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The authors focus on Heinrich events and the question of whether the arrest and restart of convection can explain the associated sudden changes in oceanic and atmospheric temperature. For this purpose, a new (mixed) dynamical-box model is developed in which the ocean and atmosphere communicate via both Ekman layers and convection. The conservation of heat, salt, volume flux, and a “convection condition” yields a system of algebraic equations that are solved analytically. As expected, it is found that as the freshwater flux increases, the convective ocean temperature decreases. The heat flux from the ocean to the atmosphere, the transport of the oceanic meridional overturning cell (MOC), and the corresponding atmospheric flow generated by the heat flux from the ocean all decrease. However, the outgoing air temperature increases with increasing freshwater flux. This counterintuitive increase is because a decreased latent and sensible heat flux (to a humid atmosphere) means a reduced temperature difference between the warmer ocean and the cooler atmosphere, implying a cooler ocean and warmer atmosphere. For each wind speed, there is a critical freshwater flux beyond which the convection collapses and the temperatures of both the ocean and the air plunge because equatorial water is no longer flowing northward to replace the frigid northern waters. The above points to a potentially new instability process that was probably active during glaciation periods—when ice and snow are abundant, even the smallest amount of freshwater flux will cause local warming which, in turn, will cause increased melting, resulting in an ever-increased freshwater flux until the critical flux is reached and the MOC collapses. The model suggests that switching convection on and off changed the glacial ocean temperature by 4°C and the glacial air temperature by 12.5°C, both consistent with the Greenland Ice Sheet Project (GISP II) ice core record and the Centre Européen de Recherche et d’Enseignement des Géosciences de l’Environnement (CEREGE) alkenone record. [ABSTRACT FROM AUTHOR]