Influence of autocorrelation on the topology of the climate network

A Revisit of Large-Scale Patterns in Middle Stratospheric Circulation Variations

Variations in stratospheric atmospheric circulation significantly impact tropospheric weather and climate. Understanding these variations not only aids in better prediction of tropospheric weather and climate but also provides guidance for the development and flight trajectories of stratospheric aircraft. Our understanding of the stratosphere has made remarkable progress over the past 100 years. However, we still lack a comprehensive perspective on large-scale patterns in stratospheric circulation, as the stratosphere is a typical complex system. To address this gap, we employed the eigen microstate approach (EMA) to revisit the characteristics of zonal wind from 70-10 hPa from 1980 to 2022, based on ERA5 reanalysis data. Our analysis focused on the three leading modes, corresponding to variations in the strength of the quasi-biennial oscillation (QBO) and the stratospheric atmospheric circulations in the Arctic and Antarctic, respectively. After filtering out high-frequency components from the temporal evolutions of these modes, a significant 11-year cycle was observed in the Antarctic stratospheric atmospheric circulation mode, potentially linked to the 11-year solar cycle. In contrast, the Arctic stratospheric atmospheric circulation mode showed a 5-6-year cycle without evidence of an 11-year periodicity. This difference is likely due to the timing of polar vortex breakdowns: the Antarctic polar vortex breaks up later, experiencing its greatest variability in late spring and early summer, making it more susceptible to solar radiation effects, unlike the Arctic polar vortex, which peaks in winter and early spring. The fourth mode exhibits characteristics of a Southern Hemisphere dipole and shows a significant correlation with the Antarctic stratospheric atmospheric circulation mode, leading it by about two months. We designed a linear prediction model that successfully demonstrated its predictive capability for the Antarctic polar vortex.

Precursors of the El Niño phenomenon: A climate network analysis

The identification of precursors of climatic phenomena has enormous practical importance. Recent work constructs a climate network based on surface air temperature data to analyze the El Niño phenomena. We utilize microtransitions which occur before the discontinuous percolation transition in the network as well as other network quantities to identify a set of reliable precursors of El Niño episodes. These precursors identify 10 out of 13 El Niño episodes occurring in the period of 1979-2018 with an average lead time of approximately 6.4 months. We also find indicators of tipping events in the data.

Climate network approach reveals the modes of CO2 concentration to surface air temperature

Increasing atmospheric carbon dioxide (CO₂) is expected to be the main factor of global warming. The relation between CO₂ concentrations and surface air temperature (SAT) has been found related to Rossby waves based on a multi-layer complex network approach. However, the significant relations between CO₂ and SAT occur in the South Hemisphere that is not that much influenced by human activities may offer not enough information to formulate targeted carbon reduction policies. Here, we address it by removing the effects of the Rossby waves to reconstruct CO₂ concentrations and SAT multi-layer complex network. We uncover that the CO₂ concentrations are strongly associated with the surrounding SAT regions. The influential regions of CO₂ on SAT occur over eastern Asia, West Asia, North Africa, the coast of North American, and Western Europe. It is shown that CO₂ over Siberia in phase with the SAT variability in eastern East Asia. Indeed, CO₂ concentration variability is causing effects on the recent warming of SAT in some middle latitude regions. Furthermore, sensitive parameters that CO₂ impacts SAT of top 15 carbon emissions countries have been identified. These countries are significantly responsible for global warming, giving implications for carbon emissions reductions. The methodology and results presented here not only facilitate further research in regions of increased sensitivity to the warming resulting from CO₂ concentrations but also can formulate strategies and countermeasures for carbon emission and carbon reduction.

Statistical physics approaches to the complex Earth system

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge of the Earth system, including climate extreme events, earthquakes and geological relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as critical phenomena, network theory, percolation, tipping points analysis, and entropy can be applied to complex Earth systems. Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics concepts and theories can be useful in the field of Earth system science.

Correlation networks of air particulate matter ( PM 2.5 ): a comparative study

Over the last decades, severe haze pollution constitutes a major source of far-reaching environmental and human health problems. The formation, accumulation and diffusion of pollution particles occurs under complex temporal scales and expands throughout a wide spatial coverage. Seeking to understand the transport patterns of haze pollutants in China, we review a proposed framework of time-evolving directed and weighted air quality correlation networks. In this work, we evaluate monitoring stations' time-series data from China and California, to test the sensitivity of the framework to region size, climate and pollution magnitude across multiple years (2014-2020). We learn that the use of hourly PM 2.5 concentration data is needed to detect periodicities in the positive and negative correlations of the concentrations. In addition, we show that the standardization of the correlation function method is required to obtain networks with more meaningful links when evaluating the dispersion of a severe haze event at the North China Plain or a wildfire event in California during December 2017. Post COVID-19 outbreak in China, we observe a significant drop in the magnitude of the assigned weights, indicating the improved air quality and the slowed transport of PM 2.5 due to the lockdown. To identify regions where pollution transport is persistent, we extend the framework, partitioning the dynamic networks and reducing the networks' complexity through node subsampling. The end result separates the temporal series of PM 2.5 in set of regions that are similarly affected through the year.

