  We study the forced response of the teleconnection between the El
Nino-Southern Oscillation (ENSO) and global precipitation in general and the
Indian summer monsoon (IM) in particular in the Max Planck Institute Grand
Ensemble. The forced response of the teleconnection is defined as the
time-dependence of a correlation coefficient evaluated over the ensemble. The
ensemble-wise variability is taken either wrt. spatial averages or dominant
spatial modes in the sense of Maximal Covariance Analysis or Canonical
Correlation Analysis or EOF analysis. We find that the strengthening of the
ENSO-IM teleconnection is robustly or consistently featured in view of all four
teleconnection representations, whether sea surface temperature (SST) or sea
level pressure (SLP) is used to characterise ENSO, and both in the historical
period and under the RCP8.5 forcing scenario. The main contributor to this
strengthening in terms of a linear regression model is the regression
coefficient, which can outcompete even a declining ENSO variability in view of
using the SLP. We also find that the forced change of the teleconnection is
typically nonlinear by (1) formally rejecting the hypothesis that ergodicity
holds, i.e., that expected values of temporal correlation coefficients with
respect to the ensemble equal the ensemble-wise correlation coefficient itself,
and also showing that (2) the trivial contributions of the forced changes of
e.g. the mean SST and/or precipitation to temporal correlations are
insignificant here. We also provide, in terms of the test statistics, global
maps of the degree of nonlinearity/nonergodicity of the forced change of the
teleconnection between local precipitation and ENSO.
