We show how a 3-D, self-consistent numerical model of the geodynamo can be used as the subjective prior information for the determination of Earth's core surface flows from the geomagnetic field and its secular variation. This is achieved by estimating those parts of the numerical model state vector hidden from the observations, through a standard Kalman filtering (or stochastic inverse) procedure, where the Kalman gain matrix is based on the multivariate statistics of the geodynamo model. To allow for a direct comparison with observations, the field variables entering these statistics are scaled following two of the scaling laws that have recently come to the fore in numerical dynamo modelling, which express the dependency of the secular variation timescale and the magnetic energy density on their respective control parameters. We perform test experiments with noisy synthetic data, showing good to excellent recovery of the hidden parts of the state vector. A geomagnetic field model parent to a candidate model to the 2010 release of IGRF is then used for a core surface flow estimation. The estimated flow confirms the presence of convective columns underneath America, whereas exhibiting a high level of equatorial symmetry. We suggest that the discrete state estimation problem considered here (in connection with the classical core flow problem) could be used generically as a means to assess the degree of geophysical realism of a given geodynamo model. More generally, this study opens the way to using scaling laws and multivariate statistics from numerical models in the broader context of geomagnetic data assimilation. Assuming that we have knowledge of the radial component of the magnetic induction B r and of its rate-of-change ∂ t B r at the top of Earth's core, the so-called core flow problem consists of trying to estimate the flow u compatible with these observations, by using the radial component of the magnetic induction equation ∂ t B r = −∇ h · (u h B r) + λr −1 ∇ 2 (r B r), (1)