Articles | Volume 30, issue 1 
            
                
                    
                    
            
            
            https://doi.org/10.5194/npg-30-49-2023
                    © Author(s) 2023. 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-30-49-2023
                    © Author(s) 2023. This work is distributed under 
the Creative Commons Attribution 4.0 License.
                the Creative Commons Attribution 4.0 License.
On the interaction of stochastic forcing and regime dynamics
Joshua Dorrington
CORRESPONDING AUTHOR
                                            
                                    
                                            Atmospheric, Oceanic, and Planetary Physics, University of Oxford, Oxford, UK
                                        
                                    
                                            Institute for Meteorology and Climate (IMK-TRO), Karlsruhe Institute of Technology, Karlsruhe, Germany
                                        
                                    Tim Palmer
                                            Atmospheric, Oceanic, and Planetary Physics, University of Oxford, Oxford, UK
                                        
                                    Related authors
Joshua Oldham-Dorrington, Camille Li, Stefan Sobolowski, and Robin Guillaume-Castel
                                        EGUsphere, https://doi.org/10.5194/egusphere-2025-4977, https://doi.org/10.5194/egusphere-2025-4977, 2025
                                    Short summary
                                    Short summary
                                            
                                                The future of heavy precipitation in Europe is uncertain, and current precipitation can be poorly represented in climate models. To understand model heavy precipitation better we break it into two steps: firstly, do weather patterns that favour precipitation occur? Secondly, does heavy precipitation occur under those weather patterns. By doing so, we are able to better understand model biases and forced changes which can make current climate models more useful and easier to improve.
                                            
                                            
                                        Joshua Dorrington, Marta Wenta, Federico Grazzini, Linus Magnusson, Frederic Vitart, and Christian M. Grams
                                    Nat. Hazards Earth Syst. Sci., 24, 2995–3012, https://doi.org/10.5194/nhess-24-2995-2024, https://doi.org/10.5194/nhess-24-2995-2024, 2024
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                                                Extreme rainfall is the leading weather-related source of damages in Europe, but it is still difficult to predict on long timescales. A recent example of this was the devastating floods in the Italian region of Emiglia Romagna in May 2023. We present perspectives based on large-scale dynamical information that allows us to better understand and predict such events.
                                            
                                            
                                        Joshua Dorrington, Kristian Strommen, and Federico Fabiano
                                    Weather Clim. Dynam., 3, 505–533, https://doi.org/10.5194/wcd-3-505-2022, https://doi.org/10.5194/wcd-3-505-2022, 2022
                                    Short summary
                                    Short summary
                                            
                                                We investigate how well current state-of-the-art climate models reproduce the wintertime weather of the North Atlantic and western Europe by studying how well different "regimes" of weather are captured. Historically, models have  struggled to capture these regimes, making it hard to predict future changes in wintertime extreme weather. We show models can capture regimes if the right method is used, but they show biases, partially as a result of biases in jet speed and eddy strength.
                                            
                                            
                                        Joshua Oldham-Dorrington, Camille Li, Stefan Sobolowski, and Robin Guillaume-Castel
                                        EGUsphere, https://doi.org/10.5194/egusphere-2025-4977, https://doi.org/10.5194/egusphere-2025-4977, 2025
                                    Short summary
                                    Short summary
                                            
                                                The future of heavy precipitation in Europe is uncertain, and current precipitation can be poorly represented in climate models. To understand model heavy precipitation better we break it into two steps: firstly, do weather patterns that favour precipitation occur? Secondly, does heavy precipitation occur under those weather patterns. By doing so, we are able to better understand model biases and forced changes which can make current climate models more useful and easier to improve.
                                            
                                            
                                        Joshua Dorrington, Marta Wenta, Federico Grazzini, Linus Magnusson, Frederic Vitart, and Christian M. Grams
                                    Nat. Hazards Earth Syst. Sci., 24, 2995–3012, https://doi.org/10.5194/nhess-24-2995-2024, https://doi.org/10.5194/nhess-24-2995-2024, 2024
                                    Short summary
                                    Short summary
                                            
