Open Mind

Known Factors

November 10, 2008 · 18 Comments

Some of the factors which affect global temperature, including the fluctuations we see on shorter time scales, are known. These include major volcanic eruptions, whose sulfate aerosols cool the planet for several years, and the el Nino phenomenon, which allows for greater or lesser heat exchange between the atmosphere and the Pacific ocean and can warm the planet (el Nino) or cool it (la Nina). Is it possible to remove these temporary influences from the temperature record, more clearly to isolate the changes which are actually part of global warming?

Not entirely. As we’ve seen before, the impact of climate forcings (and volcanic cooling is a forcing) isn’t all felt immediately because the climate system contains many components with different time scales. I’m not aware of all the components or their relevant time scales (I wonder if anyone is?), so I’ll make no attempt to compensate for that. Instead, I’ll do a multiple regression of global temperature (from GISS) since 1975 (the “modern global warming era”) against el Nino (as indicated by the Multivariate el Nino index, or MEI), volcanic forcing (as estimated by Crowley 2003), and time. Such an analysis is bound to be imperfect, so I’ll leave it to real climate scientists to judge its appropriateness; we can consider it an interesting intellectual exercise.

I actually tried several indices to represent el Nino, including the southern oscillation index (SOI) and the Nino3.4 index, but the MEI gave the best fit so I’ll go with that. Also, the Crowley data for volcanic AOD is for latitude zones, so I computed an area-weighted average to represent the globe. Furthermore, the Crowley volcanic forcing estimates only go to the end of 1999, but since we’ve had no major eruptions (that I’m aware of) since then, I simply set the volcanic forcing to zero after 2000. Finally, I allowed for a lag in the impact of volcanoes and MEI; the best-fit lags were 4 months for MEI and 8 months for volcanic forcing.

The fit turned out to be pretty good:


An interesting numerical result is that the time trend rate is 0.0164 deg.C/yr. This is 0.0009 deg.C/yr less than the estimate using linear regression alone, without accounting for el Nino and volcanoes. However, both estimates are within the error limits of the other. A possibly useful result is that the residuals from the multiple regression show less autocorrelation than those of the simple linear fit. As a result, the uncertainty level of the trend from the multiple regression is smaller than that from simple linear regression; ignoring el Nino and volcanoes gives a trend estimate of 0.0173 +/- 0.0042 deg.C/yr, but when including them the trend estimate is 0.0164 +/- 0.0022 deg.C/yr.

I also fit trends to recent subsets of the residuals; if residuals since 1997, or 1998, or whatever, show a statistically significant trend we have evidence that the rate of warming has changed (accelerated or slowed, depending on the sign of the trend). None of the intervals tested (up to starting at 2002) showed a statistically significant trend.

Removing the influence of el Nino and volcanoes with multiple regression is certaintly an imperfect procedure. But it might be a valid way to refine the statistical estimate of the rate of global warming. If any real climate scientists are reading this…

By request, here’s the GISS data after subtracting the estimated (from multiple regression) influence due to el Nino and volcanoes, together with a trend line:


Categories: Global Warming

18 responses so far ↓

  • steven mosher // November 10, 2008 at 4:43 am

    very nice tamino.

  • Leif Svalgaard // November 10, 2008 at 3:30 pm

    So you would get the AGW contribution by subtracting the fit. Can yo show a graph of that too?

    [Response: Of course it's only an approximation, which doesn't account for the time delay due to heat capacity, other factors which may cause short-term fluctuations, or nonlinearity of the response. But the graph is in the update to this post.]

  • Leif Svalgaard // November 10, 2008 at 3:51 pm

    Thanks. Perhaps, I don’t quite understand what the fit was. If i look at the last few points both the GISS and the fit, i see values for both around +0.5, so their difference should be about 0, yet the updated plot shows values around 0.5 ???

    [Response: The fit includes a linear time trend in addition to influence from MEI and volcanoes; one would presume that the term linear in time is an approximation of the AGW contribution. The impact of just MEI and volcanoes (with no term linear in time) shows no trend, just fluctuations.]

  • captdallas2 // November 10, 2008 at 4:56 pm

    Could you include PDO?

  • Deepclimate // November 10, 2008 at 5:20 pm

    Tamino, thanks for another great post.

    You could say that the remaining trend is an approximation of the overall net anthropogenic contribution, which includes warming forcings (GHGs), partly counterbalanced by cooling influences (aerosols). In other words, the portion of trend due solely to GHGs is likely even higher.

    It would be interesting to see how your analysis compares to “hindcasting” in the same time period from climate models. We’ll be all watching for comments about that …

  • Ed Davies // November 10, 2008 at 8:14 pm

    “Also, the Crowley data for volcanic AOD is for latitude zones, so I computed an area-weighted average to represent the globe.”

    Would it be being too precious to compute an insolation-weighted average? Near-polar latitude bands not only have a smaller area but also have a smaller amount of solar energy arriving per m² so have a much smaller amount of energy to bounce back into space.

