Data assimilation refers to any methodology that uses partialobservational data and the dynamics of a system for estimating themodel state or its parameters. We consider here a non classicalapproach to data assimilation based in null controllabilityintroduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography.More precisely, we are interested in developing this methodologyto recover the unknown final state value (state value at the end of the measurement period) in a quasi-geostrophicocean model from satellite altimeter data, which allows in fact tomake better predictions of the ocean circulation. The main idea ofthe method is to solve several null controllability problems for the adjoint system inorder to obtain projections of the final state on a reduced basis.Theoretically, we have to prove the well posedness of theinvolved systems associated to the method and we also need anobservability property to show the existence of null controls for the adjoint system. Tothis aim, we use a global Carleman inequality for the associatedvelocity-pressure formulation of the problem which was previouslyproved in [Fernández-Cara et al., J. Math. Pures Appl.83(2004) 1501–1542]. We present numerical simulations using a regularizedversion of this data assimilation methodology based on nullcontrollability for elements of a reduced spectral basis.After proving the convergence of the regularized solutions, weanalyze the incidence of the observatory size and noisy data inthe recovery of the initial value for a quality prediction.