Air pollution fluctuations have been found to strongly depend on the weather dynamics. Here we identify the significant atmospheric processes that affect the local daily variability of air pollution. We develop a multilayered network analysis to detect the interlinks between the 500‐hPa geopotential height and surface air pollution in both China and the United States. We find that Rossby waves significantly affect air pollution fluctuations through the development of cyclone and anticyclone systems and further affect the local stability of the air and the winds. Some of these systems are remote (∼3,000 km) and lead to air pollution 1–2 days later. Thus, the impact of Rossby waves on human life is greater than previously believed. The rapid warming of the Arctic could slow down Rossby waves, thus increasing human health risks. Our method can help to determine the risk assessment of such extreme events and can improve potential predictability.

Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A , whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as A = ∑ I = 1 r σ I U I ⨂ V I , where r = min ( N , M ) , eigenvalue σ _I behaves as the probability amplitude of the eigen microstate U _I so that ∑ I = 1 r σ I 2 = 1 and U _I evolves following V _I . In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σ _I becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate U _I in analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U _I and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.

The impact of climate change on extreme weather is one of the most concerning problems. Climate change could cause more frequent and unexpected extreme weather. Still, synchronization features of extreme weather under climate change are not fully understood. Here, we develop a climate network approach to study global synchronization patterns of extreme events based on the 500‐hPa geopotential field. We find that a positive event synchronization (PES) network is associated with the tropical circulations in the tropics; a negative event synchronization network is associated with the large‐scale atmospheric Rossby waves in mid‐latitudes. By studying temporal evolution of the PES network, we find that the synchronization strengths in the tropics are weakening under climate change in relation to the slowing down of tropical circulations. Furthermore, our results show that the strength of synchronization in Africa and the Atlantic Ocean decrease faster than other regions.

Earthquakes involve complex processes that span a wide range of spatial and temporal scales. The limited earthquake predictability is partly due to the erratic nature of earthquakes and partly due to the lack of understanding of the underlying mechanisms of earthquakes. To improve our understanding and possibly the predictability of earthquakes, we develop here a lagged conditional probability method to study the spatial and temporal long-term memory of interevent earthquakes above a certain magnitude. We find, in real data from different locations, that the lagged conditional probabilities show long-term memory for both the interevent times and interevent distances and that the memory functions obey scaling and decay slowly with time, while, at a characteristic time (crossover), the decay rate becomes faster. We also show that the epidemic-type aftershock sequence model, which is often used to forecast earthquake events, fails in reproducing the scaling function of real catalogs as well as the crossover in the scaling function. Our results suggest that aftershock rate is a critical factor to control the long-term memory.

A prominent feature of earthquakes is their empirical laws, including memory (clustering) in time and space. Several earthquake forecasting models, such as the epidemic-type aftershock sequence (ETAS) model, were developed based on these empirical laws. Yet, a recent study [1] showed that the ETAS model fails to reproduce the significant long-term memory characteristics found in real earthquake catalogs. Here we modify and generalize the ETAS model to include short- and long-term triggering mechanisms, to account for the short- and long-time memory (exponents) discovered in the data. Our generalized ETAS model accurately reproduces the short- and long-term/distance memory observed in the Italian and Southern Californian earthquake catalogs. The revised ETAS model is also found to improve earthquake forecasting after large shocks.