TY - GEN A1 - Goswami, Bedartha A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Marwan, Norbert A1 - Heitzig, Jobst A1 - Breitenbach, Sebastian Franz Martin A1 - Kurths, Jürgen T1 - Abrupt transitions in time series with uncertainties T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 576 KW - North-Atlantic climate KW - Indian monsoon KW - Holocene KW - teleconnections KW - variability KW - periods KW - records Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-423111 SN - 1866-8372 IS - 576 ER - TY - JOUR A1 - Goswami, Bedartha A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Marwan, Norbert A1 - Heitzig, Jobst A1 - Breitenbach, Sebastian Franz Martin A1 - Kurths, Jürgen T1 - Abrupt transitions in time series with uncertainties JF - Nature Communications N2 - Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an ‘uncertainty-aware’ framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-017-02456-6 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Ozturk, Ugur A1 - Marwan, Norbert A1 - Korup, Oliver A1 - Saito, H. A1 - Agarwa, Ankit A1 - Grossman, M. J. A1 - Zaiki, M. A1 - Kurths, Jürgen T1 - Complex networks for tracking extreme rainfall during typhoons JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons but mask out contributions of local convective storms. We propose a radial rank method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July. Y1 - 2018 U6 - https://doi.org/10.1063/1.5004480 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 7 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Marwan, Norbert A1 - Caesar, Levke A1 - Kurths, Jürgen T1 - Wavelet-based multiscale similarity measure for complex networks JF - The European physical journal : B, Condensed matter and complex systems N2 - In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales. KW - Statistical and Nonlinear Physics Y1 - 2018 U6 - https://doi.org/10.1140/epjb/e2018-90460-6 SN - 1434-6028 SN - 1434-6036 VL - 91 IS - 11 PB - Springer CY - New York ER - TY - JOUR A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Merz, Bruno A1 - Kurths, Jürgen T1 - Quantifying the roles of single stations within homogeneous regions using complex network analysis JF - Journal of hydrology N2 - Regionalization and pooling stations to form homogeneous regions or communities are essential for reliable parameter transfer, prediction in ungauged basins, and estimation of missing information. Over the years, several clustering methods have been proposed for regional analysis. Most of these methods are able to quantify the study region in terms of homogeneity but fail to provide microscopic information about the interaction between communities, as well as about each station within the communities. We propose a complex network-based approach to extract this valuable information and demonstrate the potential of our approach using a rainfall network constructed from the Indian gridded daily precipitation data. The communities were identified using the network-theoretical community detection algorithm for maximizing the modularity. Further, the grid points (nodes) were classified into universal roles according to their pattern of within- and between-community connections. The method thus yields zoomed-in details of individual rainfall grids within each community. KW - Complex network KW - Event synchronization KW - Rainfall network KW - Z-P approach Y1 - 2018 U6 - https://doi.org/10.1016/j.jhydrol.2018.06.050 SN - 0022-1694 SN - 1879-2707 VL - 563 SP - 802 EP - 810 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Krämer, Hauke Kai A1 - Donner, Reik Volker A1 - Heitzig, Jobst A1 - Marwan, Norbert T1 - Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀 , which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate. Y1 - 2018 U6 - https://doi.org/10.1063/1.5024914 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 8 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Wendi, Dadiyorto A1 - Marwan, Norbert T1 - Extended recurrence plot and quantification for noisy continuous dynamical systems JF - Chaos : an interdisciplinary journal of nonlinear science N2 - One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot. However, thick lines also influence the RQA measures by artificially increasing the number of diagonals and the length of vertical lines [e.g., Determinism (DET) and Laminarity (LAM) become artificially higher]. To take on this challenge, an extended RQA approach for accounting disrupted and deviated diagonal lines is proposed. The approach uses the concept of a sliding diagonal window with minimal window size that tolerates the mentioned deviated lines and also considers a specified minimal lag between points as connected. This is meant to derive a similar determinism indicator for noisy signal where conventional RQA fails to capture. Additionally, an extended local minima approach to construct RP is also proposed to further reduce artificial block structures and vertical lines that potentially increase the associated RQA like LAM. The methodology and applicability of the extended local minima approach and DET equivalent measure are presented and discussed, respectively. Y1 - 2018 U6 - https://doi.org/10.1063/1.5025485 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 8 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Öztürk, Ugur A1 - Marwan, Norbert A1 - von Specht, Sebastian A1 - Korup, Oliver A1 - Jensen, J. T1 - A new centennial sea-level record for Antalya, Eastern Mediterranean JF - Journal of geophysical research-oceans N2 - Quantitative estimates of sea-level rise in the Mediterranean Basin become increasingly accurate thanks to detailed satellite monitoring. However, such measuring campaigns cover several years to decades, while longer-term sea-level records are rare for the Mediterranean. We used a data archeological approach to reanalyze monthly mean sea-level data of the Antalya-I (1935–1977) tide gauge to fill this gap. We checked the accuracy and reliability of these data before merging them with the more recent records of the Antalya-II (1985–2009) tide gauge, accounting for an eight-year hiatus. We obtain a composite time series of monthly and annual mean sea levels spanning some 75 years, providing the longest record for the eastern Mediterranean Basin, and thus an essential tool for studying the region's recent sea-level trends. We estimate a relative mean sea-level rise of 2.2 ± 0.5 mm/year between 1935 and 2008, with an annual variability (expressed here as the standard deviation of the residuals, σresiduals = 41.4 mm) above that at the closest tide gauges (e.g., Thessaloniki, Greece, σresiduals = 29.0 mm). Relative sea-level rise accelerated to 6.0 ± 1.5 mm/year at Antalya-II; we attribute roughly half of this rate (~3.6 mm/year) to tectonic crustal motion and anthropogenic land subsidence. Our study highlights the value of data archeology for recovering and integrating historic tide gauge data for long-term sea-level and climate studies. KW - sea level KW - tide gauge KW - data archeology KW - Mediterranean Sea Y1 - 2018 U6 - https://doi.org/10.1029/2018JC013906 SN - 2169-9275 SN - 2169-9291 VL - 123 IS - 7 SP - 4503 EP - 4517 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Wendi, Dadiyorto A1 - Marwan, Norbert A1 - Merz, Bruno T1 - In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization. KW - Recurrence plot KW - phase space time delay embedding reconstruction KW - artefact avoidance Y1 - 2017 U6 - https://doi.org/10.1142/S0218127418500074 SN - 0218-1274 SN - 1793-6551 VL - 28 IS - 1 PB - World Scientific CY - Singapore ER -