Disconnect in the relationship between GMST and ECS

by Kenneth Fritsch

Abstract. An analysis is presented of  he disconnection between the CMIP5 and CMIP6 Historical and Future periods when considering the relationship of the individual model GMST changes and the climate sensitivity. I have included a simple model that can account for the period disconnection using the negative forcing of aerosol/cloud effects in the Historical period that is carried forward into the Future period.   I attribute some of the uncertainty in simulations of this simple model to endogenous model decision (selection) uncertainty that leads to variations in the changes of the negative forcing in the Historical period carried forward into the Future period.


There have been a number of references in the climate science literature (references 1 through10) concerning the disconnection between the change in the global mean surface temperature (GMST) in the Historical period (used in this analysis the time period 1850 or 1861 to 2014) and the climate sensitivity of models as measured by Equilibrium Climate Sensitivity (ECS) and Transient Climate Response (TCR) for individual CMIP5 and CMIP6 climate models. That disconnection has been made more obvious by the CMIP6 ensemble of models having higher climate sensitivities than that in the CMIP5 ensemble and yet having the near same GMST trends in the Historical period (references 11 and 12).

While there have been proposed explanations for this disconnection in the literature, mainly pointing to negative aerosol and cloud related forcing in the Historical period as probable causes, there has been neither an analysis of how this effect would carry over into the Future period (used in this analysis as the 2015-2100 time period) for individual models nor a direct comparison of the models’ GMST changes in Historical and Future periods. A theme in some of these papers suggests that direct model tuning of the Historical period warming does not account for the forcing compensation for differing model climate sensitivities but rather that it can be produced by selection from a range of parameter processes that can yield overall credible results and in turn a range of credible GMST trends. If the disconnection stems from a strictly structural difference between individual models, it would not change the concern for the models capability of reproducing the Historical GMST change translating to a capability to predict Future period GMST changes.

In this analysis I have used the energy budget equation, ΔT=(ΔF-ΔN)/λ , where ΔT is the GMST change, ΔF is the forcing change, ΔN is the change in TOA radiative imbalance and λ is the climate feedback parameter for an individual model. This relationship is further simplified by assuming that the quantity ΔF-ΔN in a correctly modeled form should be near constant for all models in a given scenario and time period and can be replaced by F2x which is the individual model radiative forcing from a doubling of atmospheric CO2 concentration.   F2x/ λ is equivalent to ECS but for the purposes of this analysis the term F2x/λ will be used since it better denotes the simplifying relationship it has to the energy budget.

This analysis uses OLS regression of ΔT versus F2x/λ for individual models for a given scenario and time period and ΔT versus ΔT for individual models for scenario versus scenario. The analysis covers the CMIP5 and CMIP6 Historical and representative Future period scenarios. Also included in the analysis, as a possible contributing factor in the Historical to Future scenario disconnections, were the results of OLS regression of ΔN versus ΔN for all scenario combinations. The critical results derived from all these regressions were the slope t values and r squared values.

It was obvious from the start of this analysis that Future scenario ensembles, where the forcing from greenhouse gases (GHG) is dominating over negative aerosol forcing and noise, should have more significant slope t and r squared values than those derived from the Historical period.  In this analysis the expectations of disconnections of the Historical ensemble results from those of the Future ensembles and how this could occur facilitated the construction of simple simulation scenario models (hereafter in this article referred to as Reproduction Models) that closely reproduce and provide a potential explanation of the differing model scenario results. I posted a previous thread here at Climate etc. (reference 13) on the disconnection between the Historical Future scenarios for CMIP5 models. That analysis did not provide a Reproduction like model showing how a negative forcing can compensate the climate sensitivities in the Historical period and be carried over into the Future period without materially reducing the correlations there. I attempt to provide that missing step in this analysis.


All time series changes in climate variables in this analysis were determined using the empirical CEEMDAN method of extracting a secular trend from periodical oscillation and noise components (references 14 and 15). This method avoids having to limit the period selections to those where the non-trend components are not thought to bias the variable change. It also allows the change to be determined for the entire time period selected.

The individual model GMST and TOA radiation data and the corresponding Pre-Industrial Controls (PIC) for this analysis were taken for the CMIP5 scenarios from KNMI Climate Explorer website (reference 16) and for CMIP6 from the ESGF Node at DKRZ (reference 17). The forcing data for CMIP5 were taken from Meinshausen (reference 18) and that for CMIP6 were from Fiedler (reference 19). The λ and F2x data were taken from Gregory and Forster (references 20 and 21) for CMIP5 and from Femke (reference 22) for CMIP6.

