International audienceWe report a calculation of time-dependent quasi-geostrophic core flows for 1940-2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely the model errors arising from interactions between unresolved core surface motions and magnetic fields. Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies at mid-latitudes and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scal...