There are also much more detailed efforts to predict the start of the next glacial cycle, like this.

I’ve seen many Ice Age models, not just this one of Paillard’s. Some of these other models actually do try to explain how Ice Ages are caused and when they will begin and end. My favorite (but still flawed) model at the moment is Sea ice switch mechanism and glacial-interglacial CO2 variations by Hezi Gildor and Eli Tziperman.

It’s interesting that so many people think that the only thing that determines climate on the Earth is the Sun, yet when you look around, you can see this isn’t true. For example, desert climates are not caused by the Sun, they are determined by proximity to mountain shadows. Arctic climates are determined by latitude. Some climates are determined by altitude, and so on. The Sun provides the energy for WEATHER but geophysical context determines CLIMATE. (I guess while I’m on this soapbox, another thing that interests me is the belief that higher temperatures everywhere mean greater storm intensity. That’s nonsense. It is temperature DIFFERENCE that determines storm intensity, and higher temperatures everywhere means higher temperatures everywhere, not in just one place).

By the way, I think you would like reading An Assessment of Climate Feedbacks in Coupled Ocean–Atmosphere Models by Brian J. Soden and Isaac M. Held as well as Conceptual Models of the Climate: 2001 Program of Study in Geophysical Fluid Dynamics, before making your next post on mathematics and climate.

Also, I want you remember that CO2 only accounts for 3% of the current Greenhouse effect, so what accounts for the rest of the Greenhouse effect? I know what it is but I wonder why very few people ever attempt to talk about that? I want you to return back to a discussion on radiation balance after taking a look at figure 4-1 at http://www.ssec.wisc.edu/library/coursefiles/04_rad_budget.pdf. It is an extremely common pictorial of the Earth’s radiation budget in visual form. Can you calculate Earth’s current temperature using just that figure alone? I can, it is a very elementary exercise and you would think that everyone would use the empirical description of the Earth’s radiation budget in that figure to base their models on, but they don’t. It is an empirical observation that tells us everything we need to know on how to calculate Earth’s current temperature so how can people in-the-know ignore such an elementary thing and yet still claim to be in-the-know?

• Andrew Revkin, The next age and the Anthropocene, Dot Earth, 8 January 2012.

The consensus seems to be that we have put enough CO₂ into the air to postpone the next glacial period, perhaps for the next 100,000 years. And this paper:

• Gary Schaffer, Long time management of fossil fuel resources to limit global warming and avoid ice age onsets, Geophys. Res. Lett. 36 (2009), L03704.

suggests that we if we save our remaining fossil fuels, we could head off the next few glacial cycles by burning them at appropriately chosen times. Another possibility would be to deliberately release more potent greenhouse gases than CO₂ whenever a glacial period was imminent.

If we were smart, we might be able to manage the Earth’s temperature for quite a while, avoiding glacial periods without turning up the heat full blast as we’re doing now.

I was a bit confused about this remark of yours:

I assume that the ice sheet needs some minimal time in order to grow and exceed the volume [...] and that the insolation maxima preceding the g–G transition must remain below the level . The g–G transition then can occur at the next insolation decrease, when it falls below .

I can think of two interpretations. One is:

1. If the Earth is in its g state and the insolation stays below some value for a time , then the Earth jumps into the G state.

2. If the Earth is in its g state and the insolation rises above , we wait until it drops below some value , and then the Earth jumps into its G state.

An alternative interpretation involves:

2′. If the Earth is in its g state and the insolation rises above , we wait until it drops below some value . Then we ‘reset the clock’ and proceed according to rule 1.

Which one is right, if either?

He replied:

The rule is:

the g-G transition is triggered when the insolation decreases below , provided the 2 following conditions are satisfied:

- the g state is longer than a minimal duration (33 kyr, which is longer than a precession cycle) = starting from the i-g transition.

- the insolation maximum preceding the g-G transition is “small” (below )

It now appears to me that, in the Nature paper, it should be written “maximum” instead of “maxima” (… maybe this is the source of confusion!!)

Your option (1) is almost correct (insolation below for more than 33 kyr) if you add that g-G happens when insolation falls below (it must be synchronous with an insolation decrease).

Indeed, insolation maxima occur about every 23 kyr, so your statement is almost equivalent to saying that the preceding maximum is below .

The basic ideas behind this model (and also the continuous one) is that the glacial-interglacial cycles are “relaxation oscillations” or switches between some “preferred states”. These 2 models are built using 3 states, but actually 2 states are sufficient. Transitions are triggered by the insolation changes (according to Milankovitch), but ice volume needs to get through a maximum (“G state”) before a major transition occurs (a termination). This is the key to the 100-kyr cycle.

Starting from an increase in northern summer sunshine and some melting of arctic ice, there was a slowdown in the Atlantic conveyor current due to the reduced salinity, which cooled the northern hemisphere but warmed the southern hemisphere. Consequent changes in winds and currents then brought more deep water to the surface of the Southern Ocean, releasing trapped CO2 and warming the whole planet.

The general idea, if I’ve understood this correctly, is that it seems initially mysterious that we have word-wide ice ages rather than northern/southern ones, given that increased summer sunshine in one hemisphere means a reduction in the other. And the proposed solution to the puzzle involves transitions in ocean circulation patterns and ocean storage of CO2.

In other words, the timer starts running when we enter the g state and resets whenever it gets warmer than ; once the timer runs out, the next time it gets colder than , we transition to G.