It may be argued that it is a necessary, though insufficient, criterion that climate models accurately reproduce the observed historical evolution of the global-mean surface temperature anomaly to lend credibility to model-based projections of future warming. Therefore, it was surprising that the latest generation of global climate models from the Coupled Model Intercomparison Project Phase 6 (CMIP6) exhibits a suppressed warming in the mid-20th century relative to the previous generation Phase 5 models (CMIP5) and to the observed historical temperature evolution (Fig. ). The CMIP5 ensemble-mean historical warming evolution is in much better agreement with the observations than the CMIP6 ensemble-mean for much of the 20th century, and particularly during the mid-century period after a warming signal has already emerged.

We suspected that stronger forcing from anthropogenic aerosols in CMIP6 relative to CMIP5 is primarily responsible for the suppressed mid-century warming . Other studies have also suggested stronger aerosol forcing as a partial or primary cause of the suppressed warming in individual models or types of models that participated in CMIP6 . Anthropogenic aerosols produce a net negative forcing and thus induce a cooling response, such that a too-strong aerosol forcing in CMIP6 appeared as a likely cause of the suppressed warming. The larger atmospheric anthropogenic aerosol burden during the pre-1970s period strongly influenced the response of the global-mean surface temperature, after which stricter air quality regulations began to reduce the aerosol burden . However, the strength of the aerosol forcing remains highly uncertain, with recent assessments estimating that the net present-day aerosol forcing falls within a likely range of -1.6 to -0.6 W m-2 or -2.0 to -0.6 W m-2 , based on multiple lines of evidence. This range is in line with previous estimates of the net aerosol forcing based on the previous CMIP generations of models and from the IPCC Fourth Assessment Report, which displayed similarly large ranges for the aerosol forcing , indicating that the uncertainty has not decreased substantially over time. The range of net aerosol forcing estimated for CMIP6 models in this study (Fig. ; Table ) and in does not diverge from previous assessments. To address this uncertainty, developed a simple model for the aerosol forcing and argued that a net forcing stronger than -1.0 W m-2 is incompatible with the warming signal observed between 1850 and 1950 and that the net forcing likely lies in the range -1.0 to -0.3 W m-2. This estimate was disputed by and , arguing that the comparison of the simple model to global climate models is flawed and that aerosol forcing stronger than -1.0 W m-2 remains plausible. updated the model developed by , including modifications based on and , and indeed found that aerosol forcing stronger than -1.0 W m-2 was consistent with the historical warming.

Aerosols may affect the radiation balance through aerosol–radiation interactions (ARIs), or the scattering and absorption of radiation directly by aerosols, and through the indirect aerosol–cloud interactions (ACIs). The ACIs include the aerosol–cloud albedo effect, also known as the first indirect or Twomey effect , and the aerosol–cloud lifetime effect, or the second indirect effect ; these interactions exist for all cloud phases. In the course of model development between CMIP5 and CMIP6, many modeling groups included ACIs in the newer versions of their models for the first time or modified their model's ACIs (; CNRM-CM6-1, ; E3SMv1, ; CESM2, ; HadGEM3-GC3.1, ; MPI-ESM1.2, ). Additionally, more CMIP6 models included ACIs for liquid clouds than for ice clouds (Table ). Recent evidence has indicated that the response to anthropogenic aerosols, in particular ACIs, may account for the suppressed warming in some CMIP6 models, rather than a stronger aerosol forcing alone. obtained a colder 20th century temperature evolution in CanESM5 using the CMIP5 rather than the CMIP6 aerosol input data set, indicating the influence of the response to anthropogenic aerosol on the suppressed warming in this model, while identified ACIs as an important driver of the suppressed warming within Earth system models that participated in CMIP6. However, the net effects of ARIs and ACIs on the forcing remain highly uncertain, and indeed the spread in ACIs was found to be one of the main contributors to the spread in the net forcing itself among the CMIP6 models, with ACIs for ice clouds specifically playing a potentially important role . also argued that aerosol forcing alone is not the cause of the suppressed warming, though; in contrast, they identified a combination of stronger aerosol forcing and weaker greenhouse gas forcing, amplified by increased climate sensitivity, in the CMIP6 ensemble-mean relative to the CMIP5 ensemble mean as the cause. The cold bias during the mid-century period previously exhibited by the UKESM1 model was much improved after updates were made to its configuration, despite an absence of substantial weakening of its present-day aerosol forcing, further indicating a cause(s) of the suppressed warming beyond only the aerosol forcing strength, at least for Earth system models .

