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1Envisat Summer School – NG 2
Inverse method for development of an advanced vegetation index
Nadine Gobron
With collaborations of:Bernard Pinty, Michel Verstraete & Jean-Luc Widlowski
2Envisat Summer School – NG 2
What is the main scientific issue in remote sensing?
• Remote sensing instruments on space platforms are but sophisticated detectors recording the occurrence of elementary events (the absorption of photons or electromagnetic waves) as variations in electrical currents or voltages.
• Users, on the other hand, require information on events and processes occurring in the geophysical environment (e.g., atmospheric pollution, oceanic currents, terrestrial net productivity, etc.)
• Extracting useful environmental information from data acquired in space is the main challenge facing remote sensing scientists.
3Envisat Summer School – NG 2
How is remote sensing exploited?
• The signals detected by the sensors are immediately converted into digital numbers and transmitted to dedicated receiving stations, where these data are heavily processed.
• The effective exploitation of remote sensing data to reliably generate useful, pertinent information hinges on the availability and performance of specific tools and techniques of data analysis and interpretation.
• A variety of mathematical models can be used for this purpose; they are implemented as computer codes that read the data or intermediary products and ultimately lead to the generation of products and services usable in specific applications.
4Envisat Summer School – NG 2
Why is remote sensing called an inverse problem?
• Since space borne instruments can only measure the properties of electromagnetic waves emitted or scattered by the Earth, scientists need first to understand where these waves originate from, how they interact with the environment, and how they propagate towards the sensor.
• To this effect, they develop models of radiation transfer, assuming that everything is known about the sources of radiation and the environment, and calculate the properties of the radiation field as the sensor should measure them. This is the so-called direct problem.
5Envisat Summer School – NG 2
Why is remote sensing called an inverse problem?
• In practice, one does acquire the measurements from the satellite, and would like to know what is going on in the environment:
à This is the inverse problem, which is much more complicated: Knowing the value of the electromagnetic measurements gathered in space, how can we derive the properties of the environment that were responsible for the radiation to reach the sensor?
6Envisat Summer School – NG 2
Measurements of interpretation (1)
• A model representing a measurement expresses the dependency of this measurement with respect to the relevant variables and processes:
where sm are the state variables of the system
• Direct problem: if values sm are know, such a model can accurately simulate the observation
• Inverse problem: Quantity is measured, and one seeks information on the states variables sm
),...,( 21 msssfz =
z)
7Envisat Summer School – NG 2
Measurements of interpretation (2)
• If a single state variable accounts for the physics of the measurement, the problem can be solved analytically or numerically, usually with great accuracy:
• In general, more than one state variable is required to describethe physics of the problem. The solution to the inverse problem then requires multiple equations and therefore multiple measurements.
)()( 11 zfssfz )) −=⇒=
8Envisat Summer School – NG 2
Role of independent variables (1)
• To acquire more information on an invariant system, it is necessary to gather different measurements by changing a variable other than the state variables.
where the independent variable x describes the changing conditions of observations.
• If the system of interest can be observed in more than one way, multiple independent variables may be defined.
• In case of RS from space, the useful independent variables are space, time, wavelength, illumination and observation geometry.
),...,;( 21 msssxfz =
9Envisat Summer School – NG 2
Role of independent variables (2)
• Multiple measurements may thus be aquired under different conditions of observation:
KMKN
KKK
MN
MN
sssxxxfz
sssxxxfz
sssxxxfz
ε
ε
ε
+=
+=
+=
),...,;,...,,(
....
),...,;,...,,(
),...,;,...,,(
2121
22122
221
2
12111
211
1
)
)
)
10Envisat Summer School – NG 2
Association of physical measurements, models & models
representing the biosphere
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
11Envisat Summer School – NG 2
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
Association of physical measurements, models & models
representing the biosphere
12Envisat Summer School – NG 2
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
Association of physical measurements, models & models
representing the biosphere
13Envisat Summer School – NG 2
Association of physical measurements, models & models
representing the biosphere
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
14Envisat Summer School – NG 2
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
Association of physical measurements, models & models
representing the biosphere
15Envisat Summer School – NG 2
The process of fitting data, as seen by Subramanian Raman in Science with a Smile.
