Open Mind

Exogenous Factors

December 31, 2009 · 19 Comments

Apparently Lucia thinks that my “estimation of uncertainty intervals without treating the effect of volcanic eruptions like Pinatubo as exogeneous is very misleading.” I’ve come to expect such foolishness from her; whenever she approaches the trend in temperature data, she reeks of desperation.

But if we do model some of the exogenous factors, we might get smaller uncertainties in our trend estimates. Yay! Let’s give that a try.

One thing we can tell right off the bat: treating volcanic forcing as an exogenous factor won’t give Lucia the “falsification” of recent warming trends she so desperately craves. That’s because there hasn’t been enough volcanic activity to have a sizeable climate impact since about 1992 (Pinatubo). Which makes you wonder whether she’s thought this through very clearly.

What might actually be “very misleading” is to cherry-pick your exogenous factors. After all, there’s another one we’re all well aware of — el Nino/la Nina — and it has shown enough activity to have a sizeable climate impact, as recently as last year. So, let’s estimate the impact of volcanic forcing and el Nino/la Nina on global temperature, then remove it to generate an “adjusted” global temperature time series. After all, it’s an “adjustment” so it should really drive ‘em crazy (even if they insisted on it). Then we can subject the adjusted data to the same analysis I did here.

For volcanic forcing I’ll use Amman et al. 2003 (Ammann, C.M., G.A. Meehl, W.M. Washington, and C. S. Zender, 2003, A monthly and latitudinally varying volcanic forcing dataset in simulations of 20th century climate, Geophysical Research Letters, 30, 1657), area-weighted to get an approximation of global volcanic forcing. For estimates after 2000 I’ll assume no volcanic forcing, which will err on the side of making it harder to establish a warming trend (we won’t be able to blame any post-2000 cooling on volcanism). For el Nino/la Nina I’ll use the MEI (Multivariate el Nino Index). Then I can do a multiple regression of global temperature since 1975 against volcanic forcing, MEI, and a time trend, allowing for a lag in the impact of volcanism and MEI. Here’s the result:

As expected, volcanic aerosols cause cooling, sometimes quite dramatically (1992-93). Also as expected, el Nino warms while la Nina cools, sometimes dramatically (1998). As expected, the fit isn’t perfect; there’s still noise in there. Of course this simple multiple regression doesn’t model the impact of either of these exogenous factors perfectly, but it does give us a good first approximation of their effect, which enables us to remove the estimated volcanic/el Nino influence from the temperature time series, creating our adjusted temperature record:

Now we can apply the same analysis we used for the unadjusted data:

In one sense, the result isn’t any different. There’s still no evidence of any recent cooling trend, in fact there’s no evidence that the trend has been any different than it’s been since 1975. The data since 1975 are still indistinguishable from a linear trend plus random noise.

But in another sense, we do have a different result. The probable error is smaller. Because of that, we’re able to get a significant result (i.e., a trend which is significantly different from zero) with less data. Without adjustment, we needed 14 years data to get a significant result, and since there’s uncertainty in parameter estimates we actually need a bit more. But with adjustment, we get a significant result with only 10 years data. So the quantitative result is indeed different, but the qualitative result — no evidence of any trend change — is the same.

One last point may be of interest. If we compute annual averages of the adjusted data, we get this (the average for 2009 is incomplete because I don’t have December data yet):

The interesting thing is that, using the adjusted data, the warmest year on record is 2009! Of course that’s just “so far,” we’ll have to wait for December data before we can compute a complete annual average.

It’s intriguing that, when we account for the two best-known exogenous factors, the previous conclusion about trends is unchanged, but we do seem to be headed for a new “hottest year ever” — this year.

Categories: Global Warming

19 responses so far ↓

  • JohnV // December 31, 2009 at 5:51 pm | Reply

    What would it look like with an adjustment for the solar cycle as well? The most accepted value seems to be about 0.1C peak-to-trough (and probably a little more with this current extended trough of solar activity). Add that to 2009 and it was a *very* warm year.

