  The runup of initial Gaussian narrow-banded and wide-banded wave fields and
its statistical characteristics are investigated using direct numerical
simulations, based on the nonlinear shallow water equations. The bathymetry
consists of the section of a constant depth, which is matched with the beach of
constant slope. To address different levels of nonlinearity, the time series
with five different significant wave heights are considered. The selected wave
parameters allow also seeing the effects of wave breaking on wave statistics.
The total physical time of each simulated time-series is 1000 hours (~360000
wave periods). The statistics of calculated wave runup heights are discussed
with respect to the wave nonlinearity, wave breaking and the bandwidth of the
incoming wave field. The conditional Weibull distribution is suggested as a
model for the description of extreme runup heights and assessment of extreme
inundations.