    [Response: My guess is that an insolation-weighted average would be a superior choice.]

  • Miguelito // November 11, 2008 at 4:42 am

    I lurk alot and don’t comment much. This blog is a good way to cut through a lot of the crap out there.

    Anyways, there’s this post on Nir Shaviv’s blog about low climate sensitivity, so low that the climate doesn’t really feel volcanic eruptions. He’s not the first: Lindzen published a paper on this and so have Douglass and Knox.

    Now, it’s horribly unscientific to say this, but my gut is telling me that Shaviv is full of BS on this. I mean: Krakatoa had a profound impact on global climate. So did Pinatubo. Or that’s what I’ve been led to believe. But, has anybody done an analysis that shows volcanic eruptions show up as statistically significant in the temperature record and aren’t just background noise? Shaviv basically points at the temperature graph and says, “You can’t see it in the noise!” Frankly, that’s not good enough for me.

    Thanks if anybody can help me.

    [Response: That idea is laughable. You can indeed "see" the influence in the temperature record, and it's easy to establish with strong statistical significance. In fact the response of earth's climate to the Pinatubo explosion provides an outstanding confirmation of the ability of computer models to simulate climate response to forcing -- a fact which probably gets Shaviv and cohorts "hot under the collar."]

  • tamino // November 11, 2008 at 1:12 pm

    Someone posted a link to an interesting paper by Lean & Rind. It was sent to the “spam cue” — which is not a problem — but I accidentally hit the “delete” button rather than the “not spam” button. Please re-submit.

  • Gavin's Pussycat // November 11, 2008 at 4:19 pm

  • lucia // November 11, 2008 at 4:50 pm

    You’ll find this paper intereting:
    “Accounting for the effects of volcanoes and ENSO in comparisons of modeled and observed temperature trends”. Santer, Wigley, Doutriaux &etc.

    Out of curiosity– are the ±uncertainty intervals you mention standard errors, or 95% confidence? Did you assume the errors are AR(1)? ARMA?

    Other than that, your results on the reduction in lag-1 autocorrelation and the reduction in uncertainty in the trend match what I’ve been getting.

    [Response: The error ranges are 2-sigma, which is effectively 95% confidence. I used an ARMA(1,1) model for the errors (and since I'm now using R, it was trivially easy to fit).]

  • Dave A // November 11, 2008 at 11:36 pm


    (and since I’m now using R, it was trivially easy to fit).]

    Sorry but hasn’t Mann said R is useless (although real statisticians would not agree with him)?

    What’s youre take on this?

    [Response: I'm not aware of any such statement. Do you have a reference?

    If he believes that, then I disagree with him.]

  • HankRoberts // November 12, 2008 at 2:08 am

    search - “Michael Mann” “R is useless” - did not match any documents.

    Perhaps you’re thinking of r2?

    “So-called “reduction of error” (RE) and “coefficient of efficiency” (CE) skill scores for the decadal reconstructions were used as metrics of validation skill as in past work (20, 32). Because of its established deficiencies as a diagnostic of reconstruction skill (32, 42), the squared correlation coefficient r2 was not used for skill evaluation. ”

    32: 1. Mann ME, 2. Rutherford S, 3. Wahl E,
    4. Ammann C
    (2007) Robustness of proxy-based climate field reconstruction methods. J Geophys Res 112:D12109.

    42: 1. Wahl ER, 2. Ammann CM (2007) Robustness of the Mann, Bradley, Hughes reconstruction of surface temperatures: Examination of criticisms based on the nature and processing of proxy climate evidence. Clim Change 85:33–69.

  • t_p_hamilton // November 12, 2008 at 3:08 am

    DaveA, you do not know what R is.

  • Dave A // November 12, 2008 at 10:32 pm


    my bad it was r2

  • lgl // November 13, 2008 at 10:50 pm


    Your MEI adjustment can not be correct and GISS is probably not the best datasource.
    There is no reason to assume pre-1995 temperature would not follow the MEI like it did post-1995, without the volcanoes.

  • DrC // November 19, 2008 at 8:37 pm

    Fabulous that you are using R. It’s amazingly powerful and the useR community is outstanding. Using R also makes you more like Steve M everyday ;)

    [Response: Smile when you say that, pardner.]

  • DrCarbon // November 20, 2008 at 4:44 am


  • lgl // December 6, 2008 at 10:53 pm

    “Shaviv basically points at the temperature graph and says, “You can’t see it in the noise!” Frankly, that’s not good enough for me.

    Thanks if anybody can help me.

    [Response: That idea is laughable”

    Not a bad idea at all. Look at the sea level, which is a good proxy for ocean heat content:
    10 years after the eruptions the heat content is probably like it would have been without the eruption. The first years the sun is blocked and energy is lost, but then the ocean has cooled and for a few years does not radiate as much energy as it would have done without the eruption, so the net loss over a decade seems close to zero.

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