climateetc--2020-08-25--New confirmation that climate models overstate atmospheric warming

Two new peer-reviewed papers from independent teams confirm that climate models overstate atmospheric warming and the problem has gotten worse over time , not better .
The papers are Mitchell et al .
( 2020 ) “ The vertical profile of recent tropical temperature trends : Persistent model biases in the context of internal variability ” Environmental Research Letters , and McKitrick and Christy ( 2020 ) “ Pervasive warming bias in CMIP6 tropospheric layers ” Earth and Space Science .
John and I didn ’ t know about the Mitchell team ’ s work until after their paper came @ @ @ @ @ @ @ t know about ours .
Mitchell et al .
look at the surface , troposphere and stratosphere over the tropics ( 20N to 20S ) .
John and I look at the tropical and global lower- and mid- troposphere .
Both papers test large samples of the latest generation ( “ Coupled Model Intercomparison Project version 6 ” or CMIP6 ) climate models , i.e .
the ones being used for the next IPCC report , and compare model outputs to post-1979 observations .
John and I were able to examine 38 models @ @ @ @ @ @ @ 48 models .
The sheer number makes one wonder why so many are needed , if the science is settled .
Both papers looked at “ hindcasts , ” which are reconstructions of recent historical temperatures in response to observed greenhouse gas emissions and other changes ( e.g .
aerosols and solar forcing ) .
Across the two papers it emerges that the models overshoot historical warming from the near-surface through the upper troposphere , in the tropics and globally .
Mitchell et al .
had , in an earlier study , examined @ @ @ @ @ @ @ amplify surface warming too much as you go up in altitude , or whether they get the vertical amplification right but start with too much surface warming .
The short answer is both .
In this Figure the box/whiskers are model-predicted warming trends in the tropics ( 20S to 20N ) ( horizontal axis ) versus altitude ( vertical axis ) .
Where the trend magnitudes cross the zero line is about where the stratosphere begins .
Red= models that internally simulate both ocean and atmosphere .
Blue : models that take observed @ @ @ @ @ @ @ simulate the air temperature trends .
Black lines : observed trends .
The blue boxes are still high compared to the observations , especially in the 100-200hPa level ( upper-mid troposphere ) .
Overall their findings are : • “ we find considerable warming biases in the CMIP6 modeled trends , and we show that these biases are linked to biases in surface temperature ( these models simulate an unrealistically large global warming ) .
” • “ we note here for the record that from 1998 to 2014 , the CMIP5 models @ @ @ @ @ @ @ times faster than the observations , and in one model the warming is 10 times larger than the observations.
” • “ Throughout the depth of the troposphere , not a single model realization overlaps all the observational estimates .
However , there is some overlap between the RICH observations and the lowermost modelled trend , which corresponds to the NorCPM1 model.
” • “ Focusing on the CMIP6 models , we have confirmed the original findings of Mitchell et al .
( 2013 ) : first , the modeled tropospheric trends are @ @ @ @ @ @ @ notably in the upper troposphere , around 200 hPa ) and , second , that these biases can be linked to biases in surface warming .
As such , we see no improvement between the CMIP5 and the CMIP6 models.
” ( Mitchell et al .
2020 ) A special prize goes to the Canadian model !
“ We draw attention to the CanESM5 model : it simulates the greatest warming in the troposphere , roughly 7 times larger than the observed trends.
” The Canadian government relies on the CanESM models “ @ @ @ @ @ @ @ climate change adaptation and mitigation in Canada and internationally.
” I would be very surprised if the modelers at UVic ever put warning labels on their briefings to policy makers .
The sticker should read : “ WARNING !
This model predicts atmospheric warming roughly 7 times larger than observed trends .
Use of this model for anything other than entertainment purposes is not recommended.
” Although the above diagram looks encouraging in the stratosphere , Mitchell et al .
found the models get it wrong too .
They predict too little cooling @ @ @ @ @ @ @ and the effects cancel in a linear trend .
The vertical “ fingerprint ” of GHG in models is warming in the troposphere and cooling in the stratosphere .
Models predict steady stratospheric cooling should have continued after late 1990s but observations show no such cooling this century .
The authors suggest the problem is models are not handling ozone depletion effects correctly .
The above diagram focuses on the 1998-2014 span .
Compare the red box/whiskers to the black lines .
The red lines are climate model outputs after feeding in observed @ @ @ @ @ @ @ .
The predicted trends don ’ t match the observed trend profile ( black line ) – there ’ s basically no overlap at all .
They warm too much in the troposphere and cool too much in the stratosphere .
Forcing models to use prescribed sea surface temperatures ( blue ) , which in effect hands the “ right ” answer to the model for most of the surface area , mitigates the problem in the troposphere but not the stratosphere .
John Christy and I had earlier compared models to observations @ @ @ @ @ @ @ of a warming bias in all models .
This is one of several papers I ’ ve done on tropical tropospheric warm biases .
The IPCC cites my work ( and others ’ ) and accepts the findings .
Our new paper shows that , rather than the problem being diminished in the newest models , it is getting worse .
The bias is observable in the lower- and mid-troposphere in the tropics but also globally .
We examined the first 38 models in the CMIP6 ensemble .
Like Mitchell et al .
@ @ @ @ @ @ @ each model .
Here are the 1979-2014 warming trend coefficients ( vertical axis , degrees per decade ) and 95 % error bars comparing models ( red ) to observations ( blue ) .
LT=lower troposphere , MT=mid-troposphere .
Every model overshoots the observed trend ( horizontal dashed blue line ) in every sample .
Most of the differences are significant at < 5 % , and the model mean ( thick red ) versus observed mean difference is very significant , meaning it ’ s not just noise or randomness .
The @ @ @ @ @ @ @ throughout the global atmosphere , even over an interval where modelers can observe both forcings and temperatures .
We used 1979-2014 ( as did Mitchell et al . )
because that ’ s the maximum interval for which all models were run with historically-observed forcings and all observation systems are available .
Our results would be the same if we use 1979-2018 , which includes scenario forcings in final years .
( Mitchell et al .
report the same thing . )
John and I found that models with higher Equilibrium Climate Sensitivity @ @ @ @ @ @ @ not surprisingly ) , but even the low-ECS group ( < 3.4K ) exhibits warming bias .
In the low group the mean ECS is 2.7K , the combined LT/MT model warming trend average is 0.21K/decade and the observed counterpart is 0.15K/decade .
This figure ( green circle added ; see below ) shows a more detailed comparison .
The horizontal axis shows the model warming trend and the vertical axis shows the corresponding model ECS .
The red squares are in the high ECS group and the blue circles are in the @ @ @ @ @ @ @ from the LT layer and open shapes are from the MT layer .
The crosses indicate the means of the four groups and the lines connect LT ( solid ) and MT ( dashed ) layers .
The arrows point to the mean observed MT ( open arrow , 0.09C/decade ) and LT ( closed arrow , 0.15 C/decade ) trends .
While the models in the blue cluster ( low ECS ) do a better job , they still have warming rates in excess of observations .
If we were to picture @ @ @ @ @ @ @ global tropospheric warming rates overlapping observations it would have to be positioned roughly in the area I ’ ve outlined in green .
The associated ECS would be between 1.0 and 2.0K .
I get it that modeling the climate is incredibly difficult , and no one faults the scientific community for finding it a tough problem to solve .
But we are all living with the consequences of climate modelers stubbornly using generation after generation of models that exhibit too much surface and tropospheric warming , in addition to running grossly exaggerated @ @ @ @ @ @ @ .
Back in 2005 in the first report of the then-new US Climate Change Science Program , Karl et al .
pointed to the exaggerated warming in the tropical troposphere as a “ potentially serious inconsistency.
” But rather than fixing it since then , modelers have made it worse .
Mitchell et al .
note that in addition to the wrong warming trends themselves , the biases have broader implications because “ atmospheric circulation trends depend on latitudinal temperature gradients.
” In other words when the models get the tropical troposphere wrong @ @ @ @ @ @ @ other features of the model atmosphere .
Even if the original problem was confined to excess warming in the tropical mid-troposphere , it has now expanded into a more pervasive warm bias throughout the global troposphere .
If the discrepancies in the troposphere were evenly split across models between excess warming and cooling we could chalk it up to noise and uncertainty .
But that is not the case : it ’ s all excess warming .
CMIP5 models warmed too much over the sea surface and too much in the tropical troposphere @ @ @ @ @ @ @ much throughout the global lower- and mid-troposphere .
That ’ s bias , not uncertainty , and until the modeling community finds a way to fix it , the economics and policy making communities are justified in assuming future warming projections are overstated , potentially by a great deal depending on the model .
Karl , T. R. , S. J. Hassol , C. D. Miller , and W. L. Murray ( 2006 ) .
Temperature Trends in the Lower Atmosphere : Steps for Understanding and Reconciling Differences .
Synthesis and Assessment Product @ @ @ @ @ @ @ Subcommittee on Global Change Research McKitrick and Christy ( 2020 ) “ Pervasive warming bias in CMIP6 tropospheric layers ” Earth and Space Science .
