1. Introduction
Potential future climate change, societal development, and climate adaptation and/or mitigation efforts are all considered in the risk assessment of future climate change [
1]. Climate change during the twenty-first century has been evaluated using global climate model (GCM) simulations from the fifth and sixth Coupled Model Intercomparison Projects (CMIP5, CMIP6) of the World Climate Research Programme [
2,
3]. The models employ a standard set of unique historical forcing functions from 1850 to 2014. The emissions from hypothetical Representative Concentration Pathways (RCPs) and Shared Socioeconomic Pathways (SSPs) scenarios are used to determine forecasts from 2015 to 2100. These span a wide range of potential outcomes that might affect how vulnerable people are to and exposed to climate change in the future. The near-term (2021–2040), mid-term (2041–2060), and long-term (2081–2100) prospective reference periods are typically used to evaluate the consequences and dangers of climate change. The pre-industrial global surface temperature is most closely represented by the reference period between 1850 and 1900.
More than 50 CMIP6 GCMs are available [
4]. Despite utilizing identical radiative forcing functions, their predictions for the twenty-first century differ greatly from one another. The fundamental issue is that a significant percentage of GCMs seem to be operating “too hot” [
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18], which suggests that climate change policy should disregard the projections from the “hot” models.
For instance, the CMIP6 GCMs evaluate that doubling atmospheric CO
2 concentrations from pre-industrial levels (from 280 to 560 ppm) will result in a global surface warming that could span from 1.8 to 5.7 °C. However, the ECS values larger than 5 °C already surpassed those of the CMIP5 GCMs [
2]. In fact, throughout the preceding 40 years, various climate models have consistently maintained an ECS range of 1.5 °C–4.5 °C.
Climate scientists are uncertain of how strong the climate’s response to greenhouse gases may be. A major dilemma is which GCMs should be utilized for climate change policy for future decades. A reasonable choice could be to utilize those models that better hindcast the global warming of the past decades. The assessment of a suitable range of climate sensitivity, which should be based on actual experimental data, is, therefore, a hot issue of discussion right now [
5].
For example, by combining a number of evidence from palaeoclimate, surface temperatures, ocean heat content, and modeling, Sherwood et al. [
19] concluded that the ECS is likely (with a 66% chance) in the range of 2.6–3.9
C, and very likely (with a 90% chance) between 2.3 and 4.7 °C. The IPCC [
1] and Hausfather et al. [
5] accepted these estimates and excluded the projections made by the too-hot models, which account for about one-third of all CMIP6 GCMs. However, Lewis [
17] reanalyzed the same data and, from multiple lines of evidences concluded that the actual ECS median should be 2.16 °C, its 17–83% range is 1.75–2.7
C, and its 5–95% range is 1.55–3.2
C. Scafetta [
12,
18] also reached a similar conclusion using a methodology that will be extended in the present paper. Lewis [
17] and Scafetta [
12,
18] would imply that about two-thirds of the CMIP6 GCMs should be screened out for the policy. Finally, McKitrick and Christy [
7] compared the tropospheric temperature records against the CMIP6 GCMs’ hindcasts and concluded that all CMIP6 GCMs are running too hot. The latter finding would require a new generation of GCMs with lower ECS values than the CMIP6 ones. This ambiguity needs to be clarified.
Additionally, it should be noted that there are several definitions of climate sensitivity. For instance, Hausfather et al. [
5] proposed the selection of suitable GCMs using not their ECS but their transient climate response (TCR). By accepting the analysis by Sherwood et al. [
19] and the choices of the IPCC [
1], they proposed to exclude the models with TCR beyond their estimated “probable” (66% probability range) range of 1.4–2.2
C. Here, I will re-assess this range as well.
The equilibrium climate sensitivity (ECS) is the long-term temperature rise (equilibrium global mean near-surface air temperature) that is expected to result from a doubling of the atmospheric CO
2 concentration [
3]. Once the CO
2 concentration has stopped rising, and the majority of the feedback has had time to fully take effect, the new global mean near-surface air temperature is predicted. However, after CO
2 has doubled, it can take centuries or even millennia to reach a new equilibrium temperature. According to the IPCC Sixth Assessment Report (AR6) [
3], there would be a high degree of confidence that ECS is between 2.5 and 4 °C, with a best estimate of 3
C, although the CMIP6 GCMs predict that the ECS could be between 1.8 and 5.7
C.
