ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In t... more ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In turn, changes in the nonlinear dynamics of sea-level variability have hardly been studied so far, even though they can provide unique information on the ocean's response to long-term changes of different atmospheric driving factors. In this work, we study seven long-term daily tide gauge records from the Baltic Sea with a set of complementary methods of linear and nonlinear time series analysis, including discrete wavelet analysis, autocorrelation-based dimension densities, time- and scale-dependent detrended fluctuation analysis, measures of complexity based on recurrence quantification analysis and recurrence networks, as well as information-theoretic approaches. The linear and nonlinear dynamical properties obtained for different records show consistent long-term variations, which are determined by changes in both local hydrological factors and the regional climatology. Time- and scale-resolved analyses reveal that temporal changes of nonlinear dynamic characteristics affect different temporal scales in different ways and are thus reflected differently by the individual measures evaluated at distinct scales. The corresponding analysis allows identifying and distinguishing long-term changes in sub-annual as well as annual to decadal-scale variability, which can be related to triggering factors acting at different temporal scales. In general, the results of all applied analyses display a consistent spatial pattern with a marked latitudinal complexity gradient, with sea-level variability being most complex close to the Baltic entrance and least complex in the central Baltic Sea.
The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal ... more The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal cycle exhibits a marked minimum in the Spring and accounts typically for about 40% of the total sea-level variability. In a climate change context changes are expected to occur not only in mean levels but also in sea-level seasonal characteristics. Such changes, even if not large in magnitude, are extremely important for ecosystems adapted to seasonal changes of the environment. Furthermore, quantifying and comprehending changes in seasonality is important to understand the mechanisms influencing regional sea level variability. Previous studies of Baltic sea-level suggested the existence of long-term changes in the seasonal cycle, in particular a possible increase of the annual amplitude. The present study addresses the quantification of changes in the seasonal cycle of sea-level in the Baltic Sea from a discrete wavelet analysis of long tide gauge records. As a pre-processing step all t...
During the last decades, the radioactive noble gas radon has found a variety of geoscientific app... more During the last decades, the radioactive noble gas radon has found a variety of geoscientific applications, ranging from its utilization as a potential earthquake precursor and proxy of tectonic stress over its specific role in volcanic environments to a wide range of applications as a tracer in marine and hydrological settings. This topical issue summarizes the current state of research as exemplified by some original research articles covering the aforementioned as well as other closely related aspects and points to some important future directions of radon application in geosciences. This editorial provides a more detailed overview of the contents of this volume, a brief summary of the rationale underlying the diverse applications, and outlines some important perspectives.
ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are availabl... more ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are available. To study complex oceanographic processes and their coupling to atmospheric dynamics it is necessary to advance beyond analyzing global mean sea-level rise or local trends. We apply a wide range of methods from linear and nonlinear time series analysis for investigating the complex dynamics of observed sea-level altimetry time series at different locations around the globe. Employing this toolkit, linear and nonlinear autodependencies (autocorrelation and auto-mutual information functions), deterministic structure (recurrence quantification and recurrence network analysis), time-reversibility characteristics (visibility graph analysis) and the relative importance of stochastic vs. deterministic dynamics (complexity-entropy plane) are studied. Combining the complimentary information from all metrics, consistent spatial patterns of sea-level dynamics are detected. Classical statistical properties such as variance, skewness and Shannon entropy of the probability distribution of sea-level reveal the special importance of western boundary currents as well as parts of the Antarctic Circumpolar Current as regions of particularly complex sea-level dynamics. In turn, the nonlinear dynamics characteristics present a somewhat different pattern exhibiting particularly high complexity in the tropics as well as the Gulf Stream and Kuroshio regions. Notably, these are also the areas where missing values due to atmospheric processes are most prominent. Further research is required to fully disentangle the dynamic complexity of sea-level from potential artifacts in the underlying altimetry data.
