Reposted by Dr. Judith Currys Climate Etc.

Posted on Nov 11, 2020 by curryja

by Kenneth Fritsch

Abstract. An analysis of the separation between the historical and future periods CMIP5 and CMIP6 is presented when the relationship between GMST changes of each model and climate sensitivity is taken into account. I have included a simple model that can account for the period interruption by negatively forcing aerosol / cloud effects in the historical period carried over to the future period. I attribute some of the uncertainty in simulations of this simple model to the endogenous uncertainty of the model decision (selection), which leads to fluctuations in changes in negative forcing in the historical period carried over into the future period.

**Introduction:**

In the climate science literature (references 1 to 10) there have been a number of references regarding the separation between the change in global mean surface temperature (GMST) over the historical period (the period 1850 or 1861 to 2014 used in this analysis). and the climate sensitivity of models, measured by equilibrium climate sensitivity (ECS) and transient climate response (TCR) for individual CMIP5 and CMIP6 climate models. This separation was made clearer by the CMIP6 ensemble of models with higher climate sensitivities than the CMIP5 ensemble and almost the same GMST trends in the historical period (references 11 and 12).

While explanations for this disruption have been suggested in the literature, mainly pointing to negative aerosol and cloud-related forces in the historical period as likely causes, it has not analyzed how this effect would carry over to the future period (used in) this analysis as Period 2015-2100) for individual models a direct comparison of the GMST changes of the models in historical and future periods. A theme in some of these papers suggests that direct modeling of the warming of the historical period does not take into account the compulsory compensation for different model climate sensitivities, but rather can be generated by selecting from a number of parameter processes that can provide credible results overall, and in turn a number credible GMST trends. If the separation was based on a strictly structural difference between individual models, this would not change the concern about the model's ability to reproduce the historical GMST change, which translates into an ability to predict future GMST changes.

In this analysis I 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 radiation 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 almost constant for all models in a certain scenario and time period and can be replaced by F2x, which is the radiative forcing of the individual model from a doubling the atmosphere is CO2 concentration. F2x / λ corresponds to ECS, but for the purposes of this analysis the term F2x / λ is used as it better describes the simplistic relationship to the energy balance.

This analysis uses the OLS regression of ΔT versus F2x / λ for individual models for a specific scenario and time period and ΔT versus ΔT for individual models for scenario versus scenario. The analysis covers the historical and representative future scenarios CMIP5 and CMIP6. The results of the OLS regression of ΔN versus ΔN for all scenario combinations were also included in the analysis as a possible factor for the separation of historical and future scenarios. The critical results derived from all of these regressions were the slope t-values and the r-squared values.

From the beginning of this analysis it was clear that future scenario ensembles, in which greenhouse gas propulsion (GHG) dominates over negative propulsion and noise from aerosols, should have more significant slope values t and r squared than those derived from the historical Period were derived. In this analysis, expectations of separating the results of the Historical Ensemble from those of the Future Ensembles and how this could be done facilitated the construction of simple simulation scenario models (hereinafter referred to as reproduction models in this article) that accurately reproduce and provide a possible explanation of the different model scenario results. I posted an earlier thread here at Climate etc. (Reference 13) about the separation between the historical future scenarios for CMIP5 models. This analysis did not provide a reproduction-like model that shows how negative forcing can compensate for climate sensitivities in the historical period and carry them over into the future period without significantly reducing the correlations there. I am trying to indicate this missing step in this analysis.

**Methods:**

All time series changes in the climate variables in this analysis were determined using the empirical CEEMDAN method to extract a secular trend from periodic oscillation and noise components (References 14 and 15). This approach avoids having to limit the period selection to those where the non-trend components are not believed to affect the variable change. In addition, the change can be determined for the entire selected period.

The individual GMST and TOA radiation data of the model and the corresponding pre-industrial controls (PIC) for this analysis were obtained for the CMIP5 scenarios from the KNMI Climate Explorer website (reference 16) and for CMIP6 from the ESGF node at the DKRZ (reference 17 ) accepted. The forcing data for CMIP5 come from Meinshausen (reference 18) and those for CMIP6 from Fiedler (reference 19). The λ and F2x data were taken from Gregory and Forster (references 20 and 21) for CMIP5 and Femke (reference 22) for CMIP6.

