Bulletin of Volcanology

, Volume 74, Issue 7, pp 1699–1712

Regional ash fall hazard I: a probabilistic assessment methodology

Authors

    • Risk Frontiers, Macquarie University
    • Department of Earth Sciences, Wills Memorial BuildingUniversity of Bristol
  • Christina Magill
    • Risk Frontiers, Macquarie University
  • John McAneney
    • Risk Frontiers, Macquarie University
  • Russell Blong
    • Risk Frontiers, Macquarie University
    • AonBenfield Australia
Research Article

DOI: 10.1007/s00445-012-0627-8

Cite this article as:
Jenkins, S., Magill, C., McAneney, J. et al. Bull Volcanol (2012) 74: 1699. doi:10.1007/s00445-012-0627-8
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Abstract

Volcanic ash is one of the farthest-reaching volcanic hazards and ash produced by large magnitude explosive eruptions has the potential to affect communities over thousands of kilometres. Quantifying the hazard from ash fall is problematic, in part because of data limitations that make eruption characteristics uncertain but also because, given an eruption, the distribution of ash is then controlled by time and altitude-varying wind conditions. Any one location may potentially be affected by ash falls from one, or a number of, volcanoes so that volcano-specific studies may not fully capture the ash fall hazard for communities in volcanically active areas. In an attempt to deal with these uncertainties, this paper outlines a probabilistic framework for assessing ash fall hazard on a regional scale. The methodology employs stochastic simulation techniques and is based upon generic principles that could be applied to any area, but is here applied to the Asia-Pacific region. Average recurrence intervals for eruptions greater than or equal to Volcanic Explosivity Index 4 were established for 190 volcanoes in the region, based upon the eruption history of each volcano and, where data were lacking, the averaged eruptive behaviour of global analogous volcanoes. Eruption histories are drawn from the Smithsonian Institution’s Global Volcanism Program catalogue of Holocene events and unpublished data, with global analogues taken from volcanoes of the same type category: Caldera, Large Cone, Shield, Lava dome or Small Cone. Simulated are 190,000 plausible eruption scenarios, with ash dispersal for each determined using an advection–diffusion model and local wind conditions. Key uncertainties are described by probability distributions. Modelled results include the annual probability of exceeding given ash thicknesses, summed over all eruption scenarios and volcanoes. A companion paper describes the results obtained for the Asia-Pacific region

Keywords

Volcanic hazardHazard assessmentProbabilistic modellingAsh dispersionRegional hazard assessmentMethodology

Introduction

Home to 25 % of the world’s volcanoes and over two billion inhabitants, the Asia-Pacific region, on the western rim of the Pacific ‘ring of fire’, is one of the world’s most densely populated areas, with many cities and communities threatened by ash falls and other volcanic hazards, often from multiple volcanoes. Parts of Honshu in Japan, for example, lie within reach of ash falls from any one of 60 different volcanoes situated within 1,000 km. Even relatively thin ash falls (∼1 mm) are capable of disrupting vital lifelines such as transport, water supply, telecommunications and electricity (Blong 1984). This study develops a regional ash hazard assessment methodology using a probabilistic modelling framework. Modelled results for the Asia-Pacific region are detailed in a companion paper (Jenkins et al. 2012).

Previous volcanic hazard assessments have typically explored the hazard or risk from a single volcano (e.g. Jenkins et al. 2008; Macedonio et al. 2008) or to a particular site (e.g. Hoblitt et al. 1987; Magill and Blong 2005). Few regional studies of volcanic hazard or risk have been attempted: exceptions include that of Ewert (2007), who, based upon 15 hazard and 10 exposure attributes, ranked 169 US volcanoes in terms of their potential threats to populations. Along a similar theme, Yokoyama et al. (1984), Arnold et al. (2005) and Small and Naumann (2001) all undertook global volcanic hazard analyses, with the latter concluding that Southeast Asia is particularly exposed to persistent volcanism.

Of those assessments where the volcanic hazard was defined spatially, a constant level of hazard is assumed within concentric circles of fixed radii extending from the source volcano. Radii have ranged from 30 km (Ewert 2007) to 200 km (Small and Naumann 2001). These analyses cannot account for different eruption magnitudes or styles from the volcano in question or for the varying dispersion of ash because of time- and altitude-varying wind conditions.

Two studies have improved upon this by attempting to take into account these factors. Spence et al. (2009) considered the population impacted by individual European volcanoes to be those within a 60° sector defined by average prevailing wind directions. Hurst and Smith (2004) carried out probabilistic ash dispersal modelling to determine the ash fall hazard from three volcanoes in the North Island of New Zealand over a 10,000-year period.

Our study builds upon these previous studies by using an ash advection–diffusion model, ASHFALL (Hurst 1994), combined with stochastic simulation techniques to analyse the ash fall hazard from 190 volcanoes in nine countries across the Asia-Pacific region (Fig. 1 and Table 1).
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Fig. 1

Locations of the 190 volcanoes and countries considered in our study

Table 1

The 190 volcanoes identified for regional hazard assessment, grouped by country

Country

Volcanoes

Australia (n = 1)

Newer volcanic province

Eastern China (n = 4)

Baitoushan, Jingbo, Longgang Group, Wudalianchi

Indonesia (n = 73)

