The Theory of Parallel Climate Realizations

Abstract

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. Keywords Climate dynamics • Nonautonomous systems • Ensembles • Snapshot attractors • Natural measures Communicated by Valerio Lucarini.

Investigating ENSO and its teleconnections under climate change in an ensemble view – a new perspective

“…, which is also chosen in Maher et al (2018) for their EOF-E analysis. To eliminate the distorting impact of the regular latitude-longitude grid in the EOF analysis, the SST fields are weighted by the square root of the cosine of the latitude, following Thompson and Wallace (2000). We consider the instantaneous ensemble-based leading SEOF mode (by which we mean the normalized eigenvectors associated with the largest eigenvalue of the covariance matrix of the SST anomaly fields) as the ENSO loading pattern and the phase of the phenomenon in each member as the corresponding principal component (PC1).…”

“…1, PC1 > 0 (PC1 < 0) corresponds to anomalously warm (cold) events associated with above (below) the ensemble average SST in the central and east-central equatorial Pacific Ocean. As in Thompson and Wallace (2000), not the normalized EOF patterns, but rather the SST regression maps are shown, computed by regressing the unweighted SST anomaly fields onto the standardized PC1 data. Therefore, the values appearing on the regression maps characterize typical amplitudes in the variability in the SST.…”

“…The applicability of this framework was also established by laboratory experiments (Vincze et al, 2017). The application of ensembles in the snapshot framework is overviewed in Tél et al (2020).…”

“…Furthermore, starting a sufficiently large ensemble of climate simulations with slightly different initial conditions has been proven to correctly cover the distribution of the possible climate states of the snapshot attractor after the transient time at any time instant; therefore, from that time on the ensemble can be used to characterize the potential states at each time instant (Drótos et al, 2015;Herein et al, 2016;Drótos et al, 2017). This ensemble can be also called parallel climate realizations (Herein et al, 2017;Tél et al, 2020). We note that it is remarkable that Leith (1978) came up with a similar idea as early as in 1978; however, Leith's work has not spread widely in the climate community.…”

Introduction to the Special Issue on the Statistical Mechanics of Climate

“…This issue is addressed in [98] using a simplified model of the ocean. Time-dependent correlations between the parallel climate realizations defining the pullback attractor are used in [118] to provide an alternative definition for teleconnections, i.e. correlation between anomalies of climatic fields in regions that are geographically very far away.…”