Complex networks reveal global pattern of extreme-rainfall teleconnections

A meta-analysis of the regional extreme rainfall events in the Indian sub-continent during the southwest monsoon period

The present review focuses on extreme rainfall events (EREs) over the Indian subcontinent during the southwest monsoon period. The evolution of ERE studies across India concentrates mainly on the regional characteristics that have influenced these events during the past decade. It evolved slowly by accounting for different indices to represent extremes, understanding causative mechanisms, and improving their forecasting. There are many methods for estimating EREs, each suited to various objectives. Rather than seeking a perfect method, the studies may adopt methodologies based on the purpose and scope. Moreover, EREs impose severe socioeconomic impacts on India, with heavy burdens on communities and resources. Factors such as low-pressure systems, Indian Ocean warming, and circulation shifts contribute to these extremes. Northwest India has seen a significant rise in ERE frequency and intensity in recent decades due to enhanced convective instability and moisture transport by various climate drivers. In contrast, Northeast India shows a decline in EREs driven by synoptic systems. EREs in the Himalayas are more complex and influenced by tropical and extratropical drivers. Regions like Kerala and the northeastern states face frequent ERE-linked flooding, while the Western Ghats show a declining trend. The ERE in the different regions show different dynamics due to their heating structure, moisture availability, and atmospheric instability factors. Thus, regional ERE forecasting is complex, but combining numerical models with machine learning can enhance accuracy and reliability. Future projections indicate a significant increase in regional EREs, but uncertainties persist due to models' biases. The findings underscore the need for improved modeling strategies and targeted policy measures to mitigate the adverse impacts of future EREs. This review offers insights into India's current state and research prospects, highlighting critical areas for further investigation and enhanced forecasting.

The circular movement of synchronous extreme precipitation preceding Kerala floods in 2018 and 2019

In 2018 and 2019, Kerala, the southernmost state in India, experienced extreme precipitation, leading to appallingly devastating floods that damaged life and property. Kerala is vulnerable to flooding due to its topography, geographical location, and meteorology. Several phenomena have been attributed to these extreme precipitations; however, no single explanation suffices to explain such complex climate phenomena. We view the occurrence of extreme precipitation that leads to floods, such as an emerging phenomenon through the lens of complex system theory. We analyze the patterns of synchrony of extreme fluctuations in precipitation, outgoing longwave radiation, and water vapor transport. We construct time-varying functional climate networks, in which the statistical similarity between the time series of extreme precipitation at different spatial locations is estimated using event synchronization. The network topology reveals that excessive precipitation during the Kerala floods was associated with a coherent pattern of synchronized extreme rainfall. In the coherent phenomena discovered, the extreme rainfall was synchronized across a wide range of length scales spanning 100-1000 km. Furthermore, it traverses a synoptic scale path. After originating in the equatorial Indian Ocean, the coherent pattern moves eastward across the Bay of Bengal. The pattern stops over the Maritime Continent and changes its direction. It moves westward toward the Indian peninsula and accumulates over southwest India. We find that the extreme precipitation was driven by enhanced convective activity, leading to cloudiness and high-vapor transport in the atmosphere. Our findings improve the understanding of intraseasonal variability in the Indian monsoon and extreme precipitation events.

A novel voting measure for identifying influential nodes in complex networks based on local structure

Identifying influential nodes in real networks is significant in studying and analyzing the structural as well as functional aspects of networks. VoteRank is a simple and effective algorithm to identify high-spreading nodes. The accuracy and monotonicity of the VoteRank algorithm are poor as the network topology fails to be taken into account.Given the nodes' attributes and neighborhood structure, this paper put forward an algorithm based on the Edge Weighted VoteRank (EWV) for identifying influential nodes in the network. The proposed algorithm draws inspiration from human voting behavior and expresses the attractiveness of nodes to their first-order neighborhood using the weights of connecting edges. Similarity between nodes is introduced into the voting process, further enhancing the accuracy of the method. Additionally, this EWV algorithm addresses the problem of influential node clustering by reducing the voting ability of nodes in the second-order neighborhood of the most influential nodes. The validity of the presented algorithm is verified through experiments conducted on 12 different real networks of various sizes and structures, directly comparing it with 7 competing algorithms.Empirical results indicate a superiority of the presented algorithm over the remaining seven competing algorithms with respect to node differentiation ability, effectiveness, and ranked list accuracy.

Coupled intelligent prediction model for medium- to long-term runoff based on teleconnection factors selection and spatial-temporal analysis

