EXPLORIS Montserrat Volcano Observatory Aspinall and Associates Risk Management Solutions An Evidence Science approach to volcano hazard forecasting Thea Hincks 1, Willy Aspinall 1,2, Gordon Woo 3, Gillian Norton 4,5

Evidence science Evidence-based medicine is the conscientious, explicit and judicious use of current best evidence in making decisions … the integration of individual expertise with the best available external evidence from systematic research After Sackett et al., 1996 Evidence Based Medicine Need to model uncertainty and make forecasts using Expert judgment & knowledge of physical system Observational evidence = highly complex system

Bayesian networks Bayesian belief networks (BBNs) Causal probabilistic network Directed acyclic graph Set of variables X i discrete or continuous Set of directed links Variables can represent hidden or observable states of a system Very useful in volcanology - our observations on internal dynamics of the volcano are indirect

Expert systems NASA data analysis MSOffice assistant… Bayesian Network applications Speech recognition Molecular Biology and Bioinformatics Medical diagnosis & decision making VOLCANIC HAZARD FORECASTING

Building a Bayesian network Sensor model:Prior and transition models Probability of observation P(Y|X) Probability of initial state P(X 0 ) Transition between states P(X 1 |X 0 ) Bayes theorem Filtering - estimate current state X t Prediction - future states X t+n Forward pass : Smoothing- past unobserved states Backward pass :

Network structure Judgment, physical models, observations factors we believe lead to instability Structure learning algorithms purely data driven model difficult to model unobserved nodes problem is NP-hard algorithms slow to compute (~ few days for 6 x ternary node graph) BN for dome collapse on Montserrat

rainfall on dome dome collapse magma flux ground deformation stability of edifice degassing pressure Factors that might lead to dome collapse: BN for dome collapse on Montserrat

rainfall on dome dome collapse magma flux ground deformation degassing stability of edifice Cant measure state directly hidden variables pressure BN for dome collapse on Montserrat

magma flux deformation SO 2 flux observed rainfall UEA & MVO rain gauges degassing stability pressure GPS, EDM and tilt Seismicity: VT earthquakes Long period earthquakes Hybrid Rockfall LP Rockfall BN for dome collapse on Montserrat use sensor models for our observations:

Data Testing with daily data from July 95 - August 04 S0 2 flux Ground deformation (4 GPS lines) 4 nodes Seismic activity (event triggered count & magnitude data) VT, Hybrid, LP, LPRF, RF 5 nodes Rainfall Collapse activity

Time dependence Structure: how are processes coupled? What is the order of the process ? Dynamic system - history is important Variables tied over several time slices Time series analysis of monitoring data Autocorrelation & partial autocorrelation functions, differenced data Approximate order for time dependent processes

Autocorrelations Computed autocorrelation function and and partial autocorrelation function for data and first differenced data check structure is sensible and estimate order of time dependence

Dynamic Bayesian Network Rainfall - 1 day autocorrelation Hidden Markov model O(1)

Dynamic Bayesian Network Pressure

Dynamic Bayesian Network Magma flux

Dynamic Bayesian Network Gas flux

Dynamic Bayesian Network Ground deformation

Dynamic Bayesian Network Structural integrity or stability of the dome is dependant on previous state prior rock fall activity prior collapse activity (also affects pressurization)

Dynamic Bayesian Network

Current model Where monitoring time series suggest higher order processes …

Current model Prior distribution Expert judgment Sensor model Transition model Expert judgment to set initial distributions Parameter learning algorithms on monitoring data P(X 0 ), P(Y 0 ) for all states X observations Y P(Y t |X t ) P(X t+1 |X t )

Results so far Parameter learning using ~9 years of data transition and sensor models 1.static BN 2.two-slice dynamic model 3.three-slice dynamic model Can estimate probability of collapse given new observations Smoothing to estimate hidden state probabilities and distributions for missing values of observed nodes

Results so far Structure learning on a small (5 node) model - observed nodes only …work still in progress!

Results so far High ground deformation Consistent, moderate hybrid activity No SO 2 observations

Results so far

Further work… Model observations with continuous nodes More monitoring data - extend network Look at full seismic record (not just event triggered data) Run structure learning algorithm on larger network Investigate second order uncertainties (model uncertainty) and scoring rules to see how well different models perform User interface for real time updating of network at MVO real time forecasting probability of collapse Longer range forecasting?

Conclusions All models are wrong (to some degree…) but some models are better than others EVIDENCE SCIENCE and BAYESIAN NETWORKS Robust, defensible procedure for combining observations, physical models and expert judgment Risk informed decision making Can incorporate new observations/phenomena as they occur Strictly proper scoring rules - unbiased assessment of performance & model uncertainty

References Druzdzel, M and van der Gaag, L., Building Probabilistic Networks: Where do the numbers come from? IEEE Transactions on Knowledge and Data Engineering 12(4):481:486 Jensen, F., An Introduction to Bayesian Networks. UCL Press. Matthews, A.J.and Barclay J., 2004 A thermodynamical model for rainfall- triggered volcanic dome collapse. GRL 31(5) Murphy, K., 2002 Dynamic Bayesian Networks: Representation, Inference and Learning. PhD Thesis, UC Berkeley. openPNL (Intel) open source C++ library for probabilistic networks/directed graphs