On Foster and Rahmstorf 2011 – Global temperature evolution 1979–2010

UPDATE 3 (January 14, 2012): I displayed my very limited understanding of statistics in this post. This was pointed out to me a great number times by many different people in numerous comments received in the WattsUpWithThat cross post.The errors in that initial portion of the post were so many and so great that they detracted from the bulk of the post, which was about the El Niño-Southern Oscillation. Please disregard this post and the WUWT cross post, and any other cross posts that may exist.

I have reissued the ENSO-related portion of the post herewith a number of additions. If Anthony Watts cross posts the new version at WattsUpWithThat, I’ll provide a link here.

Originally, when I wrote the post about Foster and Rahmstorf (2011), I had not included my error-filled discussion about their regression analysis. That was a last minute addition. Lesson learned.


UPDATE 2 (January 5, 2012): PLEASE READ. Three things: First, I did not understand that a “linear time trend” used by Foster and Rahmstorf (2011) is different than a “linear trend”. My confusion also led to confusion for many bloggers who read my post and who commented on the WattsUpWithThat cross post. My apologies. For those interested, the “linear time trend” is discussed under the heading of “Data as trend plus noise” on the Wikipedia Trend Estimationwebpage.

Second, in addition to MEI, AOD, and TSI as independent variables, I mistakenly used the values of the linear trend, which EXCEL calculated with its LINEST function from the monthly GISS data, as the fourth independent variable. And this added to the confusion of those who were interpreting the equations. In retrospect, I should not have included the equations. I should have included a table that listed the coefficients instead.

Third, in my haste to publish this post, I failed to explain the steps I used to process the data, and it may have been confusing to those who were looking at equations and graphs. I performed the regression analyses with the “raw” monthly data; then using the resulting coefficients, I made the adjustments to the monthly data. (I had prepared a graph using monthly data, similar to F&R’s Figure 4, with 1979-2010 as base years. But I felt my version was an unintelligible spaghetti graph with little value, so I didn’t include it.) I then converted the adjusted data to annual data; and last, changed the base years to 1979-2010.

The bottom line: Although I mistook a linear trend for a linear time trend, and although I did not include all of the additional data refinements used by Foster and Rahmstorf (2011), it’s difficult to see any difference between my Figure 7 and their Figure 5. There were other bloggers commenting on the thread of the WUWT cross post who got similar results using different methods. Does this mean the results of Foster and Rahmstorf (2011) are robust as some comments on the WUWT tread claimed? No. ENSO is a process, not an index, and it can’t be account for using linear regression analysis. This was illustrated clearly and discussed in detail under the heading of ENSO IS NOT AN EXOGENOUS FACTOR.

UPDATE 1(January 3, 2012):  Under the heading of ENSO IS NOT AN EXOGENOUS FACTOR, I changed the wording of a sentence, crossing out  “create” and replacing it with “recharge”.—Thanks, Steve Allen.


This post examines a curious aspect of the multiple linear regression analysis performed by Foster and Rahmstorf in their 2011 paper “Global Temperature Evolution 1979–2010”. I find it very odd that a factor upon which the paper appears to rest was not presented in detail in it. Please understand right from the start, for this portion of the post, I am not implying that there is something wrong with this specific aspect of the paper; but I’m also not agreeing with it.  I’m presenting it for discussion.

The second part of this post is a discussion of one of the exogenous factors that Foster and Rahmstorf (2011) has attempted to remove. The problem: it is not an exogenous factor. And there is a third discussion about a dataset that’s present in the spreadsheet provided by the lead author Grant Foster (aka Tamino) but, curiously, not mentioned in the paper.

Not surprisingly, Foster and Rahmstorf (2011) made the rounds at the blogs of the proponents of anthropogenic global warming. Joe Romm praised it with the post Sorry, Deniers, Study of “True Global Warming Signal” Finds “Remarkably Steady” Rate of Manmade Warming Since 1979. SkepticalScience covered the paper in their post Foster and Rahmstorf Measure the Global Warming Signal. And RealClimate gave it an honorable mention by including it as one of the topics in its Global Temperature News post.


Foster and Rahmstorf (2011) attempted to remove from 5 global temperature datasets the linear effects of 3 factors that are known to cause variations in global temperature. They covered the period of 1979 to 2010. The obvious intent of the paper is to show that anthropogenic global warming continues unabated in all of those datasets. The independent variables listed in the abstract of Foster and Rahmstorf (2011) are El Niño-Southern Oscillation, volcanic aerosols, and solar variations. Foster and Rahmstorf (2011) appears to be a much clarified version of Tamino’s (Grant Foster’s) January 20, 2011 post How Fast is Earth Warming?  After publication of the paper, Tamino discussed it in his post The Real Global Warming Signal and was kind enough to provide the source data and code in his post Data and Code for Foster & Rahmstorf 2011.  The data Tamino provided is available here.  It is a .zip file that Tamino has renamed a .xls file, as he explains, “in order to fool the wordpress software into believing that it’s an Excel file.” You will need to “Right Click and Save As” and then change the file name back to a .zip file in order to open it.

As noted above, in the abstract, Foster and Rahmstorf (2011) list the exogenous factors that are used as independent variables in the multiple regression analysis as “El Niño/southern oscillation, volcanic aerosols and solar variability.” Curiously, three paragraphs later, when they list the factors included in the multiple regression analysis again, Foster and Rahmstorf (2011) have added a fourth variable: linear trend. The last sentence of the third paragraph under the heading of “Introduction” reads:

“The influence of exogenous factors will be approximated by multiple regression of temperature against ENSO, volcanic influence, total solar irradiance (TSI) and a linear time trend to approximate the global warming that has occurred during the 32 years subject to analysis.”

