Snow Avalanche Alpha-Beta Runout (Lied-Bakkehøi)

Where does a snow avalanche stop? The honest answer is that nobody can compute it from first principles, because the flow regime changes several times on the way down and the snow itself changes with it. So in 1980 Karstein Lied and Steinar Bakkehøi did something different (Journal of Glaciology 26, 165). They surveyed 206 Norwegian avalanche paths where the extreme historical runout was known — from vegetation damage, from written records, from local knowledge — and looked for a terrain parameter that predicted it. They found one, and it is startlingly simple.

Define two angles from the top of the release area. The beta angle $\beta$ points to the first place the path flattens to a 10° gradient. The alpha angle $\alpha$ points to the distal limit of the extreme runout. Regress one on the other and you get, for Norway, $\alpha = 0.96\beta - 1.4°$, with a standard deviation of about 2.3° about the line and a correlation strong enough to be genuinely useful.

There is no physics in this at all, and that is the point. The beta point is a proxy for the entire geometry of the track — how steep the start zone is, how long the acceleration is, how abruptly the runout zone flattens — and terrain geometry turns out to predict extreme runout better than any single dynamic parameter does. The model never claimed a mechanism, never contained a friction coefficient, and never pretended to describe an individual event. Its honesty is exactly why it survived: it is a shape-to-shape correlation, stated as one.

The coefficients are regional and they do not travel. The 0.96 and the −1.4° belong to Norwegian terrain and a Norwegian maritime snow climate. Fits made in the Canadian Rockies, the Coast Mountains, Iceland, the Alps, Colorado and Japan all differ — sometimes in the slope, sometimes in the intercept, always in the scatter — because snowpack structure and terrain differ. Using the Norwegian coefficients on a continental snowpack is not conservative; it is unfounded. This page takes both coefficients as inputs and names the source rather than reproducing a table, because the tables belong to the agencies that measured them.

Note that the intercept is an angle, small and usually negative, sitting next to a slope coefficient that is a pure number. Entering it in a different angular unit from the one you read the answer in is the standard way to get this model wrong by a few degrees, and a few degrees at the toe of a long path is hundreds of metres of ground.

Now the part that is not negotiable. This is a planning tool, not permission. The alpha angle it returns is a regression estimate of where avalanches on paths of this shape have historically stopped. It does not say where the next avalanche on this path will stop, and it does not define a safe building site. The 2.3° standard deviation is not a rounding error: normal practice is to site against $\alpha$ minus one or two standard deviations, and even then it is one input among several. The model was also fitted to paths with a single well-defined beta point, and short paths, gullies, cliff-fed paths and terrain traps all violate that. It says nothing about the powder cloud, which travels further than the dense core and has destroyed buildings well beyond mapped dense-flow limits, and nothing about air blast.

Avalanche hazard mapping is regulated work in most jurisdictions with avalanche terrain, and it is done by qualified practitioners using local records, field mapping, historical vegetation evidence and dynamic models together. This page will teach you how the relation behaves. It will not tell you where it is safe to sleep.