ABSTRACT Time series analysis offers a rich toolbox for deciphering information from high-resolut... more ABSTRACT Time series analysis offers a rich toolbox for deciphering information from high-resolution geological and geomorphological archives and linking the thus obtained results to distinct climate and environmental processes. Specifically, on various time-scales from inter-annual to multi-millenial, underlying driving forces exhibit more or less periodic oscillations, the detection of which in proxy records often allows linking them to specific mechanisms by which the corresponding drivers may have affected the archive under study. A persistent problem in geomorphology is that available records do not present a clear signal of the variability of environmental conditions, but exhibit considerable uncertainties of both the measured proxy variables and the associated age model. Particularly, time-scale uncertainty as well as the heterogeneity of sampling in the time domain are source of severe conceptual problems that may lead to false conclusions about the presence or absence of oscillatory patterns and their mutual phasing in different archives. In my presentation, I will discuss how one can cope with non-uniformly sampled proxy records to detect and quantify oscillatory patterns in one or more data sets. For this purpose, correlation analysis is reformulated using kernel estimates which are found superior to classical estimators based on interpolation or Fourier transform techniques. In order to characterize non-stationary or noisy periodicities and their relative phasing between different records, an extension of continuous wavelet transform is utilized. The performance of both methods is illustrated for different case studies. An extension to explicitly considering time-scale uncertainties by means of Bayesian techniques is briefly outlined.
ABSTRACT Properly describing temporal changes in the occurrence of extremely high or low temperat... more ABSTRACT Properly describing temporal changes in the occurrence of extremely high or low temperatures has a paramount relevance for properly assessing the potential local impacts of ongoing climatic changes and estimating possible future trends. As an alternative to traditional extreme value statistics, in this work we utilize linear quantile regression to unveil long-term trends in arbitrary quantiles of the distribution of daily mean, maximum and minimum temperatures inferred from the NCEP/NCAR and ERA 40 reanalysis data sets. Our results allow identifying climatic hotspots in which extreme temperatures consistently change faster than the trend in the mean, as well as regions displaying inconsistent behavior for both data sets. In order to further validate the obtained results, a repetition of the proposed analysis for station data of surface air temperatures is outlined.
Networks with nodes embedded in a metric space have gained increasing interest in recent years. T... more Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.
ABSTRACT The time-reversibility structure of climate time series provides important information o... more ABSTRACT The time-reversibility structure of climate time series provides important information on the nature of the underlying processes. A novel statistical test for time-reversibility is employed that is based on the study of time-directed properties of visibility graphs constructed from time series and is particularly suitable for the study of irregularly sampled paleoclimate proxy records. Several oxygen isotope records of Greenland paleoclimate during the late Pleistocene and Holocene are investigated. We find that the records' time-reversibility structure changes from irreversible to reversible several 10 ky before the glacial termination. This finding suggests that strongly nonlinear (irreversible) climate dynamics (probably related to the asymmetric saw-tooth-like profile of strong Dansgaard-Oeschger and Heinrich events) during the coldest stage were followed by reversible more Holocene-like dynamics appearing well before the actual beginning of the Holocene. Hence, changes in time-reversibility structure may provide a nonlinear early warning signal for climate tipping points, complimenting features such as critical slowing down or increasing auto-correlation.
Observed recent and expected future increases in frequency and intensity of climatic extremes in ... more Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions.
Mutually intertwined supply chains in contemporary economy result in a complex network of trade r... more Mutually intertwined supply chains in contemporary economy result in a complex network of trade relationships with a highly non-trivial topology that varies with time. In order to understand the complex interrelationships among different countries and economic sectors, as well as their dynamics, a holistic view on the underlying structural properties of this network is necessary. This study employs multi-regional input-output data to decompose 186 national economies into 26 industry sectors and utilizes the approach of interdependent networks to analyze the substructure of the resulting international trade network for the years 1990-2011. The partition of the network into national economies is observed to be compatible with the notion of communities in the sense of complex network theory. By studying internal versus cross-subgraph contributions to established complex network metrics, new insights into the architecture of global trade are obtained, which allow to identify key elements of global economy. Specifically, financial services and business activities dominate domestic trade whereas electrical and machinery industries dominate foreign trade. In order to further specify each national sector's role individually, (cross-)clustering coefficients and cross-betweenness are obtained for different pairs of subgraphs. The corresponding analysis reveals that specific industrial sectors tend to favor distinct directionality patterns and that the cross-clustering coefficient for geographically close country pairs is remarkably high, indicating that spatial factors are still of paramount importance for the organization of trade patterns in modern economy. Regarding the evolution of the trade network's substructure, globalization is well-expressed by trends of several structural characteristics (e.g., link density and node strength) in the interacting network framework. Extreme events, such as the financial crisis 2008/2009, are manifested as anomalies superimposed to these trends. The marked reorganization of trade patterns, associated with this economic crisis in comparison to "normal" annual fluctuations in the network structure is traced and quantified by a new widely applicable generalization of the Hamming distance to weighted networks.
