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Avalanche Hazard
Snow Avalanche α-β Runout Distance Simulator
Use the Lied-Bakkehøi (1980) statistical regression α = 0.96β − 1.4° to predict the farthest reach (α point), peak velocity and impact pressure of a snow avalanche from path length, vertical drop, β angle and snow type. A first-screening tool for hazard mapping, building placement and avalanche defense sizing.
Parameters
Path length (release → β point)
m
Vertical drop H
m
Vertical fall from release crown to stopping point
Terrain type
Terrain correction Δα applied to α angle
β angle (10°-slope point)
°
Snow type
Release-zone width
m
Fracture depth
cm
Return period T
y
Results
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α runout angle (°)
—
β angle (°)
—
100-yr runout (m)
—
Design return-period (m)
—
Peak velocity (km/h)
—
Impact pressure (kPa)
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Avalanche path profile — release, β point, α point
Green: release zone. Blue: flowing avalanche. Orange: β point (10° gradient). Red: α point (stopping point). Animation shows the avalanche leaving the release zone, passing β and stopping at α.
β is the depression angle from the release crown to the 10° point on the runout. α is the depression angle to the stopping point. The Lied-Bakkehøi (1980) Norwegian dataset is the reference; α < β. Peak velocity follows the simplified Voellmy-Salm form, with H the vertical drop from crown to stopping point.
Impact pressure p is the dynamic pressure from density ρ and the square of peak velocity. Release mass M is the product of release-zone area A, fracture depth d and density ρ.
Professor, snow avalanches still kill skiers and mountaineers every winter. Can we actually predict how far an avalanche will reach?
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Yes — over 100 deaths a year worldwide, mainly in the Alps, the Rockies, the Norwegian fjords and the snowy mountains of Japan. Several methods exist, and the most widely used first-screening tool is the α-β model. Lied and Bakkehøi published it in 1980 after fitting a statistical regression to more than 200 Norwegian avalanche tracks.
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What do α and β represent? The formula says α = 0.96β − 1.4°…
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Draw the avalanche track in a vertical profile. The β point is where the slope first flattens to 10°; the β angle is the depression angle from the release crown to that point. The α angle is the depression angle from the same crown to the actual stopping point. Avalanches decelerate on gentle slopes, so α is always less than β. In the Norwegian data, that relation collapses neatly onto α ≈ 0.96β − 1.4°. Read β off the topographic map and α (and thus the runout) follows.
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So can we ignore regional differences and terrain?
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Good catch. The α/β ratio actually shifts with region: 0.96 in Norway, 0.85 in Iceland, 0.92 in Austria. Terrain matters too — confined gullies give longer runouts, open bowls track the standard regression, broad fans cut it short. The terrain selector in this tool adds Δα between +1° and −4° as a quick correction so you can feel that effect.
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Velocity and impact pressure also pop out. Are those from a different formula?
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Yes — α-β only answers "how far"; velocity needs the mechanical Voellmy-Salm model. Its simplified form is v_max = √(2gH(1 − tanα/tanβ)). Dynamic pressure is simply p = ρv², with ρ ≈ 280 kg/m³ for dry slab and 500 kg/m³ for wet slab. A 150 km/h dry slab carries about 500 kPa — enough to bend-fail RC walls taller than 5 m.
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How are these numbers used in real practice?
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Switzerland's SLF defines the red zone (T=300 yr, p > 30 kPa, no building), blue zone (T=300 yr, p < 30 kPa, or T=100 yr only — reinforced building only) and yellow zone (information only). Avalanche defenses — catching dams, deflectors, snow sheds, anchored steel fences, and even ANFO/Gazex artillery release — are sized from α-β runouts and Voellmy-Salm pressures. RAMMS::Avalanche and SamosAT do the detailed 3D simulation; α-β is the first cut.
Frequently Asked Questions
The α-β model (Lied & Bakkehøi, 1980) is an empirical regression built from more than 200 Norwegian avalanche events. It predicts the angle α from the release-zone crown to the final stopping point using only the geometry of the β point — the location where the slope first flattens to 10°. The standard Norwegian dataset gives α = 0.96·β − 1.4°, which is widely used as a first-screening tool in hazard zoning around the world.
Trace the longitudinal profile of the avalanche path. The β point is where the slope first drops to 10° on the way down. The β angle is the depression angle from the release-zone crown to that β point. The α angle is the depression angle from the same crown to the actual stopping point. Because avalanches decelerate on gentle slopes, α is always less than β. The α/β ratio varies by region: about 0.96 for Norway, 0.85 for Iceland and 0.92 for Austria.
Peak velocity uses the simplified Voellmy-Salm form v_max = √(2gH(1 − tanα/tanβ)), where H is the vertical drop from the release crown to the stopping point. Impact pressure (dynamic pressure) is p = ρ·v² with ρ the snow density (≈ 280 kg/m³ for dry slab, ≈ 500 kg/m³ for wet slab). At 43 m/s a dry-slab flow reaches about 520 kPa — enough to bend-fail an RC wall taller than 5 m. The Swiss SLF guideline treats 30 kPa as the lightweight-building limit and 300 kPa as the RC limit.
