- characterization of nonlinear variability patterns in time and/or frequency domain,
- quantification of various aspects of time series and big data complexity and predictability,
- identification and quantification of different flavors of statistical interdependency within and between time series,
- discrimination between mere co-variability and true causality among two or more time series,
- dimensionality/complexity reduction and identification of statistically and/or dynamically meaningful modes of (co-)variability, and
- statistical and/or dynamical modeling of time series using stochastic or deterministic approaches.
According to this broad range of potential analysis goals, there exists a continuously expanding plethora of time series and big data analysis methods. This session focusses on geoscience problems from different fields covered by the EGU community that exhibit considerable degrees of dynamical and/or structural complexity, and applications of methods that specifically address this complexity. We anticipate that the presentation of novel methodological developments and/or successful showcases of applications of complexity science concepts (like statistical complexity measures, entropies, multi-scale and cross-scale analysis, predictability quantifiers, information transfer, causal discovery or complex networks, to mention only a few examples) across various disciplines will stimulate inter-disciplinary exchange and cross-fertilization among the EGU community.
Quantifying the structure and heterogeneity of complex spatial patterns is a key challenge in the analysis of spatial data across many scientific disciplines, including geoscience and geomorphology. The complexity of spatial patterns can be analysed by considering the recurrence of specific properties. While recurrence plot based methods are well established for analysing dynamical systems, their application to spatial patterns has received less attention. Here, we propose a novel approach that combines spatial recurrence analysis with a measure from fractal geometry, lacunarity, which originally quantifies homogeneity in spatial patterns. Applied to recurrence plots, it is referred to as recurrence lacunarity (RL) and quantifies the homogeneity of recurrences. Although recurrence plots can be generated from higher-dimensional data, RL has not yet been calculated for higher-dimensional (spatial) recurrence plots. To address this gap, we evaluate the RL of spatial data by validating the method using synthetic test patterns and then applying it to analyse hillslope gradients of river catchments near the Mendocino Triple Junction. The results demonstrate that the RL effectively detects and quantifies differences in the spatial structure of the catchments, which can be related to local uplift rates and the geological setting. RL provides a robust measure for comparing diverse spatial data sets and for quantifying how their spatial structure relates to external parameters, and may also be used as features in machine-learning models, complementing existing descriptors of spatial structure.
How to cite: Bielig, C., Rheinwalt, A., Braun, T., and Marwan, N.: Recurrence Lacunarity for the Analysis of Spatial Data, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6596, https://doi.org/10.5194/egusphere-egu26-6596, 2026.
Large scale climate oscillations (COs) are major explanatory drivers modulating climate systems and water resources across the Globe. Understanding the recurring patterns of Global climate oscillations (GCOs) is crucial for developing predictive models of hydro-climatic variables and management of water resources. In this study seven prominent GCOs of 1950-2025 period namely ElNino Southern Oscillations (ENSO), Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), Indian Ocean Dipole (IOD), Atlantic Multi-decadal Oscillation (AMO) Arctic Oscillation (AO) and Southern Oscillation Index (SOI) are subjected to Recurrence Quantification Analysis (RQA). Diverse set of RQ measures like laminarity determinism, trapping time, entropy and mean diagonal length are quantified for each of the time series considering the complete time spell. The complexity measures are further quantified for pre- and post- Global climate shifts of 1977-78 and 1998-99. Nino 3.4 Index is found to be the most deterministic and stable pattern irrespective of the time spell chosen for the analysis followed by AMO and PDO indices. IOD and AO indices of post-climatic shifts are showing more complex patterns, SOI is most sensitive to climatic shift while remaining indices showed stable patterns in the post-spells of both the climatic shifts. The insights gained from the study are helpful for proceeding with in-depth studies on selection of CO drivers in predictive modeling, multi-variate risk assessment and the synchronization studies of hydro-climatic extremes.
How to cite: Haroon, M. and Sankaran, A.: Complexity evaluation of Global climatic oscillations using Recurrence Quantification Analysis, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-22026, 2026.
