Hello,
Think also that when you prescribe only the depth or the free surface elevation at an open boundary the problem is not always well posed. It is more or less correct when the flow goes out, but when the flow gets in, you lack information on the velocities, so a big eddy can enter your domain, and it is one of the infinite number of possible solutions (this stems from the theory of characteristics, with fluvial flows). In such a case of open boundaries in the sea we recommend to:
1) put this open boundary as far offshore as possible, i.e. with the largest depth and the minimum velocity.
2) use the Thompson boundary condition, that will deal with the characteristic pathlines to find, when possible, (flow exiting) the right boundary conditions.
With best regards,
Jean-Michel Hervouet