Difference between revisions of "Rayleigh scattering"
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== Formalism == | == Formalism == | ||
| − | We consider a layer | + | We consider a layer. |
dP is the difference of pressure between the two levels that define the layer. | dP is the difference of pressure between the two levels that define the layer. | ||
dN is the number of molecules per m2 & dm is the mass per m2 of the layer | dN is the number of molecules per m2 & dm is the mass per m2 of the layer | ||
| + | |||
| + | dTau is the optical depth for a given wavelength | ||
<math>m_{molecule}</math> is the mass of one molecule of the considered gas | <math>m_{molecule}</math> is the mass of one molecule of the considered gas | ||
| Line 43: | Line 45: | ||
g is the gravity | g is the gravity | ||
| − | + | sigma_mol is the Rayleigh scattering cross section of the molecule | |
| − | |||
| − | sigma_mol is the Rayleigh scattering cross section | ||
=== LMDZ formalism === | === LMDZ formalism === | ||
Revision as of 18:18, 4 October 2022
Contents
About Rayleigh scattering
The following article gives a clear overview on Rayleigh scattering cross sections :
Bodhaine (1999) On Rayleigh Optical Depth Calculations : http://web.gps.caltech.edu/~vijay/Papers/Rayleigh_Scattering/Bodhaine-etal-99.pdf
Have a look especially on equations (2) and (9).
About Rayleigh scattering in LMDZ Generic
References
LMDZ
LMDZ uses formalism from :
Hansen (1974) Light scattering in planetary atmospheres : https://ui.adsabs.harvard.edu/link_gateway/1974SSRv...16..527H/ADS_PDF
Have a look on equations (2.29) to (2.32).
exo_k
Rayleigh routine in exo_k is avalaible here :
Exo_k uses formalism from :
Caldas (2019) Effects of a fully 3D atmospheric structure on exoplanet transmission spectra: retrieval biases due to day–night temperature gradients : https://hal.archives-ouvertes.fr/hal-02005332/document
Have a look on equation (12) & appendix D
Formalism
We consider a layer.
dP is the difference of pressure between the two levels that define the layer.
dN is the number of molecules per m2 & dm is the mass per m2 of the layer
dTau is the optical depth for a given wavelength
\(m_{molecule}\) is the mass of one molecule of the considered gas
g is the gravity
sigma_mol is the Rayleigh scattering cross section of the molecule
LMDZ formalism
In LMDZ0 we have :
dTau = scalep * (tauconsti * tauvari) * dP
tauvari = tauvari(wavelength in micron)
scalep = 100 because P is in mBar in optcv.F90
exo_k formalism
dTau = sigma_mol * dN
sigma_mo = sigma_mol(wavenumber in cm-1)
which gives : dTau = sigma_mol \( \displaystyle \frac{dm}{m_{molecule}} \)
and then : dTau \( \displaystyle = \frac{\text{sigma_mol}}{g * m_{molecule}} dP\)
Relations between LMDZ & Exo_k formalisms
LMDZ & exo_k formalism are linked as following \[ \displaystyle \text{(tauconsti * tauvari)} = \frac{\text{sigma_mol}}{g * m_{molecule}} * \text{scalep}\]
Be careful with units !!! (cm-1 for wavenumbers in exo_k, microns for wavelengths in LMDZ, not to forget the scalep factor in LMDZ)
To be noticed
TAURAY(NW) is calculated in calc_rayleigh.F90.
It is in fact TAUVAR which calculated, and then averaged by the black body function for each channel to give TAURAY \[ \text{TAURAY(NW)} = \frac{\int_{\lambda' \in \text{channel}} \text{TAUVAR} (\lambda') B_{\lambda} \, \mathrm{d}\lambda'}{\int B_{\lambda} \, \mathrm{d}\lambda'} \]
TAUVAR is cut into two parts : TAUCONSTI et TAUVARI with TAUVAR = TAUCONSTI * TAUVARI
The \( \lambda \) dependence is in the TAUVARI
