EXPLORISMontserratVolcano ObservatoryAspinall and Associates

Risk Management Solutions

1

2

3

4

5

An Evidence Science approach to volcano hazard forecasting

Thea Hincks1, Willy Aspinall1,2, Gordon Woo3, Gillian Norton4,5

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 Xi discrete or continuous

Set of directed linksVariables 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(X0)

Transition between states P(X1|X0)

Bayes theorem

€

P(A | B,C) =P(B | A,C)P(A | C)

P(B | C)

Filtering - estimate current state Xt

Prediction - future states Xt+n

Forward pass :

Smoothing- past unobserved statesBackward 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

Can’t measurestate directly

hidden variablespressure

BN for dome collapse on Montserrat

magma flux

deformation

SO2 flux

observed rainfall UEA & MVO rain gauges

degassing

stability

pres

sure

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

• S02 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 modelWhere 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(X0), P(Y0)

for all states X

observations Y

P(Yt|Xt)

P(Xt+1|Xt)

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 SO2 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., 2000. Building Probabilistic Networks: Where do the numbers come from? IEEE Transactions on Knowledge and Data Engineering 12(4):481:486

Jensen, F., 1996. 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. www.ai.mit.edu

openPNL (Intel) http://sourceforge.net/projects/openpnl

open source C++ library for probabilistic networks/directed graphs