This study presents dynamic application of recurrence quantification analysis (RQA) as an alternative approach for evaluation of streamflow complexity. Daily streamflows of 67 stations positioned in two major basins namely Mahanadi and Cauvery located at northern and southern India for 1980-2020 period are considered for recurrence analysis (RA). Then a novel dynamic recurrence theory (DRT) approach is followed for evaluating the complexity of multiple streamflow segments along the time domain. The key recurrence measures such as Determinism, Laminarity, Entropy, Trapping Time along with mean diagonal length are quantified for multiple segments along the temporal domain. The temporal evolution of recurrence measures showed abrupt alternations in complexity measures in majority of stations, except for 6 stations (16 %) of Mahanadi and 5 stations (17 %) of Cauvery, mostly falling within 1985-2000 period. The drastic shifts in complexity measures are coinciding more with the anthropogenic impacts than climatic drivers. The streamflow dynamics of Cauvery basin is found to be more erratic and complex than that of Mahanadi basin. In general, the streamflow dynamics of stations located in lower reaches are more complex and controlled by flow regulations than that of the upper reaches of both the basins. The insights gained from the novel DTA approach are noted to be helpful in identifying the prominent changes in streamflow and hence giving better insights on to its predictability.
How to cite: Sankaran, A., Cheriyalicheth, H. H., and Athayakkoth, S.: Evaluation of streamflow complexity of two major Indian river basins using dynamic recurrence theoretical approach, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-7598, https://doi.org/10.5194/egusphere-egu26-7598, 2026.
Soil moisture is a complex nonlinear hydroclimatic variable playing a significant role in the hydrologic cycle. Soil moisture has great influence on land-atmospheric interactions, including triggering and shaping extreme events, especially under climate change. Therefore, identifying hidden patterns and structures in soil moisture dynamics and understanding their evolution are critical for a wide range of applications. In this study, we aim to explore the temporal dynamics of soil moisture systems across global land areas using recurrence network analysis, bridging complex networks concept and recurrence plots. We use GLDAS soil moisture data in global land areas for 1948–2024 at a spatial resolution of 1 degree x 1 degree. Recurrence networks of soil moisture systems are constructed from soil moisture time series at individual grids. The nodes of the network represent the states of the system, and the links represent the recurrence of states. The nodes of the recurrence networks are identified by delay embedding of the soil moisture time series (i.e., phase space reconstruction) in an optimum embedding dimension identified using the False Nearest Neighbour algorithm. Thereafter, the links of the networks are established by considering the closeness of the nodes in terms of Euclidean distances. Several complex network measures, such as degree centrality, betweenness centrality, shortest path length, and clustering coefficient, are used to interpret the soil moisture systems from a recurrence perspective. The results from this study suggest that the soil moisture system behavior is similar for regions characterized with similar precipitation regime. This understanding is highly relevant for identifying regions with similar land-atmospheric coupling processes.
How to cite: Prabhakar, A. and Sivakumar, B.: Recurrence networks-based analysis of soil moisture dynamics in global land areas, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-8889, https://doi.org/10.5194/egusphere-egu26-8889, 2026.
Large-scale climate oscillations influence agricultural drought by altering atmospheric circulation, moisture transport, and land–atmosphere interactions. Understanding how climate oscillations organize the spatial connectivity of agricultural drought across different time lags remains a key challenge for regional drought assessment and predictability. To address this challenge, this study investigates the lag-dependent spatial connectivity between major climate oscillations and agricultural drought using an event-based complex network framework. For implementation, agricultural droughts in India are studied. Drought events are identified using a standardized soil moisture index for the period 1951–2014. Using these identified drought events, Event Coincidence Analysis is first applied to identify statistically significant lagged relationships between drought occurrence and the phases of major climate oscillations, including the El Niño–Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), Pacific Decadal Oscillation (PDO), Atlantic Multidecadal Oscillation (AMO), and North Atlantic Oscillation (NAO), across multiple lead times (τ = 1, 3, 6, 9, and 12 months). Subsequently, these lag-specific relationships are used to construct complex networks that explicitly represent spatial connections between climate oscillations and drought events. The network analysis reveals clear and systematic regional patterns. Arid, semi-arid, and sub-humid regions consistently exhibit high network degree values, indicating strong connectivity with multiple climate oscillations, particularly at short to intermediate time lags. This suggests that droughts in these regions are driven by compound climate influences originating from different ocean basins. In contrast, humid regions display lower network degree values across all time lags, indicating weaker sensitivity to large-scale climate variability. Overall, the results demonstrate that agricultural drought across India is governed by lag-dependent and spatially organized climate influences rather than by a single dominant climate driver. The proposed framework provides a direct link between temporal climate signals and spatial drought connectivity, offering a robust basis for improving drought monitoring and early warning systems.
