Network analysis reveals strongly localized impacts of El Niño

Exploring the spatiotemporal impact and pathways of temperature and CO2 concentration based on network approach

Mitigating carbon dioxide (CO2) emissions and curbing temperature rise hold profound significance for global climate protection and economic advancement, particularly in China. From a climatic systems perspective, the interplay between temperature fluctuations and CO2 emissions remains underexplored. Based on the surface-level 1000 hPa atmospheric temperature (T) and CO2 concentration data for China from 2004 to 2020, with a spatial resolution of 3°×2°, this study introduces a multi-layer network framework with time-lag effects to investigate the interaction patterns between temperature and carbon concentration across regions in China. The study reveals the following key features. (1) The interaction between T and CO2 concentrations exhibit a one-day time lag, particularly pronounced during summer and winter. (2) The strength of these interactions weakens diminishes with increasing geographic distance, while significant links are concentrated in regions approximately 1000 km apart. (3) Directional effects of the two are identified, where CO2 concentration forms a positive influence path on T (CO2→T) to the north. (4) Although the influence path of T on CO2 concentration is sparse, its influence is stronger. Specifically, the negative correlation exhibit significant teleconnection, radiating over a region up to 2000 km from northwest to southeast. This study advances the understanding of the temperature-CO2 feedback mechanism, shedding light on the spatial-temporal dynamics of their interaction. These insights provide a scientific foundation for formulating precise carbon reduction policies and climate adaptation strategies tailored to regional characteristics.

Multiple serial correlations in global air temperature anomaly time series

Serial correlations within temperature time series serve as indicators of the temporal consistency of climate events. This study delves into the serial correlations embedded in global surface air temperature (SAT) data. Initially, we preprocess the SAT time series to eradicate seasonal patterns and linear trends, resulting in the SAT anomaly time series, which encapsulates the inherent variability of Earth's climate system. Employing diverse statistical techniques, we identify three distinct types of serial correlations: short-term, long-term, and nonlinear. To identify short-term correlations, we utilize the first-order autoregressive model, AR(1), revealing a global pattern that can be partially attributed to atmospheric Rossby waves in extratropical regions and the Eastern Pacific warm pool. For long-term correlations, we adopt the standard detrended fluctuation analysis, finding that the global pattern aligns with long-term climate variability, such as the El Niño-Southern Oscillation (ENSO) over the Eastern Pacific. Furthermore, we apply the horizontal visibility graph (HVG) algorithm to transform the SAT anomaly time series into complex networks. The topological parameters of these networks aptly capture the long-term correlations present in the data. Additionally, we introduce a novel topological parameter, Δσ, to detect nonlinear correlations. The statistical significance of this parameter is rigorously tested using the Monte Carlo method, simulating fractional Brownian motion and fractional Gaussian noise processes with a predefined DFA exponent to estimate confidence intervals. In conclusion, serial correlations are universal in global SAT time series and the presence of these serial correlations should be considered carefully in climate sciences.

Arctic weather variability and connectivity

The Arctic's rapid sea ice decline may influence global weather patterns, making the understanding of Arctic weather variability (WV) vital for accurate weather forecasting and analyzing extreme weather events. Quantifying this WV and its impacts under human-induced climate change remains a challenge. Here we develop a complexity-based approach and discover a strong statistical correlation between intraseasonal WV in the Arctic and the Arctic Oscillation. Our findings highlight an increased variability in daily Arctic sea ice, attributed to its decline accelerated by global warming. This weather instability can influence broader regional patterns via atmospheric teleconnections, elevating risks to human activities and weather forecast predictability. Our analyses reveal these teleconnections and a positive feedback loop between Arctic and global weather instabilities, offering insights into how Arctic changes affect global weather. This framework bridges complexity science, Arctic WV, and its widespread implications.

Exploring the intensity, distribution and evolution of teleconnections using climate network analysis

Teleconnections refer to long-range climate system linkages occurring over typically thousands of kilometers. Generally speaking, most teleconnections are attributed to the transmission of energy and propagation of waves although the physical complexity and characteristics behind these waves are not fully understood. To address this knowledge gap, we develop a climate network-based approach to reveal their directions and distribution patterns, evaluate the intensity of teleconnections, and identify sensitive regions using global daily surface air temperature data. Our results reveal a stable average intensity distribution pattern for teleconnections across a substantial spatiotemporal scale from 1948 to 2021, with the extent and intensity of teleconnection impacts increasing more prominently in the Southern Hemisphere over the past 37 years. Furthermore, we pinpoint climate-sensitive regions, such as southeastern Australia, which are likely to face increasing impacts due to global warming. Our proposed method offers new insights into the dynamics of global climate patterns and can inform strategies to address climate change and extreme events.

Signatures of climatic phenomena in climate networks: El Niño and La Niña

We construct climate networks based on surface air temperature data to identify distinct signatures of climatic phenomena such as El Niño and La Niña events, which trigger many climatic disruptions around the globe with severe economic and ecological consequences. The climate network has been seen to show a discontinuous phase transition in the size of the normalized largest cluster and the susceptibility during both events. The correlation matrix of the network shows a structure that has distinct characteristics for El Niño events, La Niña events, and normal conditions of the Pacific Ocean. We also identify the signatures of the El Niño southern oscillations in the heat map of the cross-correlation and network quantifiers like the betweenness centrality. The distribution of teleconnections of distinct strengths, the betweenness centrality distributions, and the geographic location of nodes of high betweenness centrality yield important insights into the structure of the network and the transfer of information between different parts. We further discuss the predictive power of these quantities.

Non-negative matrix factorization for overlapping community detection in directed weighted networks with sparse constraints

Detecting overlapping communities is essential for analyzing the structure and function of complex networks. However, most existing approaches only consider network topology and overlook the benefits of attribute information. In this paper, we propose a novel attribute-information non-negative matrix factorization approach that integrates sparse constraints and optimizes an objective function for detecting communities in directed weighted networks. Our algorithm updates the basic non-negative matrix adaptively, incorporating both network topology and attribute information. We also add a sparsity constraint term of graph regularization to maintain the intrinsic geometric structure between nodes. Importantly, we provide strict proof of convergence for the multiplication update rule used in our algorithm. We apply our proposed algorithm to various artificial and real-world networks and show that it is more effective for detecting overlapping communities. Furthermore, our study uncovers the intricate iterative process of system evolution toward convergence and investigates the impact of various variables on network detection. These findings provide insights into building more robust and operable complex systems.

Network inference from short, noisy, low time-resolution, partial measurements: Application to C. elegans neuronal calcium dynamics

Network link inference from measured time series data of the behavior of dynamically interacting network nodes is an important problem with wide-ranging applications, e.g., estimating synaptic connectivity among neurons from measurements of their calcium fluorescence. Network inference methods typically begin by using the measured time series to assign to any given ordered pair of nodes a numerical score reflecting the likelihood of a directed link between those two nodes. In typical cases, the measured time series data may be subject to limitations, including limited duration, low sampling rate, observational noise, and partial nodal state measurement. However, it is unknown how the performance of link inference techniques on such datasets depends on these experimental limitations of data acquisition. Here, we utilize both synthetic data generated from coupled chaotic systems as well as experimental data obtained from Caenorhabditis elegans neural activity to systematically assess the influence of data limitations on the character of scores reflecting the likelihood of a directed link between a given node pair. We do this for three network inference techniques: Granger causality, transfer entropy, and, a machine learning-based method. Furthermore, we assess the ability of appropriate surrogate data to determine statistical confidence levels associated with the results of link-inference techniques.

A modified extreme event-based synchronicity measure for climate time series

Extreme event-based synchronicity is a specific measure of similarity of extreme event-like time series. It is capable to capture the nonlinear interactions between climatic extreme events. In this study, we proposed a modified extreme event-based synchronicity measure that incorporates two types of extreme events (positive and negative) simultaneously in climate anomalies to characterize the synchronization and time delays. Statistical significance of the modified extreme event synchronization measure is tested by Monte-Carlo simulations. The applications of the modified extreme event-based synchronicity measure on synthetic time series verified that it was superior to the traditional event synchronicity measure. Both synchronous and antisynchronous features between climate time series could be captured by the modified measure. It is potentially applied in investigating the interrelationship between climate extremes and climate index or constructing complex networks of climate variables. In addition, this modified extreme event-based synchronicity measure could be easily applied to other types of time series just by identifying the extreme events properly.

