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Complex Earth System Models are widely utilised to make conditionalstatements about the future climate under some assumptions about changes infuture atmospheric greenhouse gas concentrations; these statements are oftenreferred to as climate projections. The models themselves are high-dimensionalnonlinear systems and it is common to discuss their behaviour in terms ofattractors and low-dimensional nonlinear systems such as the canonical Lorenz`63 system. In a non-autonomous situation, for instance due to anthropogenicclimate change, the relevant object is sometimes considered to be the pullbackor snapshot attractor. The pullback attractor, however, is a collection of {\emall} plausible states of the system at a given time and therefore does not takeinto consideration our knowledge of the current state of the Earth System whenmaking climate projections, and are therefore not very informative regardingannual to multi-decadal climate projections. In this article, we approach theproblem of measuring and interpreting the mid-term climate of a model by usinga low-dimensional, climate-like, nonlinear system with three timescales ofvariability, and non-periodic forcing. We introduce the concept of an {\emevolution set} which is dependent on the starting state of the system, andexplore its links to different types of initial condition uncertainty and therate of external forcing. We define the {\em convergence time} as the time thatit takes for the distribution of one of the dependent variables to lose memoryof its initial conditions. We suspect a connection between convergence timesand the classical concept of mixing times but the precise nature of thisconnection needs to be explored. These results have implications for the designof influential climate and Earth System Model ensembles, and raise a number ofissues of mathematical interest.

The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example