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Assessing the Impact of Structural Effects on the Radiative Signature of Vegetation

Assessing the Impact of Structural Effects on the Radiative Signature of Vegetation J-L. Widlowski, B. Pinty, T. Lavergne, N. Gobron and M. Verstraete Methods in Transport Workshop, 11 th – 16 th September 2004, Granlibakken, USA. Overview. Origin of 3-D signatures in reflectance fields

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Assessing the Impact of Structural Effects on the Radiative Signature of Vegetation

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  1. Assessing the Impact of Structural Effects on the Radiative Signature of Vegetation J-L. Widlowski, B. Pinty, T. Lavergne, N. Gobron and M. Verstraete Methods in Transport Workshop, 11th – 16th September 2004, Granlibakken, USA

  2. Overview • Origin of 3-D signatures in reflectance fields • Implications for 1-D’ RT model inversions • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields • Origin of 3-D signatures in reflectance fields • Implications for 1-D’ RT model inversions • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields

  3. R zTOC At the bottom of the canopy, z0 • Background albedo is not zero. A • Magnitude is depending on wavelength: Quasi-monotonic increase in visible & NIR. T z0 T (1- α) • Directionality of the upward reflected radiation is anisotropic. Radiation Transfer in Vegetation Canopies conditioned by two important boundary conditions: At the top of the canopy, zTOC • Impinging radiation has a • direct and a diffuse component due to atmospheric scattering Ref: Govaerts, PhD Thesis, 1996

  4. Ω ΩL • Directionality of leaf scattering depends on the leaf surface roughness, and the percentage of diffusely scattered photons from leaf interior. Ω Dicotyledon leaf: 3-D tissue representation plate model • Plate models often assume Bi-Lambertian scattering properties: - radiation is scattered according to cosine law: | ΩL ·Ω | - magnitude depends on leaf reflection and transmission values Ref: Ross, 1981 Leaf Optical Properties • Leaf reflection and transmission depend primarily on wavelength, plant species, growth condition, age and position in canopy. Ref: Govaerts et al. (1995) IEEE IGARS’95

  5. zenithal orientations, g(θL): • erectophile (grass) • planophile (water cress) • plagiophile • extremophile • uniform/spherical • time varying orientations: • heliotropism (sunflower) • para-heliotropism Directionally dependent leaf cross-section, G(Ω) Ref: Ross, 1981 Foliage Structural Properties III Vegetation foliage features characteristic leaf-normal distributions, g(ΩL) with preferred: • azimuthal orientations, g(φL)

  6. Ω For a volume of oriented, point-like scatterers (1-D or turbid medium): Λ(z) Ω0 • leaf area density [m2 / m3] σe(z, Ω) = · G(Ω) Ω = Ω0 Turbid canopy representation: 1-D • leaf cross-section along Ω BUT • Finite size of scatterer introduces: • mutual shading • enhanced retro-reflection illuminated leaf http://academic.emporia.edu/aberjame/remote/lec10/lec10.htm Hot-spot effect (i.e., Heiligenschein, opposition effect) Discrete canopy representation: 1-D’ Ref: Verstraete et al. (1990) JGR Foliage Structural Properties III In vegetation canopies the extinction coefficient is directionally variant but wavelength independent.

  7. Ω Ω0 0.08 1-D’ 0.06 Bi-directional Reflectance Factor (λ= Red) 0.04 1-D 0.02 Impacts Bi-directional reflectance field 0.00 illuminated leaf -90 -45 0 45 90 source observation zenith angle [degree] sensor Hierarchy of physical scales within vegetation layer Ref: Gobron et al. (1997) JGR Foliage Structural Properties III Extinction coefficient is wavelength independent, but directionally variant. For a volume of oriented, finite-sized scatterers (1-D’ medium): σe(z, Ω, Ω0) =Λ(z) · G(Ω)· O(z, Ω, Ω0) • Leaf area density [m2 / m3] • Interception probability along Ω • Enhanced return-probability near retro-reflection direction Ref: Pinty et al. (1997) JAS Knyazikhin et al. (1998) JGR

