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- ItemMultiresolution analysis of the spatiotemporal variability in global radiation observed by a dense network of 99 pyranometers(Katlenburg-Lindau : EGU, 2017) Madhavan, Bomidi Lakshmi; Deneke, Hartwig; Witthuhn, Jonas; Macke, AndreasThe time series of global radiation observed by a dense network of 99 autonomous pyranometers during the HOPE campaign around Jülich, Germany, are investigated with a multiresolution analysis based on the maximum overlap discrete wavelet transform and the Haar wavelet. For different sky conditions, typical wavelet power spectra are calculated to quantify the timescale dependence of variability in global transmittance. Distinctly higher variability is observed at all frequencies in the power spectra of global transmittance under broken-cloud conditions compared to clear, cirrus, or overcast skies. The spatial autocorrelation function including its frequency dependence is determined to quantify the degree of similarity of two time series measurements as a function of their spatial separation. Distances ranging from 100-m to 10-km are considered, and a rapid decrease of the autocorrelation function is found with increasing frequency and distance. For frequencies above 1-3-ming-1 and points separated by more than 1-km, variations in transmittance become completely uncorrelated. A method is introduced to estimate the deviation between a point measurement and a spatially averaged value for a surrounding domain, which takes into account domain size and averaging period, and is used to explore the representativeness of a single pyranometer observation for its surrounding region. Two distinct mechanisms are identified, which limit the representativeness; on the one hand, spatial averaging reduces variability and thus modifies the shape of the power spectrum. On the other hand, the correlation of variations of the spatially averaged field and a point measurement decreases rapidly with increasing temporal frequency. For a grid box of 10-km-×-10-km and averaging periods of 1.5-3-h, the deviation of global transmittance between a point measurement and an area-averaged value depends on the prevailing sky conditions: 2.8 (clear), 1.8 (cirrus), 1.5 (overcast), and 4.2-% (broken clouds). The solar global radiation observed at a single station is found to deviate from the spatial average by as much as 14-23 (clear), 8-26 (cirrus), 4-23 (overcast), and 31-79-Wg-mg-2 (broken clouds) from domain averages ranging from 1-km-×-1-km to 10-km-×-10-km in area.
- ItemSimilarity estimators for irregular and age-uncertain time series(München : European Geopyhsical Union, 2014) Rehfeld, K.; Kurths, J.Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.
- ItemInferring causation from time series in Earth system sciences([London] : Nature Publishing Group UK, 2019) Runge, Jakob; Bathiany, Sebastian; Bollt, Erik; Camps-Valls, Gustau; Coumou, Dim; Deyle, Ethan; Glymour, Clark; Kretschmer, Marlene; Mahecha, Miguel D.; Muñoz-MarÃ, Jordi; van Nes, Egbert H.; Peters, Jonas; Quax, Rick; Reichstein, Markus; Scheffer, Marten; Schölkopf, Bernhard; Spirtes, Peter; Sugihara, George; Sun, Jie; Zhang, Kun; Zscheischler, JakobThe heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers. © 2019, The Author(s).
- ItemAbrupt transitions in time series with uncertainties(London : Nature Publishing Group, 2018) Goswami, B.; Boers, N.; Rheinwalt, A.; Marwan, N.; Heitzig, J.; Breitenbach, S.F.M.; Kurths, J.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.
- ItemSleep apnea-hypopnea quantification by cardiovascular data analysis(San Francisco, CA : Public Library of Science (PLoS), 2014) Camargo, S.; Riedl, M.; Anteneodo, C.; Kurths, J.; Penzel, T.; Wessel, N.Sleep disorders are a major risk factor for cardiovascular diseases. Sleep apnea is the most common sleep disturbance and its detection relies on a polysomnography, i.e., a combination of several medical examinations performed during a monitored sleep night. In order to detect occurrences of sleep apnea without the need of combined recordings, we focus our efforts on extracting a quantifier related to the events of sleep apnea from a cardiovascular time series, namely systolic blood pressure (SBP). Physiologic time series are generally highly nonstationary and entrap the application of conventional tools that require a stationary condition. In our study, data nonstationarities are uncovered by a segmentation procedure which splits the signal into stationary patches, providing local quantities such as mean and variance of the SBP signal in each stationary patch, as well as its duration L. We analysed the data of 26 apneic diagnosed individuals, divided into hypertensive and normotensive groups, and compared the results with those of a control group. From the segmentation procedure, we identified that the average duration 〈L〉, as well as the average variance 〈σ2〉, are correlated to the apnea-hypoapnea index (AHI), previously obtained by polysomnographic exams. Moreover, our results unveil an oscillatory pattern in apneic subjects, whose amplitude S∗ is also correlated with AHI. All these quantities allow to separate apneic individuals, with an accuracy of at least 79%. Therefore, they provide alternative criteria to detect sleep apnea based on a single time series, the systolic blood pressure.