  • Ray Ladbury // December 31, 2009 at 6:26 pm | Reply

    Ohhh, Snap!!! I can’t wait to see the gyrations when the denialist mothership starts hearing about this!

  • cogito // December 31, 2009 at 7:32 pm | Reply

    @Ray: Is that all you are interested in?

  • Chad // December 31, 2009 at 7:36 pm | Reply

    Hey Tamino,
    I recently did a similar analysis and it’s nice to see that we’ve got similar results (meaning I didn’t screw up!) However, I included solar effects. What were your lags for MEI and the volcanic forcing? I used 4 and 11 months, respectively. It’s also worth noting that taking these effects into account seriously reduces the lag-1 serial correlation which in turn reduces the inflation adjustment to the standard errors.

    Also, how do you make your graphics look so neat and fresh? What format/size do you use? I’ve been using PNG() in R with fairly high resolution, but they don’t look sufficiently pretty.

    [Response: I selected the best-fit lags, which turned out to be 4 months for MEI and 9 for volcanic forcing.

    I did the graphics in R, expanding them to full screen and saving as jpg files, then let wordpress crunch them to smaller size. I do expand the axis markers and labels to make them more legible.]

  • Ray Ladbury // December 31, 2009 at 8:40 pm | Reply

    Cogito, Hell no, but you gotta admit that its fun to watch ‘em react to an own goal.

    I don’t attach a lot of importance to analyses like this. We already knew the “negative trend” trumped by the denialosphere had ENSO stamped all over it. This merely brings it into focus.
    My guess is that somebody in the denialsphere will start throwing every connection they can think of and use it to explain the Universe.

    Cue McI in 5, 4, 3, 2…

  • Cthulhu // January 1, 2010 at 2:57 am | Reply

    A recent paper that looks at removing natural noise like ENSO and volcanic noise from the hadcrut record:

  • Lamont // January 2, 2010 at 6:30 am | Reply

    What about MEI vs. ERSSTv3b vs. global SSTs, etc? Are there other timeseries that would be a better ‘fit’ to modelling heat transfer from ocean activity to the atmosphere?

    Deniers will also probably want this analysis done with UAH rather than GISS for surface temperature (just pointing that one out).

    And the 4 month lag from ENSO conditions to atmospheric temperature response makes sense and I’ve come across that before — but what’s the physical explanation for the 9-t0-11 month lag for volcanic forcing (not doubting it, but i’ve just never come across that before)?

  • David B. Benson // January 2, 2010 at 9:14 pm | Reply

    Lamont // January 2, 2010 at 6:30 am — That 3/4 to one year lag also appears as the response to changes in TSI. The upper 10 meters or so of the ocean rapidly mixes due to wave action, so delay in the response seems to me to be due to the time required to heat about that much water.

  • Todd Friesen // January 2, 2010 at 9:42 pm | Reply

    I’ve been doing my own modeling of climate for a couple of years, and I agree that adjusted for natural variability, 2009 is the warmest year on record. Using the GISS data, 2005 was the warmest year, and I would apply a -0.04C adjustment for solar, and a -0.05C for ENSO to adjust for 2005 to 2009. From the data, I see that 2009 is roughly 0.05C cooler than 2005. Based on my anthropogenic+natural model (adjusted for ENSO, solar, volcanoes), I would have expected both years to be roughly the same. (Anthropogenic forcings, i.e. GHGs, aerosols, various albedoes etc.) suggest about a 0.09C warming, which are roughly offset by ENSO and solar).

    The model has about a standard deviation of 0.06C between model and actual annual global anomaly. 2005 was warmer than the model by about +0.06C (+ 1 s.d.), and 2009 is warmer by a little over +0.01C.

    Prospectively, I expect 2010 will be +0.08C warmer than 2005 actual, with a land+ocean anomaly of +0.71C. Anthropogenic forcings will contribute about +0.10C of this +0.08C, solar: -0.03C, ENSO: +0.07C. (This doesn’t add up to +0.08C because 2005 actuals were +0.06C warmer than model).