But one of the bases for the paper is to illustrate how similar the trends are after the adjustments for ENSO, Total Solar Irradiance, and Volcanic Aerosols have been made, so including the linear trends of those datasets in the regression analysis seems odd. As a result, I went in search of another reason why Foster and Rahmstorf (2011) would have needed to include the linear trend in their regression analyses. As I note in the following, I’m using commercially available add-on software for EXCEL to perform the multiple regression analyses. Since I have no other means to verify the results, other than reproducing the results of one of their graphs, I’ll request that you confirm the following results if you have that capability.


The only reason that I can see that Foster and Rahmstorf (2011) needed to include the trend in the multiple regression analysis is, the adjustment factor for the solar data is the wrong sign when the multiple regression analysis uses only ENSO, Solar, and Volcanic Aerosol data as independent variables.  Let me explain in more detail.  But again, please understand, for this portion of the post, I am not implying that there is something wrong with this specific aspect of the paper; and again, I’m also not agreeing with it.  I found this interesting.

With the data provided by Tamino, I used Analyse-It for EXCEL software to perform a multiple regression analysis. (For those with EXCEL who have no means to perform a multiple linear regression analysis and want to verify my results, Analyse-It is available free on a 30-day trial basis.) My initial analysis included Tamino’s favorite global Surface Temperature dataset GISS as the dependent variable and the Multivariate ENSO Index (MEI), the Total Solar Irradiance (PMOD), and the Volcanic Aerosol Optical Depth data (AOD) as the independent variables. I lagged the MEI data by four months, the PMOD data by one month, and the AOD data by seven months, in agreement with Table 1 of Foster and Rahmstorf (2011), which is also Table 1 in this post. And in this analysis, I did not include the GISTEMP linear trend as an independent variable.

Table 1

The multiple regression analysis using only the ENSO (MEI), Solar (PMOD), and Volcanic Aerosol (AOD) data resulted in Equation 1:


GISS = 123.6 + 0.06769MEI(4m lag) – 0.09025TSI.PMOD(1m lag)– 3.837AOD (7m lag)

I highlighted the solar variable scaling factor in boldface to emphasize the fact that the sign is negative. It would need to be positive to reproduce the results of Foster and Rahmstorf (2011). The signs of the ENSO and volcanic aerosol factors are what one would expect, Figure 1. It’s only the sign of the solar coefficient that is the opposite of what Foster and Rahmstorf (2011) present, Figure 2 (which is their Figure 7).

Figure 1


Figure 2

And that makes a monumental difference to the outcome of Foster and Rahmstorf (2011). If we adjust the GISS surface temperature data with the factors presented in Equation 1, then the rise is not continuous. Refer to Figure 3. The peak year for the adjusted GISS-based global Surface Temperature data is 2002.

Figure 3

To confirm the results of Foster and Rahmstorf (2011), I added the 0.167 deg C/Decade linear trend of the GISS global surface temperature anomaly data to the independent variables. The lags of the ENSO (MEI), Solar (PMOD), and Volcanic Aerosol (AOD) data remained the same as above.

The multiple regression analysis using the ENSO (MEI), Solar (PMOD), and Volcanic Aerosol (AOD) data and the linear trend resulted in Equation 2:


GISS = -91.43 + 1.024Trend + 0.0761MEI(4m lag) + 0.06694TSI.PMOD(1m lag)– 2.334AOD (7m lag)

The sign of the Total Solar Irradiance coefficient now agrees with what Foster and Rahmstorf (2011) presented, as shown in Figure 4. Note that including the trend as an independent variable also influenced the scaling of the ENSO (MEI) and Volcanic Aerosol (AOD) data. It increased the scaling factor of the ENSO data a little, but decreased the scaling factor of Volcanic Aerosol significantly. Of course, the inclusion of the trend as an independent variable, with the change in sign of the Solar influence, also gives the adjusted GISS data results that Foster and Rahmstorf (2011) wanted, Figure 5, with the rise in temperature relatively steady over the 32 year period. And note that the trend of 0.172 deg C per decade is comparable to the findings of Foster and Rahmstorf (2011) shown in Table 1 for GISS data.

Figure 4


Figure 5

Of course, I did not include [and Foster and Rahmstorf (2011) could not have included] the trend adjustment from Equation 2 when the corrected data was presented in Figure 5. If the trend adjustment was included, the corrected data would have no trend. That means, it appears Foster and Rahmstorf (2011) needed to include the trend of the GISTEMP data in the regression analysis only to assure the sign of the solar influence they sought.

Foster and Rahmstorf (2011) would have gotten similar scaling factors for the ENSO (MEI), Solar (PMOD), and Volcanic Aerosol (AOD) data if they had simply detrended the GISS Global Surface Temperature data.


