Over the past 3.5 million years, there have been several intervals when climate conditions were warmer than during the preindustrial Holocene. Although past intervals of warming were forced differently than future anthropogenic change, such periods can provide insights into potential future climate impacts and ecosystem feedbacks, especially over centennial-to-millennial timescales that are often not covered by climate model simulations. Our observation-based synthesis of the understanding of past intervals with temperatures within the range of projected future warming suggests that there is a low risk of runaway greenhouse gas feedbacks for global warming of no more than 2 °C. However, substantial regional environmental impacts can occur. A global average warming of 1-2 °C with strong polar amplification has, in the past, been accompanied by significant shifts in climate zones and the spatial distribution of land and ocean ecosystems. Sustained warming at this level has also led to substantial reductions of the Greenland and Antarctic ice sheets, with sea-level increases of at least several metres on millennial timescales. Comparison of palaeo observations with climate model results suggests that, due to the lack of certain feedback processes, model-based climate projections may underestimate long-term warming in response to future radiative forcing by as much as a factor of two, and thus may also underestimate centennial-to-millennial-scale sea-level rise.

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We perform joint nonlinear inversions of glacial isostatic adjustment (GIA) data, including the following: postglacial decay times in Canada and Scandinavia, the Fennoscandian relaxation spectrum (FRS), late‐Holocene differential sea level (DSL) highstands (based on recent compilations of Australian sea level histories), and the rate of change of the degree 2 zonal harmonic of the geopotential, J2. Resolving power analyses demonstrate the following: (1) the FRS constrains mean upper mantle viscosity to be ∼3 × 1020 Pa s, (2) postglacial decay time data require the average viscosity in the top ∼1500 km of the mantle to be 1021 Pa s, and (3) the J2 datum constrains mean lower mantle viscosity to be ∼5 × 1021 Pa s. To reconcile (2) and (3), viscosity must increase to 1022–1023 Pa s in the deep mantle. Our analysis highlights the importance of accurately correcting the J2 observation for modern glacier melting in order to robustly infer deep mantle viscosity. We also perform a large series of forward calculations to investigate the compatibility of the GIA data sets with a viscosity jump within the lower mantle, as suggested by geodynamic and seismic studies, and conclude that the GIA data may accommodate a sharp jump of 1–2 orders of magnitude in viscosity across a boundary placed in a depth range of 1000–1700 km but does not require such a feature. Finally, we find that no 1‐D viscosity profile appears capable of simultaneously reconciling the DSL highstand data and suggest that this discord is likely due to laterally heterogeneous mantle viscosity, an issue we explore in a companion study.