A Novel Information Theoretical Criterion for Climate Network Construction

This paper presents a novel methodology for Climate Network (CN) construction based on the Kullback-Leibler divergence (KLD) among Membership Probability (MP) distributions, obtained from the Second Order Data-Coupled Clustering (SODCC) algorithm. The proposed method is able to obtain CNs with emergent behaviour adapted to the variables being analyzed, and with a low number of spurious or missing links. We evaluate the proposed method in a problem of CN construction to assess differences in wind speed prediction at different wind farms in Spain. The considered problem presents strong local and mesoscale relationships, but low synoptic scale relationships, which have a direct influence in the CN obtained. We carry out a comparison of the proposed approach with a classical correlation-based CN construction method. We show that the proposed approach based on the SODCC algorithm and the KLD constructs CNs with an emergent behaviour according to underlying wind speed prediction data physics, unlike the correlation-based method that produces spurious and missing links. Furthermore, it is shown that the climate network construction method facilitates the evaluation of symmetry properties in the resulting complex networks.

General Component Analysis (GCA): A new approach to identify Chinese corporate bond market structures

PCA has been widely used in many fields to detect dominant principle components, but it ignores the information embedded in the remaining components. As a supplement to PCA, we propose the General Component Analysis (GCA). The inverse participation ratios (IPRs) are used to identify the global components (GCs) and localized components (LCs). The mean values of the IPRs derived from the shuffled data are taken as the natural threshold, which is exquisite and novel. In this paper, the Chinese corporate bond market is analyzed as an example. We propose a novel network method to divide time periods based on micro data, which performs better in capturing the time points when the market state switches. As a result, two periods have been obtained. There are two GCs in both periods, which are influenced by terms to maturity and ratings. Besides, there are 382 LCs in Period 1 and 166 LCs in Period 2. In the LC portfolios there are two interesting bond collections which are helpful to understand the thoughts of the investors. One is the supper AAA bond collection which is believed to have implicit governmental guarantees by the investors, and the other is the overcapacity industrial bond collection which is influenced by the supply-side reform led by the Chinese government. GCA is expected to be applied to other complex systems.

Transition to reconstructibility in weakly coupled networks

Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to reflect the underlying physical interactions accurately. Here we systematically study the problem of reconstructing direct physical interaction networks from thresholding correlations. We explicate how local common cause and relay structures, heterogeneous in-degrees and non-local structural properties of the network generally hinder reconstructibility. However, in the limit of weak coupling strengths we prove that stationary systems with dynamics close to a given operating point transition to universal reconstructiblity across all network topologies.

Percolation Phase Transition of Surface Air Temperature Networks under Attacks of El Niño/La Niña

In this study, sea surface air temperature over the Pacific is constructed as a network, and the influences of sea surface temperature anomaly in the tropical central eastern Pacific (El Niño/La Niña) are regarded as a kind of natural attack on the network. The results show that El Niño/La Niña leads an abrupt percolation phase transition on the climate networks from stable to unstable or metastable phase state, corresponding to the fact that the climate condition changes from normal to abnormal significantly during El Niño/La Niña. By simulating three different forms of attacks on an idealized network, including Most connected Attack (MA), Localized Attack (LA) and Random Attack (RA), we found that both MA and LA lead to stepwise phase transitions, while RA leads to a second-order phase transition. It is found that most attacks due to El Niño/La Niña are close to the combination of MA and LA, and a percolation critical threshold Pc can be estimated to determine whether the percolation phase transition happens. Therefore, the findings in this study may renew our understandings of the influence of El Niño/La Niña on climate, and further help us in better predicting the subsequent events triggered by El Niño/La Niña.

Teleconnection Paths via Climate Network Direct Link Detection

Teleconnections describe remote connections (typically thousands of kilometers) of the climate system. These are of great importance in climate dynamics as they reflect the transportation of energy and climate change on global scales (like the El Niño phenomenon). Yet, the path of influence propagation between such remote regions, and weighting associated with different paths, are only partially known. Here we propose a systematic climate network approach to find and quantify the optimal paths between remotely distant interacting locations. Specifically, we separate the correlations between two grid points into direct and indirect components, where the optimal path is found based on a minimal total cost function of the direct links. We demonstrate our method using near surface air temperature reanalysis data, on identifying cross-latitude teleconnections and their corresponding optimal paths. The proposed method may be used to quantify and improve our understanding regarding the emergence of climate patterns on global scales.

Effects of random rewiring on the degree correlation of scale-free networks

Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature. We comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same. Consequently, the network dynamics is changed, which is proven here by means of the biased random walk.

Relating Granger causality to long-term causal effects

In estimation of causal couplings between observed processes, it is important to characterize coupling roles at various time scales. The widely used Granger causality reflects short-term effects: it shows how strongly perturbations of a current state of one process affect near future states of another process, and it quantifies that via prediction improvement (PI) in autoregressive models. However, it is often more important to evaluate the effects of coupling on long-term statistics, e.g., to find out how strongly the presence of coupling changes the variance of a driven process as compared to an uncoupled case. No general relationships between Granger causality and such long-term effects are known. Here, we pose the problem of relating these two types of coupling characteristics, and we solve it for a class of stochastic systems. Namely, for overdamped linear oscillators, we rigorously derive that the above long-term effect is proportional to the short-term effects, with the proportionality coefficient depending on the prediction interval and relaxation times. We reveal that this coefficient is typically considerably greater than unity so that small normalized PI values may well correspond to quite large long-term effects of coupling. The applicability of the derived relationship to wider classes of systems, its limitations, and its value for further research are discussed. To give a real-world example, we analyze couplings between large-scale climatic processes related to sea surface temperature variations in equatorial Pacific and North Atlantic regions.