Accurate medium- to long-term runoff forecasting is of great significance for flood control, drought mitigation, comprehensive water resource management, and ecological restoration. However, runoff formation is a complex process influenced by various natural and anthropogenic factors, resulting in nonlinearity, nonstationarity, and long prediction periods, which complicate forecasting efforts. Traditional statistical models, which primarily focus on individual runoff sequences, struggle to integrate multi-source data, limiting their predictive accuracy. This narrow approach overlooks the multifaceted variables influencing runoff, resulting in incomplete and less reliable predictions. To address these challenges, we selected and integrated Random Forest (RF), Support Vector Regression (SVR), and Multilayer Perceptron Regression (MLPR) to develop two coupled intelligent prediction models-RF-SVR and RF-MLPR-due to their complementary strengths. RF effectively removes collinear and redundant information from high-dimensional data, while SVR and MLPR handle nonlinearity and nonstationarity, offering enhanced generalization capabilities. Specifically, MLPR, with its deep learning structure, can extract more complex latent information from data, making it particularly suitable for long-term forecasting. The proposed models were tested in the Yalong River Basin (YLRB), where accurate medium- to long-term runoff forecasts are essential for ecological management, flood control, and optimal water resource allocation. The results demonstrate the following: (1) The impact of atmospheric circulation indices on YLRB runoff exhibits a one-month lag, providing crucial insights for water resource scheduling and flood prevention. (2) The coupled models effectively eliminate collinearity and redundant variables, improving prediction accuracy across all forecast periods. (3) Compared to single baseline models, the coupled models demonstrated significant performance improvements across six evaluation metrics. For instance, the RF-MLPR model achieved a 3.7%-6.5% improvement in the Nash-Sutcliffe efficiency (NSE) metric across four hydrological stations compared to the RF-SVR model. (4) Prediction accuracy decreased with longer forecast periods, with the R2 value dropping from 0.8886 for a 1-month forecast to 0.6358 for a 12-month forecast, indicating the increasing challenge of long-term predictions due to greater uncertainty and the accumulation of influencing factors over time. (5) The RF-MLPR model outperformed the RF-SVR model, demonstrating a superior ability to capture the complex, nonlinear relationships inherent in the data. For example, in terms of the R2 metric, the RF-MLPR model's performance at the Jinping hydrological station improved by 6.5% compared to the RF-SVR model. Similarly, at the Lianghekou station, for a one-month lead prediction period, the RF-MLPR model's R2 value was 7.9% higher than that of the RF-SVR model. The significance of this research lies not only in its contribution to improving hydrological prediction accuracy but also in its broader applicability. The proposed coupled prediction models provide practical tools for water resource management, flood control planning, and drought mitigation in regions with similar hydrological characteristics. Furthermore, the framework's flexibility in parameterization and its ability to integrate multi-source data offer valuable insights for interdisciplinary applications across environmental sciences, meteorology, and climate prediction, making it a globally relevant contribution to addressing water management challenges under changing climatic conditions.

Cascading spatial drought network: A complex networks approach to track propagation of meteorological droughts to agricultural droughts

Meteorological droughts often propagate to agricultural (and other) droughts, both spatially and temporally. The present study proposes a novel complex networks-based cascading spatial drought network to examine the spatial propagation of meteorological droughts in a region to agricultural droughts in other regions. This is done through: (1) establishing stable homogeneous drought communities; (2) investigating inter-community drought propagation; (3) locating drought sources; and (4) evaluating drought connections within major crop belts. The approach is implemented to study droughts in the Indian-subcontinent during the period 1948-2022. Monthly precipitation and root-zone soil moisture data from GLDAS (Global Land Data Assimilation System) are used to compute the standardized precipitation index (SPI) for meteorological droughts and standardized soil moisture index (SSI) for agricultural droughts. Primarily, the drought network is demarcated into several subsets of network communities within which clusters of localized propagation take place. Multi-community subgraphs combining different communities are also formed to understand the long-distance inter-community drought linkages. Using network centrality measures, such as degree, closeness, and clustering coefficient, network properties of scale-freeness, small-worldness, and presence of rich-clubs are checked. Although the overall network does not exhibit any of these properties, certain subgraphs have significant small-worldness, rich-clubs, and partial scale-freeness. Some of the crucial nodes that support these network properties lie in the monsoon pathways (in the Western Ghats), and others have a strong association with El Niño Southern Oscillation (ENSO) teleconnections, thus validating the ability of the drought network to capture seasonal and climatic features. Additionally, subgraphs of nodes with high productivity of different food crops are created to study drought propagation within crop belts. Barring potential shortcomings related to data dependencies, the cascading spatial drought network helps identify an impending agricultural drought that could strengthen our ability to forecast droughts.

Correlation change analysis and NDVI prediction in the Yellow River Basin of China using complex networks and GRNN-PSRLSTM

The Normalized Difference Vegetation Index (NDVI) is affected by various environmental factors, and its relationship with these factors is complex. In order to explore the complex relationship between NDVI and environmental factors, this paper adopts the complex network method to construct a correlation fluctuation network and analyze the interaction between them. It is found that temperature, precipitation, soil moisture, sunshine duration, and PM2.5 are all correlated with NDVI to varying degrees, and their combined correlation with NDVI varies over time. The correlation typically takes 3 to 6 months to change, and it tends to persist to some extent. Moreover, we fuse a generalized regression neural network (GRNN) with a long-short-term memory (LSTM) network combining phase space reconstruction (PSR) to propose a GRNN-PSRLSTM prediction model. The model achieves the prediction of monthly NDVI using the five environmental factors of the fluctuation network. The results indicate that the averages of root mean squared error (RMSE) and mean absolute percentage error (MAPE) predicted by the GRNN-PSRLSTM model in the nine provinces are 0.0232 and 0.0564 respectively. This model performs better in the assessment metrics for monthly NDVI forecasts. These findings are significant for evaluating vegetation changes and have some theoretical value for the ecological protection of the Yellow River Basin.

