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Abstract. Past warm periods provide an opportunity to evaluate climate models under extreme forcing scenarios, in particular high ( >  800 ppmv) atmospheric CO2 concentrations. Although a post hoc intercomparison of Eocene ( ∼  50  Ma) climate model simulations and geological data has been carried out previously, models of past high-CO2 periods have never been evaluated in a consistent framework. Here, we present an experimental design for climate model simulations of three warm periods within the early Eocene and the latest Paleocene (the EECO, PETM, and pre-PETM). Together with the CMIP6 pre-industrial control and abrupt 4 ×  CO2 simulations, and additional sensitivity studies, these form the first phase of DeepMIP – the Deep-time Model Intercomparison Project, itself a group within the wider Paleoclimate Modelling Intercomparison Project (PMIP). The experimental design specifies and provides guidance on boundary conditions associated with palaeogeography, greenhouse gases, astronomical configuration, solar constant, land surface processes, and aerosols. Initial conditions, simulation length, and output variables are also specified. Finally, we explain how the geological data sets, which will be used to evaluate the simulations, will be developed.

Shifts in the latitude of the intertropical convergence zone-a region of intense tropical rainfall-have often been explained through changes in the atmospheric energy budget, specifically through theories that tie rainfall to meridional energy fluxes. These quantitative theories can explain shifts in the zonal mean, but often have limited relevance for regional climate shifts, such as a period of enhanced precipitation over Saharan Africa during the mid Holocene. Here we present a theory for regional tropical rainfall shifts that utilizes both zonal and meridional energy fluxes. We first identify a qualitative link between zonal and meridional energy fluxes and rainfall variations associated with the seasonal cycle and the El Niño/Southern Oscillation. We then develop a quantitative theory based on these fluxes that relates atmospheric energy transport to tropical rainfall. When applied to the orbital configuration of the mid Holocene, our theory predicts continental rainfall shifts over Africa and Southeast Asia that are consistent with complex model simulations. However, the predicted rainfall over the Sahara is not sufficient to sustain vegetation at a level seen in the palaeo record, which instead requires an additional large energy source such as that due to reductions in Saharan surface albedo. We thus conclude that additional feedbacks, such as those involving changes in vegetation or soil type, are required to explain changes in rainfall over Africa during the mid Holocene.

The global atmospheric circulation transports energy from the equatorial regions to higher latitudes through a poleward flow of high-energy and -entropy parcels and an equatorward flow of air with lower energy and entropy content. Because of its turbulent nature, this circulation can only be described in some averaged sense. Here, we show that the total mass transport by the circulation is twice as large when averaged on moist isentropes than when averaged on dry isentropes. The additional mass transport on moist isentropes corresponds to a poleward flow of warm moist air near Earth's surface that rises into the upper troposphere within mid-latitudes and accounts for up to half of the air in the upper troposphere in polar regions.

Tropical cyclones instigate an isolated blast of vigorous mixing in the upper tropical oceans, stirring warm surface water with cooler water in the thermocline. Previous work suggests that the frequency, intensity, and lifetime of these storms may be functions of the climate state, implying that transient tropical mixing could have been stronger during warmer equable climates with higher concentrations of carbon dioxide. Stronger mixing of the tropical oceans can force the oceans' meridional heat flux to increase, cooling tropical latitudes while warming higher ones. This response differs significantly from previous modeling studies of equable climates that used static mixing; coupling mixing to climate changes the dynamic response. A parameterization of mixing from tropical cyclones is developed, and including it leads to a cooling of tropical oceans and a warming of subtropical waters compared with control cases with fixed mixing. The mixing penetration depth regulates the magnitude of the response.

