{"id":56088,"date":"2021-06-15T09:50:00","date_gmt":"2021-06-15T08:50:00","guid":{"rendered":"https:\/\/www.lse.ac.uk\/granthaminstitute\/?post_type=publication&p=56088"},"modified":"2022-06-30T10:19:57","modified_gmt":"2022-06-30T09:19:57","slug":"on-generalized-langevin-dynamics-and-the-modelling-of-global-mean-temperature","status":"publish","type":"publication","link":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/on-generalized-langevin-dynamics-and-the-modelling-of-global-mean-temperature\/","title":{"rendered":"On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature (In: \u2018Unifying Themes in Complex Systems X\u2019)"},"content":{"rendered":"\n

Climate science employs a hierarchy of models, trading the tractability of simplified energy balance models (EBMs) against the detail of Global Circulation Models. Since the pioneering work of Hasselmann, stochastic EBMs have allowed treatment of climate fluctuations and noise. However, it has recently been claimed that observations motivate heavy-tailed temporal response functions in global mean temperature to perturbations. Our complementary approach exploits the correspondence between Hasselmann’s EBM and the original mean-reverting stochastic model in physics, Langevin’s equation of 1908. We propose mapping a model well known in statistical mechanics, the Mori-Kubo Generalised Langevin Equation (GLE) to generalise the Hasselmann EBM. If present, long range memory then simplifies the GLE to a fractional Langevin equation (FLE). We describe the corresponding EBMs that map to the GLE and FLE, briefly discuss their solutions, and relate them to Lovejoy’s new Fractional Energy Balance Model.<\/p>\n\n\n\n

Watkins N.W., Chapman S.C., Chechkin A., Ford I., Klages R., Stainforth D.A. (2021) On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature. In: Braha D. et al. (eds) Unifying Themes in Complex Systems X. ICCS 2020. Springer Proceedings in Complexity. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-030-67318-5_29<\/em><\/strong><\/p>\n\n","protected":false},"excerpt":{"rendered":"\n

Our complementary approach exploits the correspondence between Hasselmann’s EBM and the original mean-reverting stochastic model in physics, Langevin’s equation of 1908. We propose mapping a model well known in statistical mechanics, the Mori-Kubo Generalised Langevin Equation (GLE) to generalise the Hasselmann EBM. <\/p>\n\n","protected":false},"author":12,"featured_media":0,"template":"","tags":[830,398],"publication-type":[238],"topic_area":[],"class_list":["post-56088","publication","type-publication","status-publish","hentry","tag-climate-change-modelling","tag-climate-sensitivity","publication-type-books"],"acf":{"exclude_from_sync":{"ref_value":"field_560538b0e7350","value":"1","type":false,"post_type":""},"downloads":{"ref_value":"field_52f16cc1a80f2","value":false,"type":"repeater","post_type":""},"rss_newsletter":{"ref_value":"field_54f5c2c1544d8","value":"","type":false,"post_type":""},"profile_link":{"ref_value":"field_52f164b5189e9","value":["nick-watkins","david-stainforth"],"type":"relationship","post_type":"profile"},"article_link":{"ref_value":"field_52eee3c7f0586","value":"https:\/\/link.springer.com\/chapter\/10.1007%2F978-3-030-67318-5_29","type":false,"post_type":""},"article_link_title":{"ref_value":"field_5322399d89d42","value":"external link to article","type":false,"post_type":""},"spotlight":{"ref_value":"field_52f80896506d3","value":"","type":false,"post_type":""}},"yoast_head":"\nOn Generalized Langevin Dynamics and the Modelling of Global Mean Temperature (In: \u2018Unifying Themes in Complex Systems X\u2019) - Grantham Research Institute on climate change and the environment<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/on-generalized-langevin-dynamics-and-the-modelling-of-global-mean-temperature\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature (In: \u2018Unifying Themes in Complex Systems X\u2019) - Grantham Research Institute on climate change and the environment\" \/>\n<meta property=\"og:description\" content=\"Our complementary approach exploits the correspondence between Hasselmann\u2019s EBM and the original mean-reverting stochastic model in physics, Langevin\u2019s equation of 1908. 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