Estimation of extreme runout frequencies based on observed short term frequencies

Kalle Kronholm

Krister Kristensen

IGS 2010, Sapporo

Hazard zoning in Norway

Level 1 (municipality): Susceptibility maps

Level 2 (regulation plan): mainly 1/1000 => purely frequency

Level 3 (building plan): if frequency >1/1000 => pressure to design and dimension

Motivation

Not rely on empirical or dynamical models alone, also use field information, as quantitatively as possible

Estimating low frequency (extreme) events based on field evidence is impossible

Traces from frequent events can be observed in field and associated return period may be estimated

Use field observations on frequent events and their runout lengths to estimate low frequency events

Classical model used: α-β model

Relate terrain parameters to run-out

Lied and Bakkehøi (1980), Bakkehøi et al. (1983)

α = 0.96β -1,4° + W, W~N(0, 2.3°)

Issue: any choice of σ can be chosen by practitioner to represent hazard zone (e.g. 1/1000)

Extended α-β model

Objective method for choosing actual hazard zone

Harbitz et al. (2001)

Additional assumptions about extreme value (Gumbel) distributions of runout angles in classical model

The annual probability of being hit by an avalanche does not exceed 1/Δtsafe

The return period of avalanches in the path is Δtrelease

Our use of the extended α-β model

1. Find a place in a path where the “safe” period Δtsafe can be estimated (e.g. 100 years)

2. Using the “extended” equations and assumptions, calculate the return period of avalanches in the path

3. Using the calculated return period, use the “extended” equations to calculate the needed Δtsafe (e.g. 1000 years)

The study area

Study area

The study area

The study area

Field evidence used

Written and oral evidence

Old maps and air photos

Destroyed trees

Vegetation types

Old farms

Plunge pools

Field evidence: Destroyed trees

Field evidence: Old farm houses

Field evidence: Plunge pools

Results

Estimated 1/100-year “safe” return periods for 31 avalanche paths from field evidence

Calculated the 1/1000-year points in paths (“extended” α-β model)

Calculated classical α-β model results, based on terrain and climate we used 0 and -1 σ

Hazard zones for 1/1000 years – the “truth”…?

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

f(x) = 0.929490789498948 x + 31.2156091868433R² = 0.919562770065685

f(x) = 1.06658895691505 x + 24.9036541941537R² = 0.867384688009377 L_alfa0

Linear (L_alfa0)L_betaLinear (L_beta)1:11:1

“Observed” 100y runout length (m)

Runo

ut le

ngth

, Bet

a, A

lfa 0

(m)

Location of the “observed” 100y point

Similar plot for the angles, large variation in runout length

Generally located between beta point and alfa 0

100y point related to topographical parameters identified in the α-β model

Flat profile which was just below 10° for long distance

Location of calculated 1000y point

Very close agreement with the alfa-1 point

Use in hazard zoning when good observations available?

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

f(x) = 1.01732442133548 x − 26.6107246356401R² = 0.938022233900649f(x) = 0.938974218219726 x − 43.198317633523R² = 0.965974838547425

L_alfa0Linear (L_alfa0)L_alfa_1Linear (L_alfa_1)1:11:1

Calculated 1000y runout length (m)

Runo

ut le

ngth

, Alfa

0, A

lfa-1

(m)

Location of the actual hazard zone

The alfa 0 runout length was used for hazard zoning with minor local adjustments (local topography, climate)

Actual hazard zone less conservative than the calculated suggestions based on the most conservative estimate

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

f(x) = 1.02799312107765 x − 49.3359453424114R² = 0.973465142584593

f(x) = 1.11213040105276 x − 25.9778879296603R² = 0.976302635540527f(x) = 1.06011561256852 x + 44.3821048070558R² = 0.988276872514022

L_1000Linear (L_1000)L_alfa_1Linear (L_alfa_1)L_alfa0Linear (L_alfa0)"1:1"1:1

Actual 1000y hazard zone (m)

Run

out 1

/100

0 ca

lcul

ated

, Alfa

0, A

lfa-1

(m)

Conclusions

Based on limited data!Need data from other climate areas and larger areas

The method is promising Theoretically appealing because it objectively uses (subjective)

information as quantitatively as possible

Method is more conservative than standard methodsThere are other interpretations of the extreme value used, we

tested the most conservative – test the others

Bad for customers, but it is a nice theoretical framework

Acknowledgements

Research was carried out through a snow avalanche research grant from OED/NVE 200905737-3