<%namespace name="tools" file="tools.tex"/>
<%! import os %>

In order to verify the 2DH hydrodynamics of XBeach when forced by directionally-spread short waves, a simulation is set up to compare model results to field measurements. In this case the DELILAH field experiment at Duck, North Carolina is selected as a suitable test location. The period that is modeled is October 13th 1990, which was a stormy day, between 16:00 and 17:00 hours. The significant wave height at 8 m water depth was 1.81 m, with a peak period of 10.8 s and a mean angle of incidence of -16$^o$ relative to the shoreward normal. This period is selected because the wave conditions are energetic enough to generate a significant infragravity wave component and the incident wave spectrum is sufficiently narrow-banded to justify the assumptions in the model boundary conditions. The model is forced with the wave spectrum measured at 8 m water depth \citep{Birkemeier1997}. A measured tidal signal is imposed on the model boundaries of which the mean level is 0.69 m above datum. The slope of the wave front in the roller model is set to 0.05, which is found to be a slight improvement over the value of 0.10 used in the previous sections. A constant grid size of 5 m in cross shore and 10 m in longshore direction is used. The resolution of the wave model in directional space is 15$^o$. The model is set to generate output at the location of the primary cross shore measurement array, gauge numbers 10, 20, 30, 40, 50, 60, 70, 80 and 90 (\autoref{fig:Delilah_199010131000_bathy}).

${tools.image(os.path.join(input_path, 'Delilah_199010131000/'), 'Delilah_199010131000_bathy.png', ' Bathymetry and measurement locations')}

The modeled time-averaged wave heights of the short waves are compared to the time-averaged wave heights measured at the gauges. These results are shown in the first panel of \autoref{fig:Delilah_hydro}. Unfortunately, no data exist for gauge number 60.

The infragravity wave height is calculated as follows \citep{VanDongeren2003}:

$H_{rms,low} = \sqrt{8 \int_{0.005 Hz}^{0.05 Hz} S df}$

\autoref{fig:Delilah_hydro} shows the infragravity wave height. The measured and modelled time-averaged longshore current are shown in the second panel of \autoref{fig:Delilah_hydro}. The correlation coefficient, scatter index, relative bias and Brier Skill Score for the simulation are shown in \autoref{tab:Delilah_199010131000_default_skills}.

% if interpret:

XBeach overestimates the infragravity wave height, but does follow the measured cross shore trend well. It can be seen that the model strongly under predicts the longshore current in the trench between measurement gauge 60 and the shore. Further calibration of the short wave and roller parameters is required in order to improve the simulated longshore current in this trough.

% endif

${tools.image('Delilah_199010131000/default/', 'hydro.eps', 'Wave height transformation and flow velocities during the DELILAH field experiment 1990', 'Delilah_hydro')}
${tools.table('Delilah_199010131000/default/', 'skills.tex')}



% if interpret:

The figure shows a migration of energy from high to low frequencies in shoreward direction in the measured spectra. The simulated spectra reproduce well the trend of increasing energy in the low frequency band in shoreward direction, but the amount of energy in the simulated low frequency band is less than in the measurements. In conclusion it can be stated that the model reproduces to a high degree of accuracy the short wave transformation in the shoaling and breaker zone. The transfer of energy from high to low frequencies in the model has qualitative skill. The longshore velocity in the nearshore requires additional calibration of the short wave and roller parameters.

% endif
