Sea ice is a multiscale composite displaying complex structure on length scales ranging over many orders of magnitude. Finding the effective properties relevant to large-scale dynamics and thermodynamics is a central challenge in modeling and predicting sea ice behavior, similar to finding macroscopic behavior from microscopic laws in statistical mechanics. Integral representations for the homogenized properties of composites, where the microstructural geometry is encoded into the spectrum of a random operator, have opened up new theoretical and computational approaches to sea ice modeling. We’ll give an overview of how they’re being used to study sea ice electromagnetics, thermal transport, wave-ice interactions, and advection diffusion processes at the floe scale. They also allow us to connect sea ice to random matrix theory, uncertainty quantification, and exotic materials such as twisted bilayer graphene.

How to cite: Golden, K.: Multiscale homogenization and random matrix theory for sea ice, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6058, https://doi.org/10.5194/egusphere-egu26-6058, 2026.

Arctic sea ice is one of the most sensitive components of the Earth's climate system and acts as a bellwether for changes in it. The ice cover grows, shrinks, and moves because of its interactions with the atmosphere and the underlying ocean. One of the principal challenges associated with modelling the atmosphere-ice-ocean interactions is the lack of definitive knowledge of the rheological properties of the ice cover at large scales. A systematic study of sea ice dynamics since the 1960s has led to the development of many rheological models, but the predictions from these models are not entirely consistent with observations.

In this work, I will consider the motion of sea ice at three different scales: (i) floe-scale or `microscopic'; (ii) mesoscopic; and (iii) continuum. Starting from the dynamics at the scale of an individual ice floe I will obtain the continuum equations by coarse graining. This approach is similar to the one used to obtain the Navier-Stokes equation from the Boltzmann equation, and allows for the determination of shear viscosity of the ice cover as an explicit function of ice concentration and mean thickness. I will compare results from the theory with observations and idealised simulations and also discuss a more general approach that accounts for phase change and mechanical deformation of ice floes.

How to cite: Toppaladoddi, S.: Sea ice motion on multiple scales, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-13703, https://doi.org/10.5194/egusphere-egu26-13703, 2026.

Complex systems such as the climate are often described in terms of linear modes of variability, but these modes cannot capture the intrinsically nonlinear organization of the dynamics. We introduce a framework for extracting topological modes of variability (TMVs) directly from observational, laboratory or simulation data. 

TMVs were introduced in the context of the templex framework [Charó et al., 2022; 2025], which represents a dynamical system through a combination of its topological structure and the way the flow in phase space moves across it. In this framework, TMVs correspond to flow patterns that are organized around special regions of an attractor, called joining loci, where different pathways merge.

Here we show how these joining loci — and the TMVs organized around them — can be recovered directly from data, without explicitly constructing a cell complex. We use dynamical indicators of local dimension and stability [Lucarini et al., 2016; Faranda et al., 2017] to locate the regions of the attractor where joining loci are expected, and we then extract the corresponding cycles from a directed graph built on a clustering of the data. By retaining only the robust transitions in this graph, we obtain a set of persistent TMVs.

We apply this approach to the El Niño–Southern Oscillation (ENSO) using Niño-3.4 sea-surface temperature anomalies from NOAA’s Oceanic Niño Index (ONI), providing new insight into ENSO variability and predictability.

How to cite: Charó, G. D., Faranda, D., Ghil, M., and Sciamarella, D.: Extracting persistent topological modes of variability in complex dynamics from data, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-13629, https://doi.org/10.5194/egusphere-egu26-13629, 2026.

Intermittent dynamics are a common feature of many Earth-system components that often interact across ample ranges of temporal and spatial scales.  Our previous work shed light on the mechanism driving intermittency and identified precursors of its onset (Barone et al., 2025). This current study moves forward, and it investigates the processes by which an intermittent component in a coupled system influences other ones that, in the absence of the coupling, would evolve quasi stationarily. In particular, we investigate a prototypical fast–slow, e.g. atmosphere-ocean, setup in which fast intermittent systems act as a unidirectional forcing on slow components characterized by a stable limit cycle.

Using a two-scale version of the Lorenz–63 model, we show that intermittent bursts in the fast dynamics induce deviations from the slow dynamics’s limit cycle, which, depending on the strength of the coupling and the timescale difference, can even fully destabilize the limit cycle and lead to a chaotic regime. We show that increasing the frequency of intermittent events does not necessarily affect the slow component response, which below a critical value retains its structural properties, highlighting the non-trivial nature of intermittent information transfer across scales. The induced transition from periodicity to chaos caused by the intermittent burst, is looked through the lens of the power spectrum decomposition (PSD) of the finite-time Lyapunov exponents, offering a unique view on the progressive loss of predictability in the slow component. The analysis is then extended to a spatially extended system based on unidirectionally coupled Kuramoto–Sivashinsky equations. As the coupling strength increases, the energy PSD of the slow and initially regular dynamics, progressively approaches that of the fast intermittent system, up to a regime in which the two become effectively indistinguishable. Remarkably, mutual information between subsystems reveals a clear latency in the slow response that increases with the degree of time-scale separation.