Differential heating of the earth's atmosphere drives a global circulation that transports energy from the tropical regions to higher latitudes. Because of the turbulent nature of the flow, any description of a ''mean circulation'' or ''mean parcel trajectories'' is tied to the specific averaging method and coordinate system. In this paper, the NCEP-NCAR reanalysis data spanning 1970-2004 are used to compare the mean circulation obtained by averaging the flow on surfaces of constant liquid water potential temperature, or dry isentropes, and on surfaces of constant equivalent potential temperature, or moist isentropes. While the two circulations are qualitatively similar, they differ in intensity. In the tropics, the total mass transport on dry isentropes is larger than the circulation on moist isentropes. In contrast, in midlatitudes, the total mass transport on moist isentropes is between 1.5 and 3 times larger than the mass transport on dry isentropes.It is shown here that the differences between the two circulations can be explained by the atmospheric transport of water vapor. In particular, the enhanced mass transport on moist isentropes corresponds to a poleward flow of warm moist air near the earth's surface in midlatitudes. This low-level poleward flow does not appear in the zonally averaged circulation on dry isentropes, as it is hidden by the presence of a larger equatorward flow of drier air at same potential temperature. However, as the equivalent potential temperature in this low-level poleward flow is close to the potential temperature of the air near the tropopause, it is included in the total circulation on moist isentropes. In the tropics, the situation is reversed: the Hadley circulation transports warm moist air toward the equator, and in the opposite direction to the flow at upper levels, and the circulation on dry isentropes is larger than that on moist isentropes.The relationship between circulation and entropy transport is also analyzed. A gross stratification is defined as the ratio of the entropy transport to the net transport on isentropic surfaces. It is found that in midlatitudes the gross stability for moist entropy is approximately the same as that for dry entropy. The gross stratification in the midlatitude circulation differs from what one would expect for either an overturning circulation or horizontal mixing; rather, it confirms that warm moist subtropical air ascends into the upper troposphere within the storm tracks.

The oceanic meridional overturning circulation (MOC) is a crucial component of the climate system, impacting heat and nutrient transport, and global carbon cycling. Past greenhouse climate intervals present a paradox because their weak equator-to-pole temperature gradients imply a weaker MOC, yet increased poleward oceanic heat transport appears to be required to maintain these weak gradients. To investigate the mode of MOC that operated during the early Cenozoic, we compare new Nd isotope data with Nd tracer-enabled numerical ocean circulation and coupled climate model simulations. Assimilation of new Nd isotope data from South Pacific Deep Sea Drilling Project and Ocean Drilling Program Sites 323, 463, 596, 865, and 869 with previously published data confirm the hypothesized MOC characterized by vigorous sinking in the South and North Pacific~70 to 30 Ma. Compilation of all Pacific Nd isotope data indicates vigorous, distinct, and separate overturning circulations in each basin until~40 Ma. Simulations consistently reproduce South Pacific and North Pacific deep convection over a broad range of conditions, but cases using strong deep ocean vertical mixing produced the best data-model match. Strong mixing, potentially resulting from enhanced abyssal tidal dissipation, greater interaction of wind-driven internal wave activity with submarine plateaus, or higher than modern values of the geothermal heat flux enable models to achieve enhanced MOC circulation rates with resulting Nd isotope distributions consistent with the proxy data. The consequent poleward heat transport may resolve the paradox of warmer worlds with reduced temperature gradients.

[1] The subtropical terminus of the Hadley circulation is interpreted as the latitude poleward of which vertical wave activity fluxes (meridional eddy entropy fluxes) become sufficiently deep to reach the upper troposphere. This leads to a sign change of the upper-tropospheric divergence of meridional wave activity fluxes (convergence of meridional eddy angular momentum fluxes) and marks the transition from the tropical Hadley cell to the extratropical Ferrel cell. A quantitative formulation for determining the depth of vertical wave activity fluxes and thus the terminus of the Hadley circulation is proposed based on the supercriticality, a measure of the slope of isentropes. The supercriticality assumes an approximately constant value at the terminus of the Hadley circulation in a series of simulations with an idealized dry general circulation model. However, it is unclear how to generalize this supercriticality-based formulation to moist atmospheres.