30 Radiative transfer algorithms

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:

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.