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

6. Aim of this section Introduce RT approach as basis to understanding optical and microwave vegetation response enable use of models enable access to literature

7. Scope of this section Introduction to background theory –RT theory –Wave propagation and polarisation –Useful tools for developing RT Building blocks of a canopy scattering model –canopy architecture –scattering properties of leaves –soil properties

8. Associated practical and reading Reading –microwave leaf model Chuah, H.T., Lee, K.Y., and Lau, T.W., 1995, “Dielectric constants of rubber and oil palm leaf samples at X-band”, IEEE Trans. Geoscience and Remote Sensing, GE-33, 221-223. –Optical leaf model Jacquemoud, S., and Baret, F., 1990, “PROSPECT: a model of leaf optical properties spectra”, Remote Sensing of Environment, 34, 75- 91. Practicals investigating leaf scattering –Optical OR microwave

9. Why build models? Assist data interpretation calculate RS signal as fn. of biophysical variables Study sensitivity to biophysical variables or system parameters Interpolation or Extrapolation fill the gaps / extend observations Inversion estimate biophysical parameters from RS aid experimental design plan experiments

10. Radiative Transfer Theory Approach optical and microwave case at same time through RT –‘relatively’ simple & well-understood –no other treatment in this way –researchers tend to specialise in either field less understanding of other field / synergy Deal with other approaches in later lectures

11. Radiative Transfer Theory Applicability –heuristic treatment consider energy balance across elemental volume –assume: no correlation between fields –addition of power not fields no diffraction/interference in RT –can be in scattering –develop common (simple) case here

12. Radiative Transfer Theory Case considered: –horizontally infinite but vertically finite plane parallel medium (air) embedded with infinitessimal oriented scattering objects at low density –canopy lies over soil surface (lower boundary) –assume horizontal homogeneity applicable to many cases of vegetation

13. Radiative Transfer Theory More accurate approach is to use Maxwell’s equations difficult to formulate will return to for object scattering but not propagation (RT)

14. Radiative Transfer Theory More accurate approach is to use Maxwell’s equations difficult to formulate will return to for object scattering but not propagation (RT)

15. Radiative Transfer Theory More accurate approach is to use Maxwell’s equations difficult to formulate use object scattering but not propagation (RT) essentially wave equation for electric field k - wavenumber = 2  / in air Plane wave

16. Radiative Transfer Theory Consider incident Electric-field E i (r) of magnitude E i in direction to a position r: incident wave sets up internal currents in scatterer that reradiate ‘scattered’ wave Remote sensing problem: –describe field received at a sensor from an area extensive ensemble average of scatterers

17. Scattering Define using scattering matrix: elements polarised scattering amplitudes –for discs: –for needles: assume scattering in far field

18. Scattering Bessel function (complex) permittivity of leaf Leaf volume Wavenumber 2 = 4  2 / 2

19. Scattering Sinc function

20. Stokes Vector Can represent plane wave polarisation by,and phase term: h,v phase equal for linear polarised wave

21. Stokes Vector More convenient to use modified Stokes vector:

22. Stokes Vector Using this, relate scattered Stokes vector to incident: N.B S 2 so 1/ 4 for discs etc

23. Stokes Vector Average Mueller matrix over all scatterers to obtain phase matrix for use in RT

24. Building blocks for a canopy model Require descriptions of: –canopy architecture –leaf scattering –soil scattering

25. Canopy Architecture 1-D: Functions of depth from the top of the canopy (z).

26. Canopy Architecture 1-D: Functions of depth from the top of the canopy (z). 1.Vertical leaf area density (m 2 /m 3 ) OR the vertical leaf number density function, N v (z) (number of particles per m 3 ) 2.the leaf normal orientation distribution function, (dimensionless). 3.leaf size distribution defined as: –area to relate leaf area density to leaf number density, as well as thickness. –the dimensions or volume of prototype scattering objects such as discs, spheres, cylinders or needles.

27. Canopy Architecture Leaf area / number density – (one-sided) m 2 leaf per m 3 –N v (z) - number of ‘particles’ per m 3 LAI

28. Canopy Architecture Leaf Angle Distribution

29. Archetype Distributions:  planophile   erectophile   spherical   plagiophile   extremophile  Leaf Angle Distribution

30. Archetype Distributions: Leaf Angle Distribution

31. Elliptical Distribution: Leaf Angle Distribution

32. Elliptical Distribution: Leaf Angle Distribution

33. RT theory: infinitessimal scatterers –without modifications (dealt with later) Scattering at microwave depends on leaf volume for given number per unit area –on leaf ‘thickness’ for given LAI In optical, leaf size affects canopy scattering in retroreflection direction –‘roughness’ term: ratio of leaf linear dimension to canopy height also, leaf thickness effects on reflectance /transmittance Leaf Dimension

34. RT theory: infinitessimal scatterers –without modifications (dealt with later) Scattering at microwave depends on leaf volume for given number per unit area –on leaf ‘thickness’ for given LAI In optical, leaf size affects canopy scattering in retroreflection direction –‘roughness’ term: ratio of leaf linear dimension to canopy height also, leaf thickness effects on reflectance /transmittance Leaf Dimension

35. Canopy element and soil spectral properties Scattering properties of leaves –scattering affected by: Leaf surface properties and internal structure; leaf biochemistry; leaf size (essentially thickness, for a given LAI).

