The Stability of Thermohaline Circulation in a Two-Box Model

Abstract

In Stommel?s simple two-box model, which has provided an insight on the thermohaline circulation and climate instability mechanisms, a linear mass transport was used. However, a scaling law based on geostrophy and advective?diffusive heat balance suggests a nonlinear mass transport relation for the oceans. By including this nonlinear mass transport relation to Stommel?s box model, it is possible to study the effects of the thermocline, which was not considered before, on the stability of the thermohaline circulation while keeping the simplicity of Stommel?s box model. The results were compared with those obtained with the traditional model using a linear mass transport relation. The thermal mode circulation of the nonlinear model is significantly more stable than that of the linear model, suggesting the thermohaline catastrophe is less likely to occur in the present North Atlantic if the thermocline is considered. In the nonlinear model, the circulation removes density anomalies rapidly so that significantly higher haline forcing is needed to initiate the thermohaline catastrophe. A linear stability analysis shows that negative feedback from the mass transport law has the strongest effect on the stability within a parameter range relevant for the present North Atlantic. The analysis also shows that freshwater flux parameterization does not have significant effect on the stability excluding artificial stability due to the details of the salinity restoring boundary condition.