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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 structures and directionalities in Monsoonal precipitation over South Asia(Göttingen : Copernicus GmbH, 2010) Malik, N.; Marwan, N.; Kurths, J.Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.
- ItemAn extended singular spectrum transformation (SST) for the investigation of Kenyan precipitation data(Göttingen : Copernicus GmbH, 2013) Itoh, N.; Marwan, N.In this paper a change-point detection method is proposed by extending the singular spectrum transformation (SST) developed as one of the capabilities of singular spectrum analysis (SSA). The method uncovers change points related with trends and periodicities. The potential of the proposed method is demonstrated by analysing simple model time series including linear functions and sine functions as well as real world data (precipitation data in Kenya). A statistical test of the results is proposed based on a Monte Carlo simulation with surrogate methods. As a result, the successful estimation of change points as inherent properties in the representative time series of both trend and harmonics is shown. With regards to the application, we find change points in the precipitation data of Kenyan towns (Nakuru, Naivasha, Narok, and Kisumu) which coincide with the variability of the Indian Ocean Dipole (IOD) suggesting its impact of extreme climate in East Africa.
- 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.