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Thermal Conductivity of Snow (Sturm 1997)

Also known as thermal conductivity of snow · Sturm 1997 snow conductivity · snow insulation value · why an igloo is warm · effective conductivity of snow · snow k value · does snow insulate · snow conductivity from density · snow thermal properties

keff=0.138−1.01 ρ∗+3.233 ρ∗2k_{\mathrm{eff}} = 0.138 - 1.01\,\rho^{*} + 3.233\,\rho^{*2}

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Constant used — built into this formula, no need to enter
ρice=917 kg/m3\rho_{\mathrm{ice}} = 917\ \text{kg/m}^{3}Density of Ice at 0 °C
See also
R-Value of a Snow Wall — The same fit turned into the number a builder wants: the R-value of a wall of a given thickness.R-Value of an Insulation Layer (R = L/k) — The general R = L/k this specialises, where k is any material you like instead of snow.Thermal Resistance of a Plane Wall — The conduction resistance underneath the R-value, in K/W rather than per square metre.Snow Water Equivalent (SWE) — The same density read as a water content instead of an insulation property.Compressive Strength of Sintered Snow — The other thing density buys — whether the wall stands up, which is a different and more dangerous question.

Learning zone

This is the page that explains why an igloo works, and the explanation is not the one most people give. It is not that ice is a good insulator — ice conducts at about 2.2 W/(m·K), roughly ninety times better than still air and comparable to a decent thermal paste. What insulates is the air trapped between the grains, held in pores small enough that convection cannot stir it. Snow is an ice skeleton whose only real job is to hold air still, and the skeleton is a liability rather than an asset: every extra gram of ice is another conduction path from the inside of the wall to the outside.

Sturm, Holmgren, König and Morris published the standard fit in the Journal of Glaciology in 1997, from 488 measurements across seasonal snow of every kind. Their quadratic, with density expressed in grams per cubic centimetre, is k=0.138−1.01ρ+3.233ρ2k = 0.138 - 1.01\rho + 3.233\rho^2, and they stated it for densities from 0.156 to 0.600 g/cm³. Run it at 300 kg/m³ — a well-settled pack, or a sintered shelter wall — and it returns about 0.126 W/(m·K). That is softwood across the grain. A wall of frozen water conducts heat about as well as a wall of pine, and it does so at a seventeenth of the conductivity of the ice it is made from.

The lower bound of the validity band is not arbitrary, and this is a lovely detail. Differentiate the quadratic and the vertex sits at 0.1562 g/cm³ — essentially exactly where the authors stopped. Below that the parabola turns back upward and claims that lighter snow conducts more, which is false. The fit does not fail gradually at the edge of its band; it fails by reversing. For lower densities the same paper gives a separate linear branch, k=0.023+0.234ρk = 0.023 + 0.234\rho, which at 50 kg/m³ returns 0.035 W/(m·K) — better than mineral wool batt, which is why a metre of fresh powder over a subnivean space is such an effective blanket, and why frost depth in soil is set more by early snow cover than by air temperature.

Now the honesty, because a three-decimal answer flatters this fit badly. Sturm's own data scatter over roughly a factor of three at any single density. Snow at 250 kg/m³ can be a rounded, well-bonded, thoroughly sintered pack with broad ice necks between the grains, or it can be a heap of faceted crystals touching at points, and the two conduct very differently while weighing the same. Density is a scalar and microstructure is not; the fit is a best line through a genuine cloud. Treat the answer as the middle of a wide range rather than as a property of the piece of snow in front of you.

Two further caveats worth carrying. The quantity is an effective conductivity: it quietly includes vapour diffusing through the pore space and recondensing, which is real heat transport, grows with temperature, and is a substantial fraction of the total near 0 °C. And it says nothing about the ice glaze that forms on the inside face of an occupied shelter, where breath and body heat melt and refreeze the surface into something an order of magnitude more conductive than the snow behind it.

Thermal Conductivity of Snow (Sturm 1997)
keff=0.138−1.01 ρ∗+3.233 ρ∗2k_{\mathrm{eff}} = 0.138 - 1.01\,\rho^{*} + 3.233\,\rho^{*2}
keffρsair
Where
  • keffk_{\mathrm{eff}}= Effective thermal conductivity (W/(m·K))
  • ρs\rho_s= Snow density (kg/m³)
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