  We study the relationship between the El Ni\~no--Southern Oscillation (ENSO)
and the Indian summer monsoon in ensemble simulations from state-of-the-art
climate models, the Max Planck Institute Earth System Model (MPI-ESM) and the
Community Earth System Model (CESM). We consider two simple variables: the
Tahiti--Darwin sea-level pressure difference and the Northern Indian
precipitation. We utilize ensembles converged to the system's snapshot
attractor for analyzing possible changes (i) in the teleconnection between the
fluctuations of the two variables, and (ii) in their climatic means. (i) With
very high confidence, we detect an increase in the strength of the
teleconnection, as a response to the forcing, in the MPI-ESM under historical
forcing between 1890 and 2005, concentrated to the end of this period. We
explain that our finding does not contradict instrumental observations, since
their existing analyses regarding the nonstationarity of the teleconnection are
either methodologically unreliable, or consider an ill-defined teleconnection
concept. In the MPI-ESM we cannot reject stationarity between 2006 and 2099
under the Representative Concentration Pathway 8.5 (RCP8.5), and in a
110-year-long 1-percent pure CO2 scenario; neither can we in the CESM between
1960 and 2100 with historical forcing and RCP8.5. (ii) In the latter ensembles,
the climatic mean is strongly displaced in the phase space projection spanned
by the two variables. This displacement is nevertheless linear. However, the
slope exhibits a strong seasonality, falsifying a hypothesis of a universal,
emergent relationship between these two climatic means, excluding applicability
in an emergent constraint.
