Radiation is treated in models using separate simulations, so-called radiative transfer models. This takes place in the following steps; the procedure may be slightly modified in the specific implementation:
First, the densities of the components of the air are transmitted to the radiation model.
The radiation properties of the matter are then calculated using these densities and tabulated spectra of the substances.
Now the spectral radiation flux density $S_{i}^{(j)}$ is calculated in $N_S\geq 1$ intervals by solving the radiative transfer equation.
By spectrally integrating the convergence of the radiation flux density, thermal power densities are determined, which are transmitted back to the dynamic core. From these, heating rates are obtained.
Since solving the radiative transfer equation would lead to a global linear system of equations, the atmosphere is divided into non-interacting columns that have at least the horizontal extent of a grid cell.
Once the vertical radiation flux densities $S_i^{(j)}$ are available for every spectral interval $j$ at every interface $i$, one can first sum the radiation flux density over all intervals:
\[ \begin{align} S_i\coloneqq\sum_{j=1}^{N_S}S_{i}^{(j)} \end{align} \]
The thermal power density $q_i^{(V)}$ can be derived from this by means of the continuity equation:
\[ \begin{align} q_i^{(V)} = S_{i+1} - S_i \end{align} \]
This power density must then be inserted into the temperature equation of the model.