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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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modeling rotational raman scattering in the earth s atmosphere

Modeling rotational Raman scattering in the Earth’s atmosphere

Rutger van Deelen

Jochen Landgraf

Otto Hasekamp

Ilse Aben

September 13, 2006, KNMI

three questions
Three questions

Multiple scattering. Multiple Raman scattering?

Polarization?

Dependence on input solar spectrum?

measured gome spectra
Measured GOME spectra

solar irradiance spectrum

Earth radiance spectrum

rotational raman scattering
Rotational Raman scattering

AIR (N2, O2)

Cabannes

96 % elastic

Raman

4 % inelastic

Raman

doubling adding approach
Perturbation theory approachDoubling-addingapproach

multiple orders of Raman scattering,

comes out naturally,

scalar

one order of Raman scattering,

fast,

vector

wP

wP

wP

wP

wP

A

rayleigh
Rayleigh

optical

thickness

tray(l)

single

scattering

albedo

wray(l)

Pray

phase

function

Q

rayleigh1
Rayleigh

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

perturbation theory approach based on the green s function1
Perturbation theory approach: based on the Green’s function

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

perturbation theory approach based on the green s function2
Perturbation theory approach: based on the Green’s function

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+ …

perturbation theory approach expansion of the green s function1
Perturbation theory approach: expansion of the Green’s function

b

a

b

a

Gray

Gray

Gray

-

D

for all

Rayleigh +

1 order of Raman

Rayleigh

perturbation theory approach expansion of the green s function2
Perturbation theory approach: expansion of the Green’s function

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

perturbation theory approach expansion of the green s function3
Perturbation theory approach: expansion of the Green’s function

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

comparison pert da1
Comparison pert - da

Filling-in

[%]

Difference

pert - da

polarization
Polarization

Stokes vector

neglect of polarization
Neglect of polarization

Error

continuum

[%]

scalar -vector

Error

filling-in

[%]

scalar -vector

conclusion
Conclusion

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 filling-in

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%.

the doubling adding product
The doubling-adding product

Involves integration over all possible angles

AND all possible wavelengths

(Use optimized wavelength grid, only relevant bins)

optimizing the wavelength grid
Optimizing the wavelength grid

w

w

(w+ww)/2

order

of

scattering

(w+ww+www)/3

wavenumber shift [cm-1]

optimizing the wavelength grid1
Optimizing the wavelength grid

w

w

threshold

(w+ww)/2

order

of

scattering

(w+ww+www)/3

wavenumber shift [cm-1]

polarization the phase matrix elements
Polarization: the phase matrix elements

P11cab

P21cab

P22cab

P33cab

P44cab

Q

Q

Q

Q

Q

P11ram

P21ram

P22ram

P33ram

P44ram

P34 = 0

how much multiple raman scattering
How much multiple Raman scattering?

reflectivity

total Raman scattering

fraction

multiple Raman

scattering fraction

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