The PIC series were tested for statistically significant trends and if none were found no adjustments were made to corresponding GMST and TOA series. There appeared no good reason to subtract non significant components (noise) from the series of interest. A with/without adjustment comparison of the final series changes over the period of interest showed no or very small differences relative to the series changes.

OLS regression was chosen for this analysis after comparing results for the slope and slope t values with Deming regressions. The small differences in the slope values for these two types of regression showed that the noise in the independent variable was not sufficient to require use of a version of Total Least Square regression. The r squared values for the regressions are reported with and without outliers along with the number of outliers found. These outliers were determined using Cook’s Distance criteria of greater than 4 times the mean of the Cook’s Distance for all the model results (reference 23). No effort was made to analyze the outliers since the motive for detecting them was not to subjectively exclude possible outliers but rather show how almost all models fit the regression line and allow comparison where all data points are used. The residuals from the OLS regressions were tested for auto correlation and fitting to a normal distribution. Based on those tests, no adjustments to the regression results were required.

Results and Discussion:

Table 1 shows the OLS regression results for the CMIP5 scenarios of Historical, RCP 4.5, RCP 6.0 and RCP 8.5 and for CMIP6 scenarios of Historical, SSP3 7.0 and the CMIP6 renditions of the CMIP5 RCP 4.5 and 8.5 scenarios. The ΔT versus ΔT regression for all scenario combinations was included with that for ΔT versus F2x/λ even though differences between the Historical and Future scenarios were expected to produce similar results with both regressions. With ΔT there were more model data available than for that with F2x/λ values and more scenario combinations to compare. The slope t and r squared values in the table show a very strong correlation for the CMIP5 and CMIP6 Future scenarios between the GMST change and the climate sensitivity parameter. The Historical scenarios for CMIP5 and CMIP6 were expected to show little correlation for these relationships and in fact show no correlation.

R is abbreviated for RCP and the 2 numbers following are the forcing change goal for that scenario, i.e. R45 stands for RCP4.5.  The R designations are carried over from CMIP5 to CMIP6.  S70 is unique to CMIP6 and has full designation as SSP3 7.0.

The results in Table 3 are from 1000 simulations of the models referred to as Reproduction Models that were constructed to reproduce the regression results of the CMIP5 and CMIP6 scenario ensembles in Table 1. The simulation models for regression used the following equations for X and Y, the independent and dependent variables, respectively:

X=(ΔR/F2x)*F2x[i]/λ[i], where X is the metric to which the individual model GMST change in the scenario should correlate without a variable negative forcing altering the relationship.

Y=(ΔR/F2x)*F2x[i]/λ[i]+rnorm(n=1, mean=K*Diff[i],sd=SD), where Y is the simulated change in the individual model GMST over the scenario time period.

In the equations, ΔR is the change in net outgoing radiation from ΔR=ΔF-ΔN with ΔF being the change in forcing and ΔN being the TOA radiative imbalance. These variables derive from the global energy budget ΔT=(ΔF-ΔN)/λ, where λ is the climate feedback parameter. The value used for ΔN is the mean for ΔN for the scenario model ensemble and was taken for CMIP5 from KNMI Climate Explore (reference 16) and for CMIP6 was taken from ESGF Node of DKRZ (reference 17). The values for ΔF changes and the aerosol/cloud forcing changes used for determining the K values were taken from pik-potsdam (reference 18), except for the special case of ssp 370 where the aerosol/cloud forcing changes were taken from Fiedler (reference 19). F2x is the mean radiative forcing for a doubling of atmospheric CO2 concentration for the scenario ensemble being considered. F2x[i] is the F2x for the individual model in the scenario. λ[i] is the individual model feedback parameter. Diff is the difference of the individual model feedback parameter from the mean of the scenario model feedback parameters. K is a tunable model parameter that determines how much the individual model feedback parameter is compensated in moderating the Historical ΔT.

There have been a number of papers in the climate science literature to justify assuming that the other tunable Reproduction model parameter, which is the standard deviation, SD, in the random normal function that adds noise to the Y variable, can be considered at least partially attributable to the different choices available to the modelers of the individual models analyzed here. The tendency of the models to compensate the GMST changes in the Historical period for varying individual model climate sensitivities in bringing the results more in line with the observed GMST changes points to modelers decisions adding to overall uncertainty of the model results. The structure variation from model to model could also determine the bounds of the potential influence of the modelers’ decisions in this matter. I have attempted to categorize the Reproduction model by searching the literature for similar examples. The best examples found were presented in one paper (reference 24) that dealt with stochastic and endogenous decision dependent uncertainty. A quote from reference 24 describes endogenous uncertainty in these models as: “A problem is classified as having endogenous uncertainty when decisions that are part of the problem to be solved, influences the uncertainty of parameters that are also part of the problem.”