Community structure of tropics emerging from spatio-temporal variations in the Intertropical Convergence Zone dynamics

The Intertropical Convergence Zone (ITCZ) is a narrow tropical belt of deep convective clouds, intense precipitation, and monsoon circulations encircling the Earth. Complex interactions between the ITCZ and local geophysical dynamics result in high climate variability, making weather forecasting and prediction of extreme rainfall or drought events challenging. We unravel the complex spatio-temporal dynamics of the ITCZ and the resulting teleconnection patterns via a novel tropical climate classification achieved using complex network analysis and community detection. We reduce the high-dimensional complex ITCZ dynamics into a simple yet insightful community structure that classifies the tropics into seven regions representing distinct ITCZ dynamics. The two largest communities, encompassing landmasses over the Northern and Southern hemispheres, are associated with coherent seasonal ITCZ dynamics and have significant long-range connections. Temporal analysis of the community structure highlights that the tropical Pacific and Atlantic Oceans communities exhibit substantial variation on multidecadal scales. Further, these communities exhibit incoherent dynamics due to atmosphere-ocean interactions driven by equatorial and coastal oceanic upwelling.

Sketching the spatial disparities in heatwave trends by changing atmospheric teleconnections in the Northern Hemisphere

Pronounced spatial disparities in heatwave trends are bound up with a diversity of atmospheric signals with complex variations, including different phases and wavenumbers. However, assessing their relationships quantitatively remains a challenging problem. Here, we use a network-searching approach to identify the strengths of heatwave-related atmospheric teleconnections (AT) with ERA5 reanalysis data. This way, we quantify the close links between heatwave intensity and AT in the Northern Hemisphere. Approximately half of the interannual variability of heatwaves is explained and nearly 80% of the zonally asymmetric trend signs are estimated correctly by the AT changes in the mid-latitudes. We also uncover that the likelihood of extremely hot summers has increased sharply by a factor of 4.5 after 2000 over areas with enhanced AT, but remained almost unchanged over the areas with attenuated AT. Furthermore, reproducing Eastern European heatwave trends among various models of the Coupled Model Intercomparison Project Phase 6 largely depends on the simulated Eurasian AT changes, highlighting the potentially significant impact of AT shifts on the simulation and projection of heatwaves.

Triadic percolation induces dynamical topological patterns in higher-order networks

Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.

SAMSGL: Series-aligned multi-scale graph learning for spatiotemporal forecasting

Spatiotemporal forecasting in various domains, like traffic prediction and weather forecasting, is a challenging endeavor, primarily due to the difficulties in modeling propagation dynamics and capturing high-dimensional interactions among nodes. Despite the significant strides made by graph-based networks in spatiotemporal forecasting, there remain two pivotal factors closely related to forecasting performance that need further consideration: time delays in propagation dynamics and multi-scale high-dimensional interactions. In this work, we present a Series-Aligned Multi-Scale Graph Learning (SAMSGL) framework, aiming to enhance forecasting performance. In order to handle time delays in spatial interactions, we propose a series-aligned graph convolution layer to facilitate the aggregation of non-delayed graph signals, thereby mitigating the influence of time delays for the improvement in accuracy. To understand global and local spatiotemporal interactions, we develop a spatiotemporal architecture via multi-scale graph learning, which encompasses two essential components: multi-scale graph structure learning and graph-fully connected (Graph-FC) blocks. The multi-scale graph structure learning includes a global graph structure to learn both delayed and non-delayed node embeddings, as well as a local one to learn node variations influenced by neighboring factors. The Graph-FC blocks synergistically fuse spatial and temporal information to boost prediction accuracy. To evaluate the performance of SAMSGL, we conduct experiments on meteorological and traffic forecasting datasets, which demonstrate its effectiveness and superiority.

How representative are air transport functional complex networks? A quantitative validation

Functional networks have emerged as powerful instruments to characterize the propagation of information in complex systems, with applications ranging from neuroscience to climate and air transport. In spite of their success, reliable methods for validating the resulting structures are still missing, forcing the community to resort to expert knowledge or simplified models of the system's dynamics. We here propose the use of a real-world problem, involving the reconstruction of the structure of flights in the US air transport system from the activity of individual airports, as a way to explore the limits of such an approach. While the true connectivity is known and is, therefore, possible to provide a quantitative benchmark, this problem presents challenges commonly found in other fields, including the presence of non-stationarities and observational noise, and the limitedness of available time series. We explore the impact of elements like the specific functional metric employed, the way of detrending the time series, or the size of the reconstructed system and discuss how the conclusions here drawn could have implications for similar analyses in neuroscience.

Exotic swarming dynamics of high-dimensional swarmalators

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.

Chemical Science Research, Elementary School Children and Their Teachers Are More Closely Related than You May Imagine: The "I Bet You Did Not Know" Project

Topics associated with the chemical sciences form a significant part of the curriculum in science at the primary school level in the U.K. In this methodology paper, we demonstrate how a wide range of research articles associated with the chemical sciences can be disseminated to an elementary school audience and how children can carry out investigations associated with cutting-edge research in the classroom. We discuss how the Primary Science Teaching Trust's (PSTT's) "I bet you did not know" (IBYDK) articles and their accompanying Teacher Guides benefit children, primary (elementary) school teachers, and other stakeholders including the researchers themselves. We define three types of research articles; ones describing how children can reproduce the research themselves without much adaptation, others where children can mirror the research using similar methods, and some where an analogy can be used to explain the research. We provide exemplars of each type and some preliminary feedback on articles written.

