The determination of smooth velocity fields from sequences of satellite images has received considerable attention in many domains in natural sciences such as atmospheric physics and physical oceanography. Two categories of methods have been discussed in the literature. The so-called maximum cross correlation approach is a feature tracking method, whereas the gradient based approach relies on the fundamental assumption that the brightness of a moving point is invariant between time t and t+dt. The method we propose is related to the second approach, but we model displacement rather than velocity directly. We use a discretization of the continuity equation and assume absence of divergence. For the estimation of the displacement field, we use a penalized least squares method. The penalty term takes observation errors into account. It includes an estimate of the noise variance based on second-order differences. We investigate how much of the day-to-day variability of total ozone of Total Ozone Mapping Spectrometer can be explained by advective displacement. ¿ 2001 American Geophysical Union