RADIATIVE TRANSFER MODEL

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RADIATIVE TRANSFER MODEL
By Nisha Upadhyay
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Points Covered

• What is Radiative Transfer Model?
• Different Types of RTM?
• What is PROSAIL?
• Inputs of PROSAIL.
• Retrieval of Biophysical Parameters using
  PROSAIL.

• Simulation of PROSAIL.
• Inversion of PROSAIL.

• Sensitivity Analysis

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Radiative Transfer Model

• Radiation transfer is the physical phenomenon of
  energy transfer in the form of electromagnetic
  radiation. The propagation of radiation through a
  medium is affected by absorption, emission, and
  scattering processes.
• Radiative Transfer Models (RTMs) calculate the
  flow of radiation (ultraviolet, visible or
  infrared light) through a plant canopy or
  planetary atmosphere.
• They can be used to predict the spectral
  transmission of the atmosphere, the light
  reflected or emitted from a plant, and the amount
  of energy absorbed or emitted at different
  levels.
• RTM is used to study spectral transmission or
  signature of plants, light reflected or emitted
  from plant and amount of energy absorbed.
• Continue...

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Radiative Transfer Model
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• Parameters that Governs RTM
• There are three main parameters that govern the
  Radiative Transfer Modeling
• Soil Structure (Soil Brightness, Roughness)
• Higher the soil roughness more the anisotropic
  reflectance
• Vegetation Architecture (LAI, Leaf Angle,etc.)
• As LAI increases, reflectance also increase in
  NIR region
• Leaf Biochemical Parameters. (Chlorophyll, Leaf
  structure)
• As Chlorophyll increase, reflectance decreases
  in Visible Band (400 nm to 725 nm)
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Radiative Transfer Model
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• Types of RTM
• There are two main categories of RTMs
• Homogeneous Models
• The landscape is represented by a constant
• horizontal distribution of absorbing and
• scattering elements (sheets, branches, etc.).
• Heterogeneous Models
• The landscape is represented by a non-uniform
• space distribution of unspecified elements of the
  
• landscape.
• e.g. deciduous and coniferous forests.

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Different Radiative Transfer Models

• SUIT Model Developed for a homogeneous canopy.
• SAIL Model A canopy re?ectance models.
• PROSPECT Model Determine leaf reflectance and
  transmittance signatures in the optical domain.
• PROSAIL Model POSPECT SAIL PROSAIL.
• GeoSAIL Model Combination of geometric model
  with SAIL model that provides the reflectance and
  transmittance of the tree crowns and radiative
  transfer within the crowns is calculated using
  SAIL.
• FLIGHT Model A three-dimensional ray-tracing
  model for the radiative transfer within crown
  boundaries and deterministic ray tracing between
  the crowns and other canopy components.

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Different Radiative Transfer Models
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• Coupled atmosphere and canopy (CAC) model An
  off nadir canopy reflectance model, was used to
  simulate multiple reflectances based on various
  combinations of canopy biophysical parameters.

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Different Radiative Transfer Models
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• SAIL (Scattering by Arbitrary Inclined Leaves)
  Model (Verhoef and Bunnik, 1981)
• It is extension of the SUIT model and uses
  fraction of leaves at discrete leaf inclination
  angle as parameter. This model is also totally
  mathematically invertible.
• One of the earliest canopy re?ectance models.
• SAIL considers the canopy as a horizontal,
  homogeneous, turbid, and infinitely extended
  vegetation layer composed of diffusely reflecting
  and transmitting elements.
• SAIL is a physics-based radiative transfer model
  used for simulating the hemispheric reflectance
  spectra of canopies under different viewing
  directions.
• Inputs to SAIL
• Structural canopy parameters (LAI, mean leaf
  inclination angle (?1), hot-spot size parameter
  (s)), measurement configuration (zenith and
  relative azimuth viewing angles (?v, ?v), zenith
  solar angle (?s)), fraction of diffuse
  illumination (skyl), and soil spectral
  reflectance (?s).
• Output of SAIL
• Canopy bidirectional reflectance.

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Different Radiative Transfer Models
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• SAIL

Canopy Parameters
LAI
Leaf Inclination Angle (?1)
hot-spot size parameter (s)
View Illumination Parameter
Zenith and Relative Azimuth angles (?v, ?v)
Zenith Solar Angle (?s)
Fraction of Diffuse Illumination (skyl)
SAIL
Soil Spectral Reflectance (?s))
Canopy Bidirectional Reflectance
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Continue
Different Radiative Transfer Models

• PROSPECT (Jacquemoud and Barret, 1990)
• PROSPECT model describing the optical properties
  of plant leaves from the visible (400 nm) to the
  shortwave infrared (2500 nm).
• It is based on representation of the leaf as one
  or several absorbing plates with rough surfaces
  giving rise to isotropic scattering.
• Relates foliar biochemistry and scattering
  parameters to leaf reflectance and transmittance
  spectra.
• It can readily be coupled with SAILH to
  facilitate direct modeling of the impact of
  chlorophyll, water and leaf dry matter
  constituents on the reflectance of a complete
  plant canopy.
• Inputs to PROSPECT
• Leaf structure parameter N, chlorophyll a b
  concentration (Cab) (µg/cm2), equivalent water
  thickness (Cw) (cm), and dry matter content (Cm)
  (g/cm2).
• Output of PROSPECT
• Leaf reflectance and transmittance signatures in
  the visible spectrum.