Our study provides a robust framework to investigate similar dynamical configurations in Earth system models, whereby a fast intermittent atmosphere induces short-living, yet impactful, changes in a slow ocean. 

A. Barone, A. Carrassi, T. Savary, J. Demaeyer, S. Vannitsem; Structural origins and real-time predictors of intermittency. Chaos 1 October 2025; 35 (10): 103119. https://doi.org/10.1063/5.0287572

How to cite: Barone, A., Carrassi, A., Demaeyer, J., and Vannitsem, S.: Breaking of stationarity by intermittency in coupled dynamics, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-19518, https://doi.org/10.5194/egusphere-egu26-19518, 2026.

We investigate the lifetime of dynamical regimes under the impact of noise motivated by models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state space faster. However, for relevant systems with complexities ranging from phenomenological toy models to models of atmospheric dynamics, this intuition has proven misleading. As long as the noise is sufficiently small, the noisy system stays in regimes of interest on average longer than its deterministic counterpart, an effect we call "stochastic inertia''. This phenomenon has been observed through extensive numerical simulations for different noise levels. We propose a numerical technique for testing the occurrence of stochastic inertia, constructing, for any fixed noise level, a Markov chain on the set of points given by a  sufficiently long trajectory of the system without noise. The method is shown to correctly predict the presence of stochastic inertia in simple systems, and its utility is demonstrated on a paradigm model of atmospheric dynamics.

How to cite: Schoeller, H., Chemnitz, R., Koltai, P., Engel, M., and Pfahl, S.: Regime persistence through noise - A data-driven approach using deterministic trajectories, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-2772, https://doi.org/10.5194/egusphere-egu26-2772, 2026.

How to cite: Brolly, M.: Trajectory-based probabilistic learning is essential for representing unresolved dynamics in chaotic systems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6847, https://doi.org/10.5194/egusphere-egu26-6847, 2026.

This study introduces a novel sequential data assimilation method that uses conditional denoising score matching (CDSM). The CDSM leverages iterative refinement of noisy samples guided by conditional score functions to achieve real-time state estimation by incorporating observational constraints at each time step. Unlike traditional methods, such as variational assimilation and Kalman ffltering, which rely on Gaussian assumptions and can be computationally expensive because of iterations or ensembles, CDSM is based on stochastic differential equations (SDEs). It does not require explicit noise addition or manipulation of probability density functions, thus simplifying the assimilation process and enhancing the computational efficiency. Here, error growth and reduction were modeled using noise addition and denoising processes based on SDEs. This transforms the data assimilation problem into a denoising problem based on conditional score matching. Our approach integrates dynamic models, performs data assimilation through Langevin dynamics at the observation times, and uses the analyzed states for subsequent integration. The noise addition process is embedded in the score model training using neural networks and is not explicitly used in the assimilation process. The results from twin experiments using the Lorenz ‘63 model demonstrate that the CDSM achieves a performance comparable to that of traditional methods in nonlinear systems. This method is robust and flexible with low requirements for training data quality. This is particularly suitable for scenarios in which the observation intervals are much larger than the model integration steps. The CDSM shows great potential for application inlarge-scale numerical and data-driven models.

How to cite: Shen, Z.: A Novel Sequential Data Assimilation by Conditional Denoising Score Matching, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6704, https://doi.org/10.5194/egusphere-egu26-6704, 2026.

One of the main issues faced by climate models is the presence of biases due to uncertainties in model parameters. Here, we set out to constrain such parameter values by reducing the mismatch between a climate model's equilibrium state and ground-truth observations through the minimisation of a cost function, using Bayesian optimisation. We illustrate this method on the parametrisation of the ocean vertical diffusivity $\kappa$, first as a proof-of-concept in a conceptual ocean model, then in VEROS, a global ocean model of intermediate complexity. In the first case, we can artificially introduce an error in $\kappa$ and show that Bayesian optimisation allows us to retrieve its true value. In the case of VEROS, we aim at improving the model's description of the Atlantic Meridional Overturning Circulation (AMOC), so we can compare the simulated AMOC strength to the measured mean AMOC strength over the past two decades.

However, the equilibrium state of a model depends on the model parameters. Since we are modifying these parameters at each Bayesian iteration, the equilibrium state of the model needs to be recomputed every time in order to be compared to observations. In climate models, equilibria are usually computed through spin-ups, or trajectories of typically several thousands of years. But this method is extremely costly and does not guarantee that all model variables have converged to the equilibrium, since they evolve on a large range of time scales. On the other hand, Anderson Acceleration (AA) is an iterative method designed to solve fixed-point equations for any dynamical system much more efficiently than using direct integration. Indeed, AA determines at each iteration an educated guess of the position of the equilibrium by combining previous iterates. Here, we combine AA and Bayesian optimisation to re-compute the model's equilibrium at every Bayesian iteration. We show that we are able to constrain the distribution of $\kappa$ values to minimise the distance to observations.