  8. RT model implementations: • Discrete foliage at small IFOVs • (growth grammars, L-systems) Local Scale • Stochastic foliage at medium to large IFOVs (allometric relationships) Widlowski et al., 2003, EUR Report 20855 Tree Structural Properties • Actual trees are very complex, featuring • species-specific patterns of: • foliage distribution • leaf orientation • crown shape and dimensions • branch & trunk structures • growth processes

  9. Gaussian hill height: 100m 500x500 m2 rainy season • tree and plant species • seasonal cycles • underlying topography • plant spatial distributions Tropical Forest dry season Deciduous tree rows in winter canopy structure affects multi-angular reflectance patterns Govaerts et al., 1997, ISPRS Symposium Widlowski et al., 2003, EUR Report 20855 Canopy Structural Properties Actual vegetation canopies include location-specific: All of which have an impact on the surface-leaving reflectance field. Widlowski et al., 2003, EUR Report 20855

  10. Largest soil fraction visible at nadir views Multi-directional surface observations Different fractionsof soil and foliagecontribute to the surface-leavingradiation if targetarea is observedfrom different viewing angles

  11. Near-Infrared Leaf scattering dominates over soil backscattering in the near-infrared Spectral Contrast between Vegetation & Background Leaf soil Reflectance Wavelength

  12. 30o Leaf scattering dominates over the soil backscattering 60o Bowl-shape BRF shapes of Heterogeneous Canopies: NIR Sparse Dense Medium Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)

  13. Near-Infrared Leaf scattering dominates over soil backscattering in the near-infrared Spectral Contrast between Vegetation & Background RED Soil back- scattering dominates over leaf scattering in the red Leaf soil Reflectance Wavelength

  14. 30o Bell-shape Soil backscattering dominates over leaf scattering 60o BRF shapes of Heterogeneous Canopies: Red Sparse Dense Medium Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)

  15. The RPV parametric model BRF(z,Ω0 Ω) =ρ0MI(k) FHG(Θ) H (ρc) ρ0 - controls amplitude level k - controls bowl/bell shape Θ - controls forward/backward scattering ρC - controls hot spot peak Ref: Rahman et al. (1993) JGR

  16. Impact of Canopy Structure on surface BRFs Is the ‘shape’ of the surface-leaving BRF field affected by the 3-D characteristics of vegetation canopies at one given wavelength? Bowl-shape • Bi-directional reflectance pattern may be classified as: • ‘Bowl’ shaped for k < 1 • ‘Lambertian’ for k = 1 • ‘Bell’ shaped for k > 1 BRF BRF k=1.18 Bell-shape k=0.65 The RPV parametric model BRF(z,Ω0 Ω) =ρ0MI(k) FHG(Θ) H (ρc) ρ0 - controls amplitude level k - controls bowl/bell shape Θ - controls forward/backward scattering ρC - controls hot spot peak Ref: Rahman et al. (1993) JGR

  17. Impact of Canopy Structure on surface BRFs SZA=30o λ=red IFOV~275 m 350 structurally different canopy architectures

  18. Impact of Canopy Structure on surface BRFs Bell shape 1.5 kred SZA=30o λ=red 1.0 IFOV~275 m 0.5 Bowl shape Ref: Widlowski et al. (2004), in print, Climatic Change

  19. Overview • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields

  20. Matching surface BRFs with 1-D’ models Assume you have a set of multi-directional observations of a surface target and - in absence of any a priori information regarding its structure - wish to utilize a 1-D’ RT model to retrieve information about that surface target. What’s the impact of the structural differences in both models? Approach: Use a large LUT (containing ~47000 candidates) spanning the entire domain of probable 1-D’ solutions, and find the best matching candidate under identical conditions of illumination and viewing.

