Removing The Effects of Natural Variables – Multiple Linear Regression-Based or “Eyeballed” Scaling Factors

Guest post by Bob Tisdale

This is the second of a series of follow-up posts to Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases?. The first follow-up was Notes On Polar Amplification.

This post discusses the impacts on global temperatures of a natural mode of Sea Surface Temperature variability: the El Niño-Southern Oscillation (ENSO). If this subject is new to you, refer to the post An Introduction To ENSO, AMO, and PDO – Part 1.

INTRODUCTION

My post Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases? was cross posted at Watts Up With That? under the same title (Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases?) In a step-by-step process, that post illustrated how I was removing the linear effects of El Niño and La Niña events and of volcanic eruptions from the global temperature record during the satellite era. I then went on to explain and provide links to more detailed explanations of the secondary effects of the ENSO process and how they impact the multidecadal trend.

There were a few comments on the WUWT thread about my use of “eyeballed” scaling factors. They wondered what I meant by “eyeballed”, expressed concern about a scaling factor that was not based on statistics, and suggested using EXCEL to determine the scaling factors.

“EYEBALLED” SCALING FACTORS

The scaling and lag I used in comparisons of the global temperatures and the ENSO and Volcano proxies were established by the visual appearance of the two variables, using the larger(est) event (the 1997/98 El Nino, and the 1991 Mount Pinatubo eruption) as reference. “Eyeballed” simply referred to the visual comparison of the impacted variable (global temperature) and the impacting variables (ENSO and Volcanic eruptions). Refer to Figure 1, which is also Figure 1 from Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases?. Note how the NINO3.4 data has been scaled (multiplied by a factor of 0.16) and lagged (moved back in time 3 months) so that the rises of the two datasets are about the same during the evolution of the 1997/98 El Niño. Notice also how the response of the global temperature data to the lesser ENSO events after 2000 doesn’t always align with the NINO3.4 SST anomalies.

http://i53.tinypic.com/deuxdz.jpg

Figure 1

The data indicates that the larger events (such as the 1997/98 El Nino) are strong enough to overcome the noise that can mask the global response to lesser events. In other words, I used the larger 1997/98 ENSO event as reference because the response to it was clearest. Statistical methods such as linear (or multiple linear) regression rely on the relationship between two (or more) datasets over the term of the data. Any additional noise in the data during the smaller ENSO events (and during the lesser volcanic eruptions) may bias the results.

If we could determine the cause or causes of that additional noise, then adding those variables to a multiple linear regression analysis would be helpful.

MULTIPLE LINEAR REGRESSION

Analyse-it for Excel is a statistical add-on package for EXCEL. (It has a 30-day free trial period). One of its features is multiple linear regression. Their Multiple linear regression webpage provides a general description of this feature: “Linear regression, or Multiple Linear regression when more than one predictor is used, determines the linear relationship between a response (Y/dependent) variable and one or more predictor (X/independent) variables. The least-squares method is used to minimize the vertical distance between the response and the fitted linear line.”

The response variable discussed in this post is global temperature (represented by GISS LOTI from 60S-60N) and the predictor variables are ENSO (represented by NINO3.4 SST anomalies) and volcanic eruptions (represented by GISS Stratospheric Aerosol Optical Thickness data: ASCII data). Figure 2 shows the differences in the variability of those three datasets.

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Figure 2

According to the EXCEL multiple regression software, the scaling factor to best fit the wiggles of the ENSO data to those in the global temperature data is 0.07262, and for the Aerosol Optical Thickness data it’s -3.191.

Note: The scaling factors determined by the regression software in this post are based on the “raw” data. I’ve used a 13-month running-average filter in the graphs after the fact to reduce the visual effects of seasonal variations and other noise.

In Figure 3, I’ve illustrated the multiple linear regression-estimated relationships between the GISS LOTI data, the NINO3.4 SST anomalies (ENSO), and the GISS Stratospheric Optical Thickness (Volcano) data. The scaling for the Volcano proxy data appears too large, while the scaling for the ENSO proxy appears too small. The global temperature anomaly (60S-60N) response to the 1997/98 El Niño almost doubled the rise in the scaled NINO3.4 SST anomalies.

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Figure 3

Figure 4 illustrates the result when we subtract scaled ENSO and Volcano proxy data from the Global Temperature data. That dataset is supposed to represent global temperature data that has been adjusted for ENSO and volcanic eruptions. I’ve also included the scaled NINO3.4 SST anomalies to show that much of the ENSO signal remains in the data. Note also how the response in global temperature lags the ENSO proxy.

http://i51.tinypic.com/20ffatc.jpg

Figure 4

Multiple linear regression does not appear to do a good job of removing the impacts of ENSO.

THREE-MONTH LAG

Referring back to Figure 1, we can see that the global temperature response during the 1997/98 El Niño lagged the NINO3.4 SST anomalies by 3 months. Let’s also look at the Volcano proxy. Figure 5 shows it and the ENSO-adjusted GISS Land-Ocean Temperature Index (LOTI) data from Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases?. (Figure 5 was Figure 2 in that post.) In order to align the leading edge of the global temperature response to the 1991 eruption of Mount Pinatubo (the larger and clearer response), I had to lag the Volcano proxy 3 months.

http://i51.tinypic.com/8vyd54.jpg

Figure 5

If we shift the NINO3.4 SST anomalies and Aerosol Optical Thickness data three months, the EXCEL Analyse-It software, of course, calculates different scaling factors: 0.08739 for the ENSO proxy and -3.495 for the Volcano proxy. The ENSO- and Volcano-adjusted data using these updated scaling factors (based on a 3-month lag) is shown in Figure 6. Again, much of the ENSO signal remains.

http://i53.tinypic.com/2q1ib7t.jpg

Figure 6

Once again, multiple linear regression appears to have done a poor job of removing the effects of ENSO.

