Some Challenges in Modelling Volcanic Occurrence Data

Mark BebbingtonIIST & Volcanic Risk Solutions, Massey University

What is an Eruption?• Arrival of solid volcanic products at surface• Events ranging from an individual explosion to

eruptive periods lasting centuries– Includes quiet periods of up to 3 months– Often `stop’ dates go unrecorded.

• `Historical’ eruptions– Presence of observers, monitoring, weather

• `Pre-historical’ eruptions– Dated, radio-carbon (to 50ka, with error ~ 25 to 1000

yr), K-Ar dating (from 50ka, with error ~ 10 to 100 ka).• VEI (Volcanic Explosivity Index)

– a logarithmic `size’ assigned to historical eruptions on the basis of: explosion size; volume; column height; classification; duration; …

CompletenessGlobally, the observance probability rises from 10% in 1500 to 100% in 1980 (assumed).

BUT

– some volcanoes are much better observed

- Big eruptions are much better observed

- what is an eruption?

Data: The good,

Etna flank eruptions: 1970 –Stationary behaviour?

Are time and size of next eruption `predictable’?

Etna: Flank eruptions 1600-Non-stationary?

60 flank eruptions- “known” onset

dates, duration, and volume

- Complete since ~1600 AD

Etna: Summit + Flank 1970-Independence?

12 summit eruptions, onset dates, durations and volumes, complete since 1970?

Any relation to the flank eruptions?

Data: The Bad,

A prediction?- The past behaviour of a volcano is the best predictor of its future activity.

“The repetitive nature of the eruptive activity at Mt St Helens during the last 4000 years, with dormant intervals typically of a few centuries or less, suggests that the current quiet period will not last a 1000 years. Instead, an eruption is likely within the next hundred years, possibly before the end of this century”

- Crandell et al., “Mt St Helens volcano: Recent and future behavior”. Science 187:438-441, 1975

- Mt St Helens erupted in 1980, having been quiescent since 1857

Data: The Ugly

VEI > 3

Vesuvius

Cycles initiated by (sub-) plinian event and terminated by repose of several centuries?

Periodicities

20151050

50

40

30

20

10

0

i

tau

_i

S 14.0130R-Sq 22.0%R-Sq(adj) 11.6%

Fitted Line Plottau_i = 30.32 - 5.096 i + 0.2796 i**2

Radiocarbon Dating• Volcanic products cannot be directly

carbon dated – they were never alive.• Date organic material in (or more often just

under) an eruptive layer. • Dates are given as

N(mu,sigma)• Conversion to

calendar years • Stratigraphic

ordering

Taveuni, Fiji

101 eruptive episodes, individually datedBUT - considerable “rounding”, large error bars

rift volcano – only one spatial dimension

120001000080006000400020000

100

80

60

40

20

0

Years BP

Co

un

t

meanup_bndlow_bnd

Variable

Eruption dates

Taranaki 103 tephras in single core –depths on all, 10 dated individually

Stars = core dates, lines 95% confidence limits

`DODGY’DATE

Taranaki II – 2 cores plus near source

Umutekai104 tephras, c. 1550BP –10100BP

Rotokare45 tephras, c.500BP – 6200BP

Near-source23 tephras, c.90BP – 2200BP

Related cycles of magma-feeding pulses, large eruptions and

eruption frequencyTaranaki

Yucca Mountain40 eruptions in last 10.5Ma. Last 80ka ago.Large error bars, and multiple eruptions with the same estimated age.Widely varying sizes- Probability of disruption of repository in 10ka?

Auckland

49 cones in last 250ka, last two much bigger, especially last (Rangitoto) – 59% of total volume.

Is there any pattern?