[MITgcm-support] Meridional overturning streamfunction and free surface

[cimatori]

Hi everybody,
I have a question that is probably obvious to those who know the details
of the advection algorithm, but I am not one of them and couldn't find
the answer myself.
I am computing the meridional overturning streamfunction (in a simple
geometry, cartesian coordinates, full cells only). It is a simple task
and the streamfunction at the bottom (integrating from the top) is
nicely close to zero when averaged in time (order of 10^-6 Sv). Just for
completeness sake, I wanted to add the effect of the (implicit) free
surface, so I summed the anomalous eta to the layer thickness of the top
layer at each time step. Unfortunately, this makes things worse at the
bottom (that is, the streamfunction is larger than in the case without
eta taken into account, order 10^-2Sv). Please note that I am working at
the cell centre (using meridional velocity at the cell centre from the
diagnostics output and \Deltax_F) so that the error is not due to the
different position of v and eta on the grid.
I think that I am misunderstanding how the free surface is actually
treated in the model. How should I include eta in the overturning
streamfunction computation?

Thanks,
Andrea