No Energy Paradox

Whatever happens today in the UK, it won’t be as awful as 1 July 2007.

So I’ll carry on where I left off yesterday.

Randall Carlson, speaking in a video about the Energy Paradox, says:

…at the end of the last ice age we have a meltdown of the great ice sheets that was inexplicably fast, beyond anything that allows itself of any kind of an explanation.

The “energy paradox” was that there simply wasn’t enough thermal energy available on the Earth to melt that much ice in less than 10,000 years. So Carlson believes that it was most likely an asteroid impact that provided the necessary heat energy.

But there’s no need to invoke any extra-terrestrial energy source to explain the meltdown. The Earth itself is perfectly able to melt any amount of ice. For when it becomes covered in a layer of insulating snow or ice, its surface temperature will start rising, and it will carry on rising until the snow or ice melts.

A simple conductive heat flow model can demonstrate this. What happens if we take the Earth as it presently is, at latitude 45º N, with a temperature ranging from a little over 0º C at the surface, and 7000º C at its core, and drop 5 km of snow on its surface?

When the snow lands, the surface rock temperatures beneath the snow immediately start rising. and keep on rising. In fact they rise by about 100º C over 500,000 years.

Ice is far more conductive than snow, but under 5 km of ice, surface rock temperatures also rise, only rather more slowly than under snow. (Surface rock relative temperature shown is the temperature relative to the initial rock temperature.)

During the last ice age, the temperature of the ice sheets would have been gradually rising until they reached 0º C, at which point they would have started melting. And when they started melting, faster in some places than others, large cracks would have opened up in the ice, exposing more of the ice to an atmosphere that was also gradually warming.

If the surface rock warming caused increased vulcanism, there would have been a rise in dust and CO2 levels in the atmosphere (which is what actually happened at the end of the last ice age). Dust deposition on the surface of the ice sheets would have lowered their albedo (reflectivity) causing their upper surfaces to warm and start melting as well. The decreasing ice albedo would have meant that the atmosphere warmed up even faster. A Milankovitch cycle solar heat gain maximum would have helped as well.

So at the very end of the ice age the ice sheets would be melting not just from below, but also from above. And if surface rock temperatures had risen above 100º C, there would also be steam rising up crevasses in the ice, attacking the ice there also. So if the ice had initially been melting very slowly, by the end of the ice age it would have been melting very rapidly.

So there’s really no need to invoke any asteroid impacts, and there is no energy paradox. There’s more than enough heat available inside the Earth to melt all the ice, even without any atmospheric warming or dust deposition.

And when the ice or snow melts, the surface rocks rapidly drop back to their original pre-glacial temperatures, and vulcanism will also subside, and the dust and CO2 in the atmosphere will diminish. Surface rock temperatures will continue to slowly cool until snow and ice can again begin to build up on top of them.

So there follows a succession of glaciations with interglacial periods between them, as shown below using 250 m thick snow sheets, producing glaciations of about 50,000 years duration, with surface rock temperatures rising and falling by about 40º C. In this simple model the snow all melts very suddenly when it changes phase from snow to water, because the whole sheet is treated as a single layer with the same temperature throughout. In reality the phase change would happen rather more gradually. No atmospheric warming or dust deposition on the top surface of the snow is assumed: the snow is melted by the heated rocks beneath. The heat flows from the warm rocks into the snow above may be very small (about 8 milliWatts / m² in this case), but over very long periods of time they still amount to enough heat to melt the snow.

These results are all from a very simple heat flow simulation model. They should be quite easy to reproduce. They are not intended to be particularly accurate, but simply to demonstrate that surface rock temperatures can rise quite sharply beneath both snow and ice, and in many cases this will generate sufficient heat to melt the  overlying snow or ice.

About Frank Davis

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3 Responses to No Energy Paradox

  1. Does the model account for Antarctic ice sheets? Possibly too small as a percentage of the surface of the world to be an effective insulator? Just wondering, it’s a great concept of yours, following with interest.

    • Frank Davis says:

      Does the model account for Antarctic ice sheets?

      The model is of a single column running from the surface of the Earth to the centre at one single latitude (as described here). I don’t have enough computing power to do multiple latitudes. All I’m trying to show at the moment is that surface rock temperatures will rise beneath (sufficiently deep) snow or ice sheets, and that this can be enough to melt the ice at that latitude.

      So I haven’t really addressed the wider question of how terrestrial glaciations might begin and end. At present I’m supposing that they start when there’s sufficient snow covering a large enough area of the Earth for long enough for the Earth’s albedo to rise, and the atmosphere to cool. Antarctica would of course be part of that snow-covered area. And I’m supposing that glaciations end when the kind of mechanisms I’ve postulated melt much of the snow or ice, causing the Earth’s albedo to fall, and the atmosphere to warm up. It does seem that there’s a step change into an ice age and out of one.

      • Sir, thankyou for the detailed response. It’s a shame your model cannot get some significant super computer time to confirm or disprove it on a larger sample area. To a layman, it sounds plausible and I thank you for sharing it.

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