Nonlinear dynamics and chaos in a vocal-ventricular fold system

In humans, ventricular folds are located superiorly to the vocal folds. Under special circumstances such as voice pathology or singing, they vibrate together with the vocal folds to contribute to the production of voice. In the present study, experimental data measured from physical models of the vocal and ventricular folds were analyzed in the light of nonlinear dynamics. The physical models provide a useful experimental framework to study the biomechanics of human vocalizations. Of particular interest in this experiment are co-oscillations of the vocal and ventricular folds, occasionally accompanied by irregular dynamics. We show that such a system can be regarded as two coupled oscillators, which give rise to various cooperative behaviors such as synchronized oscillations with a 1:1 or 1:2 frequency ratio and desynchronized oscillations with torus or chaos. The insight gained from the view of nonlinear dynamics should be of significant use for the diagnosis of voice pathologies, such as ventricular fold dysphonia.

Reconfiguration of Amazon's connectivity in the climate system

With the recent increase in deforestation, forest fires, and regional temperatures, the concerns around the rapid and complete collapse of the Amazon rainforest ecosystem have heightened. The thresholds of deforestation and the temperature increase required for such a catastrophic event are still uncertain. However, our analysis presented here shows that signatures of changing Amazon are already apparent in historical climate data sets. Here, we extend the methods of climate network analysis and apply them to study the temporal evolution of the connectivity between the Amazon rainforest and the global climate system. We observe that the Amazon rainforest is losing short-range connectivity and gaining more long-range connections, indicating shifts in regional-scale processes. Using embeddings inspired by manifold learning, we show that the Amazon connectivity patterns have undergone a fundamental shift in the 21st century. By investigating edge-based network metrics on similar regions to the Amazon, we see the changing properties of the Amazon are noticeable in comparison. Furthermore, we simulate diffusion and random walks on these networks and observe a faster spread of perturbations from the Amazon in recent decades. Our methodology innovations can act as a template for examining the spatiotemporal patterns of regional climate change and its impact on global climate using the toolbox of climate network analysis.

Compound events of wet and dry extremes: Identification, variations, and risky patterns

Compound hydrometeorological extremes have been widely examined under climate change, they have significant impacts on ecological and societal well-being. This study sheds light on a new category compound of contrasting extremes, namely compounding wet and dry extremes (CWDEs). The CWDEs are characterized as devastating dry events (EDs) accompanied by wet extremes (EWs) in a given time window. Notably, we first adopt a separate system to identify coinciding events considering the different evolving processes and impacting patterns of EDs and EWs. The peak-over-threshold and standardized index methods are used in a daily and monthly window to identify EWs and EDs respectively. Furthermore, the spatial-temporal changes and risky patterns of CWDEs are revealed by using the Mann-Kendall test, the Ordinary Least Squares, and the Global and Local Moran indices. Germany is the study case. As one major finding, the results indicate a pronounced seasonal effect and spatial clustering pattern of CWDEs. The summer is the most vulnerable period for CWDEs, and the spatial hotspots are mainly located in the southern tip of Germany, as well as in the vicinity of the capital city Berlin. Besides, robust uptrends in CWDEs across all evaluation metrics have been discovered in historical periods, and the moist climate and complex geography collectively contribute to severe CWDEs. Unexpectedly, the study finds that compounding events in dry regions are mainly driven by wet extremes, whereas they show a higher dependency on dry anomalies in wet regions. The research provides new insights into compound extremes which are composed of individual hazards with distinct features. Related findings will aid decision-makers in producing effective risk mitigation plans for prioritizing vulnerable regions. Lastly, the robust framework and open access data allow for extensive exploration of various compounding hazards in different regions.

Exploring the spatial pattern of house collapse rates caused by extreme rainfall in central China: The role of natural and social factors

The collapse of houses represents a prominent hazard associated with floods, mudslides, and other disastrous events resulting from extreme rainfall. Nevertheless, previous research in this area has been insufficiently dedicated to comprehending the factors that specifically contribute to house collapse triggered by extreme rainfall. This study endeavors to address this knowledge gap by proposing a hypothesis that the occurrence of house collapse, induced by extreme rainfall, demonstrates spatial heterogeneity and is subject to the interactive impacts of various factors. In the study, we investigate the relationship between house collapse rates and natural and social factors in the provinces of Henan, Shanxi, and Shaanxi provinces in 2021. These provinces are representative of flood-prone areas in central China. Spatial scan statistics and GeoDetector model were used to analyze spatial hotspot areas of house collapse rates and determinant power of natural and social factors on the spatial heterogeneity of house collapse rates, respectively. Our analysis reveals that the spatial hotspot areas predominantly concentrated in regions characterized by high rainfall, including areas along riverbanks and low-lying regions. Multiple factors contribute to the variations in house collapse rates. Among these factors, precipitation (q = 0.32) is the most significant, followed by the ratio of brick-concrete houses (q = 0.24), per capita GDP (q = 0.13), elevation (q = 0.13) and other factors. Notably, the interaction of precipitation and slope explains 63 % of the damage pattern, making it the strongest causal factor. The results substantiate our initial hypothesis and underscore the fact that the pattern of damage does not solely rely on a singular factor but rather on the interaction of multiple factors. These findings hold significance in advancing the formulation of more precise strategies aimed at bolstering safety measures and safeguarding properties within regions susceptible to flooding.

