Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 1 UoL MSc Remote Sensing Dr Lewis [email protected]
Mar 28, 2015
Radiative Transfer Theory at Optical wavelengths applied to vegetation canopies: part 1
UoL MSc Remote Sensing
Dr Lewis [email protected]
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– Course notes for this lecture– Reading list
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
• 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
Building blocks for a canopy model
• Require descriptions of:– canopy architecture– leaf scattering– soil scattering
Soil
H
zCanopy
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. Vertical leaf area density (m2/m3)
2. the leaf normal orientation distribution function
(dimensionless).
3. leaf size distribution (m)
( )zul
Canopy Architecture
• Leaf area / number density– (one-sided) m2 leaf per m3( )zul
( )dzzuLHz
z
l∫=
=
=0
LAI
Ωl
x
z
y
θl
φl
Inclination to vertical
azimuth
Leaf normal vector
Canopy Architecture
• Leaf Angle Distribution
( ) 12
≡ΩΩ∫ + lll dgπ
• Archetype Distributions:planophile
erectophile
spherical
plagiophile
extremophile
Leaf Angle Distribution
( ) lllg ϑϑ 2cos3=
( ) lllg ϑϑ 2sin2
3⎟⎠
⎞⎜⎝
⎛=
( ) 1=llg ϑ
( ) lllg ϑϑ 2sin8
15 2⎟⎠
⎞⎜⎝
⎛=
( ) lllg ϑϑ 2cos7
15 2⎟⎠
⎞⎜⎝
⎛=
• Archetype Distributions:
Leaf Angle Distribution
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 10 20 30 40 50 60 70 80 90
g_l(theta_l)
leaf zenith angle / degrees
spherical planophile erectophileplagiophile extremophile
• RT theory: infinitessimal scatterers– without modifications (dealt with later)
• 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
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
Dicotyledon leaf structure
opticalSpecular
from surface
Smooth (waxy) surface- strong peak
hairs, spines- more diffused
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
opticalDiffused
from scattering at internal air-cell wall interfaces
Depends on refractive index:varies: 1.5@400 nm
1.3@2500nmDepends on total areaof cell wall interfaces
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
optical
More complex structure (or thickness):- more scattering- lower transmittance- more diffuse
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 water
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
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 dimensions– optical
• increase leaf area for constant number of leaves - increase LAI
• increase leaf thickness - decrease transmittance (increase reflectance)
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 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
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
• 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
• Canopy model building blocks– canopy architecture: area/number, angle, size– leaf scattering: spectral & structural– soil scattering: roughness, type, water