Articles | Volume 32, issue 2
https://doi.org/10.5194/npg-32-131-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-32-131-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Multifractality of climate networks
Adarsh Jojo Thomas
CORRESPONDING AUTHOR
Hydrology Meteorology & Complexity (HM&Co), École nationale des ponts et chaussées, IP Paris, 6-8 Av. Blaise Pascal, Champs-sur-Marne, France
Jürgen Kurths
Department of Complexity Science, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany
Daniel Schertzer
Hydrology Meteorology & Complexity (HM&Co), École nationale des ponts et chaussées, IP Paris, 6-8 Av. Blaise Pascal, Champs-sur-Marne, France
Department of Complexity Science, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany
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Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 29, 4437–4455, https://doi.org/10.5194/hess-29-4437-2025, https://doi.org/10.5194/hess-29-4437-2025, 2025
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The hybrid variational mode decomposition–recurrent neural network (VMD-RNN) model provides a reliable one-step-ahead prediction, with better performance in predicting high and low values than the pure long short-term memory (LSTM) model. The universal multifractal technique is also introduced to evaluate prediction performance, thus validating the usefulness and applicability of the hybrid model.
Jerry Jose, Auguste Gires, Yelva Roustan, Ernani Schnorenberger, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys., 31, 587–602, https://doi.org/10.5194/npg-31-587-2024, https://doi.org/10.5194/npg-31-587-2024, 2024
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Wind energy exhibits extreme variability in space and time. However, it also shows scaling properties (properties that remain similar across different times and spaces of measurement). This can be quantified using appropriate statistical tools. In this way, the scaling properties of power from a wind farm are analysed here. Since every turbine is manufactured by design for a rated power, this acts as an upper limit on the data. This bias is identified here using data and numerical simulations.
Jerry Jose, Auguste Gires, Ernani Schnorenberger, Yelva Roustan, Daniel Schertzer, and Ioulia Tchiguirinskaia
Nonlin. Processes Geophys., 31, 603–624, https://doi.org/10.5194/npg-31-603-2024, https://doi.org/10.5194/npg-31-603-2024, 2024
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To understand the influence of rainfall on wind power production, turbine power and rainfall were measured simultaneously on an operational wind farm and analysed. The correlation between wind, wind power, air density, and other fields was obtained on various temporal scales under rainy and dry conditions. An increase in the correlation was observed with an increase in the rain; rain also influenced the correspondence between actual and expected values of power at various velocities.
Sara M. Vallejo-Bernal, Frederik Wolf, Niklas Boers, Dominik Traxl, Norbert Marwan, and Jürgen Kurths
Hydrol. Earth Syst. Sci., 27, 2645–2660, https://doi.org/10.5194/hess-27-2645-2023, https://doi.org/10.5194/hess-27-2645-2023, 2023
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Employing event synchronization and complex networks analysis, we reveal a cascade of heavy rainfall events, related to intense atmospheric rivers (ARs): heavy precipitation events (HPEs) in western North America (NA) that occur in the aftermath of land-falling ARs are synchronized with HPEs in central and eastern Canada with a delay of up to 12 d. Understanding the effects of ARs in the rainfall over NA will lead to better anticipating the evolution of the climate dynamics in the region.
Domenico Giaquinto, Warner Marzocchi, and Jürgen Kurths
Nonlin. Processes Geophys., 30, 167–181, https://doi.org/10.5194/npg-30-167-2023, https://doi.org/10.5194/npg-30-167-2023, 2023
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Despite being among the most severe climate extremes, it is still challenging to assess droughts’ features for specific regions. In this paper we study meteorological droughts in Europe using concepts derived from climate network theory. By exploring the synchronization in droughts occurrences across the continent we unveil regional clusters which are individually examined to identify droughts’ geographical propagation and source–sink systems, which could potentially support droughts’ forecast.
Arun Ramanathan, Pierre-Antoine Versini, Daniel Schertzer, Remi Perrin, Lionel Sindt, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 26, 6477–6491, https://doi.org/10.5194/hess-26-6477-2022, https://doi.org/10.5194/hess-26-6477-2022, 2022
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Reference rainfall scenarios are indispensable for hydrological applications such as designing storm-water management infrastructure, including green roofs. Therefore, a new method is suggested for simulating rainfall scenarios of specified intensity, duration, and frequency, with realistic intermittency. Furthermore, novel comparison metrics are proposed to quantify the effectiveness of the presented simulation procedure.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Atmos. Meas. Tech., 15, 5861–5875, https://doi.org/10.5194/amt-15-5861-2022, https://doi.org/10.5194/amt-15-5861-2022, 2022
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Weather radars measure rainfall in altitude whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind which affects the location of the measured field. Governing equation linking acceleration, gravity, buoyancy, and drag force is updated to account for oblateness of drops. Then multifractal wind is used as input to explore velocities and trajectories of drops. Finally consequence on radar rainfall estimation is discussed.
