Articles | Volume 6, issue 2
https://doi.org/10.5194/ascmo-6-141-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-6-141-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Nonlinear time series models for the North Atlantic Oscillation
Thomas Önskog
CORRESPONDING AUTHOR
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
Christian L. E. Franzke
Meteorological Institute and Center for Earth System Research and Sustainability, University of Hamburg, Hamburg, Germany
School of Engineering and Science, Jacobs University, Bremen, Germany
Abdel Hannachi
Department of Meteorology, Stockholm University, Stockholm, Sweden
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Sun-Seon Lee, Sahil Sharma, Nan Rosenbloom, Keith B. Rodgers, Ji-Eun Kim, Eun Young Kwon, Christian L. E. Franzke, In-Won Kim, Mohanan Geethalekshmi Sreeush, and Karl Stein
Earth Syst. Dynam., 16, 1427–1451, https://doi.org/10.5194/esd-16-1427-2025, https://doi.org/10.5194/esd-16-1427-2025, 2025
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A new 10-member ensemble simulation with the state-of-the-art Earth system model was employed to study the long-term climate response to sustained greenhouse warming through to the year 2500. The findings show that the projected changes in the forced mean state and internal variability during 2101–2500 differ substantially from the 21st-century projections, emphasizing the importance of multi-century perspectives for understanding future climate change and informing effective mitigation strategies.
Ja-Yeon Moon, Jan Streffing, Sun-Seon Lee, Tido Semmler, Miguel Andrés-Martínez, Jiao Chen, Eun-Byeoul Cho, Jung-Eun Chu, Christian L. E. Franzke, Jan P. Gärtner, Rohit Ghosh, Jan Hegewald, Songyee Hong, Dae-Won Kim, Nikolay Koldunov, June-Yi Lee, Zihao Lin, Chao Liu, Svetlana N. Loza, Wonsun Park, Woncheol Roh, Dmitry V. Sein, Sahil Sharma, Dmitry Sidorenko, Jun-Hyeok Son, Malte F. Stuecker, Qiang Wang, Gyuseok Yi, Martina Zapponini, Thomas Jung, and Axel Timmermann
Earth Syst. Dynam., 16, 1103–1134, https://doi.org/10.5194/esd-16-1103-2025, https://doi.org/10.5194/esd-16-1103-2025, 2025
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Based on a series of storm-resolving greenhouse warming simulations conducted with the AWI-CM3 model at 9 km global atmosphere and 4–25 km ocean resolution, we present new projections of regional climate change, modes of climate variability, and extreme events. The 10-year-long high-resolution simulations for the 2000s, 2030s, 2060s, and 2090s were initialized from a coarser-resolution transient run (31 km atmosphere) which follows the SSP5-8.5 greenhouse gas emission scenario from 1950–2100 CE.
Luc Hallali, Eirik Myrvoll-Nilsen, and Christian L. E. Franzke
EGUsphere, https://doi.org/10.5194/egusphere-2025-2461, https://doi.org/10.5194/egusphere-2025-2461, 2025
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We present an alternative statistical methodology to detect whether the Atlantic Ocean’s circulation system is approaching a tipping point. Our approach separates natural variability from real early warning signals of tipping, reducing false alarms. When applied to proxy of Atlantic Ocean’s circulation strength , we found significant signs that the system is ongoing destabilization . This suggests it may be approaching a tipping point, which could have major impacts on global climate patterns.
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
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In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Daniel Gliksman, Paul Averbeck, Nico Becker, Barry Gardiner, Valeri Goldberg, Jens Grieger, Dörthe Handorf, Karsten Haustein, Alexia Karwat, Florian Knutzen, Hilke S. Lentink, Rike Lorenz, Deborah Niermann, Joaquim G. Pinto, Ronald Queck, Astrid Ziemann, and Christian L. E. Franzke
Nat. Hazards Earth Syst. Sci., 23, 2171–2201, https://doi.org/10.5194/nhess-23-2171-2023, https://doi.org/10.5194/nhess-23-2171-2023, 2023
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Wind and storms are a major natural hazard and can cause severe economic damage and cost human lives. Hence, it is important to gauge the potential impact of using indices, which potentially enable us to estimate likely impacts of storms or other wind events. Here, we review basic aspects of wind and storm generation and provide an extensive overview of wind impacts and available indices. This is also important to better prepare for future climate change and corresponding changes to winds.
Herminia Torelló-Sentelles and Christian L. E. Franzke
Hydrol. Earth Syst. Sci., 26, 1821–1844, https://doi.org/10.5194/hess-26-1821-2022, https://doi.org/10.5194/hess-26-1821-2022, 2022
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Drought affects many regions worldwide, and future climate projections imply that drought severity and frequency will increase. Hence, the impacts of drought on the environment and society will also increase considerably. Monitoring and early warning systems for drought rely on several indicators; however, assessments on how these indicators are linked to impacts are still lacking. Our results show that meteorological indices are best linked to impact occurrences.
