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The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this wiggle matching by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.
The method of recurrence plots is extended to the cross recurrence plots (CRP), which among others enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of it is e.g. compressed or stretched) so that they are synchronized. An application of this method to geophysical sediment core data illustrates its suitability for real data. The rock magnetic data of two different sediment cores from the Makarov Basin can be adjusted to each other by using this method, so that they are comparable.
We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation.
The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.
Sea surface temperature (SST) patterns can – as surface climate forcing – affect weather and climate at large distances. One example is El Niño-Southern Oscillation (ENSO) that causes climate anomalies around the globe via teleconnections. Although several studies identified and characterized these teleconnections, our understanding of climate processes remains incomplete, since interactions and feedbacks are typically exhibited at unique or multiple temporal and spatial scales. This study characterizes the interactions between the cells of a global SST data set at different temporal and spatial scales using climate networks. These networks are constructed using wavelet multi-scale correlation that investigate the correlation between the SST time series at a range of scales allowing instantaneously deeper insights into the correlation patterns compared to traditional methods like empirical orthogonal functions or classical correlation analysis. This allows us to identify and visualise regions of – at a certain timescale – similarly evolving SSTs and distinguish them from those with long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like ENSO and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections like the connection between ENSO and Indian Ocean Dipole.
High resolution reconstructions of the India Summer Monsoon (ISM) are essential to identify regionally different patterns of climate change and refine predictive models. We find opposing trends of hydrological proxies between northern (Sahiya cave stalagmite) and central India (Lonar Lake) between 100 and 1300 CE with the strongest anti-correlation between 810 and 1300 CE. The apparently contradictory data raise the question if these are related to widely different regional precipitation patterns or reflect human influence in/around the Lonar Lake. By comparing multiproxy data with historical records, we demonstrate that only the organic proxies in the Lonar Lake show evidence of anthropogenic impact. However, evaporite data (mineralogy and delta O-18) are indicative of precipitation/evaporation (P/E) into the Lonar Lake. Back-trajectories of air-mass circulation over northern and central India show that the relative contribution of the Bay of Bengal (BoB) branch of the ISM is crucial for determining the delta O-18 of carbonate proxies only in north India, whereas central India is affected significantly by the Arabian Sea (AS) branch of the ISM. We conclude that the delta O-18 of evaporative carbonates in the Lonar Lake reflects P/E and, in the interval under consideration, is not influenced by source water changes. The opposing trend between central and northern India can be explained by (i) persistent multidecadal droughts over central India between 810 and 1300 CE that provided an effective mechanism for strengthening sub-tropical westerly winds resulting in enhancement of wintertime (non-monsoonal) rainfall over northern parts of the Indian subcontinent, and/or (ii) increased moisture influx to northern India from the depleted BoB source waters.
Encounters with neighbours
(2003)
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications. Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed. Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.
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.
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.
Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region.
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.
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.
A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.
Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure – the weighted degree–betweenness (WDB) measure – to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail.
The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.
Quantifying the roles of single stations within homogeneous regions using complex network analysis
(2018)
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.
We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.
We present the results of biogeochemical and mineralogical analyses on a sediment core that covers the Holocene sedimentation history of the climatically sensitive, closed, saline, and alkaline Lonar Lake in the core monsoon zone in central India. We compare our results of C/N ratios, stable carbon and nitrogen isotopes, grain-size, as well as amino acid derived degradation proxies with climatically sensitive proxies of other records from South Asia and the North Atlantic region. The comparison reveals some more or less contemporaneous climate shifts. At Lonar Lake, a general long term climate transition from wet conditions during the early Holocene to drier conditions during the late Holocene, delineating the insolation curve, can be reconstructed. In addition to the previously identified periods of prolonged drought during 4.6-3.9 and 2.0-0.6 cal ka that have been attributed to temperature changes in the Indo Pacific Warm Pool, several additional phases of shorter term climate alteration superimposed upon the general climate trend can be identified. These correlate with cold phases in the North Atlantic region. The most pronounced climate deteriorations indicated by our data occurred during 62-5.2,4.6-3.9, and 2.0-0.6 cal ka BP. The strong dry phase between 4.6 and 3.9 cal ka BP at Lonar Lake corroborates the hypothesis that severe climate deterioration contributed to the decline of the Indus Civilisation about 3.9 ka BP. (C) 2014 Elsevier B.V. All rights reserved.
Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the
Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots were developed to compare the influence of the El Nino/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has shown the stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Nina years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.