This tool applies a simple log correction, factor = 1 + 0.15·log10(T/100), giving roughly +7% runout at T=300 yr and −8% at T=30 yr relative to T=100 yr. In practice you fit a Gumbel or GEV distribution to multi-year avalanche magnitudes and pick the runout corresponding to your design return period (typically 300 yr for public buildings). Swiss SLF uses red (T=300, p>30 kPa), blue (T=300, p<30 kPa or T=100 only) and yellow zones.
Real-World Applications
Hazard maps and land-use regulation: Switzerland, Austria, Norway and Canada apply the α-β model and its extensions nationally to compute 100-to-300-year runouts and then classify red, blue and yellow zones. Red prohibits new construction, blue requires reinforced structures and yellow is informational. Japan applies similar concepts in Hakuba-mura and other high-risk municipalities in Nagano and Hokkaido.
Sizing avalanche defenses: Catching dams (avalanche dams), deflectors (guidance walls) and snow sheds along rail and road corridors are positioned and sized from α-β-predicted stopping points. Voellmy-Salm impact pressures feed the structural design, with the SLF guideline assuming 300 kPa at 5 m height as standard. Detailed work is handed off to RAMMS::Avalanche or SamosAT 2D/3D codes, where α-β supplies the boundary screening.
Ski-area and mountaineering safety: Guides and patrol teams on Mt. Hood, Mt. Manaslu and Japan's Northern Alps apply α-β on topographic maps to flag stopping zones where exposure is highest. Combined with the release width and fracture-depth estimate of the released mass, they decide how much ANFO/Gazex/Galci-Cannon artillery is needed for controlled release.
Climate change re-evaluation: Warmer winters drive a higher frequency of wet-slab events (ρ ≈ 500 kg/m³), so even an unchanged runout brings nearly double the impact pressure compared with dry slab. Several historically "blue" districts in Europe are being upgraded toward "red" after combined α-β and RAMMS re-analyses.
Common Misconceptions and Cautions
The first pitfall is treating α-β as universal without local calibration. This tool uses the Norwegian baseline α = 0.96β − 1.4°, fitted under snow, terrain and vegetation typical of Norway. Iceland (α = 0.85β), Austria (α = 0.92β − 1.3°) and parts of Hokkaido use larger α/β ratios or additional terms. The ±1° to −4° terrain corrections here are rough rules of thumb; serious design needs local regression.
The second issue is that α-β returns a single maximum runout. Real events scatter — Lied and Bakkehøi themselves report a standard deviation σ ≈ 2.3°. For design use a conservative α offset (mean − k·σ, k=1.65 for 95% one-sided), not the mean. The return-period correction here is only a coarse proxy for that probabilistic treatment, which should really integrate over an avalanche magnitude distribution.
The third trap is treating p = ρv² as the full impact load. Real avalanches form a two-layer flow — a dense basal layer and a powder cloud (200+ km/h, ρ ≈ 10 kg/m³) — and pressures at a given building elevation differ from the simple dynamic-pressure estimate. The powder cloud is low density but extremely fast; even at half the dense-flow dynamic pressure, its shock-front overpressure can blow out windows and roofs. The p reported here describes the dense flow; powder loads require a separate evaluation.
How to Use
Enter path length (horizontal distance from release to terrain end) in metres.
Input vertical drop (elevation difference between release and runout zone) in metres.
Specify beta angle (β, the angle from release point to runout terminus) and release area size in square metres.
The simulator applies Lied-Bakkehøi regression (α = 0.96β − 1.4°) to compute the alpha angle (α, the steeper angle defining maximum reach).
Review calculated runout distance for 100-year return period, design return-period distance, peak velocity, and impact pressure.
Worked Example
Alpine valley in Switzerland: path length 1800 m, vertical drop 1200 m, release area 50,000 m². Calculate β = arctan(1200/1800) ≈ 33.7°. Using α = 0.96(33.7°) − 1.4° = 31.0°. For a 100-year event with terrain friction coefficient 0.15, estimated runout distance reaches 2340 m from release point. Peak velocity at runout zone approximately 65 km/h, generating impact pressure around 18 kPa on structures. Design return-period (300-year) extends runout by 140 m due to increased release mass.
Practical Notes
β angle typically ranges 25–38° for documented European valleys; steeper paths yield higher α values and longer runouts.
Release area size directly scales peak velocity and impact pressure; 100,000 m² sites produce 45–55% greater pressures than 30,000 m² events.
Forest density and terrain roughness reduce modelled α by 2–4° in protected valleys; open scree sections show unmodified regression.
Avalanche defence structures (dams, deflection berms) shift the α-point application 300–600 m downslope; recalculate for post-construction risk.