MODEL-PREPARED SCALING FACTORS

In a 2009 paper, Thompson et al created models of global temperature responses to ENSO and Volcanic eruptions. The paper was “Identifying Signatures of Natural Climate Variability in Time Series of Global-Mean Surface Temperature: Methodology and Insights”. Link : http://www.atmos.colostate.edu/ao/ThompsonPapers/ThompsonWallaceJonesKennedy_JClimate2009.pdf

On page 2 they provided an overview of their methods: “The impacts of ENSO and volcanic eruptions on global-mean temperature are estimated using a simple thermodynamic model of the global atmospheric-oceanic mixed layer response to anomalous heating. In the case of ENSO, the heating is assumed to be proportional to the sea surface temperature anomalies over the eastern Pacific; in the case of volcanic eruptions, the heating is assumed to be proportional to the stratospheric aerosol loading.”

The same method was used in its companion paper Fyfe et al (2010), “Comparing Variability and Trends in Observed and Modelled Global-Mean SurfaceTemperature.”

http://www.atmos.colostate.edu/ao/ThompsonPapers/FyfeGillettThompson_GRL2010.pdf

Thompson et al provided a link to their “Global Mean”, “ENSO fit”, and “Volcano fit” data. Link to Data. Figure 7 shows the three Thompson et al datasets. Note: Thompson et al examined the data from 1900 to March 2009. Since we’re only looking at the change in temperature during the satellite era (dictated by the second, more recent of the two SST datasets used by GISS) I had to shift their global mean data down 0.25 degrees C to align it with the other datasets.

http://i53.tinypic.com/286zdpf.jpg

Figure 7

And Figure 8 shows what Thompson et al refer to as the “ENSO/Volcano Residual Global Mean” temperature anomalies after the ENSO and Volcano proxy signals have been removed. And, again, I’ve included the “ENSO fit” data to show how poorly it approximated the “Signatures of Natural Climate Variability in Time Series of Global-Mean Surface Temperature”. The response of their adjusted Global Mean Temperature to the 1997/98 El Niño is greater than their “ESNO fit” data, and this is after the effects of ENSO have supposedly been removed.

http://i51.tinypic.com/2z82jo8.jpg

Figure 8

In summary, linear regression and models prepared for climate studies appear to do a poor job of removing the linear effects of ENSO. If the secondary effects of ENSO were also included in the multiple linear regression, would the results be better?

These secondary effects are easy to see if we look at…

THE RESULTS USING THE EYEBALLED METHOD

As noted earlier, for the “eyeballed” method, I keyed the scaling of the ENSO and Volcano proxies visually off the leading edges of the 1997/98 El Niño and the 1991 eruption of Mount Pinatubo. Refer to Figure 9. In this example, I’ve reduced the scaling on the Volcano proxy data, so that its impact is approximately 0.2 deg C for the Mount Pinatubo eruption.

http://i55.tinypic.com/9iy1xd.jpg

Figure 9

The result when the ENSO and volcano signals are removed is shown in Figure 10. Also shown is the scaled ENSO proxy as a reference. The rises that occur after the 1986/87/88 and the 1997/98 El Niño events make it appear as though there is another lagged ENSO-related signal.

http://i54.tinypic.com/351gxds.jpg

Figure 10

And to see this signal, we invert the scaled NINO3.4 SST anomalies. Refer to Figure 11. That is, we multiply the NINO3.4 SST anomalies by a negative number (-0.1 scaling factor). The inverted ENSO data has not been lagged. But it has been shifted down 0.05 deg C to align it with the 1987/88 upward shift in the ENSO- and Volcano-adjusted global data. The two datasets diverge slightly at times between 1989 and 1996, but the adjusted global temperatures follow the inverted NINO3.4 SST anomalies reasonably well. Then there is a significant divergence during the evolution of the 1997/98 El Niño. The adjusted global temperature anomalies do not drop at that time proportionately to the El Niño. (And there is no reason global temperatures should drop a large amount. The majority of the warm water that fuels an El Niño comes from below the surface of the Pacific Warm Pool.)

http://i56.tinypic.com/2da0dx4.jpg

Figure 11

If we shift the NINO3.4 SST anomalies up 0.21 deg C, Figure 12, we can see that the adjusted global temperatures rise in response to the transition from El Niño to La Niña in 1998 and then, once again, they follow the general variations in the inverted NINO3.4 SST anomalies, but running in and out of synch with it.

http://i54.tinypic.com/msi0br.jpg

Figure 12

In other words, the vast majority of the rise in ENSO- and Volcano-Adjusted GISS Land-Ocean Temperature Index data could be explained by one or more detrended Sea Surface Temperature dataset(s) that mimicked inverted NINO3.4 SST anomalies with upward shifts, similar to what’s illustrated in Figure 13.

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Figure 13

I qualified the above statement with “detrended”. At a few alarmist blogs, I received a few negative comments about my Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases? post because I had used the trends in the SST subsets to explain the trend in global temperature. I had explained in the post why the upward trends were associated with the process of ENSO, but I received the complaints regardless. Those bloggers, of course, failed to read the explanation (It starts under the heading of “La Niña Events Are Not The Opposite Of El Niño Events”) or had elected to misrepresent my post. But in order to overcome this objection in this post, I’ll use detrended SST anomalies for the following illustrations. The same and other bloggers also complained about the minimal sizes of the Kuroshio-Oyashio Extension and South Pacific Convergence Zone (SPCZ) Extension SST subsets I used in the “Can Most” post. Those areas were used because they had the strongest warming signals during a La Niña. But since the objections exist, I’ll use SST datasets that represent larger portions of the global oceans.

There are two detrended sea surface temperature subsets covering significant portions of the global oceans that have the same upward changes in temperature during those two El Niño to La Niña transitions shown in Figure 13. But if we had relied on the scaling factors suggested by the multiple linear regression, or if we had used a model similar to the one created by Thompson et al, would we have noticed the relationship?

EAST INDIAN-WEST PACIFIC SST ANOMALIES

The first of the SST subsets is the East Indian-West Pacific Ocean. The coordinates of this dataset are 60S-60N, 80E-180E. I’ve highlighted those coordinates in the following map. Figure 14 is a correlation map of annual (January to December) East Indian-West Pacific SST anomalies and annual GISS LOTI data for 1982 to 2010. Much of the Northern Hemisphere land surface temperature anomalies vary with the East Indian-West Pacific SST anomalies. That is, when the East Indian-West Pacific SST anomalies rise in those upward ENSO-induced steps, so do those areas highly correlated with it.

