The early Eocene, from about 56 Ma, with high atmospheric CO<sub>2</sub> levels, offers an analogue for the response of the Earth's climate system to anthropogenic fossil fuel burning. In this study we present an ensemble of 50 Earth system model runs with an early Eocene palaeogeography and variation in the forcing values of atmospheric CO<sub>2</sub> and the Earth's orbital parameters. Two-dimensional model output fields are reduced to scalar values through simple summarising algorithms and by singular value decomposition. Relationships between these scalar results and the forcing parameters are identified by linear modelling, providing estimates of the relative magnitudes of the effects of atmospheric CO<sub>2</sub> and each of the orbital parameters on important climatic features, including tropical-polar temperature difference, ocean-land temperature contrast, and Asian, African and S. American monsoon rains. Our results indicate that although CO<sub>2</sub> exerts a dominant control on most of the climatic features examined in this study, the orbital parameters also strongly influence important components of the ocean-atmosphere system in a greenhouse Earth. In our ensemble, atmospheric CO<sub>2</sub> spans the range 280–3000 ppm, and this variation accounts for over 95 % of the effects on mean air temperature, southern winter high-latitude ocean-land temperature contrast and northern winter tropical-polar temperature difference. However, the variation of precession accounts for over 75 % of the influence of the forcing parameters on the Asian and African monsoon rainfall, and obliquity variation accounts for over 65 % of the effects on winter ocean-land temperature contrast in high northern latitudes. Our method gives a quantitative ranking of the influence of each of the forcing parameters on key climatic model outputs, with additional spatial information from our singular value decomposition approach providing insights into likely physical mechanisms. The results demonstrate the importance of orbital variation as an agent of change in climates of the past.