\chapter{SWASH model}

\section{1D model}

In order to find out if the reflection induced by the breakwater has an
influence on the sea state at the buoy's location, a one-dimensional model of
the zone between the buoy and the breakwater was created.

The considered domain is \SI{1450}{\m} long, with \SI{1250}{\m} between the
buoy and the breakwater, and a further \SI{200}{\m} offshore of the buoy.
The model is a 10 layers swash model accounting for porous media in near the
breakwater. The model was adapted from PA Poncet.

\subsection{Model 1}

A first run was produced in order to test the model with a water level of
\SI{0.5}{\m} using the measured spectrum from 2017-02-28 as the offshore
boundary condition and a sommerfeld radiation condition on the breakwater
boundary. The model was run over a duration of 30 minutes.

The same model was implemented without the breakwater (by forcing a minimum
depth) with an added \SI{250}{\m} sponge layer at the shorewards boundary.

The reflection coefficient at the buoy's location was computed using
a PUV method \parencite{huntley1999use}.

The results are displayed in \autoref{fig:swash_1_R}. Two methods of
calculating the reflection were used \parencite{huntley1999use}, the second one
might be wrongly implemented, and the first one might be subject to
noise-induced bias.

\begin{figure}
	\centering
	\includegraphics{R1.png}
	\includegraphics{R2.png}
	\caption{Reflection coefficient computed with Swash. 1: With breakwater; 2:
	Without breakwater.}\label{fig:swash_1_R}
\end{figure}

\subsection{Model 2}

An attempt at running the model with the correct water level (\SI{4.5}{\m}) was
made without success, as the model does not seem to be able to compute
overtopping. Changing the boundary condition at the breakwater does not fix the
issue, and the model is not able to run with water on both sides of the
breakwater as the initial condition.

\paragraph{SWASH overtopping} \cite{suzuki2011applicability,zhang2020numerical} It seems like computing wave overtopping
should be possible using the SWASH model.

Implemented model with longer domain, with water behind the breakwater; currently, model crashes when overtopping
happens.

The model DOES NOT crash if layers are disabled (depth-averaged model). No overtopping seems to appear in the results.

Resulting reflection coefficient in \autoref{fig:swash_nolay}: very high reflection coefficient, probably inaccurate.

\begin{figure}
	\centering
	\includegraphics{R_singlelayer.png}
	\caption{Reflection coefficient computed with Swash without layers (method 1, probable noise-induced
	bias.}\label{fig:swash_nolay}
\end{figure}

Model does also work with 2 layers; overtopping does appear \autoref{fig:swash_2lay}.

\begin{figure}
	\centering
	\includegraphics{R_2lay.png}
	\caption{Reflection coefficient computed with Swash 2 layers (method 1, probable noise-induced
	bias.}\label{fig:swash_2lay}
\end{figure}

Model crashes with 3 or more layers.

\subsection{Model 3}
Model: \SI{1450}{\m} offshore, \SI{300}{\m} shorewards. \SI{250}{\m} sponge layer. \SI{4.5}{\m} water level. 2 layers.
\autoref{fig:bathy}

\begin{figure}
	\centering
	\includegraphics{bathy_b.pdf}
	\includegraphics{bathy_nb.pdf}
	\caption{Bathymetry.}\label{fig:bathy}
\end{figure}

Results \autoref{fig:res45}.
\begin{figure}
	\centering
	\includegraphics{R_2lay_45.pdf}
	\caption{Results (1: breakwater; 2: no breakwater).}\label{fig:res45}
\end{figure}

\subsection{Model with measured time-series}
Using raw buoy data. Model crashes with 2 layers. Works when layers are disabled. \textbf{No overtopping!}
\autoref{fig:rests}. \SI{1}{\hour} computation time.

\begin{figure}
	\centering
	\includegraphics{R_ts.pdf}
	\caption{Results with real timeseries, no layers.}\label{fig:rests}
\end{figure}

%\subsection{2D Model}
%Working on 2D model which might work with overtopping.