Ambang, Agung, Arjuno-Welirang, Awu, Batur, Cereme, Colo [Una Una], Dempo, Dieng Volc Complex, Dukono, Ebulobo, Egon, Galunggung, Gamalama, Gamkonora, Gede, Geureudong, Guntur, Ibu, Inierie, Inielika, Ijen, Iliboleng, Iliwerung, Iya, Iyang-Argapura, Kaba, Karangetang [Api Siau], Kelimutu, Kelut, Kerinci, Kiaraberes-Gagak, Krakatau, Lamongan, Leroboleng, Lewotobi, Lewotolo, Lokon-Empung, Mahawu, Makian, Marapi, Merapi, Merbabu, Muria, Paluweh, Papandayan, Penanggungan, Peuet Sague, Ranakah, Ranau, Raung, Rinjani, Ruang, Salak, Sangeang Api, Semeru, Sempu, Seulawah Agam, Sibayak, Sinabung, Sirung, Slamet, Soputan, Sorikmarapi, Sumbing, Sundoro, Talang, Tambora, Tandikat, Tangkubanparahu, Tengger Caldera, Tongkoko, Wilis

Japan (n = 63)

Adatara, Akagi, Akan, Akita-Komaga-take, Akita-Yake-yama, Asama, Aso, Azuma, Bandai, Chokai, E-san, Fuji, Fukue-jima, Hakkoda Group, Hakone, Haku-san, Haruna, Hiuchi, Ibusuki Volc Field, Iwaki, Iwate, Izu-Tobu, Kanpu, Kikai, Kirishima, Komaga-take, Kozu-shima, Kuchinoerabu-jima, Kuju, Kurikoma, Kusatsu-Shirane, Kuttara, Mashu, Megata, Mikura-jima, Miyake-jima, Myoko, Nasu, Niigata-Yake-yama, Nii-jima, Nikko-Shirane, Nipesotsu-Maruyama, Niseko, On-take, Oshima, Oshima-Oshima, Osore-yama, Rausu, Rishiri, Sakura-jima, Shikotsu, Shiretoko-Iwo-zan, Sumiyoshi-ike, Tate-yama, Tokachi, To-shima, Towada, Tsurumi, Unzen, Usu, Yake-dake, Yotei, Zao

New Zealand (n = 11)

Auckland Field, Egmont [Taranaki], Kaikohe-Bay of Islands, Maroa, Mayor Island, Okataina, Reporoa, Ruapehu, Taupo, Tongariro, White Island

Papua New Guinea (n = 21)

Ambitle, Bagana, Balbi, Bam, Bamus, Dakataua, Garbuna Group, Hargy, Kadovar, Karkar, Lamington, Langila, Lolobau, Loloru, Long Island, Manam, Pago, Rabaul, Ritter Island, Ulawun, Victory

Philippines (n = 15)

Banáhao, Bulusan, Camiguin, Canlaon, Leonard Range, Mahagnoa, Makaturing, Mariveles, Matutum, Mayon, Parker, Pinatubo, Ragang, San Pablo Volc Field, Taal

Taiwan (n = 1)

Kueishantao

South Korea (n = 1)

Halla

In what follows, we specify how volcanoes were chosen for analysis and provide an overview of the methodology before describing key components in more detail. The paper concludes with a brief discussion of significant methodological outcomes and the limitations of our approach. The focus here is on defining a robust methodology, with the presentation and discussion of results deferred to Jenkins et al. (2012). A description of terms, acronyms and mathematical notation can be found in “Appendix 1”.

Identifying volcanoes for analysis

The methodology presented here employs the Smithsonian Institution’s Global Volcanism Program catalogue of Holocene events (Siebert and Simkin 2002-), which has been supplemented with further unpublished records provided by the Smithsonian Institution (Siebert, personal communication). The resulting database, which we refer to as the ‘global eruption database’, is used to obtain data regarding eruptive behaviour for each of the volcanoes in the Asia-Pacific region and global analogues. To be considered in our analysis, volcanoes must have had at least one recorded eruption in the Holocene. Volcanoes classified as submarine, hydrothermal, fumarolic or of unknown type were excluded, as were those that form small isolated island chains (e.g. the Marianas and Volcano Islands, South of Japan), which due to their remote locations were unlikely to significantly contribute to the regional hazard. Nearly three quarters (n = 136) of the 190 volcanoes identified are located in just two countries: Indonesia and Japan.

Modelling framework

Volcanic hazard assessments often must depend upon eruption data that are poorly constrained and highly uncertain, particularly in countries where relevant historical records and geological studies extend back only a few hundred years or less. Probabilistic methods, as proposed in this paper, attempt to deal with this some of this inherent uncertainty. For each of the 190 identified volcanoes, 1,000 ash dispersal scenarios are simulated, where every scenario is the result of a plausible eruption with an associated probability of occurrence. Due to their potential for generating thicker and more widely dispersed ash falls, and therefore greater disruption for impacted communities, we restrict our modelling to eruptions with a Volcanic Explosivity Index (VEI) ≥4. This can be assumed to correspond to a minimum bulk volume of 0.1 km3 (Newhall and Self 1982). Nevertheless, the methodology, which is described next, requires us to first estimate the likelihood of an eruptions of any VEI from each of the volcanoes in question.

Following the logic tree outline in Fig. 2, to estimate the probability and VEI of each simulated eruption we draw from the global eruption database, after considering data completeness, a point to which we will return in later discussion. To calculate the probability of an eruption from a particular volcano, we first establish: (1) the annual probability of an eruption (of any magnitude) from the volcano, (2) the relative probability, given an eruption, that it will be VEI ≤ 3, 4, 5, 6 and 7. The latter probabilities determine the proportion of simulations that will represent VEI 4, 5, 6 and 7 eruptions so that the probability of a specific-sized eruption is accounted for by the number of simulations.
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Fig. 2

Logic tree for determining eruption probabilities and the relative number of eruptions simulated for each VEI

Once the VEI of each simulated eruption and its associated probability has been determined, other key variables, such as eruption volume, wind conditions and ash settling velocities are then randomly sampled from predefined probability distributions and used as input parameters for ash dispersal simulation (see ‘Ash dispersal modelling’ section). The probability distributions dictate the magnitude and allowable range for each variable, and their relative likelihoods within this range.

