Rayleigh scattering
Contents
About Rayleigh scattering
The following article gives a clear overview on Rayleigh scattering cross sections :
Bodhaine (1999) 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) : 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) : https://hal.archives-ouvertes.fr/hal-02005332/document
Have a look on 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
We consider the channel NW
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
