Modeling rotational raman scattering in the earth s atmosphere
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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


The gome reflectivity spectrum

The GOME reflectivity spectrum


The gome reflectivity spectrum1

The GOME reflectivity spectrum

Raman


Rotational raman scattering

Rotational Raman scattering

AIR (N2, O2)

Cabannes

96 % elastic

Raman

4 % inelastic

Raman


Filling in

Filling-in


Filling in1

Filling-in


Doubling adding approach

Perturbation theory approach

Doubling-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


Doubling adding approach1

Doubling-adding approach

R

T


Doubling adding approach2

Doubling-adding approach

R

T

Rab

a

b

Tab


Perturbation theory approach based on the green s function

Perturbation theory approach: based on the Green’s function

(z’,l’,W’)

a

b

(z,l,W)


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 function

Perturbation theory approach: expansion of the Green’s function

b

a

Gray

Rayleigh


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 da

Comparison pert - da

Filling-in

[%]


Comparison pert da1

Comparison pert - da

Filling-in

[%]

Difference

pert - da


Polarization

Polarization

Stokes vector


Polarization1

Polarization


Neglect of polarization

Neglect of polarization

Error

continuum

[%]

scalar -vector

Error

filling-in

[%]

scalar -vector


The simulated ring effect depends on the input solar spectrum

The simulated Ring effect depends on the input solar spectrum


Using a retrieved solar spectrum instead

Using a retrieved solar spectrum instead

Clear sky

land


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%.


Thank you for your attention

Thank you for your attention

www.sron.nl/raman

[email protected]


Backup slides

Backup slides


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


Using the retrieved solar spectrum a

Using the retrieved solar spectrum (A)


Using the retrieved solar spectrum b

Using the retrieved solar spectrum (B)


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