arXiv subjects

Reik V. Donner

Publications and source records attributed to Reik V. Donner.

At least 19 recordsLinked to original sources

arXiv2025

The stochastic skeleton model for the Madden-Julian Oscillation with time-dependent observation-based forcing

We analyze solutions to the stochastic skeleton model, a minimal nonlinear oscillator model for the Madden-Julian Oscillation (MJO). This model has been recognized for its ability to reproduce several large-scale features of the MJO. In previous studies, the model's forcings were predominantly chosen to be mathematically simple and time-independent. Here, we present solutions to the model with time-dependent observation-based forcing functions. Our results show that the model, with these more realistic forcing functions, successfully replicates key characteristics of MJO events, such as their lifetime, extent, and amplitude, whose statistics agree well with observations. However, we find that the seasonality of MJO events and the spatial variations in the MJO properties are not well reproduced. Having implemented the model in the presence of time-dependent forcings, we can analyze the impact of temporal variability at different time scales. In particular, we study the model's ability to reflect changes in MJO characteristics under the different phases of ENSO. We find that it does not capture differences in studied characteristics of MJO events in response to differences in conditions during El Niño, La Niña, and neutral ENSO.

physics.ao-ph↗

arXiv2025

Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.

physics.data-an↗

arXiv2025

Complex network approaches to nonlinear time series analysis

In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems.

physics.data-an↗

arXiv2025

Causal pathway from AMOC to Southern Amazon rainforest indicates stabilising interaction between two climate tipping elements

Declines in resilience have been observed in several climate tipping elements over the past decades, including the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest (AR). Large-scale nonlinear and possibly irreversible changes in system state, such as AMOC weakening or rainforest-savanna transitions in the Amazon basin, would have severe impacts on ecosystems and human societies worldwide. In order to improve future tipping risk assessments, understanding interactions between tipping elements is crucial. The AMOC is known to influence the Intertropical Convergence Zone, potentially altering precipitation patterns over the AR and affecting its stability. However, AMOC-AR interactions are currently not well understood. Here, we identify a previously unknown stabilising interaction pathway from the AMOC onto the Southern AR, applying an established causal discovery and inference approach to tipping element interactions for the first time. Analysing observational and reanalysis data from 1982-2022, we show that AMOC weakening leads to increased precipitation in the Southern AR during the critical dry season, in line with findings from recent Earth system model experiments. Specifically, we report a 4.8% increase of mean dry season precipitation in the Southern AR for every 1 Sv of AMOC weakening. This finding is consistent across multiple data sources and AMOC strength indices. We show that this stabilising interaction has offset 17% of dry season precipitation decrease in the Southern AR since 1982. Our results demonstrate the potential of causal discovery methods for analysing tipping element interactions based on reanalysis and observational data. By improving the understanding of AMOC-AR interactions, we contribute toward better constraining the risk of potential climate tipping cascades under global warming.

physics.ao-ph↗

arXiv2023

Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.

cond-mat.stat-mech↗

arXiv2022

Chameleon attractors in a turbulent flow

Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence and unpredictability. All these features have prevented a full characterization of the underlying turbulent (stochastic) attractor, which will be the key object to unpin this complexity. Here we propose a novel formalism to trace the evolution of the structural characteristics of phase-space trajectories across scales, providing a full characterization of the attractor. We demonstrate that the properties of the dynamically invariant objects depend on the scale we are focusing on. In the case of laboratory experiments on fluids we observe the emergence of an intrinsic timescale, solely determined by nonlinear interactions, controlling the geometrical and topological properties of phase-space trajectories. Given the changing nature of such attractors in time and scales we term them chameleon attractors.

nlin.CD↗

arXiv2022

A novel concept of fractal dimension in deterministic and stochastic Lorenz-63 systems

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase-space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set as it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise, despite the fact that the two cases exhibit very similar stochastic attractors at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

nlin.CD↗

arXiv2021

The Effect of Time Series Distance Functions on Functional Climate Networks

Complex network theory provides an important tool for the analysis of complex systems such as the Earth's climate. In this context, functional climate networks can be constructed using a spatiotemporal climate dataset and a suitable time series distance function. The resulting coarse-grained view on climate variability consists of representing distinct areas on the globe (i.e., grid cells) by nodes and connecting pairs of nodes that present similar time series. One fundamental concern when constructing such a functional climate network is the definition of a metric that captures the mutual similarity between time series. Here we study systematically the effect of 29 time series distance functions on functional climate network construction based on global temperature data. We observe that the distance functions previously used in the literature commonly generate very similar networks while alternative ones result in rather distinct network structures and reveal different long-distance connection patterns. These patterns are highly important for the study of climate dynamics since they generally represent pathways for the long-distance transportation of energy and can be used to forecast climate variability on subseasonal to interannual or even decadal scales. Therefore, we propose the measures studied here as alternatives for the analysis of climate variability and to further exploit their complementary capability of capturing different aspects of the underlying dynamics that may help gaining a more holistic empirical understanding of the global climate system.

