How to cite: Thompson, E., Baldissera Pacchetti, M., and Jebeile, J.: Challenging the hierarchy: what could a pluralist ecosystem of climate modelling strategies look like?, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-6571, https://doi.org/10.5194/egusphere-egu25-6571, 2025.

Much climate science relies on numerical modelling to both understand the processes of the Earth system and to make predictions or projections of how it may change in the future. International climate policy relies on the outcomes of these models to make decisions which will affect the lives and livelihoods of billions of people – so it is vital that they are well understood and their use is based on robust understanding of what they can (and also what they cannot) tell us.

Spatially resolved General Circulation Models (GCMs) have evolved over recent decades in both their spatial resolution (allowing finer detail to be studied) and their process complexity (including but not limited to biogeochemistry and feedbacks between climate and ecosystems). This expansion of their capability makes them more useful and relevant than ever, but they are extremely slow to run on even the worlds most powerful super computers. Conversely very simple models exist which can be run thousands (or millions) of times, but do not include the full detail of the GCMs. Finally there are models of intermediate complexity which sit between these extremes and also make valuable contributions through differing combinations of comprehensiveness and computational efficiency.

All classes of models have something to offer – it is important to understand their strengths and weakness and to choose the most suitable tool for the job. Moreover, use of these models together can be very powerful. For example IPCC reports tend to draw firstly on complex GCMs but then through thorough calibration processes propagate their information to larger numbers of scenarios using simplified climate emulators.

In this talk I will briefly outline how this mode of use of the full modelling hierarchy has developed in the field of carbon cycle feedbacks and in quantifying the remaining carbon budget – which allows detailed planning of climate mitigation policy aligned with the goals of the Paris Agreement. I will show the development of our understanding of climate-carbon cycle feedbacks from complex models and how these have been used first to determine a simple relationship between cumulative CO₂ emissions and global warming (so called TCRE: transient climate response to carbon emissions), and then how simple models have been used in conjunction with complex models to explore the processes behind this relationship and begin to allow propagation of observational constraints.

I will end by outlining emerging knowledge on the strengths and weakness of each class of model (e.g. how simple is too simple?) and identifying research gaps for moving forward.

How to cite: Jones, C.: Climate-carbon cycle modelling hierarchy, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-17680, https://doi.org/10.5194/egusphere-egu25-17680, 2025.

Numerical models are not just numerical representations of physical phenomena. They are also software files written by humans. As such they contain unintended coding errors, termed bugs. While the size of climate model code and human imperfection suggest that these are frequently present in climate models (Pipitone and Easterbrook, 2012), bugs are seldom acknowledged in the literature. However, missing understanding of model bugs hinders our understanding of model results as well as our ability to improve modeling workflows.

With a case study of the ICON general circulation model (GCM), I elucidate the practices and considerations around model debugging. Specifically, I give examples for bugs detected in that GCM's development and report on qualitative in-depth interviews I conducted with 11 model developers (domain scientists and scientific programmers). The interviews show that dealing with bugs is not a standardised process. While the technical testing of ICON code developments is highly standardised, and for example the assignment of responsibility is standardised implicitly, the scientific testing resists standardisation. The missing standardisation makes dealing with bugs a laborious process that takes time and effort and where human influence is common.

While this study focusses on the meaning of bugs for GCMs, similar considerations may be at play for models from different rugs of the model hierarchy. Where they differ, the model hierarchy may offer a way to more systematically detect and fix bugs in models of any rug.

Pipitone, J. and Easterbrook, S.: Assessing climate model software quality: a defect density analysis of three models, Geosci. Model Dev., 5, 1009–1022, https://doi.org/10.5194/gmd-5-1009-2012, 2012.

How to cite: Proske, U.: Dealing with bugs is part of climate modeling, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-6658, https://doi.org/10.5194/egusphere-egu25-6658, 2025.

There is a long history of global climate model (GCM) studies of the response of the Atlantic Meridional Overturning Circulation to changing greenhouse gases (GHGs). Alongside this is an almost separate branch of the literature studying the AMOC’s response to fresh water input (‘hosing’) with fixed GHGs, focusing on the potential for ‘tipping’ behaviour. Some common model responses are observed among models (e.g. in GHG experiments an initial AMOC weakening associated with warming of the subsurface North Atlantic), but also considerable diversity, especially in the long-term response following stabilisation of GHG concentrations or hosing.

