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- ItemIdentification of dynamical transitions in marine palaeoclimate records by recurrence network analysis(Göttingen : Copernicus GmbH, 2011) Donges, J.F.; Donner, R.V.; Rehfeld, K.; Marwan, N.; Trauth, M.H.; Kurths, J.The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
- ItemSpatial patterns of linear and nonparametric long-term trends in Baltic sea-level variability(Göttingen : Copernicus GmbH, 2012) Donner, R.V.; Ehrcke, R.; Barbosa, S.M.; Wagner, J.; Donges, J.F.; Kurths, J.The study of long-term trends in tide gauge data is important for understanding the present and future risk of changes in sea-level variability for coastal zones, particularly with respect to the ongoing debate on climate change impacts. Traditionally, most corresponding analyses have exclusively focused on trends in mean sea-level. However, such studies are not able to provide sufficient information about changes in the full probability distribution (especially in the more extreme quantiles). As an alternative, in this paper we apply quantile regression (QR) for studying changes in arbitrary quantiles of sea-level variability. For this purpose, we chose two different QR approaches and discuss the advantages and disadvantages of different settings. In particular, traditional linear QR poses very restrictive assumptions that are often not met in reality. For monthly data from 47 tide gauges from along the Baltic Sea coast, the spatial patterns of quantile trends obtained in linear and nonparametric (spline-based) frameworks display marked differences, which need to be understood in order to fully assess the impact of future changes in sea-level variability on coastal areas. In general, QR demonstrates that the general variability of Baltic sea-level has increased over the last decades. Linear quantile trends estimated for sliding windows in time reveal a wide-spread acceleration of trends in the median, but only localised changes in the rates of changes in the lower and upper quantiles.
- ItemLong-term changes in the north-south asymmetry of solar activity: A nonlinear dynamics characterization using visibility graphs(Göttingen : Copernicus GmbH, 2014) Zou, Y.; Donner, R.V.; Marwan, N.; Small, M.; Kurths, J.Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.
- ItemCorrelation-Based characterisation of time-Varying dynamical complexity in the Earth's magnetosphere(Göttingen : Copernicus GmbH, 2013) Donner, R.V.; Balasis, G.The dynamical behaviour of the magnetosphere is known to be a sensitive indicator for the response of the system to solar wind coupling. Since the solar activity commonly displays very interesting non-stationary and multi-scale dynamics, the magnetospheric response also exhibits a high degree of dynamical complexity associated with fundamentally different characteristics during periods of quiescence and magnetic storms. The resulting temporal complexity profile has been explored using several approaches from applied statistics, dynamical systems theory and statistical mechanics. Here, we propose an alternative way of looking at time-varying dynamical complexity of nonlinear geophysical time series utilising subtle but significant changes in the linear autocorrelation structure of the recorded data. Our approach is demonstrated to sensitively trace the dynamic signatures associated with intense magnetic storms, and to display reasonable skills in distinguishing between quiescence and storm periods. The potentials and methodological limitations of this new viewpoint are discussed in some detail.