Association of physical measurements, models & models
representing the biosphere
16Envisat Summer School – NG 2
Model Inversion
• In general, the system of equations cannot be solved:
o If K < M, the system is still underterminedo If K=M, measurements errors may prevent the
identification of the exact solution.o If K>M, the system is overdetermined.
K depends on space observation strategy
M depend on the RT model
17Envisat Summer School – NG 2
Space Observation Strategies
• Mono-directional multi-spectral scanning sensor on a Sun-synchronous orbit
single view of the same target during a given day (given Sun zenith angle)
18Envisat Summer School – NG 2
Space Observation Strategies
Ref: http://rst.gsfc.nasa.gov
19Envisat Summer School – NG 2
Space Observation Strategies
Source: http://envisat.esa.int/
20Envisat Summer School – NG 2
Space Observation Strategies
Source: http://envisat.esa.int/
21Envisat Summer School – NG 2
Space Observation Strategies
• Spinning sensor on a geostationary orbit
• Mono-directional multi-spectral scanning sensor on a Sun-synchronous orbit
single view of the same target during a given day (given Sun zenith angle)
22Envisat Summer School – NG 2
Space Observation Strategies
23Envisat Summer School – NG 2
Space Observation Strategies
24Envisat Summer School – NG 2
Space Observation Strategies
25Envisat Summer School – NG 2
Space Observation Strategies
• Spinning sensor on a geostationary orbit
multiple views of the same target during a given day (various Sun zenith angles)
• Mono-directional multi-spectral scanning sensor on a Sun-synchronous orbit
single view of the same target during a given day (given Sun zenith angle)
26Envisat Summer School – NG 2
Space Observation Strategies
• Spinning sensor on a geostationary orbit
multiple views of the same target during a given day (various Sun zenith angles)
• Mono-directional multi-spectral scanning sensor on a Sun-synchronous orbit
single view of the same target during a given day (given Sun zenith angle)
• Multi-directional multi-spectral sensor on a Sun-synchronous orbit
27Envisat Summer School – NG 2
Overview of MISR
• 9 cameras at ±70.5, ±60, ±45.6, ±26.1, 0°
• Each camera at 446, 558, 672, and 866 nm
• Spatial resolution: 275 m (250 m nadir)
• Global mode: Full res. nadir and red, 1.1 km otherwise
• Local mode: Full resolution all cameras and all bands
• Swath: 360 km• Coverage: global (9 days)
Ref: http://www-misr.jpl.nasa.gov/mission/minst.html
28Envisat Summer School – NG 2 Credit: NASA/GSFC/LaRC/JPL MISR Team
Multiangle animation
Emigrant Gap Fire,California
13 August 2001
79 km
9/19/2004 29Envisat Summer School – NG 2
Design of the MERIS Global Vegetation Index
decontaminated from atmospheric and geometrical effects
30Envisat Summer School – NG 2
MERIS/ENVISAT
• Passive optical instrument of Earth Observation• Primary mission: Ocean productivity• Secondary missions: Atmosphere and
land surface characterization• Ground segment support (up to L2)
• Global coverage: = 3 days (depends on latitude)• Swath: 1150 km• Spatial resolution: ± 300 m (FR) & ± 1200 m (RR)
• Spectral band positions, widths and gains are programmable• Radiometric and spectral calibration on-board mechanisms
(white & pink Spectralon, Fraunhofer lines)
Source: http://envisat.esa.int/instruments/meris/
31Envisat Summer School – NG 2
Nominal MERIS spectral bands
Water vapour, land1090015
Atmospheric corrections1088514
Vegetation, water vapour reference2086513
Atmospheric corrections15778.7512
Oxygen absorption R-branch3.75760.62511
Vegetation, clouds7.5737.7510
Fluorescence, atmospheric corrections10708.759
Chlorophyll fluorescence peak7.5681.258
Chlorophyll absorption and fluorescence106657
Suspended sediment106206
Chlorophyll absorption minimum105605
Suspended sediment, red tides105104
Chlorophyll and other pigments104903
Chlorophyll absorption maximum10442.52
Yellow substance and detrital pigments10412.51
ApplicationsWidth [nm]Location [nm]Band
Ref: http://envisat.esa.int/instruments/meris/descr/concept.html
9/19/2004 32Envisat Summer School – NG 2
Objective•To provide useful, quantitative, reliable, accurate and low cost information on the state of terrestrial vegetation using remote sensing data
•Development of Optimized Vegetation Indices using a physically-based approach
Approach
9/19/2004 33Envisat Summer School – NG 2
Scientific Constraints
• Maximal sensitivity to the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR)
• Minimal sensitivity to atmospheric perturbations
• Minimal sensitivity to soil colour and brightness changes
• Minimal sensitivity to angular effects
34Envisat Summer School – NG 2
SeaWiFS
MISR
MODISMERIS
Spectral Sensor Properties
35Envisat Summer School – NG 2
Spectral Leaves Profile
Prospect Model
SeaWiFS
MISR
MODISMERIS
36Envisat Summer School – NG 2
Semi-discret Model
SeaWiFS
MISR
MODISMERIS
Bidirectional Reflectance Factor at Top Of Canopy : Nadir View
37Envisat Summer School – NG 2
Bidirectional Reflectance Factor at Top Of Canopy
Semi-discret Model
lai =8.lai=5.