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Figure 14

I have discussed the East Indian-West Pacific dataset in many posts over the past two years, so I do not intend to repeat the discussion here. Those posts started with Can El Niño Events Explain All of the Global Warming Since 1976? – Part 1 and Can El Niño Events Explain All of the Global Warming Since 1976? – Part 2. The most detailed explanation of why the East Indian-West Pacific SST anomalies shift upwards as a response to those two ENSO events is provided in my series of posts:

More Detail On The Multiyear Aftereffects Of ENSO – Part 1 – El Nino Events Warm The Oceans

And:More Detail On The Multiyear Aftereffects Of ENSO – Part 2 – La Nina Events Recharge The Heat Released By El Nino Events AND…During Major Traditional ENSO Events, Warm Water Is Redistributed Via Ocean Currents.

And:

More Detail On The Multiyear Aftereffects Of ENSO – Part 3 – East Indian & West Pacific Oceans Can Warm In Response To Both El Nino & La Nina Events

And for those who like visual aids, refer to the two videos included in La Niña Is Not The Opposite Of El Niño – The Videos.

Again, to overcome one of the complaints, I need to detrend the East Indian-West Pacific data. Detrending is said to eliminate the “global warming signal”. So I employed the same method used for the Atlantic Multidecadal Oscillation data. HADISST is the long-term Sea Surface Temperature anomaly dataset used by GISS in their LOTI product. The long-term HADISST (1870-2010) East Indian-West Pacific SST anomalies had a linear trend of 0.44 deg C per Century, and that’s slightly higher than the global SST anomaly trend of 0.39 deg C per century. To detrend it, I subtracted the linear trend values for each month from the East Indian-West Pacific SST data.

And as shown in Figure 15, the detrended East Indian-West Pacific SST anomalies could easily explain much of the rise in the ENSO- and Volcano-Adjusted GISS LOTI data since 1982. The similarities between the adjusted global temperature data and the East Indian-West Pacific SST anomaly data are remarkable.

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Figure 15

As discussed and illustrated in the linked posts, the upward shifts in the East Indian-West Pacific SST anomalies are secondary effects of the warm water that was leftover from the 1986/87/88 and 1997/98 El Niño events and the results of the La Niña process itself. Basically, the ENSO processes cause the SST for this part of globe to rise in response to both El Niño and La Niña events. And the effects are cumulative if a La Niña follows an El Niño. The cumulative effect can be seen in the following animation. It shows a series of maps of 12-month average global SST anomalies, and it runs from the start of the 1997/98 El Niño to the end of 1998/99/00/01 La Niña. To its right is a graph of scaled NINO3.4 SST anomalies and the SST anomalies of the East Indian-West Pacific Oceans. The data in the graph have been smoothed with a 12-month running-average filter to match the maps.

http://i51.tinypic.com/2qiwscz.jpg

Animation 1

And for reference, Animation 2 includes the Sea Surface Temperature Anomalies of the rest of the oceans (East Pacific, Atlantic, and West Indian), and this dataset includes the North Atlantic with its Atlantic Multidecadal Oscillation.

http://i51.tinypic.com/b46lph.jpg

Animation 2

The next variable is widely known, but it is often overlooked.

THE ATLANTIC MULTIDECADAL OSCILLATION (AMO)

The second dataset that matches the upward steps in the adjusted GISS LOTI data is the Atlantic Multidecadal Oscillation or AMO data. For those new to the AMO, refer to the post An Introduction To ENSO, AMO, and PDO — Part 2.

The AMO data used here is detrended North Atlantic SST anomaly data. Again, as noted in the Wikipedia Atlantic Multidecadal Oscillation webpage, “detrending is intended to remove the influence of greenhouse gas-induced global warming from the analysis.” The data is available through the NOAA Earth System Research Laboratory (ESRL) Atlantic Multidecadal Oscillation webpage (the AMO unsmooth, long: Standard PSD Format data).

Figure 16 is a correlation map of annual (January to December) Atlantic Multidecadal Oscillation (AMO) data and annual GISS LOTI data for 1982 to 2010. Like the East Indian-West Pacific SST anomalies, much of the northern hemisphere varies in temperature with the AMO. Again, this means that much of the northern hemisphere surface temperatures rise with the upward steps in the AMO data.

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Figure 16

And for those interested, Figure 17 is a GISS LOTI trend map created at the GISS Global Mapswebpage. It illustrates the rise in surface temperature anomalies from 1982 to 2010. Note the similarities between it and the correlation maps in Figures 14 and 16. For the most part, the regions where the AMO and the East Indian-West Pacific SST anomalies correlate with the Global GISS LOTI data are also where most of the rises in surface temperature occurred. There are a few areas with differences, but the maps agree quite well.

http://i56.tinypic.com/2lar62e.jpg

Figure 17

The AMO data is compared to the adjusted GISS LOTI data in Figure 18. Again, note the agreement between the AMO data and the adjusted GISS LOTI data.

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Figure 18

And if we compare the ENSO- and Volcano-adjusted GISS LOTI data to both detrended SST-based datasets, Figure 19, we can see that it wouldn’t require a lot of effort to explain most of the global warming from 1982 to 2010 using the AMO and detrended East Indian-West Pacific SST anomaly datasets.

http://i53.tinypic.com/2gt9mic.jpg

Figure 19

Let’s add the AMO and the detrended East Indian-West Pacific SST anomalies to the multiple regression analysis and see how that impacts the results.