  21. Homogeneous discrete canopy: 1-D’ e The best fitting 1-D’solution is the one with the smallest value of e Best-fitting 1-D’ solution 3-D reference data BRF VZA -75º -50º -25º 0º +25º +50º +75º Matching surface BRFs with 1-D’ models Find the 1-D’ surface that is best at mimicking the reflectance anisotropy of a 3-D target. Heterogeneous discrete canopy: 3-D Widlowski, 2001, PhD Thesis

  22. e The best fitting 1-D’solution is the one with the smallest value of e Best-fitting 1-D’ solution 3-D reference data BRF VZA -75º -50º -25º 0º +25º +50º +75º Matching surface BRFs with 1-D’ models Find the 1-D’ surface that is best at mimicking the reflectance anisotropy of a 3-D target. θ0 = 30o Fitting criteria: 7 BRF observations VZA =0, 25, 45 ,60; λ=red Widlowski et al., 2004, JGR - submitted

  23. Matching surface BRFs with 1-D’ models 1-D’ canopies that perfectly fit the surface leaving BRFs of a 3-D target may be very accurate in predicting the albedo but not the canopy absorption, transmission etc. Ref: Widlowski et al. (2004), JGR, submitted

  24. Structural impact on k across LAI gradient: SZA=30o λ=red IFOV~275 m Ref: Widlowski et al. (2004), in print, Climatic Change Impact of Canopy Structure on surface BRFs II Bell shape 1.5 kred 1.0 0.5 Bowl shape

  25. 1-D’ The 1-D’ homologue of a 3-Dsurface target features identical optical (rL, tL, αsoil), directional (Bi-Lambertian) and structural (LAI, LND, Lrad, LAD) canopy characteristics as its 3-D original with the exception of foliage clumping. 3-D Impact of Canopy Structure on surface BRFs II Leaf area index (LAI) increases Ref: Pinty et al. (2002) IEEE TGRS

  26. 1-D’ 3-Dsurface representations of intermediate vegetation coverage tend to possess bell-shapedreflectance fields At low and high vegetation coverage 3-D surfaces possess alsobowl-shapedBRF fields 1-D’surface representations (IPA) tend to be characterized bybowl-shapedBRF fields * k3-D≥k1-D’ if k3-D≥ 1 3-D Impact of Canopy Structure on surface BRFs II Ref: Pinty et al. (2002) IEEE TGRS

  27. Impact of Canopy Structure on surface BRFs 350 forest scenes • In general, the shape of the reflectance anisotropy of a ‘pure’ 3-D target tends to be different from that of its IPA or 1-D’ homologue: • k3-D≠k1-D’ * A 1-D’ canopy having a quasi-identical reflectance anisotropy shape as a 3-D target is almost certainly not its homologue! Widlowski et al., 2004, JGR, submitted

  28. 1-D’ canopy capable of mimicking BRFs of 3-D target consequently has: • enhanced soil albedo, α1D • reduced LAI (as LAI3D increases) • reduced single scattering • albedo, ω1D(as LAI3Dincreases) • increase leaf interception at large VZA (as LAI3Dincreases) * k3-D≥k1-D’ if k3-D≥ 1 Matching surface BRFs with 1-D’ models • 3-D surface targets tend to exhibit enhanced bell-shaped BRF patterns wrt. their 1-D’ homologues: • higher nadir BRFs • lower BRFs at large VZA

  29. Matching surface BRFs with 1-D’ models • 1-D’ canopy capable of mimicking BRFs of 3-D target consequently has: • enhanced soil albedo, α1D • reduced LAI (as LAI3D increases) • reduced single scattering • albedo, ω1D(as LAI3Dincreases) • increase leaf interception at large VZA (as LAI3Dincreases) Ref: Widlowski et al. (2004), JGR, submitted

  30. Matching surface BRFs with 1-D’ models • 1-D’ canopy capable of mimicking BRFs of 3-D target consequently has: • enhanced soil albedo, α1D • reduced LAI (as LAI3D increases) • reduced single scattering • albedo, ω1D(as LAI3Dincreases) • increase leaf interception at large VZA (as LAI3Dincreases) 1-D’ leaf normal distribution Ref: Widlowski et al. (2004), JGR, submitted

  31. Conversely: it is always possible to find effective state variables for a 1-D’ canopy such that it features identical absorption, transmission & reflection fluxes as a 3-D target – provided that the structure of the latter is known. • Ex: matching the multiple-scattered BRF component Ref: Pinty et al. (2004) JGR-Atmosphere (submitted) Matching surface BRFs with 1-D’ models The state variables of a 1-D’ canopy that is capable of mimicking the reflectance anisotropy of a 3-D target have to be ‘interpreted’ cautiously to account for 1) the structural differences with the 3-D target, and 2) the lack of information regarding canopy absorption & transmission. Ref: Widlowski et al. (2004), JGR, submitted

