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.

Origins of the interdecadal fluctuations of the ENSO-Indian summer monsoon (ISM) teleconnection strength measured by running window correlation coefficients have been much debated. The main question is whether it’s due mostly (i) to sampling errors, or, (ii) under internal variability decadal time scale drivers modulate it, and/or, (iii) it has undergone some forced change recently. A new statistical test does not detect any of (ii-iii) in observations. However, it does not mean that there could not be such effects, just that the data is insufficient. Large ensemble data sets are well suited to investigate these questions. Previously, (iii) was found to be small (even if possibly important) in the MPI-GE data set, and the situation is similar in the new CESM2-LE data set. This time we investigate (ii), too, and find that the decadal variability of e.g. the Dipole Mode Index (DMI*, decorrelated from Nino3) of the Indian Ocean “explains” 4% of the apparent variability of the ENSO-ISM teleconnection. If the CESM2-LE were faithful to reality, then this signal would take two millenia to have a 50% chance to detect. We also find that this apparent DMI* influence is due to heteroscedasticity, namely, to the apparent DMI* influence on ENSO variance. However, we also find that this influence is mostly apparent, indeed, as it is the ENSO variance that dominantly influences the DMI*.