Rayleigh scattering

About Rayleigh scattering in LMDZ Generic

Formalism

References

Hansen (1974) : https://ui.adsabs.harvard.edu/link_gateway/1974SSRv...16..527H/ADS_PDF

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

in optcv.F90 :

TRAY(K,NW) = TAURAY(NW) * DPR(K)

Let's write it :

TRAY \( \displaystyle = \tau_{RAY}(\lambda) dP\)

In exo_k we have :

TRAY \( \displaystyle = \sigma_{exok} dN \) with dm in kg/m2

TRAY \( \displaystyle = \sigma_{exok} \frac{dm}{m_{molecule}} \) with dm in kg/m2

TRAY \( \displaystyle = \frac{\sigma_{exok}}{g * m_{molecule}} dP\)

so

\( \displaystyle \tau_{RAY}(\lambda) = \frac{\sigma_{exok}}{g * m_{molecule}} \)

To be noticed :

We write \( \displaystyle TRAY = \tau_{RAY} dP\)

TAURAY(NW) is calculated in calc_rayleigh.F90

For each channel, it is in fact TAUVAR which calculated, and then averaged by the black body function to give TAURAY \[ \text{TAURAY(NW)} = \frac{\int_{\lambda'} \text{TAUVAR} (\lambda') B_{\lambda} \, \mathrm{d}\lambda'}{\int B_{\lambda} \, \mathrm{d}\lambda'} \]

\( \displaystyle \tau(\lambda) \) is called TAUVAR