In this study, we investigate whether systematic differences exist within the CMIP6 ensemble that could explain the suppressed warming seen in the CMIP6 ensemble mean and for individual models. CMIP6 contained a range of relatively warm to relatively cold models for the mid-century period (Fig. ), allowing these models to be differentiated based on the comparison of a model's mean mid-20th century temperature anomaly to the CMIP5 and CMIP6 ensemble-mean mid-20th century anomalies, and thereby to identify potential systematic differences in aerosol forcing, ACIs, or other parameters within CMIP6 that could cause models to exhibit suppressed warming. It should be noted that a cause for the suppressed warming related to a systematic difference between the CMIP5 and CMIP6 ensembles cannot be definitively proven here. Ground work enabling the disentanglement of the various forcing agents was done in the Radiative Forcing Model Intercomparison Project (RFMIP; ), whose experiments are available for CMIP6 models but which were not performed for CMIP5 models. Model aerosol forcing therefore cannot be directly compared between the two eras, as forcings cannot be estimated in a consistent manner.

The CMIP6 ensemble analyzed here includes 36 models, as listed in Table  along with their mean mid-20th century surface temperature anomalies and various other information. Most model output was downloaded from the Earth System Federation Grid nodes; all MPI-ESM1.2-CR simulations and the fixed-SST MPI-ESM1.2-LR simulations were conducted as part of the study. The information about aerosol input type and ice cloud ACI in Table  was found in the online CMIP documentation for individual models (https://search.es-doc.org, last access: 10 October 2022) or by contacting the relevant modeling group. The equilibrium climate sensitivity (ECS) values in Table  were taken from , , and , and the method used to compute the ECS is described in those sources.

Not only is the mid-century warming in CMIP6 colder than CMIP5 and the observations (Fig. ; Table ), but the distribution of mean mid-century temperature anomalies from CMIP6 models is also shifted towards colder anomaly magnitudes relative to the CMIP5 distribution (Fig. ; Table ). The CMIP5 and CMIP6 ensemble-mean mid-century warming magnitudes are biased cold relative to the observed warming by 0.05 and 0.19 K, respectively; 31 of 36 (86 %) CMIP6 models are colder than the lower uncertainty bound of the observed mid-century warming and 2 of 36 (6 %) CMIP6 models warmer than the upper uncertainty bound, in contrast to 17 of 27 (63 %) models colder and 7 of 27 (26 %) models warmer for CMIP5. These statistics indicate that the suppressed warming is not due to the influence of one or two very cold models. Rather, at least one systematic difference between CMIP phases potentially exists that causes the suppressed warming. Because the CMIP6 individual model warming anomalies span a large range, with some models in better agreement with the observations, some in better agreement with the CMIP6 ensemble-mean anomaly, and some models much colder than all anomalies, systematic differences may exist within the CMIP6 ensemble itself that could explain the suppressed warming.

CMIP6 Block 1 (Fig. ; Table ) includes the models with the most realistic mean mid-20th century warming when compared to the observations. This is partially a consequence of the definition for Block 1, because the observational anomaly is larger than that for the CMIP5 ensemble mean. However, it is worthwhile to note this result because good agreement for one period of the warming evolution does not necessarily imply good agreement for another period. The Block 3 models in turn exhibit the least realistic mid-century warming and have a tendency to exhibit the least realistic warming in the late 20th century and early 21st century.

The three warming blocks present weak differentiation in terms of their mean present-day greenhouse gas ERF: 2.63 (±0.20), 2.91 (±0.13), and 2.89 (±0.24) W m-2, for Blocks 1, 2, and 3, respectively (Fig. ; Table ). Block 1 includes only three models that provided the necessary simulation, Block 2 includes six models, and Block 3 includes nine models, so care must again be taken with these results. This suggests very tentatively that Block 1 models exhibit less greenhouse gas forcing, in light of the standard deviations and small sample sizes. However, if such a difference exists at all among warming blocks, then this alone would actually lead to less warming in the Block 1 models.

The range of Block 3 greenhouse gas ERF magnitudes again contains the entire range for Block 2. While Block 1 contains the smallest greenhouse gas ERF magnitude, its range also overlaps with those for Blocks 2 and 3. Block 3 appears to exhibit a correlation between the greenhouse gas forcing and mean mid-century warming, but it is not quite statistically significant at the 95 % confidence level (r=0.66, p=0.053) and is driven by the three Block 3 models with negative mean mid-20th century temperature anomalies and somewhat smaller greenhouse gas forcing magnitudes (CNRM-ESM2-1, EC-EARTH3, and UKESM1-0-LL). This suggests that a weak greenhouse gas forcing may play some role in the suppressed warming for these three very cold models specifically. However, given the lack of systematic differences among and within warming blocks, and the lack of correlations with the mid-century warming and aerosol forcing, greenhouse gas ERF again likely is not strong a cause of the suppressed mid-century warming in CMIP6.