But this process still requires running the model a large number of times at each Bayesian iteration, which remains computationally costly. To reduce the computational burden even further, we train a deep machine learning (ML) scheme to reconstruct the entire state vector of the model from a few significant fields, such as temperature and salinity, that most contribute to the large-scale dynamics of the system. This ML scheme therefore acts as an emulator of the climate model, which does not need to perfectly reproduce all processes, but mostly the model's equilibria. AA is then applied to these few fields only, while the full model state is reconstructed by the ML scheme at each AA iteration.

How to cite: Jacques-Dumas, V., Dijkstra, H. A., and Vedel, J.: Accelerated Bayesian Optimisation for bias correction in an Intermediate Complexity Climate Model, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-7720, https://doi.org/10.5194/egusphere-egu26-7720, 2026.

Occurrence of cold spells in different North American regions has been related to concurrent wet and windy extremes in Western Europe. This link is driven by an anomalous state of the North Atlantic storm track. Two dynamical pathways have been defined as potential origins of the Pan-Atlantic compound extremes. The first pathway is linked to a Rossby wave train propagating from the Pacific toward the Atlantic, associated with a pronounced Alaskan ridge. The second pathway is characterized by the presence of a high west of Greenland, that favors simultaneously a southward displacement of a trough over eastern USA and an upper level trough over South western Europe. This study investigates the predictability of flow associated with cold spells over north America from a dynamical systems perspective, with a focus on the underlying diversity of atmospheric states and wave processes.

We start by assessing the intrinsic predictability of these two pathways using the ERA5 reanalysis and dynamical systems indicators. These indicators can be used as proxies for the predictability of each pathway. We also examine the predictability of those two pathways across different climatological periods. We further explore how variations in Rossby wave behavior and stratospheric anomalies modulate the predictability of these cold spells. We complement this analysis using the ECMWF ensemble reforecasts at different lead times, and computing skill scores for the two pathways. This help to provide new insights into the dynamical precursors and sources of predictability for compound cold and windy extremes across the North Atlantic sector.

How to cite: Krouma, M. and Messori, G.: Assessment of the predictability of cold-wet-windy Pan Atlantic compound extremes, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-5109, https://doi.org/10.5194/egusphere-egu26-5109, 2026.

Heat poses a critical risk to human health around the world. Recent work has investigated how anthropogenic climate change can modulate atmospheric circulation patterns, finding that circulation patterns increasing in frequency are associated with high temperatures in Europe. Here, we investigate the role of these changes in the dynamics of the atmosphere for European heat-related mortality. Specifically, we identify circulation patterns whose occurrence has become either more or less frequent over past decades. We couple this with an epidemiological framework, which uses an advanced regression model to compute associations between temperature and mortality. This association accounts for lags extending up to three weeks, and is fit for each subnational region within our dataset, which covers almost all of Europe. This allows us to estimate the heat-related mortality burden associated with circulation patterns that have changed in frequency. We find that dynamical changes have reinforced the thermodynamic warming trend, and are associated with increased heat-related mortality in northern and central continental Europe. Furthermore, dynamical changes appear to have played an important role for the extreme temperatures of the European summer of 2003, and the associated heat-related mortality. We thus highlight the importance of considering the role of changes in atmospheric circulation patterns when investigating the role of climate change for heat events and their impacts. Furthermore, we argue that heat action plans should consider the possibility of record-shattering heat events, where dynamical changes contributing to anomalously high temperatures could coincide with the peak of the seasonal temperature cycle, as seen in 2003. 

How to cite: Holmberg, E., Ballester, J., Faranda, D., Méndez Turrubiates, R., and Messori, G.: Changes in atmospheric circulation patterns are associated with increased European heat-related mortality, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-5296, https://doi.org/10.5194/egusphere-egu26-5296, 2026.

This study introduces a new methodology for diagnosing atmospheric circulation associated with surface extremes in modal space. The approach is conceptually similar to spherical harmonics analysis but employs Hough harmonics as basis functions. These harmonics arise from the linearised primitive equations and form an orthogonal basis. Projection onto this basis yields complex Hough expansion coefficients that describe the amplitudes and phases of the modal contributions to the global three-dimensional fields. Each Hough coefficient is indexed by zonal wavenumber, meridional mode, and vertical structure function. The orthogonality of the modes allows a decomposition of the total energy into the energy of the zonal mean flow and the energies of different wave components.

The method is applied to global reanalysis datasets and to a subset of CMIP5 climate model simulations from 1980 onwards. Reconstructed circulation fields, obtained by inverse projection onto wind and geopotential using scale-selective filtering, indicate that Eurasian heatwaves (EHWs) are primarily driven by large-scale anticyclonic systems. This agrees with previous dynamical studies and supports the physical interpretability of the diagnostic. Probability distribution functions of Rossby wave energies are computed separately for the zonal mean, for planetary-scale, and for synoptic-scale zonal wavenumbers, focusing on barotropic structures in the troposphere. The corresponding energy time series are well described by chi-square distributions, and the skewness indicates about a 50% reduction in the effective degrees of freedom of planetary-scale circulation during EHWs.

