Articles | Volume 17, issue 4
https://doi.org/10.5194/gmd-17-1765-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-17-1765-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Towards variance-conserving reconstructions of climate indices with Gaussian process regression in an embedding space
Marlene Klockmann
CORRESPONDING AUTHOR
Institute for Coastal Systems – Analysis and Modelling, Helmholtz-Zentrum Hereon, Geesthacht, Germany
now at: Institute of Oceanography, Universität Hamburg, Hamburg, Germany
Udo von Toussaint
Max Planck Institute for Plasma Physics, Garching, Germany
Eduardo Zorita
Institute for Coastal Systems – Analysis and Modelling, Helmholtz-Zentrum Hereon, Geesthacht, Germany
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Cited articles
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X.: TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems, https://www.tensorflow.org/ (last access 22 February 2024), 2015. a
Barboza, L., Li, B., Tingley, M. P., and Viens, F. G.: Reconstructing past temperatures from natural proxies and estimated climate forcings using short- and long-memory models, Ann. Appl. Stat., 8, 1966–2001, 2014. a
Büntgen, U., Allen, K., Anchukaitis, K. J., Arseneault, D., Boucher, É., Bräuning, A., Chatterjee, S., Cherubini, P., Churakova, O. V., Corona, C., Gennaretti, F., Grießinger, J., Guillet, S., Guiot, J., Gunnarson, B., Helama, S., Hochreuther, P., Hughes, M. K., Huybers, P., Kirdyanov, A. V., Krusic, P. J., Ludescher, J., Meier, W. J.-H., Myglan, V. S., Nicolussi, K., Oppenheimer, C., Reinig, F., Salzer, M. W., Seftigen, K., Stine, A. R., Stoffel, M., St. George, S., Tejedor, E., Trevino, A., Trouet, V., Wang, J., Wilson, R., Yang, B., Xu, G., and Esper, J.: The influence of decision-making in tree ring-based climate reconstructions, Nat. Commun., 12, 1–10, 2021. a
Christiansen, B., Schmith, T., and Thejll, P.: A surrogate ensemble study of climate reconstruction methods: Stochasticity and robustness, J. Climate, 22, 951–976, https://doi.org/10.1175/2008JCLI2301.1, 2009. a
Clement, A., Bellomo, K., Murphy, L. N., Cane, M. A., Mauritsen, T., Rädel, G., and Stevens, B.: The Atlantic Multidecadal Oscillation without a role for ocean circulation, Science, 350, 320–324, https://doi.org/10.1126/science.aab3980, 2015. a
Duvenaud, D., Lloyd, J., Grosse, R., Tenenbaum, J., and Zoubin, G.: Structure discovery in nonparametric regression through compositional kernel search, in: International Conference on Machine Learning, edited by: Dasgupta, S. and McAllester, D., vol. 28, Proceedings of Machine Learning Research, PMLR, Atlanta, Georgia, USA, 1166–1174, https://proceedings.mlr.press/v28/duvenaud13.html (last access: 22 February 2024), 2013. a
Esper, J., Frank, D. C., Wilson, R. J., and Briffa, K. R.: Effect of scaling and regression on reconstructed temperature amplitude for the past millennium, Geophys. Res. Lett., 32, L07711, https://doi.org/10.1029/2004GL021236, 2005. a
Garuba, O. A., Lu, J., Singh, H. A., Liu, F., and Rasch, P.: On the relative roles of the atmosphere and ocean in the Atlantic multidecadal variability, Geophys. Res. Lett., 45, 9186–9196, https://doi.org/10.1029/2018GL078882, 2018. a
Gent, P. R., Danabasoglu, G., Donner, L. J., Holland, M. M., Hunke, E. C., Jayne, S. R., Lawrence, D. M., Neale, R. B., Rasch, P. J., Vertenstein, M., Worley, P. H., Yang, Z.-L., and Zhang, M.: The community climate system model version 4, J. Climate, 24, 4973–4991, https://doi.org/10.1175/2011JCLI4083.1, 2011. a, b
