Modeling the radiance field within 3 D crop

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

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

Modeling 3 D light transfer Light-leaves interactions scattering interception 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 (3)

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) (4)

First order of scattering Example of application Estimation of the clumping parameter (5)

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 3 D 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 (6)

Multiple scattering Illustrations of parcinopy uses üGeneration of reference dataset: nested radiosity, Kuusk (97), Shabanov (2000) ü Analysis of sensitivity : leaf BRDF, Plant geometry (Espana et al) an erectophile canopy lit with a zenith source ? NIR ü Study of radiative transfer: what about fluxes isotropy? scattering order? TM, LAI 4, 60°, NIR LAI 0. 5, LAI 2 LAI 3. 7 (7)

Multiple scattering A more efficient method : radiosity Borel (1991); Goel (1991), Garcia-Haro (2002), fr(x) i L(y, r) B i (radiosity) H Lambertian Thus, the radiance equation is simplified: A radiosity model consists in: ü computing the N 2 form factors between each leaf ü solving the resulting system of linear equations ÞTwo limitations of the radiosity method: § the N 2 complexity § the Lambertian approximation (8)

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… (9)

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

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

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0 ~ 1 0 <1 (14)

Sensivity to the sphere diameter : the case of maize (15)