Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model

Nonlinear Processes in Geophysics Discussions

Politi, Antonio^1^1,15,158  Carlu, Mallory^1^1,19,192  Ginelli, Francesco^1^3,37,372  Lucarini, Valerio^2^3,39,393 

[1] Binghamton University^204;New York State Education Department-Office of Professions^199;A full list of authors and their affiliations appears at the end of the paper^370;A full list of authors appears at the end of the paper^388;AIST – National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan^435;ARC Centre of Excellence in Cognition and its Disorders, Australia^177;ARC Centre of Excellence in Cognition and its Disorders, Macquarie University, Sydney, NSW, Australia^67;Academic Medical Center, University of Amsterdam, Amsterdam, the Netherlands^175;Accademia dei Georgofili – Florence, Italy^235;AgeLab, Massachusetts Institute of Technology, Cambridge, MA, USA^169;Alfred Wegener Institute, Helmholtz Center for Polar and Marine Research, 27568 Bremerhaven, Germany^408;AltaRock Energy, Seattle, WA, USA^433;Altai State University, Lenina, 61, Barnaul 656049, Russia^450;Antarctic Climate and Ecosystems CRC, University of Tasmania, Hobart, 7001, TAS, Australia^333;Antarctic Research Centre, Victoria University of Wellington, Wellington, 6140, New Zealand^390;Australian Nuclear Science and Technology Organisation, Lucas Heights 2234, Australia^250;Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, Australia^329;BRGM, Avenue C. Guillemin, 45100 Orléans, France^284;Basque Meteorology Agency (EUSKALMET), Vitoria-Gasteiz, Basque Country, Spain^231;Bassett Healthcare Network – Bassett Medical Center^200;Beijing Key Laboratory of Behavior and Mental Health, Peking University, Beijing, China^173;Berkeley Geochronology Center, 2455 Ridge Rd., Berkeley CA 94709, USA^375;Biodiversity Institute and Department of Ecology and Evolutionary Biology, The University of Kansas, Dyche Hall, Lawrence, Kansas 66045–7561, USA^458;Bioengineering Graduate Group, University of Pennsylvania, Philadelphia, PA, USA^37;Biological Psychology and Neuropsychology, University of Hamburg, Hamburg, Germany^138;British Antarctic Survey, Cambridge, CB3 0ET, UK^331;British Geological Survey, UK^364;Bundesamt für Kartographie und Geodäsie (BKG), Richard-Strauss-Allee 11, 60598 Frankfurt, Germany^310;CAS Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Beijing, China^13;CEED, University of Oslo, Oslo, Norway^334;CEN, University of Hamburg, Hamburg, Germany^464;CHRU-Nancy, Service de Neurologie, F-54000, Nancy, France^187;CIRAD, Bobo Dioulasso, Burkina Faso^211;CMLA, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France^223;CNRS (Integrative Neuroscience and Cognition Center, UMR 8002), Paris, France^193;CNRS (Laboratoire Psychologie de la Perception, UMR 8242), Paris, France^124;COMiB - Optics and Optometry Research Center, Università degli Studi di Milano-Bicocca, Milano, Italy^116;CSIR-National Institute of Oceanography, Dona Paula, Goa-403 004, India^427;California Institute of Technology, Pasadena, CA 91125, USA^409;Canadian Action and Perception Network (CAPnet)^64;Castleton University^198;Center for Advanced Marine Core Research, Kochi University, Nankoku, Japan^425;Center for Advanced Retinal and Ocular Therapeutics, University of Pennsylvania, Philadelphia, PA, USA^5;Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, USA^230;Center for Behavioral Brain Sciences, Magdeburg, Sachsen-Anhalt, Germany^103;Center for Brain Health, University of British Columbia, Vancouver, Canada^96;Center for Global Sea Level Change, NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates^227;Center for Mind and Brain, University of California, Davis, CA, USA^39;Center for Mind/Brain Sciences (CIMeC), University of Trento, Rovereto, Italy^160;Center for Neural Science, New York University, New York, NY, USA^6;Center for Visual Science, University of Rochester, Rochester, NY, USA^31;Center of Excellence for Climate Change Research, Department of Meteorology, King