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Monte Carlo Ray Tracingfor understanding Canopy Scattering
P. Lewis1,2, M. Disney1,2, J. Hillier1, J. Watt1, P. Saich1,2
1. University College London
2. NERC Centre for Terrestrial Carbon Dynamics
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Motivation: 4D plant modelling and numerical scattering simulation
● Model development– Develop understanding of canopy scattering mechanisms
● in arbitrarily complex scenes– Develop and test simpler models
● Inversion constraint– Expected development of ‘structure’ over time
● Synergy– Structure links optical and microwave
● Sensor simulation– Simulate new sensors
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Wheat Dynamic Model Developed by INRA
• ADEL-wheat
• Winter wheat (cv Soisson)
• Developed by:– monitoring development
and organ extension at two densities
– Characterising plant 3D geometry
• Driven by thermal time since planting
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Wheat Model Development:collaboration with B. Andrieu and C. Fournier
• 2004 Experiments– Test parameterisation– Develop senescence
function– Varietal study
• 2005 Experiments– Radiometric validation
Also Tree dynamic modelTreeGrow (R. Leersnijder)
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Simulation Tools: drat: Monte Carlo Ray Tracer
● Inverse ray tracer● previously called ararat
– Advanced RAdiometric Ray Tracer● Requires specification of location of primitives● Multiple object instances from cloning
– Shoot cloning on trees● Includes ‘volumetric’ primatives
– Turbid medium
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DRAT
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DRAT
•Diffuse path
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DRAT
•Direct path
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Outputs• Image from viewer
• Direct/diffuse components
• Reflectance as a function of scattering order
• First-Order Sunlit/Shaded per material’• Distance-resolved (LiDAR)
0.0001
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scattering order
co
ntr
ibu
tio
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o r
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ec
tan
ce
Canopy A Canopy B
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scattering order
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o r
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Diffuse: A Diffuse: B Direct: A Direct: B
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ecti
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eric
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ctan
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A B Leaf Single Scattering Albedo * 0.5 Soil Reflectance
• Spectral BRF/Radiance
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An alternative: Forward Ray Tracing
● E.g. Raytran● Can have same output information● Trace photon trajectories from illumination
– to all output directions● Much slower to simulate BRDF
– In fact, requires finite angular bin for simulations● Likely same speed for simulation at all view
angles
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RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm
Turbid medium
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RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm
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RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm
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RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm
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RAMI model intercomparison
● Extremely useful to community– Test of implementation– Comparison of models
● Similar results for homogeneous canopies● Some significant variations between models
– Even between numerical models for heterogeneous scenes– Partly due to specificity of geometric representations
● E.g. high spatial resolution simulations● RAMI 3 preparations under way
– Led by Pinty et al.
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A) 1500 odays B) 2000 odays
LAI 1.4 and 6.4canopy cover 51% and 97%
solar zenith angle 35o
view zenith angle 0o
How can we use numerical model solution to ‘understand’ signal?
