Bulletin of Volcanology

, Volume 66, Issue 8, pp 735–748

The size and frequency of the largest explosive eruptions on Earth

Authors

    • Department of Earth Sciences
  • David M. Pyle
    • Department of Earth Sciences
  • Clive Oppenheimer
    • Department of Geography
Research Article

DOI: 10.1007/s00445-004-0355-9

Cite this article as:
Mason, B.G., Pyle, D.M. & Oppenheimer, C. Bull Volcanol (2004) 66: 735. doi:10.1007/s00445-004-0355-9

Abstract

A compilation and analysis of the size and frequency of the largest known explosive eruptions on Earth are presented. The ‘largest’ explosive events are defined to be those eruptions yielding greater than 1015 kg of products (>150 times the mass of the 1991 eruption of Mt. Pinatubo). This includes all known eruptions with a volcanic explosivity index (VEI) of 8. A total of 47 such events, ranging in age from Ordovician to Pleistocene, are identified, of which 42 eruptions are known from the past 36 Ma. A logarithmic ‘magnitude’ scale of eruption size is applied, based on erupted mass, to these events. On this scale, 46 eruptions >1015 kg are defined to be of magnitude M8. There is one M9 event known so far, the Fish Canyon Tuff, with an erupted mass of >1016 kg and a magnitude of 9.2. Analysis of this dataset indicates that eruptions of size M8 and larger have occurred with a minimum frequency of ≈1.4 events/Ma in two pulses over the past 36 Ma. On the basis of the activity during the past 13.5 Ma, there is at least a 75% probability of a M8 eruption (>1015 kg) occurring within the next 1 Ma. There is a 1% chance of an eruption of this scale in the next 460–7,200 years. While the effect of any individual M8 or larger eruption is considerable, the time-averaged impact (i.e., erupted mass×frequency) of the very largest eruptions is small, due to their rarity. The long-term, time-averaged erupted mass flux from magnitude 8 and 9 eruptions is ~10–100 times less than for M7 eruptions; the time-averaged mass eruption rate from M7 eruptions is 9,500 kg s−1, whereas for M8 and M9 eruptions it is ~70–1,000 kg s−1. Comparison of the energy release by volcanic eruptions with that due to asteroid impacts suggests that on timescales of <100,000 years, explosive volcanic eruptions are considerably more frequent than impacts of similar energy yield. This has important implications for understanding the risk of extreme events.

Keywords

CalderaSupereruptionSupervolcanoExtremal analysisHazard

Introduction

Current understanding of the size and frequency of the Earth’s largest explosive eruptions is limited. Despite the potential impact of such events, only a handful of these eruptions have been studied in any detail. There have been few attempts to develop a systematic dataset to allow comparison between, and analysis of such events. Analyses of prehistoric eruptions indicate that pyroclastic currents with volumes of thousands of cubic kilometres of magma can be erupted in a matter of days (e.g. Smith 1960; Sparks and Wilson 1976; Wilson 2001; Branney and Kokelaar 2003). The aftermath of the very largest events may leave ash deposits across millions of square kilometres; the ~74 ka b.p.Younger Toba Tuff eruption covered more than 1% of the Earth’s surface with >10 cm of ash (Rose and Chesner 1987). The consequences of events of this scale remain poorly constrained, but it has been speculated that projected impacts may be as severe as a ‘volcanic winter’ (Rampino and Self 1992). Indeed, the Toba eruption has been implicated in the putative human ‘bottle-neck’ in civilisation around 70 ka (Ambrose 1998; Rampino and Ambrose 2000), although the global emissions and effects of Toba-scale events remain poorly understood (e.g. Pinto et al. 1989; Bekki et al. 1996; Scaillet et al. 1998; Oppenheimer 2002). Despite their potentially significant impact, little is known—even in general terms—about the global recurrence rates, potential sizes and impacts of the largest and rarest volcanic eruptions.

The problem of determining the frequency of eruptions of the largest events has only been partially addressed (Decker 1990; Rampino 2002), with previous studies based on numerically small or short-timespan datasets. While there is now a detailed inventory of volcanic calderas (e.g. Newhall and Dzurisin 1988), no such compilation exists for the largest eruptions. The frequency and impact of flood basalt eruptions has attracted more attention (Rampino et al. 1988; Courtillot 1999). However, flood basalt events are quite different from explosive caldera-forming events both in style and products (for example, they tend to be clusters of events lasting 104–106 years, rather than single events) and so are not considered further in this analysis.

Defining the ‘largest’ eruptions

Qualitative terms suggesting the ‘enormity’ of particular events abound in the literature, but are only rarely defined in terms of a quantitative measure of size. For example, Simkin and Siebert (1994) list the terms ‘cataclysmic, paroxysmal or colossal’ to describe events larger than about 0.1 km3 of tephra. On a larger scale, events ejecting ≥300 km3 of magma have been termed ‘mega eruptions’ (Zielinski et al. 1996), ‘gigantic eruptions’ (Huff et al. 1992) and ‘great eruptions’ (Rose and Chesner 1987). In recent years, the additional qualitative, but highly evocative, terms ‘supereruption’ and ‘supervolcano’ have caught the popular imagination; and these terms are now beginning to creep into the published literature (Rampino and Self 1992; Rampino 2002). This study concentrates on defining the scale of the very largest eruptions using established quantitative concepts of ‘size’ from the literature.

The most widely used index of volcanic size is the ‘volcanic explosivity index’ (or VEI) of Newhall and Self (1982). The VEI is a semi-quantitative logarithmic scale of eruption size, based on a combination of erupted tephra volume and eruption plume height. On this scale, the largest events (VEI 8) are defined as eruptions with bulk tephra volumes >1,000 km3. For eruptions of this scale, much of the erupted tephra is in the form of ignimbrites, with a lesser component of ash fallout. The last two VEI 8 eruptions occurred ~74 ka b.p.with the eruption of the Younger Toba Tuff from Toba, Sumatra (Rose and Chesner 1987), and at 26.5 ka b.p., with the Oruanui eruption, New Zealand (Wilson 2001). Since there are no historical records of eruptions within even a factor of thirty of a Toba-sized event, and since estimates of the scale of eruptive plumes are model-dependent and difficult to constrain with any certainty for ignimbrite-forming events (e.g. Woods and Wohletz 1991; Bursik and Woods 1996; Wilson 1985; Dade and Huppert 1996), the VEI scale for the largest events is based only on erupted volume.

