Upload
anjolie-bradford
View
32
Download
0
Tags:
Embed Size (px)
DESCRIPTION
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 - PowerPoint PPT Presentation
Citation preview
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
• 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
Overview
Ref: Govaerts, PhD Thesis, 1996
Radiation Transfer in Vegetation Canopies
conditioned by two important boundary conditions:
• Impinging radiation has a direct and a diffuse component due to atmospheric scattering
At the top of the canopy, zTOC
R
A
T
• Background albedo is not zero.
At the bottom of the canopy, z0
T (1- α)
• Directionality of the upward reflected radiation is anisotropic.
• Magnitude is depending on wavelength: Quasi-monotonic increase in visible & NIR.
zTOC
z0
Dicotyledon leaf: 3-D tissue representation
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
• Directionality of leaf scattering depends on the leaf surface roughness, and the percentage of diffusely scattered photons from leaf interior.
ΩL
plate model
Ω
Ω
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
Foliage Structural Properties IIIVegetation foliage features characteristic leaf-normal distributions, g(ΩL) with preferred:
• azimuthal orientations, g(φL)
• 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
For a volume of oriented, point-like scatterers (1-D or turbid medium):
σe(z, Ω) =
Turbid canopy representation: 1-D
• leaf cross-section along Ω
· G(Ω)
Foliage Structural Properties III
• leaf area density [m2 / m3]
Λ(z)
BUT
Finite size of scatterer introduces:mutual shading enhanced retro-reflection
Discrete canopy representation: 1-D’
http://academic.emporia.edu/aberjame/remote/lec10/lec10.htm
Hot-spot effect (i.e., Heiligenschein, opposition effect)
Ω = Ω0
illuminated leaf
Ω0Ω
Ref: Verstraete et al. (1990) JGR
In vegetation canopies the extinction coefficient is directionally variant but wavelength independent.
illuminated leaf
Ω0ΩFor a volume of oriented, finite-sized
scatterers (1-D’ medium):
• Interception probability along Ω
Foliage Structural Properties III
Extinction coefficient is wavelength independent, but directionally variant.
• Leaf area density [m2 / m3]
• Enhanced return-probability near retro-reflection direction
σe(z, Ω, Ω0) = Λ(z) · G(Ω)· O(z, Ω, Ω0)
Ref: Pinty et al. (1997) JASKnyazikhin et al. (1998) JGR
Impacts Bi-directional reflectance field
Ref: Gobron et al. (1997) JGR
observation zenith angle [degree]-90 -45 0 45 90
Bi-d
irect
iona
l Ref
lect
ance
Fa
ctor
(λ=
Red
)
0.08
0.06
0.04
0.02
0.00
1-D’
1-D
sourcesensor
Hierarchy of physical scales within vegetation layer
RT model implementations:
Discrete foliage at small IFOVs (growth grammars, L-systems)
Local Scale
Tree Structural Properties
Actual trees are very complex, featuringspecies-specific patterns of:
• foliage distribution• leaf orientation• crown shape and dimensions• branch & trunk structures• growth processes
Widlowski et al., 2003, EUR Report 20855
Stochastic foliage at medium to large IFOVs (allometric relationships)
Widlowski et al., 2003, EUR Report 20855
• tree and plant species
Widlowski et al., 2003, EUR Report 20855
Canopy Structural Properties
Actual vegetation canopies includelocation-specific:
• seasonal cycles
Govaerts et al., 1997, ISPRS Symposium
Tropical Forest
dry season
rainy season
• underlying topography
500x500 m2 Gaussian hillheight: 100m
• plant spatial distributions
Deciduous tree rows in winter
All of which have an impact on the surface-leaving reflectance field.
canopy structure affects multi-angular reflectance patterns
Multi-directional surface observations
Different fractionsof soil and foliage
contribute to the surface-leavingradiation if targetarea is observedfrom different viewing angles
Largest soil fraction visible at nadir views
Spectral Contrast between Vegetation & Background
Near-Infrared
Leaf scattering dominates over soil
backscattering in the near-infrared
)( m
Ref
lect
ance
Leaf
soil
Wavelength
30o
60o
Medium
BRF shapes of Heterogeneous Canopies: NIRSparse
Dense
Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)
Leaf scattering dominates over the soil
backscatteringBowl-shape
Spectral Contrast between Vegetation & Background
Near-Infrared
Leaf scattering dominates over soil
backscattering in the near-infrared
)( m
Ref
lect
ance
Leaf
soil
Wavelength
REDSoil back-scattering dominatesover leaf scattering in the red
Medium
Sparse
Dense
Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)
30o
60o
Soil backscattering dominates over leaf
scattering
Bell-shape
BRF shapes of Heterogeneous Canopies: Red
ρ0 - controls amplitude levelk - controls bowl/bell shapeΘ - controls forward/backward scatteringρC - controls hot spot peak
BRF(z,Ω0 Ω) = ρ0 MI(k) FHG(Θ) H (ρc)
The RPV parametric model
Ref: Rahman et al. (1993) JGR
ρ0 - controls amplitude levelk - controls bowl/bell shapeΘ - controls forward/backward scatteringρC - controls hot spot peak
BRF(z,Ω0 Ω) = ρ0 MI(k) FHG(Θ) H (ρc)
The RPV parametric model
Ref: Rahman et al. (1993) JGR
BRFBRF
k=1.18
k=0.65
Bi-directional reflectance pattern may be classified as:
• ‘Bowl’ shaped for k < 1• ‘Lambertian’ for k = 1• ‘Bell’ shaped for k > 1
Bowl-shape
Bell-shape
Is the ‘shape’ of the surface-leaving BRF field affected by the 3-D characteristics of vegetation canopies at one given wavelength?