This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckman... more This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (Europhys. Lett. 4 (1987), 973).
ABSTRACT The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the ... more ABSTRACT The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal cycle exhibits a marked minimum in the Spring and accounts typically for about 40% of the total sea-level variability. In a climate change context changes are expected to occur not only in mean levels but also in sea-level seasonal characteristics. Such changes, even if not large in magnitude, are extremely important for ecosystems adapted to seasonal changes of the environment. Furthermore, quantifying and comprehending changes in seasonality is important to understand the mechanisms influencing regional sea level variability. Previous studies of Baltic sea-level suggested the existence of long-term changes in the seasonal cycle, in particular a possible increase of the annual amplitude. The present study addresses the quantification of changes in the seasonal cycle of sea-level in the Baltic Sea from a discrete wavelet analysis of long tide gauge records. As a pre-processing step all tide gauge records are linearly detrended, thereby removing long-term changes in the mean (either from oceanographic or vertical land movement origin). The seasonal cycle is then extracted from a multiresolution decomposition based on the maximal overlap discrete wavelet transform and changes in both amplitude and phase are quantified. Long-term changes in the seasonal cycle are further examined by comparing the results from different methods including autoregressive-based decomposition, singular spectral analysis (SSA) and empirical mode decomposition (EMD). To assess the potential mechanisms determining the identified changes in the seasonal cycle, a coherence analysis is performed on atmospheric pressure, temperature, and precipitation reanalysis data.
We introduce a geometric method for identifying the coupling direction between two dynamical syst... more We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled R\"ossler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying $K>2$ coupled subsystems.
ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In t... more ABSTRACT Recent work on sea-level change has mainly focused on long-term trends in the mean. In turn, changes in the nonlinear dynamics of sea-level variability have hardly been studied so far, even though they can provide unique information on the ocean's response to long-term changes of different atmospheric driving factors. In this work, we study seven long-term daily tide gauge records from the Baltic Sea with a set of complementary methods of linear and nonlinear time series analysis, including discrete wavelet analysis, autocorrelation-based dimension densities, time- and scale-dependent detrended fluctuation analysis, measures of complexity based on recurrence quantification analysis and recurrence networks, as well as information-theoretic approaches. The linear and nonlinear dynamical properties obtained for different records show consistent long-term variations, which are determined by changes in both local hydrological factors and the regional climatology. Time- and scale-resolved analyses reveal that temporal changes of nonlinear dynamic characteristics affect different temporal scales in different ways and are thus reflected differently by the individual measures evaluated at distinct scales. The corresponding analysis allows identifying and distinguishing long-term changes in sub-annual as well as annual to decadal-scale variability, which can be related to triggering factors acting at different temporal scales. In general, the results of all applied analyses display a consistent spatial pattern with a marked latitudinal complexity gradient, with sea-level variability being most complex close to the Baltic entrance and least complex in the central Baltic Sea.
The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal ... more The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal cycle exhibits a marked minimum in the Spring and accounts typically for about 40% of the total sea-level variability. In a climate change context changes are expected to occur not only in mean levels but also in sea-level seasonal characteristics. Such changes, even if not large in magnitude, are extremely important for ecosystems adapted to seasonal changes of the environment. Furthermore, quantifying and comprehending changes in seasonality is important to understand the mechanisms influencing regional sea level variability. Previous studies of Baltic sea-level suggested the existence of long-term changes in the seasonal cycle, in particular a possible increase of the annual amplitude. The present study addresses the quantification of changes in the seasonal cycle of sea-level in the Baltic Sea from a discrete wavelet analysis of long tide gauge records. As a pre-processing step all t...