Table 2 below lists the parameter values used in the Reproduction Model.

The fixed parameters were used at values noted previously and taken from the literature and applied to the scenarios as reasonable weights for increasing the total net forcing in the scenario progression from Historical to R85.

The tunable noise parameter of SD was applied at different values for CMIP5 and CMIP6 but with the same values across the CMIP scenarios. The tunable parameter, K, is the crux of this entire analysis and is the essential ingredient that causes most of the disconnection between the Historical and Future scenarios and at the same time closely reproduces the actual model results. The negative K for the Historical period, that is multiplied by the difference of the individual model feedback parameter, λ, and the scenario ensemble mean of λ, produces a more negative or positive forcing that compensates the resulting GMST change, ΔT, for feedback parameters by the amount they deviate from the mean. The future scenarios with the exception of S70, have positive K values that, instead of compensating for feedback differences, enhances them.

The ratios of the K parameter for the scenarios were used in this analysis based on what was found in literature searches. In other words for CMIP5, where the Historical K is -0.30 and the Future K is approximately half that of the Historical but positive, the change in the negative forcing from aerosol and cloud effects in the Historical period became nearly two times more negative than the forcing in the Future period became less negative. Only the magnitude of K was tuned, but not the ratio between Historical and Future scenarios.

The Reproductive Models reproduce closely the results obtained from the CMIP5 and CMIP6 scenario ensembles of models even though fitting with the tunable parameters for this analysis was by no means exhaustive, but rather carried out with a few subjective iterations.

Table 4 contains the results for the Reproduction Models without the factor that compensates the individual Historical model ΔT for the differing individual model feedback parameters. The scenario model ensemble correlations are affected in this case by the differing scale for net Forcing change and the SD noise factor. It can be seen from the table that the median probability correlations for both the CMIP5 and CMIP6 models of the Historical ensemble for ΔT versus F2x/λ and scenario ΔT versus ΔT have become significant and that those for the future scenarios remain significant and with slope t and r squared values generally not as large as those with the compensating factor.

The findings here are fully consistent with those in Rotstayn and Collier (reference 25) who found that the TCR values for 14 CMIP5 models had no significant correlation with the GMST change in the Historical period (1860-2000) while in the same period the negative aerosol forcing change correlated with the GMST change with r value over 0.90. In other words the negative forcing that varied from model to model was changing what otherwise should have been a significant correlation between TCR (and ECS) and the change in GMST in the Historical period.

There have been two papers published where the individual model Historical aerosol forcing for some of the CMIP5 and CMIP6 models using a fixed SST and ocean ice covering are determined. These data provided an opportunity for the analysis here to attempt to correct the Historical GMST changes for aerosol forcing and in turn regress the adjusted GMST change against F2x/λ. There were only 12 models for these regressions but the results in Table 7 show that the adjusted GMST changes become very significant and have reasonably high r squared values. The comparison of the t and r squared values between the unadjusted and adjusted Historical GMST changes shows most definitely and directly that the aerosol forcing applied in quantitatively different amounts to the individual models is the determining factor in disconnecting the model GMST changes from the model’s climate sensitivity.                                                                             


The adjusted GMST change was derived using the following adjustment equation:

ΔTcor= ΔTHist- (F2x(i)/F2xmean)*((0.65*ΔFaer(i))/λ(i))) where ΔTcor is the individual model GMST change corrected for the individual model aerosol forcing, ΔTHist is the uncorrected derived individual model GMST change, F2x(i) is the individual model forcing for a doubling of the atmospheric CO2 concentration, F2xmean is the ensemble mean of F2x, ΔFaer(i) is the Historical individual model aerosol forcing and λ(i) is the individual model feedback parameter. The values of ΔFaer and ΔNaer were combined under the assumption that these two variables track one another

Table 8 shows the OLS regression for CMIP5 and CMIP6 scenarios for all scenario combinations of ΔN versus ΔN.

Though the Reproduction Models did not directly take into account any ΔN differences between the Historical and Future scenarios, the results are presented in the table to show another disconnection between the Historical and Future periods. While the Zelinka paper (reference 27) indicates that individual CMIP6 models could have Historical GMST compensation for differences in climate sensitivity from ΔN that is independent of the negative aerosol compensation, it is judged that the disconnect presented here between the ΔN for the Historical and Future periods is directly related to the negative aerosol compensation disconnection. The aerosol component and its effect on GMST change would have a corresponding ΔN component and thus if there is a Historical and Future disconnection due to aerosol there should be a corresponding one for ΔN. For CMIP5 scenarios the Historical to Future correlations are significantly negative for ΔN while for Future to Future scenarios the correlations are positive and high for ΔN – as they were for ΔT. For CMIP6 scenarios the results are much the same as for CMIP5 except that the Historical to Future correlations while tending towards negative are not significant.