lai=4.lai=3.
lai=2.lai=1.5
lai=1.lai=0.5
SeaWiFS
MISR
MODISMERIS
38Envisat Summer School – NG 2
Visibility : 151.58 kmVisibility : 38.33 kmVisibility : 20.22 kmVisibility : 7.74 kmVisibility : 5.11 km
Bidirectional Reflectance Factor Top Of Atmosphere: Aerosols Optical Depth
6S Model
SeaWiFS
MISR
MODISMERIS
9/19/2004 39Envisat Summer School – NG 2
Operational Constraints
• Exploit only the target’s spectral variations as measured by the satellite instruments
• Take the actual spectral response of the sensor into account
• Minimise the computational load• Require data from a single orbit only
40Envisat Summer School – NG 2
Scheme for the algorithm optimization (1)
Radiation Transfer ModelsRadiation Transfer Models
BRF TOABRF TOA BRF TOCBRF TOC FAPARFAPAR
41Envisat Summer School – NG 2
Mathematical Implementation (1)
Medium Variables Range of values Atmosphere τs 0.05, 0.3 and 0.8 Vegetation LAI
HC
Dl
LAD
0, 1, 2, 3, and 5 0.5 and 2 m 0.01 and 0.05 m Erectophile, Planophile
Soil rs 5 Soil spectra (Price, 1995)
Geophysical properties
Illumination and observation geometries
Angle Values Solar zenith (θ0) Satellite zenith (θv) Sun-Satellite relative azimuth (∆φ)
20 and 50 degrees 0, 25 and 40 degrees 0, 90 and 180 degrees
Models: • 6S atmospheric radiation transfer model (Vermote et al., 1997)• Semi-discrete vegetation radiation transfer model (Gobron et al., 1997)
42Envisat Summer School – NG 2
RT model driven improvement for FAPAR
43Envisat Summer School – NG 2
Scheme for the algorithm optimization (2)
Radiation Transfer ModelsRadiation Transfer Models
BRF TOABRF TOA BRF TOCBRF TOC FAPARFAPAR
Rectified RedRectified Red
Angular/Atmospheric effectsAngular/Atmospheric effects
Rectified NIRRectified NIR
),,,,(),,(
)(0
0~
icHGiiv
ivTOA
i kF λλλ ρλρ
λρΩΩΩΩΩ
=
44Envisat Summer School – NG 2
?0 - controls amplitude levelk - controls bowl/bell shapeT - controls forward/backward scattering?C - controls hot spot peak
BRF(z,O0 O) = ?0 MI(k) FHG(T ) H (?c)
The RPV parametric model
Ref: Rahman et al. (1993) JGR
45Envisat Summer School – NG 2
ks
ks
k
sI kM −
−−
+= 1
11
)cos(coscoscos
);,(θθ
θθθθ
),,;,(~),,,;,( 0000 kzkz cscs ΘΩ→Ω=ΘΩ→Ω ρρρρρρ
);(),();,(),,;,(~0 GHgFkMkz cHGsIcs ρθθρρ Θ=ΘΩ→Ω
2/32
2
]cos21[1
),(Θ+Θ+
Θ−=Θ
ggFHG
GGH c
c +−
+=11
1);(ρ
ρ
2/122 ]costantan2tan[tan
cossinsincoscoscos
φθθθθ
φθθθθ
ss
ss
G
g
−+=
+=
• Direct Mode
• Inverse Method when mono-angle data (MERIS)
Ø k, Θ, ρc parameters are optimized with simulated-data for each wavelenght at TOA & TOC: representative values of anisotropic atthe global scale.
