Monte Carlo Ray Tracing for understanding Canopy Scattering P. Lewis1,2, M. Disney1,2, J. Hillier1, J. Watt1, P. Saich1,2

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Monte Carlo Ray Tracingfor understanding Canopy
ScatteringP. 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 Developmentcollaboration with B.
Andrieu and C. Fournier

• 2004 Experiments
• Test parameterisation
• Develop senescence function
• Varietal study
• 2005 Experiments
• Radiometric validation

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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

• Spectral BRF/Radiance

• Reflectance as a function of scattering order

• Direct/diffuse components

• First-Order Sunlit/Shaded per material
• Distance-resolved (LiDAR)

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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/RAM
I/Phase_2/phase_2.htm
Turbid medium
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RAMI Pinty et al. 2004 http//www.enamors.org/RAM
I/Phase_2/phase_2.htm
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RAMI Pinty et al. 2004 http//www.enamors.org/RAM
I/Phase_2/phase_2.htm
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RAMI Pinty et al. 2004 http//www.enamors.org/RAM
I/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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How can we use numerical model solution to
understand signal? Decouple structural
effects from material spectral properties
LAI 1.4 and 6.4 canopy cover 51 and 97 solar
zenith angle 35o view zenith angle 0o
A) 1500 odays
B) 2000 odays
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Lumped parameter modelling

• Assume
• Scattering from leaves with s.s. albedo w
• soil with Lambertian reflectance rs
• Examine black soil scattering for non-absortive
  canopy
• w 1
• rs 0

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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. a is p term in Knyazikhin et al. (1998)
  etc. and Smolander Stenberg (2005)

recollision probability
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Canopy A
Canopy B
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Can assume To make calculation of directdiffuse
simpler
Diffuse
Direct
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direct
direct
diffuse
diffuse
But a1, a2 differ for direct/diffuse (obviously)
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Rest of signal S solution
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Rest of signal S solution
Canopy A
Canopy B
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S. solution

• Simulate w 1 rs 1 and subtract B.S. solution
  and 1st O soil-only interaction (b1)

Or more accurate if include wrs2 term as well
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Canopy A
Canopy B
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Summary

• Can simulate for w 1 rs 0
• BS solution
• And for w 1 rs 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 w , rs
  

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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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• 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
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Example Closed Sitka forest BRF
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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

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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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1-exp(-LAI/2)