How to cite: Venkatesh, K. and Sivakumar, B.: Exploring Lag-Dependent Spatial Connectivity Between Climate Oscillations and Agricultural Drought: A Complex Network Approach, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14332, 2026.
Understanding how Arctic climate variability is organized internally and how it connects to large-scale atmospheric variability remains a challenge. Approaches based on indices or dominant modes are well-suited to identifying coherent patterns but offer limited insight into localized connectivity, pathway structure, and the timing of interactions across regions. Here, we apply a climate network approach to examine the seasonal organization of Arctic atmospheric connectivity using mid-tropospheric circulation (500 hPa geopotential height, Z500) and near-surface air temperature (T2M) over 1940–2024. The analysis focuses on winter (DJF) and summer (JJA), and examines both instantaneous and time-lagged relationships in the free atmosphere and at the surface. We find a pronounced seasonal dependence in Arctic connectivity. Within the Arctic, Z500 networks exhibit strong and spatially extensive connectivity in winter, consistent with basin-scale coherence in the mid-tropospheric circulation. In summer, this structure weakens and becomes more fragmented. In both seasons, betweenness centrality is broadly distributed, suggesting that Arctic circulation variability is not dominated by a small number of preferred internal pathways. In contrast, T2M networks are more heterogeneous, with spatially uneven connectivity and localized regions of higher importance, highlighting the role of surface conditions in shaping near-surface variability. When only the strongest links (99th percentile threshold) are considered, direct Arctic large-scale connectivity is weak in both Z500 and T2M. However, time-lagged analysis shows that connectivity can emerge on delayed timescales, particularly in winter, and is more clearly expressed in the circulation field (Z500) than at the surface (T2M). Overall, this study presents a network-based diagnostic perspective on Arctic atmospheric variability, highlighting the seasonal organization and spatial connectivity that complement traditional mode-based analyses.
How to cite: kulkarni, S. and Agarwal, A.: Complex networks as a diagnostic framework for seasonal organization and spatial connectivity in the Arctic atmosphere. , EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-20175, 2026.
Detecting transient states and critical transitions in complex systems is essential for predicting abrupt shifts in phenomena such as climate stability, biological health, and financial market trends. However, identifying these transitions in real-time is particularly challenging in noisy, non-stationary data. To address this, we introduce stochasticity, defined as the square of short-term fluctuations within a sliding time window dt [1], as a time-resolved metric for capturing system instability. We demonstrate that stochasticity can serve as a highly sensitive indicator of emerging transient phases, and show that it converges more accurately than traditional drift-based measurements. This approach can identify transitions in diverse domains, including regional temperature anomalies and Parkinson’s disease progression via keystroke dynamics and thus provides a robust tool for monitoring systems where traditional methods struggle to resolve rapid changes.
This project was supported by the Czech Science Foundation, Project No. 25-18105S.
[1] Rahvar, Sepehr, et al. "Characterizing time-resolved stochasticity in non-stationary time series." Chaos, Solitons & Fractals 185 (2024): 115069.
How to cite: Manshour, P., Rahimitabar, M. R., and Paluš, M.: Leveraging Real-Time Stochasticity to Detect Transient States in Complex Systems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-9520, https://doi.org/10.5194/egusphere-egu26-9520, 2026.
Teleconnections in the climate system are a central element of internal variability, yet their degree of nonlinearity and long-term properties remain largely unexplored, especially in a paleoclimatological context. In our investigation, we perform a statistical analysis on data from the ModE-RA paleo-reanalysis to assess the spatial structure and nonlinear character of major atmospheric teleconnections over the last five centuries. We employ the mutual information measure, combined with surrogate data methods to detect statistically significant nonlinearities in the two-dimensional system formed by gridded temperature time series and indices of major modes of internal variability. This approach allows us to identify behaviour which may not be captured by linear correlation methods. Attention is also paid to the possibility of regime shifts or changes in large-scale forcings across different periods.
How to cite: Skala, P.: Nonlinearity of teleconnections in paleoclimatological data, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-7745, https://doi.org/10.5194/egusphere-egu26-7745, 2026.
