Mátyás Herein

Large-scale, slowly propagating wave-like structures have been observed in the atmosphere of Venus, but their dynamical origin remains uncertain. In laboratory experiments we investigated whether analogous structures can develop through baroclinic instability under conditions imitating the Venusian lower-to-middle cloud region. A differentially heated rotating annulus set-up was designed to conceptually imitate the planetary setting in terms of the relevant geometrical and dynamical similarity parameters, applying meridional and zonal temperature contrast as thermal forcing. Temperature time series analysis, infrared thermography, and feature tracking velocimetry were used to characterize the flow in the system. Slowly propagating, billow-like patterns were observed, similar in shape to the vortices of Venus. Wave activity was found to emerge above a critical meridional temperature contrast, but became substantially reduced when the ratio of the imposed zonal and meridional temperature contrasts exceeded approximately 1.6. The experiments indicate that the relative magnitude of meridional and day-night thermal forcing may play an important role in determining the occurrence of such wave-like atmospheric structures.

Complex systems subjected to parameter drift require an ensemble approach in their investigation. In such cases, an individual trajectory is insufficient to capture the global changes in the system. In this paper we report the first experiment on low–dimensional chaotic mechanical systems subjected to considerable drift, resulting in six measured time series. Our set–up is based on three double pendula excited through the shaker, which allows to control and drift the excitation amplitude applied to the units. The equations of motion used for this system are shown to be consistent with the experiments: any single measurement is within the band of the ensemble simulation and traverses the band occasionally, after a sufficiently long time. The evaluation of the global dynamics can be understood with the concept of snapshot attractors , arising on the route from system initialization to a time–dependent chaotic steady state. The results presented in this paper experimentally confirm earlier simulation–only studies, expanding the concept of ensemble dynamics into more practical scenarios.

Lightning activity is strongly concentrated in tropical continental “chimneys”, among which the African lightning chimney stands out as the most intense globally. However, until recently, the incomplete and spatially uneven detection efficiency of ground‐based lightning networks, together with the limited spatio‐temporal coverage of satellite observations, have constrained the quantitative characterization of African lightning activity, particularly on the daily timescales. Since July 2024, the Lightning Imager (LI) onboard the Meteosat Third Generation (MTG) satellite has provided the first continuous, high‐temporal‐resolution observations of lightning activity over Africa and Europe from geostationary orbit. In this paper, we examine, based on the first year of MTG LI observations, how consistently daily peak activity in the African lightning chimney is represented in different observational data sets. For this purpose, we use MTG LI group and flash data, together with World Wide Lightning Location Network (WWLLN) stroke observations and Schumann resonance (SR) measurements, and focus on two key parameters: the daily peak activity and its timing. We find that daily peak activity derived from MTG flashes shows a strong positive correlation with SR intensity ( r = 0.749), while WWLLN stroke observations show much weaker correspondence. The timing of the daily peak is broadly consistent across the data sets, with the best agreement observed between MTG flashes and SR intensity. For all data sets, daily peak activity is strongly correlated with total daily activity. The strong correspondence between MTG flashes and SR intensity supports the use of both data sets in characterizing the daily activity of the African lightning chimney.

In this paper, we present a new, statistical framework for understanding the dynamics of polarity reversals under time-dependent forcing. The methods are thought to be generally applicable to geodynamo models in any scenario involving a time-dependent forcing. We demonstrate this framework on a simple conceptual dynamo model, the Rikitake system, which is a classical model of polarity reversals, known for its chaotic dynamics. Here, we investigate, for the first time, a non-autonomous extension of this model, in which the coupling parameter changes in time, mimicking the gradual activation or strengthening of a geodynamo. Given the non-autonomous nature of the underlying dynamics, the typical behavior of the system can only be accurately characterized using ensemble-based statistical approaches (instead of time series-based ones), in line with the so-called snapshot attractor view of dynamical systems theory. Using ensemble simulations with a “spin-up” initialization, we analyze the statistical behavior of polarity reversals, specifically, we construct the time-dependent ensemble-based cumulative distribution functions (CDFs) of chron lengths. Results show that as the system evolves and the coupling increases, longer chrons become increasingly permitted, albeit with lower probability. This behavior can be interpreted as the analogy of very rare “superchron” events, supported by paleomagnetic evidence. We find that early-stage chron distributions follow Gaussian statistics, while later stages exhibit lognormal distributions, indicating a transition in the underlying dynamical behavior as the system evolves. An intriguing and new result is the simultaneous probabilistic coexistence of a plethora of chrons with a multitude of lengths, whose ensemble characterizes the system at each point in time. These findings highlight the importance of incorporating ensemble methods in advanced geodynamo modeling.

The Atlantic Meridional Overturning Circulation (AMOC) is a crucial climate component, as its potential collapse would constitute a significant response to Earth’s changing climate. This critical transition has been the subject of numerous studies over the years, both from the aspect of climate modeling and dynamical systems theory. In the context of the latter, climate change is a process in which a complex, chaotic-like system possesses time-dependent parameters, in the form of e.g. the growing CO2 concentration. It has been known that such systems have a chaotic attractor which is also time-dependent, a so-called snapshot attractor. Such objects, and thus the systems they describe, can only be faithfully represented by a probability distribution over an ensemble of simulations, so-called parallel climate realizations.Based on this probability distribution, we define a novel early warning indicator for crucial transitions such as an AMOC collapse. The AMOC is said to possess a multistable quasipotential landscape, and the collapse is a transition between stable states. We argue that, from the point of view of statistical physics, this is analogous to a phase transition, but in a non-adiabatic setting. As such, the variance of the distribution over the ensemble is expected to develop a local maximum around the transition point, giving rise to a potential early warning by identifying the preceding maximum of its derivative. This method is first demonstrated on a conceptual climate model, before the analysis is carried out on ensemble simulations from the ACCESS-ESM model. The analysis in the former case is simpler, while in the latter, one has to contend with the dependence of the AMOC strength on spatial coordinates, resulting in multiple early warning points for different depths and latitudes.