Mitchell et al .
( 2020 ) “ The vertical profile of recent tropical temperature trends : Persistent model biases in the context of internal variability ” Environmental Research Letters .

by Ross McKitrick
Two new peer-reviewed papers from independent teams confirm that climate models overstate atmospheric warming and the problem has gotten worse over time, not better.
The papers are Mitchell et al. (2020) “The vertical profile of recent tropical temperature trends: Persistent model biases in the context of internal variability” Environmental Research Letters, and McKitrick and Christy (2020) “Pervasive warming bias in CMIP6 tropospheric layers” Earth and Space Science. John and I didn’t know about the Mitchell team’s work until after their paper came out, and they likewise didn’t know about ours.
Mitchell et al. look at the surface, troposphere and stratosphere over the tropics (20N to 20S). John and I look at the tropical and global lower- and mid- troposphere. Both papers test large samples of the latest generation (“Coupled Model Intercomparison Project version 6” or CMIP6) climate models, i.e. the ones being used for the next IPCC report, and compare model outputs to post-1979 observations. John and I were able to examine 38 models while Mitchell et al. looked at 48 models. The sheer number makes one wonder why so many are needed, if the science is settled. Both papers looked at “hindcasts,” which are reconstructions of recent historical temperatures in response to observed greenhouse gas emissions and other changes (e.g. aerosols and solar forcing). Across the two papers it emerges that the models overshoot historical warming from the near-surface through the upper troposphere, in the tropics and globally.
Mitchell et al. 2020
Mitchell et al. had, in an earlier study, examined whether the problem is that the models amplify surface warming too much as you go up in altitude, or whether they get the vertical amplification right but start with too much surface warming. The short answer is both.
In this Figure the box/whiskers are model-predicted warming trends in the tropics (20S to 20N) (horizontal axis) versus altitude (vertical axis). Where the trend magnitudes cross the zero line is about where the stratosphere begins. Red= models that internally simulate both ocean and atmosphere. Blue: models that take observed sea surface warming as given and only simulate the air temperature trends. Black lines: observed trends. The blue boxes are still high compared to the observations, especially in the 100-200hPa level (upper-mid troposphere).
Overall their findings are:
“we find considerable warming biases in the CMIP6 modeled trends, and we show that these biases are linked to biases in surface temperature (these models simulate an unrealistically large global warming).”
“we note here for the record that from 1998 to 2014, the CMIP5 models warm, on average 4 to 5 times faster than the observations, and in one model the warming is 10 times larger than the observations.”
“Throughout the depth of the troposphere, not a single model realization overlaps all the observational estimates. However, there is some overlap between the RICH observations and the lowermost modelled trend, which corresponds to the NorCPM1 model.”
“Focusing on the CMIP6 models, we have confirmed the original findings of Mitchell et al. (2013): first, the modeled tropospheric trends are biased warm throughout the troposphere (and notably in the upper troposphere, around 200 hPa) and, second, that these biases can be linked to biases in surface warming. As such, we see no improvement between the CMIP5 and the CMIP6 models.” (Mitchell et al. 2020)
A special prize goes to the Canadian model! “We draw attention to the CanESM5 model: it simulates the greatest warming in the troposphere, roughly 7 times larger than the observed trends.” The Canadian government relies on the CanESM models “to provide science-based quantitative information to inform climate change adaptation and mitigation in Canada and internationally.” I would be very surprised if the modelers at UVic ever put warning labels on their briefings to policy makers. The sticker should read: “WARNING! This model predicts atmospheric warming roughly 7 times larger than observed trends. Use of this model for anything other than entertainment purposes is not recommended.”
Although the above diagram looks encouraging in the stratosphere, Mitchell et al. found the models get it wrong too. They predict too little cooling before 1998 and too much after, and the effects cancel in a linear trend. The vertical “fingerprint” of GHG in models is warming in the troposphere and cooling in the stratosphere. Models predict steady stratospheric cooling should have continued after late 1990s but observations show no such cooling this century. The authors suggest the problem is models are not handling ozone depletion effects correctly.
The above diagram focuses on the 1998-2014 span. Compare the red box/whiskers to the black lines. The red lines are climate model outputs after feeding in observed GHG and other forcings over this interval. The predicted trends don’t match the observed trend profile (black line) – there’s basically no overlap at all. They warm too much in the troposphere and cool too much in the stratosphere. Forcing models to use prescribed sea surface temperatures (blue), which in effect hands the “right” answer to the model for most of the surface area, mitigates the problem in the troposphere but not the stratosphere.
McKitrick and Christy 2020
John Christy and I had earlier compared models to observations in the tropical mid-troposphere, finding evidence of a warming bias in all models. This is one of several papers I’ve done on tropical tropospheric warm biases. The IPCC cites my work (and others’) and accepts the findings. Our new paper shows that, rather than the problem being diminished in the newest models, it is getting worse. The bias is observable in the lower- and mid-troposphere in the tropics but also globally.
We examined the first 38 models in the CMIP6 ensemble. Like Mitchell et al. we used the first archived run from each model. Here are the 1979-2014 warming trend coefficients (vertical axis, degrees per decade) and 95% error bars comparing models (red) to observations (blue). LT=lower troposphere, MT=mid-troposphere. Every model overshoots the observed trend (horizontal dashed blue line) in every sample.
Most of the differences are significant at <5%, and the model mean (thick red) versus observed mean difference is very significant, meaning it’s not just noise or randomness. The models as a group warm too much throughout the global atmosphere, even over an interval where modelers can observe both forcings and temperatures.
We used 1979-2014 (as did Mitchell et al. ) because that’s the maximum interval for which all models were run with historically-observed forcings and all observation systems are available. Our results would be the same if we use 1979-2018, which includes scenario forcings in final years. (Mitchell et al. report the same thing.)
John and I found that models with higher Equilibrium Climate Sensitivity (>3.4K) warm faster (not surprisingly), but even the low-ECS group (<3.4K) exhibits warming bias. In the low group the mean ECS is 2.7K, the combined LT/MT model warming trend average is 0.21K/decade and the observed counterpart is 0.15K/decade. This figure (green circle added; see below) shows a more detailed comparison.
The horizontal axis shows the model warming trend and the vertical axis shows the corresponding model ECS. The red squares are in the high ECS group and the blue circles are in the low ECS group. Filled shapes are from the LT layer and open shapes are from the MT layer. The crosses indicate the means of the four groups and the lines connect LT (solid) and MT (dashed) layers. The arrows point to the mean observed MT (open arrow, 0.09C/decade) and LT (closed arrow, 0.15 C/decade) trends.
While the models in the blue cluster (low ECS) do a better job, they still have warming rates in excess of observations. If we were to picture a third cluster of models with mean global tropospheric warming rates overlapping observations it would have to be positioned roughly in the area I’ve outlined in green. The associated ECS would be between 1.0 and 2.0K.
Concluding remarks
I get it that modeling the climate is incredibly difficult, and no one faults the scientific community for finding it a tough problem to solve. But we are all living with the consequences of climate modelers stubbornly using generation after generation of models that exhibit too much surface and tropospheric warming, in addition to running grossly exaggerated forcing scenarios (e.g. RCP8.5). Back in 2005 in the first report of the then-new US Climate Change Science Program, Karl et al. pointed to the exaggerated warming in the tropical troposphere as a “potentially serious inconsistency.” But rather than fixing it since then, modelers have made it worse. Mitchell et al. note that in addition to the wrong warming trends themselves, the biases have broader implications because “atmospheric circulation trends depend on latitudinal temperature gradients.” In other words when the models get the tropical troposphere wrong, it drives potential errors in many other features of the model atmosphere. Even if the original problem was confined to excess warming in the tropical mid-troposphere, it has now expanded into a more pervasive warm bias throughout the global troposphere.
If the discrepancies in the troposphere were evenly split across models between excess warming and cooling we could chalk it up to noise and uncertainty. But that is not the case: it’s all excess warming. CMIP5 models warmed too much over the sea surface and too much in the tropical troposphere. Now the CMIP6 models warm too much throughout the global lower- and mid-troposphere. That’s bias, not uncertainty, and until the modeling community finds a way to fix it, the economics and policy making communities are justified in assuming future warming projections are overstated, potentially by a great deal depending on the model.
References:
Karl, T. R., S. J. Hassol, C. D. Miller, and W. L. Murray (2006). Temperature Trends in the Lower Atmosphere: Steps for Understanding and Reconciling Differences. Synthesis and Assessment Product. Climate Change Science Program and the Subcommittee on Global Change Research
McKitrick and Christy (2020) “Pervasive warming bias in CMIP6 tropospheric layers” Earth and Space Science.
Mitchell et al. (2020) “The vertical profile of recent tropical temperature trends: Persistent model biases in the context of internal variability” Environmental Research Letters.
