\section{Making a Dummy THICC Atmospheric Model*}
* The naming of this section is decided by the stream name, I did not come up with this \cite{twitch}. During this stream, a lot of plotting improvements have been made, which is not the scope of
this manual and hence has been left out. The plan was to add vertical momentum and advection, though things did not go according to plan\dots

\subsection{Discovering That Things Are Broken}
While trying to add vertical momentum, it appears that some parts of the model are broken in their current state. The horizontal advection is one of the things that is broken. If you recall, 
we needed to use the Laplacian operator in the advection equations (as shown in \autoref{eq:diffusion}, diffusion is considered a part of advection since diffusion transports energy and matter
which is what advection does as well). The Laplacian operator (as shown in \autoref{alg:laplacian layer}) does not work. It is currently unknown why that is. If a fix has been found, the original
algorithm will be fixed accordingly (unless a lot of stuff changes and we need additional functions to be defined, then I will put a reference there to the section where it will be fixed). For 
now we disabled the Laplacian operator as it has a small effect on the total advection (and because it is broken).

Another thing that we found out was broken is the vertical momentum. We tried to add it, ran into problems and just set it to 0 to fix the other problems that occured. One of those problems was 
a wrong initialisation of the density. We basically told the model that the density is the same on every layer of the atmosphere, which is obviously not true. Hence we need to adjust that. The 
new initialisation is described in \autoref{alg:density}. Note that the $\rho[:,: i]$ notation means that for every index in the first and second dimension, only change the value for the index $i$
in the third dimension.

\begin{algorithm}
    $\rho[:, :, 0] \leftarrow 1.3$ \;
    \For{$i \in [1, nlevels-1]$}{
        $\rho[:, :, i] \leftarrow 0.1\rho[:, :, i - 1]$
    }
    \caption{Initialisation of the air density $\rho$}
    \label{alg:density}
\end{algorithm}