  To study the temperature in a gas subjected to electromagnetic radiations,
one may use the Radiative Transfer equations coupled with the Navier-Stokes
equations. The problem has 7 dimensions; however with minimal simplifications
it is equivalent to a small number of integro-differential equations in 3
dimensions. We present the method and a numerical implementation using an
H-matrix compression scheme. The result is a very fast: 50K physical points,
all directions of radiation and 680 frequencies require less than 5 minutes on
an Apple M1 Laptop. The method is capable of handling variable absorptioN and
scattering functionS of spatial positions and frequencies.
  The implementation is done using htool, a matrix compression library
interfaced with the PDE solver freefem++. Applications to the temperature in
the French Chamonix valley is presented at different hours of the day with and
without snow / clouds and with a variable absorption taken from the Gemini
measurements. The result is precise enough to assert temperature differences
due to increased absorption in the vibrational frequency subrange of greenhouse
gasses.

Numerical Analysis;Numerical Analysis;Analysis of PDEs