Even though the chaotic character of the atmospheric processes may never make possible to completely eliminate uncertainties in atmospheric simulations, advanced data assimilation approaches, involving model error estimation, are indicating a promise that these uncertainties can be quantified and reduced. In particular, weak constraint 4-dimensional variational and ensemble Kalman filter based data assimilation methods offer consistent mathematical approaches for addressing this problem. These approaches are rather general, applicable not only to atmospheric models, but to any dynamical or process model, as long as these models are capable of simulating observable variables. As a demonstration, experimental results employing variational and/or ensemble based data assimilation methods in application to atmospheric models of various complexity, ranging from a simple one-dimensional, to the most complex non-hydrostatic models, will be presented and discussed.