This reduction is not observed in the CMIP5 simulations, which points to systematic model deficiencies. The models reproduce present-day surface EHW characteristics and associated Rossby wave patterns reasonably well, but struggle to reproduce day-to-day circulation variability observed in reanalyses. This limitation reduces confidence in projections of future changes in heatwaves and their related large-scale circulation. The results suggest that metrics describing intrinsic variability should be included as complementary to existing ones when evaluating simulations of heatwaves and associated circulation.

Overall, the diagnostic provides a holistic dynamical view of the variability spectrum of Rossby waves linked to surface extremes. It enables scale-selective filtering of variability in physical space and reveals statistical properties in modal space, offering a useful tool for model assessment and for studying complex atmospheric dynamics.

How to cite: Strigunova, I.: Modal-space statistics of Rossby waves during Eurasian heatwaves: implications for circulation dynamics in reanalyses and climate models, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-5650, https://doi.org/10.5194/egusphere-egu26-5650, 2026.

Over the past decade there have been unprecedented events of record low sea ice concentration in the Antarctic region. Previous work has attributed these anomalous sea ice loss events to persistent anomalies in various atmospheric drivers such as the Southern Annular Mode (SAM), the Pacific South American (PSA) patterns, and the Amundsen Sea Low (ASL). The majority of such studies employ methodologies that either assume stationarity or use averages over uniform fixed periods (e.g. months). In this study we show how a machine learning method applied to multiscale climate data can extract drivers across subsystems without predefining patterns or time periods. Specifically, we employ a nonstationary data-clustering framework to coupled sea ice and atmosphere reanalysis data to extract persistent coherent events across both systems. We use time-varying Markov transition matrices to extract the dominant states over a sliding time window and identify persistence as an uninterrupted period of a dominant state for at least ten days.

Analysing three years consisting of anomalously low sea ice events, we find that our approach identifies a variety of atmospheric drivers for these events without preconditioning. The dominant drivers vary in spatial extent and duration, as opposed to many stationary methods which require an a priori selection of scales. Here each event’s spatial and temporal boundaries are determined by the optimal model itself. This nonstationary analysis is thus particularly valuable for characterizing multiscale interactions and addressing dynamics across coupled climate subsystems.

How to cite: Quinn, C., Axelsen, A., O'Kane, T., and Bassom, A.: Data-driven identification of atmospheric drivers of anomalous Antarctic sea ice loss, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-15666, https://doi.org/10.5194/egusphere-egu26-15666, 2026.

Connecting the different levels of the hierarchy of mathematical and conceptual complexity at which climate models operate, and comparing the assumptions that apply at each level, and the results produced, has led to much progress in climate science.  A particularly notable success was Klaus Hasselmann’s use of Brownian motion to inspire his linear Markovian stochastic energy balance model (EBM) and its successors . Another informative, but lateral, connection and comparison is that between either studying climate through the lens of stochastic physical models and doing so via statistical methods. This presentation showcases how comparing these approaches can sometimes surprise us.

It has been asserted that because the Hasselmann stochastic EBM has a mean-reverting term due to feedbacks, this property must also be detected in global mean temperature time series by statistical models such as the well-known Box-Jenkins ARIMA family. Conversely its absence has been taken as an indication of fundamental difficulties with anthropogenic driving. By fitting Hasselmann models, with and without anthropogenic driving, to an ARIMA model with automatically selected parameters I will show that in this instance the absence of a prominent autoregressive term can have quite the opposite meaning and  instead be a clear indication of strong driving. I will present results of our ensemble study which is examining the ability of automatic fitting to correctly infer ARIMA parameters on EBMs with realistic values of heat capacity and other system variables. Progress in extending the study to fractional EBMs and to ARFIMA models will be discussed.

How to cite: Watkins, N. W. and Stainforth, D.: What do we learn from looking at the Hasselmann model through 2 lenses ? Stochastics meets statistics, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-5791, https://doi.org/10.5194/egusphere-egu26-5791, 2026.

We consider a prior-based dimension reduction Kalman filter for state estimation in high-dimensional settings. The method extend ideas from prior-based dimension reduction in static inverse problems by projecting covariance equations to lower-dimensional space using a global reduction operator. In contrast to reduced rank Kalman filters the dimension reduction is defined entirery a priori. Here, it is constructed using standard wavelet transforms, yielding a stable and portable framework that does not depend on empirical parameter estimation to form the projection. 

The Kalman filter update step equations are projected onto a global wavelet basis, thereby avoiding explicit construction of covariance matrices in the full state space. This makes classical Kalman filtering tractable for large spatio-temporal systems otherwise computationally inaccessible. Combined with PyTorch implementation exploiting GPU acceleration, the approach leads to a drastic reduction in computational cost, while preserving the consistent filter and enabling Gaussian uncertainty quantification.

We demonstrate the method on two high-dimensional application, highlightning the wavelet representation's natural adaptation to different data patterns and structures. The first example concerns sparsely observed oceanographic data, where the reduced filter reconstructs the full state from limited measurements with uncertainty estimates with state model derived from modelled ocean current. The second focuses on satellite-derived cloud product with state dynamics provided by neural network estimates and the observations exhibit heterrogeneous quality and frequent gaps.

