I’ve moved to WordPress. This post can now be found at Removing The Effects of Natural Variables – Multiple Linear Regression-Based or “Eyeballed” Scaling Factors#########################
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.
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.
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.
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.
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.
Multiple linear regression does not appear to do a good job of removing the impacts of ENSO.
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.
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.
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.”
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.
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.
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.
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.
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.)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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?.
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.
…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.
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:
The Stratospheric Aerosol Optical Thickness data is available from GISS:
And the Atlantic Multidecadal Oscillation data is available from NOAA ESRL:
Thanks Bob, good stuff again.
I don't know if you can make use of this, but based on your Kuroshio post, I've been playing around with the similar ocean current regions around the globe (I still can't get the temp reconstruction to work good enough).
But how about discarding the AMO index and using just the Gulf Stream equivalent of the Kuroshio - they are actually the same type of current other than the Gulf Stream has a longer start-up length based on the geography of the land.
The Gulf Stream shows a clear step-change right after the 1997-98 El Nino.
Like the Kuroshio and the ENSO, the Gulf Stream has only a very, very small trend in the data going way back so one can conclude it is a natural oscillation with no global warming signal (while the AMO has a large one before detrending).
Bill Illis: Thanks. What coordinates are you using for the Gulf Stream Extension?
I've also had some very good results but using the AMO and detrended East Indian-West Pacific datasets. I should be posting about it in a few days.
I will probably have some other comments later, but first a question.
You reverse the La Niña and add it to the El Niño, with the assumption being that both have a net warming impact. But what about the smaller ENSO wiggles between the Niñas and Niños? Do they also have a cumulative warming impact? Or does ENSO have to exceed a threshold before anything happens?
Bob, I wouldnt want to put you of the software that you have already used - it probably makes the workflow very easy, but Excel does have multiple linear regression built in. (it looks like its only for single x variables but it is meant for multiple) select two or three columns of x data instead of one. In older versions its in tools... data analysis... regression. I seem to rememeber that you need to install the analysis toolpack for it to be visible.
To see the fit values click on the rediduals box and you will get predicted Y and the residuals.
A very nice and comprehensive post Bob! Its a good counter-post to this one:
Tamino claims, that AMO is due to GW, and therefore shouldn't be removed. I don't believe him, nor do many of his readers, but it isnt shown in the comments since he moderates so heavily.
Have you tried having a discussion with him?
I posted this short question earlier today but it never appeared, so I'll try again.
You've come up with a good argument that El Niños and La Niñas both cause warming. Do you think the smaller ENSO variations between the major Niño and Niña events cause cumulative warming too? Or do we have to exceed some threshold before anything happens?
Roger: Sorry for not moderating your comment. It's there.
You asked, "Do you think the smaller ENSO variations between the major Niño and Niña events cause cumulative warming too?"
The key is that an El Nino has to be followed by a La Nina. The East Indian-West Pacific continued to decline during the lesser El Nino events of 2002/03 and 2004/05, and then it started its upward responses to the combination of the2006/07 El Nino and 2007/08 La Nina.
I'll try to moderate more often, sorry.
juakola said, "Have you tried having a discussion with him [Tamino]?"
My comments have been deleted so many times at (not so)OpenMind that I don't bother to try anymore.
The AMO will contribute to the trend when looking at the short-term global temperature anomalies. For the long term, it depends when you start the analysis. If the period goes from AMO max to max, then the contribution to the trend would be little if anything. But if you were looking at a period that started at AMO min and extended to AMO max, then the AMO contributes to the trend.
Chas: Thanks for the tip. I went looking for linear regression software in EXCEL, but couldn't find it. So I tried google and that's where I found the add-on package.
Here is what I got for Hadcrut3 back to 1871 using the biggest ocean current impacts (other than the Antarctic Circumpolar Current which is too big in my opinion to include in such a model).
The main ocean climate-impacting currents occur at the equator (moving east-west) and then on the west side of the continents moving west-east at 35 to 50 latitudes.
This is simply a result of a rotating planet and the prevailing winds that occur as a result.
You can see these ocean currents in the highest resolution US Navy ocean model publicaly available - NLOM which has 1/32 degree resolution.
For the Gulf Stream, I'm using 35N to 50N; 60W to 0W but one could probably tighten that up a bit. The Gulf Stream portion of the North Atlantic has just a very small trend while the Atlantic equatorial has a very large warming trend. This is why the AMO undetrended has such a large trend, it is the equatorial trend mainly.
Just a comment on the smoothing and moving averages, I don't think the climate operates on those timescales so it is better to use monthly or weekly numbers.
I tried to reason with Tamino, so he (partly) 'answered' with a new post:
But he deleted my original comment and only partly cited it. I dont know if he will publish my new comment.
Bob, you mind to take a peek on it?
Bob, can you write a counter-post for Tamino's post at http://tamino.wordpress.com/2011/01/30/amo/
It would be beneficial to see the counterarguments (if any).
To those who have linked Tamino's recent post about the AMO, yes, I've started a reply.
Bob, you make many references to Excel in writing this post. What program did you use earlier?
Have you tried any of the other statistical packages?
Excel does not have a stellar reputation in research. See, for example, this list of elemental Excel bugs, http://blog.meteorit.co.uk/2007/10/02/excel-2007-bug-shows-wrong-answers-to-simple-multiplications/
Which Excel version do you use?
Thats very nice Bob, we'll stay tuned.
Tamino's analysis always revolves around slanted charts and slanted formulae.
He won't let one argue with him on his blog so it is a waste of time.
I don't know how anyone could view his own chart of the undetrended AMO match with the GISS and not understand the correlation.
The question is how much warming is ocurring and how much is natural cycles (mostly ocean-related).
If the actual warming is much less than the CO2-based climate models say it should be (we should be over +1.4C now) then there is a problem.
A line which has gone up by 0.7C in 130 years has to accelerate substantially to reach 3.25C in the next 90 years.
After the full affect of the La Nina builds in (and the AMO crashes) in the next several months, how will Tamino's results look then.
It's a no brainer, since he substracts detrended north atlantic SST anomalies from detrended north atlantic SST anomalies which was zero anomaly. So he proved 1-1=0, hard to argue with that.
Anonymous @ January 30, 2011 12:42 PM asked, "Which Excel version do you use?"
I do not have the problem illustrated in the linked wabpage, if that's your question.
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