Difference between revisions of "Rayleigh scattering"
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<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 | ||
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TRAY is the optical depth | TRAY is the optical depth | ||
Revision as of 16:54, 28 September 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 K & the channel NW.
DPR(K) ( or 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
\(m_{molecule}\) is the mass of one molecule of the considered gas
g is the gravity
TRAY is the optical depth
sigma_mol the Rayleigh scattering cross section
LMDZ formalism
In LMDZ, in optcv.F90 we have :
TRAY(K,NW) = TAURAY(NW) * DPR(K)
exo_k formalism
TRAY = sigma_mol * dN
which gives : TRAY = sigma_mol \( \displaystyle \frac{dm}{m_{molecule}} \)
and then : TRAY \( \displaystyle = \frac{\text{sigma_mol}}{g * m_{molecule}} dP\)
Relations between LMDZ & Exo_k formalisms
LMDZ & exo_k formalism are linked as following \[ \displaystyle \text{TAURAY} = \frac{\text{sigma_mol}}}{g * m_{molecule}} \]
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
