Summary. In this paper we discuss a numerical procedure for performing dynamic data driven simulations (DDDAS). In dynamic data driven simulations our goal is to update the solution as well as input parameters involved in the simulation based on local measurements. The updates are performed in time. In the paper we discuss (1) updating the solution using multiscale interpolation technique (2) recovering as well as updating initial conditions based on least squares approach (3) updating the permeability field using Markov Chain Monte Carlo techniques. We test our method on various synthetic examples.