1 / 37

Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 2

Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 2. UoL MSc Remote Sensing Dr Lewis plewis@geog.ucl.ac.uk. Radiative Transfer equation. Used extensively for (optical) vegetation since 1960s (Ross, 1981) Used for microwave vegetation since 1980s.

harlan
Télécharger la présentation

Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 2 UoL MSc Remote Sensing Dr Lewis plewis@geog.ucl.ac.uk

  2. Radiative Transfer equation • Used extensively for (optical) vegetation since 1960s (Ross, 1981) • Used for microwave vegetation since 1980s

  3. Radiative Transfer equation • Consider energy balance across elemental volume • Generally use scalar form (SRT) in optical • Generally use vector form (VRT) for microwave

  4. Medium 1: air z = l cos q0=lm0 q0 Medium 2: canopy in air z Pathlength l Medium 3:soil Path of radiation

  5. Scalar Radiative Transfer Equation • 1-D scalar radiative transfer (SRT) equation • for a plane parallel medium (air) embedded with a low density of small scatterers • change in specific Intensity (Radiance) I(z,W) at depth z in direction W wrt z:

  6. Scalar RT Equation • Source Function: • m - cosine of the direction vector (W) with the local normal • accounts for path length through the canopy • ke - volume extinction coefficient • P() is the volume scattering phase function

  7. Extinction Coefficient and Beers Law • Volume extinction coefficient: • ‘total interaction cross section’ • ‘extinction loss’ • ‘number of interactions’ per unit length • a measure of attenuation of radiation in a canopy (or other medium). Beer’s Law

  8. No source version of SRT eqn Extinction Coefficient and Beers Law

  9. Optical Extinction Coefficient for Oriented Leaves • Volume extinction coefficient: • ul : leaf area density • Area of leaves per unit volume • Gl : (Ross) projection function

  10. Optical Extinction Coefficient for Oriented Leaves

  11. Optical Extinction Coefficient for Oriented Leaves • range of G-functions small (0.3-0.8) and smoother than leaf inclination distributions; • planophile canopies, G-function is high (>0.5) for low zenith and low (<0.5) for high zenith; • converse true for erectophile canopies; • G-function always close to 0.5 between 50o and 60o • essentially invariant at 0.5 over different leaf angle distributions at 57.5o.

  12. Optical Extinction Coefficient for Oriented Leaves • so, radiation at bottom of canopy for spherical: • for horizontal:

  13. A Scalar Radiative Transfer Solution • Attempt similar first Order Scattering solution • in optical, consider total number of interactions • with leaves + soil • Already have extinction coefficient:

  14. SRT • Phase function: • ul - leaf area density; • m’ - cosine of the incident zenith angle •  - area scattering phase function.

  15. SRT • Area scattering phase function: • double projection, modulated by spectral terms • l : leaf single scattering albedo • Probability of radiation being scattered rather than absorbed at leaf level • Function of wavelength

  16. SRT

  17. SRT: 1st O mechanisms • through canopy, reflected from soil & back through canopy

  18. SRT: 1st O mechanisms Canopy only scattering Direct function of w Function of gl, L, and viewing and illumination angles

  19. 1st O SRT • Special case of spherical leaf angle:

  20. Multiple Scattering Contributions to reflectance and transmittance Scattering order LAI 1

  21. Multiple Scattering Contributions to reflectance and transmittance Scattering order LAI 5

  22. Multiple Scattering Contributions to reflectance and transmittance Scattering order LAI 8

  23. Multiple Scattering • range of approximate solutions available • Recent advances using concept of recollision probability, p • Huang et al. 2007

  24. i0=1-Q0 s i0 p Q0 s1=i0w(1 – p) p: recollision probability w: single scattering albedo of leaf

  25. 2nd Order scattering: i0 w2i0 p(1-p) wi0 p

  26. ‘single scattering albedo’ of canopy

  27. Average number of photon interactions: The degree of multiple scattering Absorptance p: recollision probability Knyazikhin et al. (1998): p is eigenvalue of RT equation Depends on structure only

  28. For canopy: Spherical leaf angle distribution pmax=0.88, k=0.7, b=0.75 Smolander & Stenberg RSE 2005

  29. Clumping Canopy with ‘shoots’ as fundamental scattering objects:

  30. Canopy with ‘shoots’ as fundamental scattering objects:

  31. pshoot=0.47 (scots pine) p2<pcanopy Shoot-scale clumping reduces apparent LAI pcanopy p2 Smolander & Stenberg RSE 2005

  32. Other RT Modifications • Hot Spot • joint gap probabilty: Q • For far-field objects, treat incident & exitant gap probabilities independently • product of two Beer’s Law terms

  33. RT Modifications • Consider retro-reflection direction: • assuming independent: • But should be:

  34. RT Modifications • Consider retro-reflection direction: • But should be: • as ‘have already travelled path’ • so need to apply corrections for Q in RT • e.g.

  35. RT Modifications • As result of finite object size, hot spot has angular width • depends on ‘roughness’ • leaf size / canopy height (Kuusk) • similar for soils • Also consider shadowing/shadow hiding

  36. Summary • SRT formulation • extinction • scattering (source function) • Beer’s Law • exponential attenuation • rate - extinction coefficient • LAI x G-function for optical

  37. Summary • SRT 1st O solution • use area scattering phase function • simple solution for spherical leaf angle • 2 scattering mechanisms • Multiple scattering • Recollison probability • Modification to SRT: • hot spot at optical

More Related