Overall, we demonstrate how reduced-basis Kalman filtering with a priori selected wavelet subspaces provides a general and computationally viable framework for nonstationary Gaussian inverse problems. The approach combines scalable data assimilation, uncertainty quantification, and the integration of data-driven dynamics in high-dimensional geophysical applications.

How to cite: Himanka, T. and Laine, M.: Dimension reduction Kalman filtering: examples from high-dimensional dynamical systems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-11361, https://doi.org/10.5194/egusphere-egu26-11361, 2026.

Bayesian inverse problems in Earth sciences often ask for inversion techniques capable of handling high-dimensional nonlinear forward models, and prior information that is neither Gaussian nor analytically representable. This contribution focuses on the methodological developments underlying our application of cross entropy based importance sampling for Bayesian updating (CEBU) to Antarctic tidal grounding line migration based upon Sentinel-1 line of sight offsets. In particular, we highlight how the algorithm is extended to incorporate empirical, hence, nonparametric priors, how its sequential structure enables detailed convergence diagnostics, and how its evidence estimate can support filtering and model selection.

The grounding line marks the transition from grounded ice to floating ice shelf in Antarctica’s marine-terminating glaciers. The underlying elastic beam model simulating the bending of the ice in response to tidal deflection is, among others, based on an ice thickness parameter. Its prior shall be defined by the values from a dataset of a previous study. This prior exhibits non‑Gaussian structure and parameter dependencies that cannot be captured by standard parametric assumptions. Hence, we extend the CEBU framework by introducing an isoprobabilistic transform that maps the empirical ensemble into the standard normal space in which the update is performed. The extension allows CEBU to operate directly on empirical prior information, thereby embedding physical knowledge into the Bayesian update in a fully nonparametric manner.

After the initial transformation to standard normal space, CEBU proceeds through a sequence of tempered intermediate distributions that gradually introduce the likelihood. This sequential structure provides a transparent view of convergence behavior: we introduce the Kolmogorov–Smirnov distance between each intermediate importance sampling density and the prior as a measure of information gain and respective parameter importance. This quantity provides a nonparametric and interpretable metric of which components of the parameter vector are most informed by our observations and which remain dominated by prior uncertainty. The difference of information gained per step determines the respective importance of a parameter at a particular tempering step. Hence, by the distance metric introduced, CEBU intrinsically provides a convergence curriculum used to attain the posterior distribution.

After convergence, CEBU yields a Bayesian model evidence estimate. It quantifies the conceptual fit of the data observed and the model used. Accordingly, this evidence can be used for filtering the results, e.g., if the observation data of a particular inverse problem is too noisy, i.e., does not follow the measurement error model. Further, that quantity may be used for Bayesian model selection, offering a principled mechanism for evaluating competing forward models or prior assumptions. For example, that setting can be used to decide between multiple empirical priors, and thus between competing studies.

From a computational perspective, all forward evaluations and likelihood computations are embarrassingly parallelizable. That makes the approach well suited for large‑scale inference tasks on modern high performance clusters and cloud infrastructures.

How to cite: Engel, M., Ramanath, S., Krieger, L., Wuite, J., Floricioiu, D., and Körner, M.: Extending Cross Entropy Based Importance Sampling for Bayesian Updating (CEBU) with Empirical Priors and Kolmogorov-Smirnov Based Convergence Diagnostics, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-12966, https://doi.org/10.5194/egusphere-egu26-12966, 2026.

Frontal structures, frequently observed in the vicinity of westerly jets and western boundary currents, are characterized by sharp gradients in both horizontal and vertical directions. Forecast errors associated with these fronts often exhibit non-Gaussian distributions due to biases in frontal location or magnitude stemming from sparse observation networks or misrepresented model physics. Such non-Gaussianity poses significant challenges for conventional data assimilation (DA) schemes that rely on Gaussian assumptions.
In this study, we investigate the performance of various ensemble DA methods in representing fronts using idealized simulations with a frontogenesis model (Keyser et al., 1988). The compared methods include the stochastic Ensemble Kalman Filter (EnKF), the Ensemble Adjustment Kalman Filter (EAKF), and the Nonlinear Ensemble Transform Filter (NETF). Furthermore, we propose a novel nonlinear DA approach termed the Kernelized EAKF (KEAKF). By integrating kernel ridge regression into the EAKF framework, KEAKF effectively accounts for nonlinear relationships between state variables.
To simulate realistic forecast biases, the first-guess ensembles are initialized with systematic errors in both frontal magnitude and location. DA performance is rigorously evaluated using three metrics: root mean squared error (RMSE) of temperature (state error), RMSE of the temperature gradient (magnitude error), and the modified Hausdorff distance of frontal locations (displacement error). Our results demonstrate that KEAKF outperforms all other methods across all evaluation metrics. While the EnKF shows relatively stable performance in state estimation, the EAKF is superior in capturing frontal magnitude and location. The NETF, despite its non-Gaussian formulation, shows limited performance due to particle degeneracy in this setting. Finally, we discuss the implications of these findings for maintaining dynamical balances and improving the predictability of frontal systems in more complex dynamical models.

How to cite: Nakashita, S. and Enomoto, T.: Evaluation of data assimilation methods suitable for frontal structures, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-21740, https://doi.org/10.5194/egusphere-egu26-21740, 2026.