Decouple ‘structural’ effects from material ‘spectral’ properties
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Lumped parameter modelling
● Assume:– Scattering from leaves with s.s. albedo – soil with Lambertian reflectance s
● Examine ‘black soil’ scattering for non-absortive canopy– = 1
– s = 0
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0.00001
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scattering order
co
ntr
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tio
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o r
efl
ec
tan
ce
Diffuse: A Diffuse: B Direct: A Direct: B
Scattering ‘well-behaved’ for O(2+)
Slope of Direct ~= diffuse for O(2+)Lewis & Disney, 1998
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B.S. solution
• Similar to Knyazikhin et al., (1998)
• Can model as:
• Where:
• N.B. is ‘p’ term in Knyazikhin et al. (1998) etc. and Smolander & Stenberg (2005)
1
22
1bs
2
3
Obs
Obs
‘recollision probability’
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0
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Thermal Time / degree days
se
mi-
em
pir
ica
l mo
de
l pa
ram
ete
rs
cover 1-exp(-LAI/2)
1
22
1bs
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-0.05
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wavelength / nm
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ecta
nce
Diffuse: A Diffuse: A (approx) Diffuse: A: difference*100
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wavelength / nm
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fle
cta
nc
e
Diffuse: B Diffuse: B (approx) Diffuse: B: difference
Canopy A
Canopy B
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-0.05
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wavelength / nm
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ec
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ce
Direct A Direct A (approx) Direct A: difference*10
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ec
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Direct B Direct B (approx) Direct B: difference
Can assume
To make calculation of direct+diffuse simpler
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1bs
Diffuse
Direct
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1bs
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thermal time / degree days
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direct directdiffusediffuse
But 1, 2 differ for direct/diffuse (obviously)
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Rest of signal ‘S’ solution
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scattering order
log
(co
ntr
ibu
tio
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o r
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ec
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ce
)
Diffuse: Thermal Time 1500 degree days Direct: Thermal Time 1500 degree days
Diffuse: Thermal Time 2100 degree days Direct: Thermal Time 2100 degree days
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Rest of signal ‘S’ solution
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wavelength / nm
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fle
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nc
e
Total - S solution
1st Order
2nd Order
3rd Order
4th+ Order
Total
Canopy A
Canopy B
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fle
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nc
e
Total - S solution
1st Order
2nd Order
3rd Order
4th+ Order
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S. solution
• Simulate = 1 s = 1 and subtract B.S. solution and 1st O soil-only interaction (1)
12s
rest
2
3
OS
OS
Or more accurate if include s2 term as well
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Thermal Time / degree days
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rs
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Diffuse B Direct B Diffuse B (approx) Direct B (approx)
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Diffuse A Direct A Diffuse A (approx) Direct A (approx)
Canopy A
Canopy B
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Summary
● Can simulate for = 1 s = 0 – BS solution
● And for = 1 s = 1– S solution
● Simple parametric model:
– Or include higher order soil interactions● Use 3D dynamic model to study lumped parameter terms
– And to facilitate inversion for arbitrary , s
112
22
11s
scanopy
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Inversion● Using lumped parameterisation of CR:
– ADEL-wheat simulations at 100oday intervals● Structure as a fn. of thermal time
– Optical simulations● LUT of lumped parameter terms
● Data: – 3 airborne EO datasets over Vine Farm, Cambridgeshire, UK (2002)– ASIA (11 channels) + ESAR sensor
● Other unknowns– PROSPECT-REDUX for leaf– Price soil spectral PCs
● LUT inversion – Solve for equivalent thermal time and leaf/soil parameters– Constrained by thermal time interval of observations
● +/- tolerance (100odays)
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y = 1.0134x
R2 = 0.9741
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modelled
mea
sure
d
46 Acres (plots 1-3) Linear (46 Acres (plots 1-3))
• Able to simulate mean field reflectance scattering using drat/CASM/ADEL-wheat
• Reasonable match against expected thermal time
• Processing comparisons with generalised field measures now
• Similar inversion results for optical and microwave
• so can use either
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Summary
● 4D models provide structural expectation● Can use for optical and/or microwave● Compare solutions via model intercomparison
– RAMI● Can simulate canopy reflectance via simple
parametric model– Thence inversion
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Example: Closed Sitka forest
1
lcanopy
l
a
c
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Example: Closed Sitka forest BRF
1
lcanopy
l
a
c
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Microwave modelling
● Existing coherent scattering model (CASM)– add single scattering amplitudes with appropriate phase
terms
– then ‘square’ to determine backscattering coefficient
– Attenuation based requires approximations
F f eji k r
j
i j
( ).2
4
AF F *
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Microwave modelling
● Need to treat carefully:– 3-d extinction
● esp for discontinuous forest canopies– leaf curvature
● esp for cereal crops
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ERS-2 comparisonUsing ADEL-wheat/CASM
Two roughness values (s = 0.003 and 0.005)
Note sensitivity to soil in early season but later in the season the gross features of the temporal profile are similar
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Canopy Cover Proportion
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el p
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ters
1-exp(-LAI/2)