Detrended GISS = -86.31 + 0.0759MEI(4m lag) + 0.0632TSI.PMOD(1m lag) – 2.37AOD (7m lag)


Someone is bound to ask whether the GISS Global Surface Temperature dataset is the only dataset with these results. The answer is no. If the linear trend is not included in the multiple linear regression analyses, the sign of the solar coefficient is the opposite of what Foster and Rahmstorf (2011) would had to have used for the NCDC and HADCRUT global land plus sea surface temperature datasets and for the RSS and UAH global Lower Troposphere Temperature data. The resulting equations from the linear regression analyses of the other datasets are presented in equations 4 through 7. The lags for the independent variables are as listed in Table 1 above:

EQUATION 4 (NCDC Land Plus Ocean Surface Temperature):

NCDC = 109.1 + 0.05495MEI(2m lag) – 0.0796TSI.PMOD(1m lag)– 3.113AOD (5m lag)

EQUATION 5 (Hadley Centre HADCRUT Global Surface Temperature Anomalies):

HadCRUT3v = 92.21 + 0.06421MEI(3m lag) – 0.0673TSI.PMOD(1m lag)– 3.293AOD (6m lag)

EQUATION 6 (RSS MSU Lower Troposphere Temperature Anomalies):

RSS33 = 61.44 + 0.1285MEI(5m lag) – 0.04489TSI.PMOD(0m lag)– 4.863AOD (5m lag)

EQUATION 7 (UAH MSU Lower Troposphere Temperature Anomalies):

UAH = 72.94 + 0.1332MEI(5m lag) – 0.05338TSI.PMOD(0m lag)– 5.139AOD (6m lag)

If we use those coefficients, the five datasets do not produce the nice continuous rise in Global Temperatures that Foster and Rahmstorf (2011) wanted to present, as shown in Figure 6. For the three Surface Temperature anomaly datasets (GISS, HADCRUT, NCDC) 2002 has the highest temperature. It’s only the two Lower Troposphere Temperature anomaly datasets that have 2010 as the warmest year.

Figure 6

And as one would expect, if the linear trends of the other global temperature datasets are included in the independent variables, the signs of the solar coefficients are positive. Refer to equations 8 through 11.

EQUATION 8 (NCDC Land Plus Ocean Surface Temperature, with trend):

NCDC = -106.7 + 1.085Trend + 0.06832MEI(2m lag) + 0.07813TSI.PMOD(1m lag)– 1.68AOD (5m lag)

EQUATION 9 (Hadley Centre HADCRUT Global Surface Temperature Anomalies, with trend):

HadCRUT3v = -119.2 + 1.093Trend + 0.07519MEI(3m lag) + 0.08723TSI.PMOD(1m lag)– 1.858AOD (6m lag)

EQUATION 10 (RSS MSU Lower Troposphere Temperature Anomalies, with trend):

RSS33 = -135.5 + 1.05Trend + 0.1342MEI(5m lag) + 0.09923TSI.PMOD(0m lag)– 3.479AOD (5m lag)

EQUATION 11 (UAH MSU Lower Troposphere Temperature Anomalies, with trend):

UAH = -105.7 + 0.9953Trend + 0.1381MEI(5m lag) + 0.07742TSI.PMOD(0m lag)– 3.871AOD (6m lag)

With the linear trend included in the multiple regression analyses, the coefficients in the equations above provide the adjustments that Foster and Rahmstorf (2011) presented, Figure 7. I’ve included their Figure 5 as my Figure 8 as a reference.

Figure 7


Figure 8


I’m sure some will attempt to argue that including the trend in the regression analyses is necessary since computer model-based studies have shown the rise in global surface temperature is caused by anthropogenic forcings during the period of 1979 to 2010. But of course, that argument assumes climate models can be used for determining the cause of the rise in Global Surface Temperatures during any period. We have recently illustrated and discussed that the climate models used by the IPCC in their 4th Assessment report have shown no skill at reproducing the global surface temperatures over any period during the 20th Century. Refer to the summary post ON THE IPCC’s UNDUE CONFIDENCE IN COUPLED OCEAN-ATMOSPHERE CLIMATE MODELS – A SUMMARY OF RECENT POSTS.  The second problem with their assumption is that the global oceans, which cover about 70% of the surface area of the globe, show no signs of the influence of anthropogenic global warming during the satellite era. And that brings us to…


Foster and Rahmstorf (2011) included ENSO as one of the exogenous factors they attempted to remove from the instrument temperature record. But ENSO is not an exogenous factor. ENSO is a coupled ocean-atmosphere process that periodically discharges heat to the atmosphere during an El Niño. The El Niño causes changes in atmospheric circulation patterns, which cause temperatures outside of the eastern tropical Pacific to vary, some warming, some cooling, but in total, the areas that warm exceed those that cool and global surface temperatures rise in response to an El Niño. The patterns of warming and cooling during a La Niña are similar to an El Niño, but the signs are reversed. And that’s really all that a paper such as Foster and Rahmstorf (2011) could hope to account for including ENSO in the regression analysis. But there is much more to ENSO.

ENSO is also a process that redistributes the warm water that was leftover from the El Niño itself and enhances the redistribution of the warm water that was created by the El Niño outside of the eastern tropical Pacific. The redistribution carries that warm water poleward and into adjoining ocean basins during the La Niña that follows an El Niño. La Niña events also recharge part of the warm water that was released during the El Niño. Sometimes La Niña events “overcharge” the tropical Pacific, inasmuch as they create recharge more tropical Pacific ocean heat than was discharged during the El Niño that came before it. That was the case during the 1973/74/75/76 and 1995/96 La Niña events. Refer to Figure 9. The 1973/94/75/76 La Niña provided the initial “fuel” for the 1982/83 Super El Niño and the multi-year 1986/87/88 El Niño. And the 1997/98 “El Niño of the Century” was fueled by the 1995/96 La Niña. The process of ENSO cannot be accounted for through linear regression on an index. This was illustrated and discussed at an introductory level in the post ENSO Indices Do Not Represent The Process Of ENSO Or Its Impact On Global Temperature.

