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, 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




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)


• tree and plant species


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


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


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


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








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?


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


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


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


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.


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*


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


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’ leaf normal distribution



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



• 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’




• 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’



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


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


• 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


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


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


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


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


• 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






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



Ray escapes but not within a sensor





+ P1

+ P2

+ P3

+ P4


+ P1

+ P2

+ P3

+ P4

+ P5

Each sensor has already 2 (1) contribution(s)




laverth

HERE talk about the absorbed rays





n

Prsurf. Refl.()= Lambertian, specular, etc.

Pr(x,y,z,,;d) = Prsurf.Refl.() * Prtravel(x,y,z;d)

x,y,z


n

x,y,z

Prtravel(x,y,z;d)=0

l

d

Prtravel(x,y,z;d)=f(l,v,M)

Mv

d




Prsurf. Refl.()= Lambertian, specular, etc.

Pr(x,y,z,,;d) = Prsurf.Refl.() * Prtravel(x,y,z;d)

laverth

Direct transmission through medium M





On the sensor’s side:

)cos(

);,,,,Pr(phys.inter

00

din

d

lambert

dd

d

N

RBRF

dzyxR


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

laverth

speed_up nir = 6%speed_up red =


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





Speed-up by a factor of 100





Speed-up by a factor of 100

Conclusion

THANK YOU!

assessing the impact of structural effects on the radiative signature of vegetation

Documents

d signatures

d medium

vegetation canopiesconditioned

impact of structural

dominatesover leaf scattering

surface brfs

wavelength independent

different canopy ar