  Complex Earth System Models are widely utilised to make conditional
statements about the future climate under some assumptions about changes in
future atmospheric greenhouse gas concentrations; these statements are often
referred to as climate projections. The models themselves are high-dimensional
nonlinear systems and it is common to discuss their behaviour in terms of
attractors and low-dimensional nonlinear systems such as the canonical Lorenz
`63 system. In a non-autonomous situation, for instance due to anthropogenic
climate change, the relevant object is sometimes considered to be the pullback
or snapshot attractor. The pullback attractor, however, is a collection of {\em
all} plausible states of the system at a given time and therefore does not take
into consideration our knowledge of the current state of the Earth System when
making climate projections, and are therefore not very informative regarding
annual to multi-decadal climate projections. In this article, we approach the
problem of measuring and interpreting the mid-term climate of a model by using
a low-dimensional, climate-like, nonlinear system with three timescales of
variability, and non-periodic forcing. We introduce the concept of an {\em
evolution set} which is dependent on the starting state of the system, and
explore its links to different types of initial condition uncertainty and the
rate of external forcing. We define the {\em convergence time} as the time that
it takes for the distribution of one of the dependent variables to lose memory
of its initial conditions. We suspect a connection between convergence times
and the classical concept of mixing times but the precise nature of this
connection needs to be explored. These results have implications for the design
of influential climate and Earth System Model ensembles, and raise a number of
issues of mathematical interest.
