Note added February 8, 2021: An example of a rare, high-consequence event occurred today in India: a chunk of a Himalayan glacier broke off and unleashed a flood that took out one dam and seriously affected another, took out two hydroelectric power plants and killed at least 14 with another 170+ missing. This is not only an example of a rare event, but also of a compound event: a piece of glacier fell off, created a wall of water and mud that barrelled down a valley, and destroyed dams and infrastructure. It is also a combined natural disaster and engineering disaster. More info here.
As a member of the Resilient America Roundtable of the National Academy of Sciences, Engineering and Medicine, I gave a presentation in February 2019 about low-probability events with high-consequences should they occur. Here I summarize that presentation, giving examples of such events and suggestions for research, educational, and organizational challenges. Examples that we most commonly think of when considering "rare" events are big hydrologic floods, floods from dam failures, volcanic eruptions and ash clouds, earthquakes and earthquake-induced tsunamis, landslides, and wildfires. Less frequently considered are solar eruptions with the ejection of coronal material (CMEs), meteorite impacts and combination events (e.g., and earthquake plus a tsunami in the midst of a pandemic.
Natural floods (Mississippi River): For reference, during the recent "catastrophic" flood of the Mississipi River in 2008 that severely damaged Cedar Rapids (Iowa), the discharge at St. Louis was about 700,000 cfs. In the Great Flood of 1993 it was 1,030,000 cfs and in 1844 it was 1,300,000 cfs.
Natural floods (Colorado River, Grand Canyon), see attached graphic: The catastrophic flood on the Colorado River in 1983 that nearly took out Glen Canyon Dam and caused serious environmental and geomorphic changes for nearly 300 miles, had a discharge of ~100,000 cfs. For comparison, the discharge of the 1884 flood was about 300,000 cfs and a flood in about 550AD had a discharge of ~500,000 cfs.
Unnatural floods: With the aging infrastructure of U.S. dams, we should remember the 1889 Johnston Flood (Pennsylvania) that killed 2209 people in 10 minutes; the St. Francis Dam failure in Los Angeles that killed 600 people in 1928; the 1996 Teton earthen dam failure in Idaho that caused $2B in damages, and the 2017 Oroville Dam problem in which a drenching rain filled the reservoir to 151% of normal capacity causing erosion of the interior of the dam and the emergency spillway.
Volcanic eruptions: Volcanologists have created the logarithmic Volcanic Explosivity Index (VEI scale) to express the potential magnitude/disruption of volcanic eruptions akin to the Richter (and other) scales for earthquakes. For reference, the 1980 eruption of Mount St. Helens was a VEI 5, considered "large". VEI 6 and 7 events are considered "very large" and volcanoes believed to be VEI 6-7 are Crater Lake (Oregon) and in Alaska: Novarupta in the Valley of 10,000 Smokes that erupted in 1912; Churchill, Okmok, Neniaminof. VEI 7 eruptions in the past were Santorini, Greece' Tambora, Indonesia; Valles Caldera, N.M., and the Phlegraean Fields, Naples, Italy. Eruptions in Alaska, Kamchatka, and Iceland can routinely erupt and produce economic chaos, e.g., the disruptive eruption of Eyjafjallajokull in Iceland was a VEI2.
The probability of a VEI6 event is 2 per hundred years globally; of a VEI7 event is 2 per 1000years globally. For comparison, our societies routinely plan and mitigate for longer time-spans, e.g., nuclear waste disposal for 10,000 to even 1,000,000 years.
Catastrophic landslides: A relatively small landslide into Lituya Bay in 1958 caused a megatsunami that, locally, reached 1720' in height. The potential for rare, but large, landslides exists in Hawaii: a slide off the flank of Mauna Loa 120,000 years ago had a volume of 1500-2000 cubic meters. The current south flank of Kilauea moves about 10 cm/year (the Hilina slump and involves about 10,000-12,000 cubic kilometers. It moved about 2' during the M6.9 earthquake on May 4, 2018.
Meteorite impacts: The largest impact event in recorded history as the Tunguska event of 1908. Plausibly caused by an airburst of a comet 60 m in diameter or an asteroid 190 m in diameter, it released the equivalent of 5-50 megatons TNT (by comparison, the Hiroshima bomb was 15 kilotons).
Solar storms and coronal mass ejections: In September 1859 the ejection of a mass from the sun reached the earth in only 17.6 hours, an event known as the Carrington Event. It caused auroras as far south as the Caribbean, and a glow in the sky that woke gold miners in California because they thought it was breakfast time. Northeasterners could read newspapers by the aurora's light. Telegraph systems failed throughout Europe and North America.Less severe storms occurred in 1921 and 1960, but in 1989 a storm knocked out power across large sections of Quebec. A similar event in 2012 missed the earth's orbit by 9 days. In 2013 the estimated cost of a similar event was $0.6-2.6 trillion to the U.S. alone.Combination events: In 2011 we saw probably a serious modern combination event--the Tohuku (Japan) earthquake+tsunami+ nuclear reactor failure. But other combination events are entirely plausible: What if the December 2017 Santa Barbara wildfires had occurred instead, during the dry summer season? What if a modern Carrington event hit the northern U.S., Canada and Alaska in the depth of winter in February instead of September. What will happen if the flank of Kilauea (or the Canary Islands) stops creeping or moving in slow increments and fails all at once?
Challenges: The first challenge for scientists is to get the science right. The difficulty in doing this with rare events is exactly that they are rare: it's not a laboratory problem where we can go in, repeat experiments, and change them around. It's Mother Nature doing her thing on her own time-scale. What kind of modelling (or combination of models) should be used? Deterministic? Statistical? Chaos theory? How will the "disasters" caused by "hazards" differ from past events because of population, economic, infrastructure and transportation changes?
A second challenge for scientists is communication to/from decision makers and officials. How should resources be balanced between short-term and longer-term hazards? Communication is easiest when uncertainty is low in a high-risk situation (e.g., when a lava flow is slowly approaching habitation) but is more difficult for rare events where uncertainties may be great. Scientific and engineering inputs are required when making decisions about evacuation, such as when to evacuate and how large an area should be evacuated. Regular meetings with officials and scientists help, e.g., "Cities on Volcanoes" biennial working conferences between scientists and officials.
Finally, the desire of the public for input should not be underestimated, nor should the level at which they can understand and evaluate events and their potential options.
Misc. reference of interest: Doyle, E.E.H., Johnston, D.M., Smith, R., Paton, D., Communicating model uncertainty for natural hazards: A qualitative systematic thematic review. International Journal of Disaster Risk Reduction, https://doi.org/10.1016/j.ijdrr.2018.10.02339, 449-476, 2019.