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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 INGV Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF PART I: BET model INGV 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. INGV 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) INGV 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] • … INGV 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)] INGV 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 INGV 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) INGV 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 INGV 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. INGV 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) INGV 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)] INGV 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)) INGV 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 INGV 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 INGV 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 INGV Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF