An Evidence Science approach to volcano hazard forecasting

cabbageswerveAI and Robotics

Nov 7, 2013 (4 years and 3 days ago)

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EXPLORIS

Montserrat

Volcano Observatory

Aspinall and Associates

Risk Management Solutions

1

2

3

4

5

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


Can’t 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.,
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