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climateetc--2020-08-24--New paper suggests historical period estimates of climate sensitivity are not biased low by unusual

New paper suggests historical period estimates of climate sensitivity are not biased low by unusual variability in sea surface temperature patterns

An important new paper by Thorsten Mauritsen , Associate Professor at Stockholm University [ i ] and myself has just been accepted for publication ( Lewis and Mauritsen 2020 ) [ ii ] .
Its abstract reads : Recently it has been suggested that natural variability in sea surface temperature ( SST ) patterns over the historical period causes a low bias in estimates of climate sensitivity based on instrumental records , in addition to that suggested by time-variation of the climate feedback parameter in atmospheric general circulation models ( GCMs ) coupled to dynamic oceans .
This excess , @ @ @ @ @ @ @ ( the effect of evolving surface temperature patterns on climate feedback strength ) has been found in simulations performed using GCMs driven by AMIPII SST and sea ice changes ( amipPiForcing ) .
Here we show in both amipPiForcing experiments with one GCM and through using Green ’ s functions derived from another GCM , that whether such an unforced historical pattern effect is found depends on the underlying SST dataset used .
When replacing the usual AMIPII SSTs with those from the HadISST1 dataset in amipPiForcing experiments , with sea ice changes @ @ @ @ @ @ @ effects that are indistinguishable from the forced pattern effect of the corresponding coupled GCM .
Diagnosis of pattern effects using Green ’ s functions derived from the second GCM supports this result for five out of six non-AMIPII SST reconstruction datasets .
Moreover , internal variability in coupled GCMs is rarely sufficient to account for an unforced historical pattern effect of even one-quarter the strength previously reported .
The presented evidence indicates that , if unforced pattern effects have been as small over the historical record as our findings suggest , they are @ @ @ @ @ @ @ that are based on long-term instrumental observations and account for forced pattern effects obtained from GCMs .
In this article I explain in more detail what Lewis and Mauritsen ( 2020 ) is all about and what its main findings and conclusions are .
For a full picture , please read the paper , which is open-access ; it is available in a reformatted version here .
The back-story is concerns have been expressed that accounting for changing temperature patterns increases historical period energy budget based estimates of climate sensitivity .
[ iii @ @ @ @ @ @ @ This idea is now being used in assessments of climate sensitivity to increase significantly estimates based on historical period warming ( e.g.
, Sherwood et al .
2020 [ vi ] ) .
As I explained in a detailed 2018 article , [ vii ] the key paper making and quantifying this effect ( Andrews et al 2018 ) was based on simulations driven by an observationally-based estimate of the evolution of SST and sea-ice over the historical period ( amipPiForcing experiments , over 1871–2010 ) , that showed , in six models @ @ @ @ @ @ @ , here λ ) on average to be substantially greater , and hence their effective climate sensitivity ( EffCS [ viii ] , here EffCS ) , substantially lower , than when responding to long-term CO forcing .
Only a relatively small part of the differences reported in Andrews et al .
( 2018 ) can be attributed to effective climate sensitivity to CO forcing increasing over time in most atmosphere-ocean global climate models ( AOGCMs ) .
Based on typical CMIP5 AOGCM behaviour , that factor , which is allowed for in @ @ @ @ @ @ @ , such as Lewis and Curry ( 2018 ) [ ix ] , would only account for approximately 5 % out of the 40 % shortfall in effective climate sensitivity that Andrews et al .
found , [ x ] with a further 7 % due to their use of mismatching CO forcing values.7 This implies that the bulk of the average difference they found was instead attributable to unforced ( internal ) climate variability having affected SST patterns – a ( positive ) unforced historical pattern effect .
Although I put forward @ @ @ @ @ @ @ 2018 and in my 2018 article , against claims of such an effect having occurred , such claims have become widely accepted by climate scientists .
There are other possible explanations for the differences reported in Andrews et al .
( 2018 ) .
One is that the AOGCMs ’ simulated long-term SST and sea-ice patterns , and the resulting radiative responses , are unrealistic .
Another is that the GCM radiative responses in amipPiForcing experiments are unrealistic .
In this article I shall put those questions aside .
A further possibility is @ @ @ @ @ @ @ system to the historical mixture of forcings differs significantly from that to pure CO with the same time-profile of evolving effective radiative forcing .
LC18 put forward evidence against that being the case .
Moreover , I produced evidence in a subsequent article that , in the two models for which radiative response in standard CMIP5 climate model historical experiment was accurately known , there was no evidence that the response to the mix of anthropogenic forcings differed from that to pure CO forcing .
[ xi ] I wrote in my 2018 @ @ @ @ @ @ @ of a dampening unforced historical pattern effect one would need – even assuming long-term SST and sea-ice patterns , and the radiative response to them , simulated by AOGCMs to be realistic – to establish : • that correctly-calculated EffCS estimates are adequately robust to choice of historical SST and sea-ice observational dataset ; • that the differences between climate feedback strength over the historical period in amipPiForcing simulations ( λ ) and when AOGCMs generate their own SST and sea-ice patterns in response to radiative forcing ( λ ) could feasibly be @ @ @ @ @ @ @ .
It is standard to use the AMIPII SST and sea-ice dataset [ xii ] to drive GCMs in amipPiForcing experiments .
The AMIPII sea-ice dataset is based closely on HadISST1 data throughout the historical period , with only minor modifications .
However , the AMIPII SST dataset is only based on HadISST1 data until late 1981 , after which it is based on OIv2 SST data [ xiii ] .
The OIv2 post-1980 SST dataset is based largely on the same in situ and satellite data as HadISST1 , but with different @ @ @ @ @ @ @ for reconstructing SSTs in areas lacking in situ observations .
Andrews et al .
( 2108 ) showed , in their Supporting Information , that EffCS estimates are not robust to choice of historical sea-ice observational dataset .
They found that climate feedback in amipPiForcing simulations by two UK Meteorological Office GCMs was much weaker – λ was smaller , and hence EffCS was higher [ xiv ] – when the HadISST2 rather than the AMIPII sea-ice dataset was used , in conjunction with HadISST2 SST data .
The difference was mainly due @ @ @ @ @ @ @ than in SST data , and was large enough to reverse the sign of the unforced historical pattern effect , making it negative .
[ xv ] While sea-ice variation is thus an important contributor to differences in climate feedback , we do not explore sensitivity to sea-ice dataset in Lewis and Mauritsen ( 2020 ) , caveating our results in that respect .
Instead we use consistent sea-ice data , enabling isolation of the influence of SST dataset on historical climate feedback .
Thorsten and I show in our paper that λ @ @ @ @ @ @ @ of historical SST dataset , and that when the widely used HadISST1 dataset is used in place of the AMIPII SST dataset – with unchanged AMIPII sea-ice data – λ and λ are indistinguishable : no unforced historical pattern effect is found with the models we used .
We also investigated the unforced historical pattern effect using five other SST datasets , finding a significant estimated effect only in one case .
[ xvi ] Although the Lewis and Mauritsen ( 2020 ) findings are based on simulations by only two GCMs , @ @ @ @ @ @ @ “ Green ’ s functions ” ) for CAM5.3 , [ xvii ] they are consistent with historical warming in the Indo-Pacific warm pool , relative to that over the ice-free ocean as a whole , being much higher in the AMIPII than in the HadISST1 SST dataset .
[ xviii ] There is evidence , at least in CMIP5 models , that climate feedback strength is strongly positively related to relative warming in the Indo-Pacific warm pool .
[ xix ] On physical grounds , warming in tropical ascent regions , of @ @ @ @ @ @ @ warm pool , relative to elsewhere is expected to produce a strong increase in outgoing radiation at the top of atmosphere .
[ xx ] This effect , as estimated using the CAM5.3 Green ’ s functions , is illustrated in Figure 1 of our paper , reproduced below .
Figure 1 .
CAM5.3 Green ’ s functions : panels ( a ) and ( b ) show the change in respectively global mean Ts ( K ) and in global mean R ( Wm−2 ) per 1K increase in local grid-cell SST @ @ @ @ @ @ @ the global climate feedback parameter λ ( Wm−2K−1 ) for a change in local grid-cell SST ( the ratio of the values plotted in panel ( b ) to those plotted in panel ( a ) ) .
The Lewis and Mauritsen ( 2020 ) main results are set out in its Tables 1 and 2 , reproduced below : Table 1 .
Excess Indo-Pacific warm pool SST trends and climate feedback , in ECHAM6.3 amipPiForcing simulations and in MPI-ESM1.1 coupled 1pctCO2 and historical simulations .
All values are based on ensemble mean @ @ @ @ @ @ @ AMIPII and HadISST1 SST trends and standard deviations of individual run feedback estimates ) .
Feedback estimates are from OLS regression , of pentadal mean data for amipPiForcing simulations .
Values in brackets are standard errors of the OLS regression feedback estimates , which reflect underlying deviations from a linear relationship as well as internal variability .
Table 2 .
Excess Indo-Pacific warm pool SST trends and Green ’ s function derived estimates of climate feedback in CAM5.3 AMIPII-based amipPiForcing simulations , in CESM1-CAM5 coupled 1pctCO2 and historical/RCP8.5 simulations , and for warming @ @ @ @ @ @ @ with feedback estimated from the actual CAM5.3 AMIPII-based amipPiForcing simulation data .