MULTIPLE LINEAR REGRESSION WITH ENSO, VOLCANO, AMO, AND EAST INDIAN-WEST PACIFIC SST DATA

The NINO3.4 SST anomalies, the mean optical thickness data, the AMO data, and the detrended East Indian-West Pacific (EIWP) SST anomalies were all entered into the EXCEL multiple linear regression software as predictors with the GISS LOTI data as the response variable. EXCEL determined the scaling factors listed in parentheses in Figure 20. The GISS LOTI data illustrated has been adjusted by those four scaled variables. I’ve also included the scaled NINO3.4 SST anomalies as reference. The low frequency variations in the adjusted GISS data mimic the ENSO proxy before the 1997/98 El Niño. They show little relationship from 1998 to 2007, and then they appear to mimic one another again.

http://i51.tinypic.com/f4g3ns.jpg

Figure 20

Figure 21 compares the unadjusted GISS LOTI data (60S-60N) to the data that has been adjusted by the four factors. The trend of the adjusted data is approximately 27% of the unadjusted GISS LOTI data. In other words, approximately 73% of the rise in global (60S-60N) surface temperature could be natural.

http://i51.tinypic.com/dpvhhd.jpg

Figure 21

And for the sake of discussion, I had EXCEL perform the regression analysis again, but I used “raw” East Indian-West Pacific SST anomalies instead of the detrended data. As one would expect, the multiple regression software created different scaling factors, which are listed in Figure 22. It compares the resulting adjusted global (60S-60N) temperature anomalies to the unadjusted GISS LOTI data. In this instance, the trend of the adjusted data is approximately 18% of the unadjusted data, which is similar to the result I reached using the “eyeball” method and different natural factors in Can Most Of The Rise In The Satellite-Era Surface Temperatures Be Explained Without Anthropogenic Greenhouse Gases?.

http://i51.tinypic.com/2s60p40.jpg

Figure 22

Would the eyeball method with the AMO and East Indian-West Pacific adjustments reduce the global temperature trend by similar amounts? We’ll have to look at that in another post. This one is long enough.

THANKS TO…

…Michael D Smith for suggesting EXCEL to weed out lags, scaling factors, etc. Without his suggestion, I would not have looked for the Analyse-it for Excel. I think I’m going to buy it when the trial period is done.

SOURCES

The GISS LOTI, Reynolds OI.v2 SST (for the NINO3.4 SST anomalies), and HADISST (for the detrended East Indian-West Pacific SST anomalies) data used in this post are available through the KNMI Climate Explorer:

http://climexp.knmi.nl/selectfield_obs.cgi?someone@somewhere

The Stratospheric Aerosol Optical Thickness data is available from GISS:

http://data.giss.nasa.gov/modelforce/strataer/tau_line.txt

And the Atlantic Multidecadal Oscillation data is available from NOAA ESRL:

http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data

Posted by Bob Tisdale at 5:59 AM

55 thoughts on “Removing The Effects of Natural Variables – Multiple Linear Regression-Based or “Eyeballed” Scaling Factors

  1. Good analysis.
    I reach a little bit wider, myself (and more crudely). I note that the PDO, AMO, SO, NAO, AO, and AAO all went from cool phase to warm phase one by one from 1976 to 2001.
    I think that had a significant effect on the warming.
    Since then, they’ve all been on warm phase, with the PDO beginning to flip towards the end. That would explain the flatline trend since 2001.

  2. Bob T. – You are the man!
    I particularly like the animation utilizing simultaneous geo temp chart and temp graphs. Thank you for your efforts regarding these high hanging fruit. GK

  3. Here’s how I see it. If all people were gone, and all the forests grew without us (major rise in O2). All it would take is many bolts of lightning and you would have a mass confligeration and alot more Carbon monoxide, and Carbon dioxide.

  4. It seems to me that what you are trying to do is match the detailed patterns in datasets by varying some (two or three) parameters.
    Rather than by “eyeballing” the resulting matches to estimate the best fit parameter, why don’t you calculate the correlation function between the two datasets as you vary the parameters? You then look for the peak in the correlation function which gives you the best match by a rather more quantifiable method than “eyeballing”.
    It’s possible to do this by changing one parameter at a time and repeating the process until you get the best fit – by calculation, not eyeballing. The process should end up looking pretty similar to the “eyeballing” results if the parameters you have chosen really do have something to do with the real data.
    With some (quite a bit of!) work you could also get some statistical measure of the goodness of the matches as well …

  5. John Cooke
    January 29, 2011 at 10:00 am
    What you are talking about is the very bleeding edge of math. Often, mathematical analysis tools are inspired by what we do naturally. The human mind is still the best pattern matching device we have. On the other hand, I do think tools such as wavelet analysis are under utilized in working with this type of data.

  6. Hi Bob,
    some interesting ideas and results. You stress that you do the initial calculated fits using raw data which is very good precaution. Do you do the same with your eyeball fits? I suspect not since it would not be as easy to see.
    So I have to bug you again about your use of running mean and the way it shifts peaks. This precisely what you are looking at in assessing your shift, so it is not some pedantic detail.
    As I demonstrated in an earlier thread RM will bias a peak to one side or the other dependent on the level of the surrounding data each side. It is a very poor filter.
    Especially looking at your figure 9 around 1998 , the NINO peak will be pulled left and the LOTI peak will be pulled right by the defects in RM . If you do the smoothing with a better filter you will probably find the peaks line up better and the you have to compromise less in matching events that don’t agree with each other too well.
    Equally on that graph , the ’89 troughs align well (because the data each side is fairly equal) but the ’87 peaks don’t . This will align better if you use a filter that distorts less.
    I know you don’t drop your 13m running mean , but just try it ! 😉

  7. re figure 13 and the upward shift: wasn’t there one of Hansen’s “adjustments” masked in behind the 1998 peak? Can’t link you anything off the top of my head but I probably saw it here. Something like a +0.1 “adjustment” that would have stuck out like a saw thumb except to the fact it was masked by that peak.
    could that adjustment be affecting the data you are trying to match.
    Again, be careful with pick and mix speculation. If you offset, invert and scale things you can always come up with something that fits.
    I agree it does look like the residual has a fair bit of inverted NINO in it , but that could equally be that original NINO correction was a bit too strong.
    That possibility should probably be looked at closely before scouring the globe for something else to add in.
    Keep digging.

  8. Bob have not read right thru your article. There is a lot of detail there.
    What I was looking for was a summary of the key issues and findings
    for us burnt out folk to get the essence of your piece and then go digging to find
    more detail as required. Thanks.

  9. So I guess we are seeing about 80% of the warming due to the upside of the 60 year natural cycle as expressed mainly by ocean warming, and the other 20% due to the long term ongoing warming from the LIA.

  10. P. Solar says: “re figure 13 and the upward shift: wasn’t there one of Hansen’s “adjustments” masked in behind the 1998 peak?”
    The upward shifts occur in all datasets: SST, TLT, in addition to land surface temperatures by GISS or NCDC or Hadley Centre.

