Dancing With Myself

by Charles Sheffield

  Nuclear war

  Earthquakes

  Volcanic eruptions

  Meteorite impacts

  Solar flares

  Nearby supernovas

  To provide a standard of comparison, we will first consider a natural energy source which is definitely not destructive to the biosphere: the tides.

  3.TIDAL ENERGY

  Humans harness a negligible fraction of tidal energy, although the available energy is huge. Other species do rather better, and the intertidal zones are the most biologically productive regions of the world, more so than even the tropical rain forests. On the average, waves powered by the tides deliver to the shoreline 0.335 watts per square centimeter, fifteen times as much energy as comes from the Sun. Even so, the coastal area is small compared with the open oceans, and almost all tidal energy remains untapped.

  A ballpark figure for the total energy is easy to calculate (though not easy to find in the literature). Let’s assume that the tides raise and lower the mean sea-level of Earth’s oceans by two meters, twice a day. Since the oceans cover 70% of the globe, and the total surface area of Earth is about 500 million square kilometers, the total tidal energy proves to be about 2.8 × 1026 ergs.

  This is a very large amount, but it looks even bigger than it is because the erg is a standard but very small energy unit. The daily output of a sizable (1,000 megawatt) power station is 8.64 × 1020 ergs. A one-megaton hydrogen bomb produces 4.2 × 1022 ergs, or a month and a half’s production from a large power station.

  This value of available tidal energy is probably good to within a factor of two, and we will not be trying to obtain results better than that.

  4.NUCLEAR WAR

  To compare tidal energy with the energy release of a full-scale nuclear war, we have to make some assumption about the number and size of the bombs that are available. We will employ the same figure as in the 1983 TTAPS paper, namely, 25,000 megatons of TNT equivalent. Since one million tons of TNT release 4.2 × 1022 ergs of energy, our nuclear war can produce a total of 1027 ergs (assuming all the missiles are fired, and they all work—an assumption that anyone who has had dealings with the Defense Department will have a lot of trouble swallowing).

  The available daily energy of tides is thus about one-quarter of that produced by a full-scale nuclear war. However, that tidal energy is released twice every day; nuclear war can never be a regular event.

  5.EARTHQUAKES

  Earthquakes are interesting in their own right. However, I am going to give them short shrift. Although they do tremendous damage, they do it mainly at ground (and sea) level, and they do not send finely divided material high into the atmosphere. Earthquakes are thus not going to be a major source of nuclear winter effects.

  There are two different scales used to measure the intensity of earthquakes. The better-known one, called the Richter Scale, was developed by C.F. Richter in 1935, and is now routinely reported for most earthquakes around the world. It is actually an energy scale, and a logarithmic scale, at that, so a Richter rating of, say, 7.5, releases ten times as much energy as one with a rating of 6.5, and a hundred times as much energy as one of 5.5.

  As a rule-of-thumb, property damage begins with about magnitude 5. The largest recorded earthquakes rated 8.6 on the Richter Scale. There have been four of them: Alaska, on September 10, 1899; Colombia, on January 31, 1906; India, August 15, 1950; and Alaska, March 27, 1964. Judging from the reported effects, the Lisbon earthquake on November 1, 1755, probably had a magnitude between 8.7 and 9.0. The great Chinese earthquake of July 28, 1976, killed half a million people in Tangshan, and was 8.2 on the Richter Scale. The 1906 earthquake in San Francisco was rated at 8.3.

  The other scale is called the Mercalli Scale, and it is less precise. It defines “degrees of intensity” between I and XII. An intensity II earthquake is barely perceptible to humans; intensity IX damages buildings and cracks the ground, and intensity XI shatters masonry buildings, bends railroad tracks, and destroys most free-standing structures.

  I should point out that the Mercalli scale concerns itself only with effects on manmade structures. If there are none of those around, there is no rating on the Mercalli scale. This is rather like the old question, “If a tree falls in the forest and no one hears it, does it make a sound?” Is it an earthquake, if there are no manmade objects to be affected by it? The Mercalli scale would suggest that it is not.