physics.data-an↗

arXiv2021

Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation

In the past decades, boreal summers have been characterized by an increasing number of extreme weather events in the Northern Hemisphere extratropics, including persistent heat waves, droughts and heavy rainfall events with significant social, economic and environmental impacts. Many of these events have been associated with the presence of anomalous large-scale atmospheric circulation patterns, in particular persistent blocking situations, i.e., nearly stationary spatial patterns of air pressure. To contribute to a better understanding of the emergence and dynamical properties of such situations, we construct complex networks representing the atmospheric circulation based on Lagrangian trajectory data of passive tracers advected within the atmospheric flow. For these Lagrangian flow networks, we study the spatial patterns of selected node properties prior to, during and after different atmospheric blocking events in Northern Hemisphere summer. We highlight the specific network characteristics associated with the sequence of strong blocking episodes over Europe during summer 2010 as an illustrative example. Our results demonstrate the ability of the node degree, entropy and harmonic closeness centrality based on outgoing links to trace important spatio-temporal characteristics of atmospheric blocking events. In particular, all three measures capture the effective separation of the stationary pressure cell forming the blocking high from the normal westerly flow and the deviation of the main atmospheric currents around it. Our results suggest the utility of further exploiting the Lagrangian flow network approach to atmospheric circulation in future targeted diagnostic and prognostic studies.

physics.ao-ph↗

arXiv2021

Causal coupling inference from multivariate time series based on ordinal partition transition networks

Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data.

stat.ME↗

arXiv2021

Generalization of Higuchi's fractal dimension for multifractal analysis of time series with limited length

We introduce a generalization of Higuchi's estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series. The resulting multifractal Higuchi dimension analysis (MF-HDA) method considers the order-$q$ moments of the partition function provided by the length of the time series graph at different levels of subsampling. The results obtained for different types of stochastic processes as well as real-world examples of word length series from fictional texts demonstrate that MF-HDA provides a reliable estimate of the multifractal spectrum already for moderate time series lengths. Practical advantages as well as disadvantages of the new approach as compared to other state-of-the-art methods of multifractal analysis are discussed, highlighting the particular potentials of MF-HDA to distinguish mono- from multi-fractal dynamics based on relatively short time series.

physics.data-an↗

arXiv2021

Differential imprints of distinct ENSO flavors in global patterns of very low and high seasonal precipitation

The effects of El Niño's two distinct flavors, East Pacific (EP) and Central Pacific (CP)/Modoki El Niño, on global climate variability have been studied intensively in recent years. Most of these studies have made use of linear multivariate statistics or composite analysis. Especially the former assumes the same type of linear statistical dependency to apply across different phases of the El Niño--Southern Oscillation (ENSO), which appears not necessarily a justified assumption. Here, we statistically evaluate the likelihood of co-occurrences between very high or very low seasonal precipitation sums over vast parts of the global land surface and the presence of the respective EP and CP types of both, El Niño and La Niña. By employing event coincidence analysis, we uncover differential imprints of both flavors on very low and very high seasonal precipitation patterns over distinct regions across the globe, which may severely affect, among others, agricultural and biomass production or public health. We particularly find that EP periods exhibit statistically significant event coincidence rates with hydrometeorological anomalies at larger spatial scales, whereas sparser patterns emerge along with CP periods. Our statistical analysis confirms previously reported interrelations for EP periods and uncovers additional distinct regional patterns of very high/low seasonal precipitation, such as increased rainfall over Central Asia alongside CP periods that have to our knowledge not been reported so far. Our results demonstrate that a thorough distinction of El Niño and La Niña into their two respective flavors could be crucial for understanding the emergence of strong regional hydrometeorological anomalies and anticipating their associated ecological and socioeconomic impacts.