Cited articles
Benedict, J. J., Lee, S., and Feldstein, S. B.: Synoptic view of the North Atlantic oscillation, J. Atmos. Sci., 61, 121–144, 2004.
Brock, W. A., Dechert W. D., and Sheinkman J. A.: A test of independence based on the correlation dimension, Econom. Rev., 15, 197–235, 1996.
Brockwell, P. J. and Davis, R. A.: Time series: Theory and methods, second edition, Springer, New York, https://doi.org/10.1007/978-1-4419-0320-4, 1991.
Caian M., Koenigk, T., Döscher, R., and Devasthale, A.: An interannual link between Arctic sea-ice cover and the North Atlantic Oscillation, Clim. Dynam., 50, 423–441, 2018.
Cover, T. M. and Thomas, J. A.: Elements of information theory, 2nd Edn., John Wiley & Sons, Hoboken, New Jersey, https://doi.org/10.1002/047174882X, 2012.
Cropper, T., Hanna, E., Valente, M. A., and Jónsson, T.: A daily Azores-Iceland North Atlantic Oscillation index back to 1850, Geosci. Data J., 2, 12–24, 2015.
Cropper, T. E., Hanna, E., Valente, M. A., and Jónsson, T.: A daily Azores-Iceland North Atlantic Oscillation Index back to 1850, Zenodo, https://doi.org/10.5281/zenodo.9979, 2014.
De Gooijer, J.: Elements of nonlinear time series analysis and forecasting, 1st Edn., Springer International Publishing, https://doi.org/10.1007/978-3-319-43252-6, 2017.
Feldstein, S. B.: The timescale, power spectra, and climate noise properties of teleconnection patterns, J. Climate, 13, 4430–4440, 2000.
Feldstein, S. B.: Fundamental mechanisms of the growth and decay of the PNA teleconnection pattern, Q. J. Roy. Meteor. Soc., 128, 775–796, 2002.
Feldstein, S. B.: The dynamics of NAO teleconnection pattern growth and decay, Q. J. Roy. Meteor. Soc., 129, 901–924, 2003.
Feldstein, S. B. and Franzke, C.: Atmospheric teleconnection patterns in: Nonlinear and Stochastic Climate Dynamics, edited by: Franzke, C. L. E. and O'Kane, T. J., Cambridge University Press, Cambridge, UK, 54–104, 2017.
Franzke, C.: Extremes in dynamic-stochastic systems, Chaos, 27, 012101, https://doi.org/10.1063/1.4973541, 2017.
Franzke, C. and Feldstein, S. B.: The continuum and dynamics of Northern Hemisphere teleconnection patterns, J. Atmos. Sci., 62, 3250–3267, 2005.
Franzke, C. and Woollings, T.: On the Persistence and Predictability Properties of North Atlantic Climate Variability, J. Climate, 24, 466–472, 2011.
Franzke, C., Woollings, T., and Martius, O.: Persistent Circulation Regimes and Preferred Regime Transitions in the North Atlantic, J. Atmos. Sci., 68, 2809–2825, 2011.
Franzke, C., Lee, S., and Feldstein, S. B.: Is the North Atlantic Oscillation a breaking wave?, J. Atmos. Sci., 61, 145–160, 2004.
Franzke, C. L. E., O'Kane, T. J., Monselesan, D. P., Risbey, J. S., and Horenko, I.: Systematic attribution of observed Southern Hemisphere circulation trends to external forcing and internal variability, Nonlin. Processes Geophys., 22, 513–525, https://doi.org/10.5194/npg-22-513-2015, 2015.
Franzke, C., Osprey, S. M., Davini, P., and Watkins, N. W.: A dynamical systems explanation of the Hurst effect and atmospheric low-frequency variability, Sci. Rep., 5, 9068, 2015b.
Franzke, C., Barbosa, S., Blender, R., Fredriksen, H. B., Laepple, T., Lambert, F., Nilsen, T., Rypdal, K., Rypdal, M., Scotto, M., Vannitsem, S., Watkins, N., Yang, L., and Yuan, N.: The Structure of Climate Variability Across Scales, Rev. Geophys., 58, e2019RG000657, https://doi.org/10.1029/2019RG000657, 2020.
Gámiz-Fortis, S. R., Pozo-Vázquez, D., Esteban-Parra, M. J., and Castro-Díez, Y.: Spectral characteristics and predictability of the NAO assessed through Singular Spectral Analysis, J. Geophys. Res., 107, ACC 11-1–ACC 55-15, 4685, https://doi.org/10.1029/2001JD001436, 2002.