One significant practical problem with the VEI scale, and indeed with all scales based on volume, is that it is based on estimated ‘bulk volume’ and takes no account of the deposit density. Since the density of freshly emplaced tephra deposits may vary by at least a factor of 3 (e.g. freshly fallen ash may have a density of 600–800 kg m−3, while welded ignimbrites may have densities >2,000 kg m−3), this is potentially a significant problem. For example, two eruptions of 500 km3 of rhyolitic magma might yield one set of strongly welded deposits with a bulk tephra volume of 600 km3 and another set of unconsolidated deposits with a bulk volume of >1,000 km3. In the VEI scale, the first eruption would be classed as VEI 7, the second as VEI 8 (see Fig. 1 and Table 1). ‘Volume’ scales also suffer the perennial problem of interpretation when trying to distinguish between ‘dense rock equivalent’ (DRE) and ‘bulk tephra’ volumes quoted in the published literature.
Fig. 1

The relationship between eruption magnitude, M , and Volcanic Explosivity Index, VEI, for deposits of bulk density 1,000 and 2,400 kg m−3

Table 1

Illustrative relationships between erupted volume, erupted mass and eruption magnitude scale for VEI 8 eruptions (with bulk volumes of 1000–10,000 km3), as a function of bulk deposit density, assuming a melt density of 2400 kg m−3. The magnitude M is defined by M =log (erupted mass, kg)–7.0 (see text, Eq. <equationcite>1</equationcite>)

Bulk deposit density (kg m−3)

Dense rock equivalent volume (km3)

Erupted mass (kg)

Magnitude, M

1,000

417–4,170

1–10×1015

8.0–9.0

1,500

612–6,120

1.5–15×1015

8.2–9.2

2,000

816–8,160

2–20×1015

8.3–9.3

2,400

1,000–10,000

2.4–24×1015

8.4–9.4

Assessments of erupted volumes are also prone to a number of potentially significant sources of error or omission. Large caldera-forming eruptions are associated with three main types of deposit: intracaldera ignimbrite fill; outflow ignimbrite sheets; and tephra fall-out (from Plinian and/or co-ignimbrite ash clouds). It is very rare that the volumes of all three components can be estimated: two of the few examples where this has been achieved are the ~74 ka Younger Toba Tuff eruption (Rose and Chesner 1987) and the 26.5 ka Oruanui eruption (Wilson 2001). Quoted volumes of deposits in the literature rarely include volume estimates for each of these three components, leading to potentially significant uncertainties in total volume estimates.

Lipman (1984) suggested that dense-rock equivalent (DRE) intracaldera deposit volumes (I) are approximately equal in volume to outflow deposit volumes (O). Earlier, Sparks and Walker (1977) showed that some outflow deposit volumes are approximately equal to co-ignimbrite ash volumes (A). Both of these rules-of-thumb appear to be appropriate when compared to the data from the deposits at Toba (I:O:A=1000:1000:800 km3, Rose and Chesner 1987) and Oruanui (420:320:430 km3, Wilson 2001). It is hard to assess the general applicability of this relationship to the ancient products of volcanoes whose deposits are either buried, or have been removed by erosion. It is likely, for example, that the balance between intracaldera fill and outflow volumes will depend on the timing and nature of caldera-formation (e.g. Smith and Bailey 1968; Lipman 1997). For example, in the Yellowstone field, Morgan et al. (1984) noted that intracaldera ignimbrite thicknesses are comparable to outflow sheet thicknesses, suggesting that major caldera collapse post-dated ignimbrite emplacement. Under these circumstances, depending on the scale of the caldera, caldera ‘fill’ volumes could obviously be somewhat smaller than outflow volumes. This is an issue that remains to be resolved. For the sake of consistency, and in the absence of any appropriate alternative, estimates of eruption size are tabulated here based both on quoted deposit volumes (taken from the literature) and adjusted volumes (applying the assumption that total volume=I+O+A) yielding minimum and maximum estimates of eruption sizes (Table 2).
Table 2

Compilation of volume, mass and magnitude estimates for the largest known explosive eruptions

Caldera name

Deposit name

Caldera diameter (km)

Deposit bulk volume (km3)

Deposit density (kg m−3)

Dre volume a (km3)

Mass (kg)

Volume basisb

Adjusted mass (kg)

Minimum magnitude

Maximum magnitude

Age (ma)

Reference

La Garita (Colorado, USA)

Fish Canyon Tuff

100×35

5,000

2,200

4,500

1.2×1016

O+I

1.8×1016

9.1

9.2

27.8

Lipman (1997)

Toba (Indonesia)

Younger Toba Tuff

100×30

2,800

2,400

2,700

6.9×1015

O+I+A

6.9×1015

8.8

8.8

0.074

Rose and Chesner (1987)

Unknown

Lund Tuff

N/A

2,600

2,400

2,500

6.4×1015

O+I

9.6×1015

8.8

9.0

29

Maughan et al. (2002)

Yellowstone (Wyoming, USA)

Huckleberry Ridge Tuff

100×50

2,450

2,200

2,200

5.4×1015

O+1

8.1×1015

8.7

8.9

2.0

Christiansen (1984, 2001)

La Pacana (Chile)

Atana Ignimbrite

60×35

1,600

2,400

1,600

3.9×1015

O+I

5.9×1015

8.6

8.8

4

Lindsay et al. (2001)

Unknown

Millbrig-Big Berntonite

N/A

1,509

2,400

1,500

3.7×1015

A

1.1×1015

8.6

9.0

454

Huff et al. (1996)

Unknown

Green Tuff+SAM

N/A

3,000

1,200

1,500

3.6×1015

O+A

5.4×1015

8.6

8.7

28–30

Ukstins Peate et al. (2003)

Blacktail (Snake River Plain, USA)

Blacktail Tuff

100×60

1,500

2,200

1,300

3.4×1015

O+I

5.1×1015

8.5

8.7

6.5

Morgan et al. (1984)

Emory (New Mexico, USA)

Kneeling Nun Tuff

25×55

1,310

2,200

1,200

3.2×1015

O

9.6×1015

8.5

9.0

33

Elston et al. (1975)

