On defining climate by means of an ensemble

Abstract. 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 for this is the uniqueness of the probability measure on which the definition relies. We first naively propose, in harmony with earlier work, to represent such a probability measure by the distribution of ensemble members that has, loosely speaking, converged to the natural probability measure of the so-called snapshot or pullback attractor of the dynamics; this attractor is time dependent in the presence of external forcing. Then we refine the proposal by taking a probability measure that is conditional on the (possibly time-evolving) state of modes characterized by time scales of convergence that are 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 the practically relevant probability measure may, hopefully, become accessible by a few decades of convergence after initialization; for this, initialization may perhaps need to rely on the observed state of the slower-converging modes. However, the absence of sufficient separation of time scales of convergence between modes or regime transitions in variables corresponding to slower-converging modes might preclude uniqueness, perhaps in certain subsystems. In uniqueness holds, time evolution of slower-converging modes may 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.