Alpha (Runout) Angles and Climate Regimes

The alpha angle is the angle from the end of the runout to the top of the starting zone. For a brief definition including a diagram you can see the avalanche center glossary:

Avalanche Center -> Education Center -> Glossary -> Alpha Angle

Alpha angles (used to measure runout distance) do NOT depend on climatology. Whether a mountain range is maritime or continental (or something else) does not make much difference in alpha angles. Despite what may have found its way into the popular literature. What is important isn't clear, but it's not climate. Every mountain range seems to offer its own behavior regarding maximum runout potentials, and each range must be analyzed separately.


First lets consider the use and importance of the topic, as in past blog entries. Alpha angles are used by professional engineers and scientists to help determine the most likely maximum extent of a major avalanche expected to occur infrequently. Perhaps once every 100 years. This is very important when either locating or reinforcing structures. We have information on the alpha angle and related parameters for many mountain ranges based on statistically analyzing some number of paths with a known maximum extent in a given time period. This is established from recorded historical events, direct analysis of vegetation, archived aerial photography, and perhaps other factors in some cases.

While the alpha angle is important for engineering, zoning and planning it is somewhat less useful for the typical ski tour or climb. For one thing it has to be measured in the field by sighting either straight up to the top from a vantage at the bottom (supposedly at the end of the possible runout) or by sighting from the top of a slope down. Any position offering an oblique sighting is not useful. It's also not commonly known what the average (or maximum, minimum, etc) angle is for typical avalanches on a common time scale. This would require a data set of events for the particular path. Many avalanche paths can slide frequently during storms, or shortly after most storms. This prevents the accumulation of a large slab and in many cases the avalanche will not even reach the "beta point" where the runout zone can be defined as beginning. (This is the point where the local slope angle is 10 degrees.) Alpha angles do have some potential use for locating camps or other fixed sites with a longer exposure than when a person merely passes through.

For a parameter of rather limited utility, especially in comparison to so many other things, this alpha angle business seems to have grabbed the attention of many people who seem to think it's more important than it really is. This has been largely due recently to Bruce Trempers book "Staying Alive in Avalanche Terrain". It doesn't seem emphasized to me, receiving only a page or so at the most. Unfortunately readers seem to have picked up on it, particularly the numbers he gives. And unfortunately the numbers given have no context or attribution as to where they come from.

This is another case of something people are taking at face value, repeatedly quoting, and getting wrong. The figures have been cited at least twice on one forum and questioned/refuted both times. Recently they were cited yet again but clearly there is no point in trying to set the record straight on many of these internet forums.

So, here's the deal on alpha angles and climates:

Tremper gives three ranges of alpha angle, one each for maritime, intermountain, and continental ranges. It isn't specified where this information came from or what time scale it is on. Is it a typical avalanche from a typical storm? If so what is "typical"? Is it the maximum one would expect over the course of a season? Assuming it's based on some kind of data how many paths were part of the analysis and which mountain ranges were they in? We really don't know much about these figures which seem to have been pulled out of thin air.

In the published technical literature it is a simple matter to find average alpha angles for a 100 year avalanche in each of five ranges. The numbers and sources are at the end of this blog entry, after a more graphical presentation.

If we put these various parameters on a graph of sorts this is what we get:



And now we find something interesting.

It's possible that 100 year angles are not representative of shorter term values because the 100 year value will be a large dry slab in any climate. In a maritime climate this might not be true for, say, a ten year event. So it's possible there are some climate dependencies on shorter time scales. Initially I was willing to give the book the benefit of doubt based on this or some related issue.

But a 100 year event will have the longest runout expected in 100 years, and for the most part Trempers ranges are even longer than that. So they couldn't be representative of shorter return periods. His continental range is longer in its entirety than either of the 100 yr values established statistically. The maritime range is longer than 2 of the three. We also see that the five technically established values alternate in terms of continental and maritime, showing no climate dependence on that time scale.

Sometimes statements are made based on what seems logical, and to the reader they seem to make sense. But science is often counter-intuitive. Another thing discovered in studies is that shorter slopes have a longer runout potential in relation to height than longer slopes. This is also not intuitive.

Nothing here is meant to be overly simplistic, it just addresses the bottom line. There is plenty of additional research on this topic which can be found in science and engineering journals. Likewise nothing here is meant as a review or critique of Trempers popular book. I think it was a mistake to include these figures for ranges, and it certainly appears they are flawed. But it's a small part of the book. If anything deserves critique it is certain readers who seem to pull this information out of the book and promote it (referring to the book) when it's hardly the most important topic. To either the book or to personal safety.

So here are the actual numbers for the plot above, where N is the number of paths in the data set behind that figure:

25.4 Maritime N=52 Coastal AK (Cordova - Seward)
20.1 Maritime N=90 Sierra Nevada
22.1 Continental N=130 Colorado
28.2 Maritime N=113 Western Norway
27.8 Continental N=127 Canadian Rockies and Purcells

23-25 Maritime, Tremper
20-23 Intermountain, Tremper
19-22 Continental, Tremper

And here are the references for the figures on specific ranges:

Mears; Arctic and Alpine Research; V 21 #3 1989 pp. 283-287
McClung and Mears; Cold Regions Science and Technology, (19) 1991 pp. 163-175

The broad ranges are from:

Tremper; "Staying Alive in Avalanche Terrain"

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