PDAF is open-source software (https://pdaf.awi.de) providing a unified data assimilation framework for all data assimilation applications throughout the Earth system and beyond. PDAF is already coupled to a wide range of models, including all Earth system components, and is widely used for research and operational applications. With well-defined interfaces and modularization motivated by object-oriented programming, PDAF separates the forecast model, the observation handling, and the data assimilation algorithms. This structure ensures separation of concerns and allows domain experts to perform further developments of each component independently without interfering with each other. PDAF is further designed to make the coupling to models, online in memory or offline using disk files, particularly easy so that a new assimilation system can be built quickly. 
PDAF was recently upgraded to the new major revision 3.0. In PDAF V3, the code was modernized and restructured simplifying the procedure to add further data assimilation algorithms. New features are supported including model-agnostic incremental analysis updates, new diagnostics for observations and ensembles, and the ensemble square root filter (EnsRF) and ensemble adjustment Kalman filter (EAKF). With this, PDAF now provides the full range of algorithms from domain-localized ensemble filters and smoothers to Kalman filters with serial observation processing, particle and hybrid Kalman-nonlinear filters, and 3-dimensional variational data assimilation methods. Existing users can switch to PDAF V3 with minimal effort, while a new universal interface supporting all filters is recommended for new users. The Python-interface, pyPDAF, further allows the full implementation of an assimilation program in Python, leveraging the functionality and performance provided by PDAF. We will provide an overview of PDAF and the novelties of version 3.0.

How to cite: Nerger, L., Chen, Y., Corbin, A., and Keller, J.: The Parallel Data Assimilation Framework (PDAF) - Upgrade to Version 3, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-22041, https://doi.org/10.5194/egusphere-egu26-22041, 2026.

The Atlantic meridional overturning circulation, the Greenland and Antarctic ice sheets have been identified as parts of the climate system that can potentially react nonlinearly to climate change albeit on very different time scales. While critical thresholds remain difficult to quantify from existing observations for all of these subsystems, they certainly do not stand on their own. In fact, the AMOC and polar ice sheets form an intricate network of multiscale systems, with interactions that can be stabilizing or destabilizing, the latter opening the possibility of cascading tipping events.

The interaction between Greenland ice sheet and AMOC on the larger scale shows the possibility of a collapse of the AMOC once a critical amount or rate of freshwater has entered the North Atlantic. This interaction also involves smaller scales, because the Greenland meltwater needs to reach the deep-water formation regions in the North Atlantic subpolar gyre, exhibiting substantial variability in the critical regions. Moreover, the Greenland ice sheet acts on slower time scales than the AMOC, such that these two systems can form an ‘accelerating cascade’. Specfically, when tipping of the ice is underway, the ‘coupling’, i.e. the freshwater flux into the North Atlantic is at maximum. These properties have consequences for the possibility of early warning predictions; in accelerating cascades early warning signs can break down due to lack of extrapolation.

On the other hand, West Antarctic Ice Sheet melting may be able to to stabilize the AMOC. Here, we investigate through a hierarchy of models of the AMOC and idealized forms of polar ice sheet collapse, the origin and relevance of stabilization and destabilization effects. In both deterministic and stochastic conceptual models, we find that rate- and noise-induced effects have substantial impact on the AMOC stability. Moreover, rate-induced effects can stabilize the AMOC depending on the relative timing of the peak meltwalter fluxes from both ice sheets.

How to cite: von der Heydt, A.: How stable is the Atlantic meridional ocean circulation when interacting with polar ice sheets?, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-12246, https://doi.org/10.5194/egusphere-egu26-12246, 2026.

The albedo contrast between sea ice and open ocean introduces a strong positive feedback in the surface energy balance of polar regions. Classical low-order models show that this feedback robustly produces multiple equilibria: the system can exist in either a cold, ice-covered state or a warm, ice-free state with the same external forcing.  The resulting hysteresis implies that polar regions will lose sea ice abruptly and irreversibly as external forcing increases. However, this tipping-point behavior is not observed in full-complexity climate models: in experiments where global radiative forcing is gradually ramped up until sea ice disappears, ice loss is indeed found to be relatively abrupt; but when the forcing is subsequently ramped down, sea ice reappears at the same rate, showing no sign of hysteresis or irreversibility. How do we reconcile this discrepancy between simple and complex models?

Here, I show that this reconciliation can be achieved by introducing atmospheric weather noise into the simple model. The polar ocean is modelled as a collection of points subject to local stochastic forcing, introduced as an additive white noise in the  energy balance model. This leads to a Fokker-Planck equation describing the probability distribution function (PDF) of ice thickness over the ocean basin, including a zero-thickness (ice free) class. For realistic values of noise amplitude estimated from reanalysis data, the PDF is bimodal when the global forcing supports multiple equilibria of the energy balance equation, with modes centered on the corresponding ice-free and ice covered equilibria. When global forcing is ramped up or down over long (~1000 year) timescales, the PDF evolves reversibly, showing relatively abrupt but reversible loss/recovery of sea ice. However, if the ramping timescale is shorter (~100 years), some residual irreversibility is still present. In conclusion, taking stochastic atmospheric fluctuations into account provides a promising avenue for resolving a long-standing problem in climate science.