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.

East Asian summer rainfall stimulated by subseasonal Indian monsoonal heating

The responses of the East Asian summer monsoon (EASM) to the Indian summer monsoon (ISM) have been the subject of extensive investigation. Nevertheless, it remains uncertain whether the ISM can serve as a predictor for the EASM. Here, on the basis of both observations and a large-ensemble climate model experiment, we show that the subseasonal variability of abnormal diabatic heating over India enhances precipitation over central East China, the Korean Peninsula, and southern Japan in June. ISM heating triggers Rossby wave propagation along the subtropical jet, promoting southerly winds over East Asia. The southerly winds helps steer anomalous mid-tropospheric warm advection and lower-tropospheric moisture advection toward East Asia, providing conditions preferential for rainband formation. Cluster analysis shows that, depending on jet structures, ISM heating can serve as a trigger as well as a reinforcer of the rainband.

Propagation pathways of Indo-Pacific rainfall extremes are modulated by Pacific sea surface temperatures

Intraseasonal variation of rainfall extremes within boreal summer in the Indo-Pacific region is driven by the Boreal Summer Intraseasonal Oscillation (BSISO), a quasi-periodic north-eastward movement of convective precipitation from the Indian Ocean to the Western Pacific. Predicting the spatiotemporal location of the BSISO is essential for subseasonal prediction of rainfall extremes but still remains a major challenge due to insufficient understanding of its propagation pathway. Here, using unsupervised machine learning, we characterize how rainfall extremes travel within the region and reveal three distinct propagation modes: north-eastward, eastward-blocked, and quasi-stationary. We show that Pacific sea surface temperatures modulate BSISO propagation - with El Niño-like (La Niña-like) conditions favoring quasi-stationary (eastward-blocked) modes-by changing the background moist static energy via local overturning circulations. Finally, we demonstrate the potential for early warning of rainfall extremes in the region up to four weeks in advance.

Quantifying the synchronization of the spikes emitted by coupled lasers

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers' parameters. Here, we analyze experiments done with two mutually optically coupled lasers. Due to the delay in the coupling (due to the finite time the light takes to travel between the lasers), the lasers synchronize with a lag: the intensity time traces show well-defined spikes, and a spike in the intensity of one laser may occur shortly before (or shortly after) a spike in the intensity of the other laser. Measures that quantify the degree of synchronization of the lasers from the analysis of the intensity signals do not fully quantify the synchronicity of the spikes because they also take into account the synchronization of fast irregular fluctuations that occur between spikes. By analyzing only the coincidence of the spike times, we show that event synchronization measures quantify spike synchronization remarkably well. We show that these measures allow us to quantify the degree of synchronization and, also, to identify the leading laser and the lagging one.

Climate-driven changes in the predictability of seasonal precipitation

Climate-driven changes in precipitation amounts and their seasonal variability are expected in many continental-scale regions during the remainder of the 21st century. However, much less is known about future changes in the predictability of seasonal precipitation, an important earth system property relevant for climate adaptation. Here, on the basis of CMIP6 models that capture the present-day teleconnections between seasonal precipitation and previous-season sea surface temperature (SST), we show that climate change is expected to alter the SST-precipitation relationships and thus our ability to predict seasonal precipitation by 2100. Specifically, in the tropics, seasonal precipitation predictability from SSTs is projected to increase throughout the year, except the northern Amazonia during boreal winter. Concurrently, in the extra-tropics predictability is likely to increase in central Asia during boreal spring and winter. The altered predictability, together with enhanced interannual variability of seasonal precipitation, poses new opportunities and challenges for regional water management.

GPU-based, interactive exploration of large spatiotemporal climate networks

This paper introduces the Graphics Processing Unit (GPU)-based tool Geo-Temporal eXplorer (GTX), integrating a set of highly interactive techniques for visual analytics of large geo-referenced complex networks from the climate research domain. The visual exploration of these networks faces a multitude of challenges related to the geo-reference and the size of these networks with up to several million edges and the manifold types of such networks. In this paper, solutions for the interactive visual analysis for several distinct types of large complex networks will be discussed, in particular, time-dependent, multi-scale, and multi-layered ensemble networks. Custom-tailored for climate researchers, the GTX tool supports heterogeneous tasks based on interactive, GPU-based solutions for on-the-fly large network data processing, analysis, and visualization. These solutions are illustrated for two use cases: multi-scale climatic process and climate infection risk networks. This tool helps one to reduce the complexity of the highly interrelated climate information and unveils hidden and temporal links in the climate system, not available using standard and linear tools (such as empirical orthogonal function analysis).

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

New results on adaptive fixed-time control for convex-delayed neural networks

This paper studies the adaptive fixed-time synchronization issue for convex-delayed neural networks. First, the convex delay is introduced to address the state delay of neural networks in order to reflect the impacts of multiple delay components such as input transition time and switching communication. Then, a new fixed-time control method is presented to adaptively determine multi-control gains with a unified update law. Afterward, some sufficient criteria are figured out by using Lyapunov stability theorem to ensure that the delayed neural networks are fixed-timely stable. Finally, simulated examples are adopted to validate our theoretical results.

Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis

We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs' operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.

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.

