In reality, the eastern boundary sea level is certainly not level, although it shows a smaller range than that which is observed in deep water near to western boundaries, which can exceed 1 m between tropical and subpolar latitudes. In fact, both observations and models show a drop of about 35–45 cm between a high near the equator and lows at higher latitudes, in both the Pacific and Atlantic oceans [Woodworth et al., 2012]. As we consider the impact of future climate change on coastal flooding, we need to understand the origin of this slope, and the ability of models to maintain it. This is necessary if we are to have confidence that models used in climate projections can give useful information about the boundary response to ocean warming and circulation changes. Furthermore, if we consider the eastern boundary to form the boundary condition with respect to which the open ocean transport can be found by a Sverdrup balance integral, as has been found to work well for low to middle latitudes [Wunsch, 2011; Gray and Riser, 2014; Thomas et al., 2014], the eastern boundary sea level slope may also have important implications for the ocean's general circulation and its transport of heat and tracers.

A particular exception to the geostrophic constraint, in the case of the eastern Atlantic, is the exchange with the Mediterranean through the Strait of Gibraltar at approximately 36°N. Water can flow through this gap in the eastern boundary, permitting the formation of a step in eastern boundary sea level between the southern side in Morocco and the northern side in Spain. The Strait is less than 15 km across at its narrowest, or less than a seventh of a degree of latitude,with a sill depth of about 280 m, making it poorly resolved in even the best of global ocean models.

The circulation in the Strait is a complicated exchange flow, with hydraulic control being modulated by strong barotropic and internal tidal currents [Armi and Farmer, 1985; Farmer and Armi, 1989]. The mean flow is into the Mediterranean near the surface and out at depth. Estimates of the exchange transport range from 0.72 to 1.2 Sv (1 Sv = 1 sverdrup = 10⁶m³s⁻¹), with strong evaporation over the Mediterranean leading to the outflow being some 4–7% smaller than the inflow [Criado-Aldeanueva et al., 2012]. In one set of measurements,Tsimplis and Bryden [2000] found that the mean exchange interface depth lies at 147 m, although the mean flow reverses direction at a shallower depth of about 127 m. This difference reflects the importance of tidal correlations between flow and interface depth, which in their calculation account for over 40% of the exchange flow, a value consistent with observations of transport by internal waves some distance into the Mediterranean [Kinder, 1984], though it is unlikely that such a large wave transport also occurs on the Atlantic side of the Strait as internal tides there are much more linear [Morozov et al., 2002].

We can estimate the sea level signal associated with this inflow if we assume that the depth-integrated transport is given by the surface flow multiplied by a depth H, which would typically be somewhat smaller than the exchange interface depth because the flow must decrease as it approaches that depth. Taking, for example, H = 100 m, geostrophic balance then leads to a total transport T = (η_S−η_N)(gH/f), where η_S andη_N are sea level (inverse barometer corrected) to the south and north of the Strait, respectively, g is acceleration due to gravity, and f is the Coriolis parameter at 36°N. Substituting values for g, H, and f, this leads to (η_S−η_N)/T = 8.75 cm Sv⁻¹. In other words, a 1 Sv inflow would lead to eastern boundary sea level being 8.75 cm lower on the Spanish and Portuguese coast than on the Moroccan coast. This represents a substantial fraction of the total eastern boundary sea level fall between the equator and high latitudes. This step in sea level would be smaller for a larger effective depth H, or if a substantial part of the exchange resulted from tidal correlations rather than appearing in the Eulerian mean.

The purpose of this paper is to look at how coastal sea level is influenced by the Mediterranean exchange flow, by investigating the representation of this step in sea level in a variety of global ocean models. We find a strong relationship between the step and the exchange transport across a group of nine ocean models, an associated drop in Mediterranean mean sea level compared to the North Atlantic, and an influence on coastal sea level which extends thousands of kilometers northward along the coast. We show that these relationships are consistent with sea level observations if the exchange flow is within a few tenths of a sverdrup of 0.85 Sv, consistent with previous determinations.