The transient climate response (TCR) is defined as the change in the global mean surface temperature, averaged over a 20-year period, centered at the time of atmospheric carbon dioxide doubling, in a climate model simulation in which the atmospheric CO
2 concentration increases at 1% per year [
3]. TCR is calculated using simulations with shorter time periods. Because slower feedbacks, which amplify the temperature increase, take longer to fully react to an increase in atmospheric CO
2 concentration, the transient response is smaller than the equilibrium climate sensitivity. For instance, after a perturbation, the deep ocean takes several centuries to achieve a new steady state while continuing to cool the top ocean as a heatsink. The CMIP6 GCMs predict that the TCR could be between 1.2 and 2.8
C.
Because of the quick buffering effects of the oceans, ECS is larger than TCR. In order to simulate the complete time period during which strong feedbacks, such as fully equilibrating ocean temperatures, continue to influence global temperatures in the model, the ECS is calculated using computer models that run for a duration of centuries. There are methods, nevertheless, that use less processing power.
Scafetta [
12,
18] and Lewis [
17] reevaluated the equilibrium climate sensitivity (ECS) problem utilizing information from a variety of sources. These authors reached a similar conclusion: the actual ECS should be between 1.5 and 3.0
C. This finding is important for policymakers because it suggests that the predicted risk of climate change will be moderate in the next decades and that adaptation strategies will be sufficient to address any negative effects. In fact, the low-ECS GCMs are those that project the least warming for the twenty-first century.
However, ECS could be a less relevant indicator than TCR for choosing climate change policy because of the extensive time scales needed for the climate system to reach a new equilibrium. Here, I add to the work performed by Scafetta [
11,
12,
18] by rating the CMIP6 GCMs in accordance with both their ECS and TCR values reported in the literature [
3,
5]. The risk level of climate change is then assessed using the ECS and TCR GCM sub-ensembles that appear to better hindcast the warming from 1980 to 2021.
Finally,
Section 4 touches on some unresolved issues concerning the magnitude of the global surface warming as reported by the official global surface temperature records, and the potential necessity of disregarding all of the CMIP6 GCMs when formulating climate change policies for the twenty-first century.
2. Data and Methods
The following monthly near-surface air temperature records are used: ERA5-T2m [
20,
21]; HadCRUT5 [
22]; GISTEMP v4 [
23]; NOAAGlobalTemp v5 [
24]; Japanese Meteorological Agency (JMA) [
25]; the Berkeley Earth (BE) group [
26]. These surface temperature records suggest that the global surface warming
from 1980–1990 to 2011–2021 could have varied from 0.52 to 0.59
C [
12].
Section 4 compares the above temperature records with other records to discuss the likelihood that the global surface temperature records might be warm biased [
27,
28]. To highlight this issue, the following figures show the 0.52–0.59
C range of the warming reported by the global surface temperature records together with the 0.40
C warming reported by the lower troposphere UAH-MSU-lt v6 record [
29] during the same period.
Out of all the temperature records that are currently available, the UAH-MSU-lt satellite record is explicitly used in this case mainly because it is the one that demonstrates the least rising trend and may be taken as the lowest limit provided by the scientific literature for the actual warming that has occurred at the surface. The apparent paradox of comparing a lower troposphere satellite-based temperature record to observations or model simulations at the surface is resolved by taking into consideration that the GCMs indicate that the troposphere warming should be larger than at the surface [
6,
7,
8], and that our initial assumption is that the GCMs’ assertion that greenhouse gases are the primary cause of global warming may be true. Therefore, the warming shown by the UAH-MSU-lt satellite record should theoretically be even larger than that at the surface: see also the discussion in Scafetta [
12] and the discussion in
Section 4.