Auguste Gires, Jerry Jose, Ioulia Tchiguirinskaia, and Daniel Schertzer
Earth Syst. Sci. Data, 14, 3807–3819, https://doi.org/10.5194/essd-14-3807-2022, https://doi.org/10.5194/essd-14-3807-2022, 2022
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The Hydrology Meteorology and Complexity laboratory of École des Ponts ParisTech (https://hmco.enpc.fr) has made a data set of high-resolution atmospheric measurements (rainfall, wind, temperature, pressure, and humidity) available. It comes from a campaign carried out on a meteorological mast located on a wind farm in the framework of the Rainfall Wind Turbine or Turbulence project (RW-Turb; supported by the French National Research Agency – ANR-19-CE05-0022).
Yangzi Qiu, Igor da Silva Rocha Paz, Feihu Chen, Pierre-Antoine Versini, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 25, 3137–3162, https://doi.org/10.5194/hess-25-3137-2021, https://doi.org/10.5194/hess-25-3137-2021, 2021
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Our original research objective is to investigate the uncertainties of the hydrological responses of nature-based solutions (NBSs) that result from the multiscale space variability in both the rainfall and the NBS distribution. Results show that the intersection effects of spatial variability in rainfall and the spatial arrangement of NBS can generate uncertainties of peak flow and total runoff volume estimations in NBS scenarios.
Nico Wunderling, Jonathan F. Donges, Jürgen Kurths, and Ricarda Winkelmann
Earth Syst. Dynam., 12, 601–619, https://doi.org/10.5194/esd-12-601-2021, https://doi.org/10.5194/esd-12-601-2021, 2021
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In the Earth system, climate tipping elements exist that can undergo qualitative changes in response to environmental perturbations. If triggered, this would result in severe consequences for the biosphere and human societies. We quantify the risk of tipping cascades using a conceptual but fully dynamic network approach. We uncover that the risk of tipping cascades under global warming scenarios is enormous and find that the continental ice sheets are most likely to initiate these failures.
Abhirup Banerjee, Bedartha Goswami, Yoshito Hirata, Deniz Eroglu, Bruno Merz, Jürgen Kurths, and Norbert Marwan
Nonlin. Processes Geophys., 28, 213–229, https://doi.org/10.5194/npg-28-213-2021, https://doi.org/10.5194/npg-28-213-2021, 2021
Cited articles
Agarwal, A., Marwan, N., Rathinasamy, M., Merz, B., and Kurths, J.: Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach, Nonlin. Processes Geophys., 24, 599–611, https://doi.org/10.5194/npg-24-599-2017, 2017. a
Boers, N., Goswami, B., Rheinwalt, A., Bookhagen, B., Hoskins, B., and Kurths, J.: Complex networks reveal global pattern of extreme-rainfall teleconnections, Nature, 566, 373–377, https://doi.org/10.1038/s41586-018-0872-x, 2019. a
Donges, J. F., Zou, Y., Marwan, N., and Kurths, J.: Complex networks in climate dynamics, Eur. Phys. J. Spec. Top., 174, 157–179, https://doi.org/10.1140/epjst/e2009-01098-2, 2009. a, b, c
Donnat, C. and Holmes, S.: Tracking network dynamics: A survey using graph distances, Ann. Appl. Stat., 12, 971–1012, https://doi.org/10.1214/18-AOAS1176, 2018. a
Haas, M., Goswami, B., and von Luxburg, U.: Pitfalls of Climate Network Construction – A Statistical Perspective, J. Climate, 36, 3321–3342, https://doi.org/10.1175/JCLI-D-22-0549.1, 2023. a
Hlaváčková-Schindler, K., Paluš, M., Vejmelka, M., and Bhattacharya, J.: Causality detection based on information-theoretic approaches in time series analysis, Phys. Rep., 441, 1–46, https://doi.org/10.1016/j.physrep.2006.12.004, 2007. a
Hlinka, J., Hartman, D., Vejmelka, M., Runge, J., Marwan, N., Kurths, J., and Paluš, M.: Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information, Entropy, 15, 2023–2045, https://doi.org/10.3390/e15062023, 2013. a, b
Huffman, G. J., Bolvin, D. T., Nelkin, E. J., Wolff, D. B., Adler, R. F., Gu, G., Hong, Y., Bowman, K. P., and Stocker, E. F.: The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-Global, Multiyear, Combined-Sensor Precipitation Estimates at Fine Scales, J. Hydrometeorol., 8, 38–55, https://doi.org/10.1175/JHM560.1, 2007. a
Huffman, G. J., Bolvin, D. T., Nelkin, E. J., and Adler, R. F.: TRMM (TMPA) Precipitation L3 1 day 0.25 degree x 0.25 degree V7, Goddard Earth Sciences Data and Information Services Center (GES DISC) [data set], https://doi.org/10.5067/TRMM/TMPA/DAY/7, 2016. a, b