For each eruption scenario, we calculate ash thickness at 1 km grid intervals for urban areas lying within 1,000 km of the volcanic vent. Ash accumulation more than 1,000 km from source is very rare (Blong 1984) and is therefore not likely to contribute greatly to the hazard at such distances. In the absence of any internationally agreed definition, we consider an urban area to have at least 400 residents/km2 (LandScan 2005 global database: Oak Ridge National Laboratory 2005). In this way, we focus our computing resources on determining the hazard for concentrations of population; for this study region, this comprises an area of over one million square kilometres.

Annual eruption probability

In previous probabilistic assessments of ash hazard, dispersal from a single volcano is often explored conditional upon an eruption having taken place (e.g. Bonadonna et al. 2005; Connor et al. 2001; Jenkins et al. 2008). The consequences are then estimated independently of the probability that the eruption will occur. For our study, such an approach would be invalid as the ash fall hazard at any given location may be an accumulation of the hazard from many volcanoes, all of which are likely to have different eruption probabilities, styles and magnitudes. For our purposes, it was therefore necessary to estimate the individual annual eruption probability for each volcano.

In principle, assuming past averaged eruption frequency is characteristic of future eruption frequency, the averaged annual eruption probability (λ) for a volcano is determined simply by dividing the total number of eruptions (N) from that volcano by the time period (T) for which the catalogue is thought to be complete:
$$ \lambda = N/T $$
(1)

While this approach averages temporal clustering and variations in activity over time that may be better known for individual well-studied volcanoes, it does provide a consistent methodology for the quantification of ash fall hazard across a region, where more detailed knowledge is often lacking. This study is intended as a long-term estimate of ash fall hazard and not an estimate of the next likely eruption. Values of λ have been assigned to each of the 190 study volcanoes, based on the eruption history of that volcano. This demands an estimate of the T for which the eruption catalogue is thought to be complete.

Data completeness

Over the past 200 years, a sharp increase in the number of eruptions recorded globally has been observed, a feature that closely correlates with an exponential increase in global population and more effective recording (Simkin and Siebert 1994). Clearly, correctly estimating the breakpoints from which the time series of eruptions is complete is critical: a record that is too long may lead to an underestimation of eruption frequency and therefore hazard, while too short a record would needlessly eliminate valuable data.

Ideally, data completeness analyses would be carried out on a volcano-by-volcano basis. For well-studied volcanoes with relatively complete or recently detailed eruption records, rates of activity and temporal variations, e.g. open and closed systems, can reliably be constructed (e.g. Ho 1990—Mauna Loa and Etna volcanoes; Klein 1984—Kilauea volcano); however, in the Asia-Pacific region, this level of data completeness is rare and many volcanoes simply do not have a sufficient number of recorded eruptions to allow meaningful judgements. The first eruption of Suoh caldera (Indonesia) recorded in the global eruption database was a VEI 4 eruption in 1933; similarly, Tambora (Indonesia) had no recorded eruptions prior to the VEI 7 eruption of 1812–1815. In the study region, 6 % (n = 30) of volcanoes have only one eruption recorded.

There are a number of possible strategies for estimating eruption data completeness and annual eruption frequency (e.g. Bacon 1982; Coles and Sparks 2006; Marzocchi and Zaccarelli 2006); however, for the reasons stated above and given the geographically and volcanically diverse dataset required for this assessment, a rigorous completeness analysis for all volcanoes in the Region is clearly impossible. We thus analysed completeness globally over areas defined by historical and geographical boundaries, using a ‘break-in-slope’ method.

Simkin and Siebert (1994) suggest that the record for smaller magnitude eruptions (VEI ≤ 3) is complete globally since the 1960s, while the record for larger magnitude eruptions (VEI ≥ 4) is complete for at least the last century as larger magnitude eruptions are better preserved in geological deposits as well as written and oral records. For this reason, we split the global eruption database into eruptions of VEI 4 or above (n = 618) and those of VEI 3 and below (n = 6,716) and examined each subset separately by plotting the cumulative number of eruptions against time (e.g. Fig. 3). Magnitude classifications of ‘C’ (related to caldera collapse) or ‘P’ (Plinian) were allocated to the large magnitude (VEI ≥ 4) portion of the dataset. Countries with very few eruption records (e.g. eastern China, South Korea and Taiwan), were analysed together. In total, 21 geographical areas worldwide were analysed, with completeness identified by a linear increase in the cumulative number of eruptions per unit time.
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Fig. 3

Cumulative number of large magnitude (VEI≥4; left) and small magnitude (VEI≤3) eruptions (right) over time for a Indonesia, b Philippines and c Japan. Data completeness is assumed for ages younger than that indicated by the dotted lines

For large magnitude eruptions, Indonesia and the Philippines exhibit easily definable ‘breakpoints’ at approximately 420 and 630 years before present (2006; Fig. 3a and b, left). These likely correspond with the arrival of colonisers in the area; for example, Europeans first began to document eruptions in Indonesia in 1512 (Simkin and Siebert 1994) and recorded their first large magnitude eruption (Kelut) in 1586. For some other countries, choosing this breakpoint was more problematic. In Japan, for example, a recent emphasis on tephrochronology (e.g. Machida and Arai 1992) combined with a long written history has extended completeness further back in time. The result is that a plot of the cumulative number of Japanese eruptions in the global eruption database with time increases non-linearly with time (Fig. 3c). In cases such as this, it was necessary to make a subjective choice of breakpoint by dividing the curve into two approximately linear relations. Table 2 lists our best estimates of the complete duration (T) of the small and large magnitude eruption records worldwide: the first five entries in the table refer to areas in the Asia-Pacific region.
Table 2