In recent years a few studies have emerged that use in-depth analysis frameworks to give insight into individual model responses, or into the differences between model responses. However the two branches of the literature (GHG and hosing response) have remained largely independent, and there is an increasing recognition that in real-world climate change the ‘smooth’ response to GHGs and potential abrupt ‘tipping’ responses need to be considered together. Given the diversity of model responses it will be valuable to establish whether there is a simple model framework that captures the potential mechanisms of response to GHGs and hosing that have been identified in GCMs. Such a model can then be used to characterise the types of qualitative behaviour that are possible in the more relevant scenario of tipping in a warming climate.   

We present a simple box model of thermally- and haline-driven AMOC change that aims to capture in as simple a form as possible many of the mechanisms of the AMOC responses to GHGs and hosing that have been identified in the literature. To develop this from an earlier model (that captured purely the hosing response), it was found necessary to add both a simple representation of basin-scale energy and water balances, and a simple representation of varying stratification in the sub-polar North Atlantic, increasing the dynamical degrees of freedom of the model.

We show that the model captures a wide range of behaviours seen in GCM experiments, and use it to identify circumstances in which AMOC tipping may be possible without requiring unrealistic additional water input from the Greenland Ice Sheet.

How to cite: Wood, R.: Towards a unified understanding of AMOC changes under warming and fresh water forcing, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-17881, https://doi.org/10.5194/egusphere-egu25-17881, 2025.

The Atlantic Meridional Overturning Circulation (AMOC) modulates global climate and has been identified as a potential tipping element that might collapse under future climate change. Such a collapse would have strong global consequences for the climate system, ecosystems and society. The IPCC AR6 report states that it is unlikely that the AMOC will collapse in the 21^st century which is mostly based on CMIP6 type Earth System Model results. However, these models have strong biases that can affect AMOC stability. If these models are biased towards a too stable AMOC, they might underestimate the probability of an AMOC collapse this century. To better understand the effects of freshwater biases on AMOC stability we perform experiments with the intermediate complexity Earth System Model CLIMBER-X. By introducing both positive and negative freshwater biases in the Atlantic and Indian Ocean we can gain a better understanding on how these biases affect AMOC stability. We find that introducing fresh biases in the Indian Ocean leads to an increase in stability, whereas fresh biases in the Atlantic Ocean lead to a decrease in stability. The combined effect of the biases in the Atlantic and Indian Ocean is near linear. We project the results of CLIMBER-X onto CMIP6 model biases such that we can assess whether CMIP6 models are likely simulating a too stable or too unstable AMOC.    

How to cite: Boot, A. and Dijkstra, H.: The influence of freshwater biases on AMOC stability and consequences for CMIP6 models, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-1288, https://doi.org/10.5194/egusphere-egu25-1288, 2025.

The Atlantic Meridional Overturning Circulation (AMOC), is a key tipping element of the climate system. A tipping point typically results from the interplay between external forcing (such as increased GHGs concentration or freshwater input) and the intrinsic internal variability of the system. While most studies mainly focus on identifying a critical forcing threshold (i.e. the minimal CO2 concentration or anomaly freshwater input needed for the collapse), the role of the internal climate variability remains less explored. Investigating the role of the internal variability requires performing large ensemble simulations which are  typically unfeasible with state-of-the-art models and traditional approaches. In our study, using an intermediate complexity model (PlaSIM-LSG, T21), once we assessed noise-induced collapse with a rare event algorithm, we investigated at which extent climate variability affects AMOC stability when CO2 forcing is applied. Traditionally, the AMOC stability landscape is investigated using single-realization hysteresis diagrams, driven by freshwater input in the North Atlantic. However, the effects of gradual CO2 forcing and, in particular, the impact of internal climate variability on the timing of AMOC tipping points have been less studied.  We conducted three independent hysteresis simulations, applying a slow CO2 ramp-up and ramp-down (0.2 ppm/year). Our findings reveal that internal variability strongly affects the timing of the AMOC tipping and the shape of the hysteresis cycle. In one simulation, we observed a reversed cycle, where the AMOC recovers at higher CO2 levels than at collapse. While statistical Early Warning Signals (EWS) provide some indication of approaching tipping points, the internal variability considerably reduces their predictability and introduces false positives. This suggests that AMOC behavior, when internal climate variability is considered, can differ significantly from characteristics of simpler models, and that caution is needed when interpreting results from a single-experiment realization. Moreover, the role of internal climate variability suggests that a probabilistic approach is necessary to define AMOC’s “safe operating space”, since it might not be possible to define a single critical CO2 threshold to prevent AMOC collapse.

