The verification cases so far considered solely the cross-shore dimension and assumed a longshore uniform coast. In the following cases the potential of the model to predict coastal and dune erosion in situations that include the two horizontal dimensions is further examined. A first step towards a 2DH response is to verify that the 2DH forcing by surge run-up and run-down is accurately modelled by testing not against Zelt (1986), but actually \"{O}zkan-Haller \& Kirby (1997). The reason is that Zelt modeled the NSW equations including some dispersive and dissipative terms, which the present model does not have. For that reason, we also compared our model to the results of \"{O}zkan-Haller \& Kirby (1997) who modeled the NSW equations using a Fourier-Chebyshev Collocation method, which does not have any numerical dissipation or dispersion errors. They use a moving, adapting grid with a fixed $\Delta y$ (which is equal to the present model's $\Delta y$ in this comparison) but with a spatially and temporally varying $\Delta x$ so that the grid spacing in $x$ near the shoreline is very small. In the present model $\Delta x$ is set equal to $\Delta y$, which means that we can expect to have less resolution at the shoreline than \"{O}zkan-Haller \& Kirby (1997).