Data completeness by area for the global eruption record

Area

‘Breakpoints’ (years before 2006)

Number of eruptions during ‘complete’ record

Proportion (%) of total eruptions deemed complete

Proportion (%) of total record length deemed complete

Average Recurrence Interval between eruptions (years)

VEI 0–3

VEI 4–7

VEI 0–3

VEI 4–7

VEI 0–3

VEI 4–7

VEI 0–3

VEI 4–7

VEI 0–3

VEI 4–7

Indonesia

203

420

1,047

28

89

85

3

10

2 months

15

Japan

501

3,096

892

71

83

71

5

28

7 months

44

New Zealand, SW Pacific

232

6,706

380

27

88

73

2

56

7 months

248

Papua New Guinea

134

1,866

191

23

92

82

31

20

8 months

81

Philippines

181

626

133

11

85

69

42

6

1 year 4 months

59

Africa

206

9,556

124

8

90

100

4

100

1 year 8 months

1,195

Alaska, Kamchatka, Kuriles

316

11,506

713

115

86

100

3

100

5 months

100

Azores, Madeira, Canaries

576

5,056

43

13

84

100

15

100

13 years 5 months

389

Canada, Lower 50 states USA

222

2,576

147

18

43

78

2

33

1 year 6 months

143

Chile, Argentina

448

9,426

339

17

97

100

5

100

1 year 4 months

554

Colombia

471

4,556

5,134

15

100

83

9

46

6 yrs 6 mths

304

Costa Rica, El Salvador

348

8,056

202

24

96

100

12

100

1 year 9 months

336

Ecuador

474

3,156

188

31

89

91

5

32

2 years 5 months

102

Guatemala

501

425

105

8

94

100

31

100

4 years 9 months

53

Iceland

1,156

1,106

147

26

69

72

10

9

6 years 10 months

43

Italy

1,219

4,506

242

21

87

91

12

51

5 years

215

Mexico

856

9,376

114

25

83

100

9

100

7 years 6 months

375

Nicaragua

157

8,056

130

10

85

100

33

100

1 year 2 months

806

Peru

552

3,326

39

4

91

100

10

100

14 years 2 months

832

West Indies

316

10,216

33

28

87

100

10

100

9 years 7 months

365

Few data points

366

9,356

399

16

93

100

3

100

11 months

585

Assigning eruption frequencies

Having assigned T for each country or sub-region, and each magnitude range (VEI ≤ 3 and VEI ≥ 4), we now estimate each volcano’s λ for an eruption of any magnitude (Eq. 1). Eruption probability was calculated for two magnitude subsets: small magnitude (VEI ≤ 3) and large magnitude (VEI ≥ 4). For example, volcano A has a record of four small magnitude (VEI ≤ 3) eruptions in 100 years and three large magnitude (VEI ≥ 4) eruptions in 2,000 years. The T for each subset is derived from the period over which the catalogue is thought to be complete, in this example 100 and 2,000 years. To aggregate subsets, the different record lengths were normalised to one time period, assuming a constant eruption rate. In this example, we estimate a total of 83 eruptions in a 2,000-year period ((4 × 20) + 3), giving an annual eruption probability of 0.041 and an average recurrence interval—the approximate inverse of the annual eruption probability—of 24 years for an eruption of any VEI magnitude.

In the unique case of Sumiyoshi-ike in Japan, only two small magnitude eruptions have been recorded, both approximately 8,000 years ago. These eruptions fall outside the 500-year complete portion of the small magnitude eruption database for Japan and yet we still require an Average Recurrence Interval (ARI) for this volcano. This was the only volcano in this situation in the region and we chose to consider the record from the earliest eruption, leading to an ARI of approximately 4,000 years.

Figure 4 shows the ARIs calculated for all 190 volcanoes, grouped by country and Table 3 details the five volcanoes with the smallest ARIs (rank 1–5), the five surrounding the median (rank 93–97) and the five with the largest ARIs (rank 186–190). Estimated ARIs range over nearly 4 orders of magnitude from approximately 3 years (Tongariro, New Zealand: 71 small magnitude eruptions in the last 232 years and two large and two unknown magnitude eruptions in the last 6,706 years) to 10,056 years (Inierie, Indonesia: one eruption of unknown magnitude 10,056 years ago).
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Fig. 4

Average recurrence intervals for an eruption of any magnitude, based upon the eruption history of each volcano (diamond), calculated for 190 volcanoes in the Asia-Pacific region and grouped by country

Table 3

Average recurrence intervals (ARI) calculated for an eruption of any magnitude from individual volcano histories

Volcano

Country

Number of eruptions in complete record

Volcano unique ARI (in years)

Rank

Tongariro

New Zealand

73

3

1

Mayon

Philippines

60

3

2

Manam

Papua New Guinea

42

4

3

Aso

Japan

140

4

4

Ulawun

Papua New Guinea

34

4

5

Mahawu

Indonesia

7

71

93

Tandikat

Indonesia

4

74

94

Lewotolo

Indonesia

8

79

95

Nasu

Japan

6

84

96

Tongkoko

Indonesia

7

84

97

To-shima

Japan

1

6,556

186

Niseko

Japan

1

6,906

187

Rishiri

Japan

1

7,836

188

Mayor Island

New Zealand

1

8,056

189

Inierie

Indonesia

1

10,056

190

The ARI rankings run from the shortest (1) to longest (190) and selected rankings are shown here

Some of this spread in ARI can be attributed to inconsistent quality of data recordings and preservation of deposits between volcanoes and between countries; however, much of the variation will reflect real differences in the tectonic, magmatic and environmental conditions between volcanoes.