Abdulaziz University, Jeddah, Saudi Arabia^238;Centre Européen de Recherche et d'Enseignement des Géosciences de l'Environnement, Aix-en-Provence, France^367;Centre National de la Recherche Scientifique, Toulouse Cedex, France^26;Centre for Elite Performance, Expertise and Training (CEPET), Macquarie University, Sydney, NSW, Australia^68;Centre for Elite Performance, Training & Expertise, Macquarie University, Sydney, Australia^179;Centre for Life and Environmental Sciences, University of Exeter, Penryn, UK^69;Centre for Neuroscience Studies, Queen's University, Kingston, ON, Canada^63;Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK^463;Centro de Estudios Avanzados en Zonas Áridas (CEAZA), Raúl Bitrán 1305, La Serena, Chile^266;Centro de Geociencias, Universidad Nacional Autónoma de México (UNAM), Boulevard Juriquilla No. 3001, Querétaro 76230, México^385;Climate Impacts Group, University of Washington, Seattle, WA 98105, USA^403;Cluster of Excellence, Cognitive Interaction Technology, Bielefeld University, Bielefeld, Germany^20;Cognitive Science Program and Department of Psychology, Bogazici University, Istanbul, Turkey^182;Cognitive Science Program, Bogazici University, Istanbul, Turkey^180;Cognitive Systems Group, Department of Computer Science, Reutlingen University, Germany^82;Collections and Systematics Department, Icelandic Institute of Natural History, Gardabaer, Iceland^356;College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China^313;College of Dentistry, New York University, New York, NY, USA^38;College of Marine Science, University of South Florida, Saint Petersburg, FL 33701, USA^410;Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA^168;Consiglio Nazionale delle Ricerche (CNR), Institute of Neuroscience, Pisa, Italy^77;Continental Scientific Drilling Coordination Office and LacCore Facility, N.H. Winchell School of Earth Sciences, University of Minnesota, Minneapolis, MN 55455, USA^383;Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, CO, USA^246;D.O. Terre et Histoire de la Vie, Institut royal des Sciences naturelles de Belgique, Brussels, 1000, Belgium^454;DOSECC Exploration Services, Salt Lake City, Utah, USA^357;Decker School of Nursing^203;Departament of Civil and Environmental Engineering, UPC-BarcelonaTECH, C. Jordi Girona 1–3, 08034 Barcelona, Spain^282;Departemento de Paleontología de Vertebrados, Museo de Historia Natural-Universidad, Lima, 15072, Peru^457;Department F.-A. 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Box 1047, Blindern, Oslo 0316, Norway^379;Department of Geosciences, University of Texas at Dallas, Richardson, TX 75080, USA^372;Department of Geosciences, University of Tuebingen, Wilhelmstrasse 56, 72074 Tuebingen, Germany^263;Department of Geosciences, Universität Tübingen, 72074, Germany^311;Department of Human Movement Sciences, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands^22;Department of Hydraulic Engineering, Delft University of Technology, P.O. 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Rennes, CNRS, UMR 6118, 35000 Rennes, France^446;HS Orka, Svartsengi, Iceland^436;Hawaii Groundwater and Geothermal Resources Center, University of Hawai`i at Manoa, 1680 East West Road, Honolulu, HI 96822, USA^341;Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, CA, USA^105;Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Potsdam, Germany^346;Helmholtz Centre Potsdam, German Research Center for Geosciences (GFZ), Telegrafenberg, 14473 Potsdam, Germany^259;Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ), Section 1.2: Global Geomonitoring and Gravity Field, c/o DLR Oberpfaffenhofen, Münchener Strasse 20, 82234 Wessling, Germany^305;Helmholtz Zentrum Potsdam, GeoForschungsZentrum (GFZ) Potsdam, 14473 Potsdam, Germany^256;Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum, Potsdam, Germany^339;Howard Hughes Medical Institute, New York University, New York, NY, USA^7;Human Vision and Eye Movement Laboratory, Departments of Medicine (Neurology), Ophthalmology and Visual Sciences, University of British Columbia, Vancouver, BC, Canada^111;Hungarian Meteorological Service, Budapest, Hungary^225;IMT School for Advanced Studies Lucca, Lucca, Italy^139;INGV – Osservatorio Vesuviano, Naples, Italy^438;IQ-Hydrology, Ben van Londenstraat 48, 6709 TM Wageningen, the Netherlands^320;ISAE-Supaéro, Université Fédérale de Toulouse, Toulouse, France^188;Institut Universitaire de France, Paris, France^159;Institut de Physique du Globe de Paris, Paris, France^437;Institut de Physique du Globe de Strasbourg, CNRS UMR 7516, EOST/Université de Strasbourg, 5 rue Descartes, 67084 Strasbourg CEDEX, France^278;Institut de la Vision, Paris, France^28;Institut für Erd- und Umweltwissenschaften, Universität Potsdam, 14476 Potsdam, Germany^257;Institut für Geographie und Geologie, Universität Würzburg, Würzburg, Germany^362;Institute for Computing, Information and Cognitive Systems, University of British Columbia, Vancouver, Canada^97;Institute for Environmental Analytics, Reading, UK^244;Institute for Environmental Sciences, University of Geneva, Boulevard Carl-Vogt 66, 1205 Geneva, Switzerland^288;Institute for Marine and Antarctic Studies (IMAS), University of Tasmania, Hobart, TAS 7001, Australia^417;Institute for Psychology and Otto Creutzfeldt Center for Cognitive and Behavioral Neuroscience, University of Muenster, Münster, Germany^99;Institute of Biology II, RWTH Aachen University, Aachen, Germany^153;Institute of Biology, Otto-von-Guericke University, Magdeburg, Sachsen-Anhalt, Germany^102;Institute of Biometeorology of the National Research Council (IBIMET-CNR) – Florence, Italy^233;Institute of Cognitive Neuroscience, University College London, London, UK^88;Institute of Earth and Environmental Science, Potsdam University, Potsdam, Germany^261;Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland^217;Institute of Geological Sciences, University of Bern, Baltzerstrasse 1+3, 3012, Bern, Switzerland^290;Institute of Information and Communication Technologies, Electronics, and Applied Mathematics and Institute of Neuroscience, Université catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium^62;Institute of Life Sciences and Technologies, Daugavpils University, Vienības 13, Daugavpils, 5401, Latvia^439;Institute of Mountain Hazards and Environment, Chinese Academy of Sciences and Ministry of Water Conservancy, Chengdu 610041, China^317;Institute of Neuroscience, Newcastle University, Newcastle upon Tyne, UK^60;Institute of Physics, Chemnitz University of Technology, Chemnitz, Germany^122;Institute of Psychology, Chinese Academy of Sciences, Beijing, China^130;Institute of Psychology, Westfälische Wilhelms-Universität, Münster, Germany^191;Institute of Systematics and Ecology of Animals, Siberian Branch, Russian Academy of Sciences, Frunze Street 11, Novosibirsk 630091, Russia^449;Institute of Systematics and Ecology of Animals, Siberian Branch, Russian Academy of Sciences, Frunze Street, 11, Novosibirsk 630091, Russia^440;Instituto de Ciencias Básicas e Ingeniería, Museo de Paleontología, Centro de Investigaciones Biológicas, Universidad Autónoma del Estado de Hidalgo, Mineral de la Reforma, Hidalgo, Mexico^459;Istituto Nazionale di Geofisica e Vulcanologia (INGV), 00143 Rome, Italy^398;Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokohama 236-0001, Japan^411;Jarðtaeknistofan, (GEOICE Geological Services Ltd), Hafnarfjörður, Iceland^354;Jasti V Ramanamma Children's Eye Care Center, Child Sight Institute, LV Prasad Eye Institute, Hyderabad, India^140;K.G. Jebsen Centre for Deep Sea Research, Department of Earth Science, University of Bergen, Bergen, Norway^355;Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning 530004, China^314;Kochi Institute for Core Sample Research, JAMSTEC, Nankoku, Kochi 783-8502, Japan^412;Korea Polar Research Institute, Incheon, 21990, Korea^401;Laboratoire Vision Action Cognition, EA 7326, Institut de Psychologie, Institut de Neurosciences et Cognition (INC), Université Paris Descartes, Sorbonne-Paris-Cité, Boulogne-Billancourt, France^158;Laboratoire d'Aérologie, Université de Toulouse, CNRS, UPS, Toulouse, France^228;Laboratoire de Géologie, Ecole Normale Supérieure, 24 Rue Lhomond, 75000, Paris, France^260;Laboratory of Brain Processes (LOBES), Center for Cognitive and Brain Sciences, Center for Cognitive and Behavioral Brain Imaging, and Departments of Psychology, The Ohio State University, Columbus, OH, USA^15;Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Zurich, Switzerland^215;Laboratory of Monitoring and Environmental Modelling for the Sustainable Development (LaMMA consortium) – Sesto Fiorentino – Florence, Italy^234;Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA^371;Leibniz Institute for Research on Society and Space, Erkner, Germany^208;Lemoyne College^202;Liverpool John Moores University, School of Sport and Exercise Sciences, Liverpool, UK^146;MARUM Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany^380;MINES ParisTech, PSL Research University, O.I.E. – Centre for Observation, Impacts, Energy, Antipolis, France^241;Marine Parade, Macandrew Bay, Dunedin, New Zealand^395;Martin-Luther-Universität, Halle-Wittenberg, Institut für Geowissenschaften, Von-Seckendorff-Platz 3, 06120 Halle (Saale), Germany^386;Matís, Exploration & Utilization of Genetic Resources, Reykjavík, Iceland^347;Max Planck Institute for Biological Cybernetics, Tübingen, Germany^83;McGill Vision Research, Department of Ophthalmology, McGill University, Montreal, Canada^74;McGovern Institute for Brain Research, Peking University, Beijing, China^172;Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 220 S 33rd St, Philadelphia, PA 19104, USA^287;Meridian Energy, Twizel, 7901, New Zealand^402;Met Office Hadley Centre, Exeter, UK^240;Met Éireann, 65/67 Glasnevin Hill, Dublin 9, D09Y921, Ireland^221;Meteorology Area, Energy and Environment Division, TECNALIA R & I, Vitoria-Gasteiz, Basque Country, Spain^232;Museum für Naturkunde, Leibniz-Institut für Evolutions- und Biodiversitätsforschung, Berlin, Germany^447;Museum für Naturkunde, Leibniz-Institut für Evolutions- und Biodiversitätsforschung, Invalidenstraße 43, 10115 Berlin, Germany^443;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Kanagawa, Japan^107;NYU-ECNU Institute of Brain and Cognitive Science, New York University Shanghai, Shanghai, PRC^98;Nansen Environmental and Remote Sensing Center, Bjerknes Centre for Climate Research, Thormøhlens gate 47, 5006 Bergen, Norway^265;National Centre for Antarctic and Ocean Research, Vāsco Da Gāma, Goa-403 804, India^413;National Institute of Water and Atmosphere, Wellington, 6021, New Zealand^404;National Oceanography Centre, Southampton, University of Southampton, Southampton, SO17 1BJ, UK^382;Natural History Museum of Denmark, University of Copenhagen, Copenhagen, 1350, Denmark^452;Natural History Museum of Utah and Department of Geology & Geophysics, University of Utah, Salt Lake City, UT 84108, USA^376;Netherlands Institute for Neuroscience, Amsterdam, the Netherlands^174;Neural Science Program, NYU-ECNU Institute of Brain and Cognitive Science, New York University Shanghai, Shanghai, PRC^43;NeuroMI - Milan Center for Neuroscience, Milano, Italy^112;Neurobiopsychology, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany^117;Neuropsychology Unit, IRCCS Fondazione Santa Lucia, Rome, Italy^114;Neuroscience Graduate Group, University of Pennsylvania, Philadelphia, PA, USA^36;Neuroscience Institute, NYU Langone Medical Center, New York, NY, USA^12;Neuroscience and Mental Health Institute, University of Alberta, Edmonton, Alberta, Canada^49;Neuroscience, Erasmus MC, Rotterdam, the Netherlands^52;Neurosciences Graduate Program, Stanford University, Stanford, CA, USA^59;Nordvulk, Institute of Earth Sciences, University of Iceland, Reykjavík, Iceland^343;Norsar, Gunnar Randers Vei 15, 2007 Kjeller, Norway^280;Optometry and Vision Science, University of Canberra, Canberra, Australia^126;Oregon State