Reconstructing a dataset of observed global temperatures 1950-2016 from human and natural influences

by Frank Bosse

A demonstration that multidecadal variation since 1950 leads to overestimation of the Transient Climate Response (TCR).

Introduction

Inspired by a recent paper ( Folland et.al 2018), I try to replicate the annual development of the observed global mean surface temperature (GMST) for 1950-2016 with a minimum of fitting and smoothing. Unlike it was done in Folland et.al I don't want to break the time series into sub-periods nor use monthly data when annual data seem to be sufficient.

I take account for the following factors:

1. Anthropogenic forcing. I use the forcing ERF data of Lewis&Curry (2018).
2. ENSO, solar forcing, volcano forcing. I use the data of Grant Foster aka "Tamino", released in this recent post.
3. Some internal variability of the climate system which is missed in modeled approaches as this very recent paper (Kravtsov et.al 2018) shows.

The GMST product I use is the data source of Cowtan&Way as it is described here.

The aim of the procedure is to show that one reaches an excellent agreement between the constructed dataset and the observations if natural influences are allowed for and human influence is parametrized as forcing multiplied by the sensitivity coefficients (i.e. the transit climate sensitivity) that is deduced from the observations.

Procedure

1. For the C&W dataset I downloaded annual averages for 1950…2016. Thereafter the data was passed the "Tamino- filter" (shown in fig.1 and 2 of the cited post) for eliminating the influences of ENSO, volcano and variations in the solar forcing. The data for this filter are available from it's author here. The "filter" is the difference between the "raw" and "adj." data. "Tamino" uses the index "MEI" for the tuning of ENSO- events, this introduces a trend slope into this filter due to the forcing impacting MEI.
2. The thus adjusted data were regressed vs. the anthropogenic ERF data to estimate the sensitivity of the climate system vs. the forcing. The regression slope for 1950 to 2016 is 0.335 +- 0.031 K/W/m² (95% confidence). The residuals of this regression contain a (multi) decadal signal with strong persistence (Hurst coefficient=1) as will be shown below.
3. The (multi)decadal variability is detailed modeled below.

In a previous post to model the (multi)decadal variability I used the SST of the AMO-area (25-65N; 70W-7W), as it was suggested by v. Oldenborgh et. al ( 2009), regressed on the global forcing, not the GMST as it was applied in the cited paper. However, in the discussion section of this post two years ago some doubts were expressed as to whether the residuals of this regression would still contain some forced component. Therefore I used a different approach this time, based on the SST's in the Northern Atlantic (50-65N; 60W-10W) and in the Southern Ocean (50S-65S; 70E-70W).Fig.1: The global mixed layer depth (MLD) averaged over the year. Note the depth of about 250m in the Northern Atlantic (50-65N; 60W-10W) and in the Southern Ocean (50S-65S; 70E-70W). Source: Argo

The impact of any forcing on the SST will be much more muted in these regions than in other regions of the globe because the surface warming power is mixed down into and has to warm a much bigger layer of water (Fig.1).

Therefore I used the SST (ERSSTv5) data of both areas and calculated the difference of their average which should cancel out any forced warming. The result is shown together with the residuals of the regression described in point 2:

Fig.2: The residuals (black) of the regression described in point 2 above and the SST- difference (light blue) between the North Atlantic (NA) and Southern Ocean (SO).

Note that no smoothing was applied. The best fitting coefficient to map the residuals from the SST difference is 0.105.

Synthesis of the GMST series

With the equation:

T(n)=0.335*ERF anthropogenic (n) + T tamino filter (n)+ 0.105*SST NA-SO(n) -0,33      (1)

where T is the reconstructed temperature and n the actual year of the record and tamino filter used as described in point 1 above I calculated T(n)for all years n 1950-2016.

Results

Fig. 3 compares the resulting reconstructed temperature series with the original Cowtan&Way data.

Fig. 3: The original C&W data (green) and the reconstructed data with the procedure described above (dark blue). The difference of the trend slopes for the temperatures over the time 1950…2016 is marginally (4%).

The standard error of the reconstruction is 0.008 °C.

All the characteristics described in Folland et.al (2018) are replicated: the slightly cooling to 1976, the strong warming thereafter to 1998 and the somewhat muted warming to 2014, which is likely a result of the internal variability. The overall performance: 94 % of the variance of the raw C&W data is deduced from the described reconstruction. The remaining residuals probably contain mainly weather noise (Hurst Coefficient=0.7).

Discussion

How much warming since 1950 is anthropogenic? The procedure gives 98% for this time window. The trend slopes with/without internal variability are indistinguishable. Fig.2 shows that the internal variability made an almost full swing during the 67 evaluated years.

A postulate is included: There are no other contributions than described in the introduction section, perhaps longer lasting, so that we can't identify them. This is also the case if we would include more years from the past, also due to the strong increasing uncertainties in the observed data, i.e. in the Southern Ocean.

However, in shorter time windows the internal variability described here can for sure introduce some bias regarding the sensitivity.

Fig.4: The linear amplification of the GMST trends from the internal (multi) decadal variability shown in Fig.2 with the start year on the abscissa to 2016.

The internal variability (see Fig.2 and 4)"push/pulls" the observations in this manner.

The higher trend caused by this (multi)decadal variability was likely taken into account when parameterizing climate models, introducing bias in them.

Conclusions

The annual GMST 1950-2016 are a composition of:

• Anthropogenic forcing with the sensitivity TCR=1.27 °C (best estimate, calculated with the result of Eq. (1) multiplied by 3.8 W/m² for the doubling of CO2) for the C&W product, consistent with the findings of Lewis&Curry
• Solar- , volcano forcing and ENSO- influence. The calculation follows here the cited "Tamino" post with thanks to Grant Foster for releasing the "filter".
• Some (multi) decadal internal variability with the amplitude of about 0.25°C (see fig.2) which can be well modeled by scaling the SST difference between the areas mentioned.
• Weather noise (6%).

The (multi) decadal variability mentioned in (3) will lead to estimates of TCR based on trends over periods starting after 1950, particularly trends during the satellite period (post 1978), being biased upwards.

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