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.
NPG Letters
| Highlight paper
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15 May 2025
NPG Letters | Highlight paper |
| 15 May 2025
| 15 May 2025
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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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.
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia
EGUsphere, https://doi.org/10.5194/egusphere-2023-2710, https://doi.org/10.5194/egusphere-2023-2710, 2024
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The hybrid VMD-RNN model provides a reliable one-step-ahead prediction, with better performance in predicting high and low values than the pure LSTM model. The universal multifractals technique is also introduced to evaluate prediction performance, thus validating the usefulness and applicability of the hybrid model.
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
Daniel Tesfay, Larissa Serdukova, Yayun Zheng, Pingyuan Wei, Jinqiao Duan, and Jürgen Kurths
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2020-31, https://doi.org/10.5194/npg-2020-31, 2020
Publication in NPG not foreseen
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For more than a decade, the climate has attracted stochastic dynamists with its unpredictable and complex phenomena. Our attention was attracted by the results of studies on the possibility of oceanic thermohaline circulation failure. We set the task to analyze the stability of the circulation current on-state and to predetermine what extreme events can unbalance it leading to attenuation. We also suggested possible scenarios for the resuscitation of the circulation in the event of its fading.
Ankit Agarwal, Norbert Marwan, Rathinasamy Maheswaran, Ugur Ozturk, Jürgen Kurths, and Bruno Merz
Hydrol. Earth Syst. Sci., 24, 2235–2251, https://doi.org/10.5194/hess-24-2235-2020, https://doi.org/10.5194/hess-24-2235-2020, 2020
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In the climate/hydrology network, each node represents a geographical location of climatological data, and links between nodes are set up based on their interaction or similar variability. Here, using network theory, we first generate a node-ranking measure and then prioritize the rain gauges to identify influential and expandable stations across Germany. To show the applicability of the proposed approach, we also compared the results with existing traditional and contemporary network measures.
Pierre-Antoine Versini, Filip Stanic, Auguste Gires, Daniel Schertzer, and Ioulia Tchiguirinskaia
Earth Syst. Sci. Data, 12, 1025–1035, https://doi.org/10.5194/essd-12-1025-2020, https://doi.org/10.5194/essd-12-1025-2020, 2020
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The Blue Green Wave of Champs-sur-Marne (1 ha, France) has been converted into a full-scale monitoring site devoted to studying the uses of green infrastructure in storm-water management. For this purpose, the components of the water balance have been monitored: rainfall, water content in the substrate, and discharge. These measurements are useful to better understand the processes (infiltration and retention) in hydrological performance and spatial variability.
Auguste Gires, Philippe Bruley, Anne Ruas, Daniel Schertzer, and Ioulia Tchiguirinskaia
Earth Syst. Sci. Data, 12, 835–845, https://doi.org/10.5194/essd-12-835-2020, https://doi.org/10.5194/essd-12-835-2020, 2020
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The Hydrology, Meteorology and Complexity Laboratory of École des Ponts ParisTech (hmco.enpc.fr) and the Sense-City consortium (http://sense-city.ifsttar.fr/) make available a dataset of optical disdrometer measurements stemming from a campaign that took place in September 2017 under the rainfall simulator of the Sense-City climatic chamber, which is located near Paris.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys., 27, 133–145, https://doi.org/10.5194/npg-27-133-2020, https://doi.org/10.5194/npg-27-133-2020, 2020
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This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.
Markus Drüke, Matthias Forkel, Werner von Bloh, Boris Sakschewski, Manoel Cardoso, Mercedes Bustamante, Jürgen Kurths, and Kirsten Thonicke
Geosci. Model Dev., 12, 5029–5054, https://doi.org/10.5194/gmd-12-5029-2019, https://doi.org/10.5194/gmd-12-5029-2019, 2019
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This work shows the successful application of a systematic model–data integration setup, as well as the implementation of a new fire danger formulation, in order to optimize a process-based fire-enabled dynamic global vegetation model. We have demonstrated a major improvement in the fire representation within LPJmL4-SPITFIRE in terms of the spatial pattern and the interannual variability of burned area in South America as well as in the modelling of biomass and the distribution of plant types.
