introduction to radiative t ransfer theory and models (optical … · 2014-05-15 · introduction...
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Introduction to radiative transfer theory and models (Optical Domain)
Dr. Eric VermoteNASA GSFC Code 619
.
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
https://ntrs.nasa.gov/search.jsp?R=20140005397 2020-03-15T15:22:13+00:00Z
Passive Optical Remote Sensing
source
sensor
sensor
target
source sensor
target
RADAR: radiation generated next to sensor
Atmospheric Correction of Earth Observation Data for
Environmental Monitoring: Theory
Solar Energy Paths
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
atmospheric contribution
diffuse + direct direct + diffuse multiple scattering
direct + direct
Atmospheric Correction of Earth Observation Data for
Environmental Monitoring: Theory
Solar (reflective) spectral domain
Atmospheric Correction of Earth Observation Data for
Environmental Monitoring: Theory
Observation Geometry
�s �v
n
�s-�v
Solar zenithangle View zenith
angle
Relative azimuthangle
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Solution of the Radiative Transfer in the reflective domain for non absorbing atmosphere and lambertian ground
�app �s ,�v,�� �� �atm �s ,�v,�� �� Tatm(�s )Tatm(�v )�ground
1 �groundSatm
Apparent reflectance at satellite level
Atmospheric reflectance
AtmosphericTransmissions
Atmospherespherical albedo
Ground reflectance(= albedo for lambertian)
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Perfect Lambertian Reflector
����� �),,( VSreflectorLambertian
)cos()sin()cos(),,(0
2
0ssS EddRPLF ��������
�� �
Isotropicradiation
Es
Radiance of the Perfect Lambertian Reflector
1),,( ����� VSreflectorLambertianPerfect
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Simple Radiative Transfer Equation
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE (cont.)
),,( ���� vsatm
Absorbing ground
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE (cont.)
Ei
Et
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE (cont.)
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE (cont.)
��v
Er
E0
40Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE 1 interaction (cont.)
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE 2 interactions
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
SRTE Multiple Interactions
��groundSatm < 1 so when n->���������groundSatm)n ->0
Therefore
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
STRE for non absorbing atmosphere and lambertian ground
�app �s ,�v,�� �� �atm �s ,�v,�� �� Tatm(�s )Tatm(�v )�ground
1 �groundSatm
Apparent reflectance at satellite level
Atmospheric reflectance
AtmosphericTransmissions
Atmospherespherical albedo
Ground reflectance(= albedo for lambertian)
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
The composition of the atmosphere
Permanent Constituents Variable constituents
Constituent % byvolume
Constituent % by volume
Nitrogen (N2) 78.084 Water Vapor (H2O) 0.04Oxygen (O2) 20.948 Ozone (O3) 12 x 10-4
Argon (Ar) 0.934 Sulfur dioxide (SO2)b 0.001 x 10-4
Carbon dioxide (CO2) 0.033 Nitrogen dioxide (NO2) 0.001 x 10-4
Neon (Ne) 18.18 x 10-4 Ammonia (NH3) 0.001 x 10-4
Helium (He) 5.24 x 10-4 Nitric oxide (NO) 0.0005 x 10-4
Krypton (Kr) 1.14 x 10-4 Hydrogen sulfide (H2S) 0.00005 x 10-4
Xenon (Xe) 0.089 x 10-4 Nitric acid vapor traceHydrogen (H2) 0.5 x 10-4
Methane (CH4) 1.5 x 10-4
Nitrous Oxide (N2O) 0.27 x 10-4
Carbon Monoxide (CO) 0.19 x 10-4
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Gaseous Absorption (H2O)
0.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Modified SRTE to account for absorption
�app(�s ,�v,�) � Tgothergases(m,Ugaz) �atm(�s,�v ,�) � TgH 2O(m,UH 2O)Tatm(�s )Tatm(�v )�ground
1 Satm�ground
�
������
����
m is the air mass = 1/cos(�s)+1/ cos(�v)Ugaz is the gaz concentration
In case of a pure molecular atmosphere (no aerosol) we can write:
10Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Final SRTE approximation
�app(�s ,�v,�) ~ Tgothergases(m,Ugaz )
� R(� s ,�v ,�) � TgH2O(m,UH2O/ 2)�A (�s ,�v,� )
�TgH2O (m,UH2O)TA(�s )TA (�v )TR (�s )TR (�v )
�ground1 SR�A�ground
�
��
����
��
��
����
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Water vapor effect for different sensors in the near infrared
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Scattering angle ,• The scattering angle, ��� is the relative
angle between the incident and the scattered radiation
ParticleIncident Radiation
��
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Phase function• The phase function, P(�)�� describe the
distribution of scattered radiation for one or an set of particles. It is normalized such as:
since
we have
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Rayleigh/molecular scattering 1/4
• Rayleigh or molecular scattering refers to scattering by atmospheric gases, in that case:
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Rayleigh/molecular scattering 2/4• The concentration in scatterer is better described by
the efficiency they scatter at a certain wavelength or the proportion of direct transmission which is related to the spectral optical thickness �����
E0(���
Et(���
Et(�)/ E0(�)=e- �����
• For Rayleigh �����is proportional to �-4 and for standart pressure is ~ 0.235 at 0.45 �m
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Rayleigh/molecular scattering 3/4
• The rayleigh reflectance, �R, could be crudely approximated by:
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
• Compute the reflectance of the sky (assumed clear no aerosol) at solar noon at 45degree latitude at vernal equinox looking straight up at 0.45�m, 0.55�m, 0.65�m
Rayleigh/molecular scattering 4/4
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Aerosol scattering 1/5• aerosol scattering refers to scattering by particles in suspension in the
atmosphere (not molecules). The MIE scattering theory could be applied to compute the aerosol phase function and spectral optical depth, based on size distribution, real and imaginary index.