How to cite: Corti, S., Cini, M., Zappa, G., and Ragone, F.: The Role of Internal Climate Variability in Noise-Shaped Hysteresis Cycles of the AMOC Under Rising CO2 Forcing, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-14237, https://doi.org/10.5194/egusphere-egu25-14237, 2025.

The Atlantic Meridional Overturning Circulation (AMOC) is a mechanism of great importance, as its possible collapse would constitute a dramatic response to Earth’s changing climate. The AMOC is particularly important for Northern Europe, as it plays a central role in regulating the region’s climate, and a slowdown or collapse would lead to a significant cooling of the region. This critical transition has been the subject of many studies over the years, both from the aspects of climate modeling and dynamical systems theory. In the context of the latter, climate change is nothing but a complex, chaotic-like system, which possesses a time-dependent parameter, in the shape of e.g. the growing CO2 concentration. It has been known for some time now, that such systems not only have a chaotic attractor, but one which is also time-dependent, a so-called snapshot attractor. Such objects, and thus the systems they describe, can only be faithfully represented by statistics over an ensemble of trajectories, a single one does not suffice. We perform such ensemble simulations on a conceptual climate model of the AMOC, constructed by coupling the Lorenz84 and the Stommel box models. We find that the difference between the ensemble members in the point when the collapse occurs can be up to hundreds of years, and that some trajectories can even survive with the AMOC remaining in the “on” state.  This highlights the fact that that a single trajectory is unreliable, however, with the proper ensemble statistics (e.g. standard deviations, time-dependent Lyapunov exponents, etc), a probabilistic description of the collapse can be given.

How to cite: Jánosi, D., Divinszki, F., Börner, R., and Herein, M.: Ensemble simulation of the AMOC collapse in a conceptual climate model, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-2814, https://doi.org/10.5194/egusphere-egu25-2814, 2025.

The climate system is nonlinear and affected by both natural variability and several types of forcing. The impact of anthropogenic forcing and environmental change on several of the system's nonlinear processes has led to considerable concern about the tipping of regional subsystems (e.g. Lenton, 2016), due to their potentially irreversible consequences. On the global level, these nonlinear effects have been shown to give rise to bistability (Stommel, 1961} and chaotic behavior (Lorenz, 1963) in the system's past (e.g., Boers et al, 2022), as well as having been proposed conceptually as due to occur in its future, too (e.g., Steffen et al, 2018). However, specific mechanisms for a sudden tipping to an alternate stable “hothouse”, several degrees warmer than the present climate, have not been explored so far to a satisfactory extent with ESM-based studies using aqua planets (e.g., Ferreira et al 2011, Popp et al, 2016).

   Here we show that a highly simplified energy balance model (EBM) of globally averaged temperature T representing the radiative budget, coupled with a three box-type model of global carbon dynamics, does exhibit such an alternate stable hothouse climate with T higher by roughly 10 °C than the present. This TCV model also captures quite accurately the fluxes of carbon between the separate reservoirs of the coupled atmosphere-land-ocean system, when compared with observations and with simulations by high-end models. The model includes two regional mechanisms, that trigger a global tipping to such a hothouse. The two regional mechanisms are (i) the decrease of terrestrial albedo due to the darkening of ice sheets by pervasive glacial micro algal growth (e.g., Williamson et al, 2020) not included in ESMs to date; and (ii) the limits of vegetation adapting to increased environmental stress and, hence, the reduction of its carbon absorbtion (e.g., Hammond, 2022).

