For a stationary two dimensional random field evolving in time, we derive statistical distributions of appropriately defined velocities. The results are based on a genaralisation of the Rice formula.We discuss importance of identifying the correct form of the distribution which accounts for the sampling bias. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. We present an application of the theory where the sea surface is modelled as a Gaussian field. In particular we study statistical properties of velocities both for the sea surface and  for the envelope field based on this surface. For wave and wave group velocities, numerical computations of distributions are presented and illustrated graphically.