Transcript No Slide Title

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
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
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
R
zTOC
At the bottom of the canopy, z0
• Background albedo is not zero.
• Magnitude is depending on
wavelength: Quasi-monotonic
increase in visible & NIR.
• Directionality of the upward
reflected
radiation is anisotropic.
Ref: Govaerts, PhD Thesis, 1996
A
T (1- α)
z0
Leaf Optical Properties
Ω
• Leaf reflection and transmission
depend primarily on wavelength,
plant species, growth condition,
age and position in canopy.
• Directionality of leaf scattering
depends on the leaf surface
roughness, and the percentage
of diffusely scattered photons
from leaf interior.
ΩL
Ω
plate model
Plate models often assume Bi-Lambertian scattering properties:
Dicotyledon
leaf: 3-D tissue
representation
- radiation
is scattered
according to cosine law: | ΩL · Ω |
- magnitude depends on leaf reflection and transmission values

Ref: Govaerts
et al. 1981
(1995) IEEE IGARS’95
Ref: Ross,
Foliage Structural Properties III
Vegetation 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
Foliage Structural Properties III
In vegetation canopies the extinction coefficient is directionally
variant but wavelength independent.
For a volume of oriented, point-like
scatterers (1-D or turbid medium):
σe(z, Ω) = Λ(z) · G(Ω)
• leaf area density [m2 / m3]
• leaf cross-section along Ω
BUT
Ω
Ω0
Ω = Ω0
Turbid canopy representation: 1-D
Finite size of scatterer introduces:
mutual
shading
enhanced retro-reflection
Hot-spot effect
illuminated leaf
http://academic.emporia.edu/aberjame/remote/lec10/lec10.htm
Discrete
canopy representation:
(i.e., Heiligenschein,
opposition
effect) 1-D’
Ref: Verstraete et al. (1990) JGR
Foliage Structural Properties III
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
Impacts Bi-directional reflectance field
source
sensor
Bi-directional Reflectance Factor (λ= Red)
Extinction coefficient is wavelength independent, but directionally
variant.
Ω
Ω0
0.08
1-D’
0.06
0.04
0.02
1-D
0.00
-90
-45
0
45
illuminated
leaf
observation zenith angle [degree]
Hierarchy ofRef:physical
scales
Pinty et al. (1997)
JAS within vegetation layer
Knyazikhin et al. (1998) JGR
Ref: Gobron et al. (1997) JGR
90
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
RT model implementations:

Discrete foliage at small IFOVs
Local Scale
(growth grammars, L-systems)

