  Climate response metrics are used to quantify the Earth's climate response to
anthropogenic changes of atmospheric CO2. Equilibrium Climate Sensitivity (ECS)
is one such metric that measures the equilibrium response to CO2 doubling.
However, both in their estimation and their usage, such metrics make
assumptions on the linearity of climate response, although it is known that,
especially for larger forcing levels, response can be nonlinear. Such nonlinear
responses may become visible immediately in response to a larger perturbation,
or may only become apparent after a long transient. In this paper, we
illustrate some potential problems and caveats when estimating ECS from
transient simulations. We highlight ways that very slow timescales may lead to
poor estimation of ECS even if there is seemingly good fit to linear response
over moderate timescales. Moreover, such slow timescale might lead to late
abrupt responses ("late tipping points") associated with a system's
nonlinearities. We illustrate these ideas using simulations on a global energy
balance model with dynamic albedo. We also discuss the implications for
estimating ECS for global climate models, highlighting that it is likely to
remain difficult to make definitive statements about the simulation times
needed to reach an equilibrium.