Impact of Canopy Structure on surface BRFs
Impact of Canopy Structure on surface BRFs
λ=red
SZA=30o
IFOV~275 m
350 structurally different canopy architectures
λ=red
Ref: Widlowski et al. (2004), in print, Climatic Change
SZA=30o
IFOV~275 m
1.5
1.0
0.5
Bell shape
Impact of Canopy Structure on surface BRFs
Bowl shape
kred
• Origin of 3-D signatures in reflectance fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/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 fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/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
Overview
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.
Matching surface BRFs with 1-D’ 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.
What’s the impact of the structural differences in both models?
Matching surface BRFs with 1-D’ models
Widlowski, 2001, PhD Thesis
Heterogeneous discrete canopy: 3-D
Find the 1-D’ surface that is best at mimicking the reflectance anisotropy
of a 3-D target.
-75º -50º -25º 0º +25º +50º +75º VZA
3-D reference data
BR
F
Homogeneous discrete canopy: 1-D’
Best-fitting 1-D’ solution
e
The best fitting 1-D’solution is the one with the smallest value of e
Matching surface BRFs with 1-D’ models
Widlowski et al., 2004, JGR - submitted
Find the 1-D’ surface that is best at mimicking the reflectance anisotropy
of a 3-D target.Fitting criteria: 7 BRF observationsVZA =0, 25, 45 ,60; λ=red
The best fitting 1-D’solution is the one with the smallest value of e
-75º -50º -25º 0º +25º +50º +75º VZA
3-D reference data
BR
F
Best-fitting 1-D’ solution
e
θ0 = 30o
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
λ=red
Ref: Widlowski et al. (2004), in print, Climatic Change
SZA=30o
IFOV~275 m
1.5
1.0
0.5
Bell shape
Impact of Canopy Structure on surface BRFs II
Bowl shape
kred
Structural impact on k across LAI gradient:
Ref: Pinty et al. (2002) IEEE TGRS
3-D
1-D
’
Leaf area index (LAI) increases
Impact of Canopy Structure on surface BRFs II
The 1-D’ homologue of a 3-D surface 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.
Impact of Canopy Structure on surface BRFs II
1-D’ surface representations (IPA) tend to be characterized by bowl-shaped BRF fields
At low and high vegetation coverage 3-D surfaces possess also bowl-shaped BRF fields
3-D surface representations of intermediate vegetation coverage tend to possess bell-shaped reflectance fields
Ref: Pinty et al. (2002) IEEE TGRS
3-D
1-D
’
k3-D ≥ k1-D’ if k3-D ≥ 1*
Impact of Canopy Structure on surface BRFs
Widlowski et al., 2004, JGR, submitted
A 1-D’ canopy having a quasi-identical reflectance anisotropy shape as a 3-D target is almost certainly not its homologue!
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’*
350 forest scenes
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
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*
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)
Matching surface BRFs with 1-D’ models
Ref: Widlowski et al. (2004), JGR, submitted
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)
Matching surface BRFs with 1-D’ models
Ref: Widlowski et al. (2004), JGR, submitted
1-D’ leaf normal distribution
Matching surface BRFs with 1-D’ models
Ref: Widlowski et al. (2004), JGR, submitted
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.
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)
• Origin of 3-D signatures in reflectance fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires further interpretation of state variablesGiven 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 fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires further interpretation of state variablesGiven 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
Overview
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?
