We study the suitability of an initial condition ensemble to form the conceptual basis of defining climate. We point out that the most important criterion is the uniqueness of the probability measure on which the definition relies. We first propose, in harmony with earlier work, to represent such a probability measure by the distribution of ensemble members that have converged to the probability density of the natural probability measure of the so-called snapshot or pullback attractor of the dynamics, which is time dependent in the presence of external forcing. Then we refine the proposal by taking a density that is conditional on the (possibly time-evolving) state of system components with time scales longer than the horizon of a particular study. We discuss the applicability of such a definition in the Earth system and its realistic models, and conclude that micro initialization from observations in slower system components perhaps provides the practically relevant probability density after a few decades of convergence. However, the absence of sufficient time scale separation between system components or regime transitions in slower system components might preclude uniqueness, at least in certain subsystems, and time evolution in slower system components might induce unforced climate changes, leading to the need for targeted investigations to determine the forced response. We propose an initialization scheme for studying all these issues in Earth system models.