In this analysis it was shown that there is a statistically significant disconnection between the CMIP5 and CMIP6 Historical and Future period scenarios when considering the relationship between the individual model climate sensitivities and GMST values. The correlations of changes in model GMST for scenario to scenario ensembles and ensemble scenario GMST changes to F2x/λ provide a means for analyzing the degree of disconnection between the Historical to Future scenarios and connection for Future to Future scenarios.

As an aside, using F2x/λ as a simplified version of the energy budget and obtaining high correlations with GMST changes in the Future periods indicates that ΔR is a fairly constant value for these models where model to model variations in negative aerosol/cloud forcing are not an overwhelming factor.

The model ensemble correlations for both CMIP5 and CMIP6 Historical and Future scenarios can be closely reproduced with a simple model (Reconstruction model). This model accounts for negative aerosol/cloud forcing that can compensate GMST changes for differences in individual model climate sensitivities in the Historical period while allowing carry-over that forcing effect into the Future period scenarios and maintaining the higher scenario correlations in that period. The Reproduction model can provide a probable explanation for the Historical to Future disconnection that is consistent in time and forcing. Added evidence favoring the Reproduction model comes from the result of using the model without the λ compensation factor and the observation that without inclusion of that factor there are significant changes in the Historical period correlations(higher) and smaller but noticeable ones(lower) in the Future period scenarios. The results from adjusting the GMST changes in the Historical period for aerosol forcing adds more direct evidence that the aerosol forcing is the primary cause of the Historical GMST to climate sensitivity disconnection and is well aligned with the Reproduction model results. This added evidence negates the alternative explanation that the disconnection is the result of a scaling factor for a smaller ΔR in the Historical period. It also shows that the negative aerosol/cloud forcing carried over from the Historical periods to the Future periods increases the leverage that climate sensitivity has on GMST in the Future periods and thus increases Future correlations of ΔT to F2x/λ.

It should be noted that the 95% confidence intervals for the Reproduction model simulations for the Historical Period are sufficiently wide in some cases to show statistically significant slopes and correlations (but with a low probability) in the 1000 regressions carried out. That interval is related to the size of the tunable parameter of standard deviation. That standard deviation has to include the variations in how the models and modelers handle the variable application of the negative aerosol/cloud forcing and that variation might well be truncated by some common sense judgments on selections. The Reproduction model provides a wide range of choices but the modelers of individual models as a group could very well have independently selected from near the middle of the distribution of choices and that appears to be the case.

What is the import of the disconnection of the ensembles of CMIP5 and CMIP6 models used in Historical and Future period scenarios? The process of using the Historical period model results for the climate variable of GMST change and how closely it matches the observed changes as a test of its credibility and capability of predicting future GMST changes becomes questionable if model selections of parameters and processes were aimed at better reproducing the observed GMST changes and more specifically those choices related to the resulting negative aerosol/cloud forcing and potential for compensating for models with higher (and lower) climate sensitivities.

Alternatively if increasingly more negative aerosol/cloud forcing in the Historical period is handled as a natural feature of the model and does not get used either intentionally or unintentionally to moderate GMST changes, and further, if the Future period sees the aerosol/cloud forcing getting less negative, it could be supposed that a model with a higher climate sensitivity could reasonably well reproduce the observed GMST changes. If all the models had nearly the same Historical and Future changes in the negative aerosol/cloud forcing the correlations performed in this analysis would not show the disconnections that were found. That means that only some – or none – of the models could be getting the negative forcing reasonably correct.

The finding of this analysis that the ΔN values for the ensemble Historical and Future periods do not correlate or are anti-correlated adds another independent means of the disconnection of the two periods. As stated previously the ΔN data while being an independent source of data it is not necessarily independent of the main aerosol effect.

The only practical way out of this dilemma in my view is to find, or at least keep looking for, a more precise method of determining the observed climate sensitivity with narrowed confidence intervals. The observed variables with the largest uncertainty required for the energy budget to estimate the observed climate sensitivity are the aerosol/cloud forcing and ΔN. It is these variables that are also available in the climate models to compensate GMST Historical changes for variable climate sensitivities. It is therefore those two forcing entities that need attention, in the observations and the models.

The use of more complex and informed models that include endogenous decision uncertainty for modeling selection leading to variations in negative forcing between individual models in the Historical period could provide some needed insights in this area of climate science.

References [ References]

via Climate Etc.


November 11, 2020 at 09:22PM

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