Bachelor (Colorado, USA)

Carpenter Ridge Tuff

20×28

1,200

2,200

1,100

2.9×1015

O+I

4.4×1015

8.5

8.6

27.5

Lipman et al. (1973)

Timber Mountain (Nevada, USA)

Timber Mountain Tuff—Rainier Mesa Member

25×30

1,200

2,200

1,100

2.9×1015

O

8.8×1015

8.5

8.9

11.6

Farmer et al. (1991)

Paintbrush (Nevada, USA)

Paintbrush Tuff—Topopah Spring Member

20

1,200

2,200

1,100

2.9×1015

O

8.8×1015

8.5

8.9

13.4

Farmer et al. (1991)

Bursum (New Mexico, USA)

Apache Springs Tuff

30×40

1,200

2,200

1,100

2.9×1015

O

8.8×1015

8.5

8.9

29–28

Ratte et al. (1984)

Cerro Galan (Argentina)

Cerro Galan Ignimbrite

32

1,050

2,400

1,000

2.5×1015

O+I+A

2.5×1015

8.4

8.4

2.2

Sparks et al. (1985), Francis et al. (1989)

Unknown

Kinnekulle Betonite

N/A

972

2,400

950

2.4×1015

A

7.1×1015

8.4

8.9

454

Huff et al. (1996)

Bursum (New Mexico, USA)

Bloodgood Canyon Tuff

30×40

1,050

2,200

940

2.5×1015

O

7.4×1015

8.4

8.9

29–28

Ratte et al. (1984)

Unknown

Deicke Bentonite

N/A

943

2,400

920

2.3×1015

A

6.9×1015

8.4

8.8

454

Huff et al. (1996)

Uncompahgre (Colorado, USA)

Dillon/Sapinero mesa

20×23

1,000

2,200

900

2.4×1015

O

7.1×1015

8.4

8.8

28.5

Lipman et al. (1973)

San Juan (Colorado, USA)

Sapinero Mesa Tuff

22×24

1,000

2,200

900

2.4×1015

O+I

3.5×1015

8.4

8.5

28.5

Lipman et al. (1973)

Paintbrush (Nevada, USA)

Paintbrush Tuff—Tiva Canyon Member

20

1,000

2,200

900

2.4×1015

O

7.1×1015

8.4

8.8

12.9

Farmer et al. (1991)

Chinati (Texas, USA)

Mitchel Mesa Rhyolite

20×30

1,000

2,200

900

2.4×1015

O+I

3.5×1015

8.4

8.5

32–33

Henry and Price (1984)

Yellowstone (Wyoming, USA)

Lava Creek Tuff

85×45

1,000

2,200

900

2.2×1015

O

6.6×1015

8.3

8.8

0.6

Christiansen (1984, 2001)

Timber Mountain (Nevada, USA)

Timber Mountain Tuff—Ammonia Tanks Member

25×30

900

2,200

810

2.1×1015

I+O

3.2×1015

8.3

8.5

11.4

Farmer et al. (1991)

Porsea (Toba, Indonesia)

Oldest Toba Tuff

100×30

820

2,400

800

2.0×1015

I+A

2.9×1015

8.3

8.5

0.79

Lee et al. (2004)

Kilgore (Snake River Plain, USA)

Kilgore Tuff

60×80

800

2,200

710

1.9×1015

O+I

2.8×1015

8.3

8.5

4.3

Morgan et al. (1984)

Cerro Panizos (Central Andes)

Panizos Ignimbrite

18

652

2,400

640

1.6×1015

O+I

2.4×1015

8.2

8.4

6.1

Ort (1993)

Unknown (Texas, USA)

Barrel Springs Formation

N/A

675

2,200

610

1.6×1015

O

4.8×1015

8.2

8.7

36

Parker and McDowell (1979)

Unknown (Texas, USA)

Wild Cherry Formation

N/A

675

2,200

610

1.6×1015

O

4.8×1015

8.2

8.7

36

Parker and McDowell (1979)

Pastos Grandes (Central Andes)

Sifon Ignimbrite

40×50

1,200

1,200

590

1.5×1015

O

4.4×1015

8.2

8.6

8.3

De Silva (1991)

Unknown (Central Andes)

Huaylillas Ignimbrite

10

1,100

1,200

540

1.3×1015

O+I

2.0×1015

8.1

8.3

5

De Silva (1991)

Platoro (Colorado, USA)

La Jara Canyon Member

18×22

592

2,200

530

1.4×1015

O+I

2.1×1015

8.1

8.3

30

Lipman (1975)

Taupo (New Zealand)

Oruanui

35×25

1,170

1,100

530

1.4×1015

O+I+A

1.4×1015

8.1

8.1

0.0265

Wilson (2001)

San Luis (Colorado, USA)

Nelson Mountain Tuff

18

562

2,200

510

1.3×1015

O

4.0×1015

8.1

8.6

27

Steven and Lipman (1976)

Cerro Galan (Argentina)

Real Grande and Cueva Negra

32

510

2,400

500

1.2×1015

O+I

1.8×1015

8.1

8.3

4.2

Francis et al (1989)

Turkey Creek (Arizona, USA)

Rhyolite Canyon Formation

21

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

25

Latta (1983)

Tucson Mountain (Arizona, USA)

Cat Mountain Rhyolite

25

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

73

Lipman (1976)

Long Valley (California, USA)

Bishop Tuff

20×35

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

0.7

Bailey (1976)

Minarets (California, USA)

Unamed

N/A

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

100

Fiske and Tobisch (1978)

Creede (Colorado, USA)

Snowshoe Mountain Tuff

24

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

27

Steven and Ratte (1965)

Mount Hope (Colorado, USA)

Masonic Park Tuff

15

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

29

Steven and Lipman (1976)

Ute Creek (Colorado, USA)

Ute Ridge Tuff

8

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

29

Steven and Lipman (1976)

Twin Peaks (Idaho, USA)

Challis Creek Tuff

20

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

45

Hardyman (1981)

Cowboy Rim (New Mexico, USA)

Gillespie Tuff

18×26

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

33

Erb (1979)

Juniper (New Mexico, USA)

Oak Creek Tuff

25

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

35

Erb (1979)

Organ (New Mexico, USA)

Cueva Soledad Rhyolite

16

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

32

Seager (1981)