  The location of a volcanic eruption is not usually in any doubt. Locating an earthquake is trickier, and its point of maximum intensity, or epicenter, is determined by inference. However, it is useful to note that the total amount of energy release in a large volcanic eruption and a large earthquake seem to be very comparable. This emphasizes that energy release is only one of the significant variables, and probably not the most important one, when we look at the climatic effects of natural or man-made disasters.

  6.VOLCANIC ERUPTIONS

  Volcanic eruption has been fairly well studied, but there is no equivalent of the Richter Scale for volcanoes.

  Volcanic eruptions are often divided into two groups, termed Type A and Type B. Type B eruptions are in many ways more interesting and spectacular, since they are accompanied by gigantic explosions and produce large volumes of ejecta—lava, dust and ash thrown high into the air. Krakatoa, in 1883, and Mount St. Helens, in 1980, were both Type B events. Type B eruptions, foreshadowing thoughts of nuclear winter, send their dust high into the stratosphere, to produce colorful sunsets all around the world for several months.

  Krakatoa is one of the most famous eruptions of historical times, perhaps because of the movie, “Krakatoa, East of Java” (a nice example of Hollywood’s disregard of facts; Krakatoa is an island just west of Java). The Krakatoa eruption released an estimated 1025 ergs of energy—equal to a couple of hundred one-megaton hydrogen bombs. The sound of the explosion was heard 3,000 miles away, and the atmospheric shock wave circled the globe several times. At Batavia (now Jakarta), a hundred miles from the volcano, the air was so dark with dust that lamps had to be used at midday. Fifty-foot tidal waves hit the coast of Java and killed 36,000 people.

  Yet there have been much bigger explosions. Tambora, in 1815, on the Indonesian island of Sumbawa, is estimated to have been 80 times as energetic an eruption as Krakatoa. The following year, 1816, was known as “the year without a summer,” when crops failed to ripen throughout Europe. The most likely cause was a stratospheric layer of reflective dust from Tambora.

  Biggest of all blow-ups during historical times, but one for which no eyewitness or contemporary records exist, was the destruction of the island of Thira (formerly Santorini) in the Aegean Sea north of Crete. From archaeological evidence and the examination of the shattered remnant of Thira, this eruption is estimated to have released 1027 ergs of energy. That is equal to the energy release of the worlds whole stockpile of nuclear weapons. The eruption, occurring about 1470 B.C., also produced a monstrous tidal wave, hundreds of feet high, which may have been the agent that destroyed the Cretan Minoan civilization.

  The most famous volcanic eruption of all time was probably that of Vesuvius, in A.D. 79. It covered the towns of Pompeii, Herculaneum, and Stabiae in twenty-foot layers of ash (65 feet in some places) and preserved everything nicely until systematic excavation began in 1763.

  It also, as an incidental, killed the Roman naturalist and historian, Pliny the Elder, who had sailed across the bay of Naples to take a look at the eruption and perhaps to help people. He didn’t try to leave until too late, and suffocated on the beach.

  I know how he felt. Volcanoes are seductive viewing, and they induce strange psychological effects. In 1980, driving from Portland to Seattle, a friend and I made a detour to take a good look at the recently erupted Mount St. Helens. About five miles from the crater, the road had been closed off by the police. We were very annoyed at the time, but in retrospect they were doing th
e right thing. We would have kept going until we were far too close for safety.

  The next morning, talking at breakfast, we found that we had both dreamed about that deformed, ash-covered peak, with the ominous gray smoke cloud sitting on top of it.

  On the largest scale of things, the famous eruption of Vesuvius was no big deal. It released only an estimated 1024 ergs, less than one-tenth of a Krakatoa. By contrast, the 1912 eruption of Katmai in Alaska was twenty times as energetic as Krakatoa, but since it was in a sparsely populated area at the northern end of the Alaskan Peninsula, it attracted little global attention.