Global droughts connected by linkages between drought hubs

Quantifying the spatial and interconnected structure of regional to continental scale droughts is one of the unsolved global hydrology problems, which is important for understanding the looming risk of mega-scale droughts and the resulting water and food scarcity and their cascading impact on the worldwide economy. Using a Complex Network analysis, this study explores the topological characteristics of global drought events based on the self-calibrated Palmer Drought Severity Index. Event Synchronization is used to measure the strength of association between the onset of droughts at different spatial locations within the time lag of 1-3 months. The network coefficients derived from the synchronization network indicate a highly heterogeneous connectivity structure underlying global drought events. Drought hotspot regions such as Southern Europe, Northeast Brazil, Australia, and Northwest USA behave as drought hubs that synchronize regionally and with other hubs at inter-continental or even inter-hemispheric scale. This observed affinity among drought hubs is equivalent to the 'rich-club phenomenon' in Network Theory, where 'rich' nodes (here, drought hubs) are tightly interconnected to form a club, implicating the possibility of simultaneous large-scale droughts over multiple continents.

Universality and scaling in complex networks from periods of Chinese history

Critical physical systems with large numbers of molecules can show universal and scaling behaviors. It is of interest to know whether human societies with large numbers of people can show the same behaviors. Here, we use network theory to analyze Chinese history in periods 209 BCE-23 CE and 515-618 CE) related to the Western Han-Xin Dynasty and the late Northern Wei-Sui Dynasty, respectively. Two persons are connected when they appear in the same historical event. We find that the historical networks from two periods separated about 500 years have interesting universal and scaling behaviors, and they are small-world networks; their average cluster coefficients as a function of degree are similar to the network of movie stars. In the historical networks, the persons with larger degrees prefer to connect with persons with a small degree; however, in the network of movie stars, the persons with larger degrees prefer to connect with persons with large degrees. We also find an interesting similar mechanism for the decline or collapse of historical Chinese dynasties. The collapses of the Xin dynasty (9-23 CE) and the Sui dynasty (581-618 CE) were initiated from their arrogant attitude toward neighboring states.

Study of interaction and complete merging of binary cyclones using complex networks

Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru-Kulap and Seroja-Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.

Heat Extremes Driven by Amplification of Phase-Locked Circumglobal Waves Forced by Topography in an Idealized Atmospheric Model

Heatwaves are persistent temperature extremes associated with devastating impacts on human societies and ecosystems. In the midlatitudes, amplified quasi-stationary Rossby waves have been identified as a key mechanism for heatwave occurrence. Amplified waves with preferred longitudinal locations lead to concurrent extremes in specific locations. It is therefore important to identify the essential components in the climate system that contribute to phase-locking of wave patterns. Here, we investigate the role of dry atmospheric dynamics and topography in causing concurrent heatwaves by using an idealized general circulation model. Topography is included in the model experiments as a Gaussian mountain. Our results show that amplified Rossby waves exhibit clear phase-locking behavior and a decrease in the zonal phase speed when a large-scale localized topographic forcing is imposed, leading to concurrent heat extremes at preferred locations.

Detecting the causal influence of thermal environments among climate regions in the United States

The quantification of cross-regional interactions for the atmospheric transport processes is of crucial importance to improve the predictive capacity of climatic and environmental system modeling. The dynamic interactions in these complex systems are often nonlinear and non-separable, making conventional approaches of causal inference, such as statistical correlation or Granger causality, infeasible or ineffective. In this study, we applied an advanced approach, based on the convergent cross mapping algorithm, to detect and quantify the causal influence among different climate regions in the contiguous U.S. in response to temperature perturbations using the long-term (1901-2018) climatology of near surface air temperature record. Our results show that the directed causal network constructed by convergent cross mapping algorithm, enables us to distinguish the causal links from spurious ones rendered by statistical correlation. We also find that the Ohio Valley region, as an atmospheric convergent zone, acts as the regional gateway and mediator to the long-term thermal environments in the U.S. In addition, the temporal evolution of dynamic causality of temperature exhibits superposition of periodicities at various time scales, highlighting the impact of prominent low frequency climate variabilities such as El Niño-Southern Oscillation. The proposed method in this work will help to promote novel system-based and data-driven framework in studying the integrated environmental system dynamics.

Statistical inference links data and theory in network science

The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.

Theoretical models and structures recovered from measured data serve for analysis of complex networks. The authors discuss here existing gaps between theoretical methods and real-world applied networks, and potential ways to improve the interplay between theory and applications.

Dependence Analysis of PM2.5 Concentrations in 295 Chinese Cities in the Winter of 2019–2020

Considering the current severe atmospheric pollution problems in China, a comprehensive understanding of the distribution and spatial variability of PM2.5 is critically important for controlling pollution and improving the future atmospheric environment. This study first explored the distribution of PM2.5 concentrations in China, and then developed a methodology of “dependence analysis” to investigate the relationship of PM2.5 in different cities in China. The data of daily PM2.5 concentrations were collected from the environmental monitoring stations in 295 cities in China. This study also developed a set of procedures to evaluate the spatial dependence of PM2.5 among the 295 Chinese cities. The results showed that there was a total of 154 city pairs with dependence type “11”, under a significance level of 0.5%. Dependence type “11” mainly occurred between nearby cities, and the distance between 89.0% of the dependent city pairs was less than 200 km. Furthermore, the dependent pairs mainly clustered in the North China Plain, the Northeast Plain, the Middle and Lower Yangtze Plain and the Fen-Wei Plain. The geographic conditions of the Plain areas were more conducive to the spread of PM2.5 contaminants, while the mountain topography was unfavorable for the formation of PM2.5 dependencies. The dependent city couples with distances greater than 200 km were all located within the Plain areas. The high concentration of PM2.5 did not necessarily lead to PM2.5 dependences between city pairs. The methodology and models developed in this study will help explain the concentration distributions and spatial dependence of the main atmospheric pollutants in China, providing guidance for the prevention of large-scale air pollution, and the improvement of the future atmospheric environment.