  32. Overview • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Pure 1D’ approach requires further interpretation of state variables • Given 3-D structure effective state variables can be found for 1-D’ • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Pure 1D’ approach requires further interpretation of state variables • Given 3-D structure effective state variables can be found for 1-D’ • Spatial resolution limits for pixel-based inversion • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields

  33. Spatial resolution limit RT model based interpretation of multi-angular BRF measurements of individual pixels is limited to spatial resolutions where net horizontal fluxes are close to zero: radiatively independent volume • What are the typical distances that photons travel laterally in between their points of entry and exit at the top of the canopy? • At what spatial resolution do horizontal fluxes affect pixel-based model inversions?

  34. Horizontal divergence of radiation What are the typical distances that photons travel between their points of entry and exit at the top of the canopy? Red NIR Widlowski et al., 2004, JGR, submitted

  35. Horizontal divergence of radiation What are the typical distances that photons travel between their points of entry and exit at the top of the canopy? • canopy structure controls extinction coefficient and the most likely distance, d Red - NIR • multiple-scattering makes photons in NIR travel longer distances than in red • 0.5 % (1 %) of all photons in red (NIR) have d < 100m Widlowski et al., 2004, JGR, submitted

  36. fluxes across sides that are perpendicular to the solar azimuth, φ0 • fluxes across sides that are parallel to φ0 Assessment of Horizontal Fluxes What are the typical flux quantities that travel through the lateral sides of some canopy volume, V at a spatial resolution, S? φ0 Ω0 φ0 zTOC V S

  37. +ve values→ more photons enter voxel than exit through lateral sides • absorption events inside voxel • exit through other sides φ0 • -ve values→ more photons exit voxel than enter through lateral sides • absorption events outside voxel prevent photons from entering • entry through other sides Magnitude of Net Horizontal Flux Components Red Maximum & minimum flux across the lateral sides of voxel that are perpendicular to φ0 θ0 = 0o, 15o, 30o, 55o 3D forest with 300 stem/ha Widlowski et al., 2004, JGR, submitted

  38. φ0 φ0 Magnitude of Net Horizontal Flux Components Red Maximum & minimum flux across the lateral sides of voxel that are perpendicular to φ0 Maximum & minimum flux across the lateral sides of voxel that are parallel to φ0 +ve values → more photons enter voxel than exit -ve values → more photons exit voxel than enter θ0 = 0o, 15o, 30o, 55o 3D forest with 300 stem/ha Widlowski et al., 2004, JGR, submitted

  39. φ0 Magnitude of Total Net Horizontal Flux θ0 = 30o θ0 = 60o maximum and minimum net horizontal flux into voxel maximum and minimum net horizontal flux into voxel +ve values → more photons enter voxel than exit λ= NIR, Red -ve values → more photons exit voxel than enter 3D forest with 300 stem/ha Widlowski et al., 2004, JGR, submitted

  40. Impact of Net Horizontal Fluxes Depends on magnitude ofsurface-leaving radiation! Red θ0 = 30o 18m 31m Since ΔFHor is larger in red than NIR, and F↑ larger inNIR than red: look at red +5% For sensor with BRF accuracy of 5% in red: spatial resolution > 31 mrequired for pixel-basedBRF interpretation -5% 18m 29m Tree density = 300, 600, 1200,1800 stem/ha Widlowski et al., 2004, JGR, submitted

  41. Overview • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Pure 1D’ approach requires interpretation of state variables • Given 3-D structure effective state variables can be found for 1-D’ • Spatial resolution limits for pixel-based inversion • Stay above 30 m for 5 % sensor accuracy • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields • Origin of 3-D signatures in reflectance fields • hot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopy • bowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy • Implications for 1-D’ RT model inversions • Pure 1D’ approach requires interpretation of state variables • Given 3-D structure effective state variables can be found for 1-D’ • Spatial resolution limits for pixel-based inversion • Stay above 30 m for 5 % sensor accuracy • Using ‘photon spreading’ to speed-up MC simulations of reflectance fields

