University College London NERC Centre for Terrestrial Carbon Dynamics

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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scanopy

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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