    Of course, these sorts of models don’t control for every global weather variable, just the most material ones.

    Interestingly, my model would have expected 2003 to be the warmest year, but in this case, actual was below model by 0.06C (-1 s.d.).

    Given no model bias, the chance of 2010 not breaking a new record is quite slim. A single-tail probability of less than -1.2 s.d. would be required (< 10%). The current El Nino (assuming it pans out for a few more months as per NOAA's predictions) is plenty strong enough to overcome any decline in solar irradiance relative to 2005. The 2010 El Nino impact is expected to be roughly the same as that for 1998. Not to say that the 1997-1998 El Nino was weaker (it won't be), but that much of the Nino impact from the 97-98 Nino was during the latter half of 1997.

  • Todd Friesen // January 2, 2010 at 9:54 pm | Reply


    With UAH and RSS being more sensitive to Ninos, it will be interesting what their response will be in 2010 when the impacts of the 2009-2010 Nino fully hit us. It’s convenient when you end with 2008 (a La Nina), but it won’t be nearly as convenient when they are quoting through 2010. But as has been suggested, for deniers, they tend only to make Nino adjustments when it suits them.

  • Todd Friesen // January 3, 2010 at 3:41 am | Reply

    Here is my reconstruction of 1975-2009 GISS data adjusted for the sun, volcanoes, and ENSO. Looks pretty similar to Tamino’s. Also shows 2009 as the hottest year. (I estimated 2009 with my modeled December in-month projection at +0.63C).

  • Todd Friesen // January 3, 2010 at 3:43 am | Reply

    Here is my model vs GISS record for 1880-2009.

  • Lamont // January 3, 2010 at 3:48 am | Reply

    I’m sure they’ll just move the goal posts around…

    It’ll be emotionally fun to beat on them, but they’ll come up with more rationalizations…

    But now that you mention it, you brought up another issue that I haven’t had time to read up on — why is UAH/RSS more sensitive to ENSO?

  • jyyh // January 3, 2010 at 4:39 am | Reply

    Lamont, the effects of ENSO are more notable on the tropics and the two series do not account the arctic.

    On the solar variation, the issue of lag is not clear to me. If the standard lag used with it is 4 months, and the wave effect is the only one that is used to explain this, how can we be sure there are no longer lags in the system? One might want to allow very long lags for it for the unaccounted slow downwelling and such?

  • jyyh // January 3, 2010 at 4:45 am | Reply

    sorry, the 3/4 to one year lag…

  • Todd Friesen // January 3, 2010 at 6:44 am | Reply


    I don’t know the answer, just that apparently there are sensitivity differences between the surface and the lower troposphere (4-10km above surface). Because of the irregular shape of Nino events, statisical fitting is fairly credible way to detect the Earth’s sensitivity, and my statistical fitting shows that LT sensitivity is higher by about 70% compared to the surface. For example, 2010 Nino might influence global temperatures by +0.10C on the GISS dataset (similar for HadCRU). But this would be +0.17C on the satellite datasets.

    Could it be because of the greenhouse blanket? The stratosphere doesn’t show as much senstivity to Nino. This would suggest that the heat released into space is slowed down by the greenhouse blanket, and it thus would concentrate at higher altitudes (provided they are below the blanket).

  • Slioch // January 3, 2010 at 11:47 am | Reply

    Tamino: “using the adjusted data, the warmest year on record is 2009! Of course that’s just “so far,” ”

    Not only that, but every year from 2001 to 2009 is warmer than 1998.

  • David B. Benson // January 3, 2010 at 10:55 pm | Reply

    jyyh // January 3, 2010 at 4:45 am — The 2/4 to 1 year lag is the phase delay of the fast response portion. There is also a 30 year characteristic time for the rest of the ocean done to the main thermocline.

  • David B. Benson // January 4, 2010 at 12:10 am | Reply

    “2/4″ –> “3/4″
    “done” –> “down”

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