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Continue
Different Radiative Transfer Models

• PROSPECT

Chlorophyll a b concentration (Cab)
Equivalent Water Thickness (Cw)
Dry Matter Content (Cm)
Leaf structure parameter N
PROSPECT
Hemispherical Leaf Reflectance and Transmittance
Spectrum
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Continue
Different Radiative Transfer Models

• PROSAIL (Jacquemoud 1993)
• The PROSAIL canopy reflectance model was
  developed by linking the PROSPECT leaf optical
  properties model and the SAIL canopy
  bidirectional reflectance model.
• PROSAIL uses 14 input parameters to define leaf
  pigment content, leaf water content, canopy
  architecture, soil background reflectance, hot
  spot size, solar diffusivity, and solar geometry.
• Based on these inputs, the model calculates
  canopy bidirectional reflectance from 400 to 2500
  nm in 1 nm increments.

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Continue
Different Radiative Transfer Models

• PROSAIL PROSPECT SAIL

Canopy Parameters
LAI
Leaf Inclination Angle (?1)
Hot-spot size parameter (s)
View Illumination Parameter
Zenith and Relative Azimuth angles (?v, ?v)
Zenith Solar Angle (?s)
Fraction of Diffuse Illumination (skyl)
SAIL
Soil Spectral Reflectance (?s))

Equivalent Water Thickness (Cw)
Chlorophyll a b concentration (Cab)
Leaf Reflectance and Transmittance Spectrum
Bidirectional Canopy Reflectance
Leaf structure parameter N
PROSPECT
Dry Matter Content (Cm)
PROSAIL Model
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Inputs of PROSAIL

• There are 14 input parameters to PROSAIL model
• Chlorophyll a b concentration (Cab) (µg/cm2)
  Measured using DMSO (Dimethyl Sulphoxide).
• 2. Equivalent Water Thickness (Cw) (cm)
• Cw (Fresh weight of leaf (gm) dry weight of
  leaf (gm))/Area of leaf (cm²)
• 3. Dry Matter Content (Cm)
• Cm Dry weight of leaf / Area
• 4. hSpot
• hspot Leaf length / Leaf height.
• 5. Car (µg.cm-2) carotenoid content.
• 6. Cbrown brown pigment content.

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Inputs of PROSAIL

• 8. Leaf Area Index (LAI) Leaf area per unit
  ground surface area. Structural Coefficient
  (unit less).
• 9. Average leaf angle (angl) description of the
  angular orientation of the leaves.
• 10. Soil coefficient (psoil)
• 11. Diffuse/direct radiation (skyl)
• 12. Solar zenith angle (tts) Angle between sun
  position and with respect to zenith
• 13. Observer zenith angle (tto) Angle between
  observer (sensor) position and with respect to
  zenith.
• 14. Azimuth () (psi) Angle between observer
  (sensor) position with respect to north.

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Simulation of PROSAIL

• Simulation of PROSAIL model requires 14 input
  parameters.
• Before simulation of PROSAIL , sensitivity
  analysis is to be performed. Why ?
• we will see down the line
• Simulation of PROSAIL model based on the input
  parameters LAI, Cab, Cw, Car.
• Comparison of simulated spectra and field
  measured spectra.
• RMSE calculation.
• For lowest RMSE corresponding zenith angle is
  selected as hot spot angle.

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Inversion of PROSAIL

• There are various inversion strategies have been
  proposed. They are
• Numerical optimization methods (Bicheron and
  Loroy, 1999 Goel and Thompson, 1984).
• Look Up Table based approaches (Combal et al.,
  2002 Knyazikhin et al, 1998 Weiss et al.,
  2000)
• Artificial Neural Networks (Atgberger et al,
  2003a Baret et al, 1995 Weiss et al., 2000).
• Principal Component Inversion technique
  (Satapathy and Dadwal, 2005)
• PEST algorithm
• Support vector machines regression (Durbha et
  al., 2007).
• Genetic Algorithm (GA) Jin and Wang, 1999.

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Inversion of PROSAIL
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• Inversion of PROSAIL Using Look Up Table (LUT)
• LUT generation and conversion of generated
  thousands of LUT spectras into 7 bands of MODIS
  or any required band combination by the use of
  HyperAgri.
• Inversion program of PROSAIL take 7 band
  combination and hot spot position as input to
  calculate Lai, Cab, Car parameters as output
  values.
• RMSE is calculated for field obtained values and
  values obtainaed from PROSAIL Inversion.