Giorgetta, M. A., Jungclaus, J., Reick, C., Legutke, S., Bader, J., Böttinger, M., Brovkin, V., Crueger, T., Esch, M., Fieg, K., Glushak, K., Gayler, V., Haak, H., Hollweg, H.-D., Ilyina, T., Kinne, S., Kornblueh, L., Matei, D., Mauritsen, T., Mikolajewicz, U., Mueller, W., Notz, D., Pithan, F., Raddatz, T., Rast, S., Redler, R., Roeckner, E., Schmidt, H., Schnur, R., Segschneider, J., Six, K., Stockhause, M., Timmreck, C., Wegner, J., Widmann, H., Wieners, K., Claussen, M., Marotzke, J., and Stevens, B.: Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for the Coupled Model Intercomparison Project phase 5, J. Adv. Model. Earth Sy., 5, 572–597, https://doi.org/10.1002/jame.20038, 2013. a
Gray, S. T., Graumlich, L. J., Betancourt, J. L., and Pederson, G. T.: A tree-ring based reconstruction of the Atlantic Multidecadal Oscillation since 1567 AD, Geophys. Res. Lett., 31, L12205, https://doi.org/10.1029/2004GL019932, 2004. a, b, c
Hanhijärvi, S., Tingley, M. P., and Korhola, A.: Pairwise comparisons to reconstruct mean temperature in the Arctic Atlantic Region over the last 2,000 years, Clim. Dynam., 41, 2039–2060, https://doi.org/10.1007/s00382-013-1701-4, 2013. a
Haustein, K., Otto, F. E., Venema, V., Jacobs, P., Cowtan, K., Hausfather, Z., Way, R. G., White, B., Subramanian, A., and Schurer, A. P.: A limited role for unforced internal variability in twentieth-century warming, J. Climate, 32, 4893–4917, https://doi.org/10.1175/JCLI-D-18-0555.1, 2019. a
Hensman, J., Fusi, N., and Lawrence, N. D.: Gaussian processes for Big data, in: Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, ArXiv [preprint], https://doi.org/10.48550/arXiv.1309.6835, 2013. a, b, c, d
Hunter, J. D.: Matplotlib: A 2D graphics environment, Comput. Sci. Eng., 9, 90–95, https://doi.org/10.1109/MCSE.2007.55, 2007. a
Jones, P. D. and Mann, M. E.: Climate over past millennia, Rev. Geophys., 42, RG2002, https://doi.org/10.1029/2003RG000143, 2004. a
Kilbourne, H., Yu, Z., Neukom, R., Nash, D., Gergis, J., Steig, E. J., Ge, Q., McKay, N. P., Kaufman, D. S., Curran, M. A. J., Thomas, E. R., Sigl, M., Thirumalai, K., Emile-Geay, J., Chen, M.-T., Seidenkrantz, M.-S., Turney, C., Jacques, J. S., Linderholm, H. W., Horiuchi, K., Björklund, J., Severi, M., Cook, E., Bertler, N., Isaksson, E., wahl, eugene, Leduc, G., Martrat, B., E Tierney, J., Goosse, H., Thamban, M., DeLong, K., Anchukaitis, K., Zinke, J., Uemura, R., Abram, N. J., Shao, X., Dixon, D., von Gunten, L., Wang, J., Addison, J., Evans, M. N., Henley, B., Zhixin, H., McGregor, H. V., Pederson, G. T., Stenni, B., Werner, J., Xu, C., Divine, D., Dixon, B. C., Mundo, I. A., Nakatsuka, T., Phipps, S. J., Routson, C., Tyler, J. J., Allen, K. J., Chase, B., de Jong, R., Ekaykin, A. A., Ersek, V., Filipsson, H. L., Francus, P., Freund, M., Frezzotti, M., Gaire, N., Gajewski, K., Gornostaeva, A., Grosjean, M., Hormes, A., Husum, K., Selvaraj, K., Kawamura, K., Nalan, K., Lorrey, A., Mikhalenko, V., Mortyn, G. P., Motoyama, H., Moy, A., Mulvaney, R., Munz, P., Oerter, H., Opel, T., Orsi, A., Ovchinnikov, D., Porter, T., Roop, H., Saenger, C., Sano, M., Sauchyn, D., Saunders, K., Sicre, M.-A., Sinclair, K., St George, S., Thapa, U., Viau, A., Vladimirova, D., and White, J.: A global multiproxy database for temperature reconstructions of the Common Era, figshare [data set], https://doi.org/10.6084/m9.figshare.c.3285353.v2, 2017. a
