## Kleen

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## Some numbers: energy and disasters

2010 and 2011 may not have been unusual in terms of the number of energy-related disasters, but I suspect they have at least been unusual in terms of the quantity of headline-grabbing material and TV news attention, and the ongoing disaster stemming from the earthquake and tsunami in Japan is only the most dramatic of them. With the 1-year anniversaries of the Upper Big Branch and Deepwater Horizon disasters running past along with the 25th anniversary of Chernobyl, I felt a need for some sort of quantitative comparison of these various events...

An explosion or earthquake or other disaster of that sort involves the almost instantaneous release of a large quantity of energy. For earthquakes we have a convenient measure in the Richter scale, which measures the shaking amplitude. The Richter scale increases logarithmically, so that an increase in magnitude by 1 means a shaking amplitude 10 times as large. The quantity of energy involved scales as the 3/2 power of that amplitude, so 2 magnitudes on the Richter scale corresponds to an increase in energy release by a factor of 1000. Converting energy to standard metric notation in terms of joules (1 J = 1 kg m^2/s^2), the Richter scale magnitudes come to:

Magnitude 3: 2 GJ (2x10^9 J)
Magnitude 5: 2 TJ (2x10^12 J)
Magnitude 7: 2 PJ (2x10^15 J)
Magnitude 9: 2 EJ (2x10^18 J)

Nuclear explosions are typically measured in units of kilotons of TNT, where 1 kt TNT = 4.2 TJ, i.e. a 1 kiloton explosion should be about double the energy release of a magnitude-5 earthquake, and a 1 MT (megaton) explosion around double the energy release of a magnitude-7 earthquake.

Also worth thinking about in comparison is the non-explosive use of energy, as it runs through the natural world and as we use it for our own purposes. Since a year consists of just over 3x10^7 seconds, a 1 GW power plant over the course of a year produces 3x10^16 J or 30 PJ of electrical energy. That's about 7 times the energy release of the 1 MT explosion, about 15 times the energy release of a magnitude-7 earthquake. That energy release is spread over tens of millions of seconds, not just the few seconds of an explosion, but it's good to remember it is a large quantity of energy.

Human society currently uses about 15 TW of primary energy, or 450 EJ per year. That's over 200 magnitude-9 earthquakes, almost 1 per day. That's a lot of energy.

Earth receives energy from our Sun at a rate of about 174 PW. In a year that's about 5x10^24 J, 5 YJ (yottajoules) or 5 million EJ. That's a magnitude-9 earthquake worth of energy every 12 seconds! Luckily it's spread out over the whole (day-lit) surface of the Earth, so we don't normally experience the magnitude of that energy flow in any dramatic fashion. Still, it's worth remembering how natural energy scales like this tend to dwarf whatever humans do.

So, how do our recent collection of energy-related explosions and disasters compare?