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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.
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
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.
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.
Recurrence-plot-based measures of complexity and its application to heart-rate-variability data
(2002)
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
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.
Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Niño/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.
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.
Multiple landslide clusters record quaternary climate changes in the northwestern Argentine andes
(2003)
The chronology of multiple landslide deposits and related lake sediments in the semi-arid eastern Argentine Cordillera suggests that major mass movements cluster in two time periods during the Quaternary, i.e. between 40 and 25 and after 5 14C kyr BP. These clusters may correspond to the Minchin (maximum at around 28-27 14C kyr BP) and Titicaca wet periods (after 3.9 14C kyr BP). The more humid conditions apparently caused enhanced landsliding in this environment. In contrast, no landslide-related damming and associated lake sediments occurred during the Coipasa (11.5- 10 14C yr BP) and Tauca wet periods (14.5-11 14C yr BP). The two clusters at 40-25 and after 5 14C kyr BP may correspond to periods where the El Niño-Southern Oscillation (ENSO) and Tropical Atlantic Sea Surface Temperature Variability (TAV) were active. This, however, was not the case during the Coipasa and Tauca wet periods. Lake-balance modelling of a landslide-dammed lake suggests a 10-15% increase in precipitation and a 3-4 ° C decrease in temperature at ~30 14C kyr BP as compared to the present. In addition, time-series analysis reveals a strong ENSO and TAV during that time. The landslide clusters in northwestern Argentina are therefore best explained by periods of more humid and more variable climates.
We present new measures of complexity and their application to event-related potential data. The new measures are based on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis
A statistical model describing the propensity for protein aggregation is presented. Only amino-acid hydrophobicity values and calculated net charge are used for the model. The combined effects of hydrophobic patterns as computed by the signal analysis technique, recurrence quantification, plus calculated net charge were included in a function emphasizing the effect of singular hydrophobic patches which were found to be statistically significant for predicting aggregation propensity as quantified by fluorescence studies obtained from the literature. These results suggest preliminary evidence for a mesoscopic principle for protein folding/aggregation. (C) 2004 Elsevier B.V. All rights reserved
The presence of partially folded intermediates along the folding funnel of proteins has been suggested to be a signature of potentially aggregating systems. Many studies have concluded that metastable, highly flexible intermediates are the basic elements of the aggregation process. In a previous paper, we demonstrated how the choice between aggregation and folding behavior was influenced by hydrophobicity distribution patterning along the sequence, as quantified by recurrence quantification analysis (RQA) of the Myiazawa-Jernigan coded primary structures. In the present paper, we tried to unify the "partially folded intermediate" and "hydrophobicity/charge" models of protein aggregation verifying the ability of an empirical relation, developed for rationalizing the effect of different mutations on aggregation propensity of acyl-phosphatase and based on the combination of hydrophobicity RQA and charge descriptors, to discriminate in a statistically significant way two different protein populations: (a) proteins that fold by a process passing by partially folded intermediates and (b) proteins that do not present partially folded intermediates
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time- transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements. (C) 2005 Elsevier B.V. All rights reserved
Three-dimensional quantification of structures in trabecular bone using measures of complexity
(2009)
The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (mu CT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mu CT data sets.
In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.
Complex networks in climate dynamics : comparing linear and nonlinear network construction methods
(2009)
Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.
Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.
The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.
To calibrate delta O-18 time-series from speleothems in the eastern Indian summer monsoon (ISM) region of India, and to understand the moisture regime over the northern Bay of Bengal (BoB) we analyze the delta O-18 and delta D of rainwater, collected in 2007 and 2008 near Cherrapunji, India. delta D values range from + 18.5 parts per thousand to 144.4 parts per thousand, while delta O-18 varies between +0.8 parts per thousand and 18.8 parts per thousand. The Local Meteoric Water Line (LMWL) is found to be indistinguishable from the Global Meteoric Water Line (GMWL). Late ISM (September-October) rainfall exhibits lowest delta O-18 and delta D values, with little relationship to the local precipitation amount. There is a trend to lighter isotope values over the course of the ISM, but it does not correlate with the patterns of temperature and rainfall amount delta O-18 and delta D time-series have to be interpreted with caution in terms of the 'amount effect' in this subtropical region. We find that the temporal trend in delta O-18 reflects increasing transport distance during the ISM, isotopic changes in the northern BoB surface waters during late ISM, and vapor re-equilibration with rain droplets. Using an isotope box model for surface ocean waters, we quantify the potential influence of river runoff on the isotopic composition of the seasonal freshwater plume in the northern BoB. Temporal variations in this source can contribute up to 25% of the observed changes in stable isotopes of precipitation in NE India. To delineate other moisture sources, we use backward trajectory computations and find a strong correlation between source region and isotopic composition. Palaeoclimatic stable isotope time-series from northeast Indian speleothems likely reflect changes in moisture source and transport pathway, as well as the isotopic composition of the BoB surface water, all of which in turn reflect ISM strength. Stalagmite records from the region can therefore be interpreted as integrated measures of the ISM strength.
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
(2011)
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
Purpose: We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range nodestrut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network.
Methods: Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341-349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3 x 3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region.
Results: We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r - 0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r - 0.62) between NdStr and the conventional node-terminus ratio (Nd/Tm) of Garrahan et al. The Nd/Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans.
Conclusions: The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.
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.
Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question.
We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.
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.
Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks
(2012)
We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June-September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades.
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.
We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.
Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.
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.
Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches - recurrence plots and recurrence networks -, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record.
We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy-depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India.
Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.