Jürgen Kurths, Ankit Agarwal, Roopam Shukla, Norbert Marwan, Maheswaran Rathinasamy, Levke Caesar, Raghavan Krishnan, and Bruno Merz
Nonlin. Processes Geophys., 26, 251–266, https://doi.org/10.5194/npg-26-251-2019, https://doi.org/10.5194/npg-26-251-2019, 2019
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We examined the spatial diversity of Indian rainfall teleconnection at different timescales, first by identifying homogeneous communities and later by computing non-linear linkages between the identified communities (spatial regions) and dominant climatic patterns, represented by climatic indices such as El Nino–Southern Oscillation, Indian Ocean Dipole, North Atlantic Oscillation, Pacific Decadal Oscillation and Atlantic Multi-Decadal Oscillation.
Rosa Vicari, Ioulia Tchiguirinskaia, Bruno Tisserand, and Daniel Schertzer
Nat. Hazards Earth Syst. Sci., 19, 1485–1498, https://doi.org/10.5194/nhess-19-1485-2019, https://doi.org/10.5194/nhess-19-1485-2019, 2019
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Today, when extreme weather affects an urban area, huge numbers of digital data are spontaneously produced by the population on the Web. These
digital trailscan provide insight into the relation between climate-related risks and the social perception of these risks. The experiments presented in this paper show that big data exploration techniques can amplify debated issues and actors and explore how social media users behave.
Yangzi Qiu, Abdellah Ichiba, Igor Da Silva Rocha Paz, Feihu Chen, Pierre-Antoine Versini, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2019-347, https://doi.org/10.5194/hess-2019-347, 2019
Manuscript not accepted for further review
Rosa Vicari, Ioulia Tchiguirinskaia, and Daniel Schertzer
Geosci. Commun., 2, 25–38, https://doi.org/10.5194/gc-2-25-2019, https://doi.org/10.5194/gc-2-25-2019, 2019
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The resilience of our cities to climate risks relies on the capacity of urban communities to communicate. This paper presents a study aimed at understanding how to assess the impact of public outreach campaigns on urban resilience. The paper reviews resilience assessment methods, highlights those frameworks that consider communication impacts, and presents a range of experiments aimed at testing novel
resilience communication indicators.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Earth Syst. Sci. Data, 10, 941–950, https://doi.org/10.5194/essd-10-941-2018, https://doi.org/10.5194/essd-10-941-2018, 2018
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The Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech (hmco.enpc.fr) has made a data set of optical disdrometer measurements available that come from a campaign involving three collocated devices from two different manufacturers, relying on different underlying technologies (one Campbell Scientific PWS100 and two OTT Parsivel2 instruments). The campaign took place in January–February 2016 in the Paris area (France).
Abdellah Ichiba, Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer, Philippe Bompard, and Marie-Claire Ten Veldhuis
Hydrol. Earth Syst. Sci., 22, 331–350, https://doi.org/10.5194/hess-22-331-2018, https://doi.org/10.5194/hess-22-331-2018, 2018
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This paper proposes a two-step investigation to illustrate the extent of scale effects in urban hydrology. First, fractal tools are used to highlight the scale dependency observed within GIS data inputted in urban hydrological models. Then an intensive multi-scale modelling work was carried out to confirm effects on model performances. The model was implemented at 17 spatial resolutions ranging from 100 to 5 m. Results allow the understanding of scale challenges in hydrology modelling.
Daniel Wolfensberger, Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer, and Alexis Berne
Atmos. Chem. Phys., 17, 14253–14273, https://doi.org/10.5194/acp-17-14253-2017, https://doi.org/10.5194/acp-17-14253-2017, 2017
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Precipitation intensities simulated by the COSMO weather prediction model are compared to radar observations over a range of spatial and temporal scales using the universal multifractal framework. Our results highlight the strong influence of meteorological and topographical features on the multifractal characteristics of precipitation. Moreover, the influence of the subgrid parameterizations of COSMO is clearly visible by a break in the scaling properties that is absent from the radar data.
Tim Kittel, Catrin Ciemer, Nastaran Lotfi, Thomas Peron, Francisco Rodrigues, Jürgen Kurths, and Reik V. Donner
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-69, https://doi.org/10.5194/npg-2017-69, 2017
Revised manuscript not accepted
Ankit Agarwal, Norbert Marwan, Maheswaran Rathinasamy, Bruno Merz, and Jürgen Kurths
Nonlin. Processes Geophys., 24, 599–611, https://doi.org/10.5194/npg-24-599-2017, https://doi.org/10.5194/npg-24-599-2017, 2017
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Extreme events such as floods and droughts result from synchronization of different natural processes working at multiple timescales. Investigation on an observation timescale will not reveal the inherent underlying dynamics triggering these events. This paper develops a new method based on wavelets and event synchronization to unravel the hidden dynamics responsible for such sudden events. This method is tested with synthetic and real-world cases and the results are promising.
Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer, Susana Ochoa-Rodriguez, Patrick Willems, Abdellah Ichiba, Li-Pen Wang, Rui Pina, Johan Van Assel, Guendalina Bruni, Damian Murla Tuyls, and Marie-Claire ten Veldhuis
Hydrol. Earth Syst. Sci., 21, 2361–2375, https://doi.org/10.5194/hess-21-2361-2017, https://doi.org/10.5194/hess-21-2361-2017, 2017
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Data from 10 urban or peri-urban catchments located in five EU countries are used to analyze the imperviousness distribution and sewer network geometry. Consistent scale invariant features are retrieved for both (fractal dimensions can be defined), which enables to define a level of urbanization. Imperviousness representation in operational model is also found to exhibit scale-invariant features (even multifractality). The research was carried out as part of the UE INTERREG IV RainGain project.
Finn Müller-Hansen, Manoel F. Cardoso, Eloi L. Dalla-Nora, Jonathan F. Donges, Jobst Heitzig, Jürgen Kurths, and Kirsten Thonicke
Nonlin. Processes Geophys., 24, 113–123, https://doi.org/10.5194/npg-24-113-2017, https://doi.org/10.5194/npg-24-113-2017, 2017
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Deforestation and subsequent land uses in the Brazilian Amazon have huge impacts on greenhouse gas emissions, local climate and biodiversity. To better understand these land-cover changes, we apply complex systems methods uncovering spatial patterns in regional transition probabilities between land-cover types, which we estimate using maps derived from satellite imagery. The results show clusters of similar land-cover dynamics and thus complement studies at the local scale.
Auguste Gires, Catherine L. Muller, Marie-Agathe le Gueut, and Daniel Schertzer
Hydrol. Earth Syst. Sci., 20, 1751–1763, https://doi.org/10.5194/hess-20-1751-2016, https://doi.org/10.5194/hess-20-1751-2016, 2016
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Educational activities are now a common channel to increase impact of research projects. Here, we present innovative activities for young children that aim to help them (and their teachers) grasp some of the complex underlying scientific issues in environmental fields. The activities developed are focused on rainfall: observation and modeling of rain drop size and the succession of dry and rainy days, and writing of a scientific book. All activities were implemented in classrooms.
J. F. Donges, R. V. Donner, N. Marwan, S. F. M. Breitenbach, K. Rehfeld, and J. Kurths
Clim. Past, 11, 709–741, https://doi.org/10.5194/cp-11-709-2015, https://doi.org/10.5194/cp-11-709-2015, 2015
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Paleoclimate records from cave deposits allow the reconstruction of Holocene dynamics of the Asian monsoon system, an important tipping element in Earth's climate. Employing recently developed techniques of nonlinear time series analysis reveals several robust and continental-scale regime shifts in the complexity of monsoonal variability. These regime shifts might have played an important role as drivers of migration, cultural change, and societal collapse during the past 10,000 years.
T. K. D. Peron, C. H. Comin, D. R. Amancio, L. da F. Costa, F. A. Rodrigues, and J. Kurths
Nonlin. Processes Geophys., 21, 1127–1132, https://doi.org/10.5194/npg-21-1127-2014, https://doi.org/10.5194/npg-21-1127-2014, 2014
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In the past few years, complex networks have been extensively applied to climate sciences, yielding
the new field of climate networks. Here, we generalize climate network analysis by investigating the influence of altitudes in network topology. More precisely, we verified that nodes group into different communities corresponding to geographical areas with similar relief properties. This new approach may contribute to obtaining more complete climate network models.
Y. Zou, R. V. Donner, N. Marwan, M. Small, and J. Kurths
Nonlin. Processes Geophys., 21, 1113–1126, https://doi.org/10.5194/npg-21-1113-2014, https://doi.org/10.5194/npg-21-1113-2014, 2014
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We use visibility graphs to characterize asymmetries in the dynamics of sunspot areas in both solar hemispheres. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between effects due to statistical versus dynamical properties of the observed data. Temporal changes in the hemispheric predominance of the graph connectivity are found to lag those directly associated with the total hemispheric sunspot areas themselves.
