Reliable forecasts of chaotic natural systems need methods that keep many possible states alive. This study improves a particle-based method by replacing hand-chosen mixing weights with random ones and by estimating the state before mixing changes the particle set. Tests with standard chaotic models show that the method reduces known weaknesses of the original approach and can keep accurate estimates while preserving diversity.

Earthquake faults branch into smaller and smaller pieces, like cracks within cracks. We built a mathematical model linking how many fault pieces interact to how quickly aftershocks fade, how far the stress from a quake spreads, and how earthquake sizes are distributed. The model needs no tuned settings and agrees with two recent large earthquakes, in Turkey in 2023 and Japan in 2024. It offers a simpler, physics-based way to understand aftershock patterns and earthquake hazard.

The widely used standard model for predicting how fast wildfires spread responds to wind in a way that grows without limit, which is unrealistic at high wind and has long been patched by hand. We rebuilt the wind response so it levels off naturally, grounding the change in the physics of how fuel ignites. This fixes a known flaw in how the model handles fast-moving grass fires, giving forecasters more reliable predictions of fire behaviour in strong winds.

Heavy rainfall from typhoons can trigger sudden floods, yet the most intense bursts are brief and easily missed. We measured rain every ten seconds during three 2022 typhoons in Taiwan and examined how the patterns behaved across time scales. One storm produced exceptionally concentrated, rare rainfall, while the others were limited by record length. The results show that fast measurements matter because slower instruments smooth out these peaks and can lead us to underestimate flood risk.

Inside clouds, the water droplets grow by colliding together, and as a conseqeunce, two of them merge into a larger single droplet. This process can be described by an equation involving differentials and integrals. This paper studies the growth of droplet sizes by collisions and mergers by asking how we can make it identical by rescaling time, droplet size unit, as well as the total number density, like we recreate scenes in movies by minituares.

The tropical atmosphere is found to be more predictable than other regions in the world. In the present paper, however, we show that predictability is considerably limited when considering simplified versions of the atmospheric dynamics, contrasting with the common idea. These results open therefore new questions on the specific sources of higher predictability in the tropical atmosphere.

The numerical weather prediction (NWP) is facing the challenge of development bottleneck, and this article, via a comprehensive review on application of catastrophe theory to the atmospheric science for revealing the fundamental logic why the physics-based NWP methodology would be about to approach its end with some remedial measures suggested for avoiding its finality to occur, might be helpful to promote the enhancement of NWP forecasting accuracy so as to break its development bottleneck.

We tested whether persistent homology reliably detects signals in hurricane track data. Applying three valid coordinate systems to the same storms, the method's conclusions flip between "signal" and "no signal." A calibration test confirmed systematic false-positive inflation. We propose a validation checklist before this method is trusted for hurricane analysis.

Understanding Earth system dynamics requires comparing outputs from many models and variables. Yet identifying where and when datasets agree on significant changes remains a challenge. We developed methods that combine detected signals across models and variables into shared patterns in space and time, providing robust signals from large model ensembles. Applied to Amazon rainforest simulations, we show that conclusions about Earth system change depend critically on how evidence is synthesised.

Modern Seismological networks allowed the observation of unprecedented seismic cycle characteristics. Using geophysical techniques we have identified conditions that describe eathquakes occurrence and seismic moment release complex processes. These conditions indicate that earthquakes are related over long distances and time-periods within a fractal geometry. These observations will likely improve our risk analysis capabilities and will provide better information to decision makers.

Natural hazards are often described by how much area is affected, but this can miss how the affected places are connected. This study shows that the same affected area can appear as scattered patches, several grouped zones, or one large connected region. Using observed liquefaction data and computer simulations, it shows that spatial connection gives important extra information for understanding hazard patterns and possible wider impacts.

Climate models often simplify Earth’s atmosphere and oceans to make complex calculations possible. This study examines how such simplifications can unintentionally change the mathematical structures that determine large-scale climate variability and wave behavior. Using examples from global temperature balance and ocean–atmosphere waves, the paper shows that some common approximations may alter the set of physically allowed patterns of variability rather than simply simplifying them.

We investigate how two different indicators related to measures of energy transfer can be used to assess the dynamics of tropical cyclones. One indicator is based on the energy redistribution across length-scales and the other one is based on more fundamental thermodynamic principles. This research demonstrates the potential of these indicators of being used as predictors for the intensity change of tropical cyclones even in under-resolved simulations.

Using more than 70 years of tornado records across the United States, we show that tornado damage paths follow surprisingly robust geometric patterns across a wide range of sizes. Longer tornadoes tend to become wider according to a consistent scaling law that remains stable despite major changes in observation methods over time. These results suggest that tornadoes may possess an underlying large-scale statistical organisation similar to that observed in other complex natural systems.

Modern environmental forecasting combines computer simulations with real-world observations. Most systems assume errors in these sources are independent, but in reality, they are occasionally linked. We developed a new method to estimate the hidden correlations. Using a simplified atmospheric model, we showed our method successfully identifies the correlations and significantly improves prediction accuracy. This work provides a practical path toward more reliable weather and ocean forecasts.

Many natural systems, including the atmosphere and ocean, are nonlinear, noisy, and only partly observed. We develop a continuous-time smoother that combines model dynamics with past, present, and future observations using a small ensemble, without tangent-linear or adjoint models. Using only an ensemble of order ten, the method improves hidden-state estimation, supports causal inference near extreme events, and helps discover missing model structure, offering a low-cost tool for reanalysis.

Extreme wildfire-driven pyro-cumulonimbus convection can generate long-lived stratospheric vortices, but their material coherence has been unclear. Using geodesic vortex detection on reanalysis winds from the 2019–2020 Australian bushfires, we identify a coherent vortex, Koobor, bounded by loops that resist filamentation and stretch nearly uniformly for up to 40 days. Across levels, it shows a ~60-day life cycle sustained by overlapping coherent boundaries.

This work studies a mathematical model of atmospheric convection with water condensation. We prove existence and uniqueness of a stationary solution for a nonlinear differential system governing vertical air flow. Numerical simulations reveal damped oscillations in flow intensity and liquid water content, driven by latent heat and droplet accumulation. A qualitative analogy with a Volterra integro-differential equation explains the memory-driven oscillatory dynamics underlying storm formation.

This study introduces a new method to improve images of the Earth’s subsurface using seismic data. Because seismic signals are limited and noisy, estimating underground properties is difficult and often uncertain. Our method combines seismic measurements with information from wells and geology while grouping similar rock properties. Tests on synthetic and real data show that the approach produces clearer subsurface models and helps identify geological layers more reliably.

Climate tipping systems like the Atlantic circulation, the Amazon, and Greenland ice interact in ways that standard projections miss. By analysing decades of climate model output, we show that persistent memory in the Atlantic circulation causes extreme-event risk to be understated by up to six times. The Amazon, by contrast, is well described by conventional projections. Ignoring memory hides the most dangerous cascade pathways precisely where prevention is still possible.