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BET_VH tool Laura Sandri, Roberto Tonini Istituto Nazionale di Geofisica e Vulcanologia, Italy Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 Scheme of the event tree Used for long-term hazard assessment: 1) Models (many different runs with different initial and boundary conditions, and eruption size/type and vent location) 2) Past data We have to account for the whole natural variability of the phenomenon, and properly combine ALL POSSIBLE ERUPTIVE SCENARIOS Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 At each node the probability is described by a probability density function (pdf) shaped as a BETA distribution, to account for epistemic and aleatory uncertainty Probability density function for a given node Dirac δ (no epistemic uncertainty) Uniform (max epistemic uncertainty) Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 At each node: Bayesian Inference FROM MODELS prior FROM PAST DATA likelihood BAYES THEOREM → posterior distribution Dirac δ (no epistemic uncertainty) Uniform (max epistemic uncertainty) Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 In practice, to enter such information: PRIOR PDF → the user has to provide the best guess probability p (BET_VH takes it as a mean of the BETA) and a proxy for the variance that is the “Equivalent sample size” or “number of equivalent data” Λ Example for node 6 (Phenomena): we have an empirical model telling that eruptions of a given size on average generate tephra fallout 80% of the times → p=0.8, Λ=? Λ is a subjective measure of the confidence the user has on the prior information!!! It is up to you! LIKELIHOOD FUNCTION → the user has to provide the number of past “trials” (N) and “successes” (y) Example for node 6 (Phenomena, i.e. Tephra fallout): we have as best experienced 5 eruptions of a given size, 4 of which have generated widespread Tephra fallout → N=5, y=4 Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 And now... example! We want to compute PVHA for tephra fallout for traffic disruption and for roof collapse 2 (respectively 1 and 100 kg/m of ash accumulated on the ground and on roofs) from Volcano BAUBAU (located: lon=686918m, lat=4925318m), on a region with limits: LowerLeft corner: lon=672157m; lat=4910577m UpperRight corner: lon=701751m ; lat=4940161m This volcano in historical times has produced 6 eruptions in 1200 years, grouped in 2 sizes: 5 of size SMALL and 1 of size LARGE. These eruptions have occurred from 2 vents: the SMALL ones from central crater, the LARGE one from SE flank. Respectively 50% and 90% of comparable SMALL and LARGE size at other volcanoes have produced tephra fallout. Of the 6 eruptions at BAUBAU, only for 2 we have isopach maps available (for one SMALL size eruption and for the LARGE size one); of the remaining 4, we do not know whether they produced tephra (deposits too thin, might have been washed away). We have available the results of 100 simulations of a Volcanic Ash Transport and Deposition Model (i.e., TEPHRA2, that's on Vhub), for each of the 2 sizes and for various possible vents. 2 The output of the model runs provide the accumulation at the ground (kg/m ). They must be rearranged, as we will see later, to provide, for each area around the volcano, vent location and possible size, the expected frequency of ash reaching the area and overcoming the threshold (roof or traffic). Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 Node 1-2-3: Select a time window → 1 year for long term hazard assessment No prior model Past data: N=1200, y=6 Node 4: Select a geometry → central volcano Crater: 0.5km Apron: 2.1 km Sector strike: 22 degree (for some morphological features of the volcano) Prior model: 80% in central vent, 5% equally on the lateral sectors. Past data: 5 eruptions from central vent (ventloc #1) and 1 in SE (ventloc#3) Node 5: 2 sizes Prior model: 60% size SMALL, 40% size LARGE (from analogs...) Past data: 5 SMALL, 1 LARGE Node 6: TEPHRA FALL for TRAFFIC (1kg/m2) and for ROOFS (100kg/m2) Prior model: 50% for size SMALL, 90% for size LARGE (from analogs...) Past data: 1 known SMALL has produced tephra; 1 LARGE has produced tephra Define the geometry of your region: 25 areas equally spaced on the region. File of 25 records; in each record: lat lon #area Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 Node 7&8: PRIOR: We must rearrange the output from numerical simulations in a file of N_areas * N_ventloc * N_size (25 * 5 * 2 = 250) records. In the i-th record (that is relative to an area, a ventloc and a size): p7 Λ7 p8 Λ8 where p7 frequency (from simulations) of ash reaching this area from an eruption of this size from this ventloc Λ7 Equivalent sample size on p7 p8 frequency (from simulations) of ash overcoming the threshold in this area from an eruption of this size from this ventloc Λ8 Equivalent sample size on p8 Ordering of records: Record 1: Area#1 Ventloc#1 Size#1 Record 2: Area#1 Ventloc#1 Size#2 Record 3: Area#1 Ventloc#2 Size#1 Record 4: Area#1 Ventloc#2 Size#2 … Record 9: Area#1 Ventloc#5 Size#1 Record 10: Area#1 Ventloc#5 Size#2 Record 11: Area#2 Ventloc#1 Size#1 Record 12: Area#2 Ventloc#1 Size#2 Record 13: Area#2 Ventloc#2 Size#1 Record 14: Area#2 Ventloc#2 Size#2 … Record 249: Area#25 Ventloc#5 Size#1 Record 250: Area#25 Ventloc#5 Size#2 Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013 Node 7&8: PAST DATA: We must rearrange the information from the isopach maps in a file containing, for each mapped eruption (2 for us) Ordering of records: Record 1: Vent location of mapped eruption 1 Record 2: Size of mapped eruption 1 Record 3: Ash load in Area#1 from mapped eruption 1 Record 4: Ash load in Area#2 from mapped eruption 1 … Record N_areas+2 (25+2): Ash load in Area#25 from mapped eruption 1 Record N_areas+3: Vent location of mapped eruption 2 Record N_areas+4: Size of mapped eruption 2 Record N_areas+5: Ash load in Area#1 from mapped eruption 2 Record N_areas+6: Ash load in Area#2 from mapped eruption 2 … Record 2 * (N_areas+2) (2*(25+2)=54): Ash load in Area#25 from mapped eruption 2 Vhub Workshop, IAVCEI General Assembly, Kagoshima, July 2013