Abstract. 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.

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.

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.

Topological entropy is shown to be a useful characteristic of the state of the free atmosphere. It can be determined as the stretching rate of a line segment of tracer particles in the atmosphere over a time span of about 10 days. Besides case studies, the seasonal distribution of the average topological entropy is determined in several geographical locations. The largest topological entropies appear in the mid-and high latitudes, especially in winter, owing to the greater temperature gradient between the pole and the equator and the more intense stirring and shearing effects of cyclones. The smallest values can be found in the trade wind belt. The local value of the topological entropy is a measure of the chaoticity of the state of the atmosphere and of how rapidly pollutants and contaminants spread from a given location.

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Arctic sea ice melting processes in summer due to internal atmospheric variability have recently received considerable attention. A regional barotropic atmospheric process over Greenland and the Arctic Ocean in summer (June–August), featuring either a year-to-year change or a low-frequency trend toward geopotential height rise, has been identified as an essential contributor to September sea ice loss, in both observations and the CESM1 Large Ensemble (CESM-LE) of simulations. This local melting is further found to be sensitive to remote sea surface temperature (SST) variability in the east-central tropical Pacific Ocean. Here, we utilize five available large “initial condition” Earth system model ensembles and 31 CMIP5 models’ preindustrial control simulations to show that the same atmospheric process, resembling the observed one and the one found in the CESM-LE, also dominates internal sea ice variability in summer on interannual to interdecadal time scales in preindustrial, historical, and future scenarios, regardless of the modeling environment. However, all models exhibit limitations in replicating the magnitude of the observed local atmosphere–sea ice coupling and its sensitivity to remote tropical SST variability in the past four decades. These biases call for caution in the interpretation of existing models’ simulations and fresh thinking about models’ credibility in simulating interactions of sea ice variability with the Arctic and global climate systems. Further efforts toward identifying the causes of these model limitations may provide implications for alleviating the biases and improving interannual- and decadal-time-scale sea ice prediction and future sea ice projection.

Abstract. Due to rising or descending air and due to gravity, aerosol particles carry out a complicated, chaotic motion and move downwards on average. We simulate the motion of aerosol particles with an atmospheric dispersion model called the Real Particle Lagrangian Trajectory (RePLaT) model, i.e., by solving Newton's equation and by taking into account the impacts of precipitation and turbulent diffusion where necessary, particularly in the planetary boundary layer. Particles reaching the surface are considered to have escaped from the atmosphere. The number of non-escaped particles decreases with time. The short-term and long-term decay are found to be exponential and are characterized by escape rates. The reciprocal values of the short-term and long-term escape rates provide estimates of the average residence time of typical particles, and of exceptional ones that become convected or remain in the free atmosphere for an extremely long time, respectively. The escape rates of particles of different sizes are determined and found to vary in a broad range. The increase is roughly exponential with the particle size. These investigations provide a Lagrangian foundation for the concept of deposition rates.

Using an intermediate complexity climate model (Planet Simulator), we investigate the so-called Snowball Earth transition. For certain values 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 decreased continuously in finite time, according to a parameter drift scenario, 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 on individual simulations, we find that the system stays stuck in the Snowball state. 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. 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. 1 arXiv:1906.00952v1 [physics.ao-ph] 31 May 2019 Ever since its discovery, the Snowball Earth, i.e. when the Earth's surface is nearly entirely frozen, received much attention within the climate science community. Much of the details of the transition to the planet's frozen state are still unexplored. Here, instead of focusing on the true Snowball events of Earth's history, we investigate the transition in an intermediate complexity climate model (PlaSim), with a continuously drifting solar constant (a hypothetical climate change scenario), in which a full return to the original value occurs. Using an ensemble based method we obtain both of the possible stable states as possible outcomes. We also show that the process is probabilistic and the probabilities of the corresponding outcomes are given by the ensemble's distribution. In addition, the third, unstable state (referred to as the edge state) is also recovered. I. INTRODUCTIONSnowball Earth refers to the planet's coldest possible global climate. In this state, the whole Earth, from the poles to the Equator, is covered in ice and snow. Since the thick ice covering the surface reflects much of the energy radiated by the Sun, the global average temperature is very low, around 220 K 1 .Modern findings suggest that during the Earth's history, there were periods, when such Snowball events occurred. For example, several traces of glacial activity point to the presence of glaciers along the so-called Paleoequator 2 .This suggests that also the current configuration of the Earth system may be bistable, the two stable states being the Snowball state and our current climate. To better understand the phenomenon, there are simple models available that only take the global energy balance...