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We study the relationship between the El Ni\~no--Southern Oscillation (ENSO)and the Indian summer monsoon in ensemble simulations from state-of-the-artclimate models, the Max Planck Institute Earth System Model (MPI-ESM) and theCommunity Earth System Model (CESM). We consider two simple variables: theTahiti--Darwin sea-level pressure difference and the Northern Indianprecipitation. We utilize ensembles converged to the system's snapshotattractor for analyzing possible changes (i) in the teleconnection between thefluctuations of the two variables, and (ii) in their climatic means. (i) Withvery high confidence, we detect an increase in the strength of theteleconnection, as a response to the forcing, in the MPI-ESM under historicalforcing between 1890 and 2005, concentrated to the end of this period. Weexplain that our finding does not contradict instrumental observations, sincetheir existing analyses regarding the nonstationarity of the teleconnection areeither methodologically unreliable, or consider an ill-defined teleconnectionconcept. In the MPI-ESM we cannot reject stationarity between 2006 and 2099under the Representative Concentration Pathway 8.5 (RCP8.5), and in a110-year-long 1-percent pure CO2 scenario; neither can we in the CESM between1960 and 2100 with historical forcing and RCP8.5. (ii) In the latter ensembles,the climatic mean is strongly displaced in the phase space projection spannedby the two variables. This displacement is nevertheless linear. However, theslope exhibits a strong seasonality, falsifying a hypothesis of a universal,emergent relationship between these two climatic means, excluding applicabilityin an emergent constraint.

Reconsidering the relationship of the El Ni\~no--Southern Oscillation and the Indian monsoon using ensembles in Earth system models