Network motifs shape distinct functioning of Earth's moisture recycling hubs

Earth's hydrological cycle critically depends on the atmospheric moisture flows connecting evaporation to precipitation. Here we convert a decade of reanalysis-based moisture simulations into a high-resolution global directed network of spatial moisture provisions. We reveal global and local network structures that offer a new view of the global hydrological cycle. We identify four terrestrial moisture recycling hubs: the Amazon Basin, the Congo Rainforest, South Asia and the Indonesian Archipelago. Network motifs reveal contrasting functioning of these regions, where the Amazon strongly relies on directed connections (feed-forward loops) for moisture redistribution and the other hubs on reciprocal moisture connections (zero loops and neighboring loops). We conclude that Earth's moisture recycling hubs are characterized by specific topologies shaping heterogeneous effects of land-use changes and climatic warming on precipitation patterns.

Relationships between transmission of malaria in Africa and climate factors

The spread of malaria is related to climate change because temperature and rainfall are key parameters of climate change. Fluctuations in temperature affect the spread of malaria by lowering or speeding up its rate of transmission. The amount of rainfall also affects the transmission of malaria by offering a lot of sites suitable for mosquitoes to breed in. However, a high amount of rainfall does not have a great effect. Because of the high malaria incidence and the death rates in African regions, by using malaria incidence data, temperature data and rainfall data collected in 1901-2015, we construct and analyze climate networks to show how climate relates to the transmission of malaria in African countries. Malaria networks show a positive correlation with temperature and rainfall networks, except for the 1981-2015 period, in which the malaria network shows a negative correlation with rainfall.

Partial event coincidence analysis for distinguishing direct and indirect coupling in functional network construction

Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction. In this context, the widespread use of bivariate statistical association measures often results in a false identification of links because strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers. In order to properly distinguish such direct and indirect links for the special case of event-like data, we present here a new generalization of event coincidence analysis to a partial version thereof, which is aimed at excluding possible transitive effects of indirect couplings. Using coupled chaotic systems and stochastic processes on two generic coupling topologies (star and chain configuration), we demonstrate that the proposed methodology allows for the correct identification of indirect interactions. Subsequently, we apply our partial event coincidence analysis to multi-channel EEG recordings to investigate possible differences in coordinated alpha band activity among macroscopic brain regions in resting states with eyes open (EO) and closed (EC) conditions. Specifically, we find that direct connections typically correspond to close spatial neighbors while indirect ones often reflect longer-distance connections mediated via other brain regions. In the EC state, connections in the frontal parts of the brain are enhanced as compared to the EO state, while the opposite applies to the posterior regions. In general, our approach leads to a significant reduction in the number of indirect connections and thereby contributes to a better understanding of the alpha band desynchronization phenomenon in the EO state.

Drying in the low-latitude Atlantic Ocean contributed to terrestrial water storage depletion across Eurasia

Eurasia, home to ~70% of global population, is characterized by (semi-)arid climate. Water scarcity in the mid-latitude Eurasia (MLE) has been exacerbated by a consistent decline in terrestrial water storage (TWS), attributed primarily to human activities. However, the atmospheric mechanisms behind such TWS decline remain unclear. Here, we investigate teleconnections between drying in low-latitude North Atlantic Ocean (LNATO) and TWS depletions across MLE. We elucidate mechanistic linkages and detecte high correlations between decreased TWS in MLE and the decreased precipitation-minus-evapotranspiration (PME) in LNATO. TWS in MLE declines by ~257% during 2003-2017 due to northeastward propagation of PME deficit following two distinct seasonal landfalling routes during January-May and June-January. The same mechanism reduces TWS during 2031-2050 by ~107% and ~447% under scenarios SSP245 and SSP585, respectively. Our findings highlight the risk of increased future water scarcity across MLE caused by large-scale climatic drivers, compounding the impacts of human activities.

The climatic interdependence of extreme-rainfall events around the globe

The identification of regions of similar climatological behavior can be utilized for the discovery of spatial relationships over long-range scales, including teleconnections. Additionally, it provides insights for the improvement of corresponding interaction processes in general circulation models. In this regard, the global picture of the interdependence patterns of extreme-rainfall events (EREs) still needs to be further explored. To this end, we propose a top-down complex-network-based clustering workflow, with the combination of consensus clustering and mutual correspondences. Consensus clustering provides a reliable community structure under each dataset, while mutual correspondences build a matching relationship between different community structures obtained from different datasets. This approach ensures the robustness of the identified structures when multiple datasets are available. By applying it simultaneously to two satellite-derived precipitation datasets, we identify consistent synchronized structures of EREs around the globe, during boreal summer. Two of them show independent spatiotemporal characteristics, uncovering the primary compositions of different monsoon systems. They explicitly manifest the primary intraseasonal variability in the context of the global monsoon, in particular, the "monsoon jump" over both East Asia and West Africa and the mid-summer drought over Central America and southern Mexico. Through a case study related to the Asian summer monsoon, we verify that the intraseasonal changes of upper-level atmospheric conditions are preserved by significant connections within the global synchronization structure. Our work advances network-based clustering methodology for (i) decoding the spatiotemporal configuration of interdependence patterns of natural variability and for (ii) the intercomparison of these patterns, especially regarding their spatial distributions over different datasets.

