We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.

We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we present a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.

We investigated how machine learning can forecast extreme vegetation responses to weather. Examining four models, no single one stood out as the best, though "echo state networks" showed minor advantages. Our results indicate that while these tools are able to generally model vegetation states, they face challenges under extreme conditions. This underlines the potential of artificial intelligence in ecosystem modeling, also pinpointing areas that need further research.

On February 03 2022, SpaceX launched a new group of satellites for its Starlink constellation. This launch simultaneously released 49 satellites into orbits between 200 km and 250 km height. The launches occurred during a geomagnetic storm that was followed by a second storm. There was an immediate loss of 32 satellites. The satellite losses may have been caused by an unusually high level of atmospheric drag (unexplained by current theory or modeling) or a high level of satellite collisions.

With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri  below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10^-4 m²s^-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.

The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.

We propose a novel method for the estimation of ocean surface flow properties in terms of its energy and spatial and temporal scales. The method relies on flow observations collected either at a fixed location or along the flow, as would be inferred from the trajectory of freely drifting platforms. The accuracy of the method is quantified in several experimental configurations. We innovatively demonstrate that freely drifting platforms, even in isolation, can be used to capture flow properties.

The characterisation of abrupt transitions in palaeoclimate records allows understanding of millennial climate variability and potential tipping points in the context of current climate change. In our study an algorithmic method, the matrix profile, is employed to characterise abrupt warmings designated as Dansgaard–Oeschger (DO) events and to identify the most similar transitions in the palaeoclimate time series.

We identify spatially coherent air streams into atmospheric blockings, which are important weather phenomena. By adapting mathematical methods to the atmosphere, we confirm previous findings. Our work shows that spatially coherent air streams featuring cloud formation correlate with strengthening of the blocking. The developed framework also allows for statements about the spatial behavior of the air parcels as a whole and indicates that blockings reduce the dispersion of the air parcels.

Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, diffusive back-and-forth nudging and concave–convex nonlinearity, which account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impact which method is better suited for a problem.

Seismo-electromagnetic (SEM) signals emitted prior to major earthquakes show promise as candidates for short-term earthquake prediction. Analyzing the frequency characteristics of SEM signals provides insights into pre-earthquake processes in the focal zone, such as microfracturing and electrokinetic phenomena. The combined application of fractal and multifractal methods proves to be an effective tool for analyzing these complex signals.

In this work, the multiscale dynamics of 38 oceanic and atmospheric pCO₂ time series, sea surface temperature data, and salinity data from fixed buoys recorded with 3 h resolution are considered. The Fourier scaling exponents are estimated. The differences found for three ecosystems – coastal shelf, coral reefs and open ocean  – are discussed. Multifractal properties of pCO₂ difference between ocean and atmosphere are found and characterized over the scale range from 3 h to 1 year.

We have developed a systematic approach to study the climate system at multiple scales using climate networks, which have been previously used to study correlations between time series in space at only a single scale. This new approach is used to upscale precipitation climate networks to study the Indian summer monsoon and to analyze strong dependencies between spatial regions, which change with changing scales.

Vegetation patterns in semi-arid regions arise from interactions between plants and environmental factors. This study uses a numerical model to explore how vegetation responds to changes in rainfall and random disturbances. We identify key timescales that influence resilience, showing that ecosystems rely on both stable and unstable states to adapt. These findings offer insights into the resilience mechanisms that help ecosystems maintain stability under environmental stress.

Wind energy exhibits extreme variability in space and time. However, it also shows scaling properties (properties that remain similar across different times and spaces of measurement). This can be quantified using appropriate statistical tools. In this way, the scaling properties of power from a wind farm are analysed here. Since every turbine is manufactured by design for a rated power, this acts as an upper limit on the data. This bias is identified here using data and numerical simulations.

To understand the influence of rainfall on wind power production, turbine power and rainfall were measured simultaneously on an operational wind farm and analysed. The correlation between wind, wind power, air density, and other fields was obtained on various temporal scales under rainy and dry conditions. An increase in the correlation was observed with an increase in the rain; rain also influenced the correspondence between actual and expected values of power at various velocities.

Understanding volcanic activity is crucial for uncovering the fundamental physical mechanisms governing this natural phenomenon. In this study, we show the application of multifractal and statistical analysis to investigate changes associated with volcanic activity. We aim to identify significant variations within the physical processes related to changes in volcanic activity. These methodologies offer the potential to identify pertinent changes preceding a high-energy explosion.

We investigate the stability characteristics of lightning discharge channels through their differential resistance properties. Our analysis reveals that lightning channels exhibit bistable behavior, transitioning between low- and high-conductivity states depending on channel length and electric-field conditions. This work provides new insights into lightning channel dynamics and could contribute to improved lightning protection strategies.