Eruption magnitude probability

Previous discussion has centred on the calculation of annual probabilities for each of the region’s volcanoes producing an eruption of any magnitude. Given an eruption at each volcano, we now consider the conditional probability of that eruption being VEI ≤ 3, 4, 5, 6 and 7. For many volcanoes, e.g. the Auckland Volcanic Field, New Zealand (one eruption) and Hakone, Japan (three eruptions), there are very few eruptions in the database, and even less in the portion considered complete. This may be indicative of a low eruption rate, poor historical record or a geological record that is less studied, less accessible and/or less well preserved. Of the region’s 190 volcanoes, 77 % (n = 146) have less than three eruptions during the time period for which their record is deemed complete and/or no record of both large and small magnitude eruptions. With this in mind, we propose to use records from analogous volcanoes (those of the same type category) to provide some perspective on likely eruption behaviour.

Volcano category classification

With the purpose of inferring averaged eruptive behaviour across analogous volcanoes, we follow the Smithsonian Institution classification of volcanoes by type and assign each volcano to a broad type category (Table 4) based upon its physical characteristics. The volcano type category implicitly relates to previous eruption styles and magnitudes at the volcano and is indicative of magma composition, i.e. shields and small cones tend to be less silicic, and therefore produce less explosive eruptions, than large cones, lava domes and calderas.
Table 4

Volcano counts when grouped into five type categories, based on Siebert and Simkin (2002-)

Volcano type category

Includes Smithsonian Institution definitions of:

Caldera (n = 19)

Caldera, Calderas, pyroclastic shield

Large cone (n = 150)

Complex volcano, Complex volcanoes, Compound volcano, Somma volcano, Somma volcanoes, Stratovolcano, Stratovolcanoes, Volcanic complex

Shield (n = 6)

Shield volcano, Shield volcanoes

Lava dome (n = 6)

Lava dome, Lava domes

Small cone (n = 9)

Cinder cone, Cinder cones, Cones, Crater rows, Explosion craters, Fissure vent, Fissure vents, Lava cone, Maar, Maars, Pyroclastic cone, Pyroclastic cones, Scoria cones, Tuff cones, Tuff rings, Volcanic field

For detailed descriptions, schematic profiles and figures the reader is referred to Siebert and Simkin (2002-)

Of all the volcanoes considered, 79 % (n = 151) were categorised as large cones, 9 % (n = 18) as caldera and the remaining 21 as lava dome, shield or small cone. We accept that this categorisation is problematic and that assigning a single, most dominant category does not reflect the full range of complex behaviour possible at many volcanoes. Nonetheless, the approach does allow for an indication of the relative likelihood of eruption magnitudes, with some of the uncertainty in outcomes accounted for by allowing a wide range of possible eruption magnitudes.

Assigning eruption magnitude probabilities

With each volcano assigned to a particular category (Table 4), we then examined the global eruption database to determine conditional magnitude probabilities of eruptions being VEI 4, 5, 6 and 7 relative to eruptions VEI 3 and below, for each volcano category (Table 5). These globally averaged relative probabilities were then attributed to volcanoes of the same categories in the Asia-Pacific region. To test the validity of this assumption, we compare the relative probabilities determined for individual well-studied volcanoes in the region with those averaged from global analogues. For the large cone volcanoes of Fuji, Usu and Sakura-jima in Japan, the conditional probabilities of eruptions ≥VEI 4 determined from unique eruption histories are 29, 14 and 3 % respectively, compared to the globally-averaged probability of 9 % (Table 5). Given the short timescales over which eruptions have been recorded, relative to the timescales over which volcanoes are active, it is likely that at any one volcano, the full breadth of possible eruption magnitudes is not shown in the history of recorded eruptions. This provides further motive for using global analogues and probabilistic methodologies.
Table 5

Probabilities for each volcano category assumed for an eruption of VEI 3 or below, 4, 5, 6 or 7, conditional upon an eruption occurring

Volcano type category

Data (n)

Probabilities, conditional upon an eruption of any magnitude

VEI ≤ 3

VEI 4

VEI 5

VEI 6

VEI 7

Caldera

642

0.85

0.08

0.04

0.02

4.8 × 10−3

Large cone

4,825

0.91

0.07

0.02

4.8 × 10−3

4.5 × 10−4

Shield

733

0.96

0.03

6.2 × 10−3

2.0 × 10−3

1.0 × 10−3

Lava dome

58

0.74

0.21

0.04

0.01

0

Small cone

117

0.94

0.05

8.0 × 10−3

0

0

Shield (excluding pyroclastic shield) and small cone volcanoes show the lowest conditional probability of producing an eruption of VEI 4 or larger, at 0.04 (4 % of eruptions) and 0.06 (6 %) respectively, with the vast majority being VEI 3 or lower. For large-magnitude (VEI ≤ 4) eruptions, caldera volcanoes have the highest conditional probability of producing very large-magnitude eruptions (VEI 6 or 7) at 0.03 (3 % of eruptions). Eruption frequency is accounted for by calculating the averaged λ for each volcano so that these relative VEI probabilities (Table 5) describe how likely each volcano type is to produce an eruption of each VEI, conditional upon an eruption having occurred.

