Reconstructing global overturning from meridional density gradients

Despite the complexity of the global ocean system, numerous attempts have been made to scale the strength of the meridional overturning circulation (MOC), principally in the North Atlantic, with large-scale, basin-wide hydrographic properties. In particular, various approaches to scaling the MOC with meridional density gradients have been proposed, but the success of these has only been demonstrated under limited conditions. Here we present a scaling relationship linking overturning to twice vertically-integrated meridional density gradients via the hydrostatic equation and a "rotated" form of the geostrophic equation. This provides a meridional overturning streamfunction as a function of depth for each basin. Using a series of periodically forced experiments in a global, coarse resolution configuration of the general circulation model NEMO, we explore the timescales over which this scaling is temporally valid. We find that the scaling holds well in the upper Atlantic cell (at 1000 m) for multi-decadal (and longer) timescales, accurately reconstructing the relative magnitude of the response for different frequencies and explaining over 85 % of overturning variance on timescales of 64-2048 years. Despite the highly nonlinear response of the Antarctic cell in the abyssal Atlantic, between 76 and 94 % of the observed variability at 4000 m is reconstructed on timescales of 32 years (and longer). The scaling law is also applied in the Indo-Pacific. This analysis is extended to a higher resolution, stochastically forced simulation for which correlations of between 0.79 and 0.99 are obtained with upper Atlantic MOC variability on timescales > 25 years. These results indicate that meridional density gradients and overturning are linked via meridional pressure gradients, and that both the strength and structure of the MOC can be reconstructed from hydrography on multi-decadal and longer timescales provided that the link is made in this way.