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.

A complex network approach to study the extreme precipitation patterns in a river basin

The quantification of spatial propagation of extreme precipitation events is vital in water resources planning and disaster mitigation. However, quantifying these extreme events has always been challenging as many traditional methods are insufficient to capture the nonlinear interrelationships between extreme event time series. Therefore, it is crucial to develop suitable methods for analyzing the dynamics of extreme events over a river basin with a diverse climate and complicated topography. Over the last decade, complex network analysis emerged as a powerful tool to study the intricate spatiotemporal relationship between many variables in a compact way. In this study, we employ two nonlinear concepts of event synchronization and edit distance to investigate the extreme precipitation pattern in the Ganga river basin. We use the network degree to understand the spatial synchronization pattern of extreme rainfall and identify essential sites in the river basin with respect to potential prediction skills. The study also attempts to quantify the influence of precipitation seasonality and topography on extreme events. The findings of the study reveal that (1) the network degree is decreased in the southwest to northwest direction, (2) the timing of 50th percentile precipitation within a year influences the spatial distribution of degree, (3) the timing is inversely related to elevation, and (4) the lower elevation greatly influences connectivity of the sites. The study highlights that edit distance could be a promising alternative to analyze event-like data by incorporating event time and amplitude and constructing complex networks of climate extremes.

Network-based forecasting of climate phenomena

Network theory, as emerging from complex systems science, can provide critical predictive power for mitigating the global warming crisis and other societal challenges. Here we discuss the main differences of this approach to classical numerical modeling and highlight several cases where the network approach substantially improved the prediction of high-impact phenomena: 1) El Niño events, 2) droughts in the central Amazon, 3) extreme rainfall in the eastern Central Andes, 4) the Indian summer monsoon, and 5) extreme stratospheric polar vortex states that influence the occurrence of wintertime cold spells in northern Eurasia. In this perspective, we argue that network-based approaches can gainfully complement numerical modeling.

The Study on Compound Drought and Heatwave Events in China Using Complex Networks

Compound extreme events can severely impact water security, food security, and social and economic development. Compared with single-hazard events, compound extreme events cause greater losses. Therefore, understanding the spatial and temporal variations in compound extreme events is important to prevent the risks they cause. Only a few studies have analyzed the spatial and temporal relations of compound extreme events from the perspective of a complex network. In this study, we define compound drought and heatwave events (CDHEs) using the monthly scale standard precipitation index (SPI), and the definition of a heatwave is based on daily maximum temperature. We evaluate the spatial and temporal variations in CDHEs in China from 1961 to 2018 and discuss the impact of maximum temperature and precipitation changes on the annual frequency and annual magnitude trends of CDHEs. Furthermore, a synchronization strength network is established using the event synchronization method, and the proposed synchronization strength index (SSI) is used to divide the network into eight communities to identify the propagation extent of CDHEs, where each community represents a region with high synchronization strength. Finally, we explore the impact of summer Atlantic multidecadal oscillation (AMO) and Pacific decadal oscillation (PDO) on CDHEs in different communities. The results show that, at a national scale, the mean frequency of CDHEs takes on a non-significant decreasing trend, and the mean magnitude of CDHEs takes on a non-significant increasing trend. The significant trends in the annual frequency and annual magnitude of CDHEs are attributed to maximum temperature and precipitation changes. AMO positively modulates the mean frequency and mean magnitude of CDHEs within community 1 and 2, and negatively modulates the mean magnitude of CDHEs within community 3. PDO negatively modulates the mean frequency and mean magnitude of CDHEs within community 4. AMO and PDO jointly modulate the mean magnitude of CDHEs within community 6 and 8. Overall, this study provides a new understanding of CDHEs to mitigate their severe effects.

Eigen microstates and their evolution of global ozone at different geopotential heights

Studies on stratospheric ozone have attracted much attention due to its serious impacts on climate changes and its important role as a tracer of Earth's global circulation. Tropospheric ozone as a main atmospheric pollutant damages human health as well as the growth of vegetation. Yet, there is still a lack of a theoretical framework to fully describe the variation of ozone. To understand ozone's spatiotemporal variance, we introduce the eigen microstate method to analyze the global ozone mass mixing ratio between January 1, 1979 and June 30, 2020 at 37 pressure layers. We find that eigen microstates at different geopotential heights can capture different climate phenomena and modes. Without deseasonalization, the first eigen microstates capture the seasonal effect and reveal that the phase of the intra-annual cycle moves with the geopotential heights. After deseasonalization, by contrast, the collective patterns from the overall trend, El Niño-Southern Oscillation (ENSO), quasi-biennial oscillation, and tropopause pressure are identified by the first few significant eigen microstates. The theoretical framework proposed here can also be applied to other complex Earth systems.