Depth hoar in snowpack

Why does a buried snow layer grow weaker as it ages instead of settling into something stronger?

Almost everything granular gets stronger under its own weight. Sand compacts, mud consolidates, and fresh snow does too: within days a fluffy fall settles into something you can walk on. So the deepest, oldest snow in a pack ought to be the strongest part of it.

Sometimes it is the weakest — large, hollow, cup-shaped crystals with almost nothing holding them together, under a metre of consolidated slab. Something inside the pack has been actively taking it apart. What could do that, in the dark, at temperatures where nothing melts?

Notice first that snow is not an inert solid. Ice at minus 10 degrees sits at about 96 per cent of its melting temperature on the absolute scale, a mechanically restless place to be, and a snowpack is ice, air and water vapour in constant exchange. Molecules leave grains and land on other grains continuously; the pack is always rearranging. The only question is what decides where the material goes.

There are two candidates, and which wins is the whole story.

The first is curvature. A sharply convex point has slightly higher vapour pressure than a flat or concave surface, so vapour leaves the spikes of a fresh crystal and deposits in the necks between touching grains. That is sintering: grains round off, necks thicken into bonds, the layer gains strength. Where it dominates, old snow really is strong snow.

The second is temperature, and here we should do the arithmetic. The Clausius-Clapeyron relation gives the fractional change in vapour pressure as the latent heat of sublimation divided by the gas constant for water vapour, times the temperature change over temperature squared. Using 2.83 megajoules per kilogram and 461.5 joules per kilogram per kelvin (both recalled standard values), at 258 kelvin that is 6130 divided by 66,600: about 0.09 per kelvin. Nine per cent per degree.

Sit with that. A ten-degree difference across a metre of snow means the vapour pressure at the base exceeds that at the top by a factor of e to the 0.9, roughly two and a half. The curvature effect, on grains a tenth of a millimetre across, is a fraction of one per cent. It is not a close contest, and the changeover is usually placed around 10 kelvin per metre — a rule of thumb rather than a threshold, since the real driver is the vapour-pressure gradient, which depends on absolute temperature too.

So does such a gradient exist? Almost always, and asymmetrically. The ground beneath a snowpack stays near zero, insulated by the snow itself; the surface follows the air, which on a clear winter night can be minus 20. Across 1.5 metres of snow that is 13 kelvin per metre. Across 30 centimetres it is 60. Which yields the rule that surprises people every season: a thin snowpack in a cold climate is a weak snowpack, because the same temperature difference is compressed into a shorter distance.

Now trace what the vapour does. It leaves the warmer underside of each grain, crosses the pore, and deposits on the colder underside of the grain above — a relay upward, grain to grain. Two consequences follow, and together they answer the question. Growth is fast enough that arriving molecules cannot migrate to the lowest-energy position, so the crystal grows with flat faces, steps and hollows instead of rounding off: facets, and in the extreme the striated cups called depth hoar, several millimetres across. And the material deposited on top came from somewhere — disproportionately from the necks and contacts, which are consumed rather than thickened. Grain size grows and strength falls together, which is exactly the pairing that offends intuition.

There is a feedback that makes it worse. Depth hoar is low-density and porous, so it conducts heat poorly, so more of the pack's total temperature drop falls across it — steepening the very gradient that is destroying it. The forcing is external (cold air over insulated ground); the feedback is the layer's own deteriorating conductivity, and it is positive.

How could this be wrong? The test is direct: a thermistor string through the pack, with repeat snow pits dug beside it. Faceting should appear where and only where the gradient has been sustained above roughly the changeover value — and a faceted layer later buried deeply enough for the gradient to even out should begin to round and slowly regain strength. That reversal is what forecasters watch for. Faceted growth in a near-isothermal pack, or continued rounding under a sustained strong gradient, would refute the mechanism outright.

The misconception to name is that ageing and strengthening are the same thing in snow. They are the same only when curvature is in charge. Snow metamorphism has two regimes with opposite structural outcomes, and which one a layer is in depends on a condition outside the layer — the temperature difference across it — rather than on its age or its depth.

The mechanism is a close relative of what ruins food in a freezer: vapour leaving warmer ice for colder ice, large crystals growing at the expense of small. The fixed point of difference is what the transfer costs. In a freezer it is driven by cycling and the damage is the mass that has left the food. Here the gradient is sustained and one-way, and the damage is structural — the mass never leaves the layer at all, it moves from the joints into the grains, inside a material expected to bear load.

Two honest limits. A weak layer's strength is not predictable from crystal type alone: the slab above it, its loading history, and the layer's density all matter, which is why forecasting stays probabilistic. And a season with a thin early pack and a cold spell produces a weak base, but one season says nothing about a trend — separating any change in weak-layer frequency from interannual variability would need decades of consistent snow-pit records, and I would not offer a projection.

• Why a buried melt-freeze crust so often has a weak layer directly above and below it.

Every term the collection defines is gathered in the glossary.