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

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

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