When and where do Radiative–Convective and Radiative–Advective Equilibrium regimes occur on modern Earth?

Energy balance and lapse rate regimes qualitatively characterize the low, mid, and high latitudes of Earth's modern climate. Currently we do not have a complete quantitative understanding of the spatio-temporal structure of energy balance regimes (e.g., Radiative Convective Equilibrium or RCE, and Radiative Advective Equilibrium or RAE) and their connection to lapse rate regimes. Here we use the vertically-integrated moist static energy budget to define a nondimensional number that quantifies when and where RCE and RAE are approximately satisfied in Earth's modern climate. We find RCE exists yearround in the tropics and in the Northern midlatitudes during summertime. RAE exists yearround over Antarctica and in the Arctic with the exception of early summer. We show that the lapse rates in RCE and RAE regimes in reanalyses and CMIP5 models are broadly consistent with moist adiabatic and surface inversion lapse rates, respectively. We use idealized models (energy balance and aquaplanet models) to test the following hypotheses: 1) the RCE regime occurs during midlatitude summer for land-like (small heat capacity) surface conditions and 2) sea ice is necessary for the existence of the RAE regime over a polar ocean, such as the Arctic. Consistent with the first hypothesis, an aquaplanet model configured with a shallow mixed layer depth transitions to RCE in the midlatitudes during summertime whereas it does not for a deep mixed layer depth. Furthermore, we confirm the second hypothesis using mechanism-denial aquaplanet experiments with and without thermodynamic sea ice