Warner Marzocchi, Laura Sandri INGV, Via D. Creti 12, Bologna, Italy Istituto Nazionale di Geofisica e Vulcanologia Considerazioni sulla stima del rischio associato a eventi naturali Considerazioni sulla stima del rischio associato a eventi naturali

1. Definition of RISK associated with a natural event 2. Probability and risk assessment 3. A Probabilistic approach for risk assessment: the Event Tree Outline of the Course

HAZARD: Probability of any particular area being affected by a destructive volcanic event within a given time interval. VALUE: # of human lives at stake, the capital value, and the productive capacity exposed to the destructive event. VULNERABILITY: Proportion of the value which is likely to be lost as a result of a given event. RISK = HAZARD * VULNERABILITY * VALUE 1. Risk associated with a natural event INDIVIDUAL RISK = HAZARD * VULNERABILITY

1. Risk associated with a natural event Why is risk assessment important?  For land use purposes (long-term risk mitigation)  For emergency management (mid- to short-term risk mitigation)

a. Risk assessment needs multidisciplinary competences b. Hazard assessment is often the most diffucult to address. We need to deal with the problem from an “engineeristic” point of view c. Individual risk and hazard assessments consist of providing quantitative estimates of the probability of each event d. Hazard assessment has to use all the available information 1. Risk associated with a natural event

a. Risk assessment needs multidisciplinary competences HAZARD: scientists VULNERABILITY: engineers, architects, doctors… VALUE: economists, politicians…

1. Risk associated with a natural event b. Hazard assessment has to be (often) addressed from an “engineeristic” point of view Often, our state of knowledge and available data are (very) scarce, but we must do something, as best as we can.

1. Risk associated with a natural event c. Hazard assessment consists of providing quantitative estimates of the probability of each event (individual risk) The eruptive process seems to be a typical “complex system”, therefore it is intrinsically unpredictable in a deterministic way. Therefore, we have to use a probabilistic model. The probability estimation is fundamental for decision making

1. Risk associated with a natural event d. Hazard assessment has to consider all the available information 1.Our theoretical a priori knowledge (theoretical models, state of the system, etc…) 2. Past data from the system and/or from other systems with similar behavior 3. Data from the “real-time” monitoring

1. Risk associated with a natural event About decision making…  The comparison between risks relative to different hazards  Definition of “acceptable risk” (costs/benefits balance)

2. Probability and risk assessment  The probability is the best way to describe quantitatively the occurrence of an aleatoric event (i.e., individual risk)  An aleatoric event is an event that cannot be predicted deterministically.  Almost all the natural events of interests are aleatoric events

2. Probability and risk assessment  The probability of an aleatoric event E is indicated by P(E) and it is a number (or a function) between 0 and 1.  The probability is defined in different ways (classical, frequentist, assiomatic, Bayesian).  Often, the probability estimation is very problematic.

2. Probability and risk assessment The Bayesian approach is particularly useful in practical problems characterized by few data and scarce theoretical knowledge The Bayesian approach implies that the probability is not a single value but it is a probability distribution. The probability distribution has an average (the best guess of the probability) and a standard deviation. These two parameters estimates the aleatoric and epistemic uncertainties.

2. Probability and risk assessment Bayes theorem… A posteriori Probability A priori Probability Likelihood  i = Prob. of event E i  = Observations

2. Probability and risk assessment We do not use a single value but a distribution of probability. In this way we can account for aleatoric and epistemic uncertainties.

2. Probability and risk assessment  and  are the parameters of the distribution. Their values depend on the a priori theoretical knowledge, and on the data from the past and from possible “real-time” monitoring of the system. An example: the Beta distribution

Update of a Beta distribution with new observed data… Bayesian approach Bernoulli (N trials n successes) where: ’=+n ’=+N-n 2. Probability and risk assessment

… about the ELLSBERG PARADOX URN 50 red balls 50 blue balls URN 100 unknown Combination of red and blue balls Probability Dirac’s function Probability Uniform distribution 1 Average

2. Probability and risk assessment … about the ELLSBERG PARADOX

2. Probability and risk assessment Some example of annual risk of death: - Smoking  5 x Cardiovascular disease  3.5 x Cancer  2 x Workers in construction  1.5 x Car accidents  1.5 x All accidents (US)  3.4 x Eruptions (world)  1 x 10 -7

3. A probabilistic approach for risk assessment: the Event Tree The Event Tree is a tree-like representation of events in which branches are logical steps from a general priori event through increasingly specific subsequent events (intermediate outcomes) to final outcomes. In this way, ET shows the most relevant possible outcomes of the system at a progressively higher degree of detail. The main advantage of the ET scheme consists of its intrinsic simplicity and of providing a quantitative estimation of any kind of hazard and individual risk.

