Thermodynamical constraints on the meridional overturning circulation in warming climates

In midlatitudes of present-day climate, the circulation averaged on moist isentropes is twice as strong as the circulation averaged on dry isentropes (Pauluis et al., 2010, J. Clim.). In the A1B climate scenario, Laliberte and Pauluis (2010, GRL) showed that the winter moist circulation strengthens with respect to the dry circulation, indicating that the latent heat component of the circulation increases at the expense of the sensible heat component. Climate modeling studies covering a wide range of surface temperatures support this observation and show that the overturning circulation attains a maximum and then weakens as surface temperatures rise (Caballero and Langen, 2005, GRL; Rose and Ferreira, 2012, J. Clim). The latent heat component of the circulation therefore cannot increase indefinitely with rising surface temperatures, indicating that a thermodynamical constraint might determine the maximum relative strength of the moist and dry circulations circulation attainable in warmer climates. Here, such a constraint is derived using a theoretical model describing the structure of the dry and moist isentropic circulations in the lower troposphere. The model decomposes the meridional flow in the troposphere into three contributions: a dry equatorward flow; a cold/moist equatorward flow; and a warm/moist poleward flow in the mixed layer. It is based on the joint distribution of meridional mass fluxes in potential temperature and equivalent potential temperature. It updates an existing model of the dry circulation by emphasizing the role of moisture in the mixed layer. The model is used to derive an expression for the ratio of moist to dry circulations strengths, which is used to assess the influence of surface thermodynamics on the circulations. This expression indicates that while an increase in the total heat fluxes occurs when surface temperature variability increases (via an increase in latent heat flux), it cannot increase indefinitely.