We argue that a physics experiment with systems involving drifting parameters requires a paradigm shift: the measured signal, a curve, should be compared with a band resulting from simulations. Based on earlier theoretical results, an accurate description of drifting dissipative chaotic systems can only be given by following an ensemble of trajectories. After convergence to a time-dependent attractor (to the so-called snapshot attractor), the ensemble faithfully represents the dynamics. We point out that an experimentally measured signal should wander within the spread of the converged numerical ensemble, i.e., to behave as any of the ensemble members on the snapshot attractor. If that is the case, the model (a set of ordinary differential equations) used for the simulation can be considered credible. The transient period preceding the arrival to the attractor can be divided into two phases when using two initially localized ensembles. In the first one, a quick spread of the ensembles takes place, and a plume diagram evolves. The next, intermediate phase corresponds to a convergence of the no longer localized ensembles to the same unique time-dependent attractor and lasts approximately as long as the averages and other statistical moments of the two ensembles remain distinct.

The Atlantic Meridional Overturning Circulation (AMOC) is a mechanism of great importance, as its possible collapse would constitute a dramatic response to Earth’s changing climate. The AMOC is particularly important for Northern Europe, as it plays a central role in regulating the region’s climate, and a slowdown or collapse would lead to a significant cooling of the region. This critical transition has been the subject of many studies over the years, both from the aspects of climate modeling and dynamical systems theory. In the context of the latter, climate change is nothing but a complex, chaotic-like system, which possesses a time-dependent parameter, in the shape of e.g. the growing CO2 concentration. It has been known for some time now, that such systems not only have a chaotic attractor, but one which is also time-dependent, a so-called snapshot attractor. Such objects, and thus the systems they describe, can only be faithfully represented by statistics over an ensemble of trajectories, a single one does not suffice. We perform such ensemble simulations on a conceptual climate model of the AMOC, constructed by coupling the Lorenz84 and the Stommel box models. We find that the difference between the ensemble members in the point when the collapse occurs can be up to hundreds of years, and that some trajectories can even survive with the AMOC remaining in the “on” state. This highlights the fact that that a single trajectory is unreliable, however, with the proper ensemble statistics (e.g. standard deviations, time-dependent Lyapunov exponents, etc), a probabilistic description of the collapse can be given.

In view of the growing importance of climate ensemble simulations, we propose an ensemble approach for following the dynamics of extremes in the presence of climate change. A strict analog of extreme events, a concept based on single time series and local observations, cannot be found. To study nevertheless typical properties over an ensemble, in particular if global variables are of interest, a novel, statistical approach is used, based on a ”zooming in” into the ensemble. To this end, additional sub-ensembles with initially very close members are generated around trajectories of the original ensemble. Plume diagrams initiated on the same day of a year are generated from these sub-ensembles. The trajectories within a plume diagram strongly deviate on the time scale of a few weeks. By defining the extreme deviation as the difference between the maximum and minimum values in a plume diagram, a growth rate for the extreme deviation can be extracted. An average of these taken over the original ensemble (i.e. over all sub-ensembles) characterizes the typical, exponential growth rate of extremes, and the reciprocal of this can be considered the characteristic time of the emergence of extremes. Using a climate model of intermediate complexity, these are found to be on the order of a few days, with some difference between the global mean surface temperature and pressure. Measuring the reciprocal of the growth rate in several years along the last century, results for the temperature turn out to be roughly constant, while a pronounced decaying trend is found in the last decades for the pressure.

In view of the growing importance of climate ensemble simulations, we propose an ensemble approach for following the dynamics of extremes in the presence of climate change. A strict analog of extreme events, a concept based on single time series and local observations, cannot be found. To study nevertheless typical properties over an ensemble, in particular if global variables are of interest, a novel, statistical approach is used, based on a zooming in into the ensemble. To this end, additional, small sub-ensembles are generated, small in the sense that the initial separation between the members is very small in the investigated variables. Plume diagrams initiated on the same day of a year are generated from these sub-ensembles. The trajectories within the plume diagram strongly deviate on the time scale of a few weeks. By defining the extreme deviation as the difference between the maximum and minimum values of a quantity in a plume diagram, i.e., in a sub-ensemble, a growth rate for the extreme deviation can be extracted. An average of these taken over the original ensemble (i.e., over all sub-ensembles) characterizes the typical, exponential growth rate of extremes, and the reciprocal of this can be considered the characteristic time of the emergence of extremes. Using a climate model of intermediate complexity, these are found to be on the order of a few days, with some difference between the global mean surface temperature and pressure. Measuring the extreme emergence time in several years along the last century, results for the temperature turn out to be roughly constant, while a pronounced decaying trend is found in the last decades for the pressure.