University, College of Earth, Ocean and Atmospheric Sciences, Corvallis, OR, USA^432;Organic Geochemistry Group, MARUM Center for Marine Environmental Sciences, University of Bremen, 28359 Bremen, Germany^416;Otto Creutzfeldt Center for Cognitive and Behavioral Neuroscience, Westfälische Wilhelms-Universität, Münster, Germany^192;Pacific Marine Environmental Laboratory, NOAA, Seattle, WA 98115, USA^405;Pacific Northwest National Laboratory, Richland, WA, USA^431;Paralign, Inc., San Francisco, CA, USA^151;Perception in Action Research Centre & Department of Cognitive Science, Faculty of Human Sciences, Macquarie University, Sydney, Australia^176;Perception in Action Research Centre (PARC), Department of Cognitive Science, Faculty of Human Sciences, Macquarie University, Sydney, NSW, Australia^66;Petrified Forest National Park, Petrified Forest, AZ 86028, USA^377;Preferred Mutual Insurance Company^196;Present address: Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Charlestown, MA, USA^148;Present address: Center for Perceptual Systems, The University of Texas at Austin, Austin, TX, USA^8;Present address: Department of Experimental Psychology, Ghent University, Ghent, Belgium^189;Present address: Department of Psychology, Royal Holloway, University of London, London, UK^181;Princeton Neuroscience Institute, Princeton University, Princeton, NJ, USA^104;Program in Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Ontario, Canada^91;Psychological Sciences Research Institute & Institute of Neuroscience, University of Louvain, Belgium^184;Psychology Department, University of Milano-Bicocca, Milano, Italy^115;Psychology Department, Università La Sapienza, Roma, Italy^113;Radboud University, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, the Netherlands^21;Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan^110;Research School of Earth Sciences, Australian National University, Canberra 0200, Australia^251;Research School of Earth Sciences, Australian National University, Canberra, 0200, Australia^406;Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany^448;SUNY Polytechnic^194;SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK^461;Scheie Eye Institute, Department of Ophthalmology, University of Pennsylvania, Philadelphia, PA, USA^2;Schmalhausen Institute of Zoology, National Academy of Sciences of Ukraine, B. Khmel'nyts'koho 15, Kiev 01601, Ukraine^451;School of Arts and Design, Zhengzhou University of Light Industry, Zhengzhou, Henan, China^17;School of Civil Engineering, The University of Queensland, St Lucia QLD, 4072, Australia^396;School of Earth Sciences and Environmental Sustainability, Northern Arizona University, AZ 86011, USA^400;School of Earth Sciences, University of Melbourne, Melbourne, Australia^324;School of Earth and Environmental Sciences, University of Adelaide, Adelaide, SA, Australia^328;School of Earth and Environmental Sciences, University of Wollongong, Wollongong 2522, Australia^248;School of Environment, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand^428;School of Geography, University of Melbourne, Melbourne, Australia^326;School of Geography, University of Nottingham, Nottingham, UK^327;School of Geology, Environment and Earth Sciences, Victoria University of Wellington, Wellington, 6140, New Zealand^391;School of Geosciences, The University of Sydney, Sydney, NSW2006, Australia^407;School of Information Science, Yunnan University, Kunming, China^161;School of Mathematics and Statistics, University College Dublin, Dublin, Ireland^222;School of Natural Sciences and Centre for Ore Deposit and Earth Sciences (CODES), University of Tasmania, Hobart, TAS 7001, Australia^426;School of Natural Sciences, University of Tasmania, Hobart, Australia^358;School of Natural and Built Environment, Queen's University Belfast, Belfast, UK^330;School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China^16;School of Ophthalmology and Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, China^72;School of Optometry & Vision Science, University of Auckland, Auckland, New Zealand^90;School of Optometry and Vision Science Graduate Group, University of California, Berkeley, Berkeley, CA, USA^3;School of Optometry and Vision Science, and New Zealand National Eye Centre, University of Auckland, Auckland, New Zealand^125;School of Optometry, University of California, Berkeley, Berkeley, CA, USA^55;School of Optometry, University of California–Berkeley, Berkeley, CA, USA^135;School of Psychological and Cognitive Sciences, Peking University, Beijing, China^171;School of Psychology, Cardiff University, Cardiff, Wales, UK^41;School of Psychology, The University of Sydney, New South Wales, Australia^78;School of Psychology, UNSW Sydney, Sydney, Australia^80;School of Psychology, University of Nottingham, Nottingham, UK^157;Science Division, New York University - Abu Dhabi, Abu Dhabi, United Arab Emirates^79;Section Computational Sensomotorics, Department of Cognitive Neurology, UKT, Germany^85;Section Computational Sensomotorics, Department of Cognitive Neurology, University Clinic Tübigen, Germany^86;Section Computational Sensomotorics, Department of Cognitive Neurology, University Clinic, Tübigen, Germany^81;Senckenberg Biodiversity and Climate Research Center (BiK-F), Senckenberganlage 25, 60325 Frankfurt, Germany^268;Senckenberg Biodiversity and Climate Research Centre (BiK-F), Senckenberganlage 25, 60325 Frankfurt, Germany^262;Service Géologique de Nouvelle-Calédonie, Nouméa, New Caledonia^420;Shenzhen Key Lab of Neuropsychiatric Modulation, Guangdong Key Lab of Brain Connectomics, CAS Center for Excellence in Brain Science and Intelligence Technology, the Brain Cognition and Brain Disease Institute (BCBDI), Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China^152;Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA^136;Soil Erosion and Conservation Research Group, CEBAS-CSIC, Spanish National Research Council, Campus Universitario Espinardo, 30100, P.O. Box 164, Murcia, Spain^319;State Key Laboratory of Brain and Cognitive Science, Institute of Biophysics, Chinese Academy of Sciences, Beijing, China^150;State Key Laboratory of Ophthalmology, Optometry and Vision Science, Wenzhou Medical University, Wenzhou, China^73;State Key Laboratory of Palaeobiology and Stratigraphy, Nanjing Institute of Geology and Paleontology and Center for Excellence in Life and Paleoenvironment, Nanjing 210008, China^387;Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland^213;Swiss Federal Research Institute WSL, Birmensdorf, 8903, Switzerland^323;Swiss Federal Research Institute WSL, Zürcherstrasse 111, 8903 Birmensdorf, Switzerland^289;Technische Universität Dresden, Institut für Planetare Geodäsie, 01062 Dresden, Germany^309;The Australian Archaeomagnetism Laboratory, Department of Archaeology and History, La Trobe University, Melbourne Campus, Bundoora, 3086, VIC, Australia^325;The Helen Wills Neuroscience Institute, University of California–Berkeley, Berkeley, CA, USA^137;Theoretical Neuroscience Group, Dept. of Psychology, UMR Marburg, Germany^84;Tomsk State University, Lenina Prospekt 36, Tomsk 634050, Russia^441;U.S. Geological Survey, Menlo Park, California, USA^359;UCL Institute of Ophthalmology, University College London, London, UK^127;UEA, School of Environmental Sciences, Norwich, UK^236;URPP Language and Space, University of Zürich, Zürich, Switzerland^207;Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000 Grenoble, France^279;University at Albany^195;University of Bradford, School of Engineering, Bradford, West Yorkshire, UK^143;University of Bradford, School of Health Studies, Bradford, West Yorkshire, UK^145;University of Bradford, School of Optometry and Vision Science, Bradford, West Yorkshire, UK^141;University of Hawai`i at Hilo, 200 W. 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DOI  :  10.5194/npg-26-73-2019

学科分类：地球科学(综合)

来源: Copernicus Publications

【 摘 要 】

We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models.

【 授权许可】

CC BY