Originally a guest post April 30, 2018 at Climate Etc.

*Plain language summary*

- A new paper by Andrew Dessler et al. claims, based on 100 simulations of the historical period (1850 to date) by the MPI‑ESM1.1 climate model, that estimates of climate sensitivity using the energy-budget method can vary widely due to internal climate system variability.
- I calculated what effect the uncertainty implied by the internal variability affecting the MPI‑ESM1.1 simulations had on the distribution of the primary climate sensitivity estimate in the recent Lewis & Curry energy-budget paper.
- The result was a marginal
*narrowing*of the Lewis & Curry sensitivity estimate. This is because the allowance for internal variability by Lewis & Curry is larger than internal variability in MPI‑ESM1.1. - Since historical period energy-budget sensitivity estimates are much more imprecise for other reasons, internal variability contributes little to their total uncertainty; it is an unimportant factor.
- Nothing in the new Dessler et al. paper indicates that the Lewis & Curry energy-budget climate sensitivity estimates are likely to be biased low.

** Introduction**Climate scientist Andrew Dessler has two interlinked short papers on climate sensitivity estimation out, one as an unpublished non-peer reviewed preprint. I focus here on the published study (hereafter Dessler18).

^{[1]}

The abstract reads:

Our climate is constrained by the balance between solar energy absorbed by the Earth and terrestrial energy radiated to space. This energy balance has been widely used to infer equilibrium climate sensitivity (ECS) from observations of 20th-century warming. Such estimates yield lower values than other methods and these have been influential in pushing down the consensus ECS range in recent assessments. Here we test the method using a 100- member ensemble of the MPI-ESM1.1 climate model simulations of the period 1850-2005 with known forcing. We calculate ECS in each ensemble member using energy balance, yielding values ranging from 2.1 to 3.9 K.

^{[2]}The spread in the ensemble is related to the central hypothesis in the energy budget framework: that global average surface temperature anomalies are indicative of anomalies in outgoing energy (either of terrestrial origin or reflected solar energy). We find that assumption is not well supported over the historical temperature record in the model ensemble or more recent satellite observations. We find that framing energy balance in terms of 500-hPa tropical temperature better describes the planet’s energy balance.

Of direct relevance to the new Lewis and Curry paper (hereafter LC18)^{[1]</sup3}, Dessler18 states:

With respect to precision of the estimates, our analysis shows that

λand ECS estimated from the historical record can vary widely simply due to internal variability.

Andrew Dessler has been using the Dessler18 results to criticise energy budget ECS estimates, such as that in LC18. He tweeted:

New Lewis and Curry paper is out! Unfortunately for them, it’s already shown to be wrong! Our recent paper showed that the methodology produces answers that can deviate significantly from reality.

^{[4]}

In reality, the LC18 results are untouched by the Dessler18 findings, as I shall show.

** What Dessler18 does**Dessler18 estimates climate feedback strength

*λ*from the global mean changes in surface air temperature

*T*

_{S}, effective radiative forcing

*F*and top-of-atmosphere net downwards radiation

*N*between the first and last decades of 100 MPI-ESM1.1 historical simulations, using the standard energy-balance equation:

*λ*= Δ

*R*/Δ

*T*

_{S}= (Δ

*F*− Δ

*N*) /Δ

*T*

_{S}.

^{[5]}Exact simulated Δ

*N*and Δ

*T*

_{S}values are output by the model, while Δ

*F*is estimated separately.

^{[6]}ECS is estimated as

*F*

_{2}

_{⤬}

_{CO2}/

*λ*, where

*F*

_{2}

_{⤬}

_{CO2}is taken as 3.9 Wm

^{−2}.

^{[7]}

The estimated 5-95% uncertainty range for* λ* derived from the MPI-ESM1.1 historical simulations is 1.17−1.63, with a median of 1.43 and an almost identical mean (units for *λ* are Wm^{−2 }K^{−1}). The distribution has an estimated standard deviation of 0.137 and shows no evidence of non-normality.^{[8]} The fractional standard deviation of the *λ* estimates is 0.096⤬ the median estimate.^{[9]}

** How would LC18’s results be impacted by adopting the internal variability implied by Dessler18?**One can easily work out the effect on the LC18 primary results of adopting the level of internal variability implied by the Dessler18 results. I calculate that when differences in Δ

*R*and Δ

*T*

_{S}and in the length of the base period used are allowed for, fractional standard deviations in

*λ*of 0.044 and 0.054 attributable to internal variability in respectively

*R*and

*T*

_{S}are implied.

^{[10]}This calculation uses a split, derived from the estimates of the model’s internal variability in Δ

*R*and in Δ

*T*

_{S, }of the Δ

*R*and Δ

*T*

_{S}contributions to the standard deviation in

*λ*.