36. Scattering properties of leaves Leaf surface properties and internal structure optical Specular from surface Smooth (waxy) surface - strong peak hairs, spines - more diffused

37. Scattering properties of leaves Leaf surface properties and internal structure optical Diffused from scattering at internal air-cell wall interfaces Depends on refractive index: varies: 1.5@400 nm 1.3@2500nm Depends on total area of cell wall interfaces

38. Scattering properties of leaves Leaf surface properties and internal structure optical More complex structure (or thickness): - more scattering - lower transmittance - more diffuse

39. Scattering properties of leaves Leaf surface properties and internal structure microwave Thickness (higher volume) - higher scattering

40. Scattering properties of leaves Leaf biochemstry

41. Scattering properties of leaves Leaf biochemstry

42. Scattering properties of leaves Leaf biochemstry

43. Scattering properties of leaves Leaf biochemstry

44. Scattering properties of leaves Leaf biochemstry –pigments: chlorophyll a and b,  -carotene, and xanthophyll absorb in blue (& red for chlorophyll) –absorbed radiation converted into: heat energy, flourescence or carbohydrates through photosynthesis

45. Scattering properties of leaves Leaf biochemstry –Leaf water is major consituent of leaf fresh weight, around 66% averaged over a large number of leaf types –other constituents ‘dry matter’ cellulose, lignin, protein, starch and minerals –Absorptance constituents increases with concentration reducing leaf reflectance and transmittance at these wavelengths.

46. Scattering properties of leaves Optical Models –flowering plants: PROSPECT

47. Scattering properties of leaves Optical Models –flowering plants: PROSPECT

48. Scattering properties of leaves Leaf water

49. Scattering properties of leaves Leaf water  PROSPECT:  leaf water content parameterised as equivalent water thickness (EWT)  approximates the water mass per unit leaf area.  related to volumetric moisture content (VMC, M v ) (proportionate volume of water in the leaf) by multiplying EWT by the product of leaf thickness and water density.

50. Scattering properties of leaves Microwave: –water content related to leaf permittivity, . Volume fractions Offset factor

51. Scattering properties of leaves Microwave: –water content related to leaf permittivity, . Frequency / GHz

52. Scattering properties of leaves leaf dimensions –optical increase leaf area for constant number of leaves - increase LAI increase leaf thickness - decrease transmittance (increase reflectance) –microwave leaf volume dependence of scattering –volume for constant leaf number –thickness for constant leaf area

53. Scattering properties of soils Optical and microwave affected by: –soil moisture content –soil type/texture –soil surface roughness.

54. soil moisture content Optical –effect essentially proportional across all wavelengths enhanced in water absorption bands

55. soil moisture content Microwave –increases soil dielectric constant effect varies with wavelength generally increases volume scattering –and decreases penetration depth

56. soil texture/type Optical –relatively little variation in spectral properties –Price (1985): PCA on large soil database 99.6% of variation in 4 PCs –Stoner & Baumgardner (1982) defined 5 main soil types: organic dominated minimally altered iron affected organic dominated iron dominated Microwave - affects dielectric constant

57. Soil roughness effects Simple models: –as only a boundary condition, can sometimes use simple models e.g. Lambertian e.g. trigonometric (Walthall et al., 1985)

58. Soil roughness effects Smooth surface: –Fresnel specular reflectance/transmittance –can be important at microwave due to double bounce in forest –can be important at optical for viewing in close to specular direction –Using Stokes vector:

59. Soil roughness effects Smooth surface:

60. Soil roughness effects Low roughness: –use low magnitude distribution of facets apply specular scattering over distribution –general effect: increases angular width of specular peak

61. Soil roughness effects Rough roughness: –optical surface scattering clods, rough ploughing –use Geometric Optics model (Cierniewski) –projections/shadowing from protrusions

62. Soil roughness effects Rough roughness: –optical surface scattering Note backscatter reflectance peak (‘hotspot’) minimal shadowing backscatter peak width increases with increasing roughness

63. Soil roughness effects Rough roughness: –volumetric scattering consider scattering from ‘body’ of soil –particulate medium –use RT theory (Hapke - optical) –modified for surface effects (at different scales of roughness)

64. Summary Introduction –Examined rationale for modelling –discussion of RT theory –Scattering from leaves –Stokes vector/Mueller matrix Canopy model building blocks –canopy architecture: area/number, angle, size –leaf scattering:spectral & structural –soil scattering:roughness, type, water