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Jack Frost’s underground workshop

Hoar, the medium in which Jack and Jenny Frost work on our windowpanes and other canvases, is formed by the condensation of water vapour as ice. But there is also depth hoar, a product of Jack Frost’s ingenuity underground, or rather under the surface because it forms in snow, not in the soil.

Glaciologists take a dim view of depth hoar. So do snow scientists, and so should you.

Snow is an excellent insulator, especially when it is not very dense and most of its volume is air. That is why igloos work: partly because air flows only inefficiently through the tortuous void spaces in the snow, and still or sluggish air is an even better insulator — not much use either at conducting heat or at carrying it around — than ice; and partly because, although they are better conductors of heat than the air, the snow grains are in limited contact with each other — so the contacts are thermal bottlenecks.

Good insulation means that the snow can be much warmer below the surface than at the surface. Or colder, but that doesn’t favour depth hoar. In Jenny Frost’s favourite subsurface setup, the snow at depth is near to the freezing point but the surface is very cold indeed. Because it is in close contact with lots of (frozen) water, the air at depth saturates with water vapour — no, wait, the air throughout the snowpack is saturated. The point is that the warm air below has a much higher capacity to hold water vapour than the very cold air above.

Air flow being inefficient, this gradient in concentration (saturation specific humidity, to get technical) is why water vapour diffuses upwards through the pores to a depth where, because of the cold, it condenses as the crystalline substance we know as hoar.

Crystals like to begin to grow at solid nucleation sites, and the surfaces of the snow grains are perfect for the purpose. Beyond this point, things are explained well in a classic paper by Sam Colbeck. When the temperature gradient is very steep, the crystals like to grow as plates or facets that often join to form upside-down cup-like shapes. What is more, they begin to consume the grains on which they nucleated.

A vertically elongated facet is a better conductor than the mixture of air and grains at the same depth, so its base is slightly colder than average for its depth, while the top of the grain it is consuming is slightly warmer. This means that, at the scale of single facets and their grains, vapour tends to sublimate from the grain top and diffuse downwards to the tip of the facet.

Relying on this physics, Jack Frost can make lots of depth hoar in a single cold snap, say a few days. Sometimes a half or more of the snow gets turned into depth hoar. The resulting facets and cups are commonly a few millimetres across, and single crystals the size of your fingernail are not unknown. These are giants compared to the original snow grains, whose typical sizes might well have been much less than a millimetre.

That is why we are not keen on depth hoar. The cups look cool, but they have replaced not just countless small grains of snow but countless bonds between grains. Depth hoar is weaker than the granular snow it replaces because the giant crystals haven’t had time to bond to each other, a phenomenon called “sintering”.

What are the consequences? First of all, depth hoar is so friable that it makes retrieving shallow ice cores very difficult. Second, depth hoar complicates the interpretation of microwave emissions from snow and ice which we could otherwise use to estimate the accumulation rate. And finally, layers of depth hoar are among the prime reasons for avalanches. When they collapse, they make excellent slip surfaces for the snow above.

The glaciological attitude to depth hoar is not uniformly disapproving, though. A good place to grow depth hoar is near the bottom of autumnal snowfalls that rest on the so-called summer surface — the glacier surface as it was at the end of summer. When we come along at the end of the winter, we want to measure the mass balance, that is, the mass between the summer surface and the surface at the time of measurement. The depth hoar can be very useful as a marker.

But, all things considered, life would be simpler, and safer, if Jack and Jenny Frost were to concentrate on window art.

Posted by Graham Cogley on September 1, 2010 2:00 PM | Permalink