I apply the calculated fractional standard deviations in *λ* of 0.044 and 0.054 attributable to internal variability in Δ*R* and Δ*T*_{S} to respectively the denominator and the numerator of the fraction {(*F*_{2⤬CO2} Δ*T*_{S}) / (Δ*F* − Δ*N*)} that is used to estimate ECS.^{[11]} To avoid double counting, I remove the allowances made in LC18 for internal variability in Δ*R* and Δ*T*_{S}.

The result is to change the 5–95% range for estimated ECS from 1.16–2.68 K on the original LC18 basis, to 1.19−2.65 K using internal variability corresponding to the Dessler18 results. The ECS estimate becomes slightly better constrained, not worse constrained.

It is arguable that the almost symmetrical uncertainty range for *λ* in Dessler18 implies that, because of the anticorrelation between Δ*T*_{S} and Δ*R,* almost all the variability in *λ* can be treated as arising from internal variability in its numerator variable, i.e. in Δ*R*. In that case, the fractional standard deviation of 0.096 in *λ* just needs to be scaled to allow for the higher Δ*R* value and longer base period used in LC18. The resulting fractional standard deviation in *λ* attributable to internal variability in Δ*R* is then 0.054,^{[12]} with none attributed to internal variability in Δ*T*_{S}.

I apply the 0.054 fractional standard deviation to the denominator of the ECS formula, again removing the allowances made in LC18 for internal variability in Δ*R* and Δ*T*_{S}. The result is to change the 5–95% range for estimated ECS, from 1.16–2.68 K on the original LC18 basis, to 1.20−2.64 K. Even if the calculated fractional standard deviation of 0.054 were increased by 50%, the 5–95% ECS range would still be narrower than when using the internal variability estimates adopted in LC18.

** Do Dessler18’s results have any implications for historical period energy-budget ECS estimates?**The short answer to this is no.

Andrew Dessler initially claimed that the LC18 energy budget methodology caused bias. Although, to be fair, he has since withdrawn this claim, he is still promulgating the idea that energy budget ECS estimates are biased low, writing:^{[13]}

I said several times that the Lewis and Curry method is biased, but I should’ve said it is imprecise. Our ACP paper shows that the method would give us an accurate estimate if we had 100 different realizations of the 20th century. However, The imprecision of the method means that with only one realization (the historical record), it is possible that you could get an answer that is far from true. Several other papers that have come out recently have also suggested that the pattern of warming that we experienced during the late 20th century causes energy balance estimates of ECS to be lower than the climate system’s true value.

One can quantify “far from true” based on the 100 MPI-ESM1.1 historical simulations analysed by Dessler18. Historical period energy budget ECS estimates are not limited to using 10-year averaging periods, which is what Dessler18 focuses on. Use of 20-year periods gives a better idea of how much internal variability influences energy budget ECS estimates. Dessler18 quotes a 5–95% range of 0.48 Wm^{−2} for *λ* estimated using 20-year averages. The 95th and 99th percentiles of the 100 *λ* estimates involved are respectively 0.15 Wm^{−2} and 0.18 Wm^{−2} above the median estimate, while the very highest is 0.22 Wm^{−2} above the median. Even if the LC18 *λ* median estimates of 2.25–2.3 Wm^{−2} (using globally-complete temperature data) were biased high by 0.22 Wm^{−2} due to a one-in-a-hundred realisation of internal variability, the low bias in the resulting ECS estimate would not exceed 10% – a minor amount compared to other uncertainties.

Andrew Dessler also refers to other papers suggesting that the pattern of warming that we experienced during the late 20th century causes energy balance estimates of ECS to be lower than the climate system’s true value. Even if that pattern could cause energy budget ECS estimates based just on data covering the late 20th century to be biased low, it would not follow that energy budget ECS estimates based on changes over the full historical period are also biased low. The warming pattern effect is addressed at considerable length in LC18, and evidence presented that it did not bias energy budget ECS estimates based on the full historical period.

For completeness, I will also clarify another potential bias that is often mentioned. Historical period energy-budget ECS estimates reflect climate feedbacks operating over the historical period: they estimate ‘ECS_{hist}‘. In most global climate models (GCMs), estimates of their true ECS exceed ECS_{hist} estimates.^{[14]} For the extremely similar MPI-ESM1.2 model, its true ECS appears to be between 2.9 K and 3 K. That is about 8–10% higher than the median ECS_{hist} estimate of 2.73 K from the 100 MPI-ESM1.1 historical period runs. That excess is in line with the median excess of 9.5% for current generation GCMs derived in LC18 and slightly lower than one might expect given the time-profile of MPI-ESM1-2’s response to an abrupt doubling of CO_{2} concentration.^{[15]} Whether ECS exceeds ECS_{hist} in the real climate system is unknown. LC18 provides an alternative ECS estimate that allows for it doing so, based on the ECS – ECS_{hist} relationships in current GCMs.

