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Measuring the size of large explosive eruptions
The size of large explosive eruptions is commonly measured by the volume of erupted ejecta (tephra) (or alternatively, magma measured in DRE, dense rock equivalent) and expressed on the logarithmic VEI scale.
Plinian eruptions rank VEI 5 or higher, i.e. erupt more than 1 cubic kilometer tephra. VEI 6 equals > 10 km3, VEI 7 > 100 km3.

The measurement of the volume of tephra erupted during an explosive eruption is actually a difficult task, but simplified, it can be found by integrating the surface of the deposit with its thickness.
This direct method relies heavily on a sufficiently large number of field measurements of the original, undisturbed deposit thickness in an area representative for the total deposit. This is only available for extremely few and usually recent eruptions (e.g. Mt Spurr 1992 eruption).
In most other cases, parts of the deposit need to be interpolated. To do this, is one of the main tasks of physical volcanology. Quantitative models have been developed that describe the relationship between total erupted magma volume, magma eruption rate, eruption duration, the height of the eruption column, the type of tephra involved, degree of fragmentation, the type of deposition (e.g. fall versus pyroclastic flows), wind dispersal from eruption columns, and other factors.
These models were mainly developed in the past 3 decades and could be successfully calibrated with a number of well-observed or documented eruptions (e.g. Vesuvius 79 AD, Mt. St. Helens 1980, Pinatubo 1991 etc.). In addition, they are being refined with time and each major eruption that can be used to test the model.

The size of the Minoan eruption

Distribution of the Minoan ash
Distribution of the Minoan ash
The Minoan eruption (around 1613 BC) was one of the largest plinian eruptions on earth in the past 10,000 years.
The so-far established size estimations were largely based on field data from Santorini, neighboring islands, from the sea bed, and western Turkey, where the deposit can still be found in lake deposits.
The traditional and to-date most widely accepted value of the erupted magma volume of the Minoan eruption ranges between 30-40 cu km, corresponding to a total tephra volumen of about 80-90 km3, and takes into account various field data obtained and modeling done between around 1970-1990 (e.g. Sigurdsson et al, 1990).
Recently, new outcrops of the Minoan tephra (e.g. 2 m on Anafi Island, on the sea floor around Santorini and elsewhere) have become available. These findings suggest that the eruption could be larger than originally thought, ranking in fact as VEI 7, which would make it perhaps the second largest explosive eruption in historic time on the planet (after Tambora 1815).
The following is the original press release published at the University of Rhode Island about this hypothesis.

Santorini eruption much larger than originally believed

The Minoan pumice layer at the south coast of Santorini
The Minoan pumice layer at the south coast of Santorini
An international team of scientists has found that the second largest volcanic eruption in human history, the massive Bronze Age eruption of Thera in Greece, was much larger and more widespread than previously believed.

During research expeditions in April and June, the scientists from the University of Rhode Island and the Hellenic Center for Marine Research found deposits of volcanic pumice and ash 10 to 80 meters thick extending out 20 to 30 kilometers in all directions from the Greek island of Santorini.

“These deposits have changed our thinking about the total volume of erupted material from the Minoan eruption,” said URI volcanologist Haraldur Sigurdsson.

In 1991 Sigurdsson and his URI colleague Steven Carey had estimated that 39 cubic kilometers of magma and rock had erupted from the volcano around 1600 B.C., based on fallout they observed on land. The new evidence of the marine deposits resulted in an upward adjustment in their estimate to about 60 cubic kilometers. (The eruption of Mount Tambora in Indonesia in 1815 is the largest known volcanic eruption, with approximately 100 cubic kilometers of material ejected.)

An eruption of this size likely had far-reaching impacts on the environment and civilizations in the region. The much-smaller Krakatau eruption of 1883 in Indonesia created a 100-foot-high tsunami that killed 36,000 people, as well as pyroclastic flows that traveled 40 kilometers across the surface of the seas killing 1,000 people on nearby islands. The Thera eruption would likely have generated an even larger tsunami and pyroclastic flows that traveled much farther over the surface of the sea.

“Given what we know about Krakatau, the effects of the Thera eruption would have been quite dramatic,” said Carey, a co-leader of this year’s expeditions. “The area affected would have been very widespread, with much greater impacts on the people living there than we had considered before.”
Press release by Todd McLeish / University of Rhode Island, republished with kind permission

Cited references
Sigurdsson, H., et al. (1990) "Assessment of mass, dynamics and environmental effects of the Minoan eruption of Santorini Volcano", in: Hardy, D. A., et al. "THERA AND THE AEGEAN WORLD - PROCEEDINGS OF THE 3rd INTERNATIONAL CONFERENCE", Vol. 3, p. 100-112

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