                                                Extreme rainfall is the leading weather-related source of damages in Europe, but it is still difficult to predict on long timescales. A recent example of this was the devastating floods in the Italian region of Emiglia Romagna in May 2023. We present perspectives based on large-scale dynamical information that allows us to better understand and predict such events.
                                            
                                            
                                        Bjorn Stevens, Stefan Adami, Tariq Ali, Hartwig Anzt, Zafer Aslan, Sabine Attinger, Jaana Bäck, Johanna Baehr, Peter Bauer, Natacha Bernier, Bob Bishop, Hendryk Bockelmann, Sandrine Bony, Guy Brasseur, David N. Bresch, Sean Breyer, Gilbert Brunet, Pier Luigi Buttigieg, Junji Cao, Christelle Castet, Yafang Cheng, Ayantika Dey Choudhury, Deborah Coen, Susanne Crewell, Atish Dabholkar, Qing Dai, Francisco Doblas-Reyes, Dale Durran, Ayoub El Gaidi, Charlie Ewen, Eleftheria Exarchou, Veronika Eyring, Florencia Falkinhoff, David Farrell, Piers M. Forster, Ariane Frassoni, Claudia Frauen, Oliver Fuhrer, Shahzad Gani, Edwin Gerber, Debra Goldfarb, Jens Grieger, Nicolas Gruber, Wilco Hazeleger, Rolf Herken, Chris Hewitt, Torsten Hoefler, Huang-Hsiung Hsu, Daniela Jacob, Alexandra Jahn, Christian Jakob, Thomas Jung, Christopher Kadow, In-Sik Kang, Sarah Kang, Karthik Kashinath, Katharina Kleinen-von Königslöw, Daniel Klocke, Uta Kloenne, Milan Klöwer, Chihiro Kodama, Stefan Kollet, Tobias Kölling, Jenni Kontkanen, Steve Kopp, Michal Koran, Markku Kulmala, Hanna Lappalainen, Fakhria Latifi, Bryan Lawrence, June Yi Lee, Quentin Lejeun, Christian Lessig, Chao Li, Thomas Lippert, Jürg Luterbacher, Pekka Manninen, Jochem Marotzke, Satoshi Matsouoka, Charlotte Merchant, Peter Messmer, Gero Michel, Kristel Michielsen, Tomoki Miyakawa, Jens Müller, Ramsha Munir, Sandeep Narayanasetti, Ousmane Ndiaye, Carlos Nobre, Achim Oberg, Riko Oki, Tuba Özkan-Haller, Tim Palmer, Stan Posey, Andreas Prein, Odessa Primus, Mike Pritchard, Julie Pullen, Dian Putrasahan, Johannes Quaas, Krishnan Raghavan, Venkatachalam Ramaswamy, Markus Rapp, Florian Rauser, Markus Reichstein, Aromar Revi, Sonakshi Saluja, Masaki Satoh, Vera Schemann, Sebastian Schemm, Christina Schnadt Poberaj, Thomas Schulthess, Cath Senior, Jagadish Shukla, Manmeet Singh, Julia Slingo, Adam Sobel, Silvina Solman, Jenna Spitzer, Philip Stier, Thomas Stocker, Sarah Strock, Hang Su, Petteri Taalas, John Taylor, Susann Tegtmeier, Georg Teutsch, Adrian Tompkins, Uwe Ulbrich, Pier-Luigi Vidale, Chien-Ming Wu, Hao Xu, Najibullah Zaki, Laure Zanna, Tianjun Zhou, and Florian Ziemen
                                    Earth Syst. Sci. Data, 16, 2113–2122, https://doi.org/10.5194/essd-16-2113-2024, https://doi.org/10.5194/essd-16-2113-2024, 2024
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                                                To manage Earth in the Anthropocene, new tools, new institutions, and new forms of international cooperation will be required. Earth Virtualization Engines is proposed as an international federation of centers of excellence to empower all people to respond to the immense and urgent challenges posed by climate change.
                                            
