On the Inefficiency of Moist Geostrophic Turbulence: A Theory for the Energetic Output under Subsaturated Conditions

Abstract The equator-to-pole temperature gradient has traditionally been understood as the primary driver of the midlatitude storm tracks, which derive their kinetic energy in the process of transporting sensible heat down the gradient. Latent heat, however, accounts for an estimated 30%–60% of the meridional energy transport, a portion which is likely to increase in a warmer world. The contribution of latent heat to the energetics is complicated in that it is inefficient: Only a fraction of the transported latent heat is converted into kinetic energy. Currently, there is no complete theory to explain the relationship between meridional energy transport and kinetic energy generation by midlatitudes eddies. We use a two-layer moist quasigeostrophic model to develop a theory of how the energetic output of the midlatitude atmosphere depends on the relative humidity structure. By varying the surface evaporation rate, we show that the system only reaches the maximum possible energetic output in the saturated limit, producing substantially less kinetic energy at lower evaporation rates. We quantify this reduction in kinetic energy production in terms of a moist conversion efficiency. Using a moist energetic framework, we identify that precipitation dissipation and the diffusion of moisture in subsaturated regions account for the reduction in energetic output. We then show that the moist conversion efficiency can be diagnosed from the distribution of humidity. Significance Statement The impact of humidity on the strength of midlatitude storms is not well understood. Humidity will increase as the planet warms, but it is unclear whether storms will become stronger or weaker as a result. We use an idealized computer model to learn how humidity will impact the strength of storms. We focus on the effect of evaporation at the planet’s surface, with simulations ranging from a completely dry atmosphere to one with rain everywhere. In between these two limits, it is raining in only part of the atmosphere, and storms are much weaker than in the case with rain everywhere. We discuss how to connect these results to more complex models and real-world data.