The horizontal and vertical controls on the thermal structure of the tropical troposphere

Our conceptual understanding of the tropical thermal structure is based on two complementary idealisations: one stemming from convective quasi-equilibrium (QE) and the other being the weak temperature gradient (WTG) approximation. Through QE, moist convection provides a vertical control on the thermal structure, while, under WTG, wave dynamics are assumed to provide a non-local horizontal control. While it is clear that moist convection plays an important role in setting the tropical mean stability through QE, the extent to which QE implies a local constraint on stability or whether the requirement for WTG effectively inhibits the influence of local conditions on stability remains debated. Here we hypothesise that a strong local vertical control of the thermal structure would imply a relationship between humidity and stability in the troposphere, as convection within moister regions would be less affected by entrainment of surrounding air. We utilise a combination of ERA5 reanalysis and observational data to examine the relationship between stability and local humidity across the Tropics. The results are compared with a prediction based upon a specific realisation of the theory of QE that incorporates entrainment through a simple plume model. We discover that, in convective regions, wave dynamics do not eliminate the effect of local conditions on stability, and that the resulting relationship between stability and humidity can be approximated well by the entraining plume model. Since QE is not applicable in the absence of convection, in non-convective regions the WTG, and possibly other factors, acts to set stability in the region. These results may help us understand the controls on horizontal density gradients in the tropical troposphere and the associated overturning circulations.