Radiative Transfer Theory at Optical
wavelengths applied to vegetation canopies:
part 1
UoL MSc Remote Sensing
Dr Lewis
plewis@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
– 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
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 ul  z  (m2/m3)
2. the leaf normal orientation distribution function
(dimensionless).
3. leaf size distribution (m)
Canopy Architecture
• Leaf area / number density
–
2
3
ul  z  (one-sided) m leaf per m
zH
LAI
L
 u z dz
l
z 0
Canopy Architecture
• Leaf Angle Distribution
z
Inclination to vertical
  g W d W
2 
l
l
l
1
ql
Wl
Leaf normal vector
y
fl
azimuth
x
Leaf Angle Distribution
• Archetype Distributions:
 planophile

g l l   3 cos 2 l
 erectophile

 spherical

 3
g l l     sin 2 l
 2
 plagiophile

 extremophile 
g l l   1
 15  2
g l l     sin 2l
8
 15 
g l l     cos 2 2l
7
Leaf Angle Distribution
• Archetype Distributions:
3.0
2.5
g_l(theta_l)
2.0
1.5
1.0
0.5
0.0
0
10
20
30
40
50
60
70
leaf zenith angle / degrees
spherical
plagiophile
planophile
extremophile
erectophile
80
90
Leaf Dimension
• 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
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
Dicotyledon leaf structure
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
Dicotyledon leaf structure
Depends on refractive index:
varies: 1.5@400 nm
1.3@2500nm
Scattering properties of leaves
• Leaf surface properties and internal structure
optical
More complex structure (or thickness):
- more scattering
- lower transmittance
- more diffuse
Dicotyledon leaf structure
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, 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
wavelengths.
reflectance
and
transmittance
at
these
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