  11. FrankK, summary: The post illustrated and discussed how multiple linear regression (at two time lags) and a model designed to determine the impacts of ENSO and volcanic eruptions on the global temperature anomalies leave much of the ENSO signal in the global temperature data that was supposed to be adjusted for ENSO and volcanoes.
    Using the “eyeball” method, and keying off the largest events, the adjusted global temperature anomalies reveal a signal that is inversely related to ENSO, but with significant upward shifts in response to the major ENSO events of 1986/87/88 and 1997/98. It also showed that there are two detrended SST datasets (detrended to remove the global warming signal) that have the same upward steps. One of the detrended SST datasets is the Atlantic Multidecadal Oscillation (AMO), and the second is the East Indian-West Pacific SST data. I have been discussing and illustrating the causes of the upward steps in the East Indian-West Pacific SST data for two years and provided links to detailed discussions.
    I also presented the EXCEL add-on software package that performed the multiple linear regression for the post. At the end of the post, I showed the results when I used EXCEL to determine the scaling factors for, and combined impacts of, ENSO, volcanic eruptions, the AMO, and the detrended East Indian-West Pacific SST anomalies.

  12. Bob –
    It perhaps isn’t kosher to comment before reading an article, but I have an authoring methodological comment to make:
    Thank you for asking us, the readers, if we need a primer. I’ve noticed this often here at WUWT, and at Climate Audit, too. It seems to be common among skeptics to educate the newly interested while not padding articles with fundamentals ad infinitum. Thank you.
    I’ve seen so many science articles in the MSM that are 15% new information and 85% explaining basics. Especially with news/features online, redirecting newbies like you do here should be de rigueur. Even in print, providing URLs, almost as sources, would be very helpful to keep from padding articles and letting informed readers get on to the meat of the article.

  13. Here’s the takeaway:

    In other words, approximately 73% of the rise in global (60S-60N) surface temperature could be natural.

  14. Mike McMillan says: “Isn’t this an area where we could apply principal component analysis (PCA)?”
    Many methods have been used to attempt to extract the impacts of ENSO from the global temperature record: Principal component, linear regression, rotated extended EOF. There’s a good overview of the methods that have been tried on page 2 of Compo and Sardeshmuk (2008):
    http://www.esrl.noaa.gov/psd/people/gilbert.p.compo/CompoSardeshmukh2008b.pdf
    The results of the Guan and Nigam (rotated extended EOF) are interesting. I linked two of their papers in this post:
    http://bobtisdale.blogspot.com/2010/11/guan-and-nigam-2008-and-2009.html

  15. This is not exactly what I was thinking of but this shows GISS retained more residual heating than other datasets after the 1998 event. Eyeball estimate about 0.05C ahead of the field, also note how they are lower than others pre-1900 by a good 0.1C and have lessened the troughs c 1910, 1950.
    http://wattsupwiththat.files.wordpress.com/2011/01/906_2010dataset1.png
    Fairly blatantly bending the data to fit AGW. I would hesitate to look for trends in manipulated data.

  16. Does Arctic ice extent correlate with any of these oscilations. If so would the very high temp anomaly around Labrador Greenland be caused by lack of ice rather than high global temps in the northern hemisphere and could you tell the difference?

  17. It seems to me strange, to subtract a whole bunch of sea surface temperatures, from the 60S-60N temperature anomaly, when the ocean is 70% of the earth’s surface, and then remark that 73% of the global warming signal is removed. What would one expect.
    Tamino at Open Mind, has done an analysis which subtracts out the El Nino and volcanic effects; and finds that when El Nino, Volcanic and the annual cycle are fit to the data, a similar warming signal is still present in 3 of the major temperature anomaly data sets.
    http://tamino.wordpress.com/2011/01/06/sharper-focus/
    Hence for each temperature data set, we’ll do a multiple regression of the data since 1975 (or whatever we’ve got) as a function of MEI, volcanic forcing, a 2nd-order Fourier series, and a linear time trend. We’ll allow for a time lag in the influence of MEI and volcanic forcing. Then we’ll take the original data and remove the estimated part due to MEI, volcanic forcing, and annual cycle. Finally we’ll put them all on a common baseline, using 1980.0 to 2010.0. This will give us an “adjusted” data set (a name which may give some people fits), one which is adjusted to compensate for el Nino, volcanoes, and annual cycle residue.
    The remaining global warming trend (+/- 2-sigma) is 0.0166 +/- 0.0026 for GISS, 0.0155 +/- 0.003 for RSS, and 0.0133 +/- 0.003 for UAH.
    And for those in love with hottest years, all three adjusted data sets rank 2010 as #1, and both GISS and UAH place 2009 in the #2 slot.

  18. In view of my critism of running mean for this sort of thing I ran up your nino3.4 vs giss-loti with gaussian filtering but was still unhappy about the way some peaks were not fitting whatever you do. So I tried without any smoothing. It is always better to work raw as far as possible (noting this is already seasonally adjusted).
    Now it ain’t as pretty but it does allow a better alignment of the detail of the data. It also showed that aligning the centres of some “peaks” may not be correct : eg 1987.
    It’s all rather subjective but there are so many features across the whole period that line up that I’m inclined to think there is some other factor causing the earlier rise in nino3.4 .
    My eyeball of the lag this way suggested a lag of only 0.1y against your 0.25y
    nino3.4-loti-lag

  19. Mr. Tisdale,
    Do you fear any multicolinearity involved here due to intercorrelation of any of the independent variables? Never did a multiple linear regression analysis as complex as what you have done here but have done quite a few enough to know that it can be a factor. Also am not a climatologist so do not know if the independents could be intercorrelated but suspect they could. But do agree with the comment above regarding over massage of variables and potential of creating a fit from about anything.

  20. Oh damn wordpress claims to support href and then deletes them !! try again. (mods pls edit to tidy this mess , thx)
    [IMG]http://i56.tinypic.com/2lnw9j7.png[/IMG]

  21. P. Solar says: “This is not exactly what I was thinking of but this shows GISS retained more residual heating than other datasets after the 1998 event.”
    There is little difference between the Hadley Centre, NCDC and GISS temperature anomalies for the latitudes of 60S-60N.

