Internal climate variability as a confounding factor in climate sensitivity estimates

by Frank Bosse

Towards eliminating multi-decadal natural oscillations in determination of the Transient Climate Response (TCR) to CO2.


In the last few month there have been several posts (see here , here , here, here) addressing the sensitivity of our climate to forcing that accounts for the influence of internal variability. This relation is one of the most important questions of the climate research and has far reaching impact to society as the release of carbon dioxide is the main source of planet warming.

The TCR is the most relevant climate sensitivity measure for warming in the 21st century. The mean of the CMIP5 climate models suggests a TCR of 1.8K/doubling of atmospheric CO2. However, a TCR value between 1.3 and 1.4 K is more likely from the observations as it was shown here , here, here and in the cited posts above . However, there are still some discussions in the community about the validity of the observed TCR values and the relation of man made warming to the natural variability.

Improvement of the signal to noise ratio (SNR) in the observed records is required to make progress in the attribution to the causes of warming from external forcing. In his latest blog post, Nicholas Lewis published a figure that showed the slope of the temperature rise due to forcing when the temperatures were adjusted for the AMO:


Fig. 1: The residuals of the temperatures after regression vs. the forcing, included an adjustment for the AMO, source: Fig. 1 of the cited Post.

This Figure is the starting point for this analysis.

An improved AMO index

When one correlates the global forcing data of the IPCC AR5 to the Global Mean Surface Temperature (GMST), there is an interesting signature:


Fig.2: The spatial correlation of forcing and observed temperatures (GISS). The figure was generated with the “KNMI climate explorer”, thanks to Geert-Jan v. Oldenborgh.

I excluded in all the calculations the volcano-forcing because of the well known difficulties with the (in relation to other forcings small) temperature response to this.

In Fig. 2 there are two large regions with pronounced variability, that are only weakly correlated to the forcing:  parts the northern extra tropical Atlantic and Pacific northward of 30°N. The Pacific sector is linked to the ENSO behavior, and the Atlantic region is of interest for calculating an AMO-index.The Pacific sector is linked to the ENSO behavior, and the Atlantic region is of interest for calculating an AMO-index.

Oldenborgh et al use the SST of the area 25N -60N; 70W – 7OE and regress them vs. the GMST. In light of Fig.2 , this is an incomplete approach to generate an index that is not influenced by the forcing. As Nicholas Lewis recommended, I regressed the SST (HadISST1) of the area mentioned above vs. the forcings:



Fig. 3: The AMO index (annual data) which is as little as possible influenced by the forcing. The impacts of volcano events on the SST of the northern Atlantic were manually adjusted because not every event since 1870 left a mark proportional to the global volcano-forcing there.

The Index is very similar to the Index of V. Oldenborgh et. al (2009).

Evolution of the GMST since 1951

As shown in this post, there is a long time persistence in the record of the residuals after regression of the “adjusted GMST” to ENSO, Volcano and Solar as it was recommended by “Tamino” :


Fig. 4: The smoothed (with a 15 years Loess low pass) residuals of the GMST of four records after regression of the temperatures vs. the forcing,   data from IPCC AR5.

The long time persistence of the records shown in Fig. 4 is accomplished with a Hurst analyses of the annual residuals of the linear regression.

After removing all known influences of forcing and variability, we should only see some noise in the record of the residuals, which should have a Hurst coefficient (H) near 0.5, a random walk. The residuals after removing the forcing, solar, volcano- and also ENSO-events gives H = 1, which means that there still remains strong long-term persistence.

Partial removal of multi-decadal internal variability

I removed the influence of the Atlantic variability, which is not calculated with the participation of GMST per Fig. 3 (without any smoothing), from the GMST records of “Tamino” with a factor of 0.3 which gave the best fit.


Fig. 5: The GMST records adjusted for ENSO, Solar, Volcano (by “Tamino”) and Atlantic variability (AMO, see above) after 1951. The link to the forcing (shown in black) is clearly visible.

The regression vs. forcing looks like this for the case of the “Berkeley Earth” record:


Fig. 6: The regression result. The slope of the linear trend means: A forcing of 1 W/m² generates a warming 0.357 +- 0.026 K (95% confidence).

The TCR value of 1.32 K is calculated using a factor 3.71 W/m² for a doubling of CO2. The TCR results deduced from the four GMST records do not differ much from the results of the former post —  GISS : 1.55K, HadCRUT4: 1.26K; C/W-1.33. The R² values were improved in relation to the values of the former post by about 4.5%: 0.94; 0.92; 0.92; what means for “Berkeley Earth” (see Fig.6): 92% of the variability of the temperatures comes from the variability of the forcing. The Hurst analyses for long time persistence for the records gives values near 0.8, a notable reduction versus the non AMO-adjusted data (H=1) and an important step towards eliminating the ‘noise’ from unforced natural climate variability.

Improvement of the signal-to-noise ratio

In the discussion of a former blogpost there was a very interesting aspect: the shorter the observed time span after 1951 used to determine the values of TCR, the lower the value of the TCR, as shown in the comment. This behavior suggests that the time span for a valid TCR-estimation with the regression- method, which is was also exercised in the literature, is around 60 years. Therefore I investigated the time dependency   of the results of the TCR regressions after removing the AMO also for shorter time spans:


Fig. 7: The slopes of the regressions of at least 30 years long time spans (with the averages of the four records shown in Fig.5) with AMO adjustment (blue) and without this (red).

The resulting TCR of about 1.35 is remarkably constant over time. The results for the TCR calculated from 1951 to 2015 and from 1971 to 2015 don’t differ by more than 9%. As stronger the fluctuation of the calculated values for the TCR over the time as stronger the still remaining variability in the record because the response of the climate to the forcing should be not time dependent at least in the observed time span 1870-2015.

This insensitivity to the length of the period used to determine TCR also stands if one looks at the longtime record of HadCRUT4 without any further adjustments after removing the years with volcano events:


Fig.8: The slopes of the HadCRUT4 record since 1870 calculated with annual data. The resulting TCR of the AMO-adjusted record (blue) gives 1.38 +-0.1K (95% confidence= 2 sigma) for the time span 1950…2015 with the constant start year 1870. For comparison: the results using AMO-unadjusted data (red).


1.Exclusion of the Atlantic variability Index (AMO) deduced from the SST of the extra tropical northern Atlantic and the forcing data improves the signal-to-noise ratio of the detection of the impact of the forcing on the GMST.

2.The TCR deduced from observations with AMO- adjustment is very constant over the time in the interval 1.25 — 1.55 K; the highest value is calculated from GISS, whereas HadCRUT4 and Berkeley Earth give a TCR of below 1.4 K. The TCR of 1.8 K of the mean of the CMIP5 models is not justified by the historical observations since 1870.

3.The largest remaining source of uncertainty is the forcing data, particularly in the aerosol (and cloud) forcing. The latest results could point to a higher net positive forcing.

Moderation note:  As with all guest posts, please keep your comments civil and relevant.

Filed under: Sensitivity & feedbacks

Judith Curry

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