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).

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:

giss_fit.png

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

giss_fit_long.png

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:

giss_long_corrected.png

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:

giss_long_prediction.png

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:

giss_pred2.png

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?

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Did you, or could you, run

Did you, or could you, run the model with an average to strong La Nina? That should give us the range of plausible predictions absent a large tropical volcanoe.

I didn't - based on most of

I didn't - based on most of the projections of future ENSO we seem to be coming out of the present La Nina by the middle of this year. However, I just ran the same future scenario as in "model 2" above, but switching the sign of the future ENSO, so it starts in negative phase (La Nina) getting strong again in 2012-2013. The resulting temperature predictions are:

2011: 0.576
2012: 0.591
2013: 0.596
2014: 0.768

so changing the prediction from El Nino to La Nina makes no difference in 2011, but doesn't warm much until 2014 when temperatures go roaring up (and they keep going up through the end of that year). One way or another, record warmth will return, again, and again, and again. Most likely by 2013, but possibly we'll have to wait one more year than that.

Nice work: I'd been meaning

Nice work: I'd been meaning to try something like this, but not had time.

Which sunspot cycle did you pick for your prediction? On the basis of the depth and length of the minimum, magnetic fields and such like, current predictions are for a very weak solar cycle this time round - the weakest in 200 years:
http://solarscience.msfc.nasa.gov/predict.shtml

I used cycle 14, using August

I used cycle 14, using August 1903 numbers for March 2011, and copying month by month from there. It seems to have been similar to the present cycle in a number of ways, though I'm sure these are hard to predict. It was definitely one of the weakest of the 20th century, and I believe associated with the dip in temperatures in the first decade of the 20th century.

Cycle 14 looks good. Here's

Cycle 14 looks good.

Here's another thought. I'm not totally sold on using a quadratic from 1950 because the curvature is liable to be artificially inflated by the pre-70's aerosol cooling. Which in turn forces the recent trend upwards. So my guess is that your estimates are a touch high.

The alternative would be to use the linear trend since '75. How much difference does that make?

And, more interestingly, what happens if you use both methods to forecast the temperatures from 2006-2010 or 2001-2010 based on the preceeding years. That would give an indication of which is more reasonable.

The quadratic's definitely

The quadratic's definitely not good for long-term extrapolation, but it makes only a very small difference for the next few years - less than 0.01 degree. The annual linear trend is only about 0.02 degrees/year, so adjustments to that number at even the 30% level would need a few years to make a difference. Short term change is dominated by El Nino (or a stratospheric volcano), and then solar cycle, not the trend. The trend forces temperatures back to a certain range - even the strongest El Nino can't pull temperatures too far up or down from that - so it's important, but the exact slope makes little difference for periods of less than a decade or so.

I'm not sure how you would do a forecast as you suggest. The "fit" is itself a forecast of exactly that sort, based on the ENSO etc. as they happened. If you mean replacing the actual ENSO with a cyclical estimate, and the actual solar cycle with some other form of estimate, I guess one could do that - but you can pretty much tell what it would look like from my figure 1, just move the blue (ENSO) or brown (solar) curves up or down, and the red curve would follow.

Here's a crude estimate of

Here's a crude estimate of the difference: I'd expect the linear trend on 1975-2010 to cross the quadratic on the same period at around 1982 and 2003. That gives 10 years of divergence to 2013. Guestimating the mean gradient difference over that period at 0.005 C/yr, that makes 0.05 C/yr difference in 2013. So my crude estimate of the linear result for your model 2 would be:

2011 0.548
2012 0.740
2013 0.790

So 2011 is below 2009 but still hot. 2012 and 2013 are still new records.

Very interesting and well

Very interesting and well executed. I tried the same thing in 2009, and checked back this year on my results.

My original post was here:
How hot should it have really been over the last 5 years?
http://bravenewclimate.com/2009/02/08/how-hot-should-it-have-really-been...

My follow ups:
A toy model for forecasting global temperatures – 2011 redux, part 1
http://bravenewclimate.com/2011/03/02/how-hot-2011-p1/

and

Correlates of global temperatures – part 2
http://bravenewclimate.com/2011/03/06/how-hot-2011-p2/

I was planning to continue the sequence, but then got overtaken by matters Fukushima. Maybe now I won't bother, after reading your excellent work here.

Hi Barry - I don't visit your

Hi Barry - I don't visit your blog all that often, it sounds like I should more, I had missed those posts! Anyway, definitely thinking along the same lines. My work here was almost completely based on Tamino's original posts on this, just adding on a predictive piece, so not terribly original, but still, I hope useful.

What would be nice would be to get some of those folks out there claiming "it's cooling", "no warming", etc. to put down where they think temperatures will be this year and in the next few years. That did happen way back in early 2008 (if you follow the thread of my previous predictions I linked to in the main post) when every "skeptic" seemed to be calling for a very low temperature that year, what with the coming ice age and all. But there seems to have been no revisiting, no public reckoning for those claims. I'd love for them to be some more visible way to show skeptics simply have no predictive skill. Any ideas?

What is the linear trend of

What is the linear trend of both the "fit" and just the quadratic function since 2001? Some claim that we aren't seeing enough warming, when, in fact, we are seeing the warming that we would expect to see given ENSO and the solar cycle.

Good question - you can see

Good question - you can see from eyeballing Fig 1 that there's a strong negative trend in ENSO and solar cycle from around 2001. I think this is a pretty general issue, I'd like to look into a bit moire than just that one time-span, thinking of doing a whole post on it (how the underlying trend can be masked over selected periods by spurious ENSO/solar/volcano trends).

I have a similar one here for

I have a similar one here for HadCRUT3, you can figure out what is what because it's mostly the same components (although I didn't think of checking for annual cycle - my eyeball method probably can't detect it anyway...)

