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|
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).
Since this involved some data manipulation before use of R and some pulling of data by hand out of R, I'm not going to give a full discussion of how I did all this here. All the code and data files discussed below can be found in this 'tar' file.
Data sources I used were:
Tamino's approach is a pretty naive linear model of all these factors plus several additional terms describing the trend of warming temperatures and an oscillatory component with 1-year period to capture any issues with the relative calibration of individual months in the temperature series. A more physically-based statistical model would probably apply convolution with an exponentially decaying function rather than a simple offset in matching temperature to these different sources of variation - that's the sort of thing we looked at previously here with the "two box model". But the offset approach captures at least some of the time-delay effect of the convolution, and is actually remarkably successful:
Figure 1: A fit to the GISS temperature curve from 1975 to 2011 using El Nino, Volcano, sunspots, an annual cycle and an underlying (quadratic) trend. Selected parameters of the fit are: El Nino: 0.0783 (5 month offset), Volcano: -1.687 (9 month offset), Sunspot: 0.000518 (3 month offset), Linear trend (centered on 1990): 0.0169 degrees C/year. Linear trend (2000): 0.0188
Figure 2: A fit to the GISS temperature curve from 1950 to 2011 using El Nino, Volcano, sunspots, an annual cycle and an underlying (quadratic) trend. Selected parameters of the fit are: El Nino: 0.0733 (4 month offset), Volcano: -1.588 (8 month offset), Sunspot: 0.000395 (3 month offset), Linear trend (centered on 1990): 0.0149 degrees C/year. Linear trend(2000): 0.0198
The fit does a reasonable job of matching the real temperature curve, but there is still a lot of variation left out. A look at how well we're doing can come from subtracting the exogenous components of the fit:
Figure 3: The same fit as in Figure 2, now showing annual averages (black and red lines) compared with the fitted trend. The black is before subtraction of El Nino and the other factors in the fit, the red curve after. RMS differences from the trend line have been roughly cut in half by the fit, which means that predictions of future temperature (given El Nino and the other factors) can be that much closer to what is observed.
But - we don't know El Nino in the future. The offset of 4 or 5 months means we can predict at least that far with some confidence. El Nino predictions are also published for several more months in advance, so we actually can make a reasonable guess almost a year out. I picked two alternate approaches to modeling El Nino beyond that; first, just assuming it was pegged at zero (as we have done with the volcanic forcing, assuming no major future volcanoes in the model); second by just putting in the average 5-year ENSO cycle in a sinusoidal manner, to give a flavor for what El Nino might contribute. It's behavior is far from sinusoidal, but at least the difference between the two models tells us something about how much effect ENSO variations may have on future temperatures.
Sunspots are a smaller factor in the fit than El Nino, but also make some difference. I modeled them by just pasting a cycle from the early 20th century into the 21st, starting from about where we are in the cycle right now. Sunspots do seem to be picking up again after a lull, so given the positive contribution in the fitting process this will have a small effect again to boost global temperatures.
The resulting prediction for the first model (using the fitting parameters of Figure 2) is:
Figure 4: Fit of figure 2 extrapolated through 2013 with El Nino zero beyond mid-2011. Monthly GISS temperatures rise to between 0.7 and 0.8, with annual averages of 0.576 for 2011, 0.687 in 2012 and 0.718 in 2013.
and for the second is:
Figure 5: Fit of figure 2 extrapolated through 2013 with El Nino set to a 5-year pure sinusoid beyond mid-2011. Monthly GISS temperatures rise to about 0.9 before falling back, with annual averages of 0.578 for 2011, 0.785 in 2012 and 0.840 in 2013.
Back in January 2010, commenter "fredstaples" here claimed we were in a cooling trend and predicted the average for 2010 GISS temperatures would be 0.54, while I was predicting 0.65. The actual value of 0.63 was between our two guesses, but 80% of the way to mine, so I think I won that one.
Based on the above analysis, I'm fairly confident now that the GISS temperature anomaly average for 2011 will be 0.58, plus or minus about 0.05 degrees, and that either 2012 or 2013, and very likely both, will set a new record for global warmth. Is there anybody out there willing to put their name on a significantly lower estimate for this and future years? The relentless warmth is getting pretty conclusive - even star Republican witnesses in recent hearings on climate can't avoid pointing out that it's warming, and pretty fast.
Now, when are we going to get serious about stopping it?