    These findings and the mechanistic understanding of the processes leading to a global tipping can contribute to a fruitful dialogue between the conceptual-model and ESM communities. Such a dialogue can greatly enhance our understanding of the climate system’s potential for global tipping in response to anthropogenic greenhouse gas emissions.  

How to cite: Chavez, E., Ghil, M., and Rombouts, J.: A stable hothouse triggered by a tipping mechanism, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-19722, https://doi.org/10.5194/egusphere-egu25-19722, 2025.

The influence of structural errors in general circulation models (GCMs) — stemming from missing physics, imperfect parameterizations of subgrid-scale processes, limited resolution, and numerical inaccuracies — results in systematic biases across various components of the Earth system.

In this talk, we develop an approach to correct biases in the atmospheric component of the Community Earth System Model (CESM) using convolutional neural networks (CNNs) to create a corrective model parameterization for online bias reduction. By learning to predict systematic nudging increments derived from a linear relaxation towards the ERA5 reanalysis, our method dynamically adjusts the model state, significantly outperforming traditional corrections based on climatological increments alone. Our results demonstrate substantial improvements in the root mean square error (RMSE) across all state variables, with precipitation biases over land reduced by 25-35%, depending on the season. Beyond reducing climate biases, our approach enhances the representation of major modes of variability, including the North Atlantic Oscillation (NAO) and other key aspects of boreal winter variability. A particularly notable improvement is observed in the Madden-Julian Oscillation (MJO), where the CNN-corrected model successfully propagates the MJO across the maritime continent, a challenge for many current climate models. Using trio-interaction theory, we explore the dynamic improvements to the MJO and assess whether these enhancements arise from accurate physical processes.

This advancement underscores the potential of using CNNs for real-time model correction, providing a robust framework for improving climate simulations. Our findings highlight the efficacy of integrating machine learning techniques with traditional dynamical models to enhance climate prediction accuracy and reliability. This hybrid approach offers a promising direction for future research and operational climate forecasting, bridging the gap between observed and simulated climate dynamics.

How to cite: Chapman, W. and Berner, J.: Improving climate bias and variability via CNN-based state-dependent model-error corrections, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-20624, https://doi.org/10.5194/egusphere-egu25-20624, 2025.

The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in earth sciences. Here we explicitly define multi-scale data as being characterized by spatiotemporal processes (i.e. processes acting along time and space simultaneously) with process scales acting across orders of magnitude, non-stationarity, and/or invariances such as translation and rotation. Existing methods, such as traditional analytic approaches, data-driven modeling like Dynamic Mode Decomposition (DMD), and even deep learning, are not well-suited to diagnosing multi-scale data, usually requiring supervised strategies such as human intervention, extensive tuning, or selection of ideal time periods.

We present the multi-resolution Coherent Spatio-Temporal Scale Separation (mrCOSTS), a data-driven method capable of overcoming the challenges of multi-scale data. It is a hierarchical variant of Dynamic Mode Decomposition (DMD) that enables the unsupervised extraction of spatiotemporal features in multi-scale data. It operates by decomposing the data into bands of temporal frequencies associated with coherent spatial modes. The method requires no training and functions with little to no hyperparameter tuning by instead taking advantage of the hierarchical nature of multi-scale systems.

We demonstrate mrCOSTS on multi-scale data from a range of disciplines and scales: 1) sea surface temperature of the El-Nino Southern Oscillation (ENSO), 2) Antartic sea ice concentration, and 3) directly evaluating a numerical weather model against LIDAR observations of wind speed. In each example we demonstrate how mrCOSTS can be used to gain insights into the underlying dynamics of each system, revealing missing components in the description of each system's variability, diagnosing extreme events, and provide a pathway forward for building better physical representations in models.

Using mrCOSTS, we show that ENSO is the result of 6 coherent spatio-temporal bands and use these results to explain the difference in intensity and spatial pattern of extreme 2015-2016 ENSO event relative to other extreme ENSO events. In the second example, we show that the dynamics of Antarctic sea ice concentration were found to have a negligible interannual component until 2012 when a long-term decline initiated and interannual dynamics at a decadal-scale started contributing. The large decline in sea ice concentration between 2014-2017 was almost entirely the result of the new interannual dynamics while the recent record low sea ice concentrations had a strong climate change signal. Finally, we demonstrate how mrCOSTS enables the evaluation of models directly against spatially-explicit observations. We evaluated an eddy-resolving numerical model against LIDAR observations of wind speed. The scale-aware model evaluation allowed us to easily reveal that errors at the largest scales dominated the system despite the agreement of lower order statistical moments. In each case using mrCOSTS we trivially retrieved complex dynamics that were previously difficult to resolve while additionally extracting previously unknown patterns or complexities of systems characterized by multi-scale processes.

