During the “Ice Ages” or “Snowball Earth” times, where was all the energy?

We often seem to accept the idea that there are periods of time in which the entire surface of Earth was frozen, for the most part. This implies that there are periods of time in which the entire surface was NOT frozen over. Thus there must have been heat and energy present on the surface. How did all that energy move to cause an ice age? It seems absurd for all that energy to just radiate into space or move deep into Earth.

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I am confused, since we know there periods of time where the entire earth is not frozen: present time! –  Neo Aug 27 at 19:33
Yes, I suppose I could've just asserted that. –  personjerry Aug 27 at 19:38
Don't confuse "Ice Age" with "Snowball Earth" –  Peter Jansson Aug 27 at 20:03
The heat / energy would have gone the same place it goes when summer turns to winter and the whole ground freezes in nordic countries. I'm pretty sure it doesn't just move South so yes, it would simply radiate into space. Notice that this also happens pretty quickly. –  Pooks Aug 28 at 4:27
The earth is colder at night, and in the winter, so yes, the energy in the atmosphere and the top layer of soil radiates into space fairly quickly when the sun stops shining on it. –  superluminary Aug 28 at 16:12

I'm not quite sure if the question is asking about glacial, ice ages, or snowball Earth, and whether it's about the onset or end of a glacial period. I'll try to hit all three.

Ice Ages and Milankovitch Cycles

Ice ages are long spans of time that marked by periods of time during which ice reaches far from the poles, interspersed by periods during which the ice retreats (but never quite goes away). The periods of time during which ice covers a good sized fraction of the Earth are called glacials; the periods during which ice retreats to only cover areas in the far north and far south are called interglacials. We are living in ice age conditions, right now. There's still ice on Antarctica and Greenland. We are also in an interglacial period within that larger ice age. The current ice age began about 33 million years ago while the current interglacial began about 11,700 years ago.

The Milankovitch cycles determine whether the Earth is in a glacial or interglacial period. Conditions are right for ice to form and spread when precession puts northern hemisphere summer near aphelion and winter near perihelion and when both obliquity and eccentricity are low. The Earth currently satisfies the first of those conditions, but obliquity and eccentricity are a bit too high. That makes our northern hemisphere summers are a bit too warm, our winters a bit too cold.

The Milankovitch cycles] provides several answers to the question "where does the energy go?" Those times when conditions are ripe for glaciation have energy in the northern hemisphere spread more uniformly across the year than times not conducive to glaciation. Summers are milder, which means accumulated snow doesn't melt as much. Winters are milder, which means more snow falls.

Once ice does become ubiquitous, another answer to the "where does the energy go" question is into space. Ice and snow are white. Their presence reduces the amount of sunlight absorbed by the Earth.

The first paper listed below by Hays et al. is the seminal paper that brought the concept of Milankovitch cycles to the forefront. The second paper by Abe-Ouchi et al. dicusses a recent climate simulation that successfully recovers many salient features of the most recent glaciations. Most importantly, this paper appears to have solved the 100,000 year mystery and shows why deglaciation operates so quickly.

Hays, J. D., Imbrie, J., & Shackleton, N. J. (1976, December). "Variations in the Earth's orbit: Pacemaker of the ice ages." American Association for the Advancement of Science.

Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J. I., Takahashi, K., & Blatter, H. (2013). "Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume." Nature, 500(7461), 190-193.

Icehouse Earth vs Greenhouse Earth

The Earth's climate appears to have been toggling between two climate extremes for much of the Earth's existence, one where things are cold and ice is likely to form and the other where ice is absent worldwide except maybe right at the poles. Dinosaurs roamed the arctic and Antarctica when the Earth was in one of its greenhouse phases. The Earth has been in a greenhouse phase for most of the Earth's existence.

Milankovitch cycles don't cause glaciation during greenhouse Earth periods. Ice ages happen when the Earth is in an icehouse phase. What appears to distinguish greenhouse and icehouse phases are the positions and orientations of the continents. Having a continent located over a pole helps cool the climate. Having continents oriented so they channel ocean circulation in a way that keeps the ocean cool also helps cool the climate.