The PIC series were tested for statistically significant trends and if none were found no adjustments were made to the corresponding GMST and TOA series. There did not seem to be a good reason to subtract insignificant components (noise) from the series of interest. A comparison with / without adjustment of the final series changes over the period of interest showed no or only very slight differences to the series changes.

OLS regression was chosen for this analysis after comparing the results for the slope and slope t-values to Deming regressions. The small differences in slope values for these two types of regression indicated that the noise in the independent variable was insufficient to warrant using a version of Total Least Square regression. The r-squared values for the regressions are given with and without outliers along with the number of outliers found. These outliers were identified using Cook's distance criteria, which for all model results are more than four times the mean Cook's distance (reference 23). No effort was made to analyze the outliers, as the motive for their detection was not to subjectively exclude possible outliers, but to show how almost all models fit the regression line and allow a comparison using all data points will. The residuals from the OLS regressions were tested for autocorrelation and fit to a normal distribution. No adjustments to the regression results were necessary based on these tests.

**Results and discussions:**

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

R is abbreviated for RCP and the following 2 numbers are the forced change target for this scenario; H. R45 stands for RCP4.5. The R designations are transferred from CMIP5 to CMIP6. S70 is unique to CMIP6 and has the full designation SSP3 7.0.

The results in Table 3 are obtained from 1000 simulations of the models called reproduction models that were constructed to reproduce the regression results of the CMIP5 and CMIP6 scenario ensembles in Table 1. The simulation models for the 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 GMST change of the individual model in the scenario should correlate without a variable negative forcing changing 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 Period of the scenario.

In the equations, ΔR is the change in net outgoing radiation from ΔR = ΔF-ΔN, where ΔF is the change in drive and ΔN is the TOA radiation imbalance. These variables are derived from the global energy budget ΔT = (ΔF-ΔN) / λ, where λ is the climate feedback parameter. The value used for ΔN is the mean value for ΔN for the scenario-model ensemble and was taken from KNMI Climate Explore (reference 16) for CMIP5 and from the ESGF node of DKRZ (reference 17) for CMIP6. The values for ΔF changes and the aerosol / cloud forcing changes that were used to determine the K values were taken from pik-potsdam (reference 18), with the exception of the special case of ssp 370, in which the aerosol / cloud Forcing changes were adopted by Fiedler (reference) 19). F2x is the mean radiative forcing for a doubling of the atmospheric CO2 concentration for the scenario ensemble under consideration. F2x (i) is the F2x for the individual model in the scenario. λ (i) is the single model feedback parameter. Diff is the difference between the individual model feedback parameters and the mean value of the scenario model feedback parameters. K is an adjustable model parameter that determines by how much the individual model feedback parameter is compensated for when moderating the historical ΔT.

There are a number of publications in the climate science literature that justify the assumption that the other tunable reproductive model parameter, which is the standard deviation SD in the random normal function that adds noise to the Y variable, can be at least partially accounted for is due to the different options available to the modelers of the individual models analyzed here. The tendency of the models to compensate for the GMST changes in the historical period for different climate sensitivities of individual models in order to better align the results with the observed GMST changes indicates decisions by the modelers that increase the general uncertainty of the model results. The structural variation from model to model could also determine the limits of the possible influence of the decisions made by the modelers on this matter. I tried to categorize the reproductive model by looking for similar examples in the literature. The best examples found were presented in an article (reference 24) dealing with stochastic and endogenous decision-dependent uncertainty. A quote from Ref. 24 describes the endogenous uncertainty in these models as follows: "A problem is classified as endogenously unsafe if decisions that are part of the problem to be solved influence the uncertainty of parameters that are also part of the problem."

Table 2 below lists the parameter values used in the reproductive model.

