The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and the fracture strength of quasibrittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. Our analysis employs the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the $$\kappa${}$-Weibull distribution. The upper tail of the $$\kappa${}$-Weibull distribution declines as a power law in contrast with Weibull scaling. The hazard rate function of the $$\kappa${}$-Weibull distribution decreases linearly after a waiting time ${$\tau${}}_{c}$\propto${}{n}^{1/m}$, where $m$ is the Weibull modulus and $n$ is the system size in terms of representative volume elements. We conduct statistical analysis of experimental data and simulations which show that the $$\kappa${}$ Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we demonstrate that the $$\kappa${}$-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture strength of brittle materials, maximal annual rainfall, wind speed and earthquake return times. We investigate two new distributions that exhibit weakest-link scaling, i.e., a Weibull generalization known as the κ-Weibull and a modified gamma probability function that we propose herein. We show that in contrast with the Weibull and the modified gamma, the hazard function of the κ -Weibull is non-extensive, which is a signature of inter-dependence between the links. We also investigate the impact of heterogeneous links, modeled by means of a stochastic Weibull scale parameter, on the observed probability distribution.

According to the United Nations (UN) more than 55 % of the global population resided in urban areas in 2018, a number projected to increase to an estimated 60 % of the world's population by 2030. As urbanization accelerates, degradation of air quality becomes an increasing environmental pressure to human welfare and health. To date, epidemiological studies reveal a strong connection between airborne dust and adverse health effects. This study investigates the fine-mode and coarse-mode dust particulate matter levels within the planetary boundary layer (PBL) over major cities and megacities of the world (population > 5 million), leveraging on the European Space Agency (ESA) – “LIdar climatology of Vertical Aerosol Structure” (LIVAS) multiyear satellite-based dust climate data record. Results show that current dust levels exceed World Health Organization (WHO) annual-mean air quality guidelines (AQGs) for PM_2.5 and PM₁₀ in 49.4 % and 87.7 % of the cities considered, respectively, exposing ∼ 700 million people to hazardous dust concentrations. Moreover, according to the outcomes of the study, this number is expected to increase to ∼ 850 million individuals (∼ 22 % increase) by 2030s, though due to the general declining dust tendencies the health hazard is projected to be diminished in severity. Particularly affected are cities in the regions of Middle East, Indian subcontinent, East Asia, North Africa, and the Sahel. Epidemiological models are employed to estimate associated health risks. The study provides an informative mitigation and adaptation tool to support observational-based policymaking, air quality management, and public health planning to protect human health in the context of accelerating urbanization.

Wildfires are a complex and underexplored aspect of the Earth system, significantly affecting climate, as they emit greenhouse gases and aerosols that alter the Earth’s radiative balance. This study utilizes the EC-Earth3 Earth System Model to investigate how interannual variability in biomass burning emissions influences variability in total aerosol optical depth (AOD), as well as carbon monoxide (CO) and ozone (O₃) tropospheric columns. We demonstrate that fluctuations in biomass burning emissions impact AOD, CO, and O₃ variability at regional and global scales, emphasizing the need for improved understanding of wildfires and their climate effects.