The Earth transitioned from its hothouse mode to its icehouse mode 33 million years ago or so. That's right about when two key events happened in the ocean. Up until then, Antarctica was still connected to both Australia and South America. The separation from Tasmania formed the Tasmanian Gateway, while the separation from South America formed the Drake Passage. This marked the birth of the very cold Southern Ocean, it marked the buildup of ice on Antarctica, and it marked the end of the Eocene.

Bijl, P. K., Bendle, J. A., Bohaty, S. M., Pross, J., Schouten, S., Tauxe, L., ... & Yamane, M. (2013). "Eocene cooling linked to early flow across the Tasmanian Gateway." Proceedings of the National Academy of Sciences, 110(24), 9645-9650.

Exon, N., Kennett, J., & Malone, M. Leg 189 Shipboard Scientific Party (2000). "The opening of the Tasmanian gateway drove global Cenozoic paleoclimatic and paleoceanographic changes: Results of Leg 189." JOIDES J, 26(2), 11-18.

Snowball Earth and the Faint Young Sun Paradox

Snowball Earth episodes were not your average ice age. Ice typically doesn't come near the tropics, even in the worst of ice ages. Snowball Earth means just that; the snow and ice encroached well into the tropics, possibly extending all the way to the equator.

The problem with snowball Earth isn't explaining where all the energy went. The real problem is explaining why the ancient Earth wasn't in a permanent snowball Earth condition, starting from shortly after the Earth radiated away the initial heat from the formation of the Earth.

The solar constant is not quite constant. While it doesn't change much at all from year to year, or even century to century, it changes a lot over the course of billions of years. Young G class stars produce considerably less energy than do middle aged G class stars, which in turn produce considerably less energy than do older G class stars. When our Sun was young, it produced only 75% or so as much energy than it does now.

By all rights, the Earth should have been completely covered with ice. The young Sun did not produce enough energy to support open oceans. This obviously was not the case. There is plenty of geological evidence that the Earth had open oceans even when the Earth was quite young.

This 40 year old conundrum, first raised by Carl Sagan and George Mullen, is the faint young Sun paradox. There have been a number of proposed ways out of the paradox, but none of them quite line up with the geological evidence.

One obvious way out is that the Earth's early atmosphere was very different from our nitrogen-oxygen atmosphere and contained significantly more greenhouse gases. The amount of greenhouse gases needed to avert a permanent snowball Earth is highly debated, ranging from not much at all to extreme amounts. Another way out is a reduced albedo due to the significantly smaller early continents and lack of life. The young Earth would have been mostly ocean, and ocean water is rather dark (unless it's covered with ice). Lack of life means no biogenic cloud condensation nuclei, which means fewer clouds.

Goldblatt, C., & Zahnle, K. J. (2011). "Faint young Sun paradox remains." Nature, 474(7349), E1-E1.

Kienert, H., Feulner, G., & Petoukhov, V. (2012). "Faint young Sun problem more severe due to ice‐albedo feedback and higher rotation rate of the early Earth." Geophysical Research Letters, 39(23).

Rosing, M. T., Bird, D. K., Sleep, N. H., & Bjerrum, C. J. (2010). "No climate paradox under the faint early Sun." Nature, 464(7289), 744-747.

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While this doesn't answer the question directly, I found it very interesting. Thank you! –  personjerry Aug 28 at 7:47
I answered the question you should have asked. You asked where the energy went. The answer is that energy was never there. In fact, not enough energy was present. As you can see from the selected journal articles, explaining where the energy came from to avoid a permanent snowball Earth is highly problematic. –  David Hammen Aug 28 at 8:02

Of course it isn't "absurd", and looking at the ball-park energy budget figures you'll see why:

First, I don't think anyone is claiming the Earth is completely frozen. More of a "slushy at the Equator" scenario. But let's assume an average 1 km thickness of ice for arguments sake (i.e. probably an exaggeration although polar ice would be thicker).

The current thermal budget can be found here.