Feedback estimates are from OLS regression of pentadal mean R and Ts values derived from the evolving SST warming patterns in the relevant simulation or observationally-based dataset .
Data over 1871-2010 , the amipPiForcing experiment period , is used , with data from the historical experiment extended using RCP8.5 experiment data , save in the 1pctCO2 simulation case where years 1–70 data is used .
It has been found in CMIP5 AOGCMs that on average approximately 60 % of the change @ @ @ @ @ @ @ simulations comes from the tropics ( 30°N–30°S ) , [ xxi ] due in particular to the west tropical Pacific warming significantly less than the east tropical Pacific , with the tropical pattern becoming more El Niño like as simulations progress .
However , the Green ’ s function feedback estimates for the seven observationally-based SST datasets are strongly correlated with warm pool SST trends relative to those over the tropics and mid-latitudes ( r=0.90 ) , but not relative to those over the tropics alone ( r=−0.10 ) ( Figure 2 ) @ @ @ @ @ @ @ Figure 4 of Lewis and Mauritsen ( 2020 ) .
The relationship between climate feedback strength , estimated using the CAM5.3 Green ’ s functions and pentadal regression , and the warming trend in the Indo-Pacific Warm Pool relative to that over either 30°S–30°N ( blue circles ) or 50°S–50°N ( red circles ) , both over 1871–2010 , for SST per seven observational datasets ( AMIPII , HadISST1 , HadISST2 , Had4_krig_v2 , HadSST4_krig_v2 , COBE-SST2 , ERSSTv5 ) .
The red line shows a linear fit between the warming trend in @ @ @ @ @ @ @ and estimated climate feedback strength ( r = 0.90 ) .
No equivalent fit is shown for the warming trend in the IPWP relative to that over 30°S–30°N , as the relationship is very weak ( r = −0.10 ) .
The Andrews et al .
( 2018 ) AMIPII-based λ values , which are based on regressing annual ensemble mean simulated values of outgoing radiation R on surface air temperature T , exceed our estimates on the same basis of the corresponding λ values for all six of the AGCMs involved .
@ @ @ @ @ @ @ effect in all cases when using the AMIPII dataset .
However , we found that regressing annual mean data , as is standard practice , non-negligibly biased λ estimates ( although not λ estimates ) in some cases .
We therefore used instead estimates from regressing pentadal mean data .
Using pentadal mean data substantially reduces noise in the regressor variable , which through regression dilution causes a downward bias in the slope coefficient , and also greatly diminishes the effect of responses to interannual fluctuations , thus providing more robust estimation .
@ @ @ @ @ @ @ our paper , the Andrews et al .
λ estimates are up to 9 % too strong relative to those based on pentadal mean data , due to responses to interannual fluctuations .
We show in our paper that , for the five GCMs featured in Andrews et al .
( 2018 ) for which the estimated AMIPII-based unforced historical pattern effect derived from regressing pentadal data was positive , unforced variability in preindustrial control run segments from 43 CMIP5 AOGCMs is in all but 0.06 % of cases inadequate to account for @ @ @ @ @ @ @ , in only 10 % of cases is such variability sufficient to capture unforced pattern effects of one-quarter their strength .
Of course , the realism of multidecadal internal variability in AOGCMs could be questioned .
However , we concluded that if internal variability in at least some CMIP5 AOGCMs is realistic , it seems highly probable that either the AMIPII SST dataset is flawed or at least part of the historical pattern effect detected when using AMIPII SST data is forced .
‘ In this study we have found no evidence for @ @ @ @ @ @ @ historical period , arising from internal variability , in the available sea surface temperature datasets , save for when the AMIPII and ERSSTv5 datasets are used .
Our results imply that the evidence suggesting existing constraints on EffCS from historical period energy budget considerations are biased low due to unusual internal variability in SST warming patterns is too weak to support such conclusion , and suggest that any such bias is likely to be small and of uncertain sign.
’ We also say : ‘ The various datasets try , in different ways @ @ @ @ @ @ @ observations from when they become available around 1980 .
The post-1981 AMIPII dataset interpolation method , however does so in a way that emphasizes small scale features at the expense of the large scale patterns central to the study of pattern effects ( Hurrell et al .
2008 ) .
Perhaps as a result , AMIPII warms more in the western tropical ocean basins and less in the eastern subsidence regions when compared to HadISST1 .
Earlier studies have in other contexts pointed to issues with the patterns of tropical warming in AMIPII @ @ @ @ @ @ @ results to what extent there is a robust relationship between stronger climate feedback and higher SST trends in the Indo-Pacific warm pool compared with elsewhere , at least where the comparison is limited to the tropics.
’ Originally posted here , where a pdf copy is also available [ i ] Meteorology Department .
Previously at the Max Planck Institute for Meteorology in Hamburg , where he worked closely with Bjorn Stevens .
[ ii ] Lewis , N. and Mauritsen , T. , 2020 : Negligible unforced historical pattern effect on climate @ @ @ @ @ @ @ .
Journal of Climate , 1-52 , https : //doi.org/10.1175/JCLI-D-19-0941.1 [ iii ] Gregory , J. M. , and T. Andrews , 2016 : Variation in climate sensitivity and feedback parameters during the historical period .
Geophys .
Res .
Lett.
, 43 , 3911 –3920 , https : //doi.org/10.1002/2016GL068406 [ iv ] Andrews T. et al.
, 2018 Accounting for changing temperature patterns increases historical estimates of climate sensitivity .
Geophys .
Res .
Lett .
https : //doi.org/10.1029/2018GL078887 [ v ] Gregory , J.M.
, Andrews , T. , Ceppi , @ @ @ @ @ @ @ , M.J. , 2019 .
How accurately can the climate sensitivity to CO₂ be estimated from historical climate change ?
Climate Dynamics .
https : //doi.org/10.1007/s00382-019-04991-y [ vi ] Sherwood , S. , et al .
“ An assessment of Earth ’ s climate sensitivity using multiple lines of evidence.
” Reviews of Geophysics ( 2020 ) : e2019RG000678 .
https : //doi.org/10.1029/2019RG000678 [ vii ] Warming patterns are unlikely to explain low historical estimates of climate sensitivity , 5 September 2018 .
[ viii ] Effective climate sensitivity ( EffCS ) is @ @ @ @ @ @ @ ECS ) derived by estimating climate feedback strength ( λ ) in a non-equilibrium situation and dividing it into an appropriately-derived estimate of the effective radiative forcing ( ERF ) from a doubling of preindustrial CO concentration .
In an AOGCM experiment involving a step increase in CO concentration , this equates to linearly projecting warming to the point where the Earth ’ s radiation balance has been fully restored , and then scaling it appropriately if the increase in CO was not a doubling .
[ ix ] Lewis , N. and @ @ @ @ @ @ @ of Recent Forcing and Ocean Heat Uptake Data on Estimates of Climate Sensitivity .
J .
Climate , 31 , 6051–6071 , https : //doi.org/10.1175/JCLI-D-17-0667.1 ; also Masters , T. , 2014 : Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models .
Climate Dyn.
, 42 , 2173 –2181 .
https : //doi.org/10.1007/s00382-013-1770-4 [ x ] Lewis and Curry ( 2018 ) estimated a 10 % difference when using long term EffCS estimates based on regression over years 21–150 of CMIP5 abrupt4xCO2 @ @ @ @ @ @ @ 5 % if instead basing them on regression over years 1–150 , the method used in Andrews et al .
( 2018 ) .
[ xi ] Gregory et al 2019 : Does climate feedback really vary in AOGCM historical simulations ?
31 October 2019 [ xii ] Hurrell , J.W.
, Hack , J.J. , Shea , D. , Caron , J.M .
and Rosinski , J. , 2008 : A new sea surface temperature and sea ice boundary dataset for the Community Atmosphere Model .
J .
Climate , 21 ( @ @ @ @ @ @ @ [ xiii ] Reynolds , R.W.
, Rayner , N.A.
, Smith , T.M.
, Stokes , D.C. and Wang , W. , 2002 .
An improved in situ and satellite SST analysis for climate .
Journal of climate , 15 ( 13 ) , pp.1609-1625 .
https : //doi.org/10.1175/1520-0442 ( 2002 ) 015 < 1609 : AIISAS > 2.0.CO ; 2 [ xiv ] Climate feedback strength λ is reciprocally related to EffCS .
Note that we use a positive sign convention for climate feedback , but Andrews et al .
( @ @ @ @ @ @ @ , so care is needed in interpreting their statements about it .
[ xv ] Using feedback estimated by regression over years 1-50 of the parent AOGCMs ’ abrupt4xCO2 simulations as a proxy for their forced historical feedback over 1871-2010 .
[ xvi ] We computed feedback using surface skin temperature ( Ts ) rather than near-surface air temperature ( T ) , for the reasons set out in our paper , save when working with data from Andrews et al .