  22. Duh , I just realised that the reason there is a big difference around the rise in 1982 is el chincon eruption. So the 0.1 year lag seems a pretty good fit with the obvious volacanic exceptions.
    http://i56.tinypic.com/2lnw9j7.png
    A good lesson on why to work with unsmoothed data.

  23. Would be good if you had a kind of abstract and also a conclusion. It looks like the conclusions are unstated, as if the reader is supposed to understand all your data tweaks and twiddles, then the graphs are supposed to present the results, without further verbal explanation. I’m afraid it doesn’t quite work for me.

  24. eadler says: “It seems to me strange, to subtract a whole bunch of sea surface temperatures, from the 60S-60N temperature anomaly, when the ocean is 70% of the earth’s surface, and then remark that 73% of the global warming signal is removed.”
    The North Atlantic (AMO) and East Indian-West Pacific SST anomalies are detrended.
    You continued, “Tamino at Open Mind, has done an analysis which subtracts out the El Nino and volcanic effects; and finds that when El Nino, Volcanic and the annual cycle are fit to the data, a similar warming signal is still present in 3 of the major temperature anomaly data sets.”
    I’ve carried the analysis further to show the impacts of the secondary effects of ENSO and of the AMO. And if you were wondering, there’s little difference whether you detrend the North Atlantic SST anomalies or subtract the SST anomalies for the rest of the world from them:
    http://i53.tinypic.com/2e3oar5.jpg
    Also, Tamino’s opinions about the AMO are contradicted by his associates at RealClimate:
    http://www.realclimate.org/index.php/archives/2004/11/atlantic-multidecadal-oscillation-amo/
    They write, “This pattern is believed to describe some of the observed early 20th century (1920s-1930s) high-latitude Northern Hemisphere warming and some, but not all, of the high-latitude warming observed in the late 20th century.”

  25. eadler says: “It seems to me strange, to subtract a whole bunch of sea surface temperatures, from the 60S-60N temperature anomaly, when the ocean is 70% of the earth’s surface, and then remark that 73% of the global warming signal is removed. What would one expect[?]”
    You’re assuming that the putative warming is evenly distributed, aren’t you?

  26. Very nice and thorough post. You’ve retro fitted various factors to the existing temperature data. Now you need to revisit this in 1 year, 2 years etc, and see if your model is predicting temperature better than the AGW models.
    BTW, as far as software is concerned, if you really want some power, get Mathematica. It won’t be anywhere near as easy to get started, but once you do, you will be able to do far more. I think there is a hobbyist version which doesn’t cost the earth (unlike the professional version, which does cost the earth!).

  27. Jim G says: “Do you fear any multicolinearity involved here due to intercorrelation of any of the independent variables?”
    It’s my understanding that the similarities of the independent variables does not impact the overall results of the multiple linear regression, just the independent variables. And from what I’ve seen so far, a minor change to one independent variable does change the coefficients for all of the independent variables, but the results have little impact on the simple analysis I’m doing. That is, if I make a small chnage in one indepedent variable, the linear trends created by using the different mixes of scaling factors are very similar.

  28. eadler
    Ask Tamino to only leave the volcanic forcings out.
    You’ll see there’s hardly any waming from 1990 on (Pinatubo 1991).

  29. Bob Tisdale says:
    January 29, 2011 at 7:11 pm
    eadler says: “It seems to me strange, to subtract a whole bunch of sea surface temperatures, from the 60S-60N temperature anomaly, when the ocean is 70% of the earth’s surface, and then remark that 73% of the global warming signal is removed.”
    The North Atlantic (AMO) and East Indian-West Pacific SST anomalies are detrended.
    You continued, “Tamino at Open Mind, has done an analysis which subtracts out the El Nino and volcanic effects; and finds that when El Nino, Volcanic and the annual cycle are fit to the data, a similar warming signal is still present in 3 of the major temperature anomaly data sets.”
    I’ve carried the analysis further to show the impacts of the secondary effects of ENSO and of the AMO. And if you were wondering, there’s little difference whether you detrend the North Atlantic SST anomalies or subtract the SST anomalies for the rest of the world from them:
    http://i53.tinypic.com/2e3oar5.jpg
    Also, Tamino’s opinions about the AMO are contradicted by his associates at RealClimate:
    http://www.realclimate.org/index.php/archives/2004/11/atlantic-multidecadal-oscillation-amo/
    They write, “This pattern is believed to describe some of the observed early 20th century (1920s-1930s) high-latitude Northern Hemisphere warming and some, but not all, of the high-latitude warming observed in the late 20th century.”

    The problem with using the AMO as you have done, is that you have only used 1/2 a cycle of the AMO in your regression, because you start in 1980. The 1/2 cycle portion you are using has an up trend which happens to coincide with an up trend in global temperatures. This following graph of the AMO shows this:
    http://en.wikipedia.org/wiki/File:Amo_timeseries_1856-present.svg
    If you are going to get an accurate regression coefficient for the AMO, you should include earlier time periods and go back at least to 1900 to get two full periods of the AMO, to find its real correlation with global temperatures, as they rise and fall.

  30. Too much analysis of the fine noise in the overall signal. I don’t trust this type of analysis very much. Sorry. The earlier comment about the effect of the moving mean made me think of my use of quadratic smoothing in the early days of gamma ray spectra analysis. But you have to have real peaks to do this and with some assurance of peak shape.
    Interesting anyway.

  31. eadler says: “The problem with using the AMO as you have done, is that you have only used 1/2 a cycle of the AMO in your regression, because you start in 1980. The 1/2 cycle portion you are using has an up trend which happens to coincide with an up trend in global temperatures. This following graph of the AMO shows this:
    http://en.wikipedia.org/wiki/File:Amo_timeseries_1856-present.svg”
    Your first assumption is that there is a “problem” with my use of the AMO.
    During periods when the SST anomalies of the North Atlantic naturally rise faster than the global trend, as they have since the mid-1970s, the North Atlantic contributes to the upward trend in global temperatures. And this post showed that a major portion of the “up trend in global temperatures” could in fact result from the additional natural variability of the North Atlantic.
    As an example for this post, I also used detrended East Indian-West Pacific SST anomalies to satisfy a few complaints. But as I’ve shown in numerous posts for the past two years, the upward steps in the East Indian-West Pacific SST anomalies are a naturally occurring byproduct of ENSO. So your complaint is based on an assumption that the rise in global Temperatures cannot be explained as part of natural processes, when, in fact, I’ve been showing for two years that it can be.

