Modeling rotational Raman scattering in the Earth’s atmosphere. Rutger van Deelen Jochen Landgraf Otto Hasekamp Ilse Aben. September 13, 2006, KNMI. Three questions. Multiple scattering. Multiple Raman scattering? Polarization? Dependence on input solar spectrum?. Measured GOME spectra.
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Rutger van Deelen
Jochen Landgraf
Otto Hasekamp
Ilse Aben
September 13, 2006, KNMI
Multiple scattering. Multiple Raman scattering?
Polarization?
Dependence on input solar spectrum?
Raman
Perturbation theory approach atmosphere
Doublingaddingapproachmultiple orders of Raman scattering,
comes out naturally,
scalar
one order of Raman scattering,
fast,
vector
wP
wP
wP
wP
wP
A
optical
thickness
tray(l)
single
scattering
albedo
wray(l)
Pray
phase
function
Q
Cabannes + Raman
optical
thickness
tray(l)
tray(l’) = tcab(l’) + S tram(l,l’)
l
total
elastic
inelastic
wcab(l)
inelastic
single
scattering
albedo
wram(l,l’)
wray(l)
w(l,l’)
Pray
Pcab
phase
function
Q
Q
Pram
G = G(z,l,W;z’,l’,W’)
(z’,l’,W’)
a
G
b
arrow includes multiple scattering!
(z,l,W)
describes how the atmosphere responds to light
b
a
source and
target are
fixed
G
arrow includes multiple scattering!
Dyson series
G = Gray – Gray [ D Gray ] + Gray [ D Gray ]2 – Gray [ D Gray ]3+ …
b
a
b
a
Gray
Gray
Gray

D
for all
Rayleigh +
1 order of Raman
Rayleigh
b
a
b
a
b
a
Gray
Gray
Gray
Gray
D
Gray
 ...

D
+
D
Gray
for all
for all
Rayleigh +
1 order of Raman
Rayleigh +
2 orders of Raman
Rayleigh
b
a
b
a
b
a
Gray
Gray
Gray
Gray
D
bw
Gray
 ...
+
D
+
D
Gray
for all
for all
Rayleigh +
1 order of Raman
Rayleigh +
2 orders of Raman
Rayleigh
Stokes vector
Error
continuum
[%]
scalar vector
Error
fillingin
[%]
scalar vector
Radiative transfer problem including Raman scattering involves
scattering from one direction to another direction &
from a certain wavelength to another wavelength
Challenge
Answers
1.Neglecting multiple Raman scattering: errors < 0.6 %
2.Neglecting polarization: errors < 0.2 % on fillingin
Scalar approach can be used to simulate Ring effect.
Polarization effects mainly due to elastically scattered radiation.
3. Different input solar spectra: differences up to 8%
Solution: construct a solar spectrum on a high resolution wavelength grid from the measurements. Better than 0.5%.
Involves integration over all possible angles
AND all possible wavelengths
(Use optimized wavelength grid, only relevant bins)
w
w
(w+ww)/2
order
of
scattering
(w+ww+www)/3
wavenumber shift [cm1]
w
w
threshold
(w+ww)/2
order
of
scattering
(w+ww+www)/3
wavenumber shift [cm1]
P11cab
P21cab
P22cab
P33cab
P44cab
Q
Q
Q
Q
Q
P11ram
P21ram
P22ram
P33ram
P44ram
P34 = 0
reflectivity
total Raman scattering
fraction
multiple Raman
scattering fraction