Long-term forecasting & hazard Stop Vulnerability & individual risk Short-term forecasting ? Newhall & Hoblitt (Bull. Volcanol., 64, 3-20, 2002)

3. A probabilistic approach for risk assessment: the Event Tree To estimate the general structure of the tree The structure of the tree has been shown in the previous slide To estimate the probability at each node The probability at each node is estimated through a statistical distribution (to take into account the uncertainties) To combine the probabilities of the nodes to calculate the probability of any possible event The probabilities are combined through the Bayes theorem What do we need for estimating the individual risk?

3. A probabilistic approach for risk assessment: the Event Tree At each node we assign a probability distribution with the average and standard deviation that depend on 1. Our a priori knowledge (theoretical models, and state of the system) 2. The past data (from the system and from systems with similar behavior) 3. The data from the “real-time” monitoring of the system

3. A probabilistic approach for risk assessment: the Event Tree What is the probability to kill one person that lives at 10 km North of the volcano, by a pyroclastic flow from a VEI 3 eruption? P(death VEI 3, pf ) = P(1) P(2|1) P(3|2) P(4|3) P(5|4 VEI 3 ) P(6 N |5 pf ) P(7 10 |6 N ) P(8|7 10 ) P(9|8) If we want to calculate the probability to kill the same person by a pyroclastic flow, regardless the VEI of the eruption we have P(death pf )=P(death VEI 2, pf )+P(death VEI 3, pf )+P(death VEI 4+, pf ) Those probabilities can be summed because the VEI categories are mutually exclusive In principle, we can calculate the probability of any event Combining the probability of the nodes…

3. A probabilistic approach for risk assessment: the Event Tree The event tree allows assigning “dinamically” the probability for each kind of possible event (quantitative hazard assessment) 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) The scheme considers all of the available information. The scheme takes properly into account the epistemic and aleatoric uncertainties. The procedure highlights what we know and what we do not know about the system, indicating future possible works to improve the scheme.

Estimating the volcanic hazard at Mount Vesuvius…

P(1) = Long-term probability of unrest (Restlessness) P(2|1) = Prob. of presence of magma, given unrest (Genesis) P(3|2) = Prob. of eruption, given presence of magma (Outcome) P(4|3) = Prob. of a particular VEI, given the eruption occurs (Magnitude) P(5|4) = Prob. of a particular phenomenon, given a VEI (Phenomena) P(6|5) = Prob. of a particular sector, given a specific phenomena (Sector) P(7|6) = Prob. of a particular distance, given a specific sector (Distance) P(8|7) = Prob. of presence of a structure and/or human beings, given a specific phenomena in a specific sector (Exposure) P(9|8) = Prob. of death or destruction, given the above hazard (Vulnerability) P* = Prob. to have an eruption

What is unrest? (The definition depends on the present state of the volcano considered) If  The seismicity is significantly different from the background.  Any inflation of the volcano.  Presence of a significant amount of SO 2.  The CO 2 flux is significantly different from the background.  The Temperature of the fumaroles inside the crater is significantly larger than the background. Prob. that the volcano will become restless P(1):

1. A priori knowledge: none  Uniform distribution 2. Past data: 32 years of no unrests  Beta distribution 3. If seismicity, ground deformation and/or gasses emission monitored deviate from the background  p(1)=1 Prob. that the volcano will become restless We consider two sets of thresholds: for the most conservative we have: P(1): - # earthquakes  100 /month - M d  # low-frequency events  3/month - Presence of significant SO 2 flux - CO 2 flux  5 kg m -2 d -1 - Strain rate > 0 d -1 - T > 105 o C

Prob. that the volcano will become restless P(1):

1. A priori knowledge: none  Uniform distribution (==1) 2. Past data: none  we do not use this information 3. Monitoring: - Average spectral frequency  <>  3 Hz - Strain rate   d -1 - Temperature of the fumaroles > 105 o C -  < 0.40 (ratio between average and dispersion of the depth of earthquakes) - Presence of SO 2 flux Prob. that, given unrest, the unrest is caused by magmatic intrusion P(2|1):