Stochastic foliage at medium to
large IFOVs (allometric relationships)
Widlowski et al., 2003, EUR Report 20855
Canopy Structural Properties
Actual vegetation canopies include 500x500 m2
rainy
location-specific:
season
Gaussian hill
height: 100m
• tree and plant species
• seasonal cycles
• underlying topography
• plant spatial distributions
All of which have an impact on the
surface-leaving reflectance field.
Tropical Forest
dry
season
Deciduous tree rows in winter
canopy structure affects
multi-angular reflectance patterns
Widlowski et al., 2003, EUR Report 20855
Govaerts
Widlowski
et et
al.,al.,
1997,
2003,
ISPRS
EUR Symposium
Report 20855
Multi-directional surface observations
Largest soil
fraction visible
at nadir views
Different fractions
of soil and foliage
contribute to the
surface-leaving
radiation if target
area is observed
from different
viewing angles
Spectral Contrast between Vegetation & Background
Near-Infrared
Leaf
soil
Reflectance
Leaf scattering
dominates over soil
backscattering in the
near-infrared
 ( m)
Wavelength
BRF shapes of Heterogeneous Canopies: NIR
Sparse
30o
60o
Bowl-shape
Leaf scattering
dominates over the soil
backscattering
Dense
Medium
Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)
Spectral Contrast between Vegetation & Background
RED
Near-Infrared
Soil backscattering
dominates
over leaf
scattering
in the red
Leaf
soil
Reflectance
Leaf scattering
dominates over soil
backscattering in the
near-infrared
 ( m)
Wavelength
BRF shapes of Heterogeneous Canopies: Red
Sparse
30o
60o
Bell-shape
Soil backscattering
dominates over leaf
scattering
Dense
Medium
Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)
The RPV parametric model
BRF(z,Ω0
Ω) = ρ0 MI(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
The
RPV parametric
model
Impact of
Canopy
Structure on
surface BRFs
BRF(z,Ω0
Ω) = ρ0 MI(k) FHG(Θ) H (ρc)
Is theρ ‘shape’
of
the
surface-leaving
BRF
field
- controls amplitude level
affected
by the bowl/bell
3-D characteristics
of vegetation
k - controls
shape
canopies
at oneforward/backward
given wavelength?
Θ - controls
scattering
0
ρC - controls hot spot peak
BRF
Bowl-shape
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
Ref: Rahman et al. (1993) JGR
BRF
k=1.18
Bell-shape
Impact of Canopy Structure on surface BRFs
SZA=30o
λ=red
IFOV~275 m
350 structurally
different canopy
architectures
Impact of Canopy Structure on surface BRFs
Bell shape
1.5
kred
SZA=30o
λ=red
IFOV~275 m
1.0
0.5
Bowl shape
Ref: Widlowski et al. (2004),
in print, Climatic Change
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
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.
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.
The best fitting 1-D’solution is the
one with the smallest value of e
Heterogeneous discrete canopy: 3-D
Best-fitting 1-D’ solution
3-D reference data
BRF
e
Homogeneous discrete canopy: 1-D’
-75º
-50º
-25º
0º
+25º
+50º
+75º
VZA
Widlowski, 2001, PhD Thesis
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
The best fitting 1-D’solution is the
one with the smallest value of e
BRF
e
Best-fitting 1-D’ solution
3-D reference data
-75º
-50º
-25º
0º
+25º
+50º
+75º
VZA
Widlowski et al., 2004, JGR - submitted
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
Impact of Canopy Structure on surface BRFs II
Bell shape
1.5
Structural
impact on k
across LAI
gradient:
kred
SZA=30o
λ=red
1.0
IFOV~275 m
0.5
Bowl shape
Ref: Widlowski et al. (2004),
in print, Climatic Change
Impact of Canopy Structure on surface BRFs II
3-D
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.
Leaf area index
(LAI) increases
1-D’
Ref: Pinty et al. (2002) IEEE TGRS
Impact of Canopy Structure on surface BRFs II
3-D
3-D surface representations
of intermediate vegetation
coverage tend to possess
bell-shaped reflectance fields
At low and high vegetation
coverage 3-D surfaces possess
also bowl-shaped BRF fields
1-D’ surface representations
(IPA) tend to be characterized
by bowl-shaped BRF fields
*
k3-D ≥ k1-D’
if k3-D ≥ 1
1-D’
Ref: Pinty et al. (2002) IEEE TGRS
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 ≠ k*1-D’
A 1-D’ canopy having a quasiidentical reflectance anisotropy
shape as a 3-D target is almost
certainly not its homologue!
Widlowski et al., 2004, JGR, submitted
Matching surface BRFs with 1-D’ models
3-D surface targets tend to
exhibit enhanced bellshaped BRF patterns wrt.
their 1-D’ homologues:
 higher nadir BRFs
 lower BRFs at large VZA
*
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
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
Matching surface BRFs with 1-D’ models
1-D’ leaf normal distribution
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
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.
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: Widlowski et al. (2004), JGR, submitted
Ref: Pinty et al. (2004) JGR-Atmosphere (submitted)
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
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?
• canopy structure controls
extinction coefficient and
the most likely distance, d
• 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
Red - NIR
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?
• fluxes across sides that
are perpendicular to the
solar azimuth, φ0
φ0
Ω0
φ0
zTOC
• fluxes across sides that
are parallel to φ0
V
S
Magnitude of Net Horizontal Flux Components
Red
Maximum & minimum flux across
the lateral sides of voxel that are
perpendicular to φ0
+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
3D forest with 300 stem/ha
θ0 = 0o, 15o, 30o, 55o
Widlowski et al., 2004, JGR, submitted
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
φ0
φ0
+ve values → more photons
enter voxel than exit
-ve values → more photons
exit voxel than enter
3D forest with 300 stem/ha
θ0 = 0o, 15o, 30o, 55o
Widlowski et al., 2004, JGR, submitted
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
φ0
+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
Impact of Net Horizontal Fluxes
Depends on magnitude of
surface-leaving radiation!
Red
18m
31m
Since ΔFHor is larger in red
than NIR, and F↑ larger in
NIR than red: look at red
For sensor with BRF
accuracy of 5% in red:
spatial resolution > 31 m
required for pixel-based
BRF interpretation
θ0 = 30o
+5%
-5%
18m
29m
Tree density = 300, 600, 1200, 1800 stem/ha
Widlowski et al., 2004, JGR, submitted
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
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
Ref: Govaerts (1996) EU Report 16394 EN
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
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.
Ray escapes but not within a sensor
3
2
1
4
Sensors / View directions
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 interactions is calculated and added to its radiance counter.
+ P3
+ P2
+ P1
+ P4
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.
+ P3
+ P2
+ P1
+ P4
+ P5
Each sensor has already 2 (1) contribution(s)
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.
Pr(x,y,z,q0,f0;d) = Prsurf.Refl.(q0,f0;q1,f1) * Prtravel(x,y,z;d)
n
q0
q1
x,y,z
Prsurf. Refl.(q0,f0;q1,f1)= Lambertian, specular, etc.
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.
Pr(x,y,z,q0,f0;d) = Prsurf.Refl.(q0,f0;q1,f1) * Prtravel(x,y,z;d)
n
q0
Prsurf. Refl.(q0,f0;q1,f1)= Lambertian, specular, etc.
d
d
q1
l
v
M
x,y,z
Prtravel(x,y,z;d)=0
Prtravel(x,y,z;d)=f(l,v,M)
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:
Rd 
 P r(x, y, z,q
0
, f0 ; d )
phys.inter
d
Rd
BRFd 

 lambert
N in cos(q d )
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
less rays, less BRF noise
Developing the Rayspread model
RAdiation transfer Model Intercomparison exercise (RAMI)
Mean=-0.01%
•Rayspread Linux Cluster
10 nodes (PIII 450 / 380MB Ram)
• 52 RAMI Homogeneous
(Turbid and Discrete) experiments.
Speed-up roughly 100
Overview
Conclusion
• 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
 Speed-up by a factor of 100
THANK YOU!