Socorro (New Mexico, USA)

Hells Mesa Rhyolite

25×35

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

33

Osburn and Chapin (1983)

Blue Creek (Snake River Plain, USA)

Blue Creek Tuff

30×55

500

2,200

450

1.2×1015

O

3.5×1015

8.1

8.5

5.6

Morgan et al. (1984)

aFor convenience, and to facilitate comparison, dense rock equivalent (DRE) volumes are scaled assuming a uniform density of 2450 kg/m3: the erupted mass is the important parameter

bOutflow volume ( O), intracaldera volume ( I) or ash fall volume ( A)

Caldera size has been suggested as a proxy for eruption size (e.g. Scandone 1990), and analysis of the statistics of occurrence of calderas of different scale has been used to infer frequencies of large magnitude events (e.g. Decker 1990). The use of caldera size, either as measured diameter or surface area however, is not a straightforward measure of eruption scale. Calderas may be piecemeal or nested structures (e.g. Lipman 1997) associated with single or multiple large events (e.g. Toba, 3 events—Chesner 1998; Yellowstone, 3 events—Christiansen 1984, 2001; Santorini, at least 4 eruptions—Druitt et al. 1989, 1999) and are frequently eroded, masking the original cauldron. Subsequent resurgence and infill can hide the extent of subsidence of the original caldera, making depth and volume estimates difficult. For the oldest events, any caldera that may have been associated with the eruption is invariably hard to find (e.g. the North American Ordovician Bentonites, Huff et al. 1992). In the case of other deposits such as the voluminous ignimbrites of the Bolivian and Chilean Andes, the caldera may be completely buried beneath the ignimbrite shield (Baker 1981; Francis et al. 1984; Lipman 1997).

Given the uncertainties in parameters other than direct estimates of the amount of erupted material, and the equivocal nature of ‘volume’-based estimates alone, a logarithmic magnitude scale of eruption size is preferred, that is continuous and based on erupted mass (Pyle 1995, 2000). The magnitude scale, M , is defined by:
$$M = \log _{{10}} {\left( m \right)} - 7.0$$
(1)
where m is the erupted mass in kg. The magnitude scale is defined in this manner so that the scale is close to the original definition of the VEI scale but also follows earlier definitions of magnitude (Tsuya 1955). On this scale, M8 eruptions have masses in the range 1015 kg≤ m <1016 kg, and M9 eruptions have eruptive masses 1016 kg≤ m <1017 kg. In terms of volume, M8 eruptions may have bulk tephra volumes of ~400–10,000 km3, depending on the bulk density of the deposit (which may range from 1,000–2,500 kg m−3), and dense rock equivalent (DRE) volumes, for typical rhyolitic compositions, of ~400–4,000 km3. The general relationship between the magnitude scale and the volcanic explosivity index is shown in Fig. 1, for two representative deposit densities. A representative melt density of 2,450 kg m−3 is adopted for estimating DRE volumes, based on the typical ranges of densities calculated for a number of well-studied large volume deposits (Fig. 2).
Fig. 2

Calculated magma densities for six M8 eruptions. Densities were calculated on a water-free basis using the computer program ‘Magma’ (K. Wohletz), based on the published rock composition, and at the quoted eruption temperature (http://www.ees1.lanl.gov/Wohletz/Magma.htm)

The dataset

The largest eruptions, of magnitude 8 and larger and involving eruptions of >1015 kg of magma, are considered here. A search of the published and accessible literature has revealed 47 deposits formed by eruptions of M8 or larger that have been reported to date (in fact, all deposits in Table 2 represent events larger than M8.1 or 1.2×1015 kg). The ages, locations and magnitude of these deposits are summarised in Table 2. As we discuss later, this dataset is incomplete, and will be augmented in future as new deposits are discovered, or new correlations are made between known deposits.

Of the 47 deposits described in the literature, 40 have associated calderas (Table 2). As Fig. 3 shows, there is no simple relationship between caldera size and the estimated DRE volume of the erupted products based on the estimated maximum magnitude of the eruption (Table 2; see also Fig. 4). The poor fit may be a consequence of two aspects of the data: uncertainty in the precise mass of any single deposit; and uncertainty in the scale of the individual caldera collapse event that was linked to an individual eruption. It is clear, for example, that there are many published estimates of eruption volume which may be barely more precise than an order of magnitude: as is clear from Table 2, many deposits are registered simply as having volumes of ‘500 km3’, ‘1,000 km3’ and so on. More precise data on both erupted mass and caldera size are needed before much confidence can be found in the link between the two.
Fig. 3

Log-log plot of maximum dense rock equivalent deposit volume (km3) against caldera area (km2). Contours indicate the hypothetical thickness of the layer of magma extracted during eruption, assuming that layer thickness=(erupted volume/caldera area). If the cross sectional area of the magma reservoir approximates the scale of the caldera area, most large eruptions draw down of the order of 1–10 km thickness of melt. For these very large eruptions, there is no clear relationship between erupted volume and caldera area

Fig. 4

Global map showing the general distribution of sites of large explosive eruptions and selected large silicic provinces, distinguishing between regions active over the past 17 Ma (the onset of volcanism in the Snake River Plain province) and those regions older than 25 Ma. CN California (<1 Ma) and Nevada (11–13 Ma); EP Ethiopian Plateau (27–31 Ma); SM Sierra Madre Occidental (27–34 Ma); WS Whitsunday Province (105–120 Ma); SRP-Y Snake River Plain–Yellowstone province (<16.5 Ma), SW south-western USA (Texas, Colorado, Idaho, New Mexico, Arizona; 45–25 Ma)

In the remainder of this paper, a preliminary analysis of the recurrence rates of these largest eruptions is developed, in an attempt to place reasonable limits on the expected frequencies of large magnitude eruptions. A more thorough analysis of large eruptions (>1013 kg) awaits the completion of an adequate database of such events, which is currently being compiled by the IAVCEI Commission for Explosive Volcanism (http://www-volcano.geog.cam.ac.uk/database).