The RPV parametric model
46Envisat Summer School – NG 2
ks
ks
k
sI kM −
−−
+= 1
11
)cos(coscoscos
);,(θθ
θθθθ
),,;,(~),,,;,( 0000 kzkz cscs ΘΩ→Ω=ΘΩ→Ω ρρρρρρ
);(),();,(),,;,(~0 GHgFkMkz cHGsIcs ρθθρρ Θ=ΘΩ→Ω
2/32
2
]cos21[1
),(Θ+Θ+
Θ−=Θ
ggFHG
GGH c
c +−
+=11
1);(ρ
ρ
2/122 ]costantan2tan[tan
cossinsincoscoscos
φθθθθ
φθθθθ
ss
ss
G
g
−+=
+=
• Direct Mode
• Inverse Method when multi-angles data (MISR, SPECTRA)
Ø Resolution of second order equations (Gobron and Lajas, 2002)Ø Users’ controlled accuracy of the fit (model/data)Ø Retrieval of a set of acceptable solutionsØ Selection on the most representative solutions
The RPV parametric model
47Envisat Summer School – NG 2
Ø Resolution of a linear system (Engelsen et al, 1996)Ø No predefined accuracyØ Only one solutionØ Very fast method
Parametric Model: MRPV
• Direct Mode
• Inverse Method
ks
ks
k
sI kM −
−−
+= 1
11
)cos(coscoscos
);,(θθ
θθθθ
),;,(~),,;,( 0000 kbzkbz msms Ω→Ω=Ω→Ω ρρρρ
);();();,(),,;,(~0 GHbgFkMkbz msIms ρθθρρ =Ω→Ω
)cosexp();( gbbgF mm −=
GGH
+−
+=11
1);(ρ
ρ
2/122 ]costantan2tan[tan
cossinsincoscoscos
φθθθθ
φθθθθ
ss
ss
G
g
−+=
+=
48Envisat Summer School – NG 2
Scheme for the algorithm optimization (2)
Radiation Transfer ModelsRadiation Transfer Models
BRF TOABRF TOA BRF TOCBRF TOC FAPARFAPAR
Rectified RedRectified Red
Angular/Atmospheric effectsAngular/Atmospheric effects
Rectified NIRRectified NIR)](),([
~~
1 redbluRred g λρλρρ = )](),([~~
2 nirbluRnir g λρλρρ =
),,,,(),,(
)(0
0~
icHGiiv
ivTOA
i kF λλλ ρλρ
λρΩΩΩΩΩ
= TOCiblui i
g λρλρλρ ~)](),([~~
→
49Envisat Summer School – NG 2
Scheme for the algorithm optimization (3)
50Envisat Summer School – NG 2
Mathematical Implementation (2)
• Ratios of polynomials are assumed to be appropriate to generate the “rectified channels” :
)ly,x,(f)yx,(g mn,n =
Where ln,m are the m coefficients of the polynomials, and x and y are either the measured or rectified spectral reflectances,depending on the step
51Envisat Summer School – NG 2
Cost Functions (1)
• The optimisation procedure is applied to the RED and NIR bands to find the coefficients of g1 and g2:
0]~))(~),(~([2 →−ΩΩ∑= TOCjjbluig ???g
i
ςδ
xyl)ly(l)lx(lxyl)l(yl)lx(l
)y,x(g10,2
29,28,2
27,26,2
5,22
4,23,22
2,21,22
++++++++
=
xyl)ly(l)lx(l)y,x(g 5,12
4,13,12
2,11,11 ++++=
52Envisat Summer School – NG 2
Rectification Results in the Red Band
Before After
53Envisat Summer School – NG 2
Rectification Results in the NIR Band
Before After
54Envisat Summer School – NG 2
Scheme for the algorithm optimization
Radiation Transfer ModelsRadiation Transfer Models
BRF TOABRF TOA BRF TOCBRF TOC FAPARFAPAR
Rectified RedRectified Red
Angular/Atmospheric effectsAngular/Atmospheric effects
Rectified NIRRectified NIR)](),([
~~
1 redbluRred g λρλρρ = )](),([~~
