Snowpack Settlement (Viscous Compaction)

Snow starts compacting the moment it lands and never stops while it exists. A fresh 40 cm snowfall is 30 cm by morning and 20 cm by the end of the week, with exactly the same water in it. The depth moved and the snow water equivalent did not, which is the single most useful thing to know about a snowpack and the source of a great deal of confused reporting.

Kojima's 1967 insight was that snow under load behaves as a Newtonian viscous fluid, not as an elastic solid. Load it and it does not deflect and stop; it flows, slowly and continuously, at a strain rate proportional to the stress. The constant of proportionality is a compactive viscosity, and putting mass conservation alongside it — the mass in a layer is fixed, so a fractional loss of thickness is a fractional gain of density — gives the exponential form on this page. Anderson wrote it into SNTHERM in 1976 and essentially every land-surface scheme since has carried it.

The viscosity is huge and it is worth feeling the number. Snow in compaction runs $10^7$ to $10^9$ Pa·s. Water is $1.8\times10^{-3}$; cold pitch, the stuff of the famous drop experiment, is around $10^8$. Snow is pitch. That is why settlement takes hours to see and why a snowpack looks completely static while it is in fact continuously deforming.

The loads are tiny, which is the other half of the surprise. Thirty centimetres of light snow on top of a layer is about 440 Pa — a few grams per square centimetre, less than the weight of a sheet of paper spread over a hand. That such a load visibly compacts a material in hours is a good reminder of how weak snow actually is.

What this form deliberately leaves out is substantial, and both omissions run the same way. Holding the viscosity constant over the interval is a linearisation, and it is wrong in a known direction: the viscosity climbs exponentially with density, so a real layer compacts fast at first and then decelerates hard as it stiffens. This equation therefore overstates densification, and the error grows with the interval. Use it over hours, not seasons. And temperature is missing entirely: the standard parameterisation multiplies the viscosity by $e^{0.08(T_0 - T)}$, which makes snow at −20 °C roughly five times stiffer than the same snow at −1 °C. A cold snowpack barely settles; a snowpack near melting collapses. In many winters the temperature term matters more than the density term.

Two things settlement changes that are easy to miss. It costs insulation — a settled pack conducts substantially more heat than the same snow did when it fell, so the ground under it cools faster in a warm winter than a cold one. And it buys strength, though the equation cannot see the mechanism: the grains are also sintering while they compact, welding at the necks, and that is a separate process on a similar timescale. When a quinzhee is left to sit, the compaction on this page is happening, but it is the sintering that makes the pile safe to hollow — and nothing on this page decides whether it is.