                                            
                                        Tom Kimpson, Margarita Choulga, Matthew Chantry, Gianpaolo Balsamo, Souhail Boussetta, Peter Dueben, and Tim Palmer
                                    Hydrol. Earth Syst. Sci., 27, 4661–4685, https://doi.org/10.5194/hess-27-4661-2023, https://doi.org/10.5194/hess-27-4661-2023, 2023
                                    Short summary
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                                                Lakes play an important role when we try to explain and predict the weather. More accurate and up-to-date description of lakes all around the world for numerical models is a continuous task. However, it is difficult to assess the impact of updated lake description within a weather prediction system. In this work, we develop a method to quickly and automatically define how, where, and when updated lake description affects weather prediction.
                                            
                                            
                                        Joshua Dorrington, Kristian Strommen, and Federico Fabiano
                                    Weather Clim. Dynam., 3, 505–533, https://doi.org/10.5194/wcd-3-505-2022, https://doi.org/10.5194/wcd-3-505-2022, 2022
                                    Short summary
                                    Short summary
                                            
                                                We investigate how well current state-of-the-art climate models reproduce the wintertime weather of the North Atlantic and western Europe by studying how well different "regimes" of weather are captured. Historically, models have  struggled to capture these regimes, making it hard to predict future changes in wintertime extreme weather. We show models can capture regimes if the right method is used, but they show biases, partially as a result of biases in jet speed and eddy strength.
                                            
                                            
                                        Cited articles
                        
                        Altmann, E. G. and Endler, A.: Noise-enhanced trapping in chaotic scattering,
Phys. Rev. Lett., 105, 244102,
https://doi.org/10.1103/PhysRevLett.105.244102, 2010. a, b, c, d
                    
                
                        
                        Berner, J., Jung, T., and Palmer, T. N.: Systematic Model Error: The Impact of
Increased Horizontal Resolution versus Improved Stochastic and Deterministic
Parameterizations, J. Climate, 25, 4946–4962,
https://doi.org/10.1175/JCLI-D-11-00297.1, 2012. a
                    
                
                        
                        Branstator, G.: Circumglobal Teleconnections, the Jet Stream Waveguide, and
the North Atlantic Oscillation, Tech. Rep., 14,
https://doi.org/10.1175/1520-0442(2002)015<1893:CTTJSW>2.0.CO;2, 2002. a
                    
                
                        
                        Cehelsky, P. and Tung, K. K.: Theories of multiple equilibria and weather
regimes – a critical reexamination. Part II: baroclinic two-layer models,
J. Atmos. Sci., 44, 3282–3303,
https://doi.org/10.1175/1520-0469(1987)044<3282:TOMEAW>2.0.CO;2, 1987. a
                    
                
                        
                        Champneys, A. R. and Kirk, V.: The entwined wiggling of homoclinic curves
emerging from saddle-node/Hopf instabilities, Physica D, 195, 77–105, https://doi.org/10.1016/j.physd.2004.03.004, 2004. a
                    
                
                        
                        Charney, J. G. and DeVore, J. G.: Multiple Flow Equilibria in the Atmosphere
and Blocking, J. Atmos. Sci., 36, 1205–1216,
https://doi.org/10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2, 1979. a
                    
                
                        
                        Charney, J. G. and Straus, D. M.: Form-drag instability, multiple equilibria
and propagating planetary waves in baroclinic, orographically forced,
planetary wave systems, J. Atmos. Sci., 37, 1157–1176,
https://doi.org/10.1175/1520-0469(1980)037<1157:FDIMEA>2.0.CO;2, 1980. a
                    
                
                        
                        Christensen, H. M., Moroz, I. M., and Palmer, T. N.: Simulating weather
regimes: impact of stochastic and perturbed parameter schemes in a simple
atmospheric model, Clim. Dynam., 44, 2195–2214,
https://doi.org/10.1007/s00382-014-2239-9, 2015. a
                    
                
                        