Pertinent figures:

Geothermal heat flow (vertically through the rock, primarily from radioactive decay & cooling) is ~$0.084\ \mathrm{W/m^2}$.

Solar input: $340 \mathrm{W/m^2}$ About a quarter of this is reflected back but this will vary according to conditions (e.g. ice cover, clouds, etc). Assume no reflection. (yes the presence of ice would cause reflection - but it may also reduce cloud cover due to reduced evaporation?).

Note: geothermal energy is tiny relative to solar flux, so we'll ignore it.

That 1 km of ice = 1000m3 of ice (per square meter).

Let's assume that the melting process would also involve an increase in 10C in additional to the latent heat of melting (ie. yes we melt the water but we also increase its temperature a bit).

Total energy required (per $\mathrm{m^3}$) = (Temp increase * Thermal capacity of water + Latent heat of melting) * volume.

So if we plug in our numbers, that would be:

$$(10 * 4.2 + 334) * 10^6 * 1000$$ $$= 3.8 * 10^{11}\ \mathrm{Joules}$$

Heat flux for the same area is $340\ \mathrm{J/s}$ So time for the required energy to melt the ice = $3.8 * 10^{11} / 340 = 35\ \mathrm{years}$.

You could argue about my ball-park estimates. For example there would be more albedo reflection to melt the ice (=takes longer). And you may not necessarily have to increase the temperature of the water as much ( =>takes less time), and much of the Earth would not have 1km of ice (=>takes less time). But this gives you a ball park "yes it is feasible".

Edit: I read the question a bit quickly - the above shows it is 'easy' to get from an ice planet to an ice-free planet. But the converse is also true. The amount of energy that keeps the Earth ice free can easily be added/subtracted over a timescale of a few centuries, just from solar and atmospheric effects.

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What's not been touched yet, and the current answers do cover a lot of ground, is the variability of solar input.

Even IF the amount of energy radiated out by the earth remains the same (and it probably would, roughly), solar input is highly variable and is a major factor in determining the total energy budget of the planet.
Even a small change can have far reaching consequences. Thus if the sun's output goes down by only a few percent (and that's well within its variability even over the 11 year sunspot cycle) temperatures on earth will swing with that (over that short a cycle that's pretty much averaged out by changes in ocean currents). If such a "dip" lasts longer, think a few centuries, you get a "little ice age" as we just emerged from in the 19th century (and by some accounts may be on the verge of slipping into the next, as the sun is again seemingly rather inactive).
And the sun has longer cycles, such a low activity cycle lasting a few thousand years can well drop the earth into a full scale ice age. And as the ice sheets grow, reflection goes up, less energy heats the planet, less clouds form. Until the sun enters a high activity phase again, the planet will remain (relatively) cold.
As said, this is unlikely to cause the entire planet to disappear under a blanket of ice. The last major ice age "only" came down to about the latitude of the Rhine delta in Europe for example.

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I see, so essentially small changes over long periods of time. And as winwaed's answer showed, the small changes are actually pretty big energy-wise so it doesn't take all THAT long. Thank you! –  personjerry Aug 28 at 7:51
@personjerry yes, a small change (percentage wise) of a very large number is still a LOT. And the sun provides a LOT of energy. –  jwenting Aug 28 at 7:57
Please! This is not the right answer. The variability of the solar constant across the solar cycle is about 1/10 of a percent, not "a few percent." The variability of hundreds of years is less well known, but this is far from but the leading hypothesis for the cause of the little ice age. Vulcanism coupled with the Milankovitch cycle is the leading hypothesis. Suspended aerosols increase the albedo, and the little ice age period was marked by excessive vulcanism. –  David Hammen Aug 28 at 7:58
This answer needs to have some references to support the assertions made about the magnitude of solar variability. " Until the sun enters a high activity phase again, the planet will remain (relatively) cold." this is simply incorrect, the sun and albedo are not the only thing that controls global temperatures, there is also the greenhouse effect, for a start. –  Dikran Marsupial Sep 2 at 16:28