Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET: A Probabilistic Tool for Long- and Short-term Volcanic.

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



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.



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)






The conditional probability k at the node k is factorized as:

- state of unrest at time t0 (fuzzy logic)


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






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).



THE EXAMPLE OF BET_EFTHE EXAMPLE OF BET_EF



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)



BET_EF PACKAGEBET_EF PACKAGE

Event selection (Unrest+Magmatic Intrusion+Eruption+Vent all loc +VEI=5+)

Volcano selection (Vesuvio) Hazard procedure (No monitoring)

OUTPUT



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+



THE CASE OF MONITORING THE CASE OF MONITORING OBSERVATIONS INTO BET_EFOBSERVATIONS INTO BET_EF



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



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)



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.



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.



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



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



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

Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET: A Probabilistic Tool for Long- and Short-term Volcanic.

Documents

volcanoes bet

parameter bet

example of bet

description of bet slide

aleatory bet input bet

ef slide

preliminary implemented

bet major requirements