<%namespace name="tools" file="tools.tex"/>
<%! import os %>
\chapter{Laboratory experiments: morphodynamics}
\label{sec:morphodynamic}

In this chapter, the performance of XBeach is compared to results obtained from physical model tests performed in a variety experiments (this report) and field measurements (to be added in Fase 1 of the BOI Zandige Keringen project). Many of those tests are part of fundamental research to dune erosion and other morphological processes. Research took place at different laboratory scales, mainly depending on the size of the facility used. Since large-scale experiments show a more realistic dune erosion profile, only large scale physical experiments are shown. 

The accuracy of XBeach is quantitative verified for three indicators of the morphology \citep[see][]{Deltares2020_par}. Based on the profiles on several moments in time (t), the berm slope indicator, dune retreat indicator and erosion volume are compared to the observed indicator (See \autoref{fig:overview_BOI_ds}, \autoref{fig:overview_BOI_erosion} and \autoref{fig:overview_BOI_slope}). The definition of these indicators is given in \autoref{app:MorphologyIndicators}. The relative error of these indicators is computed for every moment in time where observations are available,
\begin{equation}
	V_{rel} = (V_{xb,t}-V_{data,t})/V_{data,t_{end}}
\end{equation} 
\begin{equation}
	S_{rel} = (slope_{xb,t}-slope_{data,t})/slope_{data,t}
\end{equation} 
\begin{equation}
	dx_{rel} = (dx_{xb,t}-dx_{data,t})/dx_{data,t_{end}}
\end{equation} 
where $V$ is the erosion volume above maximum still water level, $slope$ the berm slope and $dx$ the dune retreat. The quantities computed with XBeach are indicated with  $xb$ and the observed quantities are indicated with $data$. Next to the relative error with respect to the last timestep for the erosion volumes and dune retreat, the relative errors with the corresponding time is also computed:
\begin{equation}
	V_{rel,t}  = (V_{xb,t}-V_{data,t})/V_{data,t}
\end{equation} 
\begin{equation}
	dx_{rel,t} = (dx_{xb,t}-dx_{data,t})/dx_{data,t}
\end{equation} 

The root-mean-squared value of these series of relative errors is used to obtain a single error measure per indicator for all moments in time (except for the data points in the first hour of an experiment). The relative errors in the first hour are ignored since this relative error can be large compared to the other moments in time and the fact that these initial errors are not important for the dune assessment (similar as described in \cite{Deltares2020_par}).
%%\begin{multline}
%%	error_{combined} = sign(mean(\text{rel. error V(t)})) 1/3(RMS(\text{rel. error V(t)})) + \\ RMS(\text{rel. error Slope(t)})) + RMS(\text{rel. error dx(t)}))) 
%%\end{multline} 



${tools.image(os.path.join(data_path,'indicators/'), 'overview_BOI_ds.png','Dune retreat indicator. See the Appendix for the definition of this indicator.',label='overview_BOI_ds',width=150)}

${tools.image(os.path.join(data_path,'indicators/'), 'overview_BOI_erosion.png','Definition of erosion volume. See the Appendix for the definition of this indicator.',label='overview_BOI_erosion',width=150)}

${tools.image(os.path.join(data_path,'indicators/'), 'overview_BOI_slope.png','Berm slope indicator. See the Appendix for the definition of this indicator.',label = 'overview_BOI_slope',width=150)}



\section{H4357: Delta Flume 2006}

<%include file="deltaflume2006.tex"/>
<%include file="deltaflume2006_BOI.tex"/>



\section{M1797: Delta Flume 1981}

In 1981, Delta Flume experiments were performed to gain insight in the effect of a dune revetment on the morphological behaviour of the dune, however, experiments were also carried out without a dune revetment. The profile in question is based on a stretch of coast called the Noorderstrand at Schouwen, the Netherlands \citep{Vellinga1981b}. Two large scale experiments (depth scale of 2) were performed, one with and one without dune revetment. The latter is depicted in \autoref{fig:M1797}. \autoref{tab:Deltaflume_M1797_T01_indicator} shows the results for the indicators at different moments in time.

${tools.image('Deltaflume_M1797/T01/', 'T01_BOI_profiles.png', 'Comparison of profile during experiment T01. Observed profiles are shown with a dashed line and the XBeach profiles with a solid line. The storm surge level is shown with a black dashed line.',label='M1797',width=150)}
${tools.table('Deltaflume_M1797/T01/', 'indicator.tex', 'Indicators for T01',small=True)}
${tools.image('Deltaflume_M1797/T01/', 'T01_BOI_errorTime.png', 'Temporal development of the relative error for the three indicators.')}

\section{M1263 III: Delta Flume 1980-1981}
<%include file="m1263-iii_BOI.tex"/>



\section{LIP11D: Delta Flume 1994}
<%include file="lip-2e_BOI.tex"/>


\section{Deltaflume H4731}

In the H4731 Delta flume experiments, it was studied how a collapsed dune revetment affects dune erosion \citep{VanGent2007}. Four large-scale experiments were performed in the Delta flume with a depth scale of $n_d$ equals 6. A wave height of 9 m (prototype) and peak period of 12 s (prototype) were forced at the wave maker. The test without a revetment (T14) is modelled with XBeach (\autoref{fig:H4731_T14}). The results for the indicators for different moments in time are shown in \autoref{tab:Deltaflume_H4731_T14_indicator}. Note that the observed dune retreat is zero since the dune front does not erode in the observed profiles. This means that the relative error in dune retreat cannot be computed.


${tools.image('Deltaflume_H4731/T14/', 'T14_BOI_profiles.png', 'Comparison of profile during experiment T14 Observed profiles are shown with a dashed line and the XBeach profiles with a solid line. The storm surge level is shown with a black dashed line.',label='H4731_T14',width=150)}
${tools.table('Deltaflume_H4731/T14/', 'indicator.tex', 'Indicators for T14',small=True)}
${tools.image('Deltaflume_H4731/T14/', 'T14_BOI_errorTime.png', 'Temporal development of the relative error for the three indicators.')}

\section{Grosse Wellen Kanal 1998}

<%include file="gwk98.tex"/>

