Different Depths of Snow at a Single Latitude

Next looking at how single snow layers of different depths behave at latitude 47.5ºN.

Black, red, and green lines show surface rock temperatures in degrees K. Orange/yellow shows snow depth in metres. Cyan line shows air temperature above snow in degrees K. Timescales are in years with 1e5 years equal to 100,000 years.

The model uses the same initial temperature profile of the Earth at all latiudes. This means that surface rock temperatures will initially fall at the pole, and rise at the equator. So an initial period of 12,000 years is used to stabilise surface rock temperatures before snow deposition.
single_snow_layers_at_47_5N

As snow deepens above 175 m in depth, melt time grows longer.

But below 175 m depth, melt time also grows longer. And with 5 m snow surface rock temperatures actually fall rather than rise.

This happens because as the snow layer thins, its thermal resistance falls, and it loses heat more rapidly to the colder atmosphere above. At some point the rate of heat loss to the atmosphere is equal to the rate of heat gain from the surface rocks below, and the snow doesn’t melt at all. And when the snow is still thinner, the rate of heat loss to the atmosphere is even greater than the rate of heat loss from the surface rocks, and the snow gets colder, and the surface rocks get colder too.

If this doesn’t happen with the very thinnest layers (e.g. 1 m snow), it’s probably because there’s enough heat in the surface rocks to melt the overlying snow before the surface rocks cool down enough to stop the snow melting.

All of which prompts the suggestion that ice ages don’t start with blizzards that build snow sheets hundreds of metres deep, but instead begin with shallow snow sheets over large areas of land which are only slightly too deep for them to be melted by the surface rocks beneath them, and which cause a deep freeze to set in with permafrost beneath the snow. This snow never goes away, and slowly gets deeper with subsequent snow depositions on top of it, gradually turning thicker, and compressing to form ice.

Dropping 200 Metres of Snow at Different Latitudes

The next thing, using this simple model, was to see what happened when a 200 m layer of snow was deposited at different latitudes.

Near the North Pole, the snow took many thousands of years to melt, but did eventually melt after surface rock temperatures gradually kept on rising beneath the snow. After the snow melted, surface rock temperatures fell far more rapidly than they had risen.

Black, red, and green lines show surface rock temperatures in degrees K. Orange/yellow shows snow depth in metres. Cyan line shows air temperature above snow in degrees K. Timescales are in years with 1e5 years equal to 100,000 years.

The model uses the same initial temperature profile of the Earth at all latiudes. This means that surface rock temperatures will initially fall at the pole, and rise at the equator. So an initial period of 12,000 years is used to stabilise surface rock temperatures before snow deposition.

Unsurprisingly, snow melted fastest nearer the equator than the pole. Below latitude 15º N, air temperatures were too high for snow.

What it means is that if 200 m of snow were to fall simultaneously at all latitudes, the snow would melt first at low latitudes, and then at higher latitudes until ultimately it had all melted right the way to the North Pole.

So if there’s still deep snow and ice in Antarctica and Greenland, it may simply be that it hasn’t had a long enough time in which to melt.

How long would it take for a geothermal heat flow rate of 50 milliWatts per square metre to melt 1000 metres of ice? This is a volume of 1000 cubic metres of ice, with a mass of 917,000 kg, which would require, given a latent heat of fusion of 334,000 Joules per kilogram, 3.06E11 Joules of heat to melt it. With a heat flow rate of 50 milliWatts per square metre, this would take 6.12E12 seconds, or 194,063 years.

Source: List 1