2 nirbluRnir g λρλρρ =
),,,,(),,(
)(0
0~
icHGiiv
ivTOA
i kF λλλ ρλρ
λρΩΩΩΩΩ
= TOCiblui i
g λρλρλρ ~)](),([~~
→
Optimization Procedure
Optimization Procedure
FAPAR),(0 →RnirRredg ρρ
55Envisat Summer School – NG 2
Mathematical Implementation (3)
• The index formula is generated on the basis of the rectified channel values, ρRred and ρRnir,estimated as follow:
)~,~(g 1 redbluRred ??? = )~,~(g 2 nirbluRnir ??? =
),(0 RnirRredgMGVI ρρ=
56Envisat Summer School – NG 2
Cost Functions (2)
• The coefficients of g0 are optimised so that:
0]FAPAR)([ ,02
0
→−∑= RnirRredg
??gς
δ
6,02
5,02
4,0
3,02,01,0
l)yl()xl(lxlyl
)y,x(go
+−+−−−
=
57Envisat Summer School – NG 2
MGVI Optimization
Before After
58Envisat Summer School – NG 2
RT model driven improvement for FAPAR
MGVI
59Envisat Summer School – NG 2
Scheme for the algorithm optimization
062
052
04
030201
0
11
~~
10
29
~
82
7
~
6
~~
5
24
~
32
2
~
1
~~
)()(
),(FAPAR
)()(
))(())((),(
)()(
))(())((),(
),(/),()](),([
llllll
g
ll
llllQ
l
llllP
QPg
RnirRred
RredRnir
RnirRred
njin
njnninji
jin
njnninji
jijijin
+−+−−−
=
=
++
+++=
+
+++=
=
ρρρρ
ρρ
λρλρ
λρλρλλ
λρλρ
λρλρλλ
λλλλλρλρ
Radiation Transfer ModelsRadiation Transfer Models
BRF TOABRF TOA BRF TOCBRF TOC FAPARFAPAR
Rectified RedRectified Red
Angular/Atmospheric effectsAngular/Atmospheric effects
Rectified NIRRectified NIR)](),([
~~
1 redbluRred g λρλρρ = )](),([~~
2 nirbluRnir g λρλρρ =
),,,,(),,(
)(0
0~
icHGiiv
ivTOA
i kF λλλ ρλρ
λρΩΩΩΩΩ
= TOCiblui i
g λρλρλρ ~)](),([~~
→
Optimization Procedure
Optimization Procedure
FAPAR),(0 →RnirRredg ρρ
60Envisat Summer School – NG 2
Case a Case b
Case c Case d
Sensitivity to scenes heterogeneity
61Envisat Summer School – NG 2
MERIS Global Vegetation Index
Rectified Red Rectified NIR
Angular/Atmospheric `Rectification'
)](),([~~
1 redbluRred g λρλρρ = )](),([~~
2 nirbluRnir g λρλρρ =
),,,,(),,(
)(0
0~
icHG
iiv
ivTOA
i kF λλλ ρλρ
λρΩΩΩΩΩ
=
Fapar),(0 RnirRredg ρρ=MGVI
BRF TOA View angles Sun angles
Satellite Data
L2 products
62Envisat Summer School – NG 2
Conclusions (1)
• Retrieval geophysical parameters is a coupled atmosphere-vegetation problem.
• Inverse methods depend on the space remote sensing data types (multi/mono spectral & multi/mono angular).
• Retrieval of geophysical parameters values are always associated to accuracies.
• MGVI (instantaneous) can be read in the LEVEL 2 land product (TOAVI) and represents FAPAR.
63Envisat Summer School – NG 2
Conclusions (2)
• Remote sensing products require a validation exercise through:
• Ground measurements• Inter-comparison with other sensor derived products
• Temporal & spatial scale production also depend on specific applications (global or regional).
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