Based on the theory of “snapshot/pullback attractors”, we show that important features of the climate change that we are observing can be understood by imagining many replicas of Earth that are not interacting with each other. Their climate systems evolve in parallel, but not in the same way, although they all obey the same physical laws, in harmony with the chaotic-like nature of the climate dynamics. These parallel climate realizations evolving in time can be considered as members of an ensemble. We argue that the contingency of our Earth’s climate system is characterized by the multiplicity of parallel climate realizations rather than by the variability that we experience in a time series of our observed past. The natural measure of the snapshot attractor enables one to determine averages and other statistical quantifiers of the climate at any instant of time. In this paper, we review the basic idea for climate changes associated with monotonic drifts, and illustrate the large number of possible applications. Examples are given in a low-dimensional model and in numerical climate models of different complexity. We recall that systems undergoing climate change are not ergodic, hence temporal averages are generically not appropriate for the instantaneous characterization of the climate. In particular, teleconnections, i.e. correlated phenomena of remote geographical locations are properly characterized only by correlation coefficients evaluated with respect to the natural measure of a given time instant, and may also change in time. Physics experiments dealing with turbulent-like phenomena in a changing environment are also worth being interpreted in view of the attractor-based ensemble approach. The possibility of the splitting of the snapshot attractor to two branches, near points where the corresponding time-independent system undergoes bifurcation as a function of the changing parameter, is briefly mentioned. This can lead in certain climate-change scenarios to the coexistence of two distinct sub-ensembles representing dramatically different climatic options. The problem of pollutant spreading during climate change is also discussed in the framework of parallel climate realizations.

Teleconnections are striking features of the Earth climate system which appear as statistically correlated climate-related patterns between remote geographical regions of the globe. In a changing climate, however, the strength of teleconnections might change, and an appropriate characterization of these correlations and their change (more appropriate than detrending the time series) is lacking in the literature. Here we present a novel approach, based on the theory of snapshot attractors, corresponding in our context to studying parallel climate realizations. Imagining an ensemble of parallel Earth systems, instead of the single one observed (i.e., the real Earth), the ensemble, after some time, characterizes the appropriate probabilities of all options permitted by the climate dynamics, reflecting the internal variability of the climate. We claim that the relevant quantities for characterizing teleconnections in a changing climate are correlation coefficients taken over the temporally evolving ensemble in any time instant. As a particular example, we consider the teleconnections of the North Atlantic Oscillation (NAO). In a numerical climate model, we demonstrate that this approach provides the only statistically correct characterization, in contrast to commonly used temporal correlations evaluated along single detrended time series. The teleconnections of the NAO are found to survive the climate change, but their strength might be time-dependent.

The changes in the El Niño–Southern Oscillation (ENSO) phenomenon and its precipitation-related teleconnections over the globe under climate change are investigated in the Community Earth System Model Large Ensemble from 1950 to 2100. For the investigation, a recently developed ensemble-based method, the snapshot empirical orthogonal function (SEOF) analysis, is used. The instantaneous ENSO pattern is defined as the leading mode of the SEOF analysis carried out at a given time instant over the ensemble. The corresponding principal components (PC1s) characterize the ENSO phases. By considering sea surface temperature (SST) regression maps, we find that the largest changes in the typical amplitude of SST fluctuations occur in the June–July–August–September (JJAS) season, in the Niño3–Niño3.4 (5^∘ N–5^∘ S, 170–90^∘ W; NOAA Climate Prediction Center) region, and the western part of the Pacific Ocean; however, the increase is also considerable along the Equator in December–January–February (DJF). The Niño3 amplitude also shows an increase of about 20 % and 10 % in JJAS and DJF, respectively. The strength of the precipitation-related teleconnections of the ENSO is found to be nonstationary, as well. For example, the anticorrelation with precipitation in Australia in JJAS and the positive correlation in central and northern Africa in DJF are predicted to be more pronounced by the end of the 21th century. Half-year-lagged correlations, aiming to predict precipitation conditions from ENSO phases, are also studied. The Australian and Indonesian precipitation and that of the eastern part of Africa in both JJAS and DJF seem to be well predictable based on the ENSO phase, while the southern Indian precipitation relates to the half-year previous ENSO phase only in DJF. The strength of these connections increases, especially from the African region to the Arabian Peninsula.

The Arctic Oscillation (AO) and its related wintertime phenomena are investigated under climate change by 2099 in an ensemble approach using the CESM1 Large Ensemble and the MPI-ESM Grand Ensemble with different RCP scenarios. The loading pattern of the AO is defined as the leading mode of the empirical orthogonal function (EOF) analysis of sea level pressure from 20° to 90°N. It is shown that the traditional AO index (AOI) calculation method, using a base period in a single climate realization, brings subjectivity to the investigation of the AO-related phenomena. Therefore, if an ensemble is available, the changes in the AO and its related phenomena should rather be studied by a reconsidered EOF analysis (snapshot EOF) introduced herein. This novel method is based only on the instantaneous fields of the ensemble, and hence it is capable of monitoring the time evolution of the AO’s pattern and amplitude. Furthermore, the instantaneous correlation coefficientrcan objectively be calculated between the AOI and, for example, the surface temperature, and thus the time dependence of the strength of these connections can also be revealed. Results emphasize that both the AO and the related surface temperature pattern are nonstationary and their time evolution depends on the forcing. The AO’s amplitude increases and the Pacific center strengthens considerably in each scenario. Additionally, there exist such regions (e.g., northern Europe or western North America) wherershows remarkable change (0.2–0.4) by 2099. This study emphasizes the importance of the snapshot framework when studying changes in the climate system.

Using an intermediate complexity climate model (Planet Simulator), we investigate the so-called snowball Earth transition. For certain values (including its current value) of the solar constant, the climate system allows two different stable states: one of them is the snowball Earth, covered by ice and snow, and the other one is today’s climate. In our setup, we consider the case when the climate system starts from its warm attractor (the stable climate we experience today), and the solar constant is changed according to the following scenario: it is decreased continuously and abruptly, over one year, to a state, where only the Snowball Earth’s attractor remains stable. This induces an inevitable transition or climate tipping from the warm climate. The reverse transition is also discussed. Increasing the solar constant back to its original value in a similar way, in individual simulations, depending on the rate of the solar constant reduction, we find that either the system stays stuck in the snowball state or returns to warm climate. However, using ensemble methods, i.e., using an ensemble of climate realizations differing only slightly in their initial conditions we show that the transition from the snowball Earth to the warm climate is also possible with a certain probability, which depends on the specific scenario used. From the point of view of dynamical systems theory, we can say that the system’s snapshot attractor splits between the warm climate’s and the snowball Earth’s attractor.