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
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
• 0.5 % (1 %) of all photons in red (NIR) have d < 100m
• canopy structure controls extinction coefficient and the most likely distance, d
• multiple-scattering makes photons in NIR travel longer distances than in red
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?
zTOC
V
φ0
φ0
Ω0
S
• fluxes across sides that are perpendicular to the solar azimuth, φ0
• fluxes across sides that are parallel to φ0
Magnitude of Net Horizontal Flux Components
Widlowski et al., 2004, JGR, submitted
Red
Maximum & minimum flux across the lateral sides of voxel that are perpendicular to φ0
θ0 = 0o, 15o, 30o, 55o3D forest with 300 stem/ha
φ0
+ve values → more photons enter voxel than exit through lateral sides
absorption events inside voxel exit through other sides
-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
Widlowski et al., 2004, JGR, submitted
Red
+ve values → more photons enter voxel than exit
-ve values → more photons exit voxel than enter
θ0 = 0o, 15o, 30o, 55o3D forest with 300 stem/ha
φ0
Maximum & minimum flux across the lateral sides of voxel that are perpendicular to φ0
φ0
Maximum & minimum flux across the lateral sides of voxel that are parallel to φ0
Magnitude of Total Net Horizontal Flux
Widlowski et al., 2004, JGR, submitted
θ0 = 30o
maximum and minimum net horizontal flux into voxel
+ve values → more photons enter voxel than exit
-ve values → more photons exit voxel than enter
λ = NIR, Red
θ0 = 60o
3D forest with 300 stem/ha
φ0
maximum and minimum net horizontal flux into voxel
Impact of Net Horizontal Fluxes
Widlowski et al., 2004, JGR, submitted
Red
-5%
+5%
29m18m
31m18m
Depends on magnitude ofsurface-leaving radiation!
For sensor with BRF accuracy of 5% in red: spatial resolution > 31 mrequired for pixel-basedBRF interpretation
Since ΔFHor is larger in red than NIR, and F↑ larger inNIR than red: look at red
Tree density = 300, 600, 1200, 1800 stem/ha
θ0 = 30o
• Origin of 3-D signatures in reflectance fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires interpretation of state variablesGiven 3-D structure effective state variables can be found for 1-D’
• Spatial resolution limits for pixel-based inversionStay 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 fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires interpretation of state variablesGiven 3-D structure effective state variables can be found for 1-D’
• Spatial resolution limits for pixel-based inversionStay above 30 m for 5 % sensor accuracy
• Using ‘photon spreading’ to speed-up MC simulations of reflectance fields
Overview
Ref: Govaerts (1996) EU Report 16394 EN
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 interactions until an eventual absorption or exiting from the simulated scene occurs.
Information is subsequently extracted from ray paths: BRFi = π*Ni / N*ΔΩi
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
Improving the speed of the Raytran modelOnly 7 % (18 %) of injected rays in the red (in NIR) contribute towards estimation of surface albedo & substantially less for individual BRFs.
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.
5
4
3
2
1
Sensors / View directions
3D scene
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.
Ray escapes but not within a sensor
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.
+ P1
+ P2
+ P3
+ P4
Developing the Rayspread model
+ P1
+ P2
+ P3
+ P4
+ P5
Each sensor has already 2 (1) contribution(s)
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.
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.
n
Prsurf. Refl.()= Lambertian, specular, etc.
Pr(x,y,z,,;d) = Prsurf.Refl.() * Prtravel(x,y,z;d)
x,y,z
Developing the Rayspread model
n
x,y,z
Prtravel(x,y,z;d)=0
l
d
Prtravel(x,y,z;d)=f(l,v,M)
Mv
d
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.
Prsurf. Refl.()= Lambertian, specular, etc.
Pr(x,y,z,,;d) = Prsurf.Refl.() * Prtravel(x,y,z;d)
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:
)cos(
);,,,,Pr(phys.inter
00
din
d
lambert
dd
d
N
RBRF
dzyxR
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 = 15mnTRED= 10mn
less rays, less BRF noise
Developing the Rayspread model
RAdiation transfer Model Intercomparison exercise (RAMI)
•Rayspread Linux Cluster10 nodes (PIII 450 / 380MB Ram)
• 52 RAMI Homogeneous (Turbid and Discrete) experiments.
Speed-up roughly 100
Mean=-0.01%
Overview
• Origin of 3-D signatures in reflectance fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires interpretation of state variablesGiven 3-D structure effective state variables can be found for 1-D’
• Spatial resolution limits for pixel-based inversionStay above 30 m for 5 % sensor accuracy
• Using ‘photon spreading’ to speed-up MC simulations of reflectance fields
Speed-up by a factor of 100
• Origin of 3-D signatures in reflectance fieldshot spot effect: leaf/tree & gap sizes, spectral contrast of soil/canopybowl/bell shape: leaf/tree distribution, spectral contrast of soil/canopy
• Implications for 1-D’ RT model inversionsPure 1D’ approach requires interpretation of state variablesGiven 3-D structure effective state variables can be found for 1-D’
• Spatial resolution limits for pixel-based inversionStay above 30 m for 5 % sensor accuracy
• Using ‘photon spreading’ to speed-up MC simulations of reflectance fields
Speed-up by a factor of 100
Conclusion
THANK YOU!