# Box inverse

In order to fulfil our objective of estimating transport variability across the Greenland to Portugal line, we need to estimate the velocity field perpendicular to the OVIDE line for all cruises. Since the circulation in the subpolar gyre is characterised by an energetic barotropic component, which is not captured by the thermal wind velocities, we estimated the velocity field perpendicular to the OVIDE section by constraining the barotropic component using direct velocity observations gathered by the ship ADCP. We use the following steps. First, geostrophic velocities referenced to selected levels are computed for each station pair. Then, the unknown velocities at the reference levels are estimated by minimizing the weighted sum of:

1. The squared reference level velocities,

2. The squared residuals of transport constraints derived from the SADCP and LADCP measurements,

3. The squared residual of an overall mass conservation constraint.

The output of the inverse model is a geostrophic velocity field that satisfies mass conservation and captures the barotropic component of the circulation well.

Figure: Surface-to-bottom integrated transports accumulated from Greenland to Portugal along the OVIDE 2002 line. The transports are perpendicular to the hydrographic line. In blue: transports estimated using the thermal wind balance and assuming a deep reference level. In red: transports estimated by the inverse model and constrained by the direct velocity measurements. The difference between the two estimates in the East Greenland Current and the Irminger Current are striking. The southward Ekman contribution is small.

**References**

Lherminier, P., H. Mercier, C. Gourcuff, M. Alvarez, S. Bacon, C. Kermabon, 2007: Transports across the 2002 Greenland-Portugal Ovide section and comparison with 1997. J. Geophys. Res. Oceans., 112, C07003, doi:10.1029/2006JC003716.

Lherminier, P. H. Mercier, T. Huck, C. Gourcuff, F. F. Perez, P. Morin, A. Sarafanov, 2010: The Atlantic Meridional Overturning Circulation and the subpolar gyre observed at the A25-OVIDE section in June 2002 and 2004. Deep Sea Res. I, 57, 11, 1374-1391, doi:10.1016/j.dsr.2010.07.009.