Aseel Farhat Indiana University afarhat@indiana.edu Data assimilation is the process by which observations are incorporated into a computer model of a real system. Applications of data assimilation arise in many elds of geosciences, perhaps most importantly in weather forecasting. In a joint work with M. Jolly and E. S. Titi, we present a new continuous data assimilation algorithm for the two-dimensional Benard problem based on an idea from control theory. Rather than inserting the observational measurements directly into the equations, a feedback control term is introduced that forces the model towards the reference solution. We show that the approximate solutions constructed using only observations in the velocity eld and without any measurements on the temperature converge in time to the reference solution of the two-dimensional Benard problem. In a more recent joint work with E. Lunasin and E. S. Titi, we introduce an abridged continuous data assimilation algorithm for the 2D Navier-Stokes, 2D Benard problem and 3D subgrid scale - models of turbulence. The novelty of this improved algorithm is on the reduction on the components of the observational data that needs to be measured and inserted into the model equation, in the form of a feedback control term, to recover the unknown reference solution. We show that for the 2D Navier-Stokes equations the approximate solutions constructed using observations in only one component of the velocity eld converge in time to the reference solution. In the case of the 3D Leray- model, we show that the approximate solutions constructed using only observations any two components, without any measurements on the third component, of the velocity eld converge in time to the reference solution.