Climatic Change provide robust output to characterize global atmospheric CO2, CH4, radiative forcing, GMST (Allen et al. 2009; Meinshausen et al. 2011; Myhre et al. 2013a), and GSL. This approach allows for natural and anthropogenic forcings to be included or excluded to test the relative contributions from anthropogenic emissions at policy-relevant levels of uncertainty. The model used here is based on the impulse response function approach presented in the IPCC fifth assessment report (AR5) and earlier publications (Joos et al. 2013; Myhre et al. 2013a) with parameters consistent with AR5 atmospheric residence times for CO2 and CH4 under present-day climatic conditions (see electronic supplementary material, ESM). The primary extension of the AR5 impulse-response model is the inclusion of a term scaling the time constants of the CO2 impulse-response by a parameter that scales linearly with GMST anomaly and cumulative carbon uptake by the land and ocean (Millar et al. 2016). The model was forced with natural and anthropogenic historical forcings, as detailed in ESM. In order to calculate contribution to GMST, the model also incorporates the Heede (2014) CH4 data for emissions traced back to carbon producers (ESM). Excluding the six producers that only manufacture cement, the average CH4 contribution to total (CH4 + CO2) emissions traced to each carbon producer is ∼8% (n = 84). The changes in GMST were then used to calculate the rate of GSL rise using the comprehensive semi-empirical modeling of Kopp et al. (2016). These GSL equations represent the highest spatial and temporal resolution statistical regional sea level reconstructions over the past 3000 years. Kopp et al. (2016) effectively extract the three components operating on varying timescales (1) GSL primarily from ocean thermal expansion and land ice volume changes, (2) regional shifts from slowly changing glacial isostatic adjustment, tectonics, and sediment shifts, and (3) temporally nonlinear changes such as ocean/atm dynamics. 2.3 Sensitivity tests Sensitivity tests examined three sources of uncertainty: (1) climate sensitivity, (2) lack of available data on aerosol emissions from fossil fuel combustion that could be directly traced back to individual carbon producers, and (3) removal order of carbon producers. Sensitivity tests evaluated the nonlinear feedback between thermal and carbon parameters using the low and high range of equilibrium climate sensitivity and transient climate response (ESM Tables 1 and 2). For example, equilibrium climate sensitivity (GMST at equilibrium with a doubling of atmospheric CO2 concentration) is set to the low (1.5 °C) and high (4.5 °C) values of the AR5 high confidence range (IPCC 2013). The full range of possible values for climate sensitivity and other parameters was evaluated and presented in ESM. Here, we present highlight results from best estimate parameter simulations that reflect the historical observations. In a non-linear model, the order of removal of contributions to total emissions has a potential influence on percent contributions. The range of this influence was assessed; error bars for model results represent the influence of removing each carbon producer first or last for the described set of carbon, and thermal parameters and forcing. Fossil fuel combustion releases aerosols (Shindell and Faluvegi 2010). Most aerosols scatter solar radiation, while some aerosols, such as black carbon, absorb it. The net result is that aerosols partially offset the historical greenhouse gas forcing of GMST increase (Myhre et al. 2013b). Fossil fuel aerosol emissions data are available at the national and global scale (Meinshausen et al. 2011); however, we are not aware of data tracing aerosols directly to specific carbon producers. To examine this source of uncertainty, we investigated four categories of climate simulations: (1) full historical forcing (i.e. all natural and anthropogenic forcing), (2) full historical forcing minus