How to cite: Lapo, K., Yatsyshin, P., Goger, B., Ichinaga, S., and Kutz, J. N.: An unsupervised method for extracting coherent spatiotemporal patterns in multi-scale data, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-9917, https://doi.org/10.5194/egusphere-egu25-9917, 2025.

More of Earth’s surface is covered by Stratocumulus clouds (Sc) than by any other cloud
type making them extremely important for Earth’s energy balance, mostly due to reflection of
solar radiation. However, representing Sc and their radiative impact is one of the largest chal-
lenges for global climate models because these cannot resolve the length scales of the processes
involve in its formation and evolution. For this reason, Sc clouds represent a large uncertainty
for climate projections [1].
The challenge becomes more intricate due to the organizational complexity that Sc clouds
present in a broad range of spatial scales. In particular, Sc fields over the oceans display
characteristic mesoscale patterns that can present both organized and unorganized structures.
Between these morphological types, cellular convection receives particular attention given than
cloud decks self-organize into honeycomb-like hexagonal patterns composed by closed and
open convective cells fields.
The purpose of this project is to analyze satellite images of a particular tendency of Sc to orga-
nize into spatially compact, cellular-patterned, low-reflectivity regions of open cells embedded
in closed cellular cloud fields called as pockets of open cells (POCs) [2].
We aim to propose a segmentation, cell tracking and quantitative analysis of cell shape and
behavior changes in closed and open cell fields, in particular the interaction of both cells when
POCs are formed. A statistical analysis of different POCs will be carried to describe the time
and spatial contributions of cell shape changes, transitions and rearrangements in the evolution
of cellular patterns on Sc clouds considering the local dynamics between individual cells.
We hypothesize that the interaction between cold pools that are formed when open cells pre-
cipitate triggers a rapid dynamics on open cells fields. For its part, closed cells fields present
steady morphology until perturbations are formed triggering the formation of POCs.

How to cite: Haerter, J. and Monroy, D.: Morphological cellular analysis of Pockets of Open Cells on Marine, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-20182, https://doi.org/10.5194/egusphere-egu25-20182, 2025.

The early intensification (genesis) of tropical cyclones (TCs) is challenging to predict accurately in operational settings. The difficulty in predicting TC genesis stems from an insufficient understanding of the thermodynamic-kinematic characteristics involved in the multiscale interaction between clouds and TC circulations leading to genesis. Cloud-radiative feedback (CRF) has been shown to play a critical role in accelerating intensification during genesis by initiating secondary circulations that drive moisture and momentum convergence. However, it is still challenging to identify the exact pattern in radiation that could benefit genesis the most. Traditional diagnostic approaches to isolate CRF, such as the Sawyer-Eliassen Equation, require steady-state, axisymmetric thermal forcing. As such, these diagnostics methods are likely suboptimal in studying the response of weak TCs to intermittent, spatially asymmetric thermal forcing. 

This presentation utilizes novel data-driven methodologies to identify complex three-dimensional radiative patterns and approximate the thermodynamic-kinematic feedback between such patterns and early TC intensification. Specifically, we tasked a stochastic Variational Encoder-Decoder (VED) framework to discover different predictive patterns in radiative heating and quantify how these patterns affect early TC intensification. Applying the proposed framework to ensemble WRF simulations of Typhoon Haiyan (2013), longwave radiation anomalies in the downshear quadrants of Haiyan are shown to be particularly relevant to the early intensification of that TC. The extracted patterns provide new insights into how deep convective and shallow clouds should distribute spatially to best accelerate genesis. Apart from analyzing the extracted pattern, the stochastic nature of the proposed ML architecture brings additional insights into the radiatively-driven TC genesis research problem. We can use uncertainty in the prediction of intensification rates to track the time evolution of the relevance of radiation in tropical cyclone intensification. Furthermore, the uncertainty in the extracted pattern allows us to pinpoint trustworthy regions in the discovered predictive patterns for scientific interpretation.