  Type A eruptions are often just as energetic, but they are less noisy and colorful and don’t get the same publicity. They produce great quantities of thermal energy, often heating the environment but not causing major explosions. They may involve huge lava flows, and even the creation of whole new volcanic islands. The most famous modern example is the island of Surtsey, created by a volcanic eruption off south-west Iceland, in 1963. That event was estimated to have released 2 × 1024 ergs—one-tenth the energy of the Krakatoan eruption.

  Table 1 shows values for some of the biggest and best known (and some surprisingly little known) volcanic eruptions of both types.

  Table 1: Volcanic Eruptions and Associated Energy Released

  Volcano

  Date

  Type

  Energy

  (ergs)

  Megatons

  Thira, Aegean

  Laki, Iceland

  Tambora, Indonesia

  Katmai, Alaska

  Mauna Loa, Hawaii

  Krakatoa, Indonesia

  Surtsey, Iceland

  Vesuvius, Italy

  Mount St. Helens

  1470 B.C.

  1783

  1815

  1912

  1950

  1883

  1963

  1979

  1980

  B

  A,B

  B

  B

  A

  B

  A

  B

  B

  1027

  8.6 × 1026

  8.4 × 1026

  2 × 1026

  1.4 × 1025

  1025

  1.9 × 1024

  1024

  4.2 × 1023

  24,000

  20,500

  20,000

  4,800

  333

  240

  45

  24

  10

  For comparison purposes:

  Global nuclear war

  ?

  B

  1.1 × 1027

  25,000

  Eruptions of Type A are mainly lava flows, whereas Type B eject large quantities of material with explosive force. The thermal energy of Type A eruptions is usually transferred slowly to the environment, through conduction and radiation.

  7.METEORITE AND COMET IMPACTS

  First, let us see how much energy a meteorite or a comet fragment will generate when it hits the Earth. This sounds like something that needs to be looked up in a reference work, rather than calculated directly. However, I will do it from first principles, because it is a nice example of being able to derive a result with almost no knowledge of physical constants.

  The kinetic energy of a body hitting the Earth is mv2/2, where m is the mass of the body, and v is the relative speed of the Earth and the object. We can put in any value we like for m—and we will look at various sizes of impacting object. But what about v?

  Suppose that the body is falling in towards the Sun from far away—perhaps from the Oort Cloud, which is the original home of the comets. Then its initial speed out there would be close to zero, and it would be accelerated all the way in towards the Sun by the solar gravitational field. Suppose that its speed relative to the Sun, by the time it hits the Earth, is vc. The object has picked up as kinetic energy what it lost as potential energy, so

  mvc2/2 = GmM/r

  where G is the universal gravitational constant, M is the mass of the Sun, and r the distance of the Earth from the Sun at the time of the impact, equation, we have

  vc2/2 = GM/r (1)

  It looks from equation (1) as though we need to know G, M, and r in order to determine vc. But we don’t. For the Earth to be remain in orbit around the Sun, the gravitational force of the Sun on the Earth must balance the centrifugal force generated by the Earth’s movement. This implies that if ve is the speed of the Earth in its orbit,

  ve2/2 = GM/r2,

  or ve2 = GM/r (2)

  Comparing (1) and (2), we have:

  vc2 = 2ve2 (3)

  This, a very well-known result, shows that all we need to know to determine the speed of the infalling comet is the speed of the Earth in its orbit around the Sun.

  But that is easy to calculate. In one year, the Earth travels once around the Sun. The mean distance of the earth from the Sun is about 150 million kilometers (93 million miles) and the Earth moves roughly in a circle. Since there are 86,400 seconds in a day, the Earth moves 2π × 150,000,000 kilometers in 365 × 86,400 seconds, i.e., ve = 29.89 kms/second—say, 30 kms a second, accurate enough for our purposes.

  Thus from equation (3), we at once have vc = √2ve = 42.4 kms/second.