Figure 9

Foster and Rahmstorf (2011) cited Trenberth et al (2002) Evolution of El Nino–Southern Oscillation and global atmospheric surface temperatures as one of their ENSO references. But Trenberth et al (2002) include the following disclaimer in the second paragraph of their Conclusions, (their paragraph 52, my boldface):

The main tool used in this study is correlation and regression analysis that, through least squares fitting, tends to emphasize the larger events. This seems appropriate as it is in those events that the signal is clearly larger than the noise. Moreover, the method properly weights each event (unlike many composite analyses). Although it is possible to use regression to eliminate the linear portion of the global mean temperature signal associated with ENSO, the processes that contribute regionally to the global mean differ considerably, and the linear approach likely leaves an ENSO residual.

The ENSO “residuals” are a significant contributor to the rise in Global Sea Surface Temperatures during the satellite era as we shall see. Did Foster and Rahmstorf (2011) consider these residuals in their analysis? Nope. They assumed the rise was caused by anthropogenic forcing, and they assumed a linear trend represented it.

A more recent paper was overlooked by Foster and Rahmstorf (2011). Compo and Sardeshmukh (2010) “Removing ENSO-Related Variations from the Climate Record” seems to be a step in the right direction. They write (my boldface):

An important question in assessing twentieth-century climate is to what extent have ENSO-related variations contributed to the observed trends. Isolating such contributions is challenging for several reasons, including ambiguities arising from how ENSO is defined. In particular, defining ENSO in terms of a single index and ENSO-related variations in terms of regressions on that index, as done in many previous studies, can lead to wrong conclusions. This paper argues that ENSO is best viewed not as a number but as an evolving dynamical process for this purpose.

And as Compo and Sardeshmukh have suggested, Foster and Rahmstorf (2011) have reached the wrong conclusion.

Note: Compo and Sardeshmukh missed a very important aspect of ENSO. They overlooked the significance of the huge volume of warm water that is left over from El Niño events and they failed to account for its contribution to the rise in global Sea Surface Temperature anomalies since about 1976.

Let’s not forget the much-heralded Thompson et al (2008) paper “Identifying signatures of natural climate variability in time series of global-mean surface temperature: Methodology and Insights.  Thompson et al (2008) is the basis for the new and improved HADSST3 global sea surface temperature anomaly dataset from the Hadley Centre. Thompson et al (2008), like Foster and Rahmstorf (2011), is flawed because they attempt to remove the ENSO signal from the Global Surface Temperature record and claim the remainder of the rise in surface temperature is caused by anthropogenic forcings. In the Introduction, Thompson et al (2008) write (my boldface):

In this study we exploit a series of novel methodologies to identify and filter out of the unsmoothed monthly mean time series of global-mean land and ocean temperatures the variance associated with ENSO, dynamically induced atmospheric variability, and volcanic eruptions. 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…”

That is a monumental assumption, and it’s the same flawed assumption made by Foster and Rahmstorf (2011).

But it was that specific language in Thompson et al (2008) that caused me to divide the Sea Surface Temperature anomalies of the Global Oceans into the two subsets, and those were the East Pacific from pole to pole (90S-90N, 180-80W) and of the Rest-Of-World (Atlantic-Indian-West Pacific) from pole to pole (90S-90N, 80W-180). And by coincidence, I used the Sea Surface Temperature dataset (Reynolds OI.v2) that’s used in the GISS Land-Ocean Temperature Index, which is Tamino’s favorite global Surface Temperature anomaly dataset. I first presented the Sea Surface Temperature for those two subsets in the March 3, 2011 post Sea Surface Temperature Anomalies – East Pacific Versus The Rest Of The World.  (For those who are interested, there are about a dozen additional posts that discuss ENSO and the multiyear aftereffects of specific ENSO events linked at the end of that post.)

The East Pacific Sea Surface Temperature anomalies from pole to pole, Figure 10, are dominated by the variations in tropical Pacific caused by ENSO, and as a result, the variations in the East Pacific Sea Surface Temperature anomalies mimic ENSO, represented by the scaled NINO3.4 Sea Surface Temperature anomalies. The trend of the East Pacific Sea Surface Temperature anomalies is relatively flat at 0.011 deg C/Decade.

Figure 10

The reason the trend is so flat: warm water from the surface and below the surface of the western Pacific Warm Pool is carried eastward during an El Niño and spread across the surface of the eastern tropical Pacific, raising sea surface temperatures there. And during the La Niña events that follow El Niño events, the leftover warm water is returned to the western tropical Pacific. Due to the increased strength of the trade winds during the La Nina, there is an increase in upwelling of cool subsurface waters in the eastern equatorial Pacific, so the Sea Surface Temperatures there drop. In other words, the East Pacific is simply a temporary staging area for the warm water of an El Niño event. Warm water sloshes into this dataset from the western tropical Pacific and releases heat, and then the warm water sloshes back out.

But the warm waters released from below the surface of the West Pacific Warm Pool during the El Niño are not done impacting Sea Surface Temperatures throughout the global oceans, and they cannot be accounted for by an ENSO index. That leftover warm water is returned to the West Pacific during a La Niña event that follows an El Niño, much of it remaining on the surface. The Sea Surface Temperature in the western Pacific rises as a result. At approximately 10N latitude, a slow-moving Rossby wave also carries leftover warm water from the eastern tropical Pacific back to the western Pacific during the La Niña. Ocean currents carry the warm water poleward to the Kuroshio-Oyashio Extension (KOE) east of Japan and to the South Pacific Convergence Zone (SPCZ) east of Australia, and the Indonesian Throughflow (an ocean current) carries the warm water into the tropical Indian Ocean. And as noted above, due to the increased strength of the trade winds during the La Nina, there is an increase in upwelling of cool subsurface waters in the eastern equatorial Pacific, so the Sea Surface Temperatures there drop. But that cooler-than-normal water is quickly warmed during the La Niña as it is carried west by the stronger-than-normal ocean currents that are caused by the stronger-than-normal trade winds. And the reason that water warms so quickly as it is carried west is because the stronger-than-normal trade winds reduce cloud cover, and this allows more downward shortwave radiation (visible sunlight) to warm the ocean to depth. This additional warm water helps to maintain the Sea Surface Temperatures in the West Pacific and East Indian Oceans at elevated levels during the La Niña and it also recharges the West Pacific Warm Pool for the next El Niño event. Refer again to Figure 9, but keep in mind that it presents the Ocean Heat Content for the entire tropical Pacific, not just the Pacific Warm Pool.

And what happens when a major El Niño event is followed by a La Niña event? The Sea Surface Temperature anomalies for the Atlantic, Indian, and West Pacific Oceans (the Rest-Of-The-World outside of the East Pacific) first rise in response to the El Niño; the 1986/87/88 and 1997/98 El Niño events. Then the Sea Surface Temperatures of the Atlantic, Indian, and West Pacific Oceans are maintained at elevated levels by the La Niña; the 1988/89 and 1998/99/00/01 La Niña events. The results are the apparent upward shifts in the Sea Surface Temperature anomalies of the Atlantic, Indian, and West Pacific Oceans from pole to pole (90S-90N, 80W-180), as illustrated in Figure 11.

Figure 11

The dip and rebound starting in 1991 is caused by the volcanic aerosols emitted by the explosive volcanic eruption of Mount Pinatubo. And the reason the Rest-Of-The-World Sea Surface Temperature anomalies respond so little to the 1982/83 Super El Niño is because that El Niño was counteracted by the eruption of El Chichon in 1982.

To assure readers that the upward shifts in Rest-Of-The-World Sea Surface Temperature anomalies coincide with the 1986/87/88 and 1997/98 El Niño events, I’ve included an ENSO index, NINO3.4 Sea Surface Temperature anomalies, in Figure 12. The NINO3.4 Sea Surface Temperature anomalies have been scaled (multiplied by a factor of 0.12) to allow for a better visual comparison and shifted back in time by 6 months to account for the time lag between the variations in NINO3.4 Sea Surface Temperature anomalies and the response of the Rest-Of-The-World data.

Figure 12

But the ENSO Index data is visually noisy and it detracts from the upward shifts, so in Figure 13 I’ve isolated the data between the significant El Niño events. To accomplish this, I used the NOAA Oceanic Nino Index (ONI) to determine the official months of those El Niño events. There is a 6-month lag between NINO3.4 SST anomalies and the response of the Rest-Of-The-World SST anomalies during the evolution phase of the 1997/98 El Niño. So the ONI data was lagged by six months, and the Rest-Of-The-World SST data that corresponded to the 1982/83, 1986/87/88, 1998/98, and 2009/10 El Niño events was excluded—left as black dashed lines. All other months of data remain.

Figure 13

And to help further highlight the upward shifts, the average Sea Surface Temperature anomalies between the major El Niño events are added in Figure 14.

Figure 14

Based on past posts where I’ve presented the same dataset, some comments suggest the period average temperatures are misleading and request that I illustrate the linear trends. Figure 15 illustrates how flat the trends are between the 1986/87/88 and 1997/98 El Niño events and between the 1997/98 and 2009/10 El Niño events.

Figure 15

Back to the East Pacific data: If we adjust the East Pacific Sea Surface Temperature anomalies for the effects of volcanic aerosols, Figure 16, the linear trend is slightly negative. In other words, for approximately 33% of the surface area of the global oceans, Sea Surface Temperature anomalies have not risen in 30 years.

Figure 16

Note: The method used to adjust for the volcanic eruptions is described in the post Sea Surface Temperature Anomalies – East Pacific Versus The Rest Of The World, under the heading of ACCOUNTING FOR THE IMPACTS OF VOLCANIC ERUPTIONS.

And if we adjust the Rest-Of-The-World Sea Surface Temperature anomalies for volcanic aerosols, Figure 17, we reduce the effects of the dip and rebound caused by the 1991 eruption of Mount Pinatubo. And the trend of the Rest-Of-The-World data between the 1986/87/88 and 1997/98 El Niño drops slightly compared to the unadjusted data (Figure 15), making it even flatter and slightly negative.

Figure 17

In summary, ENSO is a coupled ocean-atmosphere process and its effects on Global Surface Temperatures cannot be accounted for with linear regression of an ENSO index as attempted by Foster and Rahmstorf (2011)–and others before them. We can simply add Foster and Rahmstorf (2011) to the list of numerous papers that make the same error. Examples:

Lean and Rind (2009) How Will Earth’s Surface Temperature Change in Future Decades?


Lean and Rind (2008) How Natural and Anthropogenic Influences Alter Global and Regional Surface Temperatures: 1889 to 2006


Santer et al (2001), Accounting for the effects of volcanoes and ENSO in comparisons of modeled and observed temperature trends


Thompson et al (2008), Identifying signatures of natural climate variability in time series of global-mean surface temperature: Methodology and Insights


Trenberth et al (2002) Evolution of El Nino–Southern Oscillation and global atmospheric surface temperatures


Wigley, T. M. L. (2000), ENSO, volcanoes, and record-breaking temperatures

Additionally, Foster and Rahmstorf (2011) assumed that the global warming signal is linear and that it is caused by anthropogenic forcings, but those assumptions are not supported by the satellite-era Sea Surface Temperature record as shown above. The global warming signal is not linear, and the El Niño events of 1986/87/88 and 1997/98 are shown to be the cause of the rise in sea surface temperatures, not anthropogenic greenhouse gases.


Those who have downloaded Tamino’s allfit2.xls file here (and changed it back to a .zip file) will notice that the data in Column AA is identified as “AMO”. And yes, that is Atlantic Multidecadal Oscillation data from the NOAA Earth System Research Laboratory (ESRL) AMO website.

Note: The current AMO data and the data listed in Tamino’s file are slightly different. The reason: The ESRL AMO data is constantly evolving. Each month, when the new North Atlantic (0-70N, 80W-0) Sea Surface Temperature data are added, the data is detrended with the new data.

One could only speculate why Tamino included the AMO data in the spreadsheet–and why the data in the spreadsheet extends back to 1950, when the paper only deals with the period of 1979 to 2010. And one can also wonder why Tamino would include the ESRL AMO data, which is based on Kaplan North Atlantic Sea Surface Temperature anomaly data, when no surface temperature datasets (GISS, HADCRUT or NCDC) use Kaplan SST. It’s like subtracting the Hadley Centre’s CRUTEMP land surface temperature data from GISS LOTI data to determine the Sea Surface Temperature portion of GISTEMP LOTI data. The datasets are not the same. I’ve already pointed this error out to Tamino and his disciples in the post Comments On Tamino’s AMO Post.

But for example, let’s satisfy your curiosity. Let’s assume you were wondering what the results would be if you were to account for the impact of the AMO on Northern Hemisphere surface temperatures, using a linear regression analysis with the ESRL AMO data as the independent variable and with GISS Northern Hemisphere Surface Temperature data as the dependent variable. We’ll confine the example to the Foster and Rahmstorf (2011) time period of 1979 to 2010. Refer to Figure 18. The AMO-adjusted Northern Hemisphere surface Temperature has a linear trend that is only 41% of the unadjusted Northern Hemisphere data. Hmm. That would mean the AMO was responsible for 59% of the rise in Northern Hemisphere surface temperatures based on linear regression analysis.

Figure 18

And that’s in line with generalization made by Tamino’s associates at RealClimate in their Atlantic Multidecadal Oscillation (“AMO”)webpage. There they write that the AMO is:

A multidecadal (50-80 year timescale) pattern of North Atlantic ocean-atmosphere variability whose existence has been argued for based on statistical analyses of observational and proxy climate data, and coupled Atmosphere-Ocean General Circulation Model (“AOGCM”) simulations. 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 term was introduced in a summary by Kerr (2000) of a study by Delworth and Mann (2000).

59% is definitely “some, but not all”.

Tamino continues to complain that one can’t make adjustments for the AMO because it includes a global warming component. For example, in a response to a December 22, 2011 at 6:11 pm comment by Colin Aldridge,Tamino writes:

As for AMO, unlike ENSO (or PDO for that matter) it IS temperature. Pure and simple, nothing more nothing less. Attributing temperature change to temperature change seems kinda stupid.

Hmm. I believe Tamino misses the point that the AMO is a mode of additionalvariability and that it is detrended over the entire term of the data.

Further to this end, I discussed and illustrated for Tamino that we can subtract the “warming signal” of the Global Sea Surface Temperature anomalies excluding the North Atlantic from the North Atlantic Sea Surface Temperature anomalies. That way we’re left with only the additional variability of North Atlantic Sea Surface Temperature anomalies caused by the AMO. And that’s really how the AMO should be expressed. We’ll call the difference the North Atlantic Residual. The North Atlantic Residual has, approximately, the same trend as the AMO for the 1979 to 2010 period of Foster and Rahmstorf (2011), as shown in Figure 19.

Figure 19

Note: The North Atlantic Residual data presented in Figure 16 is based on the combination of HADISST data for the years 1979 to November 1981 and Reynolds OI.v2 SST data from December 1981 to present in agreement with the GISS recipe listed on their GISS Surface Temperature Analysis webpage. To remove the North Atlantic Sea Surface Temperature data from the Global data, the North Atlantic surface area for the coordinates of 0-70N, 80W-0 was determined to represent 11% of the surface area of the global oceans.

And as an additional check of the sign of the solar correction, I performed multiple linear regression analyses with GISS Northern Hemisphere Surface Temperature data as the dependent variable and using the AMO data as an independent variable in one instance and the North Atlantic Residual data in a second. The analyses also included the ENSO (MEI), Solar (PMOD), and Volcanic Aerosols (AOD.NH) as independent variables with the same lags as the global data. In both instances, the sign of the solar correction was the opposite of what Foster and Rahmstorf (2011) were looking for, as shown in equations 12 and 13:


GISS.NH = 62.25 + 0.001696MEI (4m lag) – 0.04528TSI.PMOD(1m lag)– 1.683AOD.NH (7m lag) + 0.866AMO (0m lag)


GISS.NH = 72.12 + 0.04751MEI (4m lag) – 0.05258TSI.PMOD(1m lag)– 2.413AOD.NH (7m lag) + 0.72N. Atl. Residual (0m lag)

A closing AMO note: For an additional discussion on how the North Atlantic impacts the Sea Surface Temperatures of the periods between the upward shifts caused by the 1986/87/88 and 1997/98 El Niño events, refer to the post Supplement To “ENSO Indices Do Not Represent The Process Of ENSO Or Its Impact On Global Temperature”.


I found the inclusion of a linear trend in the regression analyses performed by Foster and Rahmstorf (2011) to be very interesting. It appears the linear trends were included simply to cause a solar correction that was the sign the authors wanted for their adjustments. One might think, if the basic results of the paper were dependent on whether a linear trend was included in the multiple regression analyses, this would have been discussed in the paper.  And again, if you have the capability, and if you’re not satisfied with the similarities between my results and the Foster and Rahmstorf (2011) results (Figures 7 and 8), please confirm the multiple regression analyses results presented above with and without the linear trend.

This post also illustrated and discussed the error in their assumption that regression analysis can be used to remove the impacts of ENSO on Global Surface Temperature. ENSO is a process that is not fully represented by ENSO Indices. In other words, the ENSO indices only represent a small portion of the impacts of ENSO on Global Surface Temperatures. Attempting to use an ENSO index as Foster and Rahmstorf (2011) have done is like trying to provide the play-by-play for a baseball game solely from an overhead view of home plate.

The assumption made by Foster and Rahmstorf (2011) that a linear trend provides an approximate “global warming” signal was shown to be erroneous using Sea Surface Temperature data. When broken down into two logical subsets of the East Pacific and the Atlantic-Indian-West Pacific Oceans, Satellite-era Sea Surface Temperature data shows no evidence of an anthropogenic global warming signal. It only shows upward shifts associated with strong ENSO events. This would seem to complicate any attempt to justify the inclusion of the linear trend to reverse the sign of the solar adjustment.

And thanks to Tamino for including the Atlantic Multidecadal Oscillation data in his spreadsheet. It allowed me to illustrate the significant impact the AMO can have on Northern Hemisphere surface temperatures.

Happy New Year to all.

ABOUT: Bob Tisdale – Climate Observations


The spreadsheet that served as the source of the data for the regression analyses was linked to Tamino’s (Grant Foster’s) post Data and Code for Foster & Rahmstorf 2011.

To save you some time, here’s a copy of the file that contains the spreadsheet from Tamino’s blog that I’ve uploaded to mine, allfit2 as of 12-21-11.  Again, you’ll have to download the file and change it to a .zip file in order to open it.

The Reynolds OI.v2 Sea Surface Temperature data used in the ENSO discussion is available through the NOAA NOMADS website here.

The Aerosol Optical Thickness data used in the volcano adjustments of the Sea Surface Temperature data in Figures 13 and 14 is available from GISS the Stratospheric Aerosol Optical Thickness webpage here.

About Bob Tisdale

Research interest: the long-term aftereffects of El Niño and La Nina events on global sea surface temperature and ocean heat content. Author of the ebook Who Turned on the Heat? and regular contributor at WattsUpWithThat.
This entry was posted in CAGW Proponent Arguments, El Nino-La Nina Processes. Bookmark the permalink.

11 Responses to On Foster and Rahmstorf 2011 – Global temperature evolution 1979–2010

  1. ferd berple says:

    F&R 2011 – What it actually shows.

    This should be fairly simple to follow if you understand algebra and substitution.


    GISS = -91.43 + 1.024Trend + 0.0761MEI(4m lag) + 0.06694TSI.PMOD(1m lag)- 2.334AOD (7m lag)

    (1) GISS = 1.024Trend + bx + c

    (2) GISS = 1.0Trend + 0.024Trend + bx + c

    (3) GISS = (GISS + d) + 0.024Trend + bx + c

    (because y = mx + d, where m=slope=trend, d=y intercept)

    (4) 0 = 0.024Trend + bx + e

    (5) Trend = -(bx + e)/0.024

    F&R have not solved for GISS. By including Trend(GISS) as an independent variable they have eliminated GISS. What they have shown is that the Trend in GISS can be fully explained as a linear result of MEI, TSI, and AOD, without any reference to CO2.

    In other words, F&R have proven that Climate Change is fully explained by the Multivariate ENSO Index (MEI), the Total Solar Irradiance (PMOD), and the Volcanic Aerosol Optical Depth data (AOD).

    In other words, F&R have proven that CO2 has no role in climate change.

  2. Joe's World says:


    Joe’s World – Your comment had nothing to do with the content of this post. I warned you a few weeks ago that I would not allow you to discuss these topics unless I presented them in my post. When I prepare a post about planet rotation and tilt, then feel free to comment about it. But until that time, I will not allow you to try to hijack a thread.



  3. nevket240 says:


    Bob. Just a heads up on another ocean component. (social security for salty scientists)


  4. Bob Tisdale says:

    nevket240: Willis Eschenbach just had a post at WUWT about the change in the pH of the oceans. They’re not becoming more acidic. The oceans aren’t acidic now. They’re basic. With the increase in CO2, they’re becoming less basic, less alkaline. In other words, the CO2 is making them more neutral:

    And Added PS: nevket240, I forgot to thank you for the link.

  5. Pingback: Revised Post – On Foster and Rahmstorf (2011) | Bob Tisdale – Climate Observations

  6. Pingback: Tisdale on Foster and Rahmstorf – take 2 | Watts Up With That?

  7. Pingback: Tisdale on Foster and Rahmstorf – take 2 | TaJnB | TheAverageJoeNewsBlogg

  8. Pingback: Tisdale on Foster and Rahmstorf – take 2 | My Blog

  9. P. Solar says:

    Hi Bob, I decided to reply to your comment here because WUWT is far to busy to conduct any kind of dialogue.

