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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.
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.
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.
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.