Implementing a deep convective thermostat, and its effect on global and local energy balance, in weather-layer models of Jovian planets and exoplanets

Abstract:

Since Pioneer and Voyager it has been clear that Jupiter's thermal emission is much more uniform in latitude than the absorbed solar radiation. The imbalance, Jupiter's own contribution, must therefore vary inversely with the absorbed solar on the planetary scale, although it does not on the smaller scale associated with cloud changes between the belts and zones (Pirraglia 1984). Ingersoll (1976) proposed a regulation mechanism to explain this uniformity, the Jovian thermostat, based on convection that keeps the deep atmosphere close to a global adiabat.

Numerical models of Jupiter's weather layer typically include upward and downward radiation, parameterize small-scale convection within the domain, and specify an internal heat flux as a boundary condition at the bottom. Young et al. (2019) imposed a constant heat flux, which on its own would not reproduce the flat thermal emission profile, but found that the dynamics flattened the temperature considerably. Guerlet et al. (2020) imposed a meridionally varying heat flux in order to match recent temperature profiles (Fletcher et al. 2016).

Friedson & Ingersoll (1987) implemented a model thermostat for Uranus by setting a constant (potential) temperature at the bottom boundary. Here we implement a model thermostat within the dry-convection scheme of Young et al. (2019). In their scheme, a convectively unstable column is relaxed to an adiabat determined by enthalpy conservation. Convection can reach the bottom of the domain but does not cross the boundary; therefore without horizontal transport, the radiative imbalance at the top is equal to that imposed at the bottom. We modify this by relaxing any convecting column that reaches the bottom to a global deep adiabat. This change breaks enthalpy conservation (appropriately), and greatly speeds up thermal equilibration, which may be a helpful side-effect for giant-(exo)planetary modelling generally. The radiative imbalance above the convecting column is no longer imposed, and in pure radiative-convective equilibrium we find that the thermal emission is indeed much more uniform in latitude. We discuss the effect of the dynamics, and the potential impact of moist convection. We also illustrate the effect of varying the albedo on the smaller scale of belts and zones, by using a discrete reflecting layer as a simple cloud model.