  The speed of the comet relative to the Earth is found by compounding these two velocities. The motion of the Earth and the comet are roughly at right angles to each other, so the final relative velocity is (vc2 + ve2)1/2 = 52 kms/second.

  This result is something of an upper limit to the impact speed of an object hitting the Earth. It is appropriate for comet impact, but since asteroids orbit the Sun in the same direction as the Earth, and are coming from much closer than the Oort Cloud, they will hit with less speed, usually between 15 and 30 kilometers a second. On the other hand, a metallic asteroid is of higher density, has a more compact mass, and therefore delivers about as much energy as a faster-moving comet of the same size.

  Meteorites are small asteroids and have quite different orbit characteristics from comets. They move in elliptical paths, almost always staying closer to the Sun than the orbit of Jupiter, and more hit in the afternoon than in the morning, by about a 3:2 ratio. Perhaps the computers of the missile defense systems should have a special test built into their code: If you detect a major impact, did it occur in the afternoon? If so, look a little closer before you start World War III.

  The comet fragment will be traveling at 52 kms a second. A fragment one kilometer in radius and with the density of water masses about 4 billion tons. Impact with Earth generates 5 × 1028 ergs of energy—5,000 Krakatoas, or 50 full-scale nuclear wars.

  We need to know what size of fragment is reasonable, and how often such bodies are likely to hit the Earth. These are difficult questions, but we have at least a couple of available data points. First, a comet fragment5 almost certainly did hit Earth, relatively recently. It happened early in the morning, on June 30, 1908, at a remote area of Central Siberia called Tunguska. Although the fragment was estimated to be no more than a couple of hundred meters across, it flattened a thousand square miles of forest and left so much dust in the high atmosphere that colorful sunsets were produced in western Europe seven thousand miles away.

 
According to our formulas, the energy produced by the Tunguska meteorite was about 5.4 × 1025 ergs—five Krakatoas, or a thousand one-megaton hydrogen bombs.

  However, a full-sized comet should be much bigger than the Tunguska meteorite. For example, Halley’s comet has a nucleus about 10 kms across. Its impact with the Earth would release 7.1 × 1030 ergs of energy—equal to 170 million one-megaton hydrogen bombs, or 7,000 nuclear wars.

  One other point needs to be made here. The world’s most famous comets are periodic comets, like Halley’s comet or Encke’s comet. These objects do not “fall from infinity,” but are in orbits that bring them close to the Sun at regular intervals of a century or less. However, they are the exceptions of the cometary world. They were once part of the Oort Cloud, and fell in from there a long time ago; then Jupiter or one of the other planets perturbed their motion by a gravitational interaction, and gave them a less elongated orbit. Now they travel in paths that are relatively close to the Sun, and their days in the Oort Cloud are over forever.

  There is evidence that major comet impacts have happened in the past, though fortunately not in historical times. Meteorite impact is the most popular theory to explain the disappearance of the dinosaurs in the late Cretaceous period, 65 million years ago, and also for an even more massive species extinction that occurred earlier, at the Permian/Triassic boundary 250 million years ago. The idea was proposed in 1980 by Alvarez and co-workers, originally to explain anomalous levels of iridium found in sedimentary deposits all around the world. It is holding up rather well, and is now supported by the discovery of so-called “shocked quartz” grains at widely dispersed locations around the world.

  Evidence of other large meteorite impacts can be found in many places: Manicouagan Lake in Quebec, a water-filled ring crater 40 miles across, is believed to be an impact crater; so is the mile-wide Meteor Crater, Arizona, which was created about 20,000 years ago. The Sudbury nickel deposit in Ontario is also probably an “astrobleme,” or asteroid-impact structure, that created the world’s largest nickel ore body. The asteroid that hit Sudbury is estimated to have been moving at 15 kilometers a second, and have been 4 kilometers in diameter. If so, its impact delivered 3 × 1029 ergs, 300 times as much as a full nuclear war. (Note that a comet, the same size but with the density of water, would produce very much the same energy, at 4.5 × 1029 ergs.)