( 2018 ) , who used T. [ xvii ] Through @ @ @ @ @ @ @ applying Green ’ s functions derived from multiple patch-warming simulations by CAM5.3 .
The Green ’ s function approach exploits the apparent linear superpositionality in space of GCM responses to warming .
Global changes in surface temperature Ts and outgoing radiation R resulting from imposed evolving historical SST patterns can thus easily be emulated by the sums of the global responses to SST changes in individual locations weighted by time-invariant Green ’ s function values for each location , and associated climate feedback estimates derived .
Sea-ice is held constant in the CAM5.3 @ @ @ @ @ @ @ the emulated values of both Ts and R. [ xviii ] We define the Indo-Pacific warm pool as the region 15°S–15°N , 45°E–195°E , and compare its warming trend with that for the ocean from 50°S–50°N as a whole , that area being essentially ice-free all year .
[ xix ] Dong , Y. , Proistosescu , C. , Armour , K.C .
and Battisti , D.S.
, 2019 : Attributing Historical and Future Evolution of Radiative Feedbacks to Regional Warming Patterns using a Green ’ s Function Approach : The Pre-eminence of @ @ @ @ @ @ @ , ( 2019 ) .
[ xx ] That is because surface temperature in convective areas controls temperature in the tropical free troposphere , which spatially is fairly uniform , and influences temperature in the extratropics .
An increase in free tropospheric temperature relative to surface temperature in descent regions strengthens the boundary layer temperature inversion , which is known to increase low cloud cover and hence reflected solar radiation .
[ xxi ] Andrews , T. , Gregory , J. M. , and Webb , M. J. , 2015 : The dependence @ @ @ @ @ @ @ patterns of surface temperature change in climate models .
J .
Climate , 28 ( 4 ) , 1630-1648. https : //doi.org/ 10.1175/JCLI-D-14-00545.1 [ xxii ] Using the ensemble mean from a number of amipPiForcing simulation runs data does not provide an adequate solution , because the noise in the SST data used to force the GCM is the same in all runs .

By Nic Lewis
An important new paper by Thorsten Mauritsen, Associate Professor at Stockholm University[i] and myself has just been accepted for publication (Lewis and Mauritsen 2020)[ii]. Its abstract reads:
Recently it has been suggested that natural variability in sea surface temperature (SST) patterns over the historical period causes a low bias in estimates of climate sensitivity based on instrumental records, in addition to that suggested by time-variation of the climate feedback parameter in atmospheric general circulation models (GCMs) coupled to dynamic oceans. This excess, unforced, historical “pattern effect” (the effect of evolving surface temperature patterns on climate feedback strength) has been found in simulations performed using GCMs driven by AMIPII SST and sea ice changes (amipPiForcing). Here we show in both amipPiForcing experiments with one GCM and through using Green’s functions derived from another GCM, that whether such an unforced historical pattern effect is found depends on the underlying SST dataset used. When replacing the usual AMIPII SSTs with those from the HadISST1 dataset in amipPiForcing experiments, with sea ice changes unaltered, the first GCM indicates pattern effects that are indistinguishable from the forced pattern effect of the corresponding coupled GCM. Diagnosis of pattern effects using Green’s functions derived from the second GCM supports this result for five out of six non-AMIPII SST reconstruction datasets. Moreover, internal variability in coupled GCMs is rarely sufficient to account for an unforced historical pattern effect of even one-quarter the strength previously reported. The presented evidence indicates that, if unforced pattern effects have been as small over the historical record as our findings suggest, they are unlikely to significantly bias climate sensitivity estimates that are based on long-term instrumental observations and account for forced pattern effects obtained from GCMs.
In this article I explain in more detail what Lewis and Mauritsen (2020) is all about and what its main findings and conclusions are. For a full picture, please read the paper, which is open-access; it is available in a reformatted version here.
Introduction
The back-story is concerns have been expressed that accounting for changing temperature patterns increases historical period energy budget based estimates of climate sensitivity.[iii] [iv] [v] This idea is now being used in assessments of climate sensitivity to increase significantly estimates based on historical period warming (e.g., Sherwood et al. 2020[vi]).
As I explained in a detailed 2018 article,[vii] the key paper making and quantifying this effect (Andrews et al 2018) was based on simulations driven by an observationally-based estimate of the evolution of SST and sea-ice over the historical period (amipPiForcing experiments, over 1871–2010), that showed, in six models, their climate feedback strength (λ, here λ amip ) on average to be substantially greater, and hence their effective climate sensitivity (EffCS[viii], here EffCS amip ), substantially lower, than when responding to long-term CO 2 forcing.
Only a relatively small part of the differences reported in Andrews et al. (2018) can be attributed to effective climate sensitivity to CO 2 forcing increasing over time in most atmosphere-ocean global climate models (AOGCMs). Based on typical CMIP5 AOGCM behaviour, that factor, which is allowed for in some historical period energy budget based estimates, such as Lewis and Curry (2018)[ix], would only account for approximately 5% out of the 40% shortfall in effective climate sensitivity that Andrews et al. found,[x] with a further 7% due to their use of mismatching CO 2 forcing values.7 This implies that the bulk of the average difference they found was instead attributable to unforced (internal) climate variability having affected SST patterns – a (positive) unforced historical pattern effect. Although I put forward arguments, both in Lewis and Curry 2018 and in my 2018 article, against claims of such an effect having occurred, such claims have become widely accepted by climate scientists.
There are other possible explanations for the differences reported in Andrews et al. (2018). One is that the AOGCMs’ simulated long-term SST and sea-ice patterns, and the resulting radiative responses, are unrealistic. Another is that the GCM radiative responses in amipPiForcing experiments are unrealistic. In this article I shall put those questions aside. A further possibility is that the forced response of the climate system to the historical mixture of forcings differs significantly from that to pure CO 2 with the same time-profile of evolving effective radiative forcing. LC18 put forward evidence against that being the case. Moreover, I produced evidence in a subsequent article that, in the two models for which radiative response in standard CMIP5 climate model historical experiment was accurately known, there was no evidence that the response to the mix of anthropogenic forcings differed from that to pure CO 2 forcing.[xi]
I wrote in my 2018 article that to justify the a existence of a dampening unforced historical pattern effect one would need – even assuming long-term SST and sea-ice patterns, and the radiative response to them, simulated by AOGCMs to be realistic – to establish:
that correctly-calculated EffCS amip estimates are adequately robust to choice of historical SST and sea-ice observational dataset;
. that the differences between climate feedback strength over the historical period in amipPiForcing simulations (λ amip ) and when AOGCMs generate their own SST and sea-ice patterns in response to radiative forcing (λ hist ) could feasibly be due to natural internal climate system variability.
It is standard to use the AMIPII SST and sea-ice dataset[xii] to drive GCMs in amipPiForcing experiments. The AMIPII sea-ice dataset is based closely on HadISST1 data throughout the historical period, with only minor modifications. However, the AMIPII SST dataset is only based on HadISST1 data until late 1981, after which it is based on OIv2 SST data[xiii]. The OIv2 post-1980 SST dataset is based largely on the same in situ and satellite data as HadISST1, but with different bias corrections and a different interpolation method for reconstructing SSTs in areas lacking in situ observations.
Andrews et al. (2108) showed, in their Supporting Information, that EffCS amip estimates are not robust to choice of historical sea-ice observational dataset. They found that climate feedback in amipPiForcing simulations by two UK Meteorological Office GCMs was much weaker – λ amip was smaller, and hence EffCS amip was higher[xiv] – when the HadISST2 rather than the AMIPII sea-ice dataset was used, in conjunction with HadISST2 SST data. The difference was mainly due to the change in sea-ice data rather than in SST data, and was large enough to reverse the sign of the unforced historical pattern effect, making it negative.[xv] While sea-ice variation is thus an important contributor to differences in climate feedback, we do not explore sensitivity to sea-ice dataset in Lewis and Mauritsen (2020), caveating our results in that respect. Instead we use consistent sea-ice data, enabling isolation of the influence of SST dataset on historical climate feedback.
Thorsten and I show in our paper that λ amip estimates are far from robust to choice of historical SST dataset, and that when the widely used HadISST1 dataset is used in place of the AMIPII SST dataset – with unchanged AMIPII sea-ice data – λ amip and λ hist are indistinguishable: no unforced historical pattern effect is found with the models we used. We also investigated the unforced historical pattern effect using five other SST datasets, finding a significant estimated effect only in one case.[xvi]
Although the Lewis and Mauritsen (2020) findings are based on simulations by only two GCMs, directly for ECHAM6.3 and indirectly (via “Green’s functions”) for CAM5.3,[xvii] they are consistent with historical warming in the Indo-Pacific warm pool, relative to that over the ice-free ocean as a whole, being much higher in the AMIPII than in the HadISST1 SST dataset.[xviii]
There is evidence, at least in CMIP5 models, that climate feedback strength is strongly positively related to relative warming in the Indo-Pacific warm pool.[xix] On physical grounds, warming in tropical ascent regions, of which the most important is the Indo-Pacific warm pool, relative to elsewhere is expected to produce a strong increase in outgoing radiation at the top of atmosphere.[xx] This effect, as estimated using the CAM5.3 Green’s functions, is illustrated in Figure 1 of our paper, reproduced below.