Artificial intelligence (AI) has recently shown promising results in ENSO (El Niño–Southern Oscillation) forecasting, outperforming traditional models. Yet AI models deliver accurate predictions without showing the underlying mechanisms. Our study examines a specific AI model, the reservoir computer (RC). Our results show that the RC is less sensitive to initial perturbations than the traditional Zebiak–Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.

This study presents a new approach to simulating large ocean density waves that travel long distances without breaking down. This new approach ensures that these waves are depicted more accurately and realistically in our models. This is particularly useful for understanding wave behavior in lakes with distinct water layers, which can help predict natural phenomena and their effects on environments like swash zones, where waves meet the shore.

The hydrostatic approximation is the basis of most simulations of ocean and climate dynamics. It is evaluated here by using a projection method in the 4D Fourier space. The evaluation is analytic.

Fog can disrupt aviation by causing accidents and delays due to low visibility, yet it remains underresearched in Croatia. This study examined fog and mist at Pula Airport using 20 years of data and machine learning techniques. There is a declining trend in fog that is linked to changing weather patterns. Fog mainly occurs from October to March. These findings enhance knowledge about fog in Croatia and can improve weather forecasts, increasing safety at the airport.

Can multilevel Monte Carlo methods improve ensemble variational data assimilation without increasing its computational cost? By shifting part of the ensemble generation cost to coarser simulation grids, larger ensemble sizes become affordable. This gives smaller sampling errors without introducing any coarse-grid bias. Numerical experiments with a quasi-geostrophic model demonstrate the potential of the approach and highlight the challenges of operational implementation.

Our study investigates how turbulence behaves in stable conditions using direct numerical simulations. We found that rethinking how energy dissipates in these situations is crucial. By revising existing models, we uncovered limitations in understanding how temperature is transported vertically in very stable conditions. We focus on how turbulence works in extreme stability and offer new insights that could improve our understanding of natural phenomena affected by stable atmospheric conditions.

Controlling chaotic systems is a key step toward weather control. The control simulation experiment (CSE) modifies weather systems using small perturbations, as shown in studies with the Lorenz-63 model. However, the effectiveness of CSE compared to other methods is unclear. This study evaluates CSE against model predictive control (MPC). Simulations reveal that MPC achieves higher success rates with less effort under certain conditions, linking control theory and atmospheric science.

Turbulence is found in many natural systems. We study its statistics in terms of scaling laws of up to fourth-order normalized moments for the velocity or magnetic fields through their relative behavior. We show analytically using existing intermittency models that the physical dimension of structures becomes irrelevant. The strongest intermittent structure has a parabolic scaling as found previously and confirmed by long simulations. More analysis will be performed using simplified models. 

The contributing influence of SSWs (sudden stratospheric warming) on regional ionosphere through chaos theory is examined. We find that ionospheric chaos is more pronounced in the European sector compared to the African sector during an SSW. Evidence of orderliness behavior in regional ionosphere of African sector is observed. Finally, we notice that after the peak phase of an SSW, ionospheric chaos is found to be more pronounced.

In recent years, there have been more and more floods due to intense precipitation, such as the July 2021 event in Belgium. Predicting precipitation is a difficult task, even just for the next few hours. This study focuses on a tool that assesses whether a given situation is stable or not (i.e., whether it is likely to stay as it is or could evolve in an unpredictable manner).

A derivation of discrete dynamical equations for the dry atmosphere without dissipative processes based on the least action principle is presented. For a given set of generally irregularly spaced grid points and a given mode of interpolation, through the minimization of action, the algorithm ensures maximal closeness of the evolution of the discrete system to the motion of the continuous atmosphere. The spatial resolution can be adjusted while executing calculations.

 Unequal-weighted ensemble prediction (UWE) using outputs of the dynamic–statistic prediction is presented, and its possible impact factors are also analysed. Results indicate that the UWE has shown promise in improving the prediction skill of summer precipitation in China on account of the fact that UWE can overcome the shortcomings of the structural inadequacy of individual dynamic–statistic predictions, reducing formulation uncertainties and resulting in more stable and accurate predictions.

We propose ensemble-based model predictive control (EnMPC), a novel method that improves the control of complex systems like the atmosphere by integrating control theory with data assimilation. Unlike traditional methods, which are computationally expensive, EnMPC uses ensemble simulations to efficiently handle uncertainties and optimize solutions. This approach reduces computational cost while maintaining accuracy, making it a promising step toward real-world applications in dynamic system control.