April 2011

Predicting future temperatures

A few months ago Tamino at Open Mind posted a fascinating analysis of warming obtained by fitting the various observational temperature series to a linear combination of El Nino, volcano, and solar cycle variations (using sun spots as a proxy for the latter), plus an underlying trend, allowing for some offsets in time between the causative series and the temperature. Year to year global average temperatures fluctuate significantly, by several tenths of a degree. Taking into account these "exogenous" factors, however, greatly reduced the level of variation. Not only does this more clearly show the underlying trend, once the "exogenous" components are removed, but it occurred to me this also allows prediction of future temperatures with considerably more confidence than the usual guessing (though I've done well with that in the past), at least for a short period into the future.

See below for a detailed discussion of what I've done with Tamino's model, for the GISS global surface temperature series. In brief, however, I present the results of two slightly different models of the future, first with no El Nino contribution beyond mid-2011, and second with a pure 5-year-cycle El Nino (starting from zero in positive phase) from mid-2011 on.

Year Model 1 prediction for GISS Jan-Dec
global average temperature anomaly
Model 2 prediction
2011 0.576 0.578
2012 0.687 0.785
2013 0.718 0.840

While there's some variation in future years, the final average temperature for 2011 should be close to 0.58 (similar to the temperatures in 2009). Temperatures in 2012 are likely to be much warmer - at least breaking the record of 0.63 set in 2005 and 2010, possibly (model 2) by as much as 0.15 degrees. With the continued waxing of the solar cycle and continued increases from CO2 effects, however warm 2012 is, 2013 should be even warmer (unless we get a big volcano or another strong La Nina then).

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?