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Atmospheric transports, the thermohaline circulation, and flux adjustments in a simple coupled model

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Marotzke, J., & Stone, P. (1995). Atmospheric transports, the thermohaline circulation, and flux adjustments in a simple coupled model. Journal of Physical Oceanography, 25, 1350-1364. doi:10.1175/1520-0485(1995)025<1350:ATTTCA>2.0.CO;2.

A theoretical analysis of the interactions between atmospheric meridional transports and the thermohaline circulation is presented, using a four-box ocean-atmosphere model in one hemisphere. The model is a simplified version of that developed by Nakamura, Stone, and Marotzke and is amenable to analytical solutions. The ocean model is Stommel's; the atmospheric model gives the surface heat and freshwater fluxes as residuals of the atmospheric energy and moisture budgets, assumed in balance. Radiation at the top of the atmosphere depends linearly on surface temperature; atmospheric meridional heat and moisture transports are proportional to the meridional temperature gradient. A Newtonian cooling law is derived for differential surface heat flux. The restoring coefficient is proportional to the efficiency of atmospheric transports and inversely proportional to the relative ocean area compared to total surface area, Surface freshwater flux increases with increasing temperature gradient and is inversely proportional to the ratio of ocean area to catchment area. The range of stable solutions with high-latitude sinking is smaller than in related, uncoupled box models due to the dependence of freshwater flux on the temperature gradient, which leads to a positive feedback with the thermohaline circulation. A strong control of the temperature gradient by atmospheric transports enhances the positive feedback between the salinity gradient and thermohaline circulation; simultaneously, it weakens the positive feedback between atmospheric moisture transport and the thermohaline circulation. Overestimating the atmospheric moisture transport and underestimating oceanic mass transport both artificially destabilize the high-latitude sinking state. Overestimating the atmospheric heat transport and hence the Newtonian restoring coefficient can be artificially stabilizing or destabilizing. These erroneous sensitivities are not alleviated if flux adjustments are added to obtain the correct mean climate, and then held fixed in climate change experiments. We derive alternate flux adjustment schemes, which do preserve the model's stability properties for particular sources of error.