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The sixth phase of the Coupled Model Intercomparison Project (CMIP6) is the latest modeling effort for general circulation models to simulate and project various aspects of climate change. Many of the general circulation models (GCMs) participating in CMIP6 provide archived output that can be used to calculate effective climate sensitivity (ECS) and forecast future temperature change based on emissions scenarios from several Shared Socioeconomic Pathways (SSPs). Here we use our multiple linear regression energy balance model, the Empirical Model of Global Climate (EM-GC), to simulate and project changes in global mean surface temperature (GMST), calculate ECS, and compare to results from the CMIP6 multi-model ensemble. An important aspect of our study is a comprehensive analysis of uncertainties due to radiative forcing of climate from tropospheric aerosols (AER RF) in the EM-GC framework. We quantify the attributable anthropogenic warming rate (AAWR) from the climate record using the EM-GC and use AAWR as a metric to determine how well CMIP6 GCMs replicate human-driven global warming over the last 40 years. The CMIP6 multi-model ensemble indicates a median value of AAWR over 1975–2014 of 0.221 ∘C per decade (range of 0.151 to 0.299 ∘C per decade; all ranges given here are for 5th and 95th confidence intervals), which is notably faster warming than our median estimate for AAWR of 0.157 ∘C per decade (range of 0.120 to 0.195 ∘C per decade) inferred from the analysis of the Hadley Centre Climatic Research Unit version 5 data record for GMST. Estimates of ECS found using the EM-GC assuming that climate feedback does not vary over time (best estimate 2.33 ∘C; range of 1.40 to 3.57 ∘C) are generally consistent with the range of ECS of 1.5 to 4.5 ∘C given by the IPCC's Fifth Assessment Report. The CMIP6 multi-model ensemble exhibits considerably larger values of ECS (median 3.74 ∘C; range of 2.19 to 5.65 ∘C). Our best estimate of ECS increases to 3.08 ∘C (range of 2.23 to 5.53 ∘C) if we allow climate feedback to vary over time. The dominant factor in the uncertainty for our empirical determinations of AAWR and ECS is imprecise knowledge of AER RF for the contemporary atmosphere, though the uncertainty due to time-dependent climate feedback is also important for estimates of ECS. We calculate the likelihood of achieving the Paris Agreement target (1.5 ∘C) and upper limit (2.0 ∘C) of global warming relative to pre-industrial for seven of the SSPs using both the EM-GC and the CMIP6 multi-model ensemble. In our model framework, SSP1-2.6 has a 53 % probability of limiting warming at or below the Paris target by the end of the century, and SSP4-3.4 has a 64 % probability of achieving the Paris upper limit. These estimates are based on the assumptions that climate feedback has been and will remain constant over time since the prior temperature record can be fit so well assuming constant climate feedback. In addition, we quantify the sensitivity of future warming to the curbing of the current rapid growth of atmospheric methane and show that major near-term limits on the future growth of methane are especially important for achievement of the 1.5 ∘C goal of future warming. We also quantify warming scenarios assuming climate feedback will rise over time, a feature common among many CMIP6 GCMs; under this assumption, it becomes more difficult to achieve any specific warming target. Finally, we assess warming projections in terms of future anthropogenic emissions of atmospheric carbon. In our model framework, humans can emit only another 150±79 Gt C after 2019 to have a 66 % likelihood of limiting warming to 1.5 ∘C and another 400±104 Gt C to have the same probability of limiting warming to 2.0 ∘C. Given the estimated emission of 11.7 Gt C per year for 2019 due to combustion of fossil fuels and deforestation, our EM-GC simulations suggest that the 1.5 ∘C warming target of the Paris Agreement will not be achieved unless carbon and methane emissions are severely curtailed in the next 10 years.