D. Eroglu, N. Marwan, S. Prasad, and J. Kurths
Nonlin. Processes Geophys., 21, 1085–1092, https://doi.org/10.5194/npg-21-1085-2014, https://doi.org/10.5194/npg-21-1085-2014, 2014
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Anoop, S. Prasad, and J. Kurths
Nonlin. Processes Geophys., 21, 1093–1111, https://doi.org/10.5194/npg-21-1093-2014, https://doi.org/10.5194/npg-21-1093-2014, 2014
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We present a new approach to estimating sedimentary proxy records along with the proxy uncertainty. We provide analytical expressions for the proxy record, while transparently propagating uncertainties from the ages to the proxy record. We represent proxies on an error-free, precise timescale. Our approach provides insight into the interrelations between proxy variability and the various uncertainties. We demonstrate our method with synthetic examples and proxy data from the Lonar lake in India.
V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, and J. Kurths
Nonlin. Processes Geophys., 21, 901–917, https://doi.org/10.5194/npg-21-901-2014, https://doi.org/10.5194/npg-21-901-2014, 2014
K. Rehfeld, N. Molkenthin, and J. Kurths
Nonlin. Processes Geophys., 21, 691–703, https://doi.org/10.5194/npg-21-691-2014, https://doi.org/10.5194/npg-21-691-2014, 2014
L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, and J. Kurths
Nonlin. Processes Geophys., 21, 705–711, https://doi.org/10.5194/npg-21-705-2014, https://doi.org/10.5194/npg-21-705-2014, 2014
N. Molkenthin, K. Rehfeld, V. Stolbova, L. Tupikina, and J. Kurths
Nonlin. Processes Geophys., 21, 651–657, https://doi.org/10.5194/npg-21-651-2014, https://doi.org/10.5194/npg-21-651-2014, 2014
J. Hlinka, D. Hartman, N. Jajcay, M. Vejmelka, R. Donner, N. Marwan, J. Kurths, and M. Paluš
Nonlin. Processes Geophys., 21, 451–462, https://doi.org/10.5194/npg-21-451-2014, https://doi.org/10.5194/npg-21-451-2014, 2014
K. Rehfeld and J. Kurths
Clim. Past, 10, 107–122, https://doi.org/10.5194/cp-10-107-2014, https://doi.org/10.5194/cp-10-107-2014, 2014
S. Lovejoy, D. Schertzer, and D. Varon
Earth Syst. Dynam., 4, 439–454, https://doi.org/10.5194/esd-4-439-2013, https://doi.org/10.5194/esd-4-439-2013, 2013
A. Gires, I. Tchiguirinskaia, D. Schertzer, and S. Lovejoy
Nonlin. Processes Geophys., 20, 343–356, https://doi.org/10.5194/npg-20-343-2013, https://doi.org/10.5194/npg-20-343-2013, 2013
Related subject area
Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Assessing Lagrangian coherence in atmospheric blocking
Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 1: Wind turbine power and the associated biases
Multifractal analysis of wind turbine power and rainfall from an operational wind farm – Part 2: Joint analysis of available wind power and rain intensity
A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales
Stieltjes functions and spectral analysis in the physics of sea ice
Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud?
Brief communication: Climate science as a social process – history, climatic determinism, Mertonian norms and post-normality
Characteristics of intrinsic non-stationarity and its effect on eddy-covariance measurements of CO2 fluxes
How many modes are needed to predict climate bifurcations? Lessons from an experiment
Non-linear hydrologic organization
The impact of entrained air on ocean waves
Approximate multifractal correlation and products of universal multifractal fields, with application to rainfall data
Henry Schoeller, Robin Chemnitz, Péter Koltai, Maximilian Engel, and Stephan Pfahl
Nonlin. Processes Geophys., 32, 51–73, https://doi.org/10.5194/npg-32-51-2025, https://doi.org/10.5194/npg-32-51-2025, 2025
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We identify spatially coherent air streams into atmospheric blockings, which are important weather phenomena. By adapting mathematical methods to the atmosphere, we confirm previous findings. Our work shows that spatially coherent air streams featuring cloud formation correlate with strengthening of the blocking. The developed framework also allows for statements about the spatial behavior of the air parcels as a whole and indicates that blockings reduce the dispersion of the air parcels.
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.
