Chris Colose explains the hysteresis loop and climate shifts:
“Here’s an example situation to help read this. Suppose we start off in the warm climate state on the upper branch labeled W1. Now suppose you gradually lower the CO2 a bit. In this case you will get just a bit colder, say evolving toward W2, or decreasing the CO2 a bit more, to W3. This is a steady cooling you expect from lowering CO2, but it isn’t an irreversible jump, and if CO2 returns to initial conditions you can return back to W1.
However, suppose we decrease CO2 a lot, such that we reach W4 along the upper branch. This is a rather unstable case (like a ball on the top of a sharply peaked hill just getting ready to be nudged), and further tendency to cool will cause an abrupt jump to the S1 state.
Physically, this is where an ice line starts to advance and the albedo feedback becomes very powerful. Also note that the water vapor feedback becomes negligible once you get tropical temperatures near freezing.
Now if you return CO2 levels back to W2 likes conditions, you don’t actually get to the W2 temperature. Now, you only warm a tiny bit to S2. In other words, because of the ice-albedo effect, you have multiple temperature solutions for a fixed solar irradiance and CO2 levels, and what state you’re in also depends on the history to get there.”
Colose seems to consider that CO2 does not strictly equal temperature. Allowing an S curve rather than a more or less straight line running lower left to upper right. The question is how much is CO2 acting as the control variable? I think there are other factors besides greenhouse gases contributing to control.
Consider that climate is described by this S curve. Then take the S curve to a smaller scale. A Minnesota lake.
As air temperatures drop in the Fall, water temperatures follow. Usually one night ice forms across most of the lake. The lake has transitioned to its Winter state. Short term rising temperatures most likely will not be able to remove the ice until Spring. Once most of the lake is ice out, it will be very unlikely the ice will return even with extremely cold air temperatures.