A Theory of Ice Ages

What happens when a few hundred metres of snow lands on the surface of the Earth at the start of an ice age? Does the snow melt? Does the ground beneath the snow cool down? Does anything happen at all?

There’s only one way to find out: Build a model. Build a heat flow model of the snow, and the air above it, and the ground beneath it. Add in a Sun that shines daily onto the surface of the snow. Given some set of initial temperatures of air, snow, and ground, figure out the heat flows between these layers, and their new temperatures after a short interval (like one hour or one day). And then start the model running, and watch what happens.

And that’s just what I did. I built a computer simulation model of the heat flow below and inside and above a block of snow. And then I set it running. I used to build dynamic heat flow models of buildings 40 years ago, as a post-graduate and research assistant. Back then we were building electronic analogues heat flow models. I don’t know whether anyone does that any more.

I’m not a climate scientist. I’m not a glaciologist. I’m not a geologist. In fact, I’m not a scientist at all. I’m just an interested layman, and nobody has paid me to build and run my model. I just like building models of things, and watching how they behave. I’ve even got my own orbital simulation model in which I cam watch what planets and moons and asteroids do (and, needless to say, I’m not an astronomer either).

So I’m not claiming to be any kind of expert on this stuff. And I’m not asking anybody to trust me. In fact, I strongly suggest that you shouldn’t trust me at all. Really what I would suggest is that you build your own model.

If you only want to listen to experts, don’t read this blog, because I’m not an expert.

So do you want to know what happened when I dropped 400 m of superfine snow onto the surface of the Earth at latitude 47,5º N?

What happened was rather surprising.

The ground beneath the snow started to warm up. Its temperature rose steadily for thousands of years. And finally it melted all the snow.

400m_snow_meltThe 5 superimposed graphs on the right were generated at runtime by my model. They show how the temperature of three layers of granite surface rocks (black line topmost, red line, green line) varied over about 220,000 years. And how the air temperatures above the snow (cyan line) varied over the same period. All temperatures in degrees Kelvin, in which water’s freezing point is 273º K and its boiling point is 373º K. And it also shows snow thickness (yellow line) in metres. Time goes from left to right.

The model run starts without any snow present, when the surface rocks are allowed to cool down over about 12,000 years, which is about the length of a terrestrial interglacial.

And then at the 12,000 year mark, I drop 400 metres of superfine snow on top of the surface rocks, which is when snow depth jumps from 0 to 400 m.

At the same time the air temperature above the snow drops by about 60º K. That happens because the surface albedo (or reflectivity) has changed from about 0.4 for granite to 0.8 for snow, and a lot of sunlight is being reflected back out into outer space without warming either the snow or the air above it. The result is a rapid drop in air temperatures in the air column above the snow.

But the really surprising and interesting thing is the way that the surface rock temperatures start rising, and carry on rising for the next 200,000 years. Why is that happening?

Here’s the explanation. Before the snow landed, the surface rocks had reached an equilibrium temperature where they were gaining as much heat from the interior of the Earth as they were losing to the atmosphere (and to outer space) above them. But when the snow landed, while the top surface rocks carried on gaining heat from warmer layers below, they could no longer lose heat at the same rate to the atmosphere above because the snow layer offers considerable resistance to any heat flow. Snow is a very good thermal insulator. And the superfine snow I’m using here has the same thermal resistivity as the expanded polystyrene or polyurethane foam that’s found in the air gaps inside brick walls. So the topmost surface rocks are continuing to gain heat at the same rate as before from the rocks beneath them, but are no longer losing heat at the same rate through the insulating snow above them. So the surface rocks start gaining heat, and when they gain heat, their temperature rises. And that’s why we’re seeing their temperature rising. The temperature rises slowly because the heat flow rate into them is very small – only a few milliWatts/m².

And the snow above the surface rocks can’t rise above oº C (273º K). Or it takes a great deal of heat to turn solid frozen water (snow) at at 0º C to liquid water at 0º C. It’s called a phase change. One phase change is from ice to water, or water to ice. Another from water to steam, or steam to water.

So the 400 m of snow starts changing phase from ice to water as soon as its temperature rises to 0º C. And it then takes many tens of thousands of years to complete the phase change.

And that’s what happens after 212,000 years. The snow turns to water. And the water runs away. And when all the snow turns into water and runs away, the surface rocks (whose temperatures have risen 70º C over the previous 200,000 years) cease to be covered in a deep layer of thermal insulation, and so they start to rapidly cool down. And within 10,000 to 20,000 years they’re almost back to the temperatures at which they started 200,000 years earlier.  And at the same time that the snow all melts, the albedo of the Earth falls from 0.8 to 0.4, and it stops reflecting most of the sunlight back into space, and air temperatures return to what they had been before the snow appeared.

So if 400 m of snow lands on the surface of the Earth, the rocks beneath the snow will warm up and melt all the overlying snow. The Sun doesn’t melt the snow. Neither does carbon dioxide in the atmosphere melt the snow. Nor do variations in the Earth’s orbit over many thousands of years (Milankovitch cycles) melt the snow. Nor does anything else. The snow is melted by the warming rocks beneath it.

So that’s what my simulation model says what happens during an ice age, when large areas of land are covered in deep snow or ice. The rocks beneath the snow and ice heat up, and eventually they melt the snow and ice.

And this might explain the last ice age lasted about 100,000 years, and the interglacial before it only lasted about 10,000 years. It’s because the surface rocks beneath the snow heat up very slowly, but cool down fast.

In fact, it may explain how ice ages work, and why there have been these long ice ages punctuated by brief interglacial periods. During the long ice ages, the rocks beneath the snow heat up very slowly, and eventually melt the snow. And during the interglacials the surface rocks cool down again much more rapidly, and cool to the point where snow can start building up again, and the next ice age start, in a repeat never-ending cycle.

But that’s just my explanation. And I’m not a climate scientist or a glaciologist or a geologist. So you don’t have to believe me.

And it’s not an explanation you’ll find in any textbook. I’ve never seen this explanation anywhere. And I’ve never seen any graphs like the one above anywhere, showing surface rock temperatures slowly rising and then sharply falling.

In my next post, whenever I get round to writing it, I’ll discuss today’s model some more, and maybe a few other matters as well.