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A 3-box model of the thermohaline circulation is developed to study the haline-thermal mode switching observed in the 3-d circulation model. By including convective adjustment with a linear equation of state for seawater and a parameterization of the localized nature of convection, the box model shows that haline mode is unstable over a certain freshwater forcing/vertical diffusivity range. Self-sustained oscillatory thermohaline circulation, with periods ranging from centuries to several millennia, are supported.
The box model gives insight in to the basic physical mechanism of mode switching. During the haline mode, horizontal transfer of properties by large scale eddies and vertical diffusion gradually decrease the density difference between polar surface and deep ocean, until local convection is triggered, even though the zonal mean density structure is stable. Vigorous flushing in a transient thermal mode sets in. However, surface freshwater fluxes reduce surface density at the poles and ultimately suppresses polar convection. Warm, salty water then sinks from the subtropics again, and the circulation returns to a haline mode to close the limit cycle. When the amplitude of surface freshwater flux exceeds a certain threshold the haline mode stabilizes. The relation between oscillation periods and freshwater forcing/vertical diffusivity are also studied.