COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET: A Probabilistic Tool for Long- and BET: A Probabilistic Tool for Long- and Short-term Volcanic Hazard AssessmentShort-term Volcanic Hazard Assessment
Warner MARZOCCHI, Jacopo SELVA, Laura SANDRI
Istituto Nazionale di Geofisica e Vulcanologia - Bologna, Italy
Funded by INGV-DPC V4 Project: Conception, verification, and application of innovative techniques to study active volcanoes
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
What is BET?What is BET?
BET (Bayesian Event Tree)BET (Bayesian Event Tree) is a new statistical code to estimate and visualize short-term (eruption forecasting BET_EF) and long-term volcanic hazard (BET_VH) and relative uncertainties (epistemic and aleatory)
BET InputBET Input: Volcanological data, models, and/or expert opinion. These data are provided by the end-user.
BET transforms these information into probabilities BET transforms these information into probabilities
BET OutputBET Output: Time and space evolution of the probability function of each specific event in which we are interested in.
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
The method is based on three basic steps
How BET works (1)How BET works (1)
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
BibliographyBibliography
Newhall and Hoblitt, Bull. Volc. 2002 (for step 1) Marzocchi et al., JGR 2004 (for steps 2 and 3) Marzocchi et al., 2006; in press IAVCEI volume on statistics in Volcanology (for steps 2 and 3) Marzocchi et al., 2006 in preparation (full description of BET)
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
How BET works (2)How BET works (2)
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
The conditional probability k at the node k is factorized as:
- state of unrest at time t0 (fuzzy logic)
How BET works (3)How BET works (3)
k|H] = k(1)[H(1)|k
(1)H1-) k(2) [H(2)|k
(2)H
(2) Past frequency data and models;no monitoring involved(1) Only monitoring data and models
are considered
Bayes model Bayes model
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
How BET works (4)How BET works (4)
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
APPLICATION TO VOLCANOESAPPLICATION TO VOLCANOES
BET is a generic tool: all volcanoes can be uploaded in BET
Major requirements to load a volcano in BET are:
1. Models and/or theoretical believes, and/or expert elicitation (VEIs distribution, tephra fall, pyroclastic flows, lahars, etc. spatial distribution)
2. Catalog of past volcanic events and related phenomena- Target volcano
- Analog volcanoes
- Worldwide catalog
3. Monitoring parameters and threshold intervals
Until now, we have (preliminary) implemented BET_EF for Mt. Vesuvius, and we are doing the same for Campi Flegrei (INGV-DPC V3_2 and V3_4 projects).
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
THE EXAMPLE OF BET_EFTHE EXAMPLE OF BET_EF
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
EVENT TREE for BET_EFEVENT TREE for BET_EF
UNREST
NO UNREST
NODE 1
MAGMATIC INTRUSION
NON MAGMATIC UNREST
NODE 2
ERUPTION
NO ERUPTION
NODE 3
VENT LOCATION 1
VENT LOCATION 2
NODE 4
…
VENT LOCATION N
VEI 3
VEI 3+
NODE 5
VEI 4
VEI 4+
VEI 5+
Node 4 accounts for all possible locations of the vent (more important for calderas)
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGEBET_EF PACKAGE
Event selection (Unrest+Magmatic Intrusion+Eruption+Vent all loc +VEI=5+)
Volcano selection (Vesuvio) Hazard procedure (No monitoring)
OUTPUT
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGE: PROBABILITY VISUALIZATIONBET_EF PACKAGE: PROBABILITY VISUALIZATION
PROBABILITY ESTIMATION
Probability that all branches of the Event Tree happen contemporaneously
e.g. probability that in the next month un Unrest with Magmatic Intrusion that leads to an Eruption in the Vent Location 1 with VEI = 5+ happens
CONDITIONAL PROBABILITY
Probability that the selected node of the Event Tree happens given that preceding branches happened
e.g. probability that in the next month an event with a VEI 3, 4, or 5+ happens, given that un Unrest with Magmatic Intrusion that leads to an Eruption in the Vent Location 1 happened
Selection done: (1) unrest -> (2) magmatic intrusion -> (3) eruption -> (4) location all -> (5) VEI=5+
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
THE CASE OF MONITORING THE CASE OF MONITORING OBSERVATIONS INTO BET_EFOBSERVATIONS INTO BET_EF
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
For each node the end-user needs to choose:
The relevant monitoring parameters A lower and upper threshold for each parameter
BET takes the values of the monitored parameters and:
Calculate the sum Z of “anomaly degrees” Calculate the average of the a priori probability k
(1)1-exp(-Z)
k|H] = k(1)[H(1)|k
(1)H1-) k(2) [H(2)|k
(2)H
From monitoring observations to probabilitiesFrom monitoring observations to probabilities
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING THRESHOLDS: FUZZY LOGICMONITORING THRESHOLDS: FUZZY LOGIC
1. Problem of thresholds definition
2. Computation of short-term probabilities (given unrest, linked to how thresholds are overcome)
tl th Monitoring value
1
0
tl lower threshold
tl higher threshold
Probability of measured monitoring value being anomalous
FUZZY LOGIC
• Subjectivity of the thresholds choice is overcome through a convergence of expert opinion and past data analysis to define a realistic interval of values for each threshold
• Smooth variation of probabilities for small changes in monitoring parameters (smooth thresholds)
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF PACKAGE: MONITORING DATABET_EF PACKAGE: MONITORING DATA
MONITORING THRESHOLDS
Each parameter has its own threshold interval. These intervals are defined depending on the past distribution of measured data (e.g. 60th and 90th percentiles).
The threshold intervals shown here are only indicative.
INPUT MONITORING MEASURES
All measured monitoring values can be updated in BET. Depending on their values, the state of the volcano is defined and short-term probabilities are computed.
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING & FUZZY #1MONITORING & FUZZY #1ne = 0 [27-120] -> pU = 0.0025
ne = 30 -> pU = 0.033
ne = 30 & Md = 3.6 [3.5,4.1] -> pU = 0.19
Changes on the value measured for 1 parameter induce changes in probability of unrest depending on the THRESHOLDS INTERVAL
When changes occur on 2 or more parameters at the same time, the probability of unrest increases.
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
MONITORING & FUZZY #2MONITORING & FUZZY #2
ne = 100 -> pU = 0.78
ne = 150 -> pU = 1.00
ne = 75 -> pU = 0.51When the measured value approach the higher threshold, the probability reach 1
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET is a tool to calculate and to visualize probabilities related to eruption forecasting/hazard assessment
BET allows assigning “dinamically” the probability for each kind of possible event long-term: useful for land use planning of the territory, and for comparing the hazard with other different kind of hazardsshort-term: useful during emergency to help managing of short-term actions aimed to reduce risk (e.g., evacuation)
BET considers all of the available information (models, state of the volcano, geologic/volcanologic/historic data, monitoring observations, expert elicitation)
BET takes properly into account the epistemic and aleatory uncertainties. This allows to highlight what we know and what we do not know about the system, indicating future possible works to improve the scheme
BET introduces fuzzy logic to smooth the transition in probability from one state to another of the volcanic activity
FINAL REMARKS on BETFINAL REMARKS on BET
COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006
Istituto Nazionale di Geofisica e VulcanologiaIstituto Nazionale di Geofisica e Vulcanologia
BET_EF will be distributed for free this year after a pilot test BET_EF will be distributed for free this year after a pilot test carried out by volcanologists with experience in managing carried out by volcanologists with experience in managing
volcanic crises. volcanic crises.
http://www.bo.ingv.it/~warnerhttp://www.bo.ingv.it/~warner
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