Systematic differences also did not emerge in ECS among warming blocks, so it is unlikely that differences in climate feedbacks among CMIP6 models amplify or diminish the mid-century warming responses to aerosol or greenhouse gas forcings.

We have investigated the causes of the suppressed warming in CMIP6 models during the mid-20th century by examining the mean warming displayed by the models over the period 1940–1970. The models divide into three warming blocks based on where the model's mid-century warming falls relative to the CMIP5 and CMIP6 ensemble-mean warming, with Block 1 models displaying the warmest and most realistic mid-century warming and Block 3 displaying the coldest and least realistic warming. The distribution of mid-century temperature anomalies shows that CMIP6 is shifted colder relative to CMIP5, rather than a small number of unusually cold CMIP6 models affecting the CMIP6 ensemble mean.

We have not found a satisfactorily complete explanation for the suppressed warming in CMIP6. Model aerosol forcing appeared to be a reasonable culprit, as was suggested in earlier work. However, aerosol forcing was found to play an important but partial role: a systematically weaker aerosol ERF for the small subset of Block 1 models likely accounts for the more realistic mid-century warming seen in these models, and likewise systematically stronger aerosol ERF for the Block 2 and 3 models may partially account for the greater degree of suppressed warming seen in these models. Aerosol forcing, nevertheless, remains insufficient to explain all variations among the many cold-biased models. Greenhouse gas forcing was not found to play an important role in variations of the mid-century warming among CMIP6 models, which, however, does not rule out systematic differences in greenhouse gas forcing between CMIP6 and CMIP5 that influence the mid-century warming, such as found by . It should again be noted that some caution should be taken with these results, due to the small numbers of models that have submitted the necessary RFMIP simulations at the time of writing; we strongly encourage more models to perform these types of forcing experiments.

We established an expected relationship between aerosol forcing differences and mid-century warming based on the MPI-ESM1.2-CR model. Many Block 3 models fell far away from the expectation curve, and, while these models did not deviate as much as Block 3, the Block 2 models displayed much scatter about the expectation curve. This points to the importance of another process, or a set of processes, in addition to aerosol forcing that cause the suppressed warming. We thus investigated whether model aerosol representations could impact the model response to aerosol forcing, including the inclusion of ACIs for ice clouds and the type of aerosol input data set used by the model. However, despite initially deceiving divisions of CMIP6 models by aerosol input data set used or by whether ACIs for ice clouds were included in the model, these were ultimately not found to have any systematic difference among models in terms of the mid-century warming or aerosol forcing and thus are unlikely to be a cause of the suppressed warming. No other model aerosol configuration options emerged as a potential cause. However, this should not be taken to mean that ACIs, or even ARIs, must be completely ruled out as causes of the suppressed mid-century warming, but rather that they are not direct or obvious causes. This further potentially points to a more much subtle role for differences in aerosol representation among models that can impact representation of ACIs and ARIs within a model and thus remains a promising direction of investigation to uncover the missing causes of the suppressed mid-century warming within CMIP6.

Other possibilities remain for differences among models in terms of aerosol representation that could not be investigated here due to lack of inclusion in the CMIP documentation and a lack of otherwise easily accessible documentation. These include, among other possibilities, the complexity of the aerosol scheme in models and differences in how aerosol–cloud and aerosol–radiation interactions are represented. These additionally present a potentially promising avenue for further investigation of the causes of the suppressed warming.

Qualitatively consistently with recent estimates of the lower bound of aerosol ERF that remains consistent with observed warming, many CMIP6 models exhibit mid-century warming despite very strong aerosol forcing. Interestingly, several CMIP6 models exhibit substantially suppressed warming, or even mid-century cooling, despite an aerosol ERF weaker than the estimated lower-bound constraint of -1.0 W m-2, in contrast to previous work arguing that weaker aerosol forcing should be most consistent with realistic mid-century warming. Though the weak warming, or even global cooling, displayed by these models is unrealistic, warming should be implausible in these models or should have a smaller degree of warming suppression if the estimated lower bound were a strong constraint on the aerosol forcing. This result underscores the difficulty in constraining the aerosol forcing, due to the large number of uncertainties related to it and in aerosol interactions with other aspects of the climate system. This also highlights the need to disentangle whether models represent the historical warming evolution for the correct reasons. Our results partly undermine the hope for constructing a strong constraint on the aerosol forcing based on the mid-20th century warming, since a direct relationship with the mid-century warming does not emerge, even if the models that best matched the observed warming all did have weak aerosol forcing.