** Conclusions**I have shown to be incorrect the Dessler18 claim that the central hypothesis in the energy budget framework – that global average surface temperature anomalies are indicative of anomalies in outgoing energy – “is not well supported over the historical temperature record in the model ensemble”.

Importantly, the uncertainty that Dessler18 focuses on barely affects the total uncertainty of primarily observationally-based ^{[16]} energy-budget ECS estimates derived from estimated changes in Δ*T*_{S}, Δ*N* and Δ*F* over the period since 1850, which is dominated by forcing uncertainty. Using the same data as for the LC18 primary estimate but with the influence of internal variability removed, the fractional standard deviation in 1/ECS is 0.22.^{[17]} Adding uncertainty attributable to internal variability, in line with that in MPI-ESM1.1, would only increase the total fractional standard deviation to 0.23.^{[18]} So, eliminating the uncertainty that Dessler18 makes a big issue about would hardly reduce the total uncertainty in current observationally-based energy balance climate sensitivity estimates.

** Other issues raised in Dessler18**Dessler18 also asserts that “If

*T*

_{S}is a good proxy for the response

*R*–

*F*, we would expect to also see a correlation in measurements dominated by interannual variations. Observational data allow us to test this hypothesis. … These [CERES EBAF] data show that Δ

*R*is poorly correlated with Δ

*T*

_{s}in response to interannual variability (Fig. 3a), as has been noted many times in the literature.”

Dessler18 Fig. 3a actually plots *monthly* mean data and hence includes *intermonthly* variability. Nevertheless, it does show a correlation, of the expected sign. One would not expect a high correlation, because a fair amount of the shorter term variability in *R* [*N*] is caused by random fluctuations in clouds. Such fluctuations in *R* cause *T*_{S} to move in the opposite direction to that if the change in *R* had been driven by a fluctuation in *T*_{S}. It is well known that this problem confounds the estimation from shorter term data of the energy-balance based relationship of *R* and *T*_{S}.^{[19]} The problem is of limited relevance to energy balance ECS estimation, which uses multidecadal or centennial changes.

I shall make only a brief comment here on the Dessler18 proposal of replacing global surface temperature with tropical mid-tropospheric (500 hPa pressure) temperature, as being a better determinant of changes in outgoing energy. It appears to eliminate a minor source of uncertainty at the expense of introducing worse problems. Indeed, the authors admit, in the second paper,^{[20]} that a key ratio they uses to convert 500-hPa tropical temperature interannual feedback strength into long term forced-response feedback strength “comes from climate model simulations; we have no way to observationally validate it, nor any theory to guide us”.

** Nic Lewis ** April 2018

[1] Dessler, A. E., T. Mauritsen, B. Stevens, 2018. The influence of internal variability on Earth’s energy balance framework and implications for estimating climate sensitivity. *Atmos. Chem. Phys.* https://doi.org/10.5194/acp-2017-1236-RC1, 2018. I thank the authors for having publicly archived the related data and code.

[2] 1 K = 1 °C

[3] Lewis, N. ,and J. Curry, 2018: The impact of recent forcing and ocean heat uptake data on estimates of climate sensitivity. *J. Clim.* JCLI-D-17-0667 A copy of the final submitted manuscript, reformatted for easier reading, is available at my personal webpages, here. The Supporting Information is available here.

[4] https:/twitter.com/AndrewDessler/status/988898450107457536

[5] In Dessler18 *R* is used to denote the top-of-atmosphere radiative imbalance (downwards net radiation, both longwave and shortwave) rather than the usual symbol *N*, used here. *R* normally denotes the change in TOA radiative imbalance resulting from a change in surface temperature, so that (when measured downwards) Δ*R* = (Δ*F* − Δ*N*). I use that notation here, but with *R* measured upwards. Note that as uncertainty in model-simulation Δ*F* is ignored, the standard deviation in estimated Δ*R* equals that in Δ*N*.

[6] Using an ensemble of three runs with time-varying forcing but fixed preindustrial sea-surface temperatures (SST).

[7] Derived from fixed SST simulations in which CO2 increases at 1% p.a.

[8] The distribution appears to be close to normal. Its mean is almost identical to the median of 1.43, and the 5–95% range of 0.46 is 3.4⤬ its estimated standard deviation of 0.137, close to the 3.29⤬ for a normal distribution.