During the last decades, the radioactive noble gas radon has found a variety of geoscientific app... more During the last decades, the radioactive noble gas radon has found a variety of geoscientific applications, ranging from its utilization as a potential earthquake precursor and proxy of tectonic stress over its specific role in volcanic environments to a wide range of applications as a tracer in marine and hydrological settings. This topical issue summarizes the current state of research as exemplified by some original research articles covering the aforementioned as well as other closely related aspects and points to some important future directions of radon application in geosciences. This editorial provides a more detailed overview of the contents of this volume, a brief summary of the rationale underlying the diverse applications, and outlines some important perspectives.
ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are availabl... more ABSTRACT Since the advent of the satellite era, global sea-level altimetry data sets are available. To study complex oceanographic processes and their coupling to atmospheric dynamics it is necessary to advance beyond analyzing global mean sea-level rise or local trends. We apply a wide range of methods from linear and nonlinear time series analysis for investigating the complex dynamics of observed sea-level altimetry time series at different locations around the globe. Employing this toolkit, linear and nonlinear autodependencies (autocorrelation and auto-mutual information functions), deterministic structure (recurrence quantification and recurrence network analysis), time-reversibility characteristics (visibility graph analysis) and the relative importance of stochastic vs. deterministic dynamics (complexity-entropy plane) are studied. Combining the complimentary information from all metrics, consistent spatial patterns of sea-level dynamics are detected. Classical statistical properties such as variance, skewness and Shannon entropy of the probability distribution of sea-level reveal the special importance of western boundary currents as well as parts of the Antarctic Circumpolar Current as regions of particularly complex sea-level dynamics. In turn, the nonlinear dynamics characteristics present a somewhat different pattern exhibiting particularly high complexity in the tropics as well as the Gulf Stream and Kuroshio regions. Notably, these are also the areas where missing values due to atmospheric processes are most prominent. Further research is required to fully disentangle the dynamic complexity of sea-level from potential artifacts in the underlying altimetry data.
ABSTRACT Time series analysis offers a rich toolbox for deciphering information from high-resolut... more ABSTRACT Time series analysis offers a rich toolbox for deciphering information from high-resolution geological and geomorphological archives and linking the thus obtained results to distinct climate and environmental processes. Specifically, on various time-scales from inter-annual to multi-millenial, underlying driving forces exhibit more or less periodic oscillations, the detection of which in proxy records often allows linking them to specific mechanisms by which the corresponding drivers may have affected the archive under study. A persistent problem in geomorphology is that available records do not present a clear signal of the variability of environmental conditions, but exhibit considerable uncertainties of both the measured proxy variables and the associated age model. Particularly, time-scale uncertainty as well as the heterogeneity of sampling in the time domain are source of severe conceptual problems that may lead to false conclusions about the presence or absence of oscillatory patterns and their mutual phasing in different archives. In my presentation, I will discuss how one can cope with non-uniformly sampled proxy records to detect and quantify oscillatory patterns in one or more data sets. For this purpose, correlation analysis is reformulated using kernel estimates which are found superior to classical estimators based on interpolation or Fourier transform techniques. In order to characterize non-stationary or noisy periodicities and their relative phasing between different records, an extension of continuous wavelet transform is utilized. The performance of both methods is illustrated for different case studies. An extension to explicitly considering time-scale uncertainties by means of Bayesian techniques is briefly outlined.
ABSTRACT Properly describing temporal changes in the occurrence of extremely high or low temperat... more ABSTRACT Properly describing temporal changes in the occurrence of extremely high or low temperatures has a paramount relevance for properly assessing the potential local impacts of ongoing climatic changes and estimating possible future trends. As an alternative to traditional extreme value statistics, in this work we utilize linear quantile regression to unveil long-term trends in arbitrary quantiles of the distribution of daily mean, maximum and minimum temperatures inferred from the NCEP/NCAR and ERA 40 reanalysis data sets. Our results allow identifying climatic hotspots in which extreme temperatures consistently change faster than the trend in the mean, as well as regions displaying inconsistent behavior for both data sets. In order to further validate the obtained results, a repetition of the proposed analysis for station data of surface air temperatures is outlined.
Networks with nodes embedded in a metric space have gained increasing interest in recent years. T... more Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.