Our study underscores the potential use of data-driven methodologies to quantify the impact of asymmetric radiative forcing on early TC formation without relying on axisymmetric or steady-state assumptions. The successful application of VED in this presentation reveals a promising way to use data-driven methods to uncover new knowledge in weather dynamics.

Reference:

How to cite: Tam, F. I.-H., Beucler, T., and Ruppert, J.: Data-driven Discovery of Predictive Spatiotemporal Patterns leading to Tropical Cyclogenesis, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-12960, https://doi.org/10.5194/egusphere-egu25-12960, 2025.

Assessing climate predictability remains a central challenge in modeling and forecasting the climate system. Approaches from nonequilibrium statistical mechanics, particularly stochastic thermodynamics, have provided insights into non-equilibrium properties of stochastic models, which have proven useful in representing patterns of climate variability. In this work, we investigate the potential of entropy production and frenesy as tools for quantifying the predictability of non-equilibrium fluctuations in the climate system. Entropy production, a measure of the irreversibility of the system’s dynamics, is explored as an intrinsic indicator of predictability and its possible connections to the Anomaly Correlation Coefficient (ACC). Frenesy, a lesser-known quantity derived from active matter studies that captures kinetic fluctuations and dynamical activity, is assessed for its potential role in explaining non-equilibrium processes within the climate system. Thus, we aim to better understand the relationships between these thermodynamic quantities and climate oscillations, such as the El Niño-Southern Oscillation and the Madden-Julian Oscillation, with the ultimate goal of defining a new measure of climate predictability and better comprehending non-equilibrium processes in the ocean and the atmosphere.

How to cite: Benincasa, R., Weiss, J. B., Du, D., Duane, G. S., and Pinardi, N.: Non-Equilibrium Thermodynamics and Climate Predictability: Investigating Entropy Production and Frenesy, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-3266, https://doi.org/10.5194/egusphere-egu25-3266, 2025.

Response theory has been shown to be a powerful tool in determining the impact of external forcing on the earth’s climate. High sensitivity to perturbations and the slow decay of response functions is associated with critical behaviour and tipping points. Despite the nonlinear nature of the climate dynamics, a generalisation of the fluctuation-dissipation theorem provides a direct connection between these response functions and the natural variability of the system. We show how response functions for a complex dynamical system may be written as a sum of terms that depend on the eigenvalues and eigenfunctions of the Koopman operator of the system, each term corresponding to a mode of variability. We demonstrate in a number of low-dimensional examples how extended dynamic mode decomposition may be used to accurately compute response and correlation functions of various observables, given only a set of snapshot data.

How to cite: Moroney, J., Lucarini, V., and Zagli, N.: Linking response to forcing to natural variability using a Koopman operator formalism, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-19443, https://doi.org/10.5194/egusphere-egu25-19443, 2025.

Nonlinear dynamical systems are ubiquitous across scientific disciplines, yet their analysis and predictive modeling remain challenging due to their inherent complexity. Koopman operator estimation and Koopman mode decomposition are common tools for emulating and extracting modes of variability from such systems. In this work, we propose a novel method for Koopman operator estimation called the Physics-Aware Koopman Operator (PAKO). Our approach is tailored for physical consistency by introducing a regularization term based on the Hilbert-Schmidt Independence Criterion (HSIC) to enforce independence between predictions and sensitive or protected physical variables. In addition to Koopman operator estimation, we extract Koopman modes and eigenvalues through a Koopman mode decomposition. We validate PAKO on the ClimateBench dataset, demonstrating superior accuracy, robustness, and interpretability for estimating the internal variability of climate systems. Our results showcase the potential of PAKO for advancing Koopman operator estimation of complex nonlinear dynamical systems.

How to cite: Mankovich, N. and Camps-Valls, G.: Physics-aware kernel Koopman operator estimation for consistent nonlinear mode decomposition, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-9070, https://doi.org/10.5194/egusphere-egu25-9070, 2025.