1. RADIATIVE TRANSFER MODEL
By: Nisha Upadhyay

2. 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

3. 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. ”
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4. 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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5. 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.

6. Different Radiative Transfer Models
SUIT Model: Developed for a homogeneous canopy.
SAIL Model: A canopy reflectance 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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7. Different Radiative Transfer Models…
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Different Radiative Transfer Models…
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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8. Different Radiative Transfer Models…
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Different Radiative Transfer Models…
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 reflectance 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 (θ1), hot-spot size parameter (s)), measurement configuration (zenith and relative azimuth viewing angles (θv, ψv), zenith solar angle (θs)), fraction of diffuse illumination (skyl), and soil spectral reflectance (ρs).
Output of SAIL
Canopy bidirectional reflectance.
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9. Different Radiative Transfer Models…
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Different Radiative Transfer Models…
SAIL:
Canopy Parameters:
LAI
Leaf Inclination Angle (θ1)
hot-spot size parameter (s)
View & Illumination Parameter:
Zenith and Relative Azimuth angles (θv, ψv)
Zenith Solar Angle (θs)
Fraction of Diffuse Illumination (skyl)
SAIL
Soil Spectral Reflectance (ρs))
Canopy Bidirectional Reflectance
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10. PROSPECT (Jacquemoud and Barret, 1990) :
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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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11. PROSPECT: Different Radiative Transfer Models… PROSPECT Continue…
Equivalent Water Thickness (Cw)
Chlorophyll a + b concentration (Cab)
Leaf structure parameter N
Dry Matter Content (Cm)
PROSPECT
Hemispherical Leaf Reflectance and Transmittance Spectrum

12. PROSAIL (Jacquemoud 1993) :
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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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13. PROSAIL = PROSPECT + SAIL
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Different Radiative Transfer Models…
PROSAIL = PROSPECT + SAIL
Canopy Parameters:
LAI
Leaf Inclination Angle (θ1)
Hot-spot size parameter (s)
View & Illumination Parameter:
Zenith and Relative Azimuth angles (θv, ψv)
Zenith Solar Angle (θs)
Fraction of Diffuse Illumination (skyl)
SAIL
Soil Spectral Reflectance (ρs))
Equivalent Water Thickness (Cw)
Chlorophyll a + b concentration (Cab)
Leaf Reflectance and Transmittance Spectrum
Bidirectional Canopy Reflectance
Leaf structure parameter N
Dry Matter Content (Cm)
PROSPECT
PROSAIL Model

14. 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.
7. N: Structural Coefficient (unit less)

15. 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.

16. we will see down the line …
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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17. 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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18. Inversion of PROSAIL Using Look Up Table (LUT)
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Inversion of PROSAIL
Inversion of PROSAIL Using Look Up Table (LUT)
LUT generation and conversion of generated thousands of LUT spectra’s 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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19. Sensitivity Analysis Simulation of PROSAIL Continue…
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 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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20. Sensitivity Analysis for Chlorophyll
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Simulation of PROSAIL
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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21. Sensitivity Analysis for Water Content (Cw)
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Simulation of PROSAIL
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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22. Sensitivity Analysis for Carotenoid
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Simulation of PROSAIL
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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23. Sensitivity Analysis for Dry Matter Content (Cm)
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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.

24. Sensitivity Analysis for Leaf Angle
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Simulation of PROSAIL
Sensitivity Analysis for Leaf Angle
Leaf Angle
Reflectance
Wavelength (nm)
As leaf angle increases the reflectance decreases in NIR region

25. Spectra validation
RMSE
RMSE
RMSE

26. Spectra validation RMSE1 0.054230638 RMSE2 0.014782031 RMSE1 0.054231

27. Spectra validation of Wheat Crop 28 Feb 2012
RMSE RMSE RMSE
RMSE RMSE RMSE
RMSE
RMSE
RMSE

28. Spectra validation of Wheat Crop 28 Feb 2012
RMSE RMSE RMSE

29. Spectra validation of Wheat Crop 15 Mar 2012
RMSE RMSE RMSE
RMSE RMSE RMSE

30. Spectra validation of Wheat Crop 15 Mar 2012
RMSE RMSE RMSE

31. Validation of whole spectra Root Mean Square Error
22 Feb 2012
28 Feb 2012
15 Mar 2012

32. Input Parameters for LUT
Max. Range
Interval Cw
0.01 – 0.05
0.001
Cab
30 – 100 1
LAI
0.1 – 6 2

33. Inversion Results Parameters Observed Predicted 22-Feb-12 28-Feb-12
15-Mar-12 Cw
0.02
0.015
0.017
0.022
0.028
Cab 60
59.84
57.96
52.13
LAI
4.5
4.1
3.5
4.57
4.18
4.17

34. Thank You