1. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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 www.bo.ingv.it/V4

2. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 WHAT IS BET? BET (Bayesian Event Tree) 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 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 The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 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 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) HOW BET WORKS?

4. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 The absolute probability of the SELECTED PATH is the product of conditional probability i at ALL SELECTED BRANCHES: 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] … BET STRUCTURE & ABSOLUTE PROBABILITY

5. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 k (M) MONITORING PART Monitoring Data & Models k (NM) NON-MONITORING PART Non-monitoring Data, Geological & Physical Models CONDITIONAL PROBABILITY AT THE NODE: k = k (M) + (1- k (NM) MONITORING DATA State of unrest at t 0 through FUZZY LOGIC CONDITIONAL PROBABILITY [ K ] (NODE k)

6. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 At each node we account for: Models + data Epistemic and aleatoric uncertainities MODELS Prior DATA Likelihood POSTERIOR PDF k = k (.) [H (.) | k (.) H (.) Bayes theorem … EACH PART

7. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 Through FUZZY SET theory… With convergence of expert opinion and past data analysis, the user defines: 1.the SET of parameters at each node 2.INTERVAL OF VALUES as threshold for each param Smooth variation of probabilities are found for small changes in monitoring parameters (smooth thresholds) MONITORING MEASURES degree of anomaly z i measure State of unrest A priori model [ k (1) ]

8. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 BET_EF PACKAGE

9. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 EVENT TREE for BET_EF Number & geometry chosen by the user Number of size groups defined by the user

10. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 BET_EF PACKAGE Volcano selection Event selection (Unrest + Magmatic Intrusion + Eruption+Vent all loc + SIZE=4+) Hazard procedure OUTPUT

11. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 PROBABILITY VISUALIZATION ABSOLUTE PROBABILITYCONDITIONAL PROBABILITY AT THE NODE Selection done: (1) unrest -> (2) magmatic intrusion -> (3) eruption -> (4) location all -> (5) SIZE=4+ Probability that all the events in the selected path occur contemporaneously Probability that the events at the selected node occur, given previous nodes

12. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 MONITORING MEASURES Measured values are directly input in BET_EF at nodes 1, 2, 3

13. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 MONITORING AT Node 4: VENT LOCATIONS Localization of monitored parameters When possible, the user may localize the anomalous measures of monitoring parameters, to identify the most likely position for next vent location Map of vent locations percent within the location

14. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 Major requirements to load a volcano in BET_EF are: 1.Models and/or theoretical believes, and/or expert elicitation 2.Catalog of past volcanic events and related phenomena 3.Monitoring parameters and relative threshold intervals 4.Number and geometry of vent locations APPLICATION TO VOLCANOES ALL VOLCANOES can be loaded in BET_EF with the BET_UPGRADE PACKAGE 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).

15. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 BET_ UPGRADE (ES. NODE 1) modelsdatamonitoring thresholds

16. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 BET is a tool to calculate and to visualize probabilities related to eruption forecasting/hazard assessment BET dinamically manages long-term (land use planning of the territory) and short-term (during emergency to help managing of short-term actions, e.g., evacuation) probabilities for each kind of possible event 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 manage monitoring measurements smooth transitions in probability and overcome single threshold definition FINAL REMARKS on BET

17. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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

18. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 STATE OF UNREST z i degree of anomaly the i-th parameter The user: input measures at node 1 BET computes: 1 - i (1 - z i ) k = k (M) + (1- k (NM) Conditional probability at the node

19. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 FROM MONITORING TO PROBABILITY k (M) |H] = k (1) [H (1) | k (1) H z i degree of anomaly the param The user: input measures BET computes: 1 - a exp(-b (k) ) Average of k (1) Z (k) = i z i degree of anomaly at the node Monitoring factor

20. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 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 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…

21. Istituto Nazionale di Geofisica e Vulcanologia The International Merapi Workshop 2006, Yogyakarta, Indonesia, Sectember 2006 MONITORING & FUZZY #2 n e = 100 -> p U = 0.78 n e = 150 -> p U = 1.00 n e = 75 [27-120] -> p U = 0.51 When the measured value approach the higher threshold, the probability reach 1 (NODE 1: UNREST)