How to cite: Caballero, R.: Atmospheric noise removes sea-ice tipping points in a simple stochastic model, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-17941, https://doi.org/10.5194/egusphere-egu26-17941, 2026.

The Atlantic Meridional Overturning Circulation (AMOC) is a key tipping element of the climate system and can be viewed as a multistable, stochastic dynamical system subject to both external forcing and internal variability. While most modelling studies emphasize deterministic thresholds for AMOC collapse, the role of internal variability in shaping the timing, probability, and nature of transitions remains poorly constrained.

This motivates a shift toward probabilistic prediction of AMOC tipping. Transition probabilities can be estimated using direct Monte Carlo sampling with large ensembles; however, this approach is severely limited in climate applications, as simulations are computationally expensive and statistical precision improves only slowly with increasing ensemble size. Rare-event algorithms provide an efficient alternative. In particular, the Giardina–Kurchan–Tailleur–Lecomte (GKTL) and Trajectory-Adaptive Multilevel Splitting (TAMS) methods enable targeted sampling of low-probability transitions at substantially reduced computational cost.

Using the intermediate-complexity PlaSIM–LSG model, we estimate AMOC transition probabilities by comparing direct Monte Carlo sampling with GKTL and TAMS. In a 600 ppm CO₂ case study, TAMS delivers the most precise probability estimates per unit cost, outperforming both Monte Carlo and GKTL and emerging as the most reliable approach for probability estimation.

We further apply TAMS to assess the transition probability to a weak AMOC state under three SSP scenarios, revealing a strong dependence on the forcing pathway. Under the high-emissions scenario SSP5–8.5, the probability of entering the AMOC-weak state remains below 1% by 2100, increases to about 20% by 2150, and reaches roughly 95% by 2200. In contrast, lower-emission scenarios (SSP4–6.0 and SSP2–4.5) maintain substantially lower probabilities throughout. These results are consistent with recent multi-model projections, suggesting that AMOC collapse is very unlikely in the 21st century but becomes plausible in the 22nd century under sustained high forcing. Additional freshwater input from Greenland ice-sheet melt would likely further increase these probabilities and advance the transition.

Overall, when direct sampling fails to capture rare transitions, rare-event methods enable both improved probability estimation and deeper insight into the underlying physical mechanisms. GKTL is well suited for exploring multistability and multiple transitions, while TAMS provides a rigorous framework for quantifying transition probabilities. Together, these approaches help bridge the gap between theoretical concepts of multistability and their practical investigation in complex climate models.

How to cite: Cini, M., Jacques-Dumas, V., Zappa, G., Ragone, F., and Dijkstra, H. A.: Comparing Rare-Event Algorithms and Direct Sampling for Estimating the Probability of CO₂-Driven AMOC Tipping, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14650, https://doi.org/10.5194/egusphere-egu26-14650, 2026.

One of the challenges in weather forecasting is the understanding of the nonlinear interactions between the fast and slow dynamics in the atmosphere. This is related to both numerical problems, such as the choice of a stable time step, and modelling and understanding the dynamics of atmospheric phenomena, such as the Madden-Julian Oscillation. Using a Rotating Shallow Water model on the sphere, in which both fast (inertia-gravity) and slow (Rossby-Haurwitz) waves occur, the nonlinear interactions in reduced models containing three, four and five waves were analysed using Hough harmonics spectral decomposition. Considering a Galerkin expansion as a solution of the nonlinear system, equations for the dynamics of each mode were derived, along with necessary conditions in the zonal and meridional structure of the modes for three interacting waves. In this talk, we will show results of three, four and five wave system interaction, discussing the energy transfers between Rossby-Haurwitz and gravity waves. We will particularly illustrate how we can observe relevant slow oscillations emerging from fast wave dynamics in realistic parameter ranges.

How to cite: Peixoto, P., Dourado, M., Raphaldini, B., and Teruya, A.: Nonlinear wave interactions in Rotating Shallow Water Equations on the Sphere: Theory and multi-wave applications, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-10391, https://doi.org/10.5194/egusphere-egu26-10391, 2026.

It is hardly questioned today that climate can be described in theory by an ensemble of trajectories differing in their initial conditions, which is then translated to numerical ensembles in climate models. It is also widely accepted that any evolution observed within a few decades after initialization is not relevant to climate. Evolution at a later stage, instead, is then used to characterize climate and its change, under the implicit assumption that slower processes do not considerably contribute to differences between ensemble members, letting internal variability of climate be identified with these differences. However, a justification for this practice is as yet lacking. In particular, a definition of climate in support of this practice is outstanding, including the identification of the kind of time scales at play through providing an argumentation for their relevance. Our study aims at filling this gap. After pointing out that the most important criterion for a definition of climate is the uniqueness of the probability measure on which the definition relies, we first recall the naive proposal to represent such a probability measure by the distribution of ensemble members that has, loosely speaking, converged to the natural probability measure of the so-called snapshot or pullback attractor of the dynamics. We then consider the time scales of convergence and refine the proposal by taking a probability measure that is conditional on the (possibly time-evolving) state of modes characterized by convergence time scales longer than the horizon of a particular study. We design an ensemble simulation initialization scheme for studying convergence time scales and uniqueness of ensembles in Earth system models.

