University College London NERC Centre for Terrestrial Carbon Dynamics

1. Monte Carlo Ray Tracingfor understanding Canopy ScatteringP. Lewis1,2, M. Disney1,2, J. Hillier1, J. Watt1, P. Saich1,2 • University College London • NERC Centre for Terrestrial Carbon Dynamics

2. 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

3. 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

4. Also Tree dynamic model • TreeGrow (R. Leersnijder) Wheat Model Development:collaboration with B. Andrieu and C. Fournier • 2004 Experiments • Test parameterisation • Develop senescence function • Varietal study • 2005 Experiments • Radiometric validation

5. 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

6. DRAT

7. DRAT Diffuse path

8. DRAT Direct path

9. Outputs • Spectral BRF/Radiance • Image from viewer • Reflectance as a function of scattering order • Direct/diffuse components • First-Order Sunlit/Shaded per material’ • Distance-resolved (LiDAR)

10. 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

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

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

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

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

16. 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.

17. 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

18. 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

19. Scattering ‘well-behaved’ for O(2+) Slope of Direct ~= diffuse for O(2+) Lewis & Disney, 1998

20. 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’

21. cover 1-exp(-LAI/2)

22. Canopy A Canopy B

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

24. diffuse diffuse direct direct But a1, a2 differ for direct/diffuse (obviously)

25. Rest of signal ‘S’ solution

26. Rest of signal ‘S’ solution Canopy A Canopy B

27. 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

29. Canopy A Canopy B

30. 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

31. 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)

32. 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

33. 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

35. Example: Closed Sitka forest

36. Example: Closed Sitka forest BRF

37. 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

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

39. 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

40. 1-exp(-LAI/2)