Steady Snowfall on Multi-layer Snow Sheets

Real snow doesn’t appear overnight in sheets hundreds of metres deep. Instead it builds up slowly in layers.

And so in the next, slightly more realistic model, snow is dropped at a constant steady rate to form layers of snow.

Once again, as snow depth builds up, subglacial surface rock temperatures rise. At first the rate of melting of the snow at the base of the ice sheet is less than the rate at which snow is added on the surface of the ice sheet, and the ice deepens. But as the surface rock temperature rises, the rate of snow melting increases until it equals – and then exceeds – the rate of surface snow deposition. The snow sheet first gets deeper, and then gets shallower, even though snow falls at a constant rate.

snowfall_on_multilayer_snow_sheet But after a while the snow sheep gets no shallower. This because, as the snow sheet thins, its thermal resistance falls, and heat flow out of the snow sheet increases until it equals the heat flow from the rocks beneath. When heat flow in equals heat flow out, the snow sheet stops melting.

Even when the snow stops falling after 100,000 years, and most of it melts, there still remains a thin layer of snow.

If thin layers of snow don’t melt, how then did the ice age end?

Different Depths of Ice at a Single Latitude

Next looking at how single ice layers of different depths behave at latitude 62.5ºN, southern Greenland. These are just large blocks of ice dropped on the surface of the Earth.

Black and green lines show surface rock temperatures in degrees K. Red line shows ice temperature in degrees K. Orange/yellow shows snow depth in metres (off scale). Cyan line shows mean annual air temperature in degrees K. Timescales are in years with 1e5 years equal to 100,000 years.

The ice is more thermally conductive than snow, so a lot more is needed to have the same effect as snow. If ice depth is greater than about 3 km. surface rock temperatures rise, and so do ice temperatures. If ice depth is less than 2 km, subglacial surface rock temperatures fall.

Ice melting is only not shown because it takes too long to happen.

Interestingly, the current depth of Greenland glaciers is 2 – 3 km, which is in accord with the results above.

One thing this suggests is that ice ages don’t start with heavy snowfall, but instead with the deposition of thin layers of snow over very large areas of land. The effect of the snow is to raise the albedo of the surface of the Earth to 0.8 or 0.9, reflecting 80 – 90% of sunlight back into space, and causing the temperature of the atmosphere above the snow to fall precipitately. If the snow layer is only a few metres deep, the subglacial surface rock has little thermal resistance above it, and heat is rapidly conducted through the snow to the cold atmosphere. Both the snow/ice and the surface surface rocks beneath them get colder. A deep freeze sets in. There is no melting of snow or ice.

Once there’s a layer of deep-frozen snow or ice in place, subsequent depositions of snow simply result in the snow and ice getting deeper. If 1 metre of snow falls every year, after 1000 years the snow will be 1 km deep, and after 5000 years 5 km deep

As the snow or ice gets deeper, the surface rocks cease cooling and start warming, because there is sufficient thermal resistance in the overlying snow/ice to slow the heat loss to a rate lower than the geothermal heat gain by surface rocks from deeper (and hotter) rock layers.