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

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

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

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)

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

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

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

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

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…

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?

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

0 ~ 1 0 <1

Sensivity to the sphere diameter : the case of maize