[9] By comparison, the standard deviation of decadal mean *T*_{S} in the MPI-ESM1.1 piControl run is 0.061 K, which is 7% of the 1850-1860 to 1996-2005 median historical simulation Δ*T*_{S} of 0.87 K. Adding the base and final period uncertainty in quadrature implies a fractional standard deviation for Δ*T*_{S} of 0.10. The corresponding absolute standard deviation for decadal mean *N* is 0.076 Wm^{−2}. Since uncertainty in Δ*F* derived from fixed SST simulations is very small (and was ignored), the standard deviation of decadal mean Δ*R* = (Δ*F* − Δ*N*) is the same. The fractional standard deviation of Δ*R* is accordingly 6.2% of the 1850-1860 to 1996-2005 mean historical (Δ*F* − Δ*N*) of 1.23 Wm^{−2}. Adding the base and final period uncertainty in quadrature implies a fractional standard deviation for Δ*N* of 0.087. Anti-correlation of −0.47 between decadal mean Δ*N* and Δ*T* _{S}, which is expected from the response of *R* to Δ*T*_{S}, explains why the 0.096 fractional standard deviation in estimates of *λ* from the MPI-ESM1.1 historical simulations is much less than the sum in quadrature of the estimated fractional standard deviations of Δ*T*_{S} and Δ*R* based on piControl run variability, being 0.133.

[10] The LC18 base period is longer than in Dessler18; 14 rather than 10 years, so the inter-period variability should be approximately 7% lower, for both Δ*R* and Δ*T*_{S}, reducing the fractional standard deviation in *λ* estimates to 0.089.The contribution from internal variability in Δ*T*_{S} appears to be slightly lower than that from Δ*N*; attributing 57% and 43% of the scaled 0.089 fractional standard deviation in *λ*, or 0.051 and 0.038, to respectively Δ*R* and Δ*T*_{S} appears reasonable. I then multiply these by 1.4 to allow for their effects adding in quadrature, increasing them to 0.071 and 0.054 respectively. The median Δ*R* for the MPI-ESM1.1 historical simulations is 1.23 Wm^{−2}, 0.61⤬ the 2.02 Wm^{−2} for the main LC18 estimate. The fractional standard deviation in *λ* estimates of 0.071 attributable to internal variability in *R* therefore scales down to 0.044. Median warming between the first and last decades of the MPI-ESM1.1 historical period runs is 0.87 K, almost identical to the globally-complete observational data warming in the primary LC18 case (0.88 K), so no adjustment is made to the 0.054 fractional standard deviation attributable to internal variability in Δ*T*_{S}.

[11] I do so by drawing one million samples from each of two normal distributions, each having a mean of one, with standard deviations of 0.054 and 0.044, and multiplying the one million sampled LC18 ECS estimates by the ratios of the first set of samples from a normal distribution to the second set.

[12] The calculation is 0.096 * (1 − 0.07) * (1.23/2.02) = 0.054. See endnote 10.

[13] https://andthentheresphysics.wordpress.com/2018/04/27/lewis-and-curry-again/#comment-117464

[14] The estimates of ‘true’ ECS in GCMs are typically derived from the *x*-intercept when by regressing Δ*R* against Δ*T*s over years 21–150 following a simulated abrupt quadrupling of the preindustrial CO_{2} concentration. Since historical period forcing is not known in most GCMs, the estimates of ECS_{hist} are usually based on data providing similar information to that available from the historical period.

[15] Interestingly, the 2.73 K historical period ECS estimate appears to be biased low, as a result of diagnosed forcing in 1850 and 1851 being anomalously low. Using 20-year rather than 10-year averaging periods at the start and end of the historical period produces a median ECS estimate of 3.0 K, although that is probably biased high by the response to the 1991 Mount Pinatubo volcanic eruption. When periods that avoid both 1850–51 and volcanic years are used, the median ECS estimate is slightly over 2.9 K, surprisingly close to MPI-ESM1.2’s estimated true ECS. Possibly MPI-ESM1.1 has a slightly higher ECS than does MPI-ESM1.2.

[16] GCMs are used in deriving components of Δ*F* and the (small) initial value of *N*, but in the main with a strong input from observations.

[17] Uncertainty in 1/ECS rather than in ECS is given since 1/ECS is proportional to *λ* (save for uncertainty in *F*_{2}_{⤬}_{CO2}), and estimates of 1/ECS have a close to normal uncertainty distribution, unlike for ECS.

[18] Since the uncertainty attributable to internal variability is independent of other uncertainties, their standard deviations add in quadrature. Adding the allowance for internal variability in Δ*R* and Δ*T*_{S} included in the main LC18 ECS estimates would have a larger, but still small, effect.

[19] Spencer, R. W., W. D. Braswell, 2010. On the diagnosis of radiative feedback in the presence of unknown radiative forcing. *J. Geophysical Research*: Atmospheres, 115(D16).

Choi, Yong-Sang, et al., 2014: Influence of non-feedback variations of radiation on the determination of climate feedback. *Theoretical and applied climatology* 115.1-2 (2014): 355-364.

[20] Dessler, A.E., P.M. Forster, 2018. An estimate of equilibrium climate sensitivity from interannual variability. Preprint of submitted manuscript.

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