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.

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.