                        Crommelin, D. T.: Homoclinic Dynamics: A Scenario for Atmospheric
Ultralow-Frequency Variability, J. Atmos. Sci., 59,
1533–1549, https://doi.org/10.1175/1520-0469(2002)059<1533:HDASFA>2.0.CO;2, 2002. a
                    
                
                        
                        Crommelin, D. T., Opsteegh, J. D., and Verhulst, F.: A Mechanism for
Atmospheric Regime Behavior, J. Atmos. Sci., 61, 1406–1419,
https://doi.org/10.1175/1520-0469(2004)061<1406:amfarb>2.0.co;2, 2004. a
                    
                
                        
                        Cvitanović, P., Søndergaard, N., Palla, G., Vattay, G., and Dettmann,
C. P.: Spectrum of stochastic evolution operators: Local matrix
representation approach, Phys. Rev. E, 60, 3936,
https://doi.org/10.1103/PhysRevE.60.3936, 1999. a
                    
                
                        
                        Cvitanović, P., Artuso, R., Mainieri, R., Tanner, G., and Vattay, G.: Chaos:
Classical and Quantum, Niels Bohr Inst.,
http://chaosbook.org/ (last access: 3 February 2023), 2016. a
                    
                
                        
                        Dawson, A. and Palmer, T. N.: Simulating weather regimes: impact of model
resolution and stochastic parameterization, Clim. Dynam., 44,
2177–2193, https://doi.org/10.1007/s00382-014-2238-x, 2015. a
                    
                
                        
                        De Swart, H. E.: Low-order spectral models of the atmospheric circulation: A
survey, Acta Applicandae Mathematicae, 11, 49–96, https://doi.org/10.1007/BF00047114,
1988. a, b
                    
                
                        
                        Dorrington, J.: Software for “On the interaction of stochastic forcing and regime dynamics”, Zenodo [code], https://doi.org/10.5281/zenodo.7602855, 2023. a
                    
                
                        
                        Dorrington, J., Strommen, K., and Fabiano, F.: Quantifying climate model representation of the wintertime Euro-Atlantic circulation using geopotential-jet regimes, Weather Clim. Dynam., 3, 505–533, https://doi.org/10.5194/wcd-3-505-2022, 2022. a
                    
                
                        
                        Düben, P. D., McNamara, H., and Palmer, T. N.: The use of imprecise
processing to improve accuracy in weather & climate prediction, J. Comput. Phys., 271, 2–18, https://doi.org/10.1016/j.jcp.2013.10.042, 2014. a
                    
                
                        
                        Faisst, H. and Eckhardt, B.: Lifetimes of noisy repellors, Phys. Rev. E,
68, 026215, https://doi.org/10.1103/PhysRevE.68.026215, 2003. a
                    
                
                        
                        Franaszek, M. and Fronzoni, L.: Influence of noise on crisis-induced
intermittency, Phys. Rev. E, 49, 3888, https://doi.org/10.1103/PhysRevE.49.3888,
1994. a
                    
                
                        
                        Hoskins, B. J. and Ambrizzi, T.: Rossby Wave Propagation on a Realistic
Longitudinally Varying Flow, J. Atmos. Sci., 50,
1661–1671, https://doi.org/10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2, 1993. a
                    
                
                        
                        Itoh, H. and Kimoto, M.: Multiple Attractors and Chaotic Itinerancy in a
Quasigeostrophic Model with Realistic Topography: Implications for Weather
Regimes and Low-Frequency Variability, J. Atmos. Sci.,
53, 2217–2231, https://doi.org/10.1175/1520-0469(1996)053<2217:maacii>2.0.co;2, 1996. a
                    
                
                        
                        Itoh, H. and Kimoto, M.: Chaotic itinerancy with preferred transition routes
appearing in an atmospheric model, Physica D, 109,
274–292, https://doi.org/10.1016/S0167-2789(97)00064-X, 1997. a
                    
                
                        
                        Izhikevich, E. M.: Dynamical Systems in Neuroscience: The Geometry of
Excitability and Bursting, MIT Press, ISBN 978-0-262-09043-8, 2006. a
                    
                
                        