Discussion

Recurrence rates of the largest volcanic eruptions

An analysis of the frequency of eruptions of M8 and larger is a first step to understanding the likelihood of future large events. Previous workers have suggested that the ‘largest eruptions’ (defined as an eruption yielding a bulk volume ≥1,000 km3) may occur as frequently as once every 50,000 years (Decker 1990). However, Decker’s study relied on an incomplete data set, as it was based on only nine supposed VEI 8 eruptions over the past 2 Ma, many of whose volumes were estimated from gross caldera dimensions. In fact, only two of these events were sufficiently large to qualify as M8 eruptions. Decker’s ‘1 per 50,000 year’ estimate of large eruption frequency relied on a qualitative extrapolation of event frequency from the short-term record of much smaller events.

Our compilation reveals 42 known eruptions larger than M8 over the past 36 Ma. This yields a minimum time-averaged estimate of eruption frequency of 1.1 events/Maover 36 Ma. Closer inspection of the record of the last 36 Ma, however, reveals two pulses of greatly increased volcanic activity (Fig. 5). These pulses, lasting from ca. 36–25 Ma and 13.5 Ma–present, approximately coincide with increased rates of deep-sea volcanic ash sedimentation and principal global climate cooling steps in the Cenozoic (e.g. Sigurdsson 2000; Sigurdsson et al. 2000). The period from 36–25 Ma encompasses the most active phase of the San Juan volcanic field (Colorado, USA), and includes a total of 22 M8 eruptions and 1 M9 eruption, yielding and a minimum large eruption frequency of 2 events/Ma. The present ‘flare-up’ includes 19 eruptions in the last 13.5 Ma and a minimum event frequency of ~1.4 events/Ma (or 2 events/Ma for the past 6 Ma). The clustered nature of volcanism revealed by our compilation adds weight to the suggestion that the rate of occurrence of the largest eruptions is non-uniform, comprising discrete ‘packets’ of increased activity (e.g. McBirney et al. 1974; Sigurdsson 2000) that are presumably controlled by regional or global-scale tectonic changes.
Fig. 5

Histogram (at 2 Ma intervals, with age of the midpoint given on the x axis) showing the time distribution of the 42 known eruptions of M8 and larger over the past 46 Ma. Key geographical areas are highlighted (New Mexico, Colorado, Nevada are in the south-western USA; SRP is the Snake River Plain-Yellowstone province of western USA). Although the record is incomplete, the bimodal pattern of known eruptions may be real, and probably reflects the control of global tectonics on rates of occurrence of large eruptions. Known events from the past 13.5 Ma are dominated by eruptions in the Central Andes and the Snake River Plain-Yellowstone province, while events between 25 and 38 Ma are dominated by eruptions in Colorado and New Mexico, south-western USA. No large silicic provinces are known from the period 17–25 Ma

Settings of large eruptions and the completeness of the geological record

The volcanoes that produce M8 and larger eruptions are associated with several different tectonic regimes. The most significant of these is accreted continental margins associated with the extension of abnormally thick continental crust (e.g. Tertiary North America and Mexico). M8 eruptions are also known from other continental margin settings (e.g. South America, Indonesia and New Zealand) and areas of plume-related intraplate magmatism (e.g. Snake River Plain–Yellowstone; Ethiopian Plateau, Africa). Figure 5 suggests that individual provinces associated with large volume eruptions tend to have lifetimes of <6–8 Ma. The only notable exception is the 16-Ma lifetime of the Yellowstone-Snake River Plain ‘hotspot’ sequence, which comprises a time-progression of volcanism moving through a sequence of shorter-lived volcanic fields (e.g. Morgan et al. 1984; Perkins and Nash 2002).

The largest silicic volcanic provinces, in terms of gross erupted volumes, are those associated with continental breakup (e.g. Chon Aike province of South America) and back-arc related magmatism (e.g. Sierra Madre Occidental range in Mexico; see Bryan et al. 2002; Table 3, Fig. 4). These provinces are characterised by large volumes of silicic material (>104–105 km3) erupted over short periods of time (typically <5–20 Ma), with time-averaged eruption rates of the order of 0.001–0.1 km3 yr−1 (Table 3; see also Crisp 1984). Despite the potential of these provinces as sites of very large eruptions, few have yet been recognised. It is only recently, for example, that the first large magnitude (M8.6) eruption has been reported from the Oligocene of the Ethiopian Plateau (Ukstins Peate et al. 2003).
Table 3

Large silicic provinces with total estimated (bulk) volumes >104 km3, arranged in increasing age order, based on compilations by Crisp (1984) and Bryan et al. (2002)

Province

Known eruptions >M8

Total silicic magma volume (km3)

Total time span (Ma)

Eruption rate (km3 yr−1) a

Crustal thickness, km

Settingb

Ref.

(a) Provinces with one or fewer known M8 eruptions

Taupo, New Zealand

1

1.6×104

<2

8×10−3

30–40

S

1

Snake River Plain, USA

-

1.4×104c

16–8

2×10−3

30–45

I

2

Ethiopian Plateau, Africa

1

6×104

31–27

6×10−2

30–40

I

3

Sierra Madre Occidental, Mexico

3.6×105

34–27

2×10−2

55

S

4, 5

Whitsunday Volcanic Province, Australia

-

105

120–105

7×10−3

35–45

C

5

Parana-Etendeka, South America, southern Africa

-

1.6×104

132

3×10−2

n.k.

C

6

Karoo, South Africa

-

3.5×104

179

7×10−2

20–37

C

7

Chon Aike, South America

-

2.3×105

188–153

1×10−2

n.k.

C

8

(b) Provinces with five or more known M8 eruptions

Eastern Snake River Plain, Yellowstone, USA

5

104

<6.5

2×10−3

30–45

I

9, 10

Altiplano-Puna, Central Andes, South America

6

1.5×104

10–2

2×10−3

50–70

S

11

San Juan Mountains, Colorado, USA

9

1.8×104

30–27

5×10−3

45–50

S

12

aTotal silicic magma volume/province lifetime; n.b. provinces were not necessarily active over the whole timespan quoted

bTectonic setting: C Magmatism associated with continental breakup; I Intraplate magmatism; S Subduction- or back-arc-related magmatism; n.k. not known

cVolume based on distal ash fall tuff data alone

References: 1 Wilson et al. (1984); 2 Perkins and Nash (2002); 3 Ukstins Peate et al. (2003); 4 Cameron et al. (1980); 5 Bryan et al. (1997); 6 Garland et al. (1995); 7 Cleverly et al. (1984); 8 Pankhurst et al. (1998); 9 Christiansen (1984); 10 Morgan et al. (1984); 11 de Silva and Francis (1991); 12 Lipman (1984)