Robustness of Interdependent Networks with Weak Dependency Based on Bond Percolation

Real-world systems interact with one another via dependency connectivities. Dependency connectivities make systems less robust because failures may spread iteratively among systems via dependency links. Most previous studies have assumed that two nodes connected by a dependency link are strongly dependent on each other; that is, if one node fails, its dependent partner would also immediately fail. However, in many real scenarios, nodes from different networks may be weakly dependent, and links may fail instead of nodes. How interdependent networks with weak dependency react to link failures remains unknown. In this paper, we build a model of fully interdependent networks with weak dependency and define a parameter α in order to describe the node-coupling strength. If a node fails, its dependent partner has a probability of failing of 1−α. Then, we develop an analytical tool for analyzing the robustness of interdependent networks with weak dependency under link failures, with which we can accurately predict the system robustness when 1−p fractions of links are randomly removed. We find that as the node coupling strength increases, interdependent networks show a discontinuous phase transition when α<αc and a continuous phase transition when α>αc. Compared to site percolation with nodes being attacked, the crossover points αc are larger in the bond percolation with links being attacked. This finding can give us some suggestions for designing and protecting systems in which link failures can happen.

Early warning of the Indian Ocean Dipole using climate network analysis

The Indian Ocean Dipole (IOD), an air–sea coupled phenomenon over the tropical Indian Ocean, has substantial impacts on the climate, ecosystems, and society. Due to the winter predictability barrier, however, a reliable prediction of the IOD has been limited to 3 or 4 mo in advance. Our work approaches this problem from a new data-driven perspective: the climate network analysis. Using this network-based method, an efficient early warning signal for the IOD event was revealed in boreal winter. Our approach can correctly predict the IOD events one calendar year in advance (from December of the previous year) with a hit rate of higher than 70%, which strongly outperforms current dynamic models.

In recent years, the Indian Ocean Dipole (IOD) has received much attention in light of its substantial impacts on both the climate system and humanity. Due to its complexity, however, a reliable prediction of the IOD is still a great challenge. In this study, climate network analysis was employed to investigate whether there are early warning signals prior to the start of IOD events. An enhanced seesaw tendency in sea surface temperature (SST) among a large number of grid points between the dipole regions in the tropical Indian Ocean was revealed in boreal winter, which can be used to forewarn the potential occurrence of the IOD in the coming year. We combined this insight with the indicator of the December equatorial zonal wind in the tropical Indian Ocean to propose a network-based predictor that clearly outperforms the current dynamic models. Of the 15 IOD events over the past 37 y (1984 to 2020), 11 events were correctly predicted from December of the previous year, i.e., a hit rate of higher than 70%, and the false alarm rate was around 35%. This network-based approach suggests a perspective for better understanding and predicting the IOD.

Natural Gas Scarcity Risk in the Belt and Road Economies Based on Complex Network and Multi-Regional Input-Output Analysis

Natural gas scarcity poses a significant risk to the global economy. The risk of production loss due to natural gas scarcity can be transferred to downstream economies through globalized supply chains. Therefore, it is important to quantify and analyze how natural gas scarcity in some regions affects the Belt and Road (B&R) economies. The embodied natural gas scarcity risks (EGSRs) of B&R economies are assessed and the EGSR transmission network is constructed. The built network shows a small-world nature. This illustrates that any interruption in key countries will quickly spread to neighboring countries, potentially affecting the global economy. The top countries, including Turkey, China, Ukraine, and India are identified in EGSR exports, which also have relatively high values of closeness centrality. The findings illustrate that the shortage of natural gas supply in these countries may have a significant impact on downstream countries or sectors and the resulting economic losses spread rapidly. These countries are critical to the resilience of the B&R economies to natural gas scarcity. The top nations, including Turkmenistan, Macedonia, and Georgia are also identified in EGSR imports, highlighting their vulnerability to natural gas scarcity. Further, the community analysis of the network provides a fresh perspective for formulating fair and reasonable allocation policies of natural gas resources and minimizing the large-scale spread of economic losses caused by natural gas scarcity.

Natural Gas Scarcity Risk for Countries along the Belt and Road

The rapid development of the Belt and Road economics has generated a considerable energy demand. Under the general trend of the global energy transition, natural gas resources are becoming the main driving force. The limited natural gas resources are posing a significant risk to economies, and this risk may also be transferred to other distant regions through economic trade. The aim of this study is to explore the trans-regional (sectoral) transmission pattern of natural gas scarcity risk. The main contribution of this paper is the assessment of the local natural gas scarcity risk (LGSR) and cross-region transfer relationship of embodied natural gas scarcity risk (EGSR), which are evaluated for the BRI economies. In addition, the network amplification effect is considered when evaluating the cross-regional impact of natural gas scarcity risk. The results show that, at the national level, Turkey, Ukraine, and Bulgaria have significant EGSR related to exports activities. The natural gas scarcity risks (GSRs) originating from these countries are mainly transferred to Turkmenistan, Georgia, and Albania, with large EGSR imports. Moreover, by comparing the ranking changes of EGSR imports, EGSR exports, and LGSRs at the national and sectoral levels, countries or sectors with higher LGSRs also have higher EGSR exports. The Top EGSR import and export network consisting of top EGSR flow relationships can well reflect countries’ preferences in choosing EGSR transfer partners. The results suggest that upstream countries and sectors should strengthen cooperation to manage natural gas resources, and provide references for decision makers in highly vulnerable downstream countries and sectors to formulate strategies to avoid the large-scale spread of economic losses caused by natural gas scarcity.