                        Kallen, E.: The Nonlinear Effects of Orographic and Momentum Forcing in a
Low-Order, Barotropic Model, J. Atmos. Sci., 38,
2150–2163,
1981. a
                    
                
                        
                        Kallenberg, O.: Random Measures, Theory and Applications, vol. 77 of
Probability Theory and Stochastic Modelling, Springer International
Publishing, Cham, https://doi.org/10.1007/978-3-319-41598-7, 2017. a
                    
                
                        
                        Kimoto, M. and Ghil, M.: Multiple Flow Regimes in the Northern Hemisphere
Winter. Part I: Methodology and Hemispheric Regimes, J.
Atmos. Sci., 50, 2625–2644,
https://doi.org/10.1175/1520-0469(1993)050<2625:mfritn>2.0.co;2, 1993. a
                    
                
                        
                        Kondrashov, D., Ide, K., and Ghil, M.: Weather Regimes and Preferred
Transition Paths in a Three-Level Quasigeostrophic Model, J.
Atmos. Sci., 61, 568–587,
https://doi.org/10.1175/1520-0469(2004)061<0568:WRAPTP>2.0.CO;2, 2004. a
                    
                
                        
                        Kwasniok, F.: Enhanced regime predictability in atmospheric low-order models
due to stochastic forcing, Philos. T. Roy. Soc.
A, 372,
20130286–20130286, https://doi.org/10.1098/rsta.2013.0286, 2014. a, b
                    
                
                        
                        Lai, Y. C. and Tél, T.: Introduction to Transient Chaos, Appl.
Math. Sci.-Switzerland, 173, 3–35,
https://doi.org/10.1007/978-1-4419-6987-3_1, 2011a. a
                    
                
                        
                        Lai, Y. C. and Tél, T.: Noise and Transient Chaos, Appl. Math.
Sci.-Switzerland, 173, 107–143, https://doi.org/10.1007/978-1-4419-6987-3_4,
2011b. a, b, c, d
                    
                
                        
                        Lorenz, E. N.: Deterministic nonperiodic flow, Universality in Chaos, 2nd edn., 20, 367–378, https://doi.org/10.1201/9780203734636, 1963. a, b
                    
                
                        
                        Lucarini, V. and Gritsun, A.: A new mathematical framework for atmospheric
blocking events, Clim. Dynam., 54, 575–598,
https://doi.org/10.1007/S00382-019-05018-2, 2019. a
                    
                
                        
                        Maiocchi, C. C., Lucarini, V., and Gritsun, A.: Decomposing the dynamics of
the Lorenz 1963 model using unstable periodic orbits: Averages, transitions,
and quasi-invariant sets, Chaos: An Interdisciplinary Journal of Nonlinear
Science, 32, 033129, https://doi.org/10.1063/5.0067673, 2022. a
                    
                
                        
                        Meurer, A., Smith, C. P., Paprocki, M., Čertík, O., Kirpichev,
S. B., Rocklin, M., Kumar, A. T., Ivanov, S., Moore, J. K., Singh, S.,
Rathnayake, T., Vig, S., Granger, B. E., Muller, R. P., Bonazzi, F., Gupta,
H., Vats, S., Johansson, F., Pedregosa, F., Curry, M. J., Terrel, A. R.,
Roučka, Š., Saboo, A., Fernando, I., Kulal, S., Cimrman, R., and
Scopatz, A.: SymPy: Symbolic computing in python, PeerJ Comput. Sci.,
2017, e103, https://doi.org/10.7717/peerj-cs.103, 2017.
 a
                    
                
                        
                        Ott, E.: Chaotic transitions, in: Chaos in Dynamical Systems, edited by:
Ott, E., Cambridge University Press, Cambridge, 2nd edn., 283–294,
https://doi.org/10.1017/CBO9780511803260.010, 2002. a
                    
                
                        
                        Palmer, T. N. and Weisheimer, A.: Diagnosing the causes of bias in climate
models – why is it so hard?, Geophys. Astrophys. Fluid Dynam.,
105, 351–365, https://doi.org/10.1080/03091929.2010.547194, 2011. a
                    