Table 3 lists some well-known but, as yet, poorly studied areas of silicic volcanism where it is likely that deposits associated with individual large events remain to be discovered. In particular, the widely distributed ignimbrite fields of the Sierra Madre Occidental (Mexico) are thought to be among the most extensive in the world (e.g. McDowell and Clabaugh 1979) but, as yet, no deposits from any individual eruption of M8 or larger have been reported. Equally, the long-lived Yellowstone-Snake River Plain ‘hotspot’ province (Smith and Braile 1994) has an extensive ash-fall tuff record suggesting that it has experienced many tens of eruptions with volumes in excess of 250 km3 over the past 16 Ma (Perkins and Nash 2001). Volumes of associated major ash-flow tuffs have, however, only been determined for deposits of the past 8 Ma (Morgan et al. 1984; Christiansen 2001). It is likely that several large volume eruptions associated with the earlier stages of the province, between 16 and 10 Ma, remain to be identified.

The products of the three best studied large silicic provinces, the San Juan volcanic field (with 9 M8 or larger events), the Yellowstone-Snake River Plain province (5 M8 events) and the Altiplano-Puna region of the Central Andes (6 M8 events) are all dominated by deposits associated with the very largest eruptive events. Each of these fields are characterised by one M8 event per 2,000–3,000 km3 of erupted silicic magma. The Taupo region, on the other hand, has yielded one M8 event associated with ~16,000 km3 silicic magma. On this basis, a province such as the Sierra Madre Occidental volcanic field (with 3.6×105 km3) may be the site of deposits of tens of as yet uncorrelated M8 and larger eruptions, while the provinces listed in Table 3a may account for many tens of undiscovered M8 events from the past 190 Ma.

Many of the largest eruptions apparently involved the evacuation of compositionally homogenous and remarkably crystal-rich (30–45%) silicic magmas, often exhibiting abundant evidence for crystal recycling: these are the ‘monotonous intermediates’ of Hildreth (1981). This category includes several of the very largest events, notably the Fish Canyon Tuff (e.g. Whitney and Stormer 1985; Bachmann et al. 2002), the Toba Tuffs (Chesner 1998; Gardner et al. 2002) and several Andean ignimbrites (e.g. Cerro Galan: Francis et al. 1989; Atana: Lindsay et al. 2001b). This observation raises the question of whether some specific and unusual circumstances (e.g. the remobilisation of former plutons) are required for the formation, or survival, of particularly voluminous magma chambers (e.g. Bachmann and Bergantz 2003; Jellinek and DePaolo 2003). This issue, along with the question of how such large-volume eruptions are initiated, remains to be resolved.

Rates and sizes of the largest volcanic eruptions

The largest eruptions on Earth are, by their nature, rare events, whose size and frequency cannot be deduced from observations of smaller events. For example, extrapolating the power-law functions that describe the relationship between size and frequency of small to medium-sized events to assess the behaviour of rare large events is unreasonable, since this extrapolation suggests that one M8 eruption should occur about every 1,200 years (e.g. Decker 1990; Pyle 1995), yet the last known such event was at 26.5 ka.

Two approaches may be used to derive estimates of the likely scale and occurrence rate of large events. The first approach, rank order statistics, provides a method of describing the nature of the underlying distribution and thereby of estimating the ‘maximum likely scale’ of the next largest event in a distribution, even from samples of only a few tens of observations (Sornette et al. 1996; Pyle 1998). Consider a measure of size of an eruption Z, for example eruptive mass. If the N largest events observed over a period of time are ranked in order of size, Z1> Z2>.... Z n, and then plotted on a log-log graph of Z i against i, the data define a distribution from which estimates of the scale of the ‘next largest’ extreme events can be determined (Sornette et al. 1996). For a system showing where the extreme events show a power-law dependence of frequency on size, an estimate of the size of the next ‘largest’ eruption can be found by ranking the N largest events Z2> Z3>.... Z n+1and finding the value for Z1 (Pyle 1998).

Analysis of the largest eruptions of last 13.5 Ma can be used to assess the likely scale of the next eruption in the sequence. In Fig. 6, the maximum estimated magnitudes of all large eruptions for the past 13.5 Ma are plotted against rank order. The data define a coherent curve, which shows a ‘plateau’ of size for the largest (lowest ranked) events. From this, it can be seen visually that the next event in the sequence that will be larger than any event seen for the past 13.5 Ma would still not be expected to be larger than M9, i.e. erupting <1016 kg of magma.
Fig. 6

Rank-order plot (see Pyle 1998) of eruption magnitude against log(rank) for M8 events and larger for the last 13.5 Ma. The expected size of a future eruption larger than any observed in the last 13.5 Ma (which will then become rank=1 on this plot) may be estimated from the trend of this plot for the lowest ranked events; such an event would have an eruption magnitude <M9

There are clearly many fewer known M8 and M9 eruptions than would be expected from simple extrapolation of the size-frequency relationship for smaller eruptions. This is not surprising, since the scale of the very largest events must be limited by the scale of the system; for example, it is to be expected that a single eruption could not exceed the scale of the crust within which magma is stored. For this same reason, the frequencies of rare ‘large’ events such as floods and earthquakes also diminish more rapidly than expected from a simple log(number)-log(size) extrapolation (e.g. Sornette 1996). In the case of large ignimbrite eruptions, one would not expect to encounter individual events larger than of the order of the scale of the cube of the crustal thickness, or~203–303 km3.

