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\textbf{Experiment description}\newline
Hydrodynamic data were obtained along a cross-shore transect at the tail of the Dutch barrier island ‘Schiermonnikoog’ in the Wadden Sea during a measurement campaign of the department Physical Geography of Utrecht University (UU) in the winter of 2014-2015. The campaign was part of the PhD research of Anita Engelstad and Daan Wesselman. The measurements are used for the validation of the hydrodynamics in the BOI-version of the dune erosion model XBeach, with a focus on the validation of simulated infragravity waves.

The location of the measurements is indicated in \autoref{fig:Overview_schiermonnikoog}. The beach and nearshore morphology near the transect is alongshore almost uniform. The cross-shore profile is a typical Wadden Sea profile, with a mildly sloping foreshore (about 1:100) and three offshore bars. In the intertidal zone, two to three bars are present, which is also visible in the aerial photograph (\autoref{fig:Overview_schiermonnikoog}). The highest point along the transect – the beach crest – is at less than 1.8 m +NAP: no dunes are present at the tail and the tail is completely inundated several times per year. At the landward side of the beach crest, the profile gently slopes towards the Wadden Sea. The elevation along the intertidal and subtidal part of the transect has been measured with a RTK-GPS system at the beginning and the end of the field campaign. For the subtidal part, open-source yearly Jarkus transects and ‘Vaklodingen’ data of RWS are available.  

${tools.image(os.path.join(data_path,'Schiermonnikoog'), 'overview_schiermonnikoog.png', 'Overview of the Schiermonnikoog study area. Right: elevation at and surrounding Schiermonnikoog (mosaic of the ‘Vaklodingen’ of 2012-2015) and the location of the (offshore) hydraulic stations of RWS (black dots) and the transect (red line) with measurement equipment locations (red dots). Left: aerial photograph of the tail of Schiermonnikoog at 04-20-2014 (Google Earth). The coordinates are in meter (RD-new projection).',label='Overview_schiermonnikoog', width=145)}

The conditions at the case site are mesotidal, mixed-energy and tide-dominated. Generally, the offshore high water levels are about 0.7 m +NAP during neap tide and 1.2 m +NAP during spring tide, while the highest storm surge level in the last 25 years reached 3.5 m +NAP \citep{wesselman2018}. The mean offshore significant wave height ranges from 0.5 - 1 m in summer to 1 - 2 m in winter, and can increase to 8 - 11 m during (northwestern) storm events. The highest recorded storm setup at this location is approximately 3.5 - 4 m \citep{engelstad2017}.  

During the observation period, the island tail was flooded 11 times during high water due to storm setup. The highest water levels and wave heights were observed during the storm at 10 and 11-01-2015, with local wind speeds of about 19 m/s from the west and waves from the northwest. This storm is used for the XBeach simulation with BOI-settings for the hydrodynamic validation. The offshore conditions are based on RWS data shared by the UU: offshore water level data at the North Sea (‘Huibertgat’ station) and in the Wadden Sea (‘Schiermonnikoog-Oost’ station), and wave height, period and directional spreading at the North Sea (‘Schiermonnikoog-Noord’ wave buoy) with a 10-min data interval.  

The storm peak is defined as the moment with highest water levels (WL = 2.7 m +NAP at the North Sea at Huibertgat and 2.9 m +NAP in the Wadden Sea at Schiermonnikoog-Oost) and coincides with high tide. At this moment, the Hs was about 6.0 m and Ts 12 s. The highest offshore significant wave height (Hs) at the station Schiermonnikoog-Noord was 7.1 m, and occurred during the low tide (about -0.3 m NAP) in advance of the storm peak. The corresponding significant wave period (Ts or T1/3) was 13 s. The wave heights remained higher than 5 m for a full day. During the storm, the waves were more focused: the directional wave spreading decreased from more than 35° to about 23° during the storm peak and about 29° afterwards. Based on the water level, the return period of this storm is about 10 years.

During the field campaign, measurements along the transect from the North Sea to the Wadden Sea (red dots in \autoref{fig:Overview_schiermonnikoog}) were performed using among others ten stand-alone pressure transducers (PT’s) from 04-11-2014 to 31-01-2015. The PT’s recorded the water level continuously at 10 Hz with an accuracy of ~1 mbar (approximately 1 cm). Short and infragravity wave heights were determined for 15 min blocks by multiplying the standard deviation of the second-order detrended sea surface elevation with four, using a highpass filter (0.05-1 Hz) for short waves and a lowpass filter (0.005-0.05 Hz) for infragravity waves. More information on the data can be found in \citet{wesselman2018} and \citet{engelstad2017}. The processed data was made available by the UU in order to compare this with the XBeach model output.   

\textbf{Results}\newline
\autoref{fig:Schier_peak} shows the spatial patterns in the water depth and wave heights (H$_{m0}$) along the cross-section during the storm peak. \autoref{fig:Schier_P1} shows an example timeseries of the water depth and wave heights during the three tidal cycles just before and during the storm for the first measurement location at the beach (P1). The dots represent the measured values and the blue line the modelled values. \autoref{fig:Schier_scatter} shows the measured versus the modelled water depth and wave height of the short and infragravity waves for the entire model period and all locations. A quantative comparison between the model resutls and the measurements is presented in \autoref{tab:Schier} by means of goodness-of-fit indicators. 
  
${tools.image('Schiermonnikoog/', 'Cross-section_XBeach-results_PeakStorm_Zoom.eps', 'Cross-section with the modelled and measured water level and spectral significant wave height ($H_{m0}$) of high and low frequency waves during the storm peak (11-01-2015 13:00-13:30). The grey zone around the modelled $H_{m0,hf}$ indicates the minimum and maximum $H_{m0,hf}$. Note the difference between the modelled low frequency $H_{m0}$ (no frequency domain filter) (black line) and the measured infragravity $H_{m0}$ (0.005 and 0.05 Hz) at the point locations (grey-green dots).',label='Schier_peak', width=145)}
 
${tools.image('Schiermonnikoog/', 'Comparison_XBeach-measured_ModelPeriod_Timeseries_adv1.eps', 'Timeseries of measured and modelled water depth, short and infragravity spectral significant wave height including goodness-of-fit indicators for measurement location P1.',label='Schier_P1', width=145)}
  
${tools.image('Schiermonnikoog/', 'Comparison_XBeach-measured_ModelPeriod_Scatterplot_AllObservationPoints.eps', 'Scatter plot of the measured versus modelled water depth, spectral significant wave height ($H_{m0}$) of short waves (G) and infragravity waves (IG) for all measurement locations at Schiermonnikoog. The dashed line indicates a perfect fit, the continuous line represents a linear fit through the point cloud',label='Schier_scatter',width=150)}

${tools.table('Schiermonnikoog/', 'skill.tex', 'Goodness-of-fit (GoF) indicators for the modelled water depth [m] and the spectral significant wave height [m] for high frequency and infragravity waves compared to the measurements.', 'Schier',small=True)} 


 
 
		