  32. peter_ga says: “Would be good if you had a kind of abstract and also a conclusion.”
    Sorry. I’ve included an abstract in reply to FrankK above:
    http://wattsupwiththat.com/2011/01/29/removing-the-effects-of-natural-variables-multiple-linear-regression-based-or-%e2%80%9ceyeballed%e2%80%9d-scaling-factors/#comment-586321
    The conclusion: This post illustrated that scaling factors used to remove the effects ENSO and volcanic eruptions from the global temperature record can be determined using a number of methods. When multiple linear regression is used to determine the scaling factors, much of the ENSO signal remains in the adjusted global temperature anomalies. When models are used, like the one created for Thompson et al (2009), the same problem exists.
    Basing the scaling factors on the appearances (eyeballing) of ENSO and volcanic aerosols and global temperatures reveals that an ENSO-like signal remains in the adjusted global temperature anomalies, but the ENSO-like signal is inverted and includes an upward step that does not exist in the raw ENSO proxy (Figures 11, 12 & 13). There are two naturally occurring SST datasets that have the same basic curve as the adjusted global temperature data. These datasets are the East Indian-West Pacific SST anomalies and the North Atlantic SST anomalies. To satisfy earlier complaints about my use of datasets with a trend to explain the trend in the adjusted global temperature anomalies, I used detrended versions of the North Atlantic and the East Indian-West Pacific SST datasets in this post, and the results indicate that a significant portion of the rise in global temperature since 1982 can be explained with these two naturally occurring (detrended) SST anomaly datasets.

  33. Much sound and fury, signifying nothing.
    [Reply – if you have a specific criticism, please say so. In a tightening of blog policy comments that add nothing to the discussion will be deleted ~jove, mod]

  34. Das ist nicht nur nicht richtig, es ist nicht einmal falsch!
    [Reply – Wenn Sie Englisch lesen können, genug zu sagen, das ist falsch, so können Sie auf Englisch sagen ~jove, mod]

  35. Bob Tisdale says:
    January 29, 2011 at 6:52 pm
    “P. Solar: As I have said before, I do not intend to change my filtering.”
    Well if you’re happy to use a filter that distorts one set of data one way, the other set of data the other way and then “eyeball” the supposed lag between the two, you are in a free country (/irony) and that is your constitutional right.
    Just don’t imagine that what you are doing has any scientific validity or that your results “show” anything meaningful.

  36. “Figure 4 illustrates the result when we subtract scaled ENSO and Volcano proxy data from the Global Temperature data. That dataset is supposed to represent global temperature data that has been adjusted for ENSO and volcanic eruptions.”
    “Supposed” by whom ? Only your method assumes that.
    You are using a closed-source add-on package for excel where you do not even know what stats you are blindly applying ( what is this “linear regression” that you are using, is it applicable to this sort of data?).
    You seem to believe that doing some arbitrary linear regression is suitable and that it should remove the signal if you subtract it. You are correct in concluding this does not work too well but you do not say why this is “supposed” to work at all.
    Your stats package seems pretty much undocumented as to exactly what it is doing and you, apparently, do not understand what you are doing in stats. No surprise that the results are not much use.
    In that context you are correct in working by eye, which is not altogether a bad approach if done rigorously, though it’s difficult to verify and reproduce.

  37. Willis, don’t forget this is a skeptic site, expect a skeptical examination of what you are putting forward. 😉

  38. P. Solar says: “Duh , I just realised that the reason there is a big difference around the rise in 1982 is el chincon eruption. So the 0.1 year lag seems a pretty good fit with the obvious volacanic exceptions.”
    I believe we had this discussion on an earlier thread. And one of my complaints about the Gaussian filter you proposed is that it failed to properly capture the El Chichon eruption.
    http://wattsupwiththat.com/2010/12/12/tisdale-k-o-es-gisss-latest-warmest-year-nonsense/#comment-550806
    You continued, “Well if you’re happy to use a filter that distorts one set of data one way, the other set of data the other way and then “eyeball” the supposed lag between the two, you are in a free country (/irony) and that is your constitutional right.”
    You and Paul Vaughan also discussed the distortions in your proposed filtering method on that same thread linked above.
    Regards

  39. Didactylos says: “Das ist nicht nur nicht richtig, es ist nicht einmal falsch!”
    Looks like a quote of Wolfgang Pauli without attribution. And to counter the quote, this post was presented clearly, it is testable, and it is evaluatable. Feel free to do so.

  40. P. Solar says: “Your stats package seems pretty much undocumented as to exactly what it is doing and you, apparently, do not understand what you are doing in stats. No surprise that the results are not much use.”
    And if you were to look at the Thompson et al results in Figure 8, you’d find similar results. Or you could input the data I used in this post into whatever statistics model you prefer and present your findings to show that multiple linear regression does a better job than I’ve presented.
    You continued, “In that context you are correct in working by eye, which is not altogether a bad approach if done rigorously, though it’s difficult to verify and reproduce.”
    I’m not sure why you would conclude your comment with “though it’s difficult to verify and reproduce,” when the datasets are listed in the sources, and the scaling factors are shown in the illustrations. I would think it should be relatively easy “to verify and reproduce”.

  41. Bob Tisdale says:
    January 30, 2011 at 2:50 am
    eadler says: “The problem with using the AMO as you have done, is that you have only used 1/2 a cycle of the AMO in your regression, because you start in 1980. The 1/2 cycle portion you are using has an up trend which happens to coincide with an up trend in global temperatures. This following graph of the AMO shows this:
    http://en.wikipedia.org/wiki/File:Amo_timeseries_1856-present.svg”
    Your first assumption is that there is a “problem” with my use of the AMO.
    During periods when the SST anomalies of the North Atlantic naturally rise faster than the global trend, as they have since the mid-1970s, the North Atlantic contributes to the upward trend in global temperatures. And this post showed that a major portion of the “up trend in global temperatures” could in fact result from the additional natural variability of the North Atlantic.
    As an example for this post, I also used detrended East Indian-West Pacific SST anomalies to satisfy a few complaints. But as I’ve shown in numerous posts for the past two years, the upward steps in the East Indian-West Pacific SST anomalies are a naturally occurring byproduct of ENSO. So your complaint is based on an assumption that the rise in global Temperatures cannot be explained as part of natural processes, when, in fact, I’ve been showing for two years that it can be.