The fixed parameters were used at the values given previously and taken from the literature and applied to the scenarios as appropriate weights to increase total net forcing over the course of the scenario from Historic to R85.

The adjustable noise parameter of SD was applied to different values for CMIP5 and CMIP6, but with the same values in all CMIP scenarios. The adjustable parameter, K, is at the heart of this entire analysis and the essential component that causes most of the separation between the historical and future scenarios while accurately reflecting the actual model results. The negative K for the historical period, which is multiplied by the difference of the individual model feedback parameter λ and the scenario ensemble mean of λ, generates a more negative or positive drive that compensates for 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 do not compensate for the differences in feedback, but improve them.

The ratios of the K-parameter for the scenarios were used in this analysis based on the results of the literature search. In other words, for CMIP5, where the historical K is -0.30 and the future K is roughly half the historical but positive, the change in negative forcing from aerosol and cloud effects became almost twice as negative as that in the historical period Forcing in the future became less negative. Only the size of K was set, not the relationship between historical and future scenarios.

The reproduction models accurately reflect the results of the CMIP5 and CMIP6 scenario ensembles of models, although the adjustment to the adjustable parameters for this analysis was by no means exhaustive, but was carried out with a few subjective iterations.

Table 4 contains the results for the reproductive models without the factor that compensates the single historical model ΔT for the different single model feedback parameters. The correlations of the scenario-model ensemble are influenced in this case by the different scale for the net forcing change and the SD noise factor. From the table it can be seen that the median probability correlations for both the CMIP5 and the CMIP6 models of the historical ensemble for ΔT versus F2x / λ and the scenario ΔT versus ΔT have become significant and that those for the future scenarios are significant and with a slope t remain and r square values generally not as large as those with the compensation factor.

The results here are in full agreement with those in Rotstayn and Collier (Reference 25) who found that the TCR values for 14 CMIP5 models did not have a significant correlation with the GMST change over the historical period (1860-2000), while they were negative over the same period. The change in aerosol forcing correlated with the GMST change with an r-value above 0.90. In other words, the negative forcing, which varied from model to model, changed the otherwise significant correlation between TCR (and ECS) and the change in GMST over the historical period.

Two articles have been published that determine the individual historical aerosol propulsion model for some of the CMIP5 and CMIP6 models using a fixed SST and sea ice cover. These data gave the analysis the opportunity to try to correct the historical GMST changes for aerosol propulsion and to 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 fitted GMST changes become very significant and have reasonably high r-squares. The comparison of the t- and r-squared values between the unadjusted and adjusted historical GMST changes shows most clearly and directly that the aerosol forcing, which is applied in quantitatively different amounts to the individual models, is the decisive factor in determining the GMST- Separate changes to the model from the model's climate sensitivity.

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

ΔTcor = ΔTHist- (F2x (i) / F2xmean) * ((0.65 * ΔFaer (i)) / λ (i))) where ΔTcor is the GMST change of the individual model, corrected for the aerosol forcing of the individual model, ΔTH is the uncorrected derived GMST change of the single model, F2x (i) is the single model that forces a doubling of the atmospheric CO2 concentration, F2x means the ensemble mean of F2x, ΔFaer (i) is the historical single model aerosol forcing and λ (i) is the individual model feedback parameter. The values of ΔFaer and ΔNaer were combined assuming that these two variables follow each other

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

Although the reproductive models did not directly account for ΔN differences between the historical and future scenarios, the results are presented in the table to show a further separation between the historical and future periods. While the Zelinka paper (reference 27) states that individual CMIP6 models could have a historical GMST compensation for differences in the climate sensitivity of ΔN that is independent of the negative aerosol compensation, it is judged that the separation between ΔN for the historical and future periods are directly related to the interruption of the negative aerosol compensation. The aerosol component and its effect on the GMST change would have a corresponding ΔN component. So if there is a historical and future separation due to aerosol, there should be a corresponding one for ΔN. For CMIP5 scenarios, the historical-future correlations for ΔN are significantly negative, while for future-to-future scenarios the correlations for ΔN are positive and high – as for ΔT. For CMIP6 scenarios the results are similar to those for CMIP5, except that the correlations between historical and future, while tending to be negative, are not significant.

