The purpose of this test is to check the ability of the model to represent runup and rundown of non-breaking long waves. To this end, a comparison was made with the analytical solution of the NSWE by Carrier and Greenspan (1958), which describes the motion of harmonic, non-breaking long waves on a plane sloping beach without friction. 
A free long wave with a wave period of 32 seconds and wave amplitude of half the wave breaking amplitude ($a_{in} = 0.5 \cdot a_{br}$) propagates over a beach with constant slope equal to $\nicefrac{1}{25}$. The wave breaking amplitude is computed as $a_{br} = \nicefrac{1}{\sqrt{128} \cdot \pi^3} \cdot s^{2.5} \cdot T^{2.5} \cdot g^{1.25} \cdot h_0^{-0.25} = 0.0307 meter$, where s is the beach slope, $T$ is the wave period and $h_0$ is the still water depth at the seaward boundary. The grid is non uniform and consists of 160 grid points. The grid size dx is decreasing in shoreward direction and is proportional to the (free) long wave celerity ($\sqrt{g \cdot h}$).The minimum grid size in shallow water was set at $dx = 0.1 meter$. 
To compare XBeach output to the analytical solution of Carrier and Greenspan, the first are non-dimensionalized with the beach slope $s$, the acceleration of gravity $g$, the wave period T, a horizontal length scale $L_x$ and the vertical excursion of the swash motion $A$. The horizontal length scale $L_x$ is related to the wave period via $T = \sqrt{\nicefrac{L_x}{g \cdot s}}$ and the vertical excursion of the swash motion A is expressed as: $A = a_{in} \cdot \nicefrac{\pi}{\sqrt{0.125 \cdot s \cdot T \cdot \sqrt{\nicefrac{g}{h_0}}}}$