BET_VH tool
Laura Sandri, Roberto Tonini
Istituto Nazionale di Geofisica e Vulcanologia, Italy
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
Scheme of the event tree
Used for long-term hazard assessment:
1) Models (many different runs with different initial and boundary conditions, and eruption size/type and
vent location)
2) Past data
We have to account for the whole natural variability of the phenomenon, and properly
combine ALL POSSIBLE ERUPTIVE SCENARIOS
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
At each node the probability is described by a probability density function (pdf) shaped
as a BETA distribution, to account for epistemic and aleatory uncertainty
Probability density function for a given node
Dirac δ (no epistemic uncertainty)
Uniform (max epistemic uncertainty)
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
At each node: Bayesian Inference
FROM MODELS  prior
FROM PAST DATA  likelihood
BAYES THEOREM → posterior distribution
Dirac δ (no epistemic uncertainty)
Uniform (max epistemic uncertainty)
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
In practice, to enter such information:
PRIOR PDF → the user has to provide the best guess probability p (BET_VH takes it as a
mean of the BETA) and a proxy for the variance that is the “Equivalent sample size” or
“number of equivalent data” Λ
Example for node 6 (Phenomena): we have an empirical model telling that eruptions of a
given size on average generate tephra fallout 80% of the times → p=0.8, Λ=?
Λ is a subjective measure of the confidence the user has on the prior information!!! It is up
to you!
LIKELIHOOD FUNCTION → the user has to provide the number of past “trials” (N) and
“successes” (y)
Example for node 6 (Phenomena, i.e. Tephra fallout): we have as best experienced 5
eruptions of a given size, 4 of which have generated widespread Tephra fallout → N=5, y=4
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
And now... example!
We want to compute PVHA for tephra fallout for traffic disruption and for roof collapse
2
(respectively 1 and 100 kg/m of ash accumulated on the ground and on roofs) from Volcano
BAUBAU (located: lon=686918m, lat=4925318m), on a region with limits:
LowerLeft corner: lon=672157m; lat=4910577m
UpperRight corner: lon=701751m ; lat=4940161m
This volcano in historical times has produced 6 eruptions in 1200 years, grouped in 2 sizes:
5 of size SMALL and 1 of size LARGE.
These eruptions have occurred from 2 vents: the SMALL ones from central crater, the
LARGE one from SE flank.
Respectively 50% and 90% of comparable SMALL and LARGE size at other volcanoes have
produced tephra fallout. Of the 6 eruptions at BAUBAU, only for 2 we have isopach maps
available (for one SMALL size eruption and for the LARGE size one); of the remaining 4, we
do not know whether they produced tephra (deposits too thin, might have been washed
away).
We have available the results of 100 simulations of a Volcanic Ash Transport and Deposition
Model (i.e., TEPHRA2, that's on Vhub), for each of the 2 sizes and for various possible
vents.
2
The output of the model runs provide the accumulation at the ground (kg/m ).
They must be rearranged, as we will see later, to provide, for each area around the volcano,
vent location and possible size, the expected frequency of ash reaching the area and
overcoming the threshold (roof or traffic).
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
Node 1-2-3:
Select a time window → 1 year for long term hazard assessment
No prior model
Past data: N=1200, y=6
Node 4:
Select a geometry → central volcano
Crater: 0.5km
Apron: 2.1 km
Sector strike: 22 degree (for some morphological features of the volcano)
Prior model: 80% in central vent, 5% equally on the lateral sectors.
Past data: 5 eruptions from central vent (ventloc #1) and 1 in SE (ventloc#3)
Node 5:
2 sizes
Prior model: 60% size SMALL, 40% size LARGE (from analogs...)
Past data: 5 SMALL, 1 LARGE
Node 6: TEPHRA FALL for TRAFFIC (1kg/m2) and for ROOFS (100kg/m2)
Prior model: 50% for size SMALL, 90% for size LARGE (from analogs...)
Past data: 1 known SMALL has produced tephra; 1 LARGE has produced tephra
Define the geometry of your region: 25 areas equally spaced on the region.
File of 25 records; in each record:
lat lon #area
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
Node 7&8:
PRIOR: We must rearrange the output from numerical simulations in a file of
N_areas * N_ventloc * N_size (25 * 5 * 2 = 250) records.
In the i-th record (that is relative to an area, a ventloc and a size):
p7 Λ7 p8 Λ8
where
p7 frequency (from simulations) of ash reaching this area from an eruption of this size from this ventloc
Λ7 Equivalent sample size on p7
p8 frequency (from simulations) of ash overcoming the threshold in this area from an eruption of this size from this ventloc
Λ8 Equivalent sample size on p8
Ordering of records:
Record 1: Area#1 Ventloc#1 Size#1
Record 2: Area#1 Ventloc#1 Size#2
Record 3: Area#1 Ventloc#2 Size#1
Record 4: Area#1 Ventloc#2 Size#2
…
Record 9: Area#1 Ventloc#5 Size#1
Record 10: Area#1 Ventloc#5 Size#2
Record 11: Area#2 Ventloc#1 Size#1
Record 12: Area#2 Ventloc#1 Size#2
Record 13: Area#2 Ventloc#2 Size#1
Record 14: Area#2 Ventloc#2 Size#2
…
Record 249: Area#25 Ventloc#5 Size#1
Record 250: Area#25 Ventloc#5 Size#2
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013
Node 7&8:
PAST DATA: We must rearrange the information from the isopach maps in a file containing, for
each mapped eruption (2 for us)
Ordering of records:
Record 1: Vent location of mapped eruption 1
Record 2: Size of mapped eruption 1
Record 3: Ash load in Area#1 from mapped eruption 1
Record 4: Ash load in Area#2 from mapped eruption 1
…
Record N_areas+2 (25+2): Ash load in Area#25 from mapped eruption 1
Record N_areas+3: Vent location of mapped eruption 2
Record N_areas+4: Size of mapped eruption 2
Record N_areas+5: Ash load in Area#1 from mapped eruption 2
Record N_areas+6: Ash load in Area#2 from mapped eruption 2
…
Record 2 * (N_areas+2) (2*(25+2)=54): Ash load in Area#25 from mapped eruption 2
Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013