The time period between 1980 and 2021 was chosen because, during this period, the temperature datasets are characterized by the lowest statistical uncertainty. The average over an 11-year period can be estimated to be
C because from 1980 to 2022, the statistical error of the monthly or annual temperature values is smaller than 0.05 °C [
22,
23] and the error of the 11-year average is calculated by dividing it by
, if the annual data are used, or by
, if the monthly data are used. A
C error is rather small and can be neglected [
12]. It should be pointed out that, besides the statistical error of the data, the temperature record’s interannual variability is a result of real physical processes (e.g. ENSO fluctuations, volcanic eruptions, solar activity variations, anthropogenic and natural warming trends, etc.), hence it does not increase the statistical error of the mean. Moreover, the 1980–2021 period is covered by the satellite-based records that can be used for an additional comparison. The 1980–2021 period also appears to be characterized by a large 1980–2000 warming rate, which drastically decreased from 2000 to 2014 because of the so-called “pause” or “hiatus” in global warming [
2], while the anthropogenic forcing accelerated. The trending divergence between data and the GCM simulations during this period has been claimed to be due to natural oscillations not captured by the models [
11,
30,
31,
32]. Finally, I will use the global aggregated impact and risk assessments assuming low to no adaptation adopted by the IPCC [
1], which are defined as a function of global surface temperature. For the comparisons between the data and model simulations, other climatic metrics (time periods and observables) might be considered, but for the reasons mentioned above, the proposed climatic metric seems logical and useful.
I additionally examine a selection of the surface air temperature (tas) simulations from 41 distinct CMIP6 GCMs obtained using historical forcings from 1850 to 2014 and four SSP forcing scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP5-8.5) from 2015 to 2100. The computer simulations for 37 GCMs were taken from the Supplemental Materials provided by Hausfather et al. [
5]; those for other four GCMs (AWI-CM-1-1-MR, CNRM-CM6-1-HR, FGOALS-g3, and HadGEM3-GC31-MM) were downloaded from the KNMI Climate Explorer website. The total number of the examined synthetic temperature records was 152, which is more than what was previously analyzed by Scafetta [
12,
18]. See
Figure 1.
This work does not repeat Scafetta [
12]’s thorough analysis of the statistical implications of the models’ internal variability, which was found to have a modest effect. However, it should be noticed that here each GCM is represented by four simulations, which correspond to the four Hist + SSP scenarios when they are available. The differences among the four records partially reflect the dispersion caused by the internal variability of the models because the radiative forcing functions for the period from 1980 to 2022 do not differ significantly from one another.
The Equilibrium Climate Sensitivity (ECS) and Transient Climate Response (TCR) values of the CMIP6 Global Circulation Models (GCMs) were taken from the Table 7.SM.5 of the IPCC AR6 [
3] and from the Supplementary Information of Hausfather et al. [
5]. The two sets vary slightly: see
Table A1.
The analytical method that is being suggested is comparable to Scafetta [
12,
18]’s. I will attempt to identify the three best subsets of GCMs that fall into the low, medium, and high ranges of ECS and TCR values. Then, I examine the temperature changes between 1980–1990 and 2011–2021 for model validation purposes, and the temperature changes between 1850–1899, 2045–2055, and 2090–2100 predicted by these three GCM subsets models for constraining realistic global aggregated impact and risk assessments.
3. Results
Figure 1 shows the CMIP6 GCM simulations that are being examined. Low-ECS (light color) and high-ECS models (dark color) alternate in the gradient of the curves’ hues. Each panel displays simulations made with different SSP forcing functions. The four panels unmistakably demonstrate that, as ECS increases, the models often forecast more warming for the twenty-first century.
Table A1 lists the names of the 41 CMIP6 GCM models with their Equilibrium Climate Sensitivity (ECS) and Transient Climate Response (TCR) values of the CMIP6 Global Circulation Models (GCMs). The ECS-150 and TCR records suggested by Hausfather et al. [
5] appear to be the most comprehensive and will be the preferred ECS and TCR values for the upcoming statistics and tables.
Figure 2 compares the ECS versus TCR values of the CMIP6 Global Circulation Models (GCMs).
Figure 2A uses the data listed in the AR6 Table 7.SM.5 [
3].
Figure 2B uses the data listed in the Supplementary Information of Hausfather et al. [
5]. The regression analysis presented in the figure demonstrates a positive correlation between ECS and TCR, indicating that when ECS increases, TCR increases as well. The IPCC records, however, contain an anomaly for KACE-1-0-G that exhibits an exceptionally low TCR despite a high ECS (panel A) (ECS = 4.48
C, TCR = 1.41
C). These apparently anomalous values seem to have been corrected in Hausfather et al. [
5] (KACE-1-0-G: ECS = 4.75
C, TCR = 2.04
C).
