Global warming as quantified by surface air temperature has been shown to be approximately linearly related to cumulative emissions of CO2. Here, a coupled state-of-the-art Earth system model with an interactive carbon cycle (BNU-ESM) was used to investigate whether this proportionality extends to the complex Earth system model and to examine the climate system responses to different emission pathways with a common emission budget of man-made CO2. These new simulations show that, relative to the lower emissions earlier and higher emissions later (LH) scenario, the amount of carbon sequestration by the land and the ocean will be larger and Earth will experience earlier warming of climate under the higher emissions earlier and lower emissions later (HL) scenario. The processes within the atmosphere, land, and cryosphere, which are highly sensitive to climate, show a relatively linear relationship to cumulative CO2 emissions and will attain similar states under both scenarios, mainly because of the negative feedback between the radiative forcing and ocean heat uptake. However, the processes with larger internal inertias depend on both the CO2 emissions scenarios and the emission budget, such as ocean warming and sea level rise.

Oceanic variability and eddy dynamics during snowball Earth events, under a kilometer of ice and driven by a very weak geothermal heat flux, are studied using a high-resolution sector model centered at the equator, where previous studies have shown the ocean circulation to be most prominent. The solution is characterized by an energetic eddy field, equatorward-propagating zonal jets, and a strongly variable equatorial meridional overturning circulation (EMOC), on the order of tens of Sverdrups (Sv; 1 Sv 10(6) m(3) s(-1)), restricted to be very close to the equator. The ocean is well mixed vertically by convective mixing, and horizontal mixing rates by currents and eddies are similar to present-day values. There are two main opposite-sign zonal jets near the equator that are not eddy driven, together with multiple secondary eddy-driven jets off the equator. Barotropic stability analyses, the Lorenz energy cycle (LEC), and barotropic-to-baroclinic energy conversion rates together indicate that both baroclinic and barotropic instabilities serve as eddy-generating mechanisms. The LEC shows a dominant input into the mean available potential energy (APE) by geothermal heat flux and by surface ice melting and then transformation to eddy APE, to eddy kinetic energy, and finally to mean kinetic energy via eddy-jet interaction, similarly to the present-day atmosphere and unlike the present-day ocean. The EMOC variability is due to the interaction of warm plumes driven by geothermal heating that reach the ocean surface, leading to ice-melt events that change the stratification and, therefore, the EMOC. The results presented here may be relevant to the ocean dynamics of planetary ice-covered moons such as Europa and Enceladus.