  The estimation of the maximum wave sunup height is a problem of practical
importance. Most of the analytical and numerical studies are limited to a
constant slope plain shore and to the classical Nonlinear Shallow Water (NSW)
equations. However, in nature the shore is characterized by some roughness. In
order to take into account the effects of the bottom rugosity various ad-hoc
friction terms are usually used. In this paper we study the effect of the
roughness of the bottom on the maximum runup height. A stochastic model is
proposed to describe the bottom irregularity and its effect is quantified using
Monte-Carlo simulations. For the discretization of the NSW equations we employ
modern finite volume schemes. Moreover, the results of the random bottom model
are compared with the more conventional approaches.