physics.ao-ph↗

arXiv2020

Disentangling synchrony from serial dependency in paired event time series

Quantifying synchronization phenomena based on the timing of events has recently attracted a great deal of interest in various disciplines such as neuroscience or climatology. A multitude of similarity measures has been proposed for this purpose, including Event Synchronization (ES) and Event Coincidence Analysis (ECA) as two widely applicable examples. While ES defines synchrony in a data adaptive local way that does not distinguish between different time scales, ECA requires selecting a specific scale for analysis. In this paper, we use slightly modified versions of both ES and ECA that address previous issues with respect to proper normalization and boundary treatment, which are particularly relevant for short time series with low temporal resolution. By numerically studying threshold crossing events in coupled autoregressive processes, we identify a practical limitation of ES when attempting to study synchrony between serially dependent event sequences exhibiting event clustering in time. Practical implications of this observation are demonstrated for the case of functional network representations of climate extremes based on both ES and ECA, while no marked differences between both measures are observed for the case of epileptic electroencephalogram (EEG) data. Our findings suggest that careful event detection along with diligent preprocessing is recommended when applying ES while less crucial for ECA. Despite the lack of a general modus operandi for both event definition and detection of synchronization, we suggest ECA as a widely robust method, especially for time resolved synchronization analyses of event time series from various disciplines.

physics.data-an↗

arXiv2019

Correlating Paleoclimate Time Series: Sources of Uncertainty and Potential Pitfalls

Comparing paleoclimate time series is complicated by a variety of typical features, including irregular sampling, age model uncertainty (e.g., errors due to interpolation between radiocarbon sampling points) and time uncertainty (uncertainty in calibration), which, taken together, result in unequal and uncertain observation times of the individual time series to be correlated. Several methods have been proposed to approximate the joint probability distribution needed to estimate correlations, most of which rely either on interpolation or temporal downsampling. Here, we compare the performance of some popular approximation methods using synthetic data resembling common properties of real world marine sediment records. Correlations are determined by estimating the parameters of a bivariate Gaussian model from the data using Markov Chain Monte Carlo sampling. We complement our pseudoproxy experiments by applying the same methodology to a pair of marine benthic oxygen records from the Atlantic Ocean. We find that methods based upon interpolation yield better results in terms of precision and accuracy than those which reduce the number of observations. In all cases, the specific characteristics of the studied time series are, however, more important than the choice of a particular interpolation method. Relevant features include the number of observations, the persistence of each record, and the imposed coupling strength between the paired series. In most of our pseudoproxy experiments, uncertainty in observation times introduces less additional uncertainty than unequal sampling and errors in observation times do. Thus, it can be reasonable to rely on published time scales as long as calibration uncertainties are not known.

stat.AP↗

arXiv2018

Edge directionality properties in complex spherical networks

Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation and trade networks. In climate networks, our approach highlights relevant patterns like large-scale circulation cells, the El Niño--Southern Oscillation and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.

physics.soc-ph↗

arXiv2018

Dynamical anomalies in terrestrial proxies of North Atlantic climate variability during the last 2 ka

Recent work has provided ample evidence that nonlinear methods of time series analysis potentially allow for detecting periods of anomalous dynamics in paleoclimate proxy records that are otherwise hidden to classical statis- tical analysis. Following upon these ideas, in this study we systematically test a set of Late Holocene terrestrial paleoclimate records from Northern Europe for indications of intermittent periods of time-irreversibility during which the data are incompatible with a stationary linear-stochastic process. Our analysis reveals that the onsets of both the Medieval Climate Anomaly and the Little Ice Age, the end of the Roman Warm Period and the Late Antique Little Ice Age have been characterized by such dynamical anomalies. These findings may indicate qualitative changes in the dominant regime of inter-annual climate variability in terms of large-scale atmospheric circula- tion patterns, ocean-atmosphere interactions and external forcings affecting the climate of the North Atlantic region.

physics.ao-ph↗

arXiv2018

Dimension-scalable recurrence threshold estimation

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Based on our results, we recommend selecting the recurrence threshold adaptively according to a fixed quantile of this distribution. We highlight the advantages of this strategy over other previously suggested approaches by discussing the performance of selected RQA measures in detecting chaos--chaos transitions in some prototypical model system.

physics.data-an↗

arXiv2018

Common solar wind drivers behind magnetic storm-magnetospheric substorm dependency

The dynamical relationship between magnetic storms and magnetospheric substorms presents one of the most controversial problems of contemporary geospace research. Here, we tackle this issue by applying a causal inference approach to two corresponding indices in conjunction with several relevant solar wind variables. We demonstrate that the vertical component of the interplanetary magnetic field is the strongest and common driver of both, storms and substorms, and explains their the previously reported association. These results hold during both solar maximum and minimum phases and suggest that, at least based on the analyzed indices, there is no statistical evidence for a direct or indirect dependency between substorms and storms. A physical mechanism by which substorms drive storms or vice versa is, therefore, unlikely.

physics.space-ph↗