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How hard is snow?

We are all familiar with the idea of hardness. Falling on your knees is more painful if you fall on a pavement than on a lawn. But most of us would be puzzled to make the idea precise and quantitative. The geologists, thanks to Friedrich Mohs (not Moh), have a good working scale for the hardness of minerals. More surprisingly, so do the snow scientists for the hardness of snow.

Hardness can indeed be defined precisely. All those with a serious interest in the hardness of substances agree that the everyday concept is proportional to the force required to produce an indentation in the surface of the substance.

In Mohs’ hardness test, you press a series of test minerals into the mineral whose hardness is to be estimated. The one that produces an indentation, and powder when you drag it across the test surface, gives you the Mohs’ hardness of the unknown mineral. Mohs’ hardness is just a number on a scale from 1 to 10, but careful studies have shown that it is proportional to the logarithm of the force, measured in newtons, N, or preferably N m^-2 (newtons per square metre, because the size of the indenter makes a difference) that is applied to the surface.

It is the same with snow, but the test indenters are even simpler. In the classical hardness test for snow, introduced by de Quervain in 1950 and explained in last year’s new edition of The International Classification for Seasonal Snow on the Ground (search on “Fierz”), you use successively (1) your fist, (2) the ends of your four fingers, (3) just one finger, (4) the tip of a pencil and (5) the blade of a knife. You apply gentle force, and your hardness index is the number of the first list entry that penetrates the snow.

It sounds very fuzzy, doesn’t it? Surely these indenters differ in size and shape? What does “gentle” mean? Are you allowed to wear gloves? (The rugged answer to that one, apparently, is No.) Do you sharpen the pencil? The International Classification says Yes, but in the only photo I have ever seen of a pencil in snow-science service it was unsharpened. Why would people bother with a procedure with so many question marks attached?

The answer to that one, of course, is that the procedure works. It is also fast, and above all cheap. Assuming that you borrowed the pencil and somebody gave you a penknife for your birthday, the cost is nil. And in a recent paper in Annals of Glaciology, Höller and Fromm show that the hand hardness index does reproduce, with acceptable accuracy, measurements using more advanced instruments. If your fist indents the snow, the implied force is about 20 N and the implied strength or resistance about 4,000—8,000 N m^-2. If you need a knife to do the job, the implied strength is about 0.1 up to 2 million N m^-2.

Why worry about the hardness of snow? There are plenty of reasons. Soft snow, especially a lot of soft snow, is a bore if you have to walk over, or rather through, it. Skiers have a fairly obvious interest in the hardness of snow on the surface. But probably the biggest justification for snow scientists who stick their fingers into snow is the risk of avalanches.

Snow can be jerked into catastrophic motion in a range of ways, and its hardness is only one of the factors to be considered. But a safe prediction is that abrupt failure is more likely where there is a sharp discontinuity of strength between adjacent layers. More precisely, the shear strength is the ability of the snow on either side of an interior plane to resist relative motion over that plane. The hardness test, applied at regular intervals in a snow pit, measures the shear strength in a roundabout way, by measuring the compressive strength of adjacent layers.

Predicting avalanches is difficult at best, but if it were expensive then the prediction might not happen at all. So the hand hardness index has won and held a place for itself in keeping the death rate down in cold, mountainous terrain. It also tends to confirm my hypothesis that science doesn’t have to be expensive to be worthwhile.

Posted by Graham Cogley on May 24, 2010 3:00 PM | Permalink