    In your argument, it seems that you are assuming what you seek to prove. If you are going to attach a regression coefficient to the AMO, it should be valid for more than 1/2 a cycle. You need to rule out the idea that the AMO is simply coincident with an Anthropogenic global warming phenonomen. You have the tools to do this for the full 2 cycles that have occurred since 1900.

  42. P. Solar says: “Just don’t imagine that what you are doing has any scientific validity or that your results “show” anything meaningful.”
    Your comment is based on your opinion that my methods are skewed because I use a running mean filter, where you suggest I should be using a Gaussian filter. Yet you have not presented your findings that the Gaussian filter would provide any significant difference in what I presented in this post.

  43. P. Solar says: “Willis, don’t forget this is a skeptic site, expect a skeptical examination of what you are putting forward. ;)”
    I assume this belongs on the thread of the post written by Willis.

  44. John Brookes says:
    January 29, 2011 at 7:24 pm
    “Very nice and thorough post. You’ve retro fitted various factors to the existing temperature data. Now you need to revisit this in 1 year, 2 years etc, and see if your model is predicting temperature better than the AGW models.
    BTW, as far as software is concerned, if you really want some power, get Mathematica. It won’t be anywhere near as easy to get started, but once you do, you will be able to do far more. I think there is a hobbyist version which doesn’t cost the earth (unlike the professional version, which does cost the earth!).”

    John,
    There is no need to wait. Tisdale could validate his model using data from 1860 to 1980, which he has neglected to include in his fitting process.
    He seems reluctant to try this.

  45. eadler says: “Tisdale could validate his model using data from 1860 to 1980, which he has neglected to include in his fitting process.
    He seems reluctant to try this.”
    eadler, I addressed this point in the first post in this series.
    http://bobtisdale.blogspot.com/2011/01/can-most-of-rise-in-satellite-era.html
    There I wrote:
    CAN THE THIS TYPE OF EVALUATION BE EXTENDED BACK IN TIME?
    I would not expect that what was presented in this post could be extended back in time. The Pacific climate shifted in 1976/77. In the abstract of Trenberth et al (2002), they write, “The 1976/1977 climate shift and the effects of two major volcanic eruptions in the past 2 decades are reflected in different evolution of ENSO events. At the surface, for 1979–1998 the warming in the central equatorial Pacific develops from the west and progresses eastward, while for 1950–1978 the anomalous warming begins along the coast of South America and spreads westward. The eastern Pacific south of the equator warms 4–8 months later for 1979–1998 but cools from 1950 to 1978.”
    The way ENSO events interacted with the Kuroshio-Oyashsio Extension and the SPCZ Extension also appear different before and after 1979 in the correlation and regression analyses presented in that paper. Link to Trenberth et al (2002):
    http://www.cgd.ucar.edu/cas/papers/2000JD000298.pdf

  46. Bob Tisdale says:
    January 30, 2011 at 12:49 pm
    “eadler says: “Tisdale could validate his model using data from 1860 to 1980, which he has neglected to include in his fitting process.
    He seems reluctant to try this.”
    eadler, I addressed this point in the first post in this series.
    http://bobtisdale.blogspot.com/2011/01/can-most-of-rise-in-satellite-era.html
    There I wrote:
    CAN THE THIS TYPE OF EVALUATION BE EXTENDED BACK IN TIME?
    I would not expect that what was presented in this post could be extended back in time. The Pacific climate shifted in 1976/77. In the abstract of Trenberth et al (2002), they write, “The 1976/1977 climate shift and the effects of two major volcanic eruptions in the past 2 decades are reflected in different evolution of ENSO events. At the surface, for 1979–1998 the warming in the central equatorial Pacific develops from the west and progresses eastward, while for 1950–1978 the anomalous warming begins along the coast of South America and spreads westward. The eastern Pacific south of the equator warms 4–8 months later for 1979–1998 but cools from 1950 to 1978.”
    The way ENSO events interacted with the Kuroshio-Oyashsio Extension and the SPCZ Extension also appear different before and after 1979 in the correlation and regression analyses presented in that paper. Link to Trenberth et al (2002):
    http://www.cgd.ucar.edu/cas/papers/2000JD000298.pdf

    Your reply mentions ENSO.
    My comment was related to the AMO, which is a more recently discovered ocean oscillation. ENSO has many more complete oscillations to evaluate than AMO which only has an increasing half period during your evaluation.
    If your model is specific to only part of the temperature record it would seem to be a cherry picking exercise, rather than something ‘that is generally useful.
    In addition, your analysis represents a kind of tautology. The earth’s surface is warming largely because the surfaces of the oceans are getting warmer. Since the AMO does not have a regular periodic behavior, simply subtracting the temperature increase of the North Atlantic Ocean and exclaiming that global warming is reduced is a meaningless excercise which discloses nothing regarding the source of the surface warming.

  47. eadler says: “Your reply mentions ENSO.”
    Two of the datasets used and discussed in this post (ENSO & the East Indian-West Pacific SST anomalies) are discussed in that reply to you, but in order to realize that one has to know the Kuroshio-Oyashsio Extension and the SPCZ Extension are parts of the East Indian-West Pacific data. Sorry I wasn’t clearer.
    You continued, “My comment was related to the AMO…”
    But the AMO was only one of four datasets I used to describe the rise in GISS LOTI.

  48. It seems to me that you are saying that when you subtract the temperature changes observed in most of the world’s oceans global warming disappears. Since the earth is 70% ocean, we should expect this to be the case.
    What does any of this have to do with understanding the physical forcing factors governing the temperature change? How does this determine to what extent GHG’s or solar radiance or other forcing factors, aside from volcanos, which you seem to have covered, have been responsible for these temperature increases? Your analysis doesn’t deal with this at all.

  49. eadler says: :It seems to me that you are saying that when you subtract the temperature changes observed in most of the world’s oceans global warming disappears. Since the earth is 70% ocean, we should expect this to be the case.”
    The SST anomaly datasets have been detrended, eadler. Try again.

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