Hannachi, A. and Stendel, M.: Annex 1: What is NAO?, in: North Sea Region Climate Change Assessment, edited by: Quante, M. and Colijn, F., Springer Inernational Publishing, 528 pp., 55–84, 2016.
Hannachi, A., Straus, D., Franzke, C., Corti, S., and Woollings, T.: Low frequency nonlinearity and regime behavior in the Northern Hemisphere extra-tropical atmosphere, Rev. Geophys. 55, 199–234, 2017.
Horel, J. D. and Wallace, J. M.: Planetary-scale atmospheric phenomena associated with the Southern Oscillation, Mon. Weather Rev., 109, 813–829, 1981.
Horenko, I.: On the identification of nonstationary factor models and their application to atmospheric data analysis, J. Atmos. Sci., 67, 1559–1574, 2010.
Kowalski, A. M., Martín, M. T., Plastino, A., Rosso, O. A., and Casas, M.: Distances in probability space and the statistical complexity setup, Entropy, 13, 1055–1075, 2011.
Kullback, S.: Information theory and statistics, Courier Corporation, Wiley, New York, 1959.
Kullback, S. and Leibler, R. A.: On information and sufficiency, Ann. Math. Stat., 22, 79–86, 1951.
Lacasa, L., Nunez, A., Roldan, E., Parrondo, J. M., and Luque, B.: Time series irreversibility: a visibility graph approach, Euro. Phys. J. B., 85, 217, https://doi.org/10.1140/epjb/e2012-20809-8, 2012.
Majda, A. J., Franzke, C., and Crommelin, D.: Normal forms for reduced stochastic climate models, Proc. Natl. Acad. Sci. USA, 106, 3649–3653, 2009.
Mandelbrot, B. M. and Wallis, J. R.: Noah, Joseph and operational hydrology, Water Res. M., 4, 909–918, 1968.
O'Kane, T. J., Risbey, J. S., Franzke, C., Horenko, I., and Monselesan, D. P.: Changes in the metastability of the midlatitude Southern Hemisphere circulation and the utility of nonstationary cluster analysis and split-flow blocking indices as diagnostic tools, J. Atmos. Sci., 70, 824–842, 2013.
Önskog, T., Franzke, C., and Hannachi, A.: Predictability and Non-Gaussian Characteristics of the North Atlantic Oscillation, J. Climate, 31, 537–554, 2018.
Risbey, J. S., O'Kane, T. J., Monselesan, D. P., Franzke, C., and Horenko, I.: Metastability of Northern Hemisphere teleconnection modes, J. Atmos. Sci., 72, 35–54, 2015.
Rossby, C.-G.: Planetary flow patterns in the atmosphere, Q. J. Roy. Meteor. Soc., 66, 68–87, 1940.
Sardeshmukh, P. D. and Sura, P.: Reconciling non-Gaussian climate statistics with linear dynamics, J. Climate, 22, 1193–1207, 2009.
Stendel, M., van den Besselaar, E., Hannachi, A., Kent, E. C., Lefevre, C., Schenk, F., van der Schrier, G., and Woollings, T. J.: Recent Change–Atmosphere, in: North Sea Region Climate Change Assessment, edited by: Quante, M. and Colijn, F., Springer International Publishing, 528 pp., 489–493, 2016.
Walker, G. T. and Bliss, E. W.: World weather, V. Memoirs Royal Meteorol., 4, 53–84, 1932.
Wallace, J. M. and Gutzler, D. S.: Teleconnections in the geopotential height field during the Northern Hemisphere winter, Mon. Weather Rev., 109, 784–812, 1981.
Woollings, T., Czuchnicki, C., and Franzke, C.: Twentieth century North Atlantic jet variability, Q. J. Roy. Meteor. Soc., 140, 783–791, 2014.
Woollings, T., Franzke, C., Hodson, D. L. R., Dong, B., Barnes, E. A., Raible, C. C., and Pinto, J. G.: Contrasting interannual and multidecadal NAO variability, Clim. Dynam., 45, 539–556, 2015.
Woollings, T., Hannachi, A., Hoskins, B., and Turner, A.: A Regime View of the North Atlantic Oscillation and Its Response to Anthropogenic Forcing, J. Climate, 23, 1291–1307, 2010.
Wunsch, C.: The Interpretation of Short Climate Records, with Comments on the North Atlantic and Southern Oscillations, B. Am. Meteorol. Soc., 80, 245–255, 1999.
Short summary
The North Atlantic Oscillation (NAO) has a significant impact on seasonal climate and surface weather conditions throughout Europe, North America and the North Atlantic. In this paper, we study a number of linear and nonlinear models for a station-based time series of the daily winter NAO. We find that a class of nonlinear models, including both short and long lags, excellently reproduce the characteristic statistical properties of the NAO. These models can hence be used to simulate the NAO.
The North Atlantic Oscillation (NAO) has a significant impact on seasonal climate and surface...