The first panel in \autoref{fig:Zelt_Case1_default_fig1.eps} shows the vertical runup  normalized with the offshore wave height H as a function of time, which is normalized by $\sqrt{g\,h_s}/L_y$ at the 5 cross-sections indicated in \autoref{fig:zeltbath.png}. The solid lines represent the present model results, while the dashed lines denotes Ozkan \& Kirby (1997)'s numerical results. We should see that the agreement is generally good, except that the present model does not capture the second peak in the time series at $y/Ly = 1$ very well. This secondary peak or ``ringing'' is due to the wave energy that is trapped along the coast and propagates towards the midpoint of the bay (Zelt, 1986). It is suspected that this focusing mechanism is not properly captured, because the present method approximates the shoreline as a staircase pattern, which in effect lengthens the shoreline. Also, the spatial derivatives are not evaluated parallel and perpendicular to the actual shoreline but in the fixed $x$ and $y$ directions. The agreement at the locations $y/Ly = 0.25$, $y/Ly = 0.5$ and $y/Ly = 0.75$ is generally good despite the large gradient of the local shoreline relative to our grid.