Atmospheric effect in the solar spectrum

Vermote et al.

University of Maryland/ Dept of Geography and

NASA/GSFC Code 614.5

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

s

),,( VSreflectorLambertian

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

2

0

ssS EddRPLF

Isotropicradiation

Es

Radiance of the Perfect Lambertian Reflector

1),,( VSreflectorLambertianPerfect

Simple Radiative Transfer Equation

ground

atmosphere

sv

SRTE (cont.)

atmosphere

sv ),,( vsatm

Absorbing ground

SRTE (cont.)

s Ei

Et

Tatm(s ) Et

Ei

SRTE (cont.)

Et Er groundEt

SRTE (cont.)

v

Er

E0

Tatm(v) Eo

Er

40

SRTE 1 interaction (cont.)

ground

atmosphere

sv

app atm Eo

Ei

Eo

Ei

T(v )Er

Ei

T(v )groundEt

Ei

T(v )groundT(s )

app atm T(v )groundT(s )

SRTE 2 interactions

ground

atmosphere albedo =Satm

Ei

EiT(s )

EiT(s )ground

EiT(s )groundSatm

EiT(s )groundSatmground

EiT(s )groundSatmgroundT(v)

SRTE Multiple Interactions

app atm T(s )T(v )ground 1 groundSatm groundSatm 2 groundSatm 3...

app atm Tatm(s )Tatm(v )ground

1 groundSatm

1 r r2 r 3 ...r n 1 1 r n

1 r

groundSatm < 1 so when n->∞ then (groundSatm)n ->0

Therefore 1 groundS groundS 2 groundS 3... 1

1 groundS

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)

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 Satmground

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:

10

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 )

ground

1 SRAground

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

scattered 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:

P( )d 40

0

2

P( )sin( )dd 0

0

2

2 P()sin()d0

P() sin( )d0

2

since

we have

Rayleigh/molecular scattering 1/4

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

P() 3

41 cos 2()

00.20.40.60.8

11.21.41.6

0

30

6090

120

210

240270

300

330

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

Rayleigh/molecular scattering 3/4

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

R (s ,v ,) ~

R P()

4cos(s )cos(v )

• Compute the reflectance of the sky (assumed clear no aerosol) at solar noon at 45degree latitude at vernal equinox looking straight up at 0.45m, 0.55m, 0.65m

Rayleigh/molecular scattering 4/4

R0.45m(45 ,0 , )

0.235P(45 )

4cos(45 )cos(0)

0.235x0.75(1 cos2 (45))

4 cos(45 )cos(0 )

0.265

2.8~ 0.1

R0.55m 0.1x(0.45/ 0.55)4 ~ 0.1x0.4 0.04

R0.65m 0.04x(0.55/ 0.65)4 ~ 0.04x0.5 0.02

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 3/5

A (s ,v ,) ~

A A

P()

4cos(s )cos(v )

single scattering albedo(0.2-1.0) to account for absorbingparticles

Aerosol scattering 4/5Continental aerosol optical thickness spectral variation

60

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

Atmospheric effect: Vegetation 1/3

Atmospheric effect: Vegetation 2/3

No absorption, Continental aerosol

Atmospheric effect: Vegetation 3/3

Absorption tropical atmosphere, Continental aerosol

Atmospheric effect: Ocean 1/2

Atmospheric effect: Ocean 2/2

Perfect Lambertian Reflector

s

RPLF(S ,V,) ES cos(S )

RPLF(S ,,)0

2

0

cos( )sin()dd Es cos(s )

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

Su

rfac

e R

efle

ctan

ce

Scatterin

g An

gle (°)

View Zenith Angle (°)

0.645 m

0.555 m

0.469 m

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

S

STT

tttete

ee

sv

vs

1

)()(

)()(')()(

),,(),,(),,(

2

//

//

')',,(

')',,()',,(),,( 2

0

1

0

2

0

1

0

ddL

ddL

satm

vssatm

vss

),,(),,(' vssvss ),,('),,( vssvss

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

S

Tv

)(

1

)( /

drddr

rdFre

2

0 0

)(),(

2

1

Adjacency effect correction (practical implementation)

)()( vatmsatm

atmappi TT

iatm

is S

1

inf

eatmvatm

evdatms

i ST

te v

1)(

)(/

ve

tST evdatmeatmvatmi

s /

)(1)(

),()),(( inf ji

dr

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)

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)

G S F C

B a l t i m o r e / W a s h i n g t o n P a r k w a yH a r v e s t e dC o r n f i e l d

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)

Conclusions

• Review of atmospheric effect including the BRDF-coupling and the adjacency effect

• Current version of MOD09 (Collection 4) does not include the BRDF-coupling or adjacency effect correction

• Collection 5 (start scheduled in Jan06), will include adjacency correction for 250m bands. BRDF-coupling correction is still being evaluated.