<p>A new algorithm to estimate river discharges from altimetry measurements only is designed. A first estimation is obtained by an artificial neural network trained from the altimetry large scale water surface measurements plus drainage area information. The combination of this purely data-based estimation and a dedicated algebraic flow model provides a first physically-consistent estimation. The latter is next employed as the first guess of an advanced variational data assimilation formulation. The final estimation is highly accurate for rivers presenting features within the learning partition; for rivers far outside the learning partition, the space-time variations of discharge remain accurately approximated however the global estimation presents a potential bias. Indeed, it is shown that if the estimation is based on the hydrodynamics models only, the inverse problem may be well-defined but up to a bias only (the bias scales the global estimation). This bias is removed thanks to the ANN but for rivers in the learning partition only. For rivers outside the learning partition, any mean value (eg. annual, seasonal) enables to remove the bias. Finally, the present hybrid and hierarchical inversion strategy seems to provide much more accurate estimations compared to the state-of-the-art for the considered 29 heterogeneous river portions.</p>