How to cite: Drótos, G. and Bódai, T.: Can we define climate by means of an ensemble? A tale of time scales of convergence, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-9626, https://doi.org/10.5194/egusphere-egu26-9626, 2026.

A signal-to-noise "paradox" was first described in the context of ensemble forecasts on seasonal timescales. It refers to a situation in which the correlation between the ensemble mean and the actual verification is larger than the correlation between the ensemble mean and individual ensemble members. A noted problem of the signal-to-noise paradox remains that the signal-to-noise ratio itself, or equivalently the ratio of predictable components (RPC), which are used to diagnose the signal-to-noise paradox, has poorly understood statistical properties, rendering reliable identification of the signal-to-noise paradox difficult.

In this contribution, a generalised concept of the RPC is discussed based on proper scoring rules. This definition is the natural generalisation of the classical RPC, yet it allows one to define and analyse the signal-to-noise properties of any type of forecast that is amenable to scoring, thus drastically widening the applicability of these concepts. The methodology is illustrated for ensemble forecasts, scored using the continuous ranked probability score (CRPS), and for probability forecasts of a binary event, scored using the logarithmic score. Numerical examples demonstrate that the classical and new RPC statistic agree regarding which data sets exhibit anomalous signal-to-noise ratios, but exhibit different variance, indicating different statistical properties.

How to cite: Broecker, J. and Bach, E.: A generalisation of the signal-to-noise ratio using proper scoring rules, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14157, https://doi.org/10.5194/egusphere-egu26-14157, 2026.

Data-driven emulation of chaotic dynamics in the Earth system is a central challenge in modern climate science. Low-dimensional systems such as the Lorenz-63 model, derived in the context of atmospheric convection, are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up to machine precision: using ordinary least squares regression on high-degree polynomial features with 512-bit arithmetic, our system-agnostic method matches the accuracy of standard numerical ODE solvers using the systems' governing equations. For the Lorenz-63 system, we obtain valid prediction times of 36 Lyapunov times, and even up to 105 Lyapunov times with favorable precision configurations, dramatically outperforming prior work, which reaches 13 Lyapunov times at most. We further validate our results on Thomas' Cyclically Symmetric Attractor, a non-polynomial chaotic system that is considerably more complex than the Lorenz-63 model, and show that similar results extend to higher dimensions using the spatiotemporally chaotic Lorenz-96 model. Our findings suggest that learning low-dimensional chaotic systems from noise-free data is a solved problem.

How to cite: Schötz, C. and Boers, N.: Machine-Precision Prediction of Low-Dimensional Chaotic Systems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-4443, https://doi.org/10.5194/egusphere-egu26-4443, 2026.

The problem of forced response estimation from a single realization was addressed in the recent ForceSMIP project [Wills et al. 2025], which compiles many state-of-the-art statistical methods, including both methods supervised by large Earth System Model (ESM) ensembles and methods that use only a single target climate realization. Single-realization estimation is frequently approached using various linear filtering techniques, in particular Linear Inverse Models (LIMs) and Dynamic Mode Decomposition (DMD) [Penland et al. 1995 and Schmid 2010]. Standard LIM and DMD do not explicitly account for external forcing. DMD with control (DMDc) naturally extends these methods to incorporate essential external forcing information as a control variable [Proctor et al. 2016].

We investigate how these forcing inputs can be incorporated into the DMDc model to estimate forced responses. This results in three variants of DMDc for forced response estimation. One variant was already used in Tier 1 of the ForceSMIP project, while the other two have yet to be tested. We evaluate all three methods using near-surface air temperature (tas) and sea-level pressure (psl) from four Earth system models (CanESM5, MIROC6, MPI-ESM, and MPI-ESM1-2-LR) using data from MMLEA v2 [Maher et al. 2025]. Specifically, we analyze their ability to recover forced responses and characterize the DMDc variants across these Earth system models and variables.

References:

    Maher, Nicola, et al. "The Updated Multi-Model Large Ensemble Archive and the Climate Variability Diagnostics Package: New Tools for the Study of Climate Variability and Change." Geoscientific Model Development 18.18 (2025): 6341-6365.

    Penland, Cécile, and Prashant D. Sardeshmukh. "The Optimal Growth of Tropical Sea Surface Temperature Anomalies." Journal of Climate 8.8 (1995): 1999-2024.

    Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic Mode Decomposition with Control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161.

    Schmid, Peter J. "Dynamic Mode Decomposition of Numerical and Experimental Data." Journal of Fluid Mechanics 656 (2010): 5-28.

    Wills, Robert CJ, et al. "Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP)." Authorea Preprints (2025).

How to cite: Mankovich, N., Gavrilov, A., and Camps-Valls, G.: Dynamic Mode Decomposition with Control for Forced Response Estimation, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-11895, https://doi.org/10.5194/egusphere-egu26-11895, 2026.