kronholm igs 2010, sapporo
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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
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