We use the Empirical Model of Global Climate (EM-GC) to show that human activity has been responsible for ~0.14 °C/decade (range: 0.08 to 0.20) of warming from 1979 to 2010. This EM-GC based quantification of Attributable Anthropogenic Warming Rate (AAWR) is constrained by the observed global mean surface temperature and ocean heat content records; the largest contribution to the uncertainty in our estimate of AAWR is imprecise knowledge of the radiative forcing due to tropospheric aerosols (AER RF). Our value of AAWR is noticeably lower than the mean value from the IPCC 2013 models, 0.22 °C/decade (range: 0.08 to 0.32) with no overlap of interquartile ranges. We also compute probabilistic forecasts of the rise in GMST where again the largest source of uncertainty is AER RF, and cast results in terms of the likelihood of achieving either 1.5 °C or 2.0 °C warmings relative to pre-industrial. We show that the likelihoods of limiting global warming to 2°C are 92%, 50%, and 20% if greenhouse gases follow the RCP 2.6, 4.5, and 6.0 scenarios; the likelihoods of limiting warming to 1.5°C drop to 67%, 10%, and 0.1% for these same three RCPs. Warming forecasts based upon our EM-GC are more optimistic than found by CMIP5 GCMs, following how many GCMs exhibit faster warming than inferred from the recent climate record. Our EM-GC forecasts show that aggressive controls on emissions of both CO₂ and CH₄ starting this decade are needed to limit global warming to 1.5°C with high probability.