Identifying regime shifts in paleoclimate proxy records remains challenging when time series are short and irregularly sampled. Such characteristics are common in paleoclimate archives and often limit the applicability of traditional linear statistical methods for quantifying regime transitions. In this study, we focus on the Younger Dryas event using a unique, biomarker stable isotope-based paleoclimate proxy dataset derived from two distinct lake sediment records that were hydrologically connected in the paleoenvironment. The proxy signals from both sediment cores exhibit strong similarities but also notable differences. We therefore use them as a ‘replicate’ sample, providing a natural framework for comparative analysis.
Recurrence plots and recurrence quantification analysis are employed to characterize nonlinear variability and to compare structural patterns between the two records. The recurrence plots capture the overall temporal extent of the Younger Dryas event in both proxies, while revealing small offsets in its onset and termination. These differences suggest potential influence of local environmental conditions on the lake systems and provide additional insights into site-specific responses. By analyzing the residual differences between the two proxy records, smaller-scale features can be identified, potentially reflecting local processes hidden by the large-scale climatic signal.
How to cite: Lyu, Z., Sachse, D., Marwan, N., and Tang, H.: Detecting Climate Transitions with Recurrence Plots: A Case Study of the Younger Dryas, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-6824, https://doi.org/10.5194/egusphere-egu26-6824, 2026.
Precipitation is a crucial component of the hydrological cycle and is essential for water supply, ecosystems, and climate dynamics.
In this context, the monsoon-driven rainfall patterns of the Indian Peninsular (IP) region exhibit a distinct spatio-temporal variability due to its strong seasonality, complex topography, and regional heterogeneity. Consequently, a key challenge is to identify local rainfall regimes and assess how their temporal evolution and recurrence patterns vary across space and seasons.
To address this, we leverage the recurrence analysis framework to comprehend the non-linear rainfall dynamics in terms of their deterministic behavior.
We apply singular value decomposition and agglomerative hierarchical clustering to extract spatial communities with similar recurrence characteristics. In addition, Laplacian centrality is used to determine central hubs within each community. Furthermore, to analyze long-term trends in predictability and persistence of rainfall dynamics, we employ a bootstrapping framework based on recurrence quantification analysis measures, comparing periods before and after 1991.
The study uncovers four communities within the IP region, which are generally shifting towards less predictable dynamics over time. The overall cluster organization varies substantially in terms of season and time period, while the spatial locations of the central hubs within each community remain stable. In particular, the community located in the western region exhibits a pronounced decline in recurrence.
In summary, these findings indicate that rainfall dynamics in the IP region is undergoing both a temporal shift towards reduced predictability and a spatial reorganization. The study exemplifies the applicability of recurrence analysis to characterize the intrinsic nonlinear dynamics of the climate system, detect regime transitions, and provide insights that support disaster preparedness and adaptation planning.
How to cite: Janzen, M., Ganapathiraju, S. A., and Marwan, N.: Recurrence Analysis of Communities from Precipitation Patterns over the Indian Peninsula, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-9506, https://doi.org/10.5194/egusphere-egu26-9506, 2026.
Natural phenomena, such as air–sea interactions, result from complex interactions among many components. Faithfully capturing such interactions is essential for improving predictive and inferential skills. However, identifying variable relationships directly in multivariate time series remains highly challenging. To address this, we specifically prioritize causality, defined as temporal precedence and directed influence, not mere correlation. This is key to identifying mechanisms governing time evolution.
In our previous work, we used transfer entropy (TE) to infer causal structure and reconstruct nonlinear dynamical models exemplified by the Lorenz system from multivariate time series [1]. Through this approach, linear terms were accurately recovered, but multiplicative nonlinear terms proved difficult to reconstruct. We attribute this limitation to the fact that TE primarily quantifies directed information flow between two variables [2], but does not explicitly decompose multi-variable interaction effects (e.g., multiplicative couplings) within the information transfer. This shortcoming motivates the use of a causality framework that can separate redundant, unique, and synergistic contributions, thereby isolating nonlinear interaction effects. Synergistic-Unique-Redundant Decomposition (SURD) decomposes causality into redundant, unique, and synergistic information components in multivariate time series [3]. We use SURD as a causal analysis tool to validate its applicability to data-driven modeling and event-focused observational analysis relevant to tipping or critical transition dynamics.