                
                        
                        Pickl, M., Lang, S. T., Leutbecher, M., and Grams, C. M.: The effect of
stochastically perturbed parametrisation tendencies (SPPT) on rapidly
ascending air streams, Q. J. Roy. Meteor.
Soc., 148, 1242–1261, https://doi.org/10.1002/QJ.4257, 2022. a
                    
                
                        
                        Pusuluri, K. and Shilnikov, A.: Homoclinic chaos and its organization in a
nonlinear optics model, Phys. Rev. E, 98, 040202,
https://doi.org/10.1103/PhysRevE.98.040202, 2018. a
                    
                
                        
                        Reimann, P.: Noisy one-dimensional maps near a crisis. I. Weak Gaussian white
and colored noise, J. Statist. Phys., 82, 1467–1501,
https://doi.org/10.1007/BF02183392, 1996. a, b, c
                    
                
                        
                        Reinhold, B. B. and Pierrehumbert, R. T.: Dynamics of Weather Regimes:
Quasi-Stationary Waves and Blocking, Mon. Weather Rev., 110,
1105–1145, https://doi.org/10.1175/1520-0493(1982)110<1105:dowrqs>2.0.co;2, 1982. a
                    
                
                        
                        Romeiras, F. J., Grebogi, C., and Ott, E.: Multifractal properties of snapshot
attractors of random maps, Phys. Rev. A, 41, 784–799,
https://doi.org/10.1103/PhysRevA.41.784, 1990. a
                    
                
                        
                        Rossby, C. G.: Planetary flow patterns in the atmosphere, Q. J. Roy.
Meteor. Soc., 66, 68–87,
1940. a
                    
                
                        
                        Selten, F. M. and Branstator, G.: Preferred Regime Transition Routes and
Evidence for an Unstable Periodic Orbit in a Baroclinic Model, J.
Atmos. Sci., 61, 2267–2282,
https://doi.org/10.1175/1520-0469(2004)061<2267:prtrae>2.0.co;2, 2004. a
                    
                
                        
                        Shen, B. W., Pielke, R. A., Zeng, X., Baik, J. J., Faghih-Naini, S., Cui, J.,
and Atlas, R.: Is weather chaotic? Coexistence of chaos and order within a
generalized lorenz model, B. Am. Meteorol. Soc.,
102, E148–E158, https://doi.org/10.1175/BAMS-D-19-0165.1, 2021. a
                    
                
                        
                        Shilnikov, A., Nicolis, G., and Nicolis, C.: Bifurcation and predictability
analysis of a low-order atmopsheric circulation model, Int. J. Bifurcation and Chaos, 05, 1701–1711, https://doi.org/10.1142/S0218127495001253,
1995. a, b
                    
                
                        
                        Strommen, K., Chantry, M., Dorrington, J., and Otter, N.: A topological perspective on weather regimes, Clim. Dynam., https://doi.org/10.1007/s00382-022-06395-x, 2022. a
                    
                
                        
                        Wackerbauer, R. and Kobayashi, S.: Noise can delay and advance the collapse of
spatiotemporal chaos, Phys. Rev. E, 75, 066209,
https://doi.org/10.1103/PhysRevE.75.066209, 2007. a
                    
                
                        
                        Yang, S., Reinhold, B., and Källé, E.: Multiple Weather Regimes
and Baroclinically Forced Spherical Resonance, J. Atmos.
Sci., 54, 1397–1409,
https://doi.org/10.1175/1520-0469(1997)054<1397:MWRABF>2.0.CO;2, 1997. a
                    
                Short summary
            Atmospheric models often include random forcings, which aim to replicate the impact of processes too small to be resolved. Recent results in simple atmospheric models suggest that this random forcing can actually stabilise certain slow-varying aspects of the system, which could provide a path for resolving known errors in our models. We use randomly forced simulations of a 
            toychaotic system and theoretical arguments to explain why this strange effect occurs – at least in simple models.
Atmospheric models often include random forcings, which aim to replicate the impact of processes...
            
         
 
             
             
            