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

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

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

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)

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

DRAT

DRAT

•Diffuse path

DRAT

•Direct path

Outputs• Image from viewer

• Direct/diffuse components

• Reflectance as a function of scattering order

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

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Canopy A Canopy B

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A B Leaf Single Scattering Albedo * 0.5 Soil Reflectance

• Spectral BRF/Radiance

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

RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm

Turbid medium

RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm

RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm

RAMI: Pinty et al. 2004 http://www.enamors.org/RAMI/Phase_2/phase_2.htm

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.

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

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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Diffuse: A Diffuse: B Direct: A Direct: B

Scattering ‘well-behaved’ for O(2+)

Slope of Direct ~= diffuse for O(2+)Lewis & Disney, 1998

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)

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‘recollision probability’

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Canopy B

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Can assume

To make calculation of direct+diffuse simpler

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But 1, 2 differ for direct/diffuse (obviously)

Rest of signal ‘S’ solution

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Diffuse: Thermal Time 1500 degree days Direct: Thermal Time 1500 degree days

Diffuse: Thermal Time 2100 degree days Direct: Thermal Time 2100 degree days

Rest of signal ‘S’ solution

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Total - S solution

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Canopy B

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Total - S solution

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S. solution

• Simulate = 1 s = 1 and subtract B.S. solution and 1st O soil-only interaction (1)

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Or more accurate if include s2 term as well

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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

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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)

y = 1.0134x

R2 = 0.9741

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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

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

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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AF F *

Microwave modelling

● Need to treat carefully:– 3-d extinction

● esp for discontinuous forest canopies– leaf curvature

● esp for cereal crops

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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