Figure 1. CAM5.3 Green’s functions: panels (a) and (b) show the change in respectively global mean Ts (K) and in global mean R (Wm−2) per 1K increase in local grid-cell SST, while panel (c) shows the global climate feedback parameter λ (Wm−2K−1) for a change in local grid-cell SST (the ratio of the values plotted in panel (b) to those plotted in panel (a)).
Our results
The Lewis and Mauritsen (2020) main results are set out in its Tables 1 and 2, reproduced below:
Table 1. Excess Indo-Pacific warm pool SST trends and climate feedback, in ECHAM6.3 amipPiForcing simulations and in MPI-ESM1.1 coupled 1pctCO2 and historical simulations. All values are based on ensemble mean Ts and R data (save for AMIPII and HadISST1 SST trends and standard deviations of individual run feedback estimates). Feedback estimates are from OLS regression, of pentadal mean data for amipPiForcing simulations. Values in brackets are standard errors of the OLS regression feedback estimates, which reflect underlying deviations from a linear relationship as well as internal variability.
Table 2. Excess Indo-Pacific warm pool SST trends and Green’s function derived estimates of climate feedback in CAM5.3 AMIPII-based amipPiForcing simulations, in CESM1-CAM5 coupled 1pctCO2 and historical/RCP8.5 simulations, and for warming in six observational SST datasets, along with feedback estimated from the actual CAM5.3 AMIPII-based amipPiForcing simulation data. Feedback estimates are from OLS regression of pentadal mean R and Ts values derived from the evolving SST warming patterns in the relevant simulation or observationally-based dataset. Data over 1871-2010, the amipPiForcing experiment period, is used, with data from the historical experiment extended using RCP8.5 experiment data, save in the 1pctCO2 simulation case where years 1–70 data is used.
It has been found in CMIP5 AOGCMs that on average approximately 60% of the change in feedback parameter over time during abrupt4×CO2 simulations comes from the tropics (30°N–30°S),[xxi] due in particular to the west tropical Pacific warming significantly less than the east tropical Pacific, with the tropical pattern becoming more El Niño like as simulations progress. However, the Green’s function feedback estimates for the seven observationally-based SST datasets are strongly correlated with warm pool SST trends relative to those over the tropics and mid-latitudes (r=0.90), but not relative to those over the tropics alone (r=−0.10) (Figure 2).
Figure 2: a reproduction of Figure 4 of Lewis and Mauritsen (2020). The relationship between climate feedback strength, estimated using the CAM5.3 Green’s functions and pentadal regression, and the warming trend in the Indo-Pacific Warm Pool relative to that over either 30°S–30°N (blue circles) or 50°S–50°N (red circles), both over 1871–2010, for SST per seven observational datasets (AMIPII, HadISST1, HadISST2, Had4_krig_v2, HadSST4_krig_v2, COBE-SST2, ERSSTv5). The red line shows a linear fit between the warming trend in the IPWP relative to that over 50°S–50°N and estimated climate feedback strength (r = 0.90). No equivalent fit is shown for the warming trend in the IPWP relative to that over 30°S–30°N, as the relationship is very weak (r = −0.10).
The Andrews et al. (2018) AMIPII-based λ amip values, which are based on regressing annual ensemble mean simulated values of outgoing radiation R on surface air temperature T, exceed our estimates on the same basis of the corresponding λ hist values for all six of the AGCMs involved. That implies a positive unforced historical pattern effect in all cases when using the AMIPII dataset. However, we found that regressing annual mean data, as is standard practice, non-negligibly biased λ amip estimates (although not λ hist estimates) in some cases. We therefore used instead estimates from regressing pentadal mean data. Using pentadal mean data substantially reduces noise in the regressor variable, which through regression dilution causes a downward bias in the slope coefficient, and also greatly diminishes the effect of responses to interannual fluctuations, thus providing more robust estimation.[xxii] As we show in our paper, the Andrews et al. λ amip estimates are up to 9% too strong relative to those based on pentadal mean data, due to responses to interannual fluctuations.
We show in our paper that, for the five GCMs featured in Andrews et al. (2018) for which the estimated AMIPII-based unforced historical pattern effect derived from regressing pentadal data was positive, unforced variability in preindustrial control run segments from 43 CMIP5 AOGCMs is in all but 0.06% of cases inadequate to account for that unforced historical pattern effect. Moreover, in only 10% of cases is such variability sufficient to capture unforced pattern effects of one-quarter their strength. Of course, the realism of multidecadal internal variability in AOGCMs could be questioned. However, we concluded that if internal variability in at least some CMIP5 AOGCMs is realistic, it seems highly probable that either the AMIPII SST dataset is flawed or at least part of the historical pattern effect detected when using AMIPII SST data is forced.
Conclusions
Our principle conclusion is:
‘In this study we have found no evidence for a substantial unforced pattern effect over the historical period, arising from internal variability, in the available sea surface temperature datasets, save for when the AMIPII and ERSSTv5 datasets are used. Our results imply that the evidence suggesting existing constraints on EffCS from historical period energy budget considerations are biased low due to unusual internal variability in SST warming patterns is too weak to support such conclusion, and suggest that any such bias is likely to be small and of uncertain sign.’
We also say:
‘The various datasets try, in different ways, to take advantage of the satellite observations from when they become available around 1980. The post-1981 AMIPII dataset interpolation method, however does so in a way that emphasizes small scale features at the expense of the large scale patterns central to the study of pattern effects (Hurrell et al. 2008). Perhaps as a result, AMIPII warms more in the western tropical ocean basins and less in the eastern subsidence regions when compared to HadISST1. Earlier studies have in other contexts pointed to issues with the patterns of tropical warming in AMIPII’
and
‘It is unclear from our results to what extent there is a robust relationship between stronger climate feedback and higher SST trends in the Indo-Pacific warm pool compared with elsewhere, at least where the comparison is limited to the tropics.’
Nicholas Lewis 24 August 2020
Originally posted here, where a pdf copy is also available
[i] Meteorology Department. Previously at the Max Planck Institute for Meteorology in Hamburg, where he worked closely with Bjorn Stevens.
[ii] Lewis, N. and Mauritsen, T., 2020: Negligible unforced historical pattern effect on climate feedback strength found in HadISST-based AMIP simulations. Journal of Climate, 1-52, https://doi.org/10.1175/JCLI-D-19-0941.1
[iii] Gregory , J. M. , and T. Andrews , 2016 : Variation in climate sensitivity and feedback parameters during the historical period . Geophys. Res. Lett., 43 , 3911 –3920 , https://doi.org/10.1002/2016GL068406
[iv] Andrews T. et al., 2018 Accounting for changing temperature patterns increases historical estimates of climate sensitivity. Geophys. Res. Lett. https://doi.org/10.1029/2018GL078887
[v] Gregory, J.M., Andrews, T., Ceppi, P., Mauritsen, T. and Webb, M.J., 2019. How accurately can the climate sensitivity to CO₂ be estimated from historical climate change? Climate Dynamics. https://doi.org/10.1007/s00382-019-04991-y
[vi] Sherwood, S., et al. “An assessment of Earth’s climate sensitivity using multiple lines of evidence.” Reviews of Geophysics (2020): e2019RG000678. https://doi.org/10.1029/2019RG000678
[vii] Warming patterns are unlikely to explain low historical estimates of climate sensitivity, 5 September 2018.
[viii] Effective climate sensitivity (EffCS) is an estimate of equilibrium climate sensitivity (ECS) derived by estimating climate feedback strength (λ) in a non-equilibrium situation and dividing it into an appropriately-derived estimate of the effective radiative forcing (ERF) from a doubling of preindustrial CO 2 concentration. In an AOGCM experiment involving a step increase in CO 2 concentration, this equates to linearly projecting warming to the point where the Earth’s radiation balance has been fully restored, and then scaling it appropriately if the increase in CO 2 was not a doubling.
[ix] Lewis, N. and J. Curry, 2018: The Impact of Recent Forcing and Ocean Heat Uptake Data on Estimates of Climate Sensitivity. J. Climate, 31, 6051–6071, https://doi.org/10.1175/JCLI-D-17-0667.1; also Masters, T., 2014: Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models. Climate Dyn., 42, 2173 –2181. https://doi.org/10.1007/s00382-013-1770-4
[x] Lewis and Curry (2018) estimated a 10% difference when using long term EffCS estimates based on regression over years 21–150 of CMIP5 abrupt4xCO2 simulations, but that would reduce to 5% if instead basing them on regression over years 1–150, the method used in Andrews et al. (2018).
