Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV BET: a probabilistic tool for Eruption Forecasting and Volcanic Hazard Assessment W. Marzocchi, L. Sandri, J. Selva INGV-Bologna BET: a probabilistic tool for Eruption Forecasting and Volcanic Hazard Assessment W. Marzocchi, L. Sandri, J. Selva INGV-Bologna Project INGV-DPC V4: “Innovative techniques to study active volcanoes” (W.Marzocchi, INGV-Bo, A. Zollo, Univ. of Naples)

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV PART I: BET model PART I: BET model

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV What is BET? BET (Bayesian Event Tree)statistical code eruption forecasting (BET_EF) (BET_VH)epistemicaleatory 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 Output: BET Output: Time and space evolution of the probability function of each specific event in which we are interested in. 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

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV The method is based on three basic steps 1.Design of a generic Bayesian Event Tree Bibliography Newhall and Hoblitt, Bull. Volc (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)Bibliography Newhall and Hoblitt, Bull. Volc (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) How BET works? 2. Estimate the conditional probability at each node 3. Combine the probabilities of each node to obtain probability distribution of any relevant event

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV The probability  of the SELECTED PATH is the product of conditional probability  i at ALL SELECTED BRANCHES:  1 ] [  2 ] [  3 ] [  4 ] [  5 ] … The probability  of the SELECTED PATH is the product of conditional probability  i at ALL SELECTED BRANCHES:  1 ] [  2 ] [  3 ] [  4 ] [  5 ] … BET Structure & Probability Eruption Forecasting: we focus on…

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV  k (M)  MONITORING PART Monitoring Data & Models  k (M)  MONITORING PART Monitoring Data & Models  k (NM)  NON-MONITORING PART Non-monitoring Data, Geological & Physical Models  k (NM)  NON-MONITORING PART Non-monitoring Data, Geological & Physical Models CONDITIONAL PROBABILITY AT THE NODE:  k  =   k (M)  + (1-  k (NM)  CONDITIONAL PROBABILITY AT THE NODE:  k  =   k (M)  + (1-  k (NM)  MONITORING DATA State of unrest  at t 0 through a FUZZY approach MONITORING DATA State of unrest  at t 0 through a FUZZY approach Conditional Probability [  K ] (Node k)

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV MODELS Prior MODELS Prior DATA Likelihood … each part  k (.)  (monitoring and non-monitoring) POSTERIOR PDF  k  =  k (.)  [H (.) |  k (.)  H (.)  (no epistemic uncertainty) In each factor, at each node, we account for: 1.Models + data 2.Epistemic and aleatoric uncertainities In each factor, at each node, we account for: 1.Models + data 2.Epistemic and aleatoric uncertainities Bayes theorem

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV A priori information: a probability (guess) and its weight in terms of number of equivalent data (p and  ). 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) What does BET accept in input? Non-monitoring info

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV Node 5: probability of a specific size (3 sizes: VEI 3, VEI 4, VEI 5+) Node 5: probability of a specific size (3 sizes: VEI 3, VEI 4, VEI 5+) Non-monitoring: Example A priori information: We assume a power law. Our initial guess will be: v P(VEI 3) = 0.60 v P(VEI 4) = 0.30 v P(VEI 5+) = 0.10 The weight assigned is  =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 v N = total number of eruptions v n(VEI 3) = number of VEI 3 eruptions v n(VEI 4) = number of VEI 4 eruptions v n(VEI 5+) = number of VEI 5+ eruptions

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV 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. What does BET accept in input? Monitoring info

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV Node 2: probability of a “magmatic” unrest Monitoring: Example A priori information: List of “indicators” of a magmatic unrest. v Presence of magmatic gases (e.g., SO 2 ) [>;1;1] v Number of LP events deeper than 5 km per day [>;0;5] v Largest magnitude M [>;3.6;4.5]  Uplift rate d  /dt [>;10;30 cm/month] Past data information: We need to put in input v N = total number of monitored eruptions v The values of the parameters for each monitored unrest v The nature of the unrest (magmatic or not)

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV Through expert opinion and/or looking at “analogs” (need of WOVOdat!), the user defines INTERVAL OF THRESHOLD for each “indicator” 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) … going into some details : including monitoring degree of anomaly z i measure State of unrest  A priori model [  k (1) ] surely NOT ANOMALOUS surely ANOMALOUS Thresholds are processed through FUZZY SET theory…

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV … going into some details: from monitoring to probability  k (M) |H] =  k (1)  [H (1) |  k (1)  H   Z (k) =  i w i z i degree of anomaly at the node  1 - exp(-  (k) ) Average of  k (1)  Monitoring part z i degree of anomaly of i-th parameter BET computes: The user: input measures

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV Cost/Benefit analysis Some useful considerations… v “Eruption forecasting” means to estimate probabilities v Typical requirement from end-users: YES or NOT (but the Nature seems not to much interested in playing deterministically) v How to interpret and to use probabilities? COMPARING THEM WITH MORE USUAL EVENTS

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV P x L > C 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 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 Cost/Benefit analysis

Eruption Forecasting through the Bayesian Event Tree: the software package BET_EF INGV More on BET: CoV5: -Oral 12-O-11, Nov. 22 (Thu) Hall A, 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.), The Bayesian Event Tree for short- and long-term eruption forecasting at Campi Flegrei, Italy, Other… Marzocchi, W., Sandri, L., Selva J., BET_EF: a probabilistic tool for long- and sort-term eruption forecasting, Bull. Volcanol., DOI /s y More on BET: CoV5: -Oral 12-O-11, Nov. 22 (Thu) Hall A, 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.), The Bayesian Event Tree for short- and long-term eruption forecasting at Campi Flegrei, Italy, Other… Marzocchi, W., Sandri, L., Selva J., BET_EF: a probabilistic tool for long- and sort-term eruption forecasting, Bull. Volcanol., DOI /s y