ABSTRACT The time-reversibility structure of climate time series provides important information o... more ABSTRACT The time-reversibility structure of climate time series provides important information on the nature of the underlying processes. A novel statistical test for time-reversibility is employed that is based on the study of time-directed properties of visibility graphs constructed from time series and is particularly suitable for the study of irregularly sampled paleoclimate proxy records. Several oxygen isotope records of Greenland paleoclimate during the late Pleistocene and Holocene are investigated. We find that the records' time-reversibility structure changes from irreversible to reversible several 10 ky before the glacial termination. This finding suggests that strongly nonlinear (irreversible) climate dynamics (probably related to the asymmetric saw-tooth-like profile of strong Dansgaard-Oeschger and Heinrich events) during the coldest stage were followed by reversible more Holocene-like dynamics appearing well before the actual beginning of the Holocene. Hence, changes in time-reversibility structure may provide a nonlinear early warning signal for climate tipping points, complimenting features such as critical slowing down or increasing auto-correlation.
Observed recent and expected future increases in frequency and intensity of climatic extremes in ... more Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions.
Mutually intertwined supply chains in contemporary economy result in a complex network of trade r... more Mutually intertwined supply chains in contemporary economy result in a complex network of trade relationships with a highly non-trivial topology that varies with time. In order to understand the complex interrelationships among different countries and economic sectors, as well as their dynamics, a holistic view on the underlying structural properties of this network is necessary. This study employs multi-regional input-output data to decompose 186 national economies into 26 industry sectors and utilizes the approach of interdependent networks to analyze the substructure of the resulting international trade network for the years 1990-2011. The partition of the network into national economies is observed to be compatible with the notion of communities in the sense of complex network theory. By studying internal versus cross-subgraph contributions to established complex network metrics, new insights into the architecture of global trade are obtained, which allow to identify key elements of global economy. Specifically, financial services and business activities dominate domestic trade whereas electrical and machinery industries dominate foreign trade. In order to further specify each national sector's role individually, (cross-)clustering coefficients and cross-betweenness are obtained for different pairs of subgraphs. The corresponding analysis reveals that specific industrial sectors tend to favor distinct directionality patterns and that the cross-clustering coefficient for geographically close country pairs is remarkably high, indicating that spatial factors are still of paramount importance for the organization of trade patterns in modern economy. Regarding the evolution of the trade network's substructure, globalization is well-expressed by trends of several structural characteristics (e.g., link density and node strength) in the interacting network framework. Extreme events, such as the financial crisis 2008/2009, are manifested as anomalies superimposed to these trends. The marked reorganization of trade patterns, associated with this economic crisis in comparison to "normal" annual fluctuations in the network structure is traced and quantified by a new widely applicable generalization of the Hamming distance to weighted networks.
This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckman... more This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (Europhys. Lett. 4 (1987), 973).
ABSTRACT The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the ... more ABSTRACT The seasonal cycle is an ubiquitous feature in sea-level records. In the Baltic Sea the seasonal cycle exhibits a marked minimum in the Spring and accounts typically for about 40% of the total sea-level variability. In a climate change context changes are expected to occur not only in mean levels but also in sea-level seasonal characteristics. Such changes, even if not large in magnitude, are extremely important for ecosystems adapted to seasonal changes of the environment. Furthermore, quantifying and comprehending changes in seasonality is important to understand the mechanisms influencing regional sea level variability. Previous studies of Baltic sea-level suggested the existence of long-term changes in the seasonal cycle, in particular a possible increase of the annual amplitude. The present study addresses the quantification of changes in the seasonal cycle of sea-level in the Baltic Sea from a discrete wavelet analysis of long tide gauge records. As a pre-processing step all tide gauge records are linearly detrended, thereby removing long-term changes in the mean (either from oceanographic or vertical land movement origin). The seasonal cycle is then extracted from a multiresolution decomposition based on the maximal overlap discrete wavelet transform and changes in both amplitude and phase are quantified. Long-term changes in the seasonal cycle are further examined by comparing the results from different methods including autoregressive-based decomposition, singular spectral analysis (SSA) and empirical mode decomposition (EMD). To assess the potential mechanisms determining the identified changes in the seasonal cycle, a coherence analysis is performed on atmospheric pressure, temperature, and precipitation reanalysis data.
We introduce a geometric method for identifying the coupling direction between two dynamical syst... more We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled R\"ossler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying $K>2$ coupled subsystems.
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