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Simulation of PROSAIL

• Sensitivity Analysis
• Sensitivity analysis is performed to study the
  effect of LAI, cab, Car on the spectra of
  vegetation.
• These three are the main biophysical parameter
  which governs the spectra of a vegetation.
• Sensitivity Analysis for LAI

• LAI is dominant in NIR Region i.e. 700-1000 nm.
• Why?
• Due to the canopy structural development and
  multiple scattering which is particularly
  important at these wavelengths.
• When LAI increases reflectance also increases.
• After a certain increase in LAI value the changes
  in LAI spectra are very small because of shadow
  effect of plant leaves.
• A inverse effect is noted for SWIR (2000 2300
  nm) in LAI spectra. Why?
• For every increase in LAI value the spectral
  response is very low. This is because in SWIR
  region soil reflectance effect is dominant and
  with increase in LAI (more coverage of ground)
  the effect of soil reflectance decreases because
  of canopy shadow effect.

Reflectance
Wavelength (nm)
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Simulation of PROSAIL
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• Sensitivity Analysis for Chlorophyll

• Chlorophyll interactions with radiation are
  limited to the optical domain ranging from 400 nm
  to 725 nm.
• Chlorophyll content derives about 60 of
  reflectance variation in visible range.
• Lower chlorophyll value, higher the reflectance
  and vice versa.
• Why ?
• Increase in chlorophyll results in high
  absorption of sun light and hence lower
  reflection. Where as decrease in chlorophyll
  pigments results in lesser absorption of sun
  light and high reflectance.

Reflectance
Wavelength (nm)

• Combined effects of LAI and Chlorophyll occur
  over the red edge region where LAI and
  chlorophyll density increase contribute to the
  shift of the red edge position.

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Simulation of PROSAIL
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• Sensitivity Analysis for Water Content (Cw)

Reflectance
Wavelength (nm)

• Water content is a dominating factor in SWIR
  region of Vegetation Spectrum.
• Higher the water content value lower the
  reflectance.
• Effects of water content on leaf reflectance
  showed that sensitivity of leaf reflectance to
  
• water content was greatest in spectral
  bands centered at 1450, 1940, and 2500 nm.

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Simulation of PROSAIL
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• Sensitivity Analysis for Carotenoid

Reflectance
Wavelength (nm)

• When Carotenoids increases reflectance
  decreases.
• Spectral variation for different ranges of
  carotenoids has been noticed for 500nm -560nm.

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Continue
Simulation of PROSAIL
Sensitivity Analysis for Dry Matter Content (Cm)
Cm
Cm Dry weight/Leaf Area
Reflectance
Wavelength (nm)

• Dry matter content is a dominating factor in NIR
  region.
• Higher the value lower the reflectance.

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Simulation of PROSAIL
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Sensitivity Analysis for Leaf Angle
Leaf Angle
Reflectance
Wavelength (nm)
As leaf angle increases the reflectance decreases
in NIR region
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Spectra validation
RMSE1 0.015965 RMSE2 0.014256 RMSE3
0.025233
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Spectra validation
RMSE1 0.054230638 RMSE2 0.014782031 RMSE3
0.020301355
RMSE1 0.054231 RMSE2 0.014782 RMSE3
0.020301
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Spectra validation of Wheat Crop 28 Feb 2012
RMSE1 0.01990675 RMSE2 0.01666175 RMSE3
0.02420385
RMSE1 0.020182894 RMSE2 0.011387273 RMSE3
0.019610445
RMSE1 0.019149 RMSE2 0.016087 RMSE3
0.027433
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Spectra validation of Wheat Crop 28 Feb 2012
RMSE1 0.032717 RMSE2 0.039955 RMSE3
0.038231
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Spectra validation of Wheat Crop15 Mar 2012
RMSE1 0.049089561 RMSE2 0.049377422 RMSE3
0.010035917
RMSE1 0.038534 RMSE2 0.0417963 RMSE3
0.0090401
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Spectra validation of Wheat Crop15 Mar 2012
RMSE1 0.036355 RMSE2 0.037048 RMSE3
0.008087
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Validation of whole spectraRoot Mean Square Error
22 Feb 2012
28 Feb 2012
15 Mar 2012
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Input Parameters for LUT
Parameters Max. Range Interval
Cw 0.01 0.05 0.001
Cab 30 100 1
LAI 0.1 6 2
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Inversion Results
Parameters  Observed Observed Observed Predicted Predicted Predicted
Parameters  22-Feb-12 28-Feb-12 15-Mar-12 22-Feb-12 28-Feb-12 15-Mar-12
Cw 0.02 0.02 0.015 0.017 0.022 0.028
Cab 60 60 60 59.84 57.96 52.13
LAI 4.5 4.1 3.5 4.57 4.18 4.17
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Thank You