Figure 3 displays the temperature changes for the CMIP6 Global Circulation Models (GCMs) from 1980–1990 to 2011–2021 using panel (A), the ECS–150 values, and panel (B), the TCR values, from Hausfather et al. [
5].
Table A2 summarizes the information for each model. Cyan boxes represent the warming ranges shown by the global surface temperature records (T2m), from 0.52 to 0.59
C, and by the lower troposphere UAH-MSU-lt v6 record (ST), from 0.39 to 0.41
C.
Figure 3A largely replicates the outcomes reported by Scafetta [
12,
18], with a few minor variations.
The radiative forcing functions (Hist+SSP scenarios) throughout the studied period (1980–2021) are almost equal, and the variations in the simulations for the four SSP scenarios for each model roughly reflect the internal variability of the models themselves, as also noted by Scafetta [
12,
18]. Thus,
Figure 3 and
Table A2 demonstrate that the performance of the models dramatically declines as ECS or TCR rise. Generally speaking, only the sub-ensembles of GCMs with low-ECS and low-TCR GCM seem to fit the observations best.
CNRM-ESM2-1 and IPSL-CM6A-LR are two high-ECS models that seem to match the global surface temperature record from 1980 to 2021. However, CNRM-ESM2-1 appears to match the data because it has a low TCR despite having a high ECS (ECS = 4.79 C, TCR = 1.83 C). IPSL-CM6A-LR seems to be a bit of an outlier (ECS = 4.70 C, TCR = 2.35 C).
Figure 3 also demonstrates that if the lower troposphere UAHMSU-lt (ST) more closely mimics the actual warming, almost all GCMs would have overpredicted the warming from 1980–1990 to 2011–2021. In this case, CAMS-CSM1-0 (ECS = 2.29
C, TCR = 1.73
C) would be the only model that seems to match the temperature data.
Figure 3 suggests that, in accordance with low, medium, and high ECS and TCR ranges, the CMIP6 models can be divided into low, medium, and high climate sensitivity groups. However, only the low-sensitivity GCM sub-ensemble appears to best suit the surface temperature data and might be utilized for policy. The three ranges could be chosen as: low-ECS 1.83–3.02
C, low-TCR 1.22–1.83
C; medium-ECS 3.02–4.36
C, medium-TCR 1.90–2.35
C; high-ECS 4.66–5.64
C, high-TCR 2.46–2.77
C.
Table A3 and
Table A4 report the temperature change from 1850–1899 to 2045–2055 and 2090–2100, respectively, for the CMIP6 Global Circulation Models (GCMs) using the ranking of the ECS-150 and TCR values from Hausfather et al. [
5]. The tables show that the warming hindcasted by the models increases along with an increase in ECS and TCR. The Min–Max intervals for each of the three ECS sub-ensembles are listed in
Table A5 for the four Hist + SSP scenarios and for the temperature change from 1850 to 1899 to 2045 to 2055 and 2090 to 2100 that were produced using the CMIP6 GCMs.
Figure 4 shows the same warming ranges using boxplots that also demonstrates that the TCR-based ranges tend to be better separated from one another, supporting the possibility that a TCR-based selection could be better suitable than the ECS-based one.
5. Discussion and Conclusions
The low ECS and TCR GCM sub-ensembles seem to be the group that does the greatest job in hindcasting the warming reported from 1980–1990 to 2011–2021 by the global surface temperature records usually used to assess global warming, as shown in
Figure 3.
The decision to adopt a specific metric (the global temperature change from 1980–1990 to 2011–2021) to assess GCM performance was not arbitrary. It considered the time period with the lowest statistical uncertainty in the data, the availability of alternative temperature records (such as the satellite ones for an indirect comparison), the potential implication for long-range oscillating patterns (such as the effect of a quasi 60-year cycle [
30,
32,
52,
60]), and the fact that the global surface temperature is the most significant global climatic index, which is also directly related to the global aggregated impact and risk assessments assuming low to no adaptation [
1]. Additionally, it may be fair to select models that better predict historical global warming when formulating policies to address the risks associated with climate change in the coming decades.