The annual probability of a volcano producing a certain magnitude eruption (EVEI) can now be simply determined by multiplying the λ occurring at that volcano by the probability that the eruption will be of the given magnitude (MVEI; Table 5 and nodes 2 and 3 of Fig. 2). Thus for each simulation:
$$ P\left[ {{E_{\text{VEI}}}} \right] \approx \lambda .{P_{{{\text{Volcano}}\,{\text{Type}}}}}\left[ {\left. {{M_{\text{VEI}}}} \right|{\text{eruption}}\,{\text{of}}\,{\text{any}}\,{\text{magnitude}}} \right] $$
(2)
In the case of Merapi, a large cone volcano in Indonesia, λ was calculated to be 0.25, on the basis of its eruptive history. Given an eruption, the probability of it being VEI 4, for example, is 0.07 (Table 5), and so:
$$ \matrix{ {P\left[ {{E_{{{\text{VEI}}4}}}} \right] \approx \lambda .{P_{{{\text{Large}}\,{\text{Cone}}}}}\left[ {\left. {{M_{{{\text{VEI}}4}}}} \right|{\text{eruption}}\,{\text{of}}\,{\text{any}}\,{\text{magnitude}}} \right]} \\ { \approx 0.25 \times 0.07} \\ { \approx 1.78 \times {{10}^{{ - 2}}}} \\ }<!end array> $$
(3)
Thus, based upon the eruption history of Merapi and the averaged eruptive behaviour of analogous volcanoes, the annual probability of an eruption of VEI 4 is established to be 1.78 × 10−2, equivalent to an ARI of around 57 years. The probability of an eruption of VEI 4 or greater is lower at 44 years and for small magnitude (VEI ≤ 3) eruptions at Merapi, the ARI is calculated as approximately 4 years, which is consistent with previous estimates (e.g. Newhall et al. 2000; Thouret et al. 2000; Voight et al. 2000). Following from this, for every 1,000 eruptions simulated at Merapi, 732 will be VEI 4, 210 VEI 5, 53 VEI 6 and 5 will be VEI 7. Calculated probabilities for each simulation are summed for each grid cell where ash fall is simulated so that the annual probability a grid cell (x) will be impacted by a VEI 4 eruption (EVEI 4) from Merapi is given by:
$$ {P_{\text{Merapi}}}{\left[ {{E_{{{\text{VEI}}4}}}} \right]_x} \approx \sum\limits_{{i = 1}}^{{i = S}} {\left( {\left( {{P_{\text{Merapi}}}\left[ {{E_{{{\text{VEI}} \geqslant 4}}}} \right]} \right)/{\text{Tota}}{{\text{l}}_S}} \right)} $$
(4)

Where S is the number of simulations that produce thicknesses exceeding the defined thresholds in grid cell x (≤732 for a VEI 4 eruption), EVEI ≥ 4 is the probability of an eruption of VEI 4, 5, 6 or 7 and TotalS is the total number of eruptions simulated, in this case 1,000. Therefore, if we assume that all VEI 4 simulated eruptions from Merapi impact location x, the ARI for that grid cell will be approximately 57 years (1/1.78 × 10−2); however, if only half of simulated VEI 4 eruptions impact the grid cell, the ARI for that cell will rise to approximately 114 years. Clearly, wind conditions are not constant and so the annual probability will vary between grid cells, with those downwind showing higher probabilities than those impacted by more unusual wind conditions.

Ash dispersal modelling

The extent and thickness of ash fall is strongly influenced by the vertical profile of wind speed and direction, eruption magnitude and the physical characteristics of ash particles. Having assigned an annual probability and VEI to each simulated eruption scenario from each volcano, we use the ash advection–diffusion model ASHFALL (Hurst 1994) to simulate the distribution and thickness of ash deposition. ASHFALL is a two-dimensional semi-analytical model that has fast runtimes (1–2 min per simulation on a single processor) making it well suited to probabilistic assessments. The spatial distribution and thickness of ash is obtained by calculating how ash falling out of the column is affected by wind. The following sections detail the probability distributions and relationships determined for the remaining input parameters.

Eruption volume

Eruption volumes follow directly from the VEI classification scheme. For a given VEI eruption, the model randomly samples volumes to be equally probable between the lower and upper limits on a logarithmic scale, i.e. a power law distribution. For example, a VEI 4 eruption would sample log10 volume randomly from a Uniform distribution ranging between −1 (log100.1) and 0 (log101) so that smaller volumes within the range are preferentially simulated.

Eruption column height

Higher eruption columns will result in ash particles taking longer to reach the ground and thus dispersed further. For each simulation, the eruption column height H (in kilometres) is calculated from an assumed relationship with eruption volume, V (in cubic kilometres):
$$ H = 8.67{\log_{{10}}}(V) + 20.20 $$
(5)

This relation is similar to that found by Carey and Sigurdsson (1989) for Plinian eruptions and is derived from a regression analysis (r2 = 0.57) of large magnitude global Holocene events with a VEI of 4 or greater (Jenkins et al. 2007).

Ash settling velocities

Terminal settling velocities are extrapolated from particle size and density. Particle size is modelled (in phi) from a normal distribution with limits 4 and −6 phi, i.e. a truncated log-normal distribution. To account for uncertainty in this estimation, the mean is sampled uniformly between −2.5 phi and 1 phi and the standard deviation between 2 phi and 3 phi. Particle density is fixed at 900 kg/m3 with the range in settling velocities accounted for by varying particle size estimates. Particle size distributions and uncertainty (Fig. 5) follow empirical evidence and theoretical arguments made by Woods and Bursik (1991).
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Fig. 5

Probability density distributions for settling velocity classes used in ash dispersal modelling

We use 50 classes of terminal settling velocity, each represented by its relative probability of occurrence within the ejected mass. ASHFALL analyses each settling velocity class individually and then sums thicknesses calculated at each grid point to give total thickness for the eruption.

