Radiative Transfer Theory at Optical and Microwavelengths applied

Radiative Transfer Theory at Optical and Microwavelengths applied to vegetation canopies: part 1 Uo. L MSc Remote Sensing course tutors: Dr Lewis Dr Saich plewis@geog. ucl. ac. uk psaich@geog. ucl. ac. uk

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

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

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

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

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

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

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

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)

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)

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 p/l in air Plane wave

Radiative Transfer Theory • Consider incident Electric-field Ei(r) of magnitude Ei 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

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

Scattering Bessel function (complex) permittivity of leaf Wavenumber 2 = 4 p 2/l 2 Leaf volume

Scattering Sinc function

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

Stokes Vector • More convenient to use modified Stokes vector:

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

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

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

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

Canopy Architecture • 1 -D: Functions of depth from the top of the canopy (z). 1. 2. 3. Vertical leaf area density (m 2/m 3) OR the vertical leaf number density function, Nv(z) (number of particles per m 3) the leaf normal orientation distribution function, (dimensionless). 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.

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

Canopy Architecture • Leaf Angle Distribution

Leaf Angle Distribution • Archetype Distributions: · planophile · erectophile · spherical · plagiophile · extremophile

Leaf Angle Distribution • Archetype Distributions:

Leaf Angle Distribution • Elliptical Distribution:

Leaf Angle Distribution • Elliptical Distribution:

Leaf Dimension • 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 • 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

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).

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

Scattering properties of leaves • Leaf surface properties and internal structure optical Diffused from scattering at internal air-cell wall interfaces Depends on total area of cell wall interfaces Depends on refractive index: varies: 1. 5@400 nm 1. 3@2500 nm

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

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

Scattering properties of leaves • Leaf biochemstry

Scattering properties of leaves • Leaf biochemstry

Scattering properties of leaves • Leaf biochemstry

Scattering properties of leaves • Leaf biochemstry

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

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.

Scattering properties of leaves • Optical Models – flowering plants: PROSPECT

Scattering properties of leaves • Optical Models – flowering plants: PROSPECT

Scattering properties of leaves • Leaf water

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, Mv) (proportionate volume of water in the leaf) by multiplying EWT by the product of leaf thickness and water density.

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

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

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

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

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

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

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

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)

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:

Soil roughness effects • Smooth surface:

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

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

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

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)

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