Karlie N. Rees, Timothy J. Garrett, Thomas D. DeWitt, Corey Bois, Steven K. Krueger, and Jérôme C. Riedi
Nonlin. Processes Geophys., 31, 497–513, https://doi.org/10.5194/npg-31-497-2024, https://doi.org/10.5194/npg-31-497-2024, 2024
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The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.
Kenneth M. Golden, N. Benjamin Murphy, Daniel Hallman, and Elena Cherkaev
Nonlin. Processes Geophys., 30, 527–552, https://doi.org/10.5194/npg-30-527-2023, https://doi.org/10.5194/npg-30-527-2023, 2023
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Our paper tours powerful methods of finding the effective behavior of complex systems, which can be applied well beyond the initial setting of sea ice. Applications include transport properties of porous and polycrystalline media, such as rocks and glacial ice, and advection diffusion processes that arise throughout geophysics. Connections to random matrix theory establish unexpected parallels of these geophysical problems with semiconductor physics and Anderson localization phenomena.
Shaun Lovejoy
Nonlin. Processes Geophys., 30, 311–374, https://doi.org/10.5194/npg-30-311-2023, https://doi.org/10.5194/npg-30-311-2023, 2023
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How big is a cloud?and
How long does the weather last?require scaling to answer. We review the advances in scaling that have occurred over the last 4 decades: (a) intermittency (multifractality) and (b) stratified and rotating scaling notions (generalized scale invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.
Hans von Storch
Nonlin. Processes Geophys., 30, 31–36, https://doi.org/10.5194/npg-30-31-2023, https://doi.org/10.5194/npg-30-31-2023, 2023
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Climate science is, as all sciences, a social process and as such conditioned by the zeitgeist of the time. It has an old history and has attained different political significances. Today, it is the challenge of anthropogenic climate change – and societies want answers about how to deal with it. In earlier times, it was mostly the ideology of climate determinism which led people to construct superiority and eventually colonialism.
Lei Liu, Yu Shi, and Fei Hu
Nonlin. Processes Geophys., 29, 123–131, https://doi.org/10.5194/npg-29-123-2022, https://doi.org/10.5194/npg-29-123-2022, 2022
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We find a new kind of non-stationarity. This new kind of non-stationarity is caused by the intrinsic randomness. Results show that the new kind of non-stationarity is widespread in small-scale variations of CO2 turbulent fluxes. This finding reminds us that we need to handle the short-term averaged turbulent fluxes carefully, and we also need to re-screen the existing non-stationarity diagnosis methods because they could make a wrong diagnosis due to this new kind of non-stationarity.
Bérengère Dubrulle, François Daviaud, Davide Faranda, Louis Marié, and Brice Saint-Michel
Nonlin. Processes Geophys., 29, 17–35, https://doi.org/10.5194/npg-29-17-2022, https://doi.org/10.5194/npg-29-17-2022, 2022
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Present climate models discuss climate change but show no sign of bifurcation in the future. Is this because there is none or because they are in essence too simplified to be able to capture them? To get elements of an answer, we ran a laboratory experiment and discovered that the answer is not so simple.
Allen Hunt, Boris Faybishenko, and Behzad Ghanbarian
Nonlin. Processes Geophys., 28, 599–614, https://doi.org/10.5194/npg-28-599-2021, https://doi.org/10.5194/npg-28-599-2021, 2021
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The same power law we previously used to quantify growth of tree roots in time describes equally the assemblage of river networks in time. Even the basic length scale of both networks is the same. The one difference is that the basic time scale is ca. 10 times shorter for drainage networks than for tree roots, since the relevant flow rate is 10 times faster. This result overturns the understanding of drainage networks and forms a basis to organize thoughts about surface and subsurface hydrology.
Juan M. Restrepo, Alex Ayet, and Luigi Cavaleri
Nonlin. Processes Geophys., 28, 285–293, https://doi.org/10.5194/npg-28-285-2021, https://doi.org/10.5194/npg-28-285-2021, 2021
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A homogenization of Navier–Stokes to wave scales allows us to determine that air bubbles suspended near the ocean surface modify the momentum equation, specifically enhancing the vorticity in the flow. A model was derived that relates the rain rate to the production of air bubbles near the ocean surface. At wave scales, the air bubbles enhance the wave dissipation for small gravity or capillary waves.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys., 27, 133–145, https://doi.org/10.5194/npg-27-133-2020, https://doi.org/10.5194/npg-27-133-2020, 2020
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This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.
Cited articles
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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
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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
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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...