Wind conditions

Ten years of wind data (January 1997 to December 2006) were obtained from the National Centres for Environmental Protection (NCEP) and Atmospheric Research (NCAR) global reanalysis project at 2.5° intervals (200–275 km). Data, available for 17 pressure levels, were interpolated to 35 even height intervals between 1 and 34 km above sea level. For each volcano, the resultant record comprises 14,608 profiles—10 years of 6-h profiles (12 am, 6 am, 12 pm and 6 pm)—of wind speed and direction. So as not to bias simulations towards particular seasonal or diurnal wind conditions, for each volcano and for each of the 1,000 eruption scenarios simulated, wind conditions were sampled randomly from this record at the location closest to the volcano, i.e. within 1.25°. Therefore, closely spaced volcanoes may utilise the same wind records.

Using NCEP/NCAR wind profiles, ASHFALL accounts for vertical, but not horizontal, changes in wind conditions with distance from the volcano. Incorporating horizontal changes in wind conditions requires the use of complex atmospheric or hybrid models, which are computationally intensive and therefore currently unsuitable for probabilistic modelling. An analysis of the variation in wind speed and direction horizontally shows that mean wind direction and speed downwind does not vary by more than 1 SD over the maximum extent ash dispersion is modelled (1,000 km): there is greater variation in wind conditions vertically within the one profile. The change in mean wind conditions across Indonesia, which has the greatest number of volcanoes and therefore the greatest number of eruptions simulated as part of this study, is shown in Fig. 6 for approximately ground, tropopause and mid-stratosphere levels and demonstrates that incorporating varying wind conditions horizontally (through more complex models) is unlikely to have a strong influence on simulated ash dispersion.
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Fig. 6

Wind profile locations (blue arrows) across central Indonesia from 105° to 130° longitude and at −7.5° latitude, with reference to volcano locations (red triangles). The mean speed along profiles is shown for three height levels: near-surface (1,000 mb), tropopause (250 mb) and mid-stratosphere (20 mb). Wind roses at the same pressure levels show variations in wind direction (where wind blows from) and thus dispersal direction, within the 10 year record for three selected locations

A more influential variable affecting the distribution of ash following an eruption is the height-varying profile of wind speed and direction at the time of the eruption. Considerable variation in vertical wind profiles across the Asia-Pacific region means that some locations experience a complete reversal in wind direction between the troposphere and stratosphere (Fig. 7). This is accounted for within the model by using profiles that describe wind speed and direction at 1-km intervals vertically through the eruption column.
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Fig. 7

Mean wind directions and speeds over the Asia-Pacific region at near surface, tropopause and mid-stratosphere pressure levels (1,000, 250 and 20 mb) for the 10-year period 1997–2006. Individual 6-hourly wind profiles at 2.5° intervals are utilised, with each simulation sampling randomly from the 10-year record, for the point closest to the volcano. Figures generated using the NOAA/ESRL Physical Sciences Division website (http://www.cdc.noaa.gov/)

Hazard outcomes

Estimating annual exceedance probabilities for ash fall thicknesses

For each 1 km2 cell defined as urban area, the ash fall hazard is identified by accumulating all simulations from each volcano that impacts the grid cell. We then calculate for each cell, from each volcano, the probability of reaching 1, 10 and 100 mm accumulation thresholds: chosen to represent the approximate onset of various forms of damage or disruption to communities, infrastructure and economies (see part II for more detail). Many cells have the potential to be impacted by ash from multiple volcanoes, even from volcanoes in adjacent countries and even for thicknesses exceeding 100 mm. Independent eruptions are combined by summing the associated annual simulated eruption probabilities over all relevant eruptions (i), potentially from a number of volcanoes. The Annual Exceedance Probability (AEP) at any grid cell (x) is then calculated for each ash thickness threshold (z) by:
$$ {\text{AE}}{{\text{P}}_x}\left[ {Z \geqslant z} \right] \approx {\sum\nolimits_i {\Pr }_x}\left[ {\left. {Z \geqslant z} \right|{\text{eruptio}}{{\text{n}}_i}} \right] $$
(6)
where Z is the simulated ash thickness. As an example, the annual cumulative probability that a cell within Tokyo will receive an ash fall exceeding 1 mm is the sum of the annual probabilities that eruptions from Fuji and Hakone and On-Take (and others) will produce ash thicknesses exceeding 1 mm. The possibility that contemporaneous eruptions from multiple volcanoes results in accumulated ash thicknesses affecting a grid cell is taken as negligible.
This procedure is shown in schematic form in Fig. 8 where by way of example we assess the probability for ash thicknesses greater than 10 mm in the Philippines, arising from eruptions at Pinatubo volcano in the first example and Pinatubo and Taal together in the second example. We display results in terms of the ARI, approximately the inverse of the AEP:
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Fig. 8

