Global temperature responses from different abrupt CO2 change experiments participating in Coupled Model Intercomparison Project Phase 6 (CMIP6) and LongRunMIP are systematically compared in order to study the linearity of the responses. For CMIP6 models, abrupt-4xCO2 experiments warm on average 2.2 times more than abrupt-2xCO2 experiments. A factor of about 2 can be attributed to the differences in forcing, and the rest is likely due to nonlinear responses. Abrupt-0p5xCO2 responses are weaker than abrupt-2xCO2, mostly because of weaker forcing. CMIP6 abrupt CO2 change experiments respond linearly enough to well reconstruct responses to other experiments, such as 1pctCO2, but uncertainties in the forcing can give uncertain responses. We derive also a generalised energy balance box model that includes the possibility of having oscillations in the global temperature responses. Oscillations are found in some models, and are connected to changes in ocean circulation and sea ice. Oscillating components connected to a cooling in the North Atlantic can counteract the long-term warming for decades or centuries and cause pauses in global temperature increase.

A new algorithm is proposed for estimating time-evolving global forcing in climate models. The method is a further development of the work of Forster et al. (2013), taking into account the non-constancy of the global feedbacks. We assume that the non-constancy of this global feedback can be explained as a time-scale dependence, associated with linear temperature responses to the forcing on different time scales. With this method we obtain stronger forcing estimates than previously assumed for the representative concentration pathway experiments in the Coupled Model Intercomparison Project Phase 5 (CMIP5). The reason for the higher future forcing is that the global feedback parameter is more negative at shorter time scales than at longer time scales, consistent with the equilibrium climate sensitivity increasing with equilibration time. Our definition of forcing provides a clean separation of forcing and response, and we find that linear temperature response functions estimated from experiments with abrupt quadrupling of CO$_2$ can be used to predict responses also for future scenarios. In particular, we demonstrate that for most models, the response to our new forcing estimate applied on the 21st century scenarios provides a global surface temperature up to year 2100 consistent with the output of coupled model versions of the respective model.

We present new estimates of the forcing for models participating in Coupled Model Intercomparison Project 6 (CMIP6) by applying the method developed in Fredriksen et al. (2021). Validating our approach, these estimates are overall consistent with the fixed-SST estimates available for a small subset of the models. We estimate forcing for experiments with abrupt changes of CO2, 1% increase of CO2, historical forcings, and future scenarios. Furthermore, we compare our new estimates to CMIP5 forcing, and demonstrate that CMIP6 forcing is lower than CMIP5 forcing at the end of the historical period, but grows faster than CMIP5 in the future scenarios, ending up at higher levels than CMIP5 at the end of the 21st century. The radiative efficiency of CO2 has not changed, suggesting that the stronger future increase in CO2 concentrations in CMIP6 compared to CMIP5 explains the forcing difference.

We examine the response of the Community Earth System Model versions 1 and 2 (CESM1 and CESM2) to abrupt quadrupling of atmospheric CO$_2$ concentrations (4xCO2) and to 1% annually increasing CO2 concentrations (1%CO2). Different estimates of equilibrium climate sensitivity (ECS) for CESM1 and CESM2 are presented. All estimates show that the sensitivity of CESM2 has increased by 1.5K or more over that of CESM1. At the same time the transient climate response (TCR) of CESM1 and CESM2 derived from 1%CO2 experiments has not changed significantly - 2.1K in CESM1 and 2.0K in CESM2. Increased initial forcing as well as stronger shortwave radiation feedbacks are responsible for the increase in ECS seen in CESM2. A decomposition of regional radiation feedbacks and their contribution to global feedbacks shows that the Southern Ocean plays a key role in the overall behavior of 4xCO2 experiments, accounting for about 50% of the total shortwave feedback in both CESM1 and CESM2. The Southern Ocean is also responsible for around half of the increase in shortwave feedback between CESM1 and CESM2, with a comparable contribution arising over tropical ocean. Experiments using a thermodynamic slab-ocean model (SOM) yield estimates of ECS that are in remarkable agreement with those from fully-coupled earth system model (ESM) experiments for the same level of CO2 increase. Finally, we show that the similarity of TCR in CESM1 and CESM2 masks significant regional differences in warming that occur in the 1%CO2 experiments for each model.

The latest generation of coupled models, the sixth Coupled Models Intercomparison Project (CMIP6), is used to study the changes in the El Niño Southern Oscillation (ENSO) in a warming climate. For the four future scenarios studied, the sea surface temperature variability increases in most CMIP6 models, but to varying degrees. This increase is linked to a weakening of the east-west temperature gradient in the tropical Pacific Ocean, which is evident across all models. Just as in previous generations of climate models, we find that many characteristics of future ENSO remain uncertain. This includes changes in dominant timescale, extra-tropical teleconnection patterns and amplitude of El Niño and La Niña events. For models with the strongest increase in future variability, the majority of the increase happens in the Eastern Pacific, where the strongest El Niño events usually occur.