Spatial–Temporal Patterns of Historical, Near-Term, and Projected Drought in the Conterminous United States

Major droughts in the United States have heavily impacted the hydrologic system, negatively effecting energy and food production. Improved understanding of historical drought is critical for accurate forecasts. Data from global climate models (GCMs), commonly used to assess drought, cannot effectively evaluate local patterns because of their low spatial scale. This research leverages downscaled (~4 km grid spacing) temperature and precipitation estimates from nine GCMs’ data under the business-as-usual scenario (Representative Concentration Pathway 8.5) to examine drought patterns. Drought severity is estimated using the Palmer Drought Severity Index (PDSI) with the Thornthwaite evapotranspiration method. The specific objectives were (1) To reproduce historical (1966–2005) drought and calculate near-term to future (2011–2050) drought patterns over the conterminous USA. (2) To uncover the local variability of spatial drought patterns in California between 2012 and 2018 using a network-based approach. Our estimates of land proportions affected by drought agree with the known historical drought events of the mid-1960s, late 1970s to early 1980s, early 2000s, and between 2012 and 2015. Network analysis showed heterogeneity in spatial drought patterns in California, indicating local variability of drought occurrence. The high spatial scale at which the analysis was performed allowed us to uncover significant local differences in drought patterns. This is critical for highlighting possible weak systems that could inform adaptation strategies such as in the energy and agricultural sectors.

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.

Epidemic spreading and control strategies in spatial modular network

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the susceptible-infected-recovered model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.

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.

Spatiotemporal data analysis with chronological networks

The number of spatiotemporal data sets has increased rapidly in the last years, which demands robust and fast methods to extract information from this kind of data. Here, we propose a network-based model, called Chronnet, for spatiotemporal data analysis. The network construction process consists of dividing a geometric space into grid cells represented by nodes connected chronologically. Strong links in the network represent consecutive recurrent events between cells. The chronnet construction process is fast, making the model suitable to process large data sets. Using artificial and real data sets, we show how chronnets can capture data properties beyond simple statistics, like frequent patterns, spatial changes, outliers, and spatiotemporal clusters. Therefore, we conclude that chronnets represent a robust tool for the analysis of spatiotemporal data sets.

Extracting central information from ever-growing data generated in our lives calls for new data mining methods. Ferreira et al. show a simple model, called chronnets, that can capture frequent patterns, spatial changes, outliers, and spatiotemporal clusters.

Complexity-based approach for El Niño magnitude forecasting before the spring predictability barrier

The El Niño Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. Early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the "spring predictability barrier" remains a great challenge for long-lead-time (over 6 mo) forecasting. To overcome this barrier, here we develop an analysis tool, System Sample Entropy (SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Niño 3.4 region. When applying this tool to several near-surface air temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Niño and the previous calendar year's SysSampEn (complexity). We show that this correlation allows us to forecast the magnitude of an El Niño with a prediction horizon of 1 y and high accuracy (i.e., root-mean-square error = 0.23° C for the average of the individual datasets forecasts). For the 2018 El Niño event, our method forecasted a weak El Niño with a magnitude of 1.11±0.23° C. Our framework presented here not only facilitates long-term forecasting of the El Niño magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.

Climate network percolation reveals the expansion and weakening of the tropical component under global warming

Global climate warming poses a significant challenge to humanity; it is associated with, e.g., rising sea level and declining Arctic sea ice. Increasing extreme events are also considered to be a result of climate warming, and they may have widespread and diverse effects on health, agriculture, economics, and political conflicts. Still, the detection and quantification of climate change, both in observations and climate models, constitute a main focus of the scientific community. Here, we develop an approach based on network and percolation frameworks to study the impacts of climate changes in the past decades using historical models and reanalysis records, and we analyze the expected upcoming impacts using various future global warming scenarios. We find an abrupt transition during the evolution of the climate network, indicating a consistent poleward expansion of the largest cluster that corresponds to the tropical area, as well as the weakening of the strength of links in the tropic. This is found both in the reanalysis data and in the Coupled Model Intercomparison Project Phase 5 (CMIP5) 21st century climate change simulations. The analysis is based on high-resolution surface (2 m) air temperature field records. We discuss the underlying mechanism for the observed expansion of the tropical cluster and associate it with changes in atmospheric circulation represented by the weakening and expansion of the Hadley cell. Our framework can also be useful for forecasting the extent of the tropical cluster to detect its influence on different areas in response to global warming.

Relation of El Niño and La Niña phenomena to precipitation, evapotranspiration and temperature in the Amazon basin

Weather phenomena El Niño and La Niña are observed by meteorological variables, which allows you to track climate change and its possible effects in certain regions. The objective of this study was to analyze the behavior of rainfall, temperature and evapotranspiration in the Amazon river basin (Latitudes 5° N to 20° S and Longitudes 50° W to 80° W), comparing them with the occurrence of El Niño and La Niña phenomena, from January 2000 to December 2016. The values referring to the meteorological variables were obtained from the TRMM and MODIS orbital sensors. After data pre-processing, the data were separated into monthly and annual scales and per period according to the presence or absence of El Niño and La Niña phenomena. Based on the results obtained, it was observed that the studied variables were affected by modification of both phenomena. The modifications are more noticeable in the distinction between the more and less rainy periods. Among the variables studied, the evapotranspiration was severely affected in the rainiest months, the La Niña phenomenon, and the least rainy months, El Niño. Thus, it was possible to conclude that, in general, the presence of La Niña increased precipitation values in comparison to the Neutral period, but the inverse occurs in the presence of El Niño. The methodology applied in the present study was adequate for the analysis of the modifications of the meteorological variables coming from the El Niño and La Niña phenomena, being able to be adapted to other variables and regions.

Percolation framework of the Earth's topography

Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on high-resolution, 1 arc min, ETOPO1 global relief records. We find some evidence for abrupt transitions that occurred during the evolution of the Earth's relief network, indicative of a continental/cluster aggregation. We apply finite-size-scaling analysis based on a coarse-graining procedure to show that the observed transition is most likely discontinuous. Furthermore, we study the percolation on two-dimensional fractional Brownian motion surfaces with Hurst exponent H as a model of long-range correlated topography, which suggests that the long-range correlations may play a key role in the observed discontinuity on Earth. Our framework presented here provides a theoretical model to better understand the geometrical phase transition on Earth, and it also identifies the critical nodes that will be more exposed to global climate change in the Earth's relief network.

Resilience of networks with community structure behaves as if under an external field

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic- paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

Unpacking the polarization of workplace skills

Economic inequality is one of the biggest challenges facing society today. Inequality has been recently exacerbated by growth in high- and low-wage occupations at the expense of middle-wage occupations, leading to a "hollowing" of the middle class. Yet, our understanding of how workplace skills drive this process is limited. Specifically, how do skill requirements distinguish high- and low-wage occupations, and does this distinction constrain the mobility of individuals and urban labor markets? Using unsupervised clustering techniques from network science, we show that skills exhibit a striking polarization into two clusters that highlight the specific social-cognitive skills and sensory-physical skills of high- and low-wage occupations, respectively. The connections between skills explain various dynamics: how workers transition between occupations, how cities acquire comparative advantage in new skills, and how individual occupations change their skill requirements. We also show that the polarized skill topology constrains the career mobility of individual workers, with low-skill workers "stuck" relying on the low-wage skill set. Together, these results provide a new explanation for the persistence of occupational polarization and inform strategies to mitigate the negative effects of automation and offshoring of employment. In addition to our analysis, we provide an online tool for the public and policy makers to explore the skill network: skillscape.mit.edu.

Constructing regional climate networks in the Amazonia during recent drought events

Climate networks are powerful approaches to disclose tele-connections in climate systems and to predict severe climate events. Here we construct regional climate networks from precipitation data in the Amazonian region and focus on network properties under the recent drought events in 2005 and 2010. Both the networks of the entire Amazon region and the extreme networks resulted from locations severely affected by drought events suggest that network characteristics show slight difference between the two drought events. Based on network degrees of extreme drought events and that without drought conditions, we identify regions of interest that are correlated to longer expected drought period length. Moreover, we show that the spatial correlation length to the regions of interest decayed much faster in 2010 than in 2005, which is because of the dual roles played by both the Pacific and Atlantic oceans. The results suggest that hub nodes in the regional climate network of Amazonia have fewer long-range connections when more severe drought conditions appeared in 2010 than that in 2005.