(’=1.3 ’=0.7) (’=1.7 ’=0.3) (’=1.88 ’=0.12) (’=0.5 ’=1.5) Prob. that, given unrest, the unrest is caused by magmatic intrusion P(2|1):

1. A priori knowledge: none  Uniform distribution (==1) 2. Past data: none  we do not use this information (analogs?) 3. Monitoring: Prob. that, given a magmatic intrusion, magma will erupt - Rate of average spectral frequency, d(<>)/dt < 0 (hours to few weeks) - Strain acceleration > 0 d -2 (hours to few days) -  < 0.40 (hours to weeks) - Acceleration of seismic energy released (hours to few days) - Cumulative strain > (hours to weeks) - Sudden reversals of at least one of the parameters (hours to few days) - Phreatic explosion (days to months) - Sudden increase of HF or HCl over SO 2 (few days) Time interval considered ONE MONTH: but the NEW probability P(3|2) is almost reached in FEW days. P(3|2):

Experience on the global volcanism and on critical systems show that the magnitude of the eruption probably have some kind of a power-law distribution. The power-law distribution is probably different in the open and closed conduit regime. (Probably, the most critical point) Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3): 1. A priori knowledge

Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

Data from historical activity of Mt. Vesuvius. Data from the so-called “analogs” Data from worldwide volcanoes Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3): 2. Past data

“Analogs” are chosen by taking into account similarities in A pronounced different/alternation between open and closed conduit behavior in the volcano’s geological or historical record The viscosity of the magma contained in a range that excludes the most acid (e.g., rhyolites) and the most basic (e.g., basalts) magma. We have identified 17 “analogs” of Mount Vesuvius Suwanose-jima, Sakura-jima, Popocatepetl, Shikotsu-Tarumai, Fuji, Alaid, Shiveluch, Trident, Komaga-take, Asama, Colima, Fuego, Mayon, Arenal, Cotopaxi, Tungurahua, Merapi. Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

The basic point is the role of the “repose time” (i.e., Poisson vs. some kind of “memory” process). We consider different standards… A4 – Data from worldwide volcanoes with 60<RT<200 B4 – Data from “analogs” with 60<RT<200 C4 – Data from Mt. Vesuvius with 60<RT<200 D4 – Data from worldwide volcanoes with RT>60 E4 – Data from “analogs” with RT>60 F4 – Data from Mt. Vesuvius with RT>60 Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

F E D C B A4 VEI  5 VEI=4VEI=3Standard 60<RT<200 MEE Average  10% 60<RT Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

 The deformation can suggest the opening of lateral vents We do not use (yet!) the monitoring data to implement the distribution  The degassing seems very promising to modify the probability of small and large eruptive events (cf. Newhall, 2003)  It seems that the precursors are not indicative of the size of the impending eruption. 3. Monitoring data Prob. that, given a magmatic eruption, it will be of a specified explosive size P(4|3):

A possible future pre-eruptive scenario… Feb. 1: No unrest observed Feb. 4: Slight inflation of the volcano (5 x /d) Mar. 1: The slight inflation continues. Occurrence of a swarm of LF at 2.5 km depth, with an average spectral frequency of 3 Hz. Mar. 15: The same as March 1, but the hypocenter of LF events are at 1 km depth and the average spectral frequency is 1-2 hz.

P=P(1)*P(2|1)*P(3|2)*P(4|3) P=P(2|1)*P(3|2)*P(4|3) Long-term forecasting Short-term forecasting Probability of occurrence of an eruption with a specific VEI

 Tephra Fall (TF)  Pyroclastic Flow or Surge (PF)  Lahar (LA)  Lava Flow (LF) Types of phenomena that we consider: Prob. that, given an eruption of a specified explosive size, it will generate a phenomenon P(5|4): For now, we consider these onesVEITFPFLALF = (Dirac Delta) 0.35 (=0.7 =1.3)0.25 (= 0.5 =1.5)0.6 (= 1.2 =0.8)  4 4 4 41.0 (Dirac Delta)0.70 (=1.4 =0.6)0.55 (= 1.1 =0.9)0.45 (= 0.9 =1.1) Data from Newhall and Hoblitt (2002)

We modify the probability distributions for TF and PF according to their past frequency during Vesuvius eruptions. Prob. that, given an eruption of a specified explosive size, it will generate a phenomenon P(5|4): For each VEI, we count how many eruptions (N) occurred and, of these, how many (n) produced, for example, TF. We use these N and n to update the  and  of the Beta distribution. ’=+n ’=+N-n

Prob. that, given an eruption of a specified explosive size, it will generate a phenomenon P(5|4):Eruption Average conditioned probability of a TF Average conditioned probability of a PF VEI=31 (Dirac Delta) 0.35 (we have no past data, so ) (we have no past data, so ’= and ’= ) VEI=41 (Dirac Delta) 0.85 (’=1.7 ’=0.3) VEI  5 1 (Dirac Delta) 0.88 (’=1.76 ’=0.24)

Definition of a spatial domain P(6|5) and p(7|6):

Prob. that, given an eruption of a specified explosive size and generating a particular phenomenon, THE NEXT episode will move in a certain sector P(6|5): N NE W SW S SE E NW

Prob. that, given an eruption of a specified explosive size and generating a particular phenomenon, THE NEXT episode will move in a certain sector P(6|5): TF: the dispersion of tephra fall depends solely on the wind field at the time of the eruption. We start by assuming equiprobability on all the sectors, and update the probability distributions according to the past frequency of TF in each sector. The result is a higher probability in Eastern sectors (in agreement with the wind field statistics, which tell us that the prevailing winds are Eastward).

Prob. that, given an eruption of a specified explosive size and generating a particular phenomenon, THE NEXT TF will move in a certain sector P(6|5): TF

Prob. that, given an eruption of a specified explosive size and generating a particular phenomenon, THE NEXT episode will move in a certain sector P(6|5): PF:  for VEI=3 eruptions, Mt Somma represents an inviolable barrier N and NE sectors have 0 probability. For the remaining sectors, we start by assuming equiprobability, and update according to the past frequency of PF in each sector.  for larger eruptions, we start by assuming equiprobability on all the sectors, and update according to the past frequency of PF in each sector.

Prob. that, given an eruption of a specified explosive size and generating a particular phenomenon, THE NEXT PF will move in a certain sector P(6|5): PF (No new data)

Prob. that, given an eruption of a specified explosive size and generating THE NEXT particular phenomenon, it will reach a certain distance P(7|6): TF: the risk associated to TF is mainly related to roof collapse. In Vesuvius surroundings, the roof maximum load is approximately Kg/m 2. Up to now we assume that a layer 10 cm thick might cause roof collapse. TF risk might also be related to traffic jamming. In this case, even few cm layer of TF might cause serious problems. PF: the risk associated to PF is related to its occurrence, regardless its intensity or the thickness of the deposit left.

Prob. that, given an eruption of a specified explosive size and generating THE NEXT TF, it will reach a certain distance P(7|6): We start from Newhall and Hoblitt (2002) 0-5 Km 5-10 Km Km Km Km VEI=30.70 ( ( =1.4 =0.6)0.45 ( ( =0.9 =1.1)0.35 ( ( =0.7 =1.3)0.25 ( ( =0.5 =1.5)0.20 ( ( =0.4 =1.6) VEI  ( ( =1.9 =0.1)0.93 ( ( =1.86 =0.14)0.90 ( ( =1.8 =0.2)0.85 ( ( =1.7 =0.3)0.80 ( ( =1.6 =0.4) TF

Prob. that, given an eruption of a specified explosive size and generating THE NEXT TF, it will reach a certain distance P(7|6):

Prob. that, given an eruption of a specified explosive size and generating THE NEXT PF, it will reach a certain distance We start from Newhall and Hoblitt (2002) 0-5 Km 5-10 Km Km Km Km VEI=30.80 ( ( =1.6 =0.4)0.20 ( ( =0.4 =1.6)0.01 ( ( =0.02 =1.98) VEI  ( ( =1.74 =0.26)0.64 ( ( =1.28 =0.72)0.45 ( ( =0.9 =1.1)0.24 ( ( =0.48 =1.52)0.16 ( ( =0.32 =1.68) PF

P(6|5): PF (No new data) P(7|6): Prob. that, given an eruption of a specified explosive size and generating THE NEXT PF, it will reach a certain distance