The model hindcasts appear to fail for the GCM sets with both the medium and high ECS or TCR, making these models inappropriate for directing climate change policy to address future climate change dangers. A TCR-based choice might even be more appropriate, as shown in
Figure 4. The findings suggest that a GCM sub-ensemble comprised of 14 low-ECS GCMs (1.83–3.02
C) or 16 low TCR GCMs (1.22–1.83
C) on the 41 examined CMIP6 GCMs could be employed most effectively for climate change policy.
By merging the two sets, the best performing GCM sub-ensemble should be made of 17 GCMs, which are: FGOALS-f3-L, CNRM-ESM2-1, MPI-ESM1-2-LR, GISS-E2-1-G, CAMS-CSM1-0, MRI-ESM2-0, IITM-ESM, MPI-ESM1-2-HR, GFDL-ESM4, MIROC6, BCC-CSM2-MR, FGOALS-g3, NorESM2-LM, MIROC-ES2L, INM-CM5-0, INM-CM4-8, and NorESM2-MM. The average simulations by these 17 GCMs are depicted in
Figure 6.
Table A5 and
Figure 4 demonstrate how choosing GCM sub-ensembles significantly affects the GCM predicted warming for the 21st century. For example, by using the Hist-SSP2-4.5 and Hist-SSP3-7.0 scenarios and selecting the low-ECS range, the predicted warming for 2045–2055 varies from 1.41 to 2.46
C; selecting the medium-ECS range, the predicted warming for 2045–2055 varies from 1.85 to 2.68
C; and selecting the high-ECS range, the predicted warming for 2045–2055 varies from 1.95 to 3.61
C. Similarly, by selecting the low-TCR range, the predicted warming for 2045–2055 varies from 1.41 to 2.21
C; selecting the medium-TCR range, the predicted warming for 2045–2055 varies from 2.00 to 3.15
C; and selecting the high-TCR range, the predicted warming for 2045–2055 varies from 2.22 to 3.61
C.
These differences are significant because local climate adaptation strategies should be adequate to manage any form of climate change danger if the expected warming for 2045–2055 is, let us say, 1.4–2.5 °C [
1]. This result is also confirmed in
Figure 4, which also shows the global aggregated impact and risk assessments assuming low to no adaptation [
1]. This risk scale measures the impacts on socio-ecological systems that can be aggregated globally into a single metric, such as monetary damages, lives affected, species lost, or ecosystem degradation at a global scale.
However, a crucial issue is still open. If the lower troposphere UAH-MSU-lt v6 record more precisely reproduces the warming that really happened from 1980 to 2021, then the only CMIP6 model that would seem to fit the temperature data would be CAMS-CSM1-0 (ECS = 2.29
C, TCR = 1.73
C). In general, all of the CMIP6 GCMs seem to have a persistent warming bias in the tropospheric layers [
7,
8] and, actually, they fail in many climatic hindcasts (e.g. they poorly reproduce the Northern Hemisphere snow-cover trends from 1967 to 2018 [
61]). In this situation, all the CMIP6 GCMs would be inadequate and even misleading to serve as a guide for climate change policies for the twenty-first century because to agree with the actual observations, the low ECS or TCR GCM simulations should be reduced, on average, by one-third, which would also drastically reduce their warming forecasts for the 21st century and, consequently, the relative climatological risk assessments [
12].
Finally,
Section 4 discusses a few points that could call into doubt how much the global surface temperature has been warming. In fact, there are several indications that a global warming has really taken place during the past 150 years, albeit it may have been less than the 1.09 °C indicated by the official global surface temperature data from 1850–1900 to 2011–2020 [
3]. The reported warming may have been overestimated due to urban heat biases and other local influences that might have skewed the data [
27,
28,
40]. The presented evidences briefly discuss and compare the global surface temperature records against a number of alternative temperature reconstructions from lower troposphere satellite measurements, tree-ring-width chronologies, and surface temperature records based on rural stations alone. Thus, it is possible, as claimed by McKitrick and Christy [
7], that the actual ECS and TCR could be lower than what is simulated by the CMIP6 GCMs. Very low ECS and TCR values (around 0.5–2.0
C) are actually suggested by some authors [
30,
32,
56,
57,
58,
59], and this eventuality should be further investigated. If true, new climate models could be required to develop reliable climate change policies for the twenty-first century.