Difference between revisions of "Rayleigh scattering"
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<math> \text{TAURAY(NW)} = \frac{\int_{\lambda' \in \text{channel}} \text{TAUVAR} (\lambda') B_{\lambda} \, \mathrm{d}\lambda'}{\int B_{\lambda} \, \mathrm{d}\lambda'} </math> | <math> \text{TAURAY(NW)} = \frac{\int_{\lambda' \in \text{channel}} \text{TAUVAR} (\lambda') B_{\lambda} \, \mathrm{d}\lambda'}{\int B_{\lambda} \, \mathrm{d}\lambda'} </math> | ||
| − | TAUVAR is cut into two parts : TAUCONSTI et TAUVARI | + | TAUVAR is cut into two parts : TAUCONSTI et TAUVARI with TAUVAR = TAUCONSTI * TAUVARI |
The <math> \lambda </math> dependence is in the TAUVARI | The <math> \lambda </math> dependence is in the TAUVARI | ||
Revision as of 15:31, 28 September 2022
Contents
About Rayleigh scattering in LMDZ Generic
References
LMDZ
Hansen (1974) : https://ui.adsabs.harvard.edu/link_gateway/1974SSRv...16..527H/ADS_PDF equations (2.29) to (2.32)
exo_k
Rayleigh routine in exo_k : http://perso.astrophy.u-bordeaux.fr/~jleconte/exo_k-doc/_modules/exo_k/rayleigh.html#Rayleigh.sigma_mol
Exo_k uses formalism from : Caldas (2019) : https://hal.archives-ouvertes.fr/hal-02005332/document equation (12) & appendix D
Formalism
We consider a layer .
DPR(K) is the difference of pressure between the two levels that define the layer.
dm is the mass per m2 of the layer
LMDZ formalism
In LMDZ, in optcv.F90 we have :
TRAY(K,NW) = TAURAY(NW) * DPR(K)
exo_k formalism
TRAY \( \displaystyle = \sigma_{exok} dN \) with \( \displaystyle \sigma_{exok} \) the cross section and dN in molecules/m2
which gives : TRAY \( \displaystyle = \sigma_{exok} \frac{dm}{m_{molecule}} \) with dm in kg/m2
and then : TRAY \( \displaystyle = \frac{\sigma_{exok}}{g * m_{molecule}} dP\)
Relations between LMDZ & Exo_k formalisms
LMDZ & exo_k formalism are linked as following \[ \displaystyle \text{TAURAY} = \frac{\sigma_{exok}}{g * m_{molecule}} \]
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
