My blog philosophy is to consider all possible physical explanations for the data we are examining, and see whether or not they seem to explain the data. As many know, climatologists tell us that much of variability in global mean surface temperature is driven by the ENSO cycle (i.e. the El Nino/La Nina cycle.) In particular, some speculate the recent “flat” or “down” trend in global mean surface temperatures (GMST) is due to the recent La Nina. So, they suggest the recent falsification of the IPCC AR4 ‘best estimate’ prediction of 2C/century is not falsified by the current data, because we have not accounted for ENSO.

Certainly, we agree that La Nina has driven down temperatures, but we also observe the temperature went flat long before this La Nina, and we have had several El Nino/ La Nina switches since Jan. 2001, the start date I use to test the IPCC AR prediction for warming.

Recently, I did a “back of the envelope” type computation to estimate the effect of ENSO, and found this phenomena could not be sufficiently strong to explain away the flat trend in the data.

One of my blog readers, Roger W Cohen, did me one better and decided to add the ENSO MEI indicator as a variable in the Cochrane-Orcutt fit to the recent monthly data. Neither he nor I have done a full analysis of the uncertainty, but it currently appears that if we include ENSO explicitly one finds:

1. It explains roughly 0.2C of the negative trend.
2. By accounting for some of the periodicity autocorrelation, it makes the falsification stronger.

Roger’s results look entirely plausible. If Roger’s analysis is correct, this result is quite strong because:

• the correlation between ENSO and GMST is widely accepted,
• the correlation was suggested by critics who doubt the falsification of the IPCC AR4 predictions and who insisted ENSO would overturn the falsification. That is: this is not a correlation “fished out of the soup” by those hunting around for ways to prove themselves right,
• other than adding a widely used index to correlate with the temperature changes due to ENSO, no “fiddling” was involved in the basic method to fit GMST data to a trend line and
• this statistical method is not fancy. (Believe it or not: not fancy is a good thing in statistical inference. It tends to indicate the analyst didn’t go hunting through the catalog of every method until they found a method that works.)

Why am I not more forceful?

I don’t have real estimates of the uncertainty yet. The reason we do not have complete estimates of the uncertainty are:
1) I need to look into how we incorporate the uncertainty introduced due to Roger’s estimate of the lag between the ENSO MEI index and the GMST. (I believe he used a 2 month lag. )
2) I need to account for the new, reduced amount of serial autocorrelation in residuals on the uncertainty in the estimated trend and
3) I mostly just need to digest this a bit more, and add in more recent data, check numbers etc. (No, I didn’t check Rogers numbers or audit them. 🙂 )

But the main result –by way of Roger is–: Accounting for ENSO explicitly suggests the falsification of IPCC projections is stronger than found when ENSO is treated as “weather noise”. (I treated it as weather noise.)

The remainder of the post will consist primarily of quotes from Roger’s blog comments and email.

Roger W Cohen’s Figures and Explanation

Roger describes this figure as follows:

The first figure shows the data from January 2001. The black line is the OLS fit corresponding to the -0.83 deg/century trend with an r 2 of 0.03. The red line is the fit with the control for the MEI index. The fit, being linear, is actually a plane in the 3D-space of Temperature-Time-MEI, and what you’re looking at is the projection on the time axis of a particular path in that plane. The path follows the actual MEI for each time increment. The underlying trend is now -0.65 deg/century, and the r 2 is up to 0.33. You can see the improved correlation visually. The deduced temperature swing from ENSO effects over this period is actually fairly large – more than 0.2 deg C.

He continues, explaining his results:

As I said in the note to your blog, including the second variable makes hypothesis testing more definitive. There are two reasons for this. First is the immediate reduction in the standard deviation of the underlying climate trend. For example, if I use the analysis (no C-O) to estimate the statistic against the IPCC prediction of “about” 2, one gets:

Time only: (2 + 0.83) / 0.51 = 5.4
Time and MEI: (2 + 0.65) / 0.42 = 6.3

Second, since serial correlations are reduced, the application of a correction procedure such as C-O to this analysis as a starting point is expected to give a smaller increase in the uncertainty of climate trend slope, so you should end up with a firmer conclusion.

For readers unfamiliar with statistics, I will note three things:

1. When Roger says “2” he is referring to 2 C/century. The statistic is a “t”
2. Roger does find that ENSO has a detectable effect on temperature.
3. The “standard deviation” mentioned by Roger is the primary variable dictating the diameter of the scatter range in the “dartboard” illustrations I discussed yesterday. So, Roger is saying that, by incorporating phenomenology (called “the physics” in blog posts) into the statistics, we reduce the “scatter” when we try to estimate the trend. In words, if the standard deviation is cut in half, we expect the diameter of the circles in those “dart boards” to be cut in half.
4. The “serial autocorrelation” in residuals that Roger refers to is the factor that Tamino is discussing in his blog post, and which he uses to justify inflating the error bars in his analysis. It is a complicating factor in any statistical analysis. Tamino’s current approach is to do the crudest analysis possible, and insist on large error bars.

   Roger is suggesting we incorporate known physical explanations for the statistical artifact, and reduce the error bars in this way. Roger’s method is generally preferred by those wishing to understand data, predict trends, understand phenomena, or test hypotheses.

Roger describes the characteristics of the residuals:

The second figure shows the residuals. While correlations are reduced from the time-only case, they are still evident (rho1=0.46). Presumably this is due to (1) inadequacies of using MEI as surrogate for ENSO-induced global temperature change; and/or (2) something else going on over timeframes of months.

What’s left to do?

Based on Roger’s analysis, I plan to incorporate the MEI index into my fit, and then account for serial autocorrelation in the remaining residuals. The magnitude of these residuals is reduced when ENSO is included explicitly, so we anticipate this could reduce uncertainty intervals. Moreover, since ENSO explains a large amount of the correlation at large lag times, we might anticipate that the remaining climate process will be approximately AR(1). (Of course, none of this can be known until the analysis is done.)

I plan a boring post to explain why AR(1) might describe variations in GMST, at least over short time scale. Very simple models for the climate, such as those used by Steve Schwartz of Brookhaven National Laboratory, suggest AR(1) may be a a reasonable approximation for the remaining climate process. However, I noted that when the noise in the data are excessive, there will be difficulties applying AR(1) to the data. This is because measurements of the earth’s surface temperature are not precisely the same thing as the earth’s temperature. The result is the physical model and the data model (used for statistics) are related but not identical. (I discuss this a bit in My comment on Steven Schwartz’s estimate of the climate time constant. The relevant portion is my discussion of the relatively mistake Tamino made when criticizing Schwartz’ analysis. Basically: Tamino mistook the physical model for the data model. )

So, not to leave you hanging… but the ENSO topic, and the issue of serial autocorrelation in the residuals is “to be continued”. 🙂