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Simple climate models can be valuable if they are able to replicate aspects of complex fully coupled earth system models. Larger ensembles can be produced, enabling a probabilistic view of future climate change. A simple emissions-based climate model, FAIR, is presented which calculates atmospheric concentrations of greenhouse gases and effective radiative forcing (ERF) from greenhouse gases, aerosols, ozone precursors and other agents. The ERFs are integrated into global mean surface temperature change. Model runs are constrained to observed temperature change from 1880 to 2016 and produce a range of future projections under the Representative Concentration Pathway (RCP) scenarios. For the historical period the ERF time series in FAIR emulates the results in the IPCC Fifth Assessment Report (AR5), whereas for RCP historical and future scenarios, the greenhouse gas concentrations in FAIR closely track the observations and projections in the RCPs. The constrained estimates of equilibrium climate sensitivity (ECS) of 2.79 (1.97 to 4.08) K, transient climate response (TCR) of 1.47 (1.03 to 2.23) K and transient climate response to cumulative CO2 emissions (TCRE) of 1.43 (1.01 to 2.16) K (1000 GtC)-1 (median and 5-95 % credible intervals) are in good agreement, with tighter uncertainty bounds, than AR5 (1.5 to 4.5 K, 1.0 to 2.5 K, and 0.8 to 2.5 K respectively). The ranges of future projections of temperature and ranges of estimates of ECS, TCR and TCRE are moderately sensitive to the historical temperature dataset used to constrain, prior distributions of ECS/TCR parameters, aerosol radiative forcing relationship and ERF from a doubling of CO2. Taking these sensitivities into account, there is no evidence to suggest that the median and credible range of observationally constrained TCR or ECS differ from climate model-derived estimates. However, the range of temperature projections under the RCP scenarios for 2081-2100 in the constrained FAIR model ensemble are lower than the emissions-based estimates reported in AR5. [ABSTRACT FROM AUTHOR]