The complexity of dynamical laws governing 3D atmospheric flows associated to incomplete and noisy observations makes very difficult the recovery of atmospheric dynamics from satellite images sequences. In this paper, we face the challenging problem of joint estimation of time-consistent horizontal motion fields and pressure maps at various atmospheric depths. Based on a vertical decomposition of the atmosphere, we propose a dense motion estimator relying on a multi-layer dynamical model. Noisy and incomplete pressure maps obtained from satellite images are reconstructed according to shallow-water model on each cloud layer using a framework derived from data assimilation. While reconstructing dense pressure maps, this variational process estimates time-consistent horizontal motion fields related to the multi-layer model. The proposed approach is validated on a synthetic example and applied to a real world meteorological satellite image sequence.