Kurths, J., Agarwal, A., Shukla, R., Marwan, N., Rathinasamy, M., Caesar, L., Krishnan, R., and Merz, B.: Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach, Nonlin. Processes Geophys., 26, 251–266, https://doi.org/10.5194/npg-26-251-2019, 2019. a
Lavallée, D., Lovejoy, S., Schertzer, D., and Schmitt, F.: On the Determination of Universal Multifractal Parameters in Turbulence, in: Topological Aspects of the Dynamics of Fluids and Plasmas, edited by: Moffatt, H. K., Zaslavsky, G. M., Comte, P., and Tabor, M., NATO ASI Series, Springer Netherlands, Dordrecht, 463–478, https://doi.org/10.1007/978-94-017-3550-6_27, 1992. a
Lovejoy, S. and Schertzer, D.: The Weather and Climate: Emergent Laws and Multifractal Cascades, Cambridge University Press, Cambridge, https://doi.org/10.1017/CBO9781139093811, 2013. a
Lovejoy, S., Tuck, A. F., and Schertzer, D.: Horizontal cascade structure of atmospheric fields determined from aircraft data, J. Geophys. Res.-Atmos., 115, D13105, https://doi.org/10.1029/2009JD013353, 2010. a
Malik, N., Bookhagen, B., Marwan, N., and Kurths, J.: Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks, Clim. Dynam., 39, 971–987, https://doi.org/10.1007/s00382-011-1156-4, 2012. a, b
Mandelbrot, B. B.: Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, J. Fluid Mech., 62, 331–358, https://doi.org/10.1017/S0022112074000711, 1974. a
Frisch, U. and Parisi, G.: Fully Developed Turbulence and Intermittency, in: Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by: Ghil, M., Benzi, R. and Parisi, G., North-Holland, New York, 84–88, https://www.researchgate.net/publication/284646749_On_the_singularity_structure_of_fully_developed_turbulence_in_Turbulence_and_predictability_in_geophysical_fluid_dynamics_and_climate_dynamics (last access: 17 July 2024), 1985. a
Richardson, L. F.: Weather Prediction by Numerical Process, Cambridge University Press, Cambridge, https://doi.org/10.1017/CBO9780511618291, 1922. a
Schertzer, D. and Lovejoy, S.: Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res.-Atmos., 92, 9693–9714, https://doi.org/10.1029/JD092iD08p09693, 1987. a, b, c, d
Schertzer, D. and Lovejoy, S.: Generalised scale invariance and multiplicative processes in the atmosphere, Pure Appl. Geophys., 130, 57–81, https://doi.org/10.1007/BF00877737, 1989. a
Schertzer, D. and Lovejoy, S.: Nonlinear Geodynamical Variability: Multiple Singularities, Universality and Observables, in: Non-Linear Variability in Geophysics: Scaling and Fractals, edited by: Schertzer, D. and Lovejoy, S., Springer Netherlands, Dordrecht, 41–82, https://doi.org/10.1007/978-94-009-2147-4_4, 1991. a, b
Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., and Marsan, D.: Multifractal Cascade Dynamics and Turbulent Intermittency, Fractals, 05, 427–471, https://doi.org/10.1142/S0218348X97000371, 1997. a, b
Tsonis, A. A. and Roebber, P. J., The architecture of the climate network, Phys. A-Stat. Mech. Appl., 333, 497–504, https://doi.org/10.1016/j.physa.2003.10.045, 2004. a, b
Yaglom, A. M.: Fluctuations in energy dissipation as influencing the shape of turbulence characteristics in an inertial interval, Dokl. Akad. Nauk SSSR, 166, 49–52, https://www.mathnet.ru/eng/dan32002 (last access: 1 July 2024), 1966. a
Executive editor
This letter aims to synergistically combine multifractals and climate network theory to better understand geophysical processes. Multifractals quantify their own variability and intermittency across a wide range of scales, while climate networks reveal their own long-range nonlinear dependencies at the observational scale. This novel methodology is introduced in the context of the Indian Monsoon, highlighting the multifractality of climate networks and showing how to upscale them.
This letter aims to synergistically combine multifractals and climate network theory to better...
Short summary
We have developed a systematic approach to study the climate system at multiple scales using climate networks, which have been previously used to study correlations between time series in space at only a single scale. This new approach is used to upscale precipitation climate networks to study the Indian summer monsoon and to analyze strong dependencies between spatial regions, which change with changing scales.
We have developed a systematic approach to study the climate system at multiple scales using...