Ah — perhaps I simply misinterpreted the meaning of “Milankovitch cycles became more influential.” From what you write, it seems the phrase just means their combined effect shifted to a pattern when warming periods were longer and cooling periods shorter.

Dr Snyder says:

“… [ESS] is likely state dependent, and thus I focused on comparing my new estimate to estimates from previous research on the late Quaternary. I also was able to investigate the state dependence of the metric within the last 800,000 years and found that it was lower in deep glacial states. This is an interesting finding, as some people have assumed that the ESS metric would be higher at the glacial maxima (e.g., the LGM) than during interglacials. That is not what the data shows.”

Reasoning from inference then, ESS will increase still further when there is little or no cryosphere at all. The PETM, which took off from an already hot, essentially ice-free climate state, appears to indicate an ESS of ~5C – 6C in response to what may have been a doubling (or less) of CO2 (eg. RealClimate PETM weirdness).

I’m not confusing the PETM with the subsequent Early Eocene Climate Optimum but Anagnostou et al. (2016) provides valuable context for considering plausible conditions just before the onset of the PETM. Arguably, it supports Zeebe et al.’s assumption that Palaeocene CO2 was about 1000ppm.

Back to the Holocene, with its ice: the suggestion is that state-dependent ESS now is probably not as high as 9C but closer to 5C – 6C, as other studies have estimated.

This is, of course, just thinking out loud, and dependent on accepting an estimate of PETM warming (above Palaeocene background) of ~5C.

As I understand it, two factors may have been in play:

First, the gradual decline in atmospheric CO2 that broadly characterises the entire Cenozoic after the Early Eocene Climate Optimum ~51Ma. This gradually cooled the climate and may have been the trigger which started the Pleistocene glaciation at about 2.75Ma.

Pleistocene glaciation seems to have been interrupted every 41ka at maximum obliquity, which strongly increases summer insolation at high N latitude. This 41ka cycle is dominant from 2.75Ma until about 0.9Ma, after which it begins to break down. The dominant cycle shifts to ~100ka by about 0.6Ma and continues until the present Holocene interglacial.

It seems as though the NH ice sheets grew larger and lasted longer in a progressively cooler, lower CO2 world. The shift from 41ka to ~100ka interglacials (the Mid-Pleistocene Transition, MPT) may have been aided by ice sheet behaviour itself.

One hypothesis is that the gradual scouring of soil by successive glaciations leading up to the MPT actually caused ice sheets to grow. Ice sheets grounded on soil are fundamentally unstable and prone to slippage as their mass increases. This keeps the sheet low and relatively thin and so easier to melt during insolation maxima.

But eventually, glacial scouring of soils exposes huge areas of bedrock and new ice sheets form with far more stable foundations, frozen fast directly to the rock beneath. This allows them to become thicker, elevating their surface high enough to significantly reduce average temperature atop the ice sheet. This thicker, more stable sheet is inherently more resistant to melting and collapse by insolation maxima and so begins to ‘skip’ some of the 41ka obliquity cycles. The post-MPT glacial cycle emerges.

It can’t be the Sun. Although sunlight is getting gradually stronger, the change over 2 million years wouldn’t have an appreciable effect.

It couldn’t be the distribution of land masses, for the same reason.

I’m fairly sure there was no asteroid impact in this time period big enough to shift Earth’s orbit or attitude significantly.

About the only thing I can think of would be a change in something else on Earth. What could it be — a new species of plant which is better at capturing CO2? Something which lowers Earth’s albedo? I’m grasping at straws here…