Kingma, D. P. and Ba, J.: Adam: A method for stochastic optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 2014. a
Knudsen, M. F., Jacobsen, B. H., Seidenkrantz, M.-S., and Olsen, J.: Evidence for external forcing of the Atlantic Multidecadal Oscillation since termination of the Little Ice Age, Nat. Commun., 5, 1–8, https://doi.org/10.1038/ncomms4323, 2014. a
Kopp, R. E., Kemp, A. C., Bittermann, K., Horton, B. P., Donnelly, J. P., Gehrels, W. R., Hay, C. C., Mitrovica, J. X., Morrow, E. D., and Rahmstorf, S.: Temperature-driven global sea-level variability in the Common Era, P. Natl. Acad. Sci. USA, 113, E1434–E1441, https://doi.org/10.1073/pnas.1517056113, 2016. a
Landrum, L., Otto-Bliesner, B. L., Wahl, E. R., Conley, A., Lawrence, P. J., Rosenbloom, N., and Teng, H.: Last millennium climate and its variability in CCSM4, J. Climate, 26, 1085–1111, https://doi.org/10.1175/JCLI-D-11-00326.1, 2013. a
Mann, M. E., Zhang, Z., Hughes, M. K., Bradley, R. S., Miller, S. K., Rutherford, S., and Ni, F.: Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia, P. Natl. Acad. Sci. USA, 105, 13252–13257, https://doi.org/10.1073/pnas.0805721105, 2008. a
Mann, M. E., Steinman, B. A., Brouillette, D. J., and Miller, S. K.: Multidecadal climate oscillations during the past millennium driven by volcanic forcing, Science, 371, 1014–1019, https://doi.org/10.1126/science.abc5810, 2021. a
Mann, M. E., Steinman, B. A., Brouillette, D. J., Fernandez, A., and Miller, S. K.: On The Estimation of Internal Climate Variability During the Preindustrial Past Millennium, Geophys. Res. Lett., 49, e2021GL096596, https://doi.org/10.1029/2021GL096596, 2022. a
Mansfield, L. A., Nowack, P. J., Kasoar, M., Everitt, R. G., Collins, W. J., and Voulgarakis, A.: Predicting global patterns of long-term climate change from short-term simulations using machine learning, npj Clim. Atmos. Sci., 3, 1–9, https://doi.org/10.1038/s41612-020-00148-5, 2020. a
Matthews, A. G. d. G., Van Der Wilk, M., Nickson, T., Fujii, K., Boukouvalas, A., León-Villagrá, P., Ghahramani, Z., and Hensman, J.: GPflow: A Gaussian Process Library using TensorFlow, J. Mach. Learn. Res., 18, 1–6, 2017. a
Mead, A.: Review of the Development of Multidimensional Scaling Methods, J. Roy. Stat. Soc. Ser. D, 41, 27–39, https://doi.org/10.2307/2348634, 1992. a, b
Meehl, J.: CCSM4 coupled run for CMIP5 historical (1850–2005), World Data Center for Climate (WDCC) at DKRZ [data set], https://doi.org/10.1594/WDCC/CMIP5.NRS4hi, 2014. a, b
Mette, M. J., Wanamaker Jr, A. D., Retelle, M. J., Carroll, M. L., Andersson, C., and Ambrose Jr., W. G.: Persistent multidecadal variability since the 15th century in the southern Barents Sea derived from annually resolved shell-based records, J. Geophys. Res.-Oceans, 126, e2020JC017074, https://doi.org/10.1029/2020JC017074, 2021. a
Michel, S., Swingedouw, D., Chavent, M., Ortega, P., Mignot, J., and Khodri, M.: Reconstructing climatic modes of variability from proxy records using ClimIndRec version 1.0, Geosci. Model Dev., 13, 841–858, https://doi.org/10.5194/gmd-13-841-2020, 2020. a, b
Miles, M. W., Divine, D. V., Furevik, T., Jansen, E., Moros, M., and Ogilvie, A. E.: A signal of persistent Atlantic multidecadal variability in Arctic sea ice, