On defining climate by means of an ensemble

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.