Anticipated future warming of the climate system increases the need for accurate climate projections. A central problem are the large uncertainties associated with these model projections, and that uncertainty estimates are often based on expert judgment rather than objective quantitative methods. Further, important climate model parameters are still given as poorly constrained ranges that are partly inconsistent with the observed warming during the industrial period. Here we present a neural network based climate model substitute that increases the efficiency of large climate model ensembles by at least an order of magnitude. Using the observed surface warming over the industrial period and estimates of global ocean heat uptake as constraints for the ensemble, this method estimates ranges for climate sensitivity and radiative forcing that are consistent with observations. In particular, negative values for the uncertain indirect aerosol forcing exceeding –1.2 Wm–2 can be excluded with high confidence. A parameterization to account for the uncertainty in the future carbon cycle is introduced, derived separately from a carbon cycle model. This allows us to quantify the effect of the feedback between oceanic and terrestrial carbon uptake and global warming on global temperature projections. Finally, probability density functions for the surface warming until year 2100 for two illustrative emission scenarios are calculated, taking into account uncertainties in the carbon cycle, radiative forcing, climate sensitivity, model parameters and the observed temperature records. We find that warming exceeds the surface warming range projected by IPCC for almost half of the ensemble members. Projection uncertainties are only consistent with IPCC if a model-derived upper limit of about 5 K is assumed for climate sensitivity.