Schematic diagrams illustrating the accumulation of hypothetical eruption scenarios at each grid cell for a single and a multiple volcano hazard assessment: each ellipse represents the area affected by ash falls exceeding a certain thickness threshold given one hypothetical eruption simulation. Accumulation of the three hypothetical simulations from each volcano (red triangle) to give impact probabilities for each cell follows Eq. 4, with TotalS being 3. The annual probability that a grid cell is impacted by ash falls from both volcano A and B (lower right hand schematic) is then the sum of the accumulated simulation impact probabilities, with impact ARIs calculated using Eq. 7. These schematics are conceptual and do not represent actual modelling results. To account for differing eruption properties, probability of occurrence and wind conditions, the modelling methodology in this paper actually simulates 1,000 separate scenarios for each volcano (as shown in the example maps to the right); however, just three simulations for each volcano are shown in the schematic diagrams to illustrate the concept. Modelling results for Pinatubo alone (upper example) and Pinatubo and Taal volcanoes together (lower example) in the Philippines are presented as an example. The ARI in Manila decreases from 18,000 years when falls from Pinatubo are considered to 1,500 years when falls from Taal and Pinatubo are considered. The star shows the centre of Manila, the capital of Philippines, and white grid cells reflect areas where there are no modelling results, e.g. the sea or cells containing less than 400 people

$$ {\text{AR}}{{\text{I}}_x}\left[ {Z \geqslant z} \right] \approx - 1/\ln \left( {1 - {\text{AE}}{{\text{P}}_x}\left[ {Z \geqslant z} \right]} \right) $$
(7)

The ARI at a given location is the estimated average time (in years) between ash falls exceeding a given thickness: smaller thickness thresholds will result in shorter ARIs. When considering the ARI for falls exceeding 10 mm in Manila (Fig. 8), values decrease from 18,000 years for falls from Pinatubo to 1,500 years when falls from Taal are also considered. This average is calculated over a long time period or, in this study, over a large number of simulations where each simulation is treated as an independent eruption.

Model limitations

As indicated earlier, our data completeness assessments suggest that more effective reporting of eruptions is limited to the past 200 years of volcanism, although this varies considerably between areas. Our estimates of data completeness, and therefore calculation of eruption probabilities, are subject to uncertainty, particularly in areas where breakpoints between complete and incomplete subsets of data are difficult to identify. It is possible that longer eruption records are dominated by intensive studies at particular volcanoes, which is not accounted for in assuming consistent recording across a geographical area.

Volcanoes with no recorded eruptions in the Holocene (approximately the last 10,000 years) are not included in our assessment. As quiescent intervals between major eruptions at some volcanoes can be thousands of years (Simkin 1993), and with many historical records shorter than this, our assessment may ignore some volcanoes which have the potential to impact the region in the future. However, the probability-weighted contribution to the hazard from volcanoes with ARIs of the order 10,000 years will likely be minimal.

In assigning probabilities to eruption magnitudes, we have used a crude form of volcanic profiling. The physical appearance of a volcano is the product of its past eruptive history and so volcanoes of a similar type category share many structural and eruptive characteristics; however, certain volcanoes may fall within different categories at various stages of their evolution. For example, the Okataina Volcanic Centre in New Zealand is classified here as a lava dome, while according to Nairn (2005) the centre is best described by a complex of lava domes within a caldera. Our categorisation may therefore underestimate the possible peril from this centre. Conversely, Krakatau, Indonesia, is classified as a caldera, whereas we may expect near future eruptions to be more typical of smaller magnitude cone formation eruptions (Simkin and Fiske 1983). While the type classification assigned by the Smithsonian Institution may not always reflect the predominant style of an eruption, at this particular juncture we have adopted their classification scheme. A more detailed volcano-by-volcano assessment is beyond the scope of this study.

Each volcano is assigned a constant annual probability of eruption, regardless of the time elapsed since the last eruption. Accordingly, we have not accounted for time-varying probability such as the possibility of eruptions being temporally clustered (e.g. Auckland Volcanic Field: Bebbington and Cronin 2011) or changes in the magmatic system and thus eruption style.

Ideally, ASHFALL should be calibrated against past eruptions for each of our volcanoes of interest. Due to a lack of preserved deposits, such a study would not be possible for many of the volcanoes and certainly lies well outside the scope of the present investigation. Nonetheless, we believe the use of this model is justified here in a broad assessment of ash fall hazard across the region, allowing us to identify areas at highest risk and those which may benefit from further, more detailed, study.

Conclusions

A methodology has been developed to assess the relative ash fall hazard across the Asia-Pacific region. Eruption probabilities are based on a global eruption database constructed from the Smithsonian Institution Global Volcanism Program catalogue augmented by the Institution’s unpublished data. The annual eruption probability for each of the 190 volcanoes considered draws information from the eruption history of the specific volcano and, where data are lacking, from global analogues, classified here as volcanoes of the same type category. The database is characterised by widely varying degrees of completeness, both temporally and spatially, with some areas (e.g. Japan) exhibiting long and comprehensive records of 3,000 years or more, while others (e.g. Indonesia) only show complete records for the last 500 years or less. By identifying periods of completeness within the database for each area and for different classes of eruption magnitude, and by then only calculating eruption statistics over these periods, we reduce the influence of poor data records upon key input variables, especially eruption frequencies. While our approach simplifies certain attributes that may be known for a few well-studied volcanoes, it nonetheless imposes a consistent methodology on the quantification of ash fall hazard across the region. The methodology provides a regional view of the ash fall hazard in a way that has not been attempted previously. More detailed study of individual volcanic centres should be taken prior to use of the results as the basis for planning or insurance underwriting decisions. In part II, we explore the modelled ash fall hazard results for eruptions with VEI ≥4 and the associated exposure of populations to this hazard in the Asia-Pacific region.

Acknowledgments

The authors would like to thank Lee Siebert (Smithsonian Institution) for providing unpublished data and for helpful discussions regarding volcano type categorisation and Tony Hurst (GNS Science) for the ASHFALL source code. We also sincerely thank Costanza Bonadonna and Warner Marzocchi for providing detailed and very valuable reviews of the manuscripts and the editors of Bulletin of Volcanology for their support. This research was carried out while Susanna Jenkins was holding an International Macquarie University Research Scholarship.

Copyright information

© Springer-Verlag 2012