This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June-September), post-monsoon (October-December), and pre-monsoon (March-May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction.
Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.
Extreme Rainfall of the South American Monsoon System: A Dataset Comparison Using Complex Networks
(2015)
In this study, the authors compare six different rainfall datasets for South America with a focus on their representation of extreme rainfall during the monsoon season (December February): the gauge-calibrated TRMM 3B42 V7 satellite product; the near-real-time TRMM 3B42 V7 RT, the GPCP 1 degrees daily (1DD) V1.2 satellite gauge combination product, the Interim ECMWF Re-Analysis (ERA-Interim) product; output of a high-spatial-resolution run of the ECHAM6 global circulation model; and output of the regional climate model Eta. For the latter three, this study can be understood as a model evaluation. In addition to statistical values of local rainfall distributions, the authors focus on the spatial characteristics of extreme rainfall covariability. Since traditional approaches based on principal component analysis are not applicable in the context of extreme events, they apply and further develop methods based on complex network theory. This way, the authors uncover substantial differences in extreme rainfall patterns between the different datasets: (i) The three model-derived datasets yield very different results than the satellite gauge combinations regarding the main climatological propagation pathways of extreme events as well as the main convergence zones of the monsoon system. (ii) Large discrepancies are found for the development of mesoscale convective systems in southeastern South America. (iii) Both TRMM datasets and ECHAM6 indicate a linkage of extreme rainfall events between the central Amazon basin and the eastern slopes of the central Andes, but this pattern is not reproduced by the remaining datasets. The authors' study suggests that none of the three model-derived datasets adequately captures extreme rainfall patterns in South America.
Hydrological and climatological controls on radiocarbon concentrations in a tropical stalagmite
(2016)
Precisely-dated stalagmites are increasingly important archives for the reconstruction of terrestrial paleoclimate at very high temporal resolution. In-depth understanding of local conditions at the cave site and of the processes driving stalagmite deposition is of paramount importance for interpreting proxy signals incorporated in stalagmite carbonate. Here we present a sub-decadally resolved dead carbon fraction (DCF) record for a stalagmite from Yok Balum Cave (southern Belize). The record is coupled to parallel stable carbon isotope (delta C-13) and U/Ca measurements, as well as radiocarbon (C-14) measurements from soils overlying the cave system. Using a karst carbon cycle model we disentangle the importance of soil and karst processes on stalagmite DCF incorporation, revealing a dominant host rock dissolution control on total DCF. Covariation between DCF, delta C-13, and U/Ca indicates that karst processes are a common driver of all three parameters, suggesting possible use of delta C-13 and trace element ratios to independently quantify DCF variability. A statistically significant multi-decadal lag of variable length exists between DCF and reconstructed solar activity, suggesting that solar activity influenced regional precipitation in Mesoamerica over the past 1500 years, but that the relationship was non-static. Although the precise nature of the observed lag is unclear, solar-induced changes in North Atlantic oceanic and atmospheric dynamics may play a role. (C) 2016 Elsevier Ltd. All rights reserved.
Non-linear time series analysis of precipitation events using regional climate networks for Germany
(2016)
Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.
The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20 degrees S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20 degrees S and the Puna Plateau originates from southeastern South America.
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.
Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.
Northeastern (NE) India experiences extraordinarily pronounced seasonal climate, governed by the Indian summer monsoon (ISM). The vulnerability of this region to floods and droughts calls for detailed and highly resolved paleoclimate reconstructions to assess the recurrence rate and driving factors of ISM changes. We use stable oxygen and carbon isotope ratios (delta O-18 and delta C-13) from stalagmite MAW-6 from Mawmluh Cave to infer climate and environmental conditions in NE India over the last deglaciation (16-6ka). We interpret stalagmite delta O-18 as reflecting ISM strength, whereas delta C-13 appears to be driven by local hydroclimate conditions. Pronounced shifts in ISM strength over the deglaciation are apparent from the delta O-18 record, similarly to other records from monsoonal Asia. The ISM is weaker during the late glacial (LG) period and the Younger Dryas, and stronger during the BOlling-Allerod and Holocene. Local conditions inferred from the delta C-13 record appear to have changed less substantially over time, possibly related to the masking effect of changing precipitation seasonality. Time series analysis of the delta O-18 record reveals more chaotic conditions during the late glacial and higher predictability during the Holocene, likely related to the strengthening of the seasonal recurrence of the ISM with the onset of the Holocene.
The presence of a low-to mid-latitude interhemispheric hydrologic seesaw is apparent over orbital and glacial-interglacial timescales, but its existence over the most recent past remains unclear. Here we investigate, based on climate proxy reconstructions from both hemispheres, the inter-hemispherical phasing of the Intertropical Convergence Zone (ITCZ) and the low-to mid-latitude teleconnections in the Northern Hemisphere over the past 2000 years. A clear feature is a persistent southward shift of the ITCZ during the Little Ice Age until the beginning of the 19th Century. Strong covariation between our new composite ITCZ-stack and North Atlantic Oscillation (NAO) records reveals a tight coupling between these two synoptic weather and climate phenomena over decadal-to-centennial timescales. This relationship becomes most apparent when comparing two precisely dated, high-resolution paleorainfall records from Belize and Scotland, indicating that the low-to mid-latitude teleconnection was also active over annual-decadal timescales. It is likely a combination of external forcing, i.e., solar and volcanic, and internal feedbacks, that drives the synchronous ITCZ and NAO shifts via energy flux perturbations in the tropics.
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.
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.
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.
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.
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system’s state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.
Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀
, which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate.