(not only canopy reflectance)
+ Canopy BRDF, gap fraction,…
+ Profile of mean fluxes, radiance distrib°
+ virtual sensors
+ polygons irradiance
each variable may be given by scattering order
* Estimation of the variance of each output
Few assumptions, but Computing-time consuming

7. Illustrations of parcinopy uses
Multiple scattering
Illustrations of parcinopy uses
Generation of reference dataset: nested radiosity, Kuusk (97), Shabanov (2000)
Analysis of sensitivity : leaf BRDF, Plant geometry (Espana et al)
an erectophile canopy lit with a zenith source
NIR ?
Study of radiative transfer: what about fluxes isotropy? scattering order?
LAI 0.5,
LAI 2
LAI 3.7
TM, LAI 4, 60°, NIR

8. A more efficient method : radiosity
Multiple scattering
A more efficient method : radiosity
Borel (1991); Goel (1991), Garcia-Haro (2002),
fr(x)
 i
H Lambertian
L(y,r)
B i (radiosity)
Thus, the radiance equation is simplified:
A radiosity model consists in:
computing the N2 form factors between each leaf
solving the resulting system of linear equations
Two limitations of the radiosity method:
the N2 complexity
the Lambertian approximation

9. A dedicated radiosity method for canopy
Multiple scattering
A dedicated radiosity method for canopy
the nested radiosity (Chelle et Andrieu, 1998)
 For each triangle, a sphere defines the close objects
 The far radiations are estimated by a TM model: SAIL
Designed to estimate leaf irradiances,
a Z-buffer projection may be used to estimate canopy BRDF from these…

10. Modeling 3D light transfer Several questions remains:
What about the 3D structure accuracy?
Quid about moving plants ?
How detailed should be the optical properties ?
Are these approaches also suitable for forest canopy?
What about needles?
Experimental dataset ?
Should the 3D approaches be restricted to the theoretical studies
to improve efficient TM models (hot spot, clumping,…)
or be used to design operational methods?

11. Conclusion Combining accurate 3D canopies and 3D RT tools
Provide tools to investigate light-canopy interactions and the properties of resulting fluxes
Provide reference dataset
Basis to develop
efficient, but correct RT models
to analyze remote sensing data

14. 0 ~ 1
0 <1

15. Sensivity to the sphere diameter : the case of maize