The Center of Mass of the Ocean as an Index of the General Stratification and Its Relation to the Overturning Circulation

Abstract The height anomaly, defined as the height of the ocean’s center of mass relative to the height of a fully mixed state, provides an index of the strength of the global stratification. In this paper, we propose a definition of the height anomaly accounting for compressibility effects, using the seawater Boussinesq approximation. A budget equation for the height anomaly is derived, tracking which processes control the stratification—diffusive and convective mixing and conversion into kinetic energy. To test our framework, we analyze model simulations in a rectangular-shaped basin with applied wind and buoyancy forcings. The height anomaly adjusts on time scales ranging from years to centuries due to a combination of deep convection, energy conversion, and interior mixing, reaching a value of −26 cm at equilibrium. The buoyancy forcing, which generates the ocean’s mean stratification through a balance between high-latitude convection and interior mixing, is the primary controlling factor. Wind pumping plays a secondary role here. Near equilibrium, a substantial correlation is found between the height anomaly and the meridional overturning transport, at decadal to centennial time scales. In general, a lower center of mass is associated with an increased global overturning flow, making it a useful index to study overturning circulations.