  42. Raytran: a 3-D Monte Carlo ray-tracing model Raytran describes the radiation transfer on a ray-by-ray basis, following individual ray-trajectories from their source through all relevant interactionsuntil an eventual absorption or exitingfrom the simulated scene occurs. Information is subsequently extracted from ray paths: BRFi = π*Ni / N*ΔΩi Ref: Govaerts (1996) EU Report 16394 EN

  43. Improving the speed of the Raytran model Only 7 % (18 %) of injected rays in the red (in NIR) contribute towards estimation of surface albedo & substantially less for individual BRFs. • Enhance the contribution of individual photons in Raytran model via the ‘photon spreading’ variance reduction technique: • Ross & Marshak, 1988 • “Calculation of Canopy Bidirectional Reflectance Using the Monte Carlo Method” • absorption is probabilistic (photons carry weights) • “fictitious flight” towards detectors yields BRF • Thompson & Goel, 1998 • “Two Models for Rapidly Calculating Bidirectional Reflectance of Complex Vegetation Scenes: Photon Spread (PS) model and Statistical Photon Spread (SPS) Model” • absorption is deterministic (Monte Carlo scheme); • “photon spreading” towards detectors yields BRF

  44. At each physical interaction in themain ray path, a secondary “spreading ray” is aimed at each sensor. The probability of reaching the detector without physical interactionsis calculated and added to its radiance counter. Ray escapes but not within a sensor 3 2 4 Sensors / View directions 1 5 3D scene Developing the Rayspread model Principle of Rayspread. At each physical interaction in the main ray path, a secondary “spreading ray” is aimed at each sensor. The probability of reaching the detector without physical interactionsis calculated and added to its radiance counter.

  45. Developing the Rayspread model Principle of Rayspread. At each physical interaction in themain ray path, a secondary “spreading ray” is aimed at each sensor. The probability of reaching the detector without physical interactionsis calculated and added to itsradiance counter. + P3 + P2 + P4 + P1

  46. Developing the Rayspread model Principle of Rayspread. At each physical interaction in themain ray path, a secondary “spreading ray” is aimed at each sensor. The probability of reaching the detector without physical interactionsis calculated and added to itsradiance counter. + P3 + P2 + P4 + P1 + P5 Each sensor has already 2 (1) contribution(s)

  47. Developing the Rayspread model Principle of Rayspread. At each physical interaction in the main ray path, a secondary “spreading ray” is aimed at each sensor. Theprobability of reaching the detectorwithout physical interactionsis calculated and added to its radiance counter. Pr(x,y,z,q0,f0;d) = Prsurf.Refl.(q0,f0;q1,f1) * Prtravel(x,y,z;d) Prsurf. Refl.(q0,f0;q1,f1)= Lambertian, specular, etc. n q0 q1 x,y,z

  48. Developing the Rayspread model Principle of Rayspread. At each physical interaction in the main ray path, a secondary “spreading ray” is aimed at each sensor. Theprobability of reaching the detectorwithout physical interactionsis calculated and added to its radiance counter. Pr(x,y,z,q0,f0;d) = Prsurf.Refl.(q0,f0;q1,f1) * Prtravel(x,y,z;d) Prsurf. Refl.(q0,f0;q1,f1)= Lambertian, specular, etc. n d q0 d q1 l v M x,y,z Prtravel(x,y,z;d)=0 Prtravel(x,y,z;d)=f(l,v,M)

  49. Developing the Rayspread model Principle of Rayspread. At each physical interaction in the main ray path, a secondary “spreading ray” is aimed at each sensor. The probability of reaching the detector without physical interactions is calculated and added to its radiance counter. On the sensor’s side:

  50. less rays, less BRF noise Developing the Rayspread model 50mx50m forest scene. 250 trees. 153000 objects Raytran 400 million rays: TNIR = 16h20 (980mn) TRED= 8h24 (504mn) Rayspread 50,000 rays: TNIR = 15mn TRED= 10mn

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