Snow Water Equivalent (SWE)

Also known as snow water equivalent · SWE · snow to water ratio · ten to one rule · how much water is in snow · snow depth to water depth · melt equivalent of snow · snow density from depth and water · inches of water from inches of snow

SWE=dρsρw\mathrm{SWE} = d \, \frac{\rho_s}{\rho_w}

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

Snow depth is not a measurement of snow. It is a measurement of how much space the snow is taking up, and how much space a given amount of water occupies as snow varies by more than a factor of ten. Two storms can leave identical marks on a depth board and differ fourfold in the water they delivered. Everything downstream of that — the spring runoff, the reservoir filling, the flood forecast, the irrigation allocation — depends on the water, not on the depth. Snow water equivalent is the conversion, and it is nothing more complicated than a density ratio.

The ten-to-one rule is a density claim in disguise, and it is a poor one. "Ten inches of snow is one inch of water" says exactly one thing: that snow has a density of 100 kg/m³. It is a climatological average over a great many storms in a great many places, and it is wrong in both directions by a lot. Cold, dry, still-air continental powder falls at 30 to 50 kg/m³ — the same water makes twenty-five or thirty inches, not ten. A wet coastal snowfall, or anything that has been worked by wind into a slab, runs 300 to 500 kg/m³, and the same water makes two or three inches. A forecaster who applies ten-to-one to a lake-effect event and to a Pacific storm has made two different errors in opposite directions using one rule.

The density is not one number even within a single snowpack. A seasonal pack is a stratigraphy, not a substance: a wind-hardened crust at 400 kg/m³ over settled snow at 250 over a layer of depth hoar at 180, each of which formed under different weather and behaves like a different material. Take a full-depth core and you get an average that describes none of the layers and predicts the mechanical behaviour of none of them. For water accounting that average is exactly right, because water does not care which layer it was in. For anything mechanical — strength, conductivity, whether a slope will slide — it is close to useless.

The measurement itself is genuinely simple and worth knowing, because it is the honest alternative to guessing a density. Push a tube of known cross-section down through the pack to the ground, pull the core, and weigh it. Mass divided by the tube's area gives the water equivalent directly, in units of depth, with no density step at all — which is why the federal snow tube has survived a century of technology. The automated version is the snow pillow: a fluid-filled bladder on the ground reads the pressure of everything above it, which is the same quantity again. Both measure water. Neither measures depth, and that is the point.

One thing that does not change, and it catches people every winter: settlement moves depth without moving water. A pack that reads 20 cm shallower in the morning has not lost a gram — the same water is sitting in less space, because snow compacts under its own weight from the moment it lands. A hydrologist tracking depth will conclude that snow disappeared overnight when nothing did. Track the water.

Snow Water Equivalent (SWE)
SWE=dρsρw\mathrm{SWE} = d \, \frac{\rho_s}{\rho_w}
dρsρwSWE
Where
  • SWE\mathrm{SWE}= Snow water equivalent (mm)
  • dd= Snow depth (cm)
  • ρs\rho_s= Snow density (kg/m³)
Missing one of these? Work it out first, then come back