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

2. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 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 Input 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 BET Output: Time and space evolution of the probability function of each specific event in which we are interested in.

3. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 The method is based on three basic steps 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 Bibliography â Newhall and Hoblitt, Bull. Volc. 2002 (for step 1) ã Marzocchi et al., JGR 2004 (for steps 2 and 3) ã Marzocchi et al., 2006; in press IAVCEI volume on statistics in Volcanology (for steps 2 and 3) ã Marzocchi et al., 2006 in preparation (full description of BET)

4. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 How BET works (2)

5. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 The conditional probability k at the node k is factorized as: - state of unrest at time t 0 (fuzzy logic) How BET works (3) k |H] = k (1) [H (1) | k (1) H 1- ) 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

6. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 How BET works (4)

7. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 APPLICATION 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).

8. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 THE EXAMPLE OF BET_EF

9. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 EVENT 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)

10. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET_EF PACKAGE Event selection (Unrest+Magmatic Intrusion+Eruption+Vent all loc +VEI=5+) Volcano selection (Vesuvio) Hazard procedure (No monitoring) OUTPUT

11. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET_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+

12. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 THE CASE OF MONITORING OBSERVATIONS INTO BET_EF

13. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 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) H 1- ) k (2) [H (2) | k (2) H From monitoring observations to probabilities

14. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 MONITORING THRESHOLDS: FUZZY LOGIC 1.Problem of thresholds definition 2.Computation of short-term probabilities (given unrest, linked to how thresholds are overcome) tltl thth Monitoring value 1 0 t l lower threshold t l 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)

15. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET_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.

16. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 MONITORING & FUZZY #1 n e = 0 [27-120] -> p U = 0.0025 n e = 30 -> p U = 0.033 n e = 30 & M d = 3.6 [3.5,4.1] -> p U = 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.

17. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 MONITORING & FUZZY #2 n e = 100 -> p U = 0.78 n e = 150 -> p U = 1.00 n e = 75 -> p U = 0.51 When the measured value approach the higher threshold, the probability reach 1

18. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 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 hazards short-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 BET

19. Istituto Nazionale di Geofisica e Vulcanologia COV4 meeting - Quito, Ecuador, Jan. 23-27, 2006 BET_EF will be distributed for free this year after a pilot test carried out by volcanologists with experience in managing volcanic crises. http://www.bo.ingv.it/~warner