To make a quantitative assessment of the frequency of large eruptions requires application of ‘Extreme Value Theory’ (see for example Embrechts et al. 1997; Woo 1999). This is a statistical approach that uses a general mathematical function to describe the ‘tail’ of size-frequency distributions, and has the general form
$$F{\left( x \right)} = \exp {\left( { - {\left( {1 - k{\left( {x - \mu } \right)}/\sigma } \right)}^{{1/k}} } \right)}$$
(2)
where the parameters of the distribution μ and k are real numbers, and σ >0 (see, for example, Woo 1999, p. 110). Distributions with k =0 are known as Gumbel distributions, Weibull distributions are those with k >0, while Frechet distributions have k <0.
Given that the system is likely to have an upper limit of size, one may use the Weibull function to describe the tail of this distribution (Embrechts et al. 1997, p. 34). In this case, the relative frequency F of eruptions larger than magnitude M may be described by F =exp(- aM b) where a >0, b >1. Approximate ‘upper limit’ fits of a Weibull distribution to the large eruption data from 0–13.5 Ma, and for the period 25–36 Ma, are shown in Fig. 7. These illustrative fits are based on the maximum estimated magnitudes (Table 2), and are considered to give upper bounds for the frequency of large eruptions.
Fig. 7

Illustrative fits of the Weibull function (see text) to the tail of the volcanic eruption size-frequency diagram for the largest events. In these plots we estimated the fraction of events larger than any threshold size by calculating the expected total number of events of M2 and larger, assuming a similar rate of volcanism as at the present. These fits represent likely upper limits to the true size-frequency pattern as the magnitudes used here are based on the inferred maximum erupted mass, from Table 2. The Weibull function that describes the tail of a bounded distribution is given by F =exp(- aM b) where a >0, b >1 and M is the magnitude (Embrechts et al. 1997, p. 34). In these two plots: a =0.065, b= 2.6 for the period 0–13.5 Ma; and a =0.0625, b =2.6 for 25–36 Ma

From this analysis, the upper and lower bounds for the size-frequency relationships of eruptions of M8 and larger may be found. Our best estimate of the ‘lower’ bound has Weibull parameters a=0.0249, and b=3.13, and predicts a frequency for M8 eruptions of 1.4 events/Ma, and M9 eruptions of <10−4 events/Ma. The upper bound has Weibull parameters a=0.0625 and b=2.6, and predicts a frequency for M8 eruptions of 22 events/Ma, and M9 eruptions of 0.15 events/Ma. The upper bound derived here (22 events/Ma, or 1 event per 45 ka) is close to Decker’s (1990) estimate of large eruption frequencies.

The size-frequency relationships for all eruptions larger than M4 are summarised in Fig. 8. This figure is based on compiled eruption rates for the past 2,000 years for eruptions of up to magnitude 7, and on the data compiled here for larger events. From the approximate Weibull curves, shown on Fig. 8, one can estimate a ‘practical’ limit of eruption size–being the scale of event for which the frequency falls to less than one event over Earth history. For the ‘low’ frequency curve, which might apply to the current state of the Earth, the practical upper limit to eruption size is a magnitude of 9.2 (~1.6×1016 kg)–or an eruption of about the scale of the Fish Canyon Tuff. For the ‘high’ estimate, this limit equates to an eruption magnitude of 10.1 (~1.2×1017 kg), an equivalent volume of 363 km3.
Fig. 8

Composite size- frequency plot for explosive volcanic eruptions larger than M4. Rates of occurrence of eruptions of M4–M7 are based on analysis of datasets for eruptions of the past 2,000 years (Simkin and Siebert 1994; Pyle 1995). Illustrative ‘high’ and ‘low’ Weibull fits to the extremal eruption data are used to provide upper and lower bounds on rates of eruptions >M7 (see text)

Comparative rates of occurrence of large volcanic eruptions and asteroid impacts

The estimates of the rates of occurrence of large explosive eruptions derived above allow a direct comparison between the scale and frequency of these events and other large magnitude natural phenomena, such as bolide impacts, hurricanes and earthquakes. Analysis of the potential scale and effects of bolide impacts on the earth has provoked a good deal of interest and analysis (e.g. Morrison et al. 1994; Grady et al. 1998; Chapman 2002). Of course, there have never been any documented fatalities from asteroid impacts, compared to the >250,000 known to have died in volcanic eruptions of the past four centuries (Simkin et al. 1994; Simkin et al. 2001). How does the size and frequency of the largest volcanic events compare with bolides?

Energy release is one parameter that may be used, at least approximately, to gauge the relative scale of bolide impacts with large eruptions (a similar analysis has been carried out for earthquakes and impactors; e.g. Grieve 1998). The energy released during a volcanic eruption comprises two main components; the kinetic energy of the ejecta, and thermal energy. Seismic energy release is negligible in comparison (Pyle 2000). In even the most violent volcanic eruptions, the kinetic energy term is relatively small, probably <5% of the total energy release (e.g. Yokoyama 1957; Hedervari 1963; Pyle 2000). Thermal energy release from volcanic eruptions results from cooling of melt from high temperatures, and, to a smaller extent, from solidification. Allowing for ~10% release of latent heat ( L) during eruption, the enthalpy release from magma on eruption is given approximately by
$$H = {\left( {C_{p} \Delta T + 0.1\,L} \right)}m$$
(3)
where C pis the specific heat capacity, ΔT is the temperature difference between the magma and its surroundings, L is the latent heat and m is the erupted mass. For rhyolite, given these assumptions, the enthalpy release on eruption is ~1.05 MJ kg−1 (Pyle 1995), while the kinetic energy, assuming eruption of material at the local speed of sound (~300 m s−1 in a dusty gas), is ~0.045 MJ kg−1. One other factor that will contribute to the eruption energy is the condensation of magmatic water vapour, which will release latent heat of ~0.02 MJ per kg of rock for every wt% of dissolved water released, or a total of ~0.1 MJ kg−1 for water-rich magmas. The total energy yield of a rhyolitic eruption is therefore ~1–1.2 MJ kg−1.

In an eruption plume dominated by fine particles much of this energy is available directly to be converted into work, driving buoyant rise of the eruption plume (e.g. Sparks et al. 1997). On this basis, the largest volcanic eruptions (>1015–1016 kg) will involve a total energy release of >1021–1022 J.

In terms of energy release per event, large volcanic eruptions are the largest high-intensity terrestrial phenomena known. The other terrestrial phenomena whose primary impact extends across lengthscales of 103 km or more include large earthquakes (largest events release ~1019 J, Kanamori 1977) and hurricanes (total potential energy as latent heat of up to ~1021 J, of which kinetic energy comprises ~1%; Rodgers et al. 1995). For comparison, the total energy stored in the world’s nuclear arsenal is ~1020 J (Grieve 1998). The rate at which energy is released during these events is similar, ranging from ~1017 W for a Richter magnitude 9.5 earthquake lasting ~100 s, to 1016 W for a large eruption lasting ~105 s.

