Transcript Document

Project INGV-DPC V4: “Innovative techniques to study active
volcanoes” (W.Marzocchi, INGV-Bo, A. Zollo, Univ. of Naples)
BET: a probabilistic tool for Eruption
Forecasting and Volcanic Hazard Assessment
W. Marzocchi, L. Sandri, J. Selva
INGV-Bologna
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
PART I: BET model
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
What is BET?
BET (Bayesian Event Tree) is a new statistical code to estimate and visualize
short- to long-term eruption forecasting (BET_EF) and volcanic hazard
(BET_VH) and relative uncertainties (epistemic and aleatory)
BET Input: Volcanological data, models, and/or expert opinion. These data are
provided by the end-user.
BET transforms these information into probabilities
BET Output: Time and space evolution of the probability function of each specific
event in which we are interested in.
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
How BET works?
The method is based on three basic steps
1. Design of a generic Bayesian Event Tree
2. Estimate the conditional probability at each node
3. Combine the probabilities of each node to obtain probability
distribution of any relevant event
Bibliography
• Newhall and Hoblitt, Bull. Volc. 2002 (for step 1)
•
•
Marzocchi et al., JGR 2004 (for steps 2 and 3)
Marzocchi et al., 2006; IAVCEI volume on statistics in Volcanology (for steps 2
and 3)
• Marzocchi et al., 2007, Bull. Volcan., in press (full description of BET_EF,
available online)
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
BET Structure & Probability
Eruption Forecasting: we
focus on…
The probability
probability
p of the SELECTED PATH is the product of conditional
i at ALL SELECTED BRANCHES:
[p] = [1] • [2] • [3] • [4] • [5] • …
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Conditional Probability [K] (Node k)
[k(M)]
MONITORING PART
Monitoring Data & Models
[k(NM)] NON-MONITORING PART
Non-monitoring Data, Geological &
Physical Models
MONITORING DATA
State of unrest  at t0
through a FUZZY approach
CONDITIONAL PROBABILITY AT THE NODE:
[k] =  [k(M)] + (1-) [k(NM)]
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
… each part [k(.)] (monitoring and non-monitoring)
In each factor, at each node, we account for:
1. Models + data
2. Epistemic and aleatoric uncertainities
POSTERIOR PDF
[k] = [k(.)] [H(.)|k(.)] 1/[H(.)]
MODELS
Prior
(no epistemic uncertainty)
Bayes theorem
DATA
Likelihood
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Non-monitoring info
What does BET accept in input?
A priori information: a probability (guess) and its weight in
terms of number of equivalent data (p and L). If no information
are available BET starts from maximum ignorance (uniform
distribution)
Past data information: total number of cases and the number
of “successes” (N and n)
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Non-monitoring: Example
Node 5: probability of a specific size
(3 sizes: VEI 3, VEI 4, VEI 5+)
A priori information: We assume a power law. Our initial guess will be:
 P(VEI 3) = 0.60
 P(VEI 4) = 0.30
 P(VEI 5+) = 0.10
The weight assigned is L=1. This means that our a priori belief has the
same weight f 1 single datum. Few data can change our estimation.
Past data information: The eruptive catalog. We need to put in input
 N = total number of eruptions
 n(VEI 3) = number of VEI 3 eruptions
 n(VEI 4) = number of VEI 4 eruptions
 n(VEI 5+) = number of VEI 5+ eruptions
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Monitoring info
What does BET accept in input?
A priori information: list of monitored parameters relevant at
the node considered, with lower and upper thresholds, and
possibly the weight of each parameter. (NOTE: the parameters
have to be measured frequently at the volcano)
Past data information: Total number of past monitored cases
(N). For each case, BET requires the values of the monitored
parameters, and the “successfulness” of the considered case.
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Monitoring: Example
Node 2: probability of a “magmatic” unrest
A priori information: List of “indicators” of a magmatic unrest.
 Presence of magmatic gases (e.g., SO2) [>;1;1]
 Number of LP events deeper than 5 km per day [>;0;5]
 Largest magnitude M [>;3.6;4.5]
 Uplift rate d/dt [>;10;30 cm/month]
Past data information: We need to put in input
 N = total number of monitored eruptions
 The values of the parameters for each monitored unrest
 The nature of the unrest (magmatic or not)
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
… going into some details: including monitoring
Thresholds are processed through FUZZY SET theory…
Through expert opinion and/or looking at “analogs” (need of
WOVOdat!), the user defines INTERVAL OF THRESHOLD for
each “indicator”
surely ANOMALOUS
measure
We assure smooth transitions (for small changes) and
uncertainty on the definition of the state of anomaly (three sets:
surely not anomalous, uncertain, surely anomalous)
surely NOT ANOMALOUS
•
State of unrest 
degree of
anomaly zi
A priori model [k(1)]
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
… going into some details: from
monitoring to probability
[k(M)|H] = [k(1)] [H(1)|k(1)] 1/[H(1)]
Monitoring part
The user: input measures
BET computes:
zi degree of anomaly of i-th
parameter
Z(k) = i wi zi degree of anomaly at the node
<k(1)>=1 - exp(-Z (k))
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Average of [k(1)]
Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Cost/Benefit analysis
Some useful considerations…
 “Eruption forecasting” means to estimate probabilities
 Typical requirement from end-users: YES or NOT (but the
Nature seems not to much interested in playing
deterministically)
 How to interpret and to use probabilities? COMPARING
THEM WITH MORE USUAL EVENTS
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
Cost/Benefit analysis
Let’s make the example of an evacuation (SIMPLIFIED!!!)
L: cost of human lives lost due to an eruption
C: cost of an evacuation
P: prob. of the deadly event (i.e., prob. of a pyroclastic flow)
If
PxL>C
the cost of human lives “probably” lost exceeds the cost of an
evacuation. Therefore, the evacuation might be called when
P>C/L
The evacuation will be called when the probability of
the deadly event will overcome a threshold defined a
priori by Civil Protection
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF
More on BET:
CoV5:
-Oral 12-O-11, Nov. 22 (Thu) Hall A, 1450-1510
Integrating Eruption Forecasting and Cost/benefit Analysis for decision making
During an Emergency: the Case of BET_EF Applied to Vesuvius in the
MESIMEX Experiment
-poster 21b-P-18, Nov. 22 (Thu.), 1640-1800
The Bayesian Event Tree for short- and long-term eruption forecasting at
Campi Flegrei, Italy,
Other…
- http://www.bo.ingv.it/bet
- Marzocchi, W., Sandri, L., Selva J., BET_EF: a probabilistic tool for long- and
sort-term eruption forecasting, Bull. Volcanol., DOI 10.1007/s00445-0070157-y
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Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF