The effect of Atlantic internal variability on TCR estimation – an unfinished study

A guest article by Frank Bosse (posted by Nic Lewis)

A recent paper by the authors Stolpe, Medhaug and Knutti (thereafter S. 17) deals with a longstanding question: By how much are the Global Mean Surface Temperatures (GMST) influenced by the internal variability of the Atlantic (AMV/AMO) and the Pacific (PMV/PDO/IPO)?

The authors analyze the impacts of the natural up’s and down’s of both basins on the temperature record HadCRUT4.5.

A few months ago this post of mine was published which considered the influence of the Atlantic variability.

I want to compare some of the results.

In the beginning I want to offer some continuing implications of S. 17.

The key figure of S. 17 (fig. 7a) describes most of the results. It shows a variability- adjusted HadCRUT4.5 record:

Fig.1: The Fig. 7a from S. 17 shows the GMST record (orange) between
1900 and 2005, adjusted for the Atlantic & Pacific variability.


Unfortunately I couldn’t find the data, therefore I digitized the orange graph and synthesized the annual data. Foremost I wanted to check this sentence from the conclusion:

“With a contribution of less than 10%, the measured global warming during the second half of the 20th century is not much affected by Atlantic and Pacific variability, underlining that most of this observed  warming is caused by anthropogenic forcings.”

 At first I calculated the regression of the variability adjusted HadCRUT4.5 record on the forcing (IPCC AR5), which is very impressive:




Fig. 2: The correlation between the forcing and the Temperature change
of S 17. 91% of the temperature variance is due to the forcing changes.


The unadjusted HadCRUT4.5 record (also from 1900…2005 and smoothed with a 10-year loess) gives R²=0.85. This implies for the whole time span:  6% of the variance of the temperatures is due to the AMV&PMV, calculated in S.17.

The slope of the linear Trend (multiplied with 3.71 W/m² for the IPCC forcing due to 2*CO2) results in a TCR of 1.35 K, for the unadjusted record of HadCRUT4.5 it’s almost the same value: 1.36 K. This is no surprise because over the long time span the influence of the decadal variability will cancel out.

The cited sentence from the conclusions in S.17 is valid only for the second half of the 20th century.

Therefore I calculated the slopes (see Fig.2) for every year from 1950 to 1976 with the constant end year 2005 and multiplied them with 3.71 to estimate the TCR.


Fig. 3: The TCR to 2005 calculated for each year from 1950 to 1976 with the results of S.17


Note in Fig.3 that the TCR of the adjusted record is relatively flat till around 1970 in contrast to the unadjusted record. For the S.17- adjusted record of HADCRUT4.5 the TCR from 1970 to 2005 is 1.33 K. For the unadjusted HADCRUT4.5 this value is 1.74 K. The reduction is due to the internal variability of the oceans as it was calculated in S 17.  The relative difference of the TCR values:



Fig.  4: The percentage of the influence of AMV and PMV on the TCR after 1950 following S.17.


If one interprets the cited sentence from the conclusions of S.17 literally, it’s correct: the second half of the 20th century began in 1950 and the influence on TCR in S.17 is well below 10% (it’s 7%). For the more critical years for the tuning of the CMIP5- models after 1970 it reaches up to 24%. This overestimation is the result of the AMV&PMV as the result of S.17 shows. The mean TCR in the CMIP5 models is 1.8 K.


Comparisons with the formerly proposed method

In the time since the release I considered some new findings from the literature and advanced some details.

  1. Selection of data

GMST: In S.17 they use HadCRUT4.5 as the temperature record. This is questionable due to some gaps in the spatial coverage of this record. In this blogpost Nic Lewis examined the GISS-record and recommended the record  of Cowtan/Way for model vs. observation comparisons. In the following discussion it was mentioned that the BEST record is also very helpful.  Therefore I use the average of both records.

Atlantic variability: In S. 17 they use an Index from this study. There are some disadvantages from the inclusion of the tropical part of the Atlantic it’s shown in v. Oldenborgh (2009). Therefore I use the SST 25…60°N; 70…7°W (HadSST3) regressed on the forcing (NOT on the GMST) to generate the AMO index.

Forcing: The basis is the record of the IPCC (AR5). In the following years some improvements were released ( see here and here  ) which are now  included in the used forcing-record.  The volcano forcing is excluded for all calculations.


  1. The internal variability of the GMST

The GMST are regressed on the forcing for the time span from 1871 to 2016 with annual data. The residuals of this regression:



Fig. 5: The unforced variability of the GMST (GMSTV) filtered with a 10a-Loess smoother. One can
notice that the volcanic influence and the ENSO-imprints are relatively small due to the smoothing.


The regression of the GMSTV on the AMO record  (see fig.  3 of the discussed post) shows a significant trend:



Fig. 6: The relationship between the GMSTV and the AMO with annual unsmoothed data.


In S.17 they also include the Pacific Internal Variability. The authors use the Tripole(IPO) Index . Unfortunately I could not find any statistically valid inference between this index (and also the PDO index) and the GMSTV which also rises some doubts on the results of this recent paper . Therefore I wasn’t able to include a decadal Pacific variability due to the lack of any significance.


  1. The TCR-estimation after removing the Atlantic internal variability

After removing the weighted AMO Influence (see Fig.6) on the GMST the adjustment shows this result:



Fig. 7: The raw- and AMO-adjusted GMST filtered with a 10a Loess smoother. Note that the longtime trend is not influenced and that the adjustments produce only a difference of about 0.1K at maximum.  The often discussed “hiatus” vanished.


For the estimation of the TCR in the years with stronger forcing from 1950 and following I calculated the trends of GMST vs. Forcing to the constant end year 2015. The year 2016 is excluded as it was strongly influenced by an ENSO-event (see Fig. 5). To calculate the TCR from the feedback I multiplied these lambda-data with 3.8W/m² for a doubling of CO2.



Fig. 8: The TCR estimated from the raw GMST and AMO adjusted GMST. Observe the stability
of the TCR with no significant trend. The mean for the calculated trends from 1950 to 1985
with the end in 2015 gives 1.29 +-0.04 K/2*CO2 with 95% confidence (2*Sigma).


A more detailed uncertainty analyses which would also include the GMST, Forcing- and AMO- uncertainties is beyond the scope of this post .

Finally I calculated the percentage of the influence of the variability on the TCR to compare it with Fig.4.

Fig. 9: The percentage of the influence of the variability on the TCR. Note the similarity in the years to 1970
to the estimation included in S.17. The longer record (to 2015) makes the estimation more valid up to 1985.



Considering the internal variability reduces the calculated TCR for the years after 1970 by about 25%. It solves the problem, that the TCR is significant lower for the time span 1950…2015 than for the time span 1975…2015.

The inclusion of the Pacific decadal variability does not improve the result, confirming some recent findings.

This actual paper about the west-tropical Pacific confirms the “Iris-effect” from observations with the implication that the ECS is estimated at about 2K for the doubling of CO2. Into the same direction points this study about the mid-latitude cloud response to the forcing. The discussed result from this post seems to be also a strong argument for a sensitivity of the GMST to Carbon Dioxide at the lower end of the IPCC AR5 1.5-4.5 K range.


Note: Frank Bosse and I have been cooperating in investigating isolating the impact of Atlantic multidecadal variability (AMO/AMV) on TCR estimation. This post reflects an approach that we both consider to be defensible; it removes any anthropogenic forcing signal from the measure of AMO/AMV.  English is not Frank’s mother tongue, so please avoid criticisms about English language usage, except where something is unclear. Nic Lewis


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