  We present a novel approach to determine the evolution of level sets under
uncertainties in the velocity fields. This leads to a stochastic description of
the level sets. To compute the quantiles of random level sets, we use the
stochastic Galerkin method for a hyperbolic reformulation of the level-set
equations. A novel intrusive Galerkin formulation is presented and proven
hyperbolic. It induces a corresponding finite-volume scheme that is
specifically taylored for uncertain velocities.