The energy released by a bolide impact may be estimated from the kinetic energy necessary to create the craters observed on the Earth’s surface (e.g. Shoemaker 1983; Hughes 2003). Most impacts are thought to be due to stony meteorites or asteroids that typically strike the Earth at ~20 km s−1 (Chapman and Morrison 1994; Hughes 2003). A 2 km diameter impactor, for example, will have a kinetic energy of ~1021 J.

In Fig. 9, the energy release and frequency of impacts and large volcanic eruptions are compared. Despite the uncertainty, it is clear that simply in terms of energy release per event, volcanic events with energies of 1020–1022 J (1014–1016 kg, or M7–M9) are considerably more frequent than impact events of the same energy. On timescales of ~100 ka and less, the largest volcanic eruptions (M7 and M8) involve a greater energy release than the largest expected impactor. While it is not clear how simple energy release might scale with environmental effects, this analysis suggests that the hazard from impactors exceeds that due to large-scale terrestrial phenomena only for events with a typical return period of >105 years.
Fig. 9

Comparison of the energy and frequency of large volcanic eruptions and impacting asteroids. The impactor curve is based on estimates of the rate of cratering of Earth’s surface over the recent past (Hughes 2000). The volcanic eruption curves are based on the upper and lower estimates of eruption frequencies of 22 events/Ma (high) and 1.4 events/Ma (low). For event energies of up to about 1021–1022 J (a frequency of ~10 events/Ma) volcanic eruptions are more frequent than asteroid collisions of equivalent energy

Time-averaged mass eruption rates and probability of occurrence of M8 and larger events

Our analysis of the frequency of occurrence of the largest volcanic eruptions allows us to compare the time-averaged mass flux of magma from these events to that from smaller eruptions, and also allows us to quantify the likelihood of future large magnitude events. Our best estimate for the frequency of M8 and larger events is that it lies between the bounds ~1.4 and 22 events/Ma. This corresponds to a time-averaged erupted magma flux of ~60–1,000 kg s−1 (Table 4). This is significantly less than from eruptions of magnitude 7, for example, and accounts for <3% of the total time-averaged flux of magma from explosive volcanic eruptions. Thus, the largest volcanic eruptions are individually significant events with considerable impacts, but they account for relatively minor time-averaged fluxes of energy and matter to the Earth’s surface due to their rarity.
Table 4

Time-averaged mass eruption rates from explosive eruptions of magnitude 2 and larger, assuming frequencies of M8 events of 1.4 to 22 events/Ma, and M9 of <0.02 to 0.15 events/Ma. Data for magnitudes 2 to 7 from Pyle (1995)

Magnitude

Tephra mass flux (kg s−1)

2

2,800

3

3,700

4

4,700

5

6,000

6

7,600

7

9,500

8

60–1,000

9

<6–50

Total

34,000–35,000

During the past 13.5 Ma, there have been 19 eruptions of M8 and larger, i.e. a minimum eruption rate of ~1.4 events/Ma. Assuming an independent process and a constant mean occurrence rate (λ), the binomial distribution may be found during a period δ where δ is divided into q small intervals Δt (e.g. De La Cruz Reyna 1996). In the limit Δt → 0, q → ∞, the discrete Poisson distribution is found:
$$P{\left( x \right)} = {\left( {\lambda \delta } \right)}^{x} \exp {\left( { - \lambda \delta } \right)}/x!$$
(4)
If it is assumed that during the past 13.5 Ma, large eruptions can be described as a homogeneous Poisson process with parameter λ ~1.4 events/Ma, it is possible to derive some order of magnitude assessments of the probability of ≥ N large magnitude eruptions (where x = N) occurring in the near future (where x =the time period considered, Table 5).
Table 5

Likelihood of future large magnitude eruptions, assuming homogeneous Poisson behaviour. A frequency of 1.4 events/Ma corresponds to the known (minimum) large eruption rate since 13.5 Ma; 2 events/Ma is approximately the known large eruption rate between 25 and 36 Ma, and for the period 0–6 Ma

Eruptions M8 and larger

Poisson λ

1.4 events/Ma

2 events/Ma

22 events/Ma

Probability of ≥1 event in next 100 years (%)

0.014

0.02

0.2

Probability of ≥1 event in next 1 Ma (%)

75

86

100

Time for 1% chance of an eruption (years)

7,200

5,000

460

Time to 95% probability of an eruption (Ma)

2.1

1.5

0.14

On the basis of our compiled record of past eruptions, there is at least a 75% probability of one M8 eruption occurring within the next million years, while there is a 1% chance of an M8 eruption occurring within the next 460–7,200 years.

Conclusions

A compilation of all known eruptions larger than 1015 kg (magnitude ≥M8) reveals 47 such events from the Ordovician to the present, and 42 eruptions of M8 and larger in two ‘packets’ of activity over the last 36 Ma. Many of the largest volcanic eruptions are associated with voluminous silicic magmatic provinces, with relatively thick continental crust and high time-averaged eruption rates.

Analysis of the recurrence rates of M8 and larger events suggest that, during periods of widescale magmatism (or ‘flare-ups’), such events occur with a frequency of 1.4–22 events/Ma. The rapid drop of eruption frequency with eruption size suggests that there is an upper limit to the scale of the largest event possible, imposed either by the maximum sustainable magma chamber size or crustal thickness. At the current time, this upper limit is ~1.6×1016 kg, or M9.2.

In terms of energy release, large volcanic eruptions are more frequent on all timescales up to ~100 ka than impact events of a similar energy. On a time-averaged basis, though, M8 and larger eruptions contribute <3% of all the magma erupted explosively at Earth’s surface. Further work is needed to better understand the potential environmental effects of individual large (M8 and M9) eruptions and the implications for hazard and risk assessment of the frequent M7 eruptions.

Acknowledgements

We would like to thank Shan De Silva, Chris Newhall, Peter Lipman and Roberto Scandone for providing data. We would also like to thank Steve Sparks, Brian Dade, Steve Self, Paul Cole and Guido Giordano for discussion. We thank R. Cioni, K. Cashman, R. Santacroce and J. Stix for reviews that helped to improve the quality of the manuscript. BGM is supported by the Natural Environmental Research Council.

Copyright information

© Springer-Verlag 2004