Monte Carlo Ray Tracing for understanding Canopy Scattering P. Lewis 1,2, M. Disney 1,2, J. Hillier 1, J. Watt 1, P. Saich 1,2 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 model TreeGrow (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

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) 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 Turbid medium

RAMI: Pinty et al

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 o daysB) 2000 o days LAI 1.4 and 6.4 canopy cover 51% and 97% solar zenith angle 35 o view zenith angle 0 o 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

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) ‘recollision probability’

cover1-exp(-LAI/2)

Canopy A Canopy B

Can assume To make calculation of direct+diffuse simpler Diffuse Direct

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

Rest of signal ‘S’ solution

Canopy A Canopy B

S. solution Simulate  = 1  s = 1 and subtract B.S. solution and 1 st O soil-only interaction (  1 ) Or more accurate if include  s 2 term as well

Canopy A Canopy B

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

Inversion ● Using lumped parameterisation of CR: – ADEL-wheat simulations at 100 o day 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 (100 o days)

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

Example: Closed Sitka forest BRF

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

Microwave modelling ● Need to treat carefully: – 3-d extinction ● esp for discontinuous forest canopies – leaf curvature ● esp for cereal crops

ERS-2 comparison Using ADEL- wheat/CASM Two roughness values (s = and 0.005) Note sensitivity to soil in early season but later in the season the gross features of the temporal profile are similar

1-exp(-LAI/2)