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Aerosol scattering 2/5Continental aerosol phase function
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Aerosol scattering 3/5single scattering albedo(0.2-1.0) to account for absorbingparticles
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Aerosol scattering 4/5Continental aerosol optical thickness spectral variation
60Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Aerosol scattering 5/5Continental aerosol single scattering albedo spectral variation
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Atmospheric effect: Vegetation 1/3
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Atmospheric effect: Vegetation 2/3
No absorption, Continental aerosolAtmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Atmospheric effect: Vegetation 3/3
Absorption tropical atmosphere, Continental aerosolAtmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Atmospheric effect: Ocean 1/2
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Atmospheric effect: Ocean 2/2
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Perfect Lambertian Reflector
Isotropicradiation
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Different Types of Reflectors
Specular reflector (mirror) diffuse reflector (lambertian)
nearly diffuse reflectorNearly Specular reflector (water)
Hot spot reflection
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Sun glint as seen by MODIS
Gray level temperature image
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
MODIS data illustrating the hot-spot over dense vegetation
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
179
179.2
179.4
179.6
179.8
180
23.50 24.00 24.50 25.00 25.50 26.00
Surf
ace
Ref
lect
ance
Scattering Angle (°)
View Zenith Angle (°)
0.645 �m
0.555 �m
0.469 �m
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
BRDF atmosphere coupling correction
�app �s ,�v,�� �� �atm �s ,�v,�� �� Tatm(�s )Tatm(�v )�ground
1 �groundSatm
Lambertian infinite target approximation
BDRF atmosphere coupling approximation
� �satm
satmvARsatm
ssdvdsvdssd
vssvsatmvsapp
SSTT
tttete
eesv
vs
����
�������
����������������
����
�
���
��
�
1)()(
)()(')()(
),,(),,(),,(
2
//
//
')',,(
')',,()',,(),,( 2
0
1
0
2
0
1
0
������
���������������
ddL
ddL
satm
vssatmvss
� �� �
�
� �
),,(),,(' �������� vssvss �),,('),,( �������� vssvss �
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Adjacency effect correction
�app �s ,�v,�� �� �atm �s ,�v,�� �� Tatm(�s )Tatm(�v )�ground
1 �groundSatm
Lambertian infinite target approximation
adjacency effect approximation
� �evdatms
eatm
satmatmapp te
ST
v ����
��� �� )(1
)( / �
��
���
�
drddrrdFre � �
�
�2
0 0
)(),(21
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Adjacency effect correction (practical implementation)
)()( vatmsatm
atmappi TT ��
���
�
iatm
is S �
���
�1
inf
� �eatmvatm
evdatms
i STte v
������
��
�
�
1)()(/
� �ve
tST evdatmeatmvatmi
s ��
������ /)(1)(
�
),()),(( inf jidr
jirdFs
n
nj
n
nie �� � �
� �
�
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Adjacency effect correction (testing)
(a) (b) (c) (d)
Synthetic data set for surface reflectance in the blue (a), green (b) and red (c), and in
RGB (d) corresponding to bright soil (yellow squares) and dense vegetation (green
squares).
(a) (b) (c) (d)
Typical atmospheric effect on the synthetic surface reflectance shown above
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Adjacency effect correction (testing)
0
0.05
0.1
0.15
0.2
0 1 2 3 4 5 6 7
reflec
tance
in the
blue
distance [kilometer]
Reflectance’s observed over a horizontal transect on the checkerboard. The red bars are the “true” surface reflectance, the blue bars correspond to the top of the atmosphere signal including adjacency effect. The green bars correspond to the corrected data using the infinite target assumption. The open square correspond to the data corrected for the adjacency effect using the operational method developed.
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises
Adjacency effect correction (validation)
600
800
1000
1200
1400
1600
1800
2000
400.00 450.00 500.00 550.00 600.00 650.00 700.00
ETM+ surface reflectance (adj. corr.)ASD surface reflectance measurementsETM+ surface reflectance (no adj. corr)
Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises