Radiative Transfer for Atmospheres with Clouds

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. A numerical implementation using an ℋ-matrix compression scheme allows us to measure the effect of clouds and airplane contrails on the temperature in the atmosphere. The result is very fast and the method is capable of handling variable absorption and scattering functions of spatial positions and frequencies.