## Section:
Application Domains2>
### Shallow Water3>

Prediction of shallow water equations in realistic application depends on the level of complexity used for the physical modelling (such as for example, for the fricton coefficient) and on a set of empirical coefficients that are usually chosen in order to fit the experimental data. Then, input environmental conditions, topography and modelling involve a certain degree of uncertainty. The capability to take into account these uncertainties in the numerical simulation is of great importance in order to correctly predict extreme flood events. Stochastic modeling of long-wave propagation demands a robust shallow-water model in order to characterize the physical processes. We coupled a residual distribution scheme for shallow water equations with some stochastic methods in order to take into account uncertainties in the numerical simulation. Preliminary results showed that influence of uncertainties is stronger after the phase interaction indicating the need for a stochastic simulation in order to have a correct prediction of the numerical solution.