Global climate dynamics in a highly parameterized radiative-convective-macroturbulent energy balance model

We present a one-layer global energy balance climate model with highly parameterized radiation, convection, and large-scale atmosphere/ocean macroturbulence. Planetary heat content is parameterized by a 2D in latitude-longitude layer characterized by a temperature field and a uniform constant heat capacity. Radiation is parameterized by mean-annual zonal average top-of-atmosphere solar irradiance. Radiative heating and cooling are parameterized by a uniform constant albedo and Stefan-Boltzmann emission with uniform constant emissivity. Convection is parameterized by a temperature threshold for convection which restricts the layer from warming beyond the threshold, effectively cooling the layer. Macroturbulence is parameterized by 2D barotropic turbulence forced at small scales and damped by Rayleigh friction. Energy conservation is maintained by balancing the convective cooling of the layer with the turbulent kinetic energy forcing, resulting in tropical forcing, while the frictional loss of kinetic energy is balanced by frictional heating of the layer. The parameterized energy transforming processes are characterized by timescales, which, for Earth-like planets, are ordered as t_radiation > t_{macroturbulence} > t_convection.

We investigate the model’s equilibrium climate state in terms of the meridional heat transport (MHT), the resulting zonally averaged temperature profile, and their fluctuations by simulating the system over many radiation times. For Earth-like parameters, despite the model’s extremely simplified dynamics, our simulations reveal a MHT profile comparable to the observed, annually averaged MHT on Earth, featuring a maximum in the mid-latitudes of approximately 5PW, a form of Bjerknes compensation.