In this study, we apply SURD-based causal decomposition to time series data generated from low-dimensional nonlinear differential equations. Synergy-dominant driver pairs are used to screen candidate multiplicative terms, which then constrain a sparse model-identification step (e.g., SINDy), improving recovery of nonlinear terms compared with pairwise TE-guided screening alone. While Martínez-Sánchez et al. (2024) primarily established SURD as a causality decomposition framework [3], the present study examines how SURD outputs can be leveraged to support reconstruction of nonlinear model equations, following our previous work, in which we implemented a data-driven approach to identify basis functions to reproduce multivariate time series [1].
We demonstrate this approach on the Lorenz63 and Rössler systems and satellite observation datasets. Concretely, we define the effect variables in the causal analysis as instantaneous tendencies (e.g., dx/dt = (x(t+∆t) − x(t))/∆t) rather than one-step-ahead states. We then quantify how candidate drivers contribute to each tendency using an appropriate lag time ∆t corresponding to causal delay. In this setting, synergistic components highlight interaction effects as nonlinear terms that require joint knowledge of multiple drivers. Unique components support single-source linear term contributions, whereas redundant components capture shared explanatory information among drivers. Moreover, we find that applying SURD to time windows extracted immediately before and after tipping yields more discriminative synergy signatures and further improves the reconstruction accuracy of multiplicative nonlinear terms.
Acknowledgments
We thank ALD Lab for the SURD framework (https://github.com/ALD-Lab/SURD) used in this study.
References
[1] K. Kohyama, R. Irie, and M. Hisada, Causal analysis of time series data for modeling nonlinear phenomena, EGU General Assembly 2025, EGU25-3480 (2025).
[2] T. Schreiber, Measuring information transfer, Physical Review Letters, 85(2), 461 (2000).
[3] C. Martínez-Sánchez, G. Arranz, and A. Lozano-Durán, Decomposing causality into its synergistic, unique, and redundant components, Nature Communications, 15(1), 9296 (2024).
How to cite: Kohyama, K., Araki, R., Irie, R., Stewart, H., and Hisada, M.: SURD-based causal decomposition for nonlinear modeling from multivariate time series, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-17143, 2026.
In an era often referred to as 'the Great Acceleration', it is becoming increasingly urgent to identify causal structures in intertwined Earth system processes. This has led to the development of a wide range of causal inference methods that aim to accurately distinguish causal influences from pure correlation. Many of the established tools fall within two methodological families: state-space approaches, which reconstruct deterministic dynamics, and information-theoretic approaches, which are formulated for coupled stochastic processes. Despite their widespread use, clear guidance on the conditions under which these different approaches are appropriate, and on the associated trade-offs, remains fragmented.
Here, we present a systematic comparison of two representatives from these methodologically different backgrounds. We focus on convergent cross mapping, a deterministic approach, and transfer entropy, a stochastic approach. Both are commonly used for identifying and quantifying interactions in the Earth system from time series data. We assess their performance using (i) synthetic coupled systems with a known causal structure and (ii) real-world meteorological data on the Walker circulation, for which there exists an established physical understanding that can be used as a benchmark. Furthermore, we evaluate the impact of typical challenges related to the data (e.g. observation length, noise) and the underlying dynamics (e.g. latent drivers, causal delay) on detection ability and reliability, and test the sensitivity of the results to initial configuration choices.
Through this work, our aim is to provide a practical workflow and a set of recommendations that clarify the strengths, limitations, and potential synergies of these two conceptually distinct approaches. Finally, we outline and discuss potential use cases in current Earth system research.
How to cite: Schilling, N., Fetzer, I., Rehfeld, K., and Zoller, H.: Comparing deterministic and stochastic methods to infer causal Earth system interactions, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-11122, 2026.
In 1988, Tomoyuki Higuchi introduced an algorithmic approximation of the box-counting dimension of the graph of a real-valued univariate function or time series (Higuchi, 1988). This Higuchi fractal dimension has since become very popular as a simple fractal dimension estimator allowing the characterization of the scaling behavior of univariate time series. Besides numerous applications across various fields of science, several extensions of the classical framework have been developed during the past years, including a recent generalization to numerically estimating multifractal spectra from time series (Carrizales-Velazquez et al., 2022).
Here, we propose a novel extension of this multifractal Higuchi dimension analysis (MF-HDA) from one-dimensional time-series to two-dimensional image objects. We start by analyzing the properties of a recent two-dimensional generalization of the classical monofractal Higuchi method (Spasic, 2014), revealing some potentially misinterpreted geometric aspects of that original work. A minor modification is proposed to replace the concept of area by a new quantity that has a straightforward connection with the one-dimensional version of the Higuchi fractal dimension and thus provides the basis for a scaling analysis. Subsequently, we present a general mathematical framework for one- and two-dimensional Higuchi fractal dimension estimates and their generalizations to multifractal spectra, following the ideas underlying our previous one-dimensional MF-HDA.
