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Simulations of the CMIP6 historical period 1850–2014, characterized by the emergence of anthropogenic climate drivers like greenhouse gases, are presented for different configurations of the NASA Goddard Institute for Space Studies (GISS) Earth System ModelE2.1. The GISS‐E2.1 ensembles are more sensitive to greenhouse gas forcing than their CMIP5 predecessors (GISS‐E2) but warm less during recent decades due to a forcing reduction that is attributed to greater longwave opacity in the GISS‐E2.1 pre‐industrial simulations. This results in an atmosphere less sensitive to increases in opacity from rising greenhouse gas concentrations, demonstrating the importance of the base climatology to forcing and forced climate trends. Most model versions match observed temperature trends since 1979 from the ocean to the stratosphere. The choice of ocean model is important to the transient climate response, as found previously in CMIP5 GISS‐E2: the model that more efficiently exports heat to the deep ocean shows a smaller rise in tropospheric temperature. Model sea level rise over the historical period is traced to excessive drawdown of aquifers to meet irrigation demand with a smaller contribution from thermal expansion. This shows how fully coupled models can provide indirect observational constraints upon forcing, in this case, constraining irrigation rates with observed sea level changes. The overall agreement of GISS‐E2.1 with observed trends is familiar from evaluation of its predecessors, as is the conclusion that these trends are almost entirely anthropogenic in origin. Plain Language Summary: Measurements show clear evidence of warming over the twentieth century and up to the present day. Our anticipation of future change comes from computer models of climate. These are based upon well‐established physical principles like Newton's laws of motion and radiative transfer theory; the models are closely related to those used for weather forecasting. We can never predict the weather on a particular day, 50 years in the future, but we can calculate whether that future decade will be warmer than our present climate. Part of our confidence in such a forecast comes from testing a climate model's ability to reproduce warming and other changes measured over the past century. We use observations of atmospheric composition and the sunlight received by our planet to calculate how the model responds to their changes. The climate model of the NASA Goddard Institute for Space Studies, GISS‐E2.1, closely follows changes measured in the ocean and atmosphere as the concentrations of greenhouse gases and other pollutants rise. This agreement suggests that future warming by greenhouse gases will be reliably predicted by GISS‐E2.1. This suggests that the warming we already experience is due to our consumption of fossil fuels that has led to the increase of carbon dioxide and other greenhouse gases in the atmosphere over the past two centuries. Key Points: Tropospheric warming and ocean heat uptake by 2014 are smaller in GISS‐E2.1 and closer to observed trends than in its CMIP5 predecessorGISS‐E2.1 climate sensitivity is higher than in CMIP5 GISS‐E2, but forcing by greenhouse gases is smallerAtmospheric trends vary among model configurations with the storage of heat beneath the thermocline [ABSTRACT FROM AUTHOR]