Troy's Scratchpad

May 23, 2011

Comparing Nino-Adjusted HadCRUT to CMIP3 A1B MMM projections

Filed under: Uncategorized — troyca @ 8:19 pm

In previous posts, I had used the difference between the multi-model mean and observations in the 20th century to try and determine a simple noise model, and then extend this to see what kind of confidence intervals we could expect for the 21st century A1B projections.  The result of this AR(1) process used to simulate noise was pretty successful for the 20th century, in that it gave tighter bounds around the MMM but still seemed to keep the observations inside the 54 runs.  Extending it to the include 2001-2010 projection suggested that observations were on the lower end for the 2001-2010 period, but the major three datasets were within the 2.5% – 97.5 % confidence interval.

However, one of the things that the models do a poor job of simulating are ENSO variations.  This can have an effect on a multi-year period, and certainly affects annual anomalies.  So, I was curious about removing the ENSO component from the variations and seeing how that affected the error in the hindcast.  In fact, this was part of the reason why I recently ran some regressions at different lag times with various other factors.

For this, I took a slightly different approach, which was to assume that the bulk of the error between the “forced component”/MMM and actual observations was simply the result of ENSO (since the model hindcasts include solar and volcanic forcings) and regressed the error against the Nino 3.4 index.  Because the MMM does not properly simulate at sub-annual time scales I had to aggregate to the annual level after lagging Nino3.4 by a few months.  This method is cheating a bit because the way this is set up means that removing a Nino3.4 component could never increase the error.  However, it would probably not be accurate to regress against the entire 20th century and assume an underlying linear trend, particularly because we’d need to include solar, man-made aerosol, and volcanic forcings as well to determine what ENSO has contributed.  Besides, this is more of a what-if situation where we’re wondering what extra noise would look like IF the MMM represents the “forced component” and IF the remainder of the error is primarily the result of ENSO.

Anyhow, the script is available here.

After regressing the 20th century annual errors against Nino3.4, the best fit I get is .082 * Nino3.4 (lagged 5 months):

The variance of the error between the unadjusted HadCRUT obs and the MMM is about .0150, compared to .0118 when we adjust HadCRUT for ENSO based on our fit.  Not a giant improvement, and so it is doubtful that ENSO itself would explain the errors in the models around the 1940-1960 period.

But from about 1975 on the errors shrink quite a bit, improved significantly by the Nino fit:

During this time period, the best fit is .089 * Nino3.4 (lagged 6 months), so fairly similar to our entire period, and a similar coefficient/magnitude to what we were getting for Nino in the regressions solely against observations in the previous post.  Here the variance in errors goes from .00769 to .00261 when we perform the ENSO adjustment, a pretty large improvement even considering the lower DF.  Running AR on the residuals suggests that the noise here is more likely to be white than from an AR(1) process, and the small variance in the residuals further suggests we can get yet tighter bounds during this more “accurate” 1975-1999 period.

The distribution of these remaining errors don’t look quite normal, but I’ll use the approximation anyway for my MC sims:

Similar to what I did previously, I will create new “runs” of the models based on the MMM + noise for bootstrapping the confidence interval.  First, a look at 1975-2010 if I use this white noise model with the above variance:

As can be seen, the yellow “model runs” are much tighter around the MMM than both the AR(1) noise model runs did and the actual CMIP3 individual runs.  However, what is interesting is that while the black line representing the observations often jumps outside these bounds in the 1975-1999 period, the green ENSO-adjusted observations stay much closer within it.  It is only in recent years that they have left the area.

So, what do our trends look like from 2000-2010 if we use this white noise model?

The resulting confidence interval for 2.5% – 97% is [0.112, 0.290] C/decade, and the Nino3.4 adjusted trend for HadCRUTv3 is well outside of it at .0037.

Of course, we have fitted Nino3.4 to the 1975-2000 errors, so it’s no surprise that we get a smaller error there than we would expect for the 21st century projections, which have not been used for training.  Furthermore, the models don’t have solar and volcanic forcings for the forecast the way they did for the hindcast, so that might be another source of divergence.  Then there is the question of whether actual forcings have tracked the A1B scenario, and of course there are other temperature data sets (I may try this with GISS).

Still, what’s interesting to me is how small of a noise model would explain the errors between the MMM and the ENSO-adjusted HadCRUT observations from 1975-2000.  It seems particularly surprising given the way the projections and actual observations diverge early in the 21st century.



  1. If you try it with GISTEMP, you’ll likely find a better agreement, since the “hump” starting in 1998 is less, and the temps in recent years is more.

    Also, Hansen’s new draft paper has updated ModelE forcings, and shows a decline since the AR4 runs were made.

    He says this:
    “In summary, precipitous decline in the growth rate of GHG forcing about 25 years ago caused a decrease in the rate of growth of the total climate forcing and thus a flattening of the planetary energy imbalance over the past two decades. That flattening allows the small forcing due to the solar cycle minimum, a delayed bounceback effect from Pinatubo cooling, and recent small volcanoes to cause a decrease of the planetary energy imbalance over the past decade.”

    A lot of that was apparent when the AR4 runs were done, but the abnormal decline in solar was not, and perhaps the “airborne fraction” remaining at ~55% wasn’t obvious either.

    FWIW, he also believes that the AR4 models understate negative aerosol forcing, while overstate ocean mixing.

    Comment by cce — June 20, 2011 @ 2:04 am

    • Thanks for stopping by, cce. You are correct that a similar analysis with GISTemp does not suggest the AR4 MMM is running quite as high. Here is a picture that shows why — first, as you mentioned, the temperature trend in the 21st century is higher for GISTemp; and second, the Nino index used does not quite have the same explanatory power in errors of GISTemp vs. MMM as it did with HadCRUT, thus resulting in a wider range of possible trends. The results can be seen here…basically, I get a confidence interval of [.072,..329] for the 2.5%-97.5%, with a median of .198 C /decade for the MMM + white noise. The GISTemp 21st century trend of .102 is on the lower end, but certainly within it. Since you’ve forced me to do the extra work (which I should’ve done by now anyhow), I might as well put the link to the modified script here 🙂

      Also, thanks for the link. I’m not particularly surprised that he believes the models understate negative aerosol forcing, as the primary other option would be that they overestimate GHG warming. Do you know if this paper is slated to be published? I was surprised by some of the language found in it, e.g. “In that event, humanity has made itself a Faustian bargain more dangerous than commonly supposed.”, which seemed more like it was heading for grey literature than peer review?

      Comment by troyca — June 20, 2011 @ 10:37 pm

  2. According to the note linking to the draft, it hasn’t been submitted yet. As for the language, that’s Hansen being Hansen. I suspect (hope?) it will be toned down whenever the paper is published. The references to his grandchildren are especially distasteful.

    Comment by cce — June 21, 2011 @ 9:41 pm

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