[xi] Gregory et al 2019: Does climate feedback really vary in AOGCM historical simulations? 31 October 2019
[xii] Hurrell, J.W., Hack, J.J., Shea, D., Caron, J.M. and Rosinski, J., 2008: A new sea surface temperature and sea ice boundary dataset for the Community Atmosphere Model. J. Climate, 21(19), 5145-5153. https://doi.org/10.1175/2008JCLI2292.1
[xiii] Reynolds, R.W., Rayner, N.A., Smith, T.M., Stokes, D.C. and Wang, W., 2002. An improved in situ and satellite SST analysis for climate. Journal of climate, 15(13), pp.1609-1625. https://doi.org/10.1175/1520-0442(2002)015<1609:AIISAS>2.0.CO;2
[xiv] Climate feedback strength λ is reciprocally related to EffCS. Note that we use a positive sign convention for climate feedback, but Andrews et al. (2018) use a negative sign convention, so care is needed in interpreting their statements about it.
[xv] Using feedback estimated by regression over years 1-50 of the parent AOGCMs’ abrupt4xCO2 simulations as a proxy for their forced historical feedback over 1871-2010.
[xvi] We computed feedback using surface skin temperature (Ts) rather than near-surface air temperature (T), for the reasons set out in our paper, save when working with data from Andrews et al. (2018), who used T.
[xvii] Through amipPiForcing simulations by ECHAM6.3, and through applying Green’s functions derived from multiple patch-warming simulations by CAM5.3. The Green’s function approach exploits the apparent linear superpositionality in space of GCM responses to warming. Global changes in surface temperature Ts and outgoing radiation R resulting from imposed evolving historical SST patterns can thus easily be emulated by the sums of the global responses to SST changes in individual locations weighted by time-invariant Green’s function values for each location, and associated climate feedback estimates derived. Sea-ice is held constant in the CAM5.3 patch-warming simulations, which reduces changes in the emulated values of both Ts and R.
[xviii] We define the Indo-Pacific warm pool as the region 15°S–15°N, 45°E–195°E, and compare its warming trend with that for the ocean from 50°S–50°N as a whole, that area being essentially ice-free all year.
[xix] Dong, Y., Proistosescu, C., Armour, K.C. and Battisti, D.S., 2019: Attributing Historical and Future Evolution of Radiative Feedbacks to Regional Warming Patterns using a Green’s Function Approach: The Pre-eminence of the Western Pacific. Journal of Climate, (2019).
[xx] That is because surface temperature in convective areas controls temperature in the tropical free troposphere, which spatially is fairly uniform, and influences temperature in the extratropics. An increase in free tropospheric temperature relative to surface temperature in descent regions strengthens the boundary layer temperature inversion, which is known to increase low cloud cover and hence reflected solar radiation.
[xxi] Andrews, T., Gregory, J. M., and Webb, M. J., 2015: The dependence of radiative forcing and feedback on evolving patterns of surface temperature change in climate models. J. Climate, 28(4), 1630-1648. https://doi.org/ 10.1175/JCLI-D-14-00545.1
[xxii] Using the ensemble mean from a number of amipPiForcing simulation runs data does not provide an adequate solution, because the noise in the SST data used to force the GCM is the same in all runs.
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climateetc--2020-08-19--Emergent constraints on TCR and ECS from historical warming in CMIP5 and CMIP6 models

This is a brief comment on a new paper [ i ] by a mathematician in the Exeter Climate Systems group , Femke Nijsse , and two better known colleagues , Peter Cox and Mark Williamson .
I note that Earth Systems Dynamics published the paper despite one of the two peer reviewers recommending against acceptance without further major revisions .
But neither of the reviewers appear to have raised the issue that I focus on here .
“ Emergent constraints ” methods relate observable climate trends , variations or other variables to climate system properties of interest , such @ @ @ @ @ @ @ , in an ensemble of models .
They then use the observed values of the variable ( s ) involved to estimate ECS or the other properties of interest .
I ’ m not a great fan of emergent constraints studies , the results of which are often sensitive to the model ensemble used .
Here the emergent constraint is the relationship , assumed linear , between transient climate response ( TCR ) and global warming from 1975 onwards .
The authors thereby derive , from a CMIP6 26 model ensemble , a @ @ @ @ @ @ @ % ‘ likely ’ range 1.29–2.05 K , 5-95 % range 1.0–2.3 K ) using warming up to 2019 .
The paper states that using instead warming up to 2014 , thereby enabling use of a larger set of CMIP6 models , reduces the TCR estimate to 1.54 K ( 5-95 % range 0.76–2.30 K ) , but don ’ t mention that in their abstract or conclusions .
The authors also derive an estimated likely range for ECS of 1.9–3.4 K ( 5–95 % range 1.5–4.0 K ) from CMIP6 models , @ @ @ @ @ @ @ to 2019 .
Based on warming up to 2014 in the larger ensemble of CMIP6 models , the median ECS estimate is 1.9 K ( 5–95 % range 1.0–3.3 K ) .
Again , the result from the larger ensemble is not mentioned in the abstract or conclusions .
I am very doubtful about estimating ECS by comparing observed and simulated historical warming .
Without also using observational data on ocean heat update , to estimate changes in the Earth ’ s energy imbalance , it is impossible to distinguish satisfactorily between ECS @ @ @ @ @ @ @ and them both being low – either combination can produce the same historical warming .
So I would not place any reliance on their ECS ranges , even if they don ’ t look unreasonable .
On the other hand , one would expect historical warming in climate models to have a close to linear relationship with their TCR , since pre-1975 ‘ warming in the pipeline ’ is fairly negligible and post 1975 forcing is reasonably close to the quasi-linear ramp forcing used to measure TCR , and similarly of multidecadal length @ @ @ @ @ @ @ , to which models and the real climate system may respond differently , is a possible confounding factor , although use of the difference between 1975–1985 and the 2009–2019 means to measure warming excludes years affected by the 1991 Mount Pinatubo eruption .
There is also the issue that the mean change in effective radiative forcing ( ERF ) in climate models between those two periods may not equal the ERF change in the real climate system .
For CMIP5 models at least , I suspect that their mean ERF change falls somewhat @ @ @ @ @ @ @ would induce an upwards bias in the emergent constraint TCR estimate .
Regardless of the above considerations , there is a fatal problem with the regression method used to relate TCR with warming .
If a model has a TCR of zero , then it would be expected to show zero historical warming .
The authors appear to recognise this , writing “ As no warming would be expected if climate sensitivity were zero , we expect the regression to pass through the intercept ” .
They actually mean pass through the origin @ @ @ @ @ @ @ as their equations ( A3 ) and ( A4 ) make clear .
And their equation ( 3 ) theoretical relationship between TCR and warming , TCR = s ΔT , has no offset term .
It is therefore physically inappropriate to use regression with a y-intercept term being estimated .
However , despite admitting that a zero y-intercept is physically appropriate , the study estimates a regression fit using a y-intercept as well as a slope coefficient parameter .
Moreover , the resulting best-fit line does not pass at all close to @ @ @ @ @ @ @ climate models with a TCR of ~0.7 K would have simulated zero post-1975 warming .
Their Figure 4 ( a ) , reproduced as Figure 1 below , shows this .
Figure 1 .
Reproduction of Figure 4 ( a ) of Nijsse et al .
( 2020 ) .
Emergent constraint on TCR against historical warming ΔT .
ΔT is calculated from the difference between 1975–1985 and 2009–2019 of a time series of GMSAT .
Linear regression is performed with all CMIP5 and CMIP6 simulations .
Shaded areas indicate a 90 % @ @ @ @ @ @ @ is the mean value of the observations , and the y axis shows the probability distribution of both generations of ensembles .
A quite involved and not very clearly described hierarchical Bayesian model regression method is used , which makes it difficult to reproduce exactly the study ’ s results .
Remarkably , the numerical value and uncertainty range of the observed warming estimate is nowhere stated .
I therefore measured it off their Figure 4 ( a ) , as 0.606 K , and took the shading as showing a normally distribution @ @ @ @ @ @ @ Based on a simple ordinary least squares ( OLS ) with-intercept regression of TCR on model-ensemble mean simulated historical warming , across the multimodel combined CMIP5 and CMIP6 ensemble , I estimate a median TCR estimate of 1.62 K ( or 1.66 K using the CMIP6 ensemble alone – marginally lower than their 1.68 K ) .
If I repeat the exercise but without estimating a y-intercept , thereby forcing the regression fit to match a zero TCR with zero historical warming , the emergent constraint gives a TCR best estimate of 1.43 @ @ @ @ @ @ @ ( R2 = 0.97 ) .
There is little regression dilution when no y-intercept is estimated .
Regressing warming on TCR rather than vice versa gives an emergent constraint TCR best estimate of 1.47 K. Regressing TCR on warming just across the CMIP5 ensemble gives a slightly lower TCR estimate of 1.37 K ( R2 = 0.97 ) .
Doing so across the CMIP6 ensemble alone gives a TCR estimate of 1.50 K ( ( R2 = 0.98 ) .
The slope coefficient standard errors imply that there is only a 3.1 % @ @ @ @ @ @ @ same in the CMIP5 and CMIP6 ensembles .
It is unclear which regression method is more accurate .
