Satellite image sequences permit to visualise oceans' surface and their underlying dynamics. Processing these images is then of major interest in order to better understanding of the observed processes. As demonstrated by state-of-the-art, image assimilation allows to retrieve surface motion from image sequences, based on assumptions on the dynamics. In this paper we demonstrate that a simple heuristics, such as the Lagrangian constancy of velocity, can be used, and successfully replaces the complex physical properties described by the Navier-Stokes equations, for assessing surface circulation from satellite images. A data assimilation method is proposed that includes an additional term a(t) to this Lagrangian constancy equation. That term summarises all physical processes other than advection. A cost function is designed, which quantifies discrepancy between satellite data and model values. The cost function is minimised by the BFGS solver with a dual method of data assimilation. The result is the motion field and the additional term a(t). This last component models the forces, other than advection, that contribute to surface circulation. The approach has been tested on Sea Surface Temperature of Black Sea. Results are given on four image sequences and compared with state-of-the-art methods.