    Firstly, I did read the latter part of your article rather quickly but did catch sight of the La Nina charging El Nino claim. You have presented this before and I found it unconvincing so I did not dwell on it. Neither do I agree with the “overcharging” idea that you state without any real evidence.

    Having said that I don’t think you are totally wrong about all this. Here’s how I see it.

    El Nino is an upsurge of warmer water from deeper ocean. This warms the surface waters, which in turn leads to some warming of the atmosphere via evaporation and convection, however much of the ocean heat energy will escape to space, either directly or indirectly. El Nino is in fact a _cooling_ event in terms of global energy budget.

    La Nina brings cooler water to the surface, this reduces evaporation and convective cooling and marginally reduces radiative loss (ignoring temporarily any cloud changes). This is different from the previous case since the atmosphere will have negligible ability to warm the oceans. It is not symmetrical. However, the temperature will not affect the amount of solar energy absorbed at the surface. So by reducing the heat loss alone this will result in a net increase in OHC. All of this before considering cloud variations.

    Your comments on trade winds removing cloud seems rather speculative in the absence of any proof. It may be more justified to use the established link between evaporation and tropical cloud cover which would operate in the same sense as the preceding effects. More cloud as a result of El Nino would enhance the energy deficit, accelerating the net loss of global energy and acting as a negative feedback that would cool the surface waters. Similarly, decreased cloud during La Nina will accentuate the energy gain and warm the cooler surface waters even quicker. Again a negative feedback on the original variation is surface temperature.

    The heat transfer to and from the atmosphere is asymmetrical but that does not mean either of the two parts of the cycle dominate the energy budget, it could go either way and almost certainly does at different times.

    I find your conclusion that La Nina _causes_ El Nino to be totally unfounded (unless you presented something else that I missed).

    These are just two phases of an oscillation in ocean currents, the root cause of which remains undetermined. To suggest either causes the other would seem similar to saying the day _causes_ the night.

    I think a more proper conclusion is that both parts of the cycle have a notable effect on both energy budget and global mean surface temperatures and whatever causes / controls the El Nino / Nina variations will have a mechanism to cause both decadal and longer term changes in OHC and surface climate.

    I don’t think this is at odds with your work, except that you see it as the cause rather than the mechanism of the changes.

    My own speculation as to root cause would be solar+planetary motion. Tidal effects on colder, denser, deep ocean water periodically bringing it to the surface. Scafetta has already demonstrated a strong cyclic component to climate, this could be the mechanism.

    Best regards.

  10. Bob Tisdale says:

    P. Solar: Your detailed discussion of ENSO is very good. There are a few things I would add but all in all it was very good. Regarding cloud cover and the recharge phase during La Niña events, Trenberth et al (2002) makes a brief mention of it when they write:

    “The negative feedback between SST and surface fluxes can be interpreted as showing the importance of the discharge of heat during El Nino events and of the recharge of heat during La Nina events. Relatively clear skies in the central and eastern tropical Pacific allow solar radiation to enter the ocean, apparently offsetting the below normal SSTs, but the heat is carried away by Ekman drift, ocean currents, and adjustments through ocean Rossby and Kelvin waves, and the heat is stored in the western Pacific tropics. This is not simply a rearrangement of the ocean heat, but also a restoration of heat in the ocean.”

    That was presented in the following post:

    And so was the 2008 Pavlakis et al paper “ENSO Surface Shortwave Radiation Forcing over the Tropical Pacific” which documents the variations in DSR there:

    Click to access acpd-8-6697-2008-print.pdf

    Also refer to the discussion of the 1995/96 La Niña in that post. The “overcharging” of the tropical Pacific OHC is a recent description of mine, but it falls in line with the Trenberth discussion above and the curious 1995/96 upsurge in tropical Pacific OHC. That event was explained in McPhaden (1999) “Genesis and Evolution of the 1997-98 El Nino.”

    He states it is the result of “stronger than normal trade winds associated with a weak La Nina in 1995–96.”

    Again, the stronger-than-normal trade winds decrease cloud cover, which, in turn, increases downward shortwave radiation, warming the tropical Pacific.

    Regarding ocean currents, I assume your comment about phases in ocean currents has to do with the strengthening and weakening of the North and South Equatorial Currents in the Pacific and my discussion of them. There is also another ocean current there that has to be included in a discussion of ENSO. It’s the Equatorial Countercurrent. I illustrated its variations in the following post. Its strength can increase drastically during an El Niño. Keep in mind, during La Niña and ENSO-neutral phases, the sea surface height in the western tropical Pacific is measurably higher in the west than it is in the east. The warm water is held there by the trade winds. When the trade winds relax, gravity causes the warm water in the west to flow eastward against the normal direction of flow, and this can be seen in the increased size of the Equatorial Countercurrent. The warm water to depth in the west Pacific Warm Pool is drawn eastward.

    See how those factors influence your interpretation of ENSO, and we can pursue other differences.

    A question: Do you want me to move this discussion to my more current post on F&R? I’m not sure if and how I can relocate your comment other than cutting and pasting, but I’ll give it a shot if you want them moved.


  11. Doug Cotton says:

    In 1981 NASA’s Dr Hansen made a huge mistake in assuming the Earth’s surface radiates like a blackbody. A further assumption was made that radiation from a colder atmosphere can be converted to thermal energy by a significantly warmer surface. It cannot be, and so it cannot warm or slow the rate of cooling. See http://climate-change-theory.com for more detail.

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