Using the geometrical mean of the estimates regressing each way , as is sometimes recommended , gives a TCR best estimate of 1.45 K from the combined CMIP5/CMIP6 ensemble .
A crude estimate of uncertainty can be obtained by using , for each type of regression , the standard error in the slope estimate and the observational uncertainty to form a large number of randomly sampled TCR estimates , combining the two resulting sets of @ @ @ @ @ @ @ gives a median TCR estimate of 1.45 K , with a 16–84 % range of 1.29–1.62 K and a 5–95 % range of 1.18–1.74 K. However , this does not account for all sources of uncertainty .
Interestingly , when fitting a relationship between ECS and post-1975 warming , and between ECS and TCR , the authors didn ’ t use a y-intercept term , resulting in those fits passing through the origin .
My key point is that an analysis method that results in a physically reasonable estimated relationship between the variables @ @ @ @ @ @ @ estimated relationship that implies zero warming with a positive TCR , and significant cooling with a zero TCR , is unphysical .
Therefore , the results of the Nijsse et al .
paper are unreliable and should be discounted .
Thanks to a commenter pointing out that it was erroneous , in the third paragraph I have removed the statement ‘ Unfortunately , the study does not provide a results table for their TCR estimates and the 5-95 % TCR range is not stated.
’ , stated that range and also corrected the @ @ @ @ @ @ @ In the fifth from last paragraph I have added the TCR estimate that I derive using the CMIP6 ensemble on its own .
[ i ] Njisse et al.
, 2020 : Emergent constraints on transient climate response ( TCR ) and equilibrium climate sensitivity ( ECS ) from historical warming in CMIP5 and CMIP6 models , Earth Syst .
Dynam.
, 11 , 737–750 , 2020 https : //doi.org/10.5194/esd-11-737-2020 Originally posted here , where a pdf copy is also available

By Nic Lewis
This is a brief comment on a new paper[i] by a mathematician in the Exeter Climate Systems group, Femke Nijsse, and two better known colleagues, Peter Cox and Mark Williamson. I note that Earth Systems Dynamics published the paper despite one of the two peer reviewers recommending against acceptance without further major revisions. But neither of the reviewers appear to have raised the issue that I focus on here.
“Emergent constraints” methods relate observable climate trends, variations or other variables to climate system properties of interest, such as equilibrium climate sensitivity (ECS), in an ensemble of models. They then use the observed values of the variable(s) involved to estimate ECS or the other properties of interest. I’m not a great fan of emergent constraints studies, the results of which are often sensitive to the model ensemble used. Here the emergent constraint is the relationship, assumed linear, between transient climate response (TCR) and global warming from 1975 onwards.
The authors thereby derive, from a CMIP6 26 model ensemble, a TCR estimate of 1.68 K (16-84% ‘likely’ range 1.29–2.05 K, 5-95% range 1.0–2.3 K) using warming up to 2019.
The paper states that using instead warming up to 2014, thereby enabling use of a larger set of CMIP6 models, reduces the TCR estimate to 1.54 K (5-95% range 0.76–2.30 K), but don’t mention that in their abstract or conclusions.
The authors also derive an estimated likely range for ECS of 1.9–3.4 K (5–95% range 1.5–4.0 K) from CMIP6 models, median estimate 2.6 K, from warming to 2019. Based on warming up to 2014 in the larger ensemble of CMIP6 models, the median ECS estimate is 1.9 K (5–95% range 1.0–3.3 K). Again, the result from the larger ensemble is not mentioned in the abstract or conclusions.
I am very doubtful about estimating ECS by comparing observed and simulated historical warming. Without also using observational data on ocean heat update, to estimate changes in the Earth’s energy imbalance, it is impossible to distinguish satisfactorily between ECS and ocean heat uptake both being high and them both being low – either combination can produce the same historical warming. So I would not place any reliance on their ECS ranges, even if they don’t look unreasonable.
On the other hand, one would expect historical warming in climate models to have a close to linear relationship with their TCR, since pre-1975 ‘warming in the pipeline’ is fairly negligible and post 1975 forcing is reasonably close to the quasi-linear ramp forcing used to measure TCR, and similarly of multidecadal length. The existence of episodic volcanic forcing, to which models and the real climate system may respond differently, is a possible confounding factor, although use of the difference between 1975–1985 and the 2009–2019 means to measure warming excludes years affected by the 1991 Mount Pinatubo eruption. There is also the issue that the mean change in effective radiative forcing (ERF) in climate models between those two periods may not equal the ERF change in the real climate system. For CMIP5 models at least, I suspect that their mean ERF change falls somewhat short of the actual change. That would induce an upwards bias in the emergent constraint TCR estimate.
Regardless of the above considerations, there is a fatal problem with the regression method used to relate TCR with warming. If a model has a TCR of zero, then it would be expected to show zero historical warming. The authors appear to recognise this, writing “As no warming would be expected if climate sensitivity were zero, we expect the regression to pass through the intercept”. They actually mean pass through the origin (have a zero y-intercept), as their equations (A3) and (A4) make clear. And their equation (3) theoretical relationship between TCR and warming, TCR = s ΔT, has no offset term. It is therefore physically inappropriate to use regression with a y-intercept term being estimated.
However, despite admitting that a zero y-intercept is physically appropriate, the study estimates a regression fit using a y-intercept as well as a slope coefficient parameter. Moreover, the resulting best-fit line does not pass at all close to the origin. Their estimate implies that climate models with a TCR of ~0.7 K would have simulated zero post-1975 warming. Their Figure 4(a), reproduced as Figure 1 below, shows this.
Figure 1. Reproduction of Figure 4(a) of Nijsse et al. (2020). Emergent constraint on TCR against historical warming ΔT . ΔT is calculated from the difference between 1975–1985 and 2009–2019 of a time series of GMSAT. Linear regression is performed with all CMIP5 and CMIP6 simulations. Shaded areas indicate a 90% prediction interval. The vertical dashed line is the mean value of the observations, and the y axis shows the probability distribution of both generations of ensembles.
A quite involved and not very clearly described hierarchical Bayesian model regression method is used, which makes it difficult to reproduce exactly the study’s results. Remarkably, the numerical value and uncertainty range of the observed warming estimate is nowhere stated. I therefore measured it off their Figure 4(a), as 0.606 K, and took the shading as showing a normally distribution 5–95% range, width 0.225 K. Based on a simple ordinary least squares (OLS) with-intercept regression of TCR on model-ensemble mean simulated historical warming, across the multimodel combined CMIP5 and CMIP6 ensemble, I estimate a median TCR estimate of 1.62 K (or 1.66 K using the CMIP6 ensemble alone – marginally lower than their 1.68 K).
If I repeat the exercise but without estimating a y-intercept, thereby forcing the regression fit to match a zero TCR with zero historical warming, the emergent constraint gives a TCR best estimate of 1.43 K. The regression fit is very good (R2 = 0.97). There is little regression dilution when no y-intercept is estimated. Regressing warming on TCR rather than vice versa gives an emergent constraint TCR best estimate of 1.47 K. Regressing TCR on warming just across the CMIP5 ensemble gives a slightly lower TCR estimate of 1.37 K (R2 = 0.97). Doing so across the CMIP6 ensemble alone gives a TCR estimate of 1.50 K ((R2 = 0.98). The slope coefficient standard errors imply that there is only a 3.1% chance that the TCR–warming relationship is the same in the CMIP5 and CMIP6 ensembles.
It is unclear which regression method is more accurate. Using the geometrical mean of the estimates regressing each way, as is sometimes recommended, gives a TCR best estimate of 1.45 K from the combined CMIP5/CMIP6 ensemble. A crude estimate of uncertainty can be obtained by using, for each type of regression, the standard error in the slope estimate and the observational uncertainty to form a large number of randomly sampled TCR estimates, combining the two resulting sets of estimates and computing quantiles. Doing so gives a median TCR estimate of 1.45 K, with a 16–84% range of 1.29–1.62 K and a 5–95% range of 1.18–1.74 K. However, this does not account for all sources of uncertainty.
Interestingly, when fitting a relationship between ECS and post-1975 warming, and between ECS and TCR, the authors didn’t use a y-intercept term, resulting in those fits passing through the origin.
My key point is that an analysis method that results in a physically reasonable estimated relationship between the variables being studied should be used. An estimated relationship that implies zero warming with a positive TCR, and significant cooling with a zero TCR, is unphysical. Therefore, the results of the Nijsse et al. paper are unreliable and should be discounted.
Nicholas Lewis 19 August 2020
Update 20 August 2020
Thanks to a commenter pointing out that it was erroneous, in the third paragraph I have removed the statement ‘Unfortunately, the study does not provide a results table for their TCR estimates and the 5-95% TCR range is not stated.’, stated that range and also corrected the reference to the model ensemble involved. In the fifth from last paragraph I have added the TCR estimate that I derive using the CMIP6 ensemble on its own.
[i] Njisse et al., 2020: Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models, Earth Syst. Dynam., 11, 737–750, 2020 https://doi.org/10.5194/esd-11-737-2020
Originally posted here, where a pdf copy is also available
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