an evidence science approach to volcano hazard forecasting

7/27/2019 An Evidence Science approach to volcano hazard forecasting

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EXPLORISMontserratVolcano ObservatoryAspinall and Associates

Risk Management Solutions

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An Evidence Science approach to

volcano hazard forecasting

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


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Evidence science

Evidence-based medicine is the conscientious, explicit and judicioususe of current best evidence in making decisions

the integration of individual expertise with the best available external

evidence from systematic researchAfter Sackett et al., 1996Evidence Based Medicine

Need to model uncertainty and make

forecasts using

Expert judgment & knowledge of

physical system

Observational evidence

= highly complex system


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Bayesian networks

Bayesian belief networks (BBNs)Causal probabilistic network

Directed acyclic graph

Set of variables Xi

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


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Expert systems

NASA data analysis

MSOffice assistant

Bayesian

Network

applications

Speech recognition

Molecular Biology

and Bioinformatics

Medical diagnosis& decision making

VOLCANIC

HAZARD

FORECASTING


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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 XtPrediction - future states Xt+n

Forward pass :

Smoothing-past unobserved states

Backward pass :


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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


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rainfall ondome dome collapse

magma flux

ground

deformation

stability

of edifice

degassing

pressure

Factors that might lead to dome collapse:



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rainfall ondome dome collapse

magma flux

ground

deformation

degassing

stability

of edifice Cant measurestate directly hidden variablespressure



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magma flux

deformation

SO2 flux

observed rainfallUEA & MVO rain gauges

degassing

stability

pressure

GPS, EDM and tilt

Seismicity: VTearthquakes

Long periodearthquakes

Hybrid

Rockfall

LP Rockfall


use sensor models forour observations:


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Data

Testing with daily data from July 95 - August 04

S02 flux

Ground deformation (4 GPS lines) 4 nodes

Seismic activity (event triggered count & magnitudedata) VT, Hybrid, LP, LPRF, RF 5 nodes

Rainfall

Collapse activity


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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 ser ies analys is of m oni tor ing data

Autocorrelation & partial autocorrelation functions, differenced data

Approximate order for time dependent processes


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Autocorrelations

Computed

autocorrelationfunction and and

partial

autocorrelation

function for data

and firstdifferenced data

check structureis sensible and

est imate order of

t ime dependence


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Dynamic Bayesian Network

Rainfall - 1 day autocorrelation

Hidden Markov model O(1)


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Pressure


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Magma flux


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Gas flux


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Ground deformation


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Structural integrity or stability

of the dome is dependant on

previous state

prior rock fall activity

prior collapse activity(also affects pressurization)


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Current model

Where monitoring time series suggest higher order processes


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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)


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Results so far

Parameter learning using ~9 years of data

transition and sensor models

1. static BN2. 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 formissing values of observed nodes


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Results so far

Structure learning on a small (5 node) model - observed nodes only

work still in progress!


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Results so far

High ground deformation

Consistent, moderate hybrid activity

No SO2 observations


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Results so far


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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?


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Conclusions

All models are wrong (to some degree)but some models are better than others

EVIDENCE SCIENCE and BAYESIAN NETWORKSRobust, 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


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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., 2004A thermodynamical model for rainfall-

triggered volcanic dome collapse. GRL 31(5)

Murphy, K., 2002Dynamic 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

an evidence science approach to volcano hazard forecasting

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