- ItemProbing the Statistical Properties of Unknown Texts: Application to the Voynich Manuscript(San Francisco, CA : Public Library of Science (PLoS), 2013) Amancio, D.R.; Altmann, E.G.; Rybski, D.; Oliveira Jr., O.N.; da Costa, L.F.While the use of statistical physics methods to analyze large corpora has been useful to unveil many patterns in texts, no comprehensive investigation has been performed on the interdependence between syntactic and semantic factors. In this study we propose a framework for determining whether a text (e.g., written in an unknown alphabet) is compatible with a natural language and to which language it could belong. The approach is based on three types of statistical measurements, i.e. obtained from first-order statistics of word properties in a text, from the topology of complex networks representing texts, and from intermittency concepts where text is treated as a time series. Comparative experiments were performed with the New Testament in 15 different languages and with distinct books in English and Portuguese in order to quantify the dependency of the different measurements on the language and on the story being told in the book. The metrics found to be informative in distinguishing real texts from their shuffled versions include assortativity, degree and selectivity of words. As an illustration, we analyze an undeciphered medieval manuscript known as the Voynich Manuscript. We show that it is mostly compatible with natural languages and incompatible with random texts. We also obtain candidates for keywords of the Voynich Manuscript which could be helpful in the effort of deciphering it. Because we were able to identify statistical measurements that are more dependent on the syntax than on the semantics, the framework may also serve for text analysis in language-dependent applications.
- ItemChange in the embedding dimension as an indicator of an approaching transition(San Francisco, CA : Public Library of Science (PLoS), 2014) Neuman, Y.; Marwan, N.; Cohen, Y.Predicting a transition point in behavioral data should take into account the complexity of the signal being influenced by contextual factors. In this paper, we propose to analyze changes in the embedding dimension as contextual information indicating a proceeding transitive point, called OPtimal Embedding tRANsition Detection (OPERAND). Three texts were processed and translated to time-series of emotional polarity. It was found that changes in the embedding dimension proceeded transition points in the data. These preliminary results encourage further research into changes in the embedding dimension as generic markers of an approaching transition point.
- ItemAdvances in Time Series Analysis and Its Applications(New York, NY : Hindawi Publishing Corporation, 2016) Gao, Z.-K.; Small, M.; Donner, R.; Meng, D.; Ghaffari, H.O.
- ItemA Rigorous Statistical Assessment of Recent Trends in Intensity of Heavy Precipitation Over Germany(Lausanne : Frontiers Media, 2019) Passow, Christian; Donner, Reik V.Comprehensive and robust statistical estimates of trends during heavy precipitation events are essential in understanding the impact of past and future climate changes in the hydrological cycle. However, methods commonly used in extreme value statistics (EVS) are often unable to detect significant trends, because of their methodologically motivated reduction of the sample size and strong assumptions regarding the underlying distribution. Here, we propose linear quantile regression (QR) as a complementary and robust alternative to estimating trends in heavy precipitation events. QR does not require any assumptions on the underlying distribution and is also able to estimate trends for the full span of the distribution without any reduction of the available data. As an example, we study here a very dense and homogenized data set of daily precipitation amounts over Germany for the period between 1951 and 2006 to compare the results of QR and the so-called block maxima approach, a classical method in EVS. Both methods indicate an overall increase in the intensity of heavy precipitation events. The strongest trends can be found in regions with an elevation of about 500 m above sea level. In turn, larger spatial clusters of moderate or even decreasing trends can only be found in Northeastern Germany. In conclusion, both methods show comparable results. QR, however, allows for a more flexible and comprehensive study of precipitation events. © Copyright © 2019 Passow and Donner.
- ItemOrder patterns networks (orpan) - A method to estimate time-evolving functional connectivity from multivariate time series(Lausanne : Frontiers Research Foundation, 2012) Schinkel, S.; Zamora-López, G.; Dimigen, O.; Sommer, W.; Kurths, J.Complex networks provide an excellent framework for studying the function of the human brain activity. Yet estimating functional networks from measured signals is not trivial, especially if the data is non-stationary and noisy as it is often the case with physiological recordings. In this article we propose a method that uses the local rank structure of the data to define functional links in terms of identical rank structures. The method yields temporal sequences of networks which permits to trace the evolution of the functional connectivity during the time course of the observation. We demonstrate the potentials of this approach with model data as well as with experimental data from an electrophysiological study on language processing.