To demonstrate the appropriate behavior of our new two-dimensional MF-HDA, we numerically estimate the multifractal spectra of different paradigmatic examples of mono- as well as multifractal two-dimensional model systems. For the special case of the two-dimensional binomial multifractal cascade model, we show that the results obtained by our new approach are largely consistent with the analytical multifractal spectra. Moreover, we find that our new approach does not exhibit an artificial widening of the multifractal spectra that is observed when applying a two-dimensional multifractal detrended fluctuation analysis as a numerical benchmark algorithm. Finally, we present some selected examples of applications of our approach to different two-dimensional geoscientific and environmental datasets like satellite images, illustrating the potential of systematic applications of our new two-dimensional MF-HDA method.
C. Carrizales-Vazquez, R.V. Donner & L. Guzman-Vargas, Generalization of Higuchi’s fractal dimension for multifractal analysis of time series with limited length, Nonlinear Dynamics, 108, 417-431, 2022.
T. Higuchi, Approach to an irregular time series on the basis of the fractal theory, Physica D, 31, 277-283, 1988.
S. Spasic, On 2D generalization of Higuchi’s fractal dimension, Chaos, Solitons & Fractals, 69, 179-187, 2014.
How to cite: Carrizales-Velazquez, C., Guzmán-Vargas, L., and Donner, R. V.: A new two-dimensional extension of the generalized Higuchi estimator for multifractal data: Theory and application to geoscience problems, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-14733, 2026.
Detrended fluctuation analysis (DFA), introduced by Peng et al. in 1994, along with its numerous algorithmic variants and multifractal extensions have become standard tools in nonlinear time series analysis and have found a vast body of applications across a wide range of scientific disciplines. However, many successful applications have in common that the time series under study are of sufficient length and exhibit unique scaling characteristics that are not overprinted by the action of any external dynamical factors. However, the latter two conditions can be violated in the context of complex geoscientific time series. In this work, we are interested in how such situations affect the general behavior of the resulting detrended fluctuation functions and attempt to provide a mechanistic explanation of the observed features, expanding on previous works that have largely been based on the thorough analysis of different kinds of stochastic model systems.
As a paradigmatic example for geoscientific data with particularly complex variability properties, we focus on a time series of satellite altimetry based global mean absolute sea-level variations (GMSL), which is available for the period from 1993 to present day at multi-day temporal resolution. This time series exhibits a variety of non-trivial fluctuation properties, including seasonality and a long-term nonlinear trend, but also reflections of nonlinear inter-annual climate variability modes like the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO). While the first two components can be largely removed from the time series by standard approaches like phase averaging and detrending/smoothing, the latter two manifest in GMSL in more subtle manners. We show that the resulting fluctuation functions of GMSL obtained with different orders of local detrending indeed do not exhibit simple and unique scaling characteristics across the full range of accessible scales, even when being subject to de-seasoning and de-trending prior to analysis. Instead, we find that depending on the scale considered, the scale-local fluctuation exponents exhibit a marked pattern, with consistent values across different DFA orders exclusively being observed below multi-annual to sub-decadal time scales. We present a simplistic explanation of those findings by studying the fluctuation functions for different types of stochastic signals with superposed oscillatory components with periodicities resembling those of the different variability modes in GMSL. Additionally, we discuss the potentials and limitations of different statistical approaches (including regression on potential external drivers as well as different time-scale decomposition techniques) to remove the effects of complex externally driven oscillatory modes from the original time series to obtain a more realistic picture of the intrinsic stochastic fluctuation properties of GMSL.
This work was partially supported by INESC TEC via the International Visiting Researcher Programme 2024 and by CMUP - Centro de Matemática da Universidade do Porto, member of LASI, which is financed by national funds through FCT - Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UID/00144/2025. Doi: https://doi.org/10.54499/UID/00144/2025.
How to cite: Donner, R. V. and Matos, J.: Potentials and limitations of detrended fluctuation analysis for complex geoscientific time series: The case of global mean sea-level, EGU General Assembly 2026, Vienna, Austria, 3–8 May 2026, EGU26-19726, 2026.
