Forty years ago I was in university working on energy conservation in buildings. I worked with an electronic analogue simulation model in which thermal resistance was represented by electrical resistance, temperature by voltage, heat flow by current. My job was to control the model with one of the new microcomputers that had become available. I spent a lot of my time with a soldering iron and wires and Veroboards, getting DACs and ADCs and other bits of electronics working.
Eventually the money ran out, and I left the university, and became a freelance software engineer, working on all sorts of stuff unrelated to energy conservation.
But I never forgot what I’d learned during that time. And so I’ve always been interested in Anthropogenic Global Warming, because it’s essentially all about heat flow, although in the Earth’s atmosphere rather than in the walls and rooms of buildings. And it’s prompted me to try to build my own simple atmospheric simulation models. Regular readers will have noticed my periodic occasional unsuccessful attempts (for instance here). The trouble is that I simply don’t know enough about atmospheric physics to do it.
But I keep going back to have another try. And over the past month or so I’ve been thinking not so much about the atmosphere (which I don’t know how to model) but the Earth beneath the atmosphere (which is much easier to model, because it’s all conductive heat flow of a kind with which I was very familiar in my university days).
And I was thinking about ice ages. We’re currently living in a warm interglacial period, at the end of an ice age which lasted about 100,000 years. Our current interglacial has only lasted for 12,000 years, during which time us humans have emerged from a Stone Age into a Bronze Age and an Iron Age. And since the last interglacial, 100,000 years ago, only lasted for 10 – 15,000 years before the ice returned, many people believe that our own interglacial is due to come to an end sometime soon. Others think that it could last for another 30,000 years or more. And of course Global Warming alarmists are far more worried about global warming than global cooling. But it’s always seemed to me that we should be much more worried in the long term about the return of an ice age than any temporary warming that may be happening.
And a few weeks ago I had an idea about how the Earth might alternate between ice ages and interglacials. It was a very simple idea, and one that anyone will be able to understand. Here it is:
During an ice age, when the Earth is covered in ice which may be 3 – 4 km deep, the ice acts as a layer of insulation on the surface of the Earth. And because the Earth has a hot core, from which heat is flowing out through the surface, the effect of this layer of insulation is to warm the rock underlying the ice sheets. And so the temperature of the underlying rock gradually rises. And it keeps on rising, and begins to melt the ice at the very bottom of the ice sheet. And eventually the hot rock under the ice completely melts all the ice. And when the hot rock meets the atmosphere, it warms the atmosphere, and begins to itself cool down. Eventually (and in fact quite rapidly) the rock cools back down to its original temperature. And then the snow and ice falling on it stops melting, and remains freezing, and a new layer of ice starts growing. In this manner the cycle repeats itself, again and again and again.
Very simple. Almost too simple. Think of the ice as a garment that the Earth dons and gets warmer, and then takes off and gets colder.
But would it work? I set out to build a heat flow simulation model of it. To simplify things, I constructed a little 50 km radius asteroid made of granite at 5000ºK (somewhere around the temperature of the core of the Earth), and allowed the heat stored in it to radiate away into space from its hot surface. Over several million years, the surface of the asteroid gradually fell until it was near the temperature where ice melts, 273ºK (0ºC).
And then I started to drop a steady rain of lumps of ice onto its surface.
Initially the ice melted very quickly. But as the asteroid continued to cool, it took longer and longer for the ice to melt. And finally, after it had cooled down enough, the asteroid remained covered in a steadily deepening layer of ice, which was melting at its base where it was in contact with the still-warm asteroid below, while further layers of ice were being added at the top.
But the really interesting thing was what happened during the period when the asteroid was neither too hot (and quickly melted the ice falling on it) nor too cold (and didn’t melt the ice at all). For during this period I found that the ice would build up for a while, and then melt away completely. And during the times when it was covered in ice, the surface of the asteroid would warm up, and during the periods when there was no ice the surface of the asteroid would cool down. Here’s a plot of the almost thermostatic cycling of the asteroid rock surface temperature (T1 red) and the outer radiating surface temperature (Ts white), and ice thickness (ice green). 40 years ago I was looking at oscilloscopes showing exactly these sorts of growth and decay curves every day.
In this manner I watched a succession of ice ages alternating with interglacial periods. And as the asteroid cooled, the ice ages got longer and longer, and the interglacials shorter and shorter, until finally the ice age never ended.
And this, more or less, is what has also been happening on the surface of the Earth for the past several million years. There have been a succession of ice ages, with the duration of the ice ages gradually getting longer and longer. Currently they seem to last about 100,000 years, but before that they lasted about 40,000 years, and before that they were even shorter. So maybe the exact same thing is happening with the Earth as happened with my asteroid.
But the other interesting thing is that my asteroid had no atmosphere above its surface (because I don’t know how to model atmospheres). And it had no sunlight falling on it either. It was just a bare rock radiating heat into space. Yet despite that, there was still a long succession of ice ages with interglacials between them. The ice ages on my little asteroid happened completely independently of any atmosphere or sun. And so maybe terrestrial ice ages are independent of sun and atmosphere as well? Or very nearly completely independent.
But the oddest thing of all is that I have never heard of this particular theory of ice ages. It simply doesn’t seem to exist in the literature at all. Wikipedia’s Ice age has no mention of anything like it. It gives:
6 Causes of ice ages
6.1 Changes in Earth’s atmosphere
6.1.1 Human-induced changes
6.2 Position of the continents
6.3 Fluctuations in ocean currents
6.4 Uplift of the Tibetan plateau and surrounding mountain areas above the snowline
6.5 Variations in Earth’s orbit (Milankovitch cycles)
6.6 Variations in the Sun’s energy output
It seems that climate scientists haven’t been considering heat flow from inside the Earth at all. Or rather, they’ve been dismissing it as unimportant, as I found one academic doing:
Although there is nothing wrong with the statement that the Earth is truly very hot at its center (actually as hot as the surface of the sun) the notion that it is a significant source of heat at the surface is easily dismissed with a little critical thinking. If the inner heat were really the dominant factor, then surely the day-night cycle would not be what it is, nor would you expect such variation in climates over seasons and latitudes. How can the south pole be covered with thousands of meters of ice with all this heat supposedly bubbling up from the surface? Why would a little lower angle of sunlight cause the average temperature to drop from +20°C in the summer to -20°C in the winter?
The fact of the matter is, solid rock is an extremely good insulator and the heat from the mantle propagates up very slowly and diminishes very quickly (at about 20°C/km) to almost nothing by the time it is at the surface. At the surface, the earth is releasing less than one-tenth of one Watt/m2. If you could somehow capture all of the energy coming up from the earth’s core into the foundation of an average-sized home, you might have enough to power one 15W light bulb! Not a lot of of juice when you compare it to the sun, which provides on average some 342W/m2 of energy to the earth’s surface.
Well, he’s quite right that the present heat flow from inside the Earth is only about 0.1 watts/square metre. But this heat flow isn’t a constant, and we’re looking at the heat flow 12,000 years after the beginning of our present interglacial, when we should have expected to see hot rocks cooling, and heat flow diminishing.
Anyway, I’m now planning to scale up my asteroid to the size of the Earth, and add some sort of simple atmosphere on its surface (no idea how), and some sunshine as well, and see what happens then. Maybe I’ll find that the ice is melted by all the sun and CO2 and stuff in the atmosphere above. But at the moment I think it’s going to carry on being the Earth beneath the ice that will melt the ice, as it warms and cools.