I used a curved trend just to demonstrate it kind of works. The whole point of making these graphs at the time was to try and visually convince some people that "warming has stopped" is not a good conclusion to draw from the recent flatness of the HadCRUT3 record. The curve is to show that what's happened could even be compatible with ongoing acceleration.

The solar data is different from yours (I think) http://solarscience.msfc.nasa.gov/greenwch/spot_num.txt and stratospheric aerosols are from http://data.giss.nasa.gov/modelforce/RadF.txt

I used MEI index for ENSO. I shift it foward about 3 months. The different components are eyeball scaled, so not great but I don't yet have the statistics ability to do it properly.

I also made a graph during the 2010 El Nino that predicted future ENSO. Funnily enough this prediction isn't too bad for what actually happened with ENSO, as far as the depth of the La Nina goes. This one was made as a visual aid to convince the same people that even a strong La Nina would only delay the inevitable.

I also plotted the relationship going forward out to 2100 (I had to generate some ENSO and solar data for this but on that scale such variation doesn't matter anyway). I showed this to them so they could see that 3C warming by 2100 isn't incompatible with what's happened in recent years.

I have been updating this as data comes in. The latest one I uploaded goes up to Jan 2011:

I have also done this with UAH and it's the same kind of deal.

I haven't done it with GISTEMP and after seeing your post I guess I don't need to anymore.

Very nice, thanks for posting

Very nice, thanks for posting this - do you have a link to your blog or somewhere that you've posted this before? I don't remember seeing this previously!

I have no blog to put this

I have no blog to put this stuff up. I have been posting these graphs around a few bulletin boards. One that contained a long explanation on a particular board seems to have been lost, so I have created a blog as a replacement and so I can update the graph monthly:
http://zzzbbb.blogspot.com/

I got fed up having to guess names that weren't already taken so zzzbbb it is.

OK, here's a thought... All

OK, here's a thought...

All these analyses assume that the ENSO indices will behave the same way in future as they have in the past, and in particular that there is no trend in the index.

But could we imaging a situation in which there is a trend? For example, an impact of recent warming leading to a shift in the behaviour leading to a running mean of the index which is consistently negative? In which case, there would be a corresponding offset on subsequent temperatures.

My initial reaction was no, because the underlying effect here is the Earth's energy balance, and El Nino can't affect that (assuming the critiques of Lindzen are correct). I can see one other possibility: if energy is being channelled preferentially into the oceans rather than the air, then that would lead to a temporary supression of the temperature trend owing to the greater heat capacity of water.

I'm not convinced, but I can't absolutely rule it out.

Hi Arthur, I think an annual

Hi Arthur,
I think an annual modulation of the volcanic forcing improves the fit significantly.
this means
(a+b*cos(..)+c*sin(..))*volc
instead of
a*volc
for some coefficents a,b,c. I think it is because of the asymetry solar insulation between summer and winter and the asymetric land/ocean distribution.
Can you confirm this?

From GISS, the first 7 months

From GISS, the first 7 months of 2011 average to 0.50 C temperature anomaly. It's possible I overestimated 2011 temperatures with this model - it'll be interesting to see. The remaining 5 months will have to average 0.69 C anomaly to meet the 0.58 C guess in this post. The hottest so far is July, at 0.60. But the trend looks good! The minor cooling in December 2010 and the beginning of 2011 has definitely dissipated as has the La Nina; we'll see where things go from here. ENSO predictions for the rest of the year look very flat, possibly even heading into another La Nina.

And now, 2011 is over and

And now, 2011 is over and GISS has posted the final number for the year - down in the bottom under J-D for 2011 we have "52" which means an anomaly of 0.52 C. So - the prediction of this post, made after only the first 2 months data for the year were available, was too high by 0.056 C for the year - a tad worse than my previous guesses, but not that bad overall.

The reason the final number for the year is on the low side is almost certainly because ENSO went negative again starting around the middle of 2011 - when I was using predictions from early in the year that it should stay roughly neutral or slightly positive. As noted in the April 5th comment above, even if ENSO stays negative (La Nina conditions) we should see 2012 slightly hotter than 2011 - and temperatures zooming up shortly after. The latest ENSO forecast sees La Nina conditions probably through May or June of 2012. We'll see!

2011 wasn't close to your

2011 wasn't close to your previous prediction of 0.75C for 2011! The official GISS land sea temperature was 0.51C not 0.52C so your prediction where you stated "I'm fairly confident now that the GISS temperature anomaly average for 2011 will be 0.58, plus or minus about 0.05 degrees" is also a bust. It seems to me that missing by 0.07C in just 8 months is a pretty big miss considering you gave yourself a 0.1C window.

I have a feeling that 2012 won't come close to setting a record either since the La Nina is forecast to continue. 2013? Who knows, if a strong El Nino forms it's possible.

When I wrote this post only 2

When I wrote this post only 2 months of GISS data had been posted, not 4 - so it's 10 months rather than 8 months of "prediction". And I really did not expected the La Nina to roar back as quickly as it did - I put too much trust in the average of the model projections without looking more closely at the distribution of different scenarios. Ah well.

Even if 2012 continues La Nina, it's going to be hotter than 2011.

And I do see the NASA press release says 0.51 C anomaly - nevertheless, their data table, which is the reference I have used for all other comparisons here, says 0.52. So 0.52 is the relevant number relative to my guesses or predictions - it's whatever the number is in the January-December column at the end of the year. Now maybe they'll update that a little as they do sometimes, as more stations report in. I'll check in later this month and see.

Did you account for the

Did you account for the change to GISTEMP v3? Try rerunning your model with the new numbers, as of Feb 2011.