ENSO teleconnections are widely studied, but their forced changes remain poorly understood. This work stands apart: its nearest neighbors in the archive concern El Niño prediction, neural-network drought forecasts, ecosystem rhythms, and quantum entanglement, indicating an interdisciplinary but weakly overlapping context. Unlike previous studies that use time series from a single scenario, here an ensemble approach is applied, which correctly isolates the forced response by separating it from internal variability. This is important because traditional methods based on trends in a single realization can yield biased estimates.
The analysis is conducted on data from the large MPI-GE ensemble (63 members), using sea surface temperature (SST) and sea level pressure (SLP) to characterize ENSO, as well as Indian monsoon rainfall. The teleconnection is represented in four ways: classical indices (Niño3, Niño3.4, SOI, box-SOI) and leading modes of variability obtained via snapshot EOF, Maximum Covariance Analysis (SMCA), and Canonical Correlation Analysis (SCCA). Correlation is computed across the ensemble for each year, yielding a time series of the forced response. The Mann–Kendall test is used to assess the significance of changes. Non-ergodicity is detected using a dedicated statistical test based on comparing temporal and ensemble correlations.
The strengthening of the ENSO–Indian monsoon teleconnection is robust across all four representations, using both SST and SLP, and in both the historical period and the RCP8.5 scenario. The main contribution to the strengthening comes from an increase in the regression coefficient (link), which can outweigh even a decline in ENSO variability. The forced change in the teleconnection is nonlinear: the ergodicity hypothesis is formally rejected, and trivial contributions from changes in mean SST and precipitation are insignificant. Global maps of the degree of non-ergodicity for the link between local precipitation and ENSO are constructed: regions with high non-ergodicity are found not only in the tropics but also worldwide, with a maximum in the center of ENSO variability.
This work differs from its neighbors in method: instead of analyzing time series from a single scenario, it uses an ensemble approach that correctly isolates the forced response and its nonlinearity. This is the first test of non-ergodicity for teleconnections in a large ensemble, providing a new tool for assessing biases in traditional temporal correlations. The results show that the strengthening of the link is not reducible to changes in ENSO variability but is associated with an increase in the regression coefficient, pointing to the importance of dynamical and thermodynamical processes in shaping the teleconnection.
The topic could develop toward a physical interpretation of the identified statistical changes. It is necessary to investigate which processes (thermodynamic or dynamic) are responsible for the increase in the regression coefficient and the nonlinearity. Also promising is the application of the developed non-ergodicity test to other teleconnections and climate variables to uncover hidden nonlinearities in forced changes.
The results will affect climate modeling and prediction, especially the assessment of teleconnection changes under anthropogenic warming. The practical significance relates to improved forecasts of the Indian monsoon and associated rainfall.
Next steps include applying the non-ergodicity test to other climate models and ensembles to check the universality of the results, as well as a detailed analysis of the physical mechanisms behind the nonlinear teleconnection changes.
This work touches on a fundamental problem in climatology: how to separate the forced signal from internal variability under nonstationarity. The non-ergodicity shown for teleconnections implies that traditional estimates from time series may be biased, casting doubt on the interpretation of observed trends. This connects to the unresolved question of why model and observed changes in the ENSO–monsoon link diverge.
The non-ergodicity test showed that even if the correlation changes linearly over time, biases can arise if mean values or standard deviations change. In this case, these trivial contributions turned out to be insignificant, confirming the true nonlinearity of the forced response.