The adjoint method is used to assimilate observations into a quasi-geostrophic ocean model for a midlatitude jet. The domain has four open boundaries. Control variables used in this study are the lateral boundary values of stream function and relative vorticity. As a basic step, simulated data are assimilated (''identical-twin'' approach), and the effects of reducing the amount of observations as well as changing their distribution in space and time are investigated. Special attention is paid to the problem of how well the unobserved parts of the model trajectory are resolved. First, data are assimilated as two-dimensional maps at certain time intervals. Subsequently, continuous assimilation is performed along satellite ground tracks. The solution deteriorates somewhat in the satellite scenario, for which the data set is relatively sparse. However, the model can still be well fitted to the ''truth.'' It is also shown that the deeper layers are constrained by the upper layer information. ¿ American Geophysical Union 1993