A Coupled Leaf/Canopy Turbid Medium Radiative Transfer Model Barry D. Ganapol

1. A Coupled Leaf/Canopy Turbid Medium Radiative Transfer Model Barry D. Ganapol Departments of Hydrology and Water Resources and Aerospace and Mechanical Engineering University of Arizona 520/621-4728 ganapol@cowboy.ame.arizona.edu Presented 9/12/04 at The Granlibakken Transport Invitational

2. Fundamental science issue? Light is transmitted through the atmosphere and reflected from vegetation canopy elements and background to an air or space borne sensor. reliably ^ Can the reflected information be interpreted through the vegetation canopy reflectance?

3. nRole of vegetation-- in the global climate + primary mechanism for exchange of atmospheric O2 and CO2 + conversion of energy fluxes to photosynthetic activity + source of nutrient production in tactical military operations + CC&D nRole of canopy reflectance (CR) modeling + to interpret remotely sensed observations of vegetation canopies + to estimate canopy biophysical parameters

4. What social implications will the reliable interpretation of reflected information from foliage have? n Basic Science + Photosynthesis + Establish ecological principles n Precision Agriculture + Improved crop yield + Improved crop management n Global climate change prediction + Terrestrial surface reflectance + GCM verification and validation nPrecision Battlefield Engagement (PBE) + Warfighter asset management + Adversary asset strength and location

5. General CR Modeling Considerations nVegetation signatures: + Spectral l: Wavelength response of canopy element (Rf, Tn, Ab) + Spatial (x,y): arrangement of scattering objects within canopy + Temporal (t): intra- and inter- annual variability + Directional (W): anisotropy resulting from surface roughness + Polarization: (Q): polarized state of surface reflected photons nFactors influencing reflectance: + size, shape and distribution of canopy phytoelements + biophysical parameters: Leaf Area Index (LAI) fAPAR leaf optical properties Leaf Angle Distribution (LAD)

6. Overview of Canopy Reflectance Modeling • Empirical Models + Canopy viewed as a rough surface • + Fit surface scattering effect to observed data • -- Lambertian reflection -- Walthall Model + Limited range of application + Lacks physical insight

7. nPhysically-based First Principle Models + Turbid medium - Application of Radiative Transfer (RT) theory for participating media (Green- gas model) - Requires additional continuum and far field assumptions - Contrast of discrete nature of scattering centers and RT description + Shadowing not part of model + Best for dense canopies - Will feature LCM2

8. + Geometric-optic (GO) Models - Canopy treated as an assemblage of vegetation-filled 3D objects - RT within assemblages/Shadowing in-between - Pixel becomes a mix of sun-lit and shaded elements

9. Computer Simulation Models • + Radiosity • - From heat transfer - Plates "see" scattering areas - More computationally intensive than ray tracing

10. + Ray Tracing - Volume rendering of a scene • - Also computationally expensive • Inversion virtually impossible • - Can generate exceptional results

11. Example BPMS Simulation by Lewis and Disney RAMI (RAdiation Transfer Model Intercomparison) Exercise ‘01 + Determine strengths and weaknesses of CR models + Ray tracing most flexible + Botanical Plant Modeling System (BPMS) most effective

12. Presentation: n Focus on turbid medium model LCM2 m Describe the microscopic leaf radiative transfer model m Describe the macroscopic leaf radiative transfer model in the canopy mLCM2Polarization (LCM2P) algorithm n Demonstrate application of LCM2

13. Radiative Transfer (RT) considerations: + Intra-leaf + Inter-leaf scattering and absorption General Turbid Medium Canopy Modeling Considerations Elements of a canopy reflectance model + Phytoelements Broadleaves Needleleaves + Leaf canopy Complicated participating medium + Not a well posed RT problem + Ignorant of biophysical properties and configurations + Must rely on natural averaging and a little luck

14. cuticular wax Palisade Parenchyma Chlorophylls Vein Carotenoid Pigments Anthocyain Pigments cuticular wax Spongy Mesophyll Typical anatomical structure of a leaf Leaf Scattering + Air-epicuticular wax interface (upper epidermis) - thin wax film - multilayered membrane of pectin, cellulose, cutin and wax + Palisade Parenchyma + Spongy Mesophyll + Epicuticular wax -air interface (lower epidermis)

15. S = Ss+Sa DL = dLS n Leaf Scattering Phase Function (Microscopic) + Microscopic leaf radiative transfer dL

16. Solution by Siewert’s FN Method BRDF DH-R Isotropic Scattering Assumed DL DH-T BRTF Required data: -- the scattering and absorption coefficients

17. + Calibration of leaf scattering coefficient LOPEX Leaf Data Set Reference leaf Database of leaf HHr and t Leaves of interest HH-R and HH-T: For an isotropic source

18. Chlorotic maple rch = 0.5 x 38.8 mg/cm2 and Water Stressed maple rw =0.5 x 0.723 gm/cm3 and Example: Consider a nominal maple canopy dL = 1.34mm rw = 0.723 gm/cm3 rch = 38.8 mg/cm2 Plus protein and cellulose and lignin Representative maple leaf from LOPEX dL= 0.94mm

20. macro Leaf micro Leaf Angle Distribution (LAD) + Macroscopic diffuse leaf radiative transfer model Leaf: Bi-Lambertian diffuse surface phase function Area scattering phase function (2-angle)

21. Area scattering phase function (1-angle) For HH- Reflectance and Transmittance Quadrature approximation

22. g g Air-leaf cuticular layer interfacial surface nLeaf phase function for specular reflectionand polarization + Specular reflection Fresnel Formula Two-angle: One-angle:

23. + Phase function for the linearly polarized component -- Experimental evidence indicates that polarization originates predominately at the leaf surface from specular reflection. (V2) -- Use the vector transport equation to describe the intensity and the linearly polarized component.

24. Intensity: Second Stokes Component: Phase Function: Phase function for the linearly polarized component: the mathematical model

25. Uncollided component: Intercept function: The Radiative Transport Algorithm with Leaf Polarization nThe Vector Transport Equation +BC Collided component: Degree of polarization of Target

26. tj h tj+1 Discretized spatial domain n The SN/Romberg Algorithm for Intensity Sweep - Sweep + Discretizations: Romberg iteration:

27. n Numerical implementation and convergence Evaluation of area scattering phase functions Iteration Strategy-- (1) Increment SN order and quadrature order Lmc (2) Perform SN sweeps to convergence (3) Monitor reflectance and transmittance for both components (4) Apply Wynn-epsilon acceleration (5) Go to (1) until (4) converges

29. Rf RfQ

30. LCM2 IPA mode

39. f Dp0 R

41. UAV FOR PRECISION AGRICULTURE: • UAV: Unmanned Aerial Vehicle (Air Tower) • Helios and Pathfinder plus prototypes • NASA technology transfer concept • New way of doing agriculture

42. Multiple Neural Networks Decision Block DPT Block Field Image Minimum distance comparison NN 1 NN 1 NN 1 NN 27 Neural Network archive 27 networks stored Cherries % Under-Ripe Mask Ripe Over-Ripe Multiple NNs and DPT Coupled Algorithm

43. 408 410 406 Processing the UAV images: Fields and Blocks

44. NN prediction vs Parchment data & Branch Count

45. NN Ripeness Prediction Maps: Field 408 Block 4

46. The future challenges in CR Modeling + 3D canopy transport formulations + Parallel implementation of transport algorithms + Effective inversion strategies + Establishment of leaf optical property libraries + Integration of stochastic leaf transport with fractal canopy transport + Fusion of long/short wave modalities + Integration of CR information into the hydrologic/biogeochemical/climatological cycle