**Conclusions:**

In this analysis it was shown that there is a statistically significant separation between the historical and future CMIP5 and CMIP6 scenarios when the relationship between the climate sensitivities of the individual models and the GMST values is taken into account. The correlations of changes in the model GMST for scenario-to-scenario ensembles and ensemble-scenario GMST changes in F2x / λ provide a way to analyze the degree of separation between the historical-future scenarios and the connection for scenarios from Future to future.

That being said, using F2x / λ as a simplified version of the energy budget and getting high correlations with GMST changes in the future periods shows that ΔR is a fairly constant value for these models, where model-to-model variations in the negative Aerosol / cloud forcing is not an overwhelming factor.

The correlations of the model ensemble for historical and future CMIP5 and CMIP6 scenarios can be precisely reproduced with a simple model (reconstruction model). This model takes into account negative aerosol / cloud forcing, which can compensate GMST changes for differences in the climate sensitivities of individual models in the historical period, while this forcing effect can be transferred to the scenarios of the future period and the higher scenario correlations can be maintained in this period. The reproductive model can provide a likely explanation for the temporally and forcibly consistent separation of history and future. Additional evidence for the reproductive model arises from the result of using the model without the λ compensation factor and the observation that without this factor there are significant changes in the correlations of the historical period (higher) and smaller but noticeable (lower) in the Future period scenarios. The results from adjusting the historical period GMST changes for aerosol forcing provide more direct evidence that aerosol forcing is the primary cause of the historical GMST disruption of climate sensitivity and agrees well with the reproductive model results. This additional evidence negates the alternative explanation that the separation 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 the future correlations of ΔT to F2x / λ increased.

It should be noted that the 95% confidence intervals for the reproductive model simulations for the historical period are in some cases sufficiently wide to show statistically significant slopes and correlations (but with low probability) in the 1000 regressions performed. This interval is related to the size of the adjustable parameter of the standard deviation. This standard deviation must include the variations in the way the models and modelers deal with the variable application of negative aerosol / cloud forcing, and this variation could potentially be cut off by some reasonable judgment about choices. The reproductive model offers a wide choice, but the modelers of individual models as a group could very well have chosen independently from the middle of the selection distribution, and this appears to be the case.

What is the significance of the separation of the ensembles of CMIP5 and CMIP6 models used in historical and future 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 to test their credibility and ability to predict future GMST changes becomes questionable when the model selection of parameters and processes Better efforts were made to reproduce the observed GMST changes and, in particular, the choices in connection with the resulting negative aerosol / cloud forcing and the potential to compensate for models with higher (and lower) climate sensitivities.

Alternatively, if in the historical period increasingly more negative aerosol / cloud forcing is treated as a natural feature of the model and is neither intentionally nor inadvertently used to moderate GMST changes, and if in the future period aerosol / cloud forcing increases less negatively could be assumed that a model with a higher climate sensitivity could reproduce the observed GMST changes fairly well. If all models had nearly the same historical and future negative aerosol / cloud changes, the correlations performed in this analysis would not indicate the separations found. This means that only some – or none – of the models could get the negative drive reasonably correctly.

The finding of this analysis that the ΔN values for the historical and future periods of the ensemble do not correlate or are anti-correlate adds another independent means of separating the two periods. As already mentioned, the ΔN data are an independent data source, but not necessarily independent of the main aerosol effect.

In my opinion, the only practical way out of this dilemma is to find a more precise method of determining the observed climate sensitivity with narrower confidence intervals, or at least to look further. The observed variables with the greatest uncertainty that are 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 for GMST historical changes for variable climate sensitivities. It is therefore these two imperative units that need attention in the observations and models.

The use of more complex and informed models that contain endogenous decision-making uncertainties for model selection and lead to variations in negative forcing between individual models over the historical period could provide some necessary insights in this area of climate science.

**References** (References)

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