introduction to radiative t ransfer theory and models (optical … · 2014-05-15 · introduction...

Introduction to radiative transfer theory and models (Optical Domain)

Dr. Eric VermoteNASA GSFC Code 619

[email protected]

.

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 contribution

diffuse + direct direct + diffuse multiple scattering

direct + direct



Solar (reflective) spectral domain



Observation Geometry

�s �v

n

�s-�v

Solar zenithangle View zenith

angle

Relative azimuthangle


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)


Perfect Lambertian Reflector

�� ),,( VSreflectorLambertian

)cos()sin()cos(),,(0

2

0ssS EddRPLF ��

��

Isotropicradiation

Es

Radiance of the Perfect Lambertian Reflector

1),,( �� VSreflectorLambertianPerfect


Simple Radiative Transfer Equation


SRTE (cont.)

),,( �� vsatm

Absorbing ground


SRTE (cont.)

Ei

Et


SRTE (cont.)


SRTE (cont.)

��v

Er

E0

40Atmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises

SRTE 1 interaction (cont.)


SRTE 2 interactions


SRTE Multiple Interactions

��groundSatm < 1 so when n->��groundSatm)n ->0

Therefore


STRE for non absorbing atmosphere and lambertian ground


1 �groundSatm

Apparent reflectance at satellite level

Atmospheric reflectance

AtmosphericTransmissions

Atmospherespherical albedo

Ground reflectance(= albedo for lambertian)


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


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


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:


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

�

��

��

��

��

��


Water vapor effect for different sensors in the near infrared


Scattering angle ,• The scattering angle, �� is the relative

angle between the incident and the scattered radiation

ParticleIncident Radiation

��


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


Rayleigh/molecular scattering 1/4

• Rayleigh or molecular scattering refers to scattering by atmospheric gases, in that case:


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



• The rayleigh reflectance, �R, could be crudely approximated by:


• 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



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.


Aerosol scattering 2/5Continental aerosol phase function


Aerosol scattering 3/5single scattering albedo(0.2-1.0) to account for absorbingparticles


Aerosol scattering 4/5Continental aerosol optical thickness spectral variation


Aerosol scattering 5/5Continental aerosol single scattering albedo spectral variation


Atmospheric effect: Vegetation 1/3



No absorption, Continental aerosolAtmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises


Absorption tropical atmosphere, Continental aerosolAtmospheric Correction of Earth Observation Data for Environmental Monitoring: Theory and Best Practises

Atmospheric effect: Ocean 1/2


Atmospheric effect: Ocean 2/2


Perfect Lambertian Reflector

Isotropicradiation


Different Types of Reflectors

Specular reflector (mirror) diffuse reflector (lambertian)

nearly diffuse reflectorNearly Specular reflector (water)

Hot spot reflection


Sun glint as seen by MODIS

Gray level temperature image


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


BRDF atmosphere coupling correction


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 �


Adjacency effect correction


1 �groundSatm

Lambertian infinite target approximation

adjacency effect approximation

� �evdatms

eatm

satmatmapp te

ST

v ��

�� )(1

)( / �

��

��

�

drddrrdFre � �

�

�2

0 0

)(),(21


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 ��

� �

�


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


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.


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)


introduction to radiative t ransfer theory and models (optical … · 2014-05-15 · introduction...

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