atmospheric effect in the solar spectrum vermote et al. university of maryland/ dept of geography...
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Atmospheric effect in the solar spectrum
Vermote et al.
University of Maryland/ Dept of Geography and
NASA/GSFC Code 614.5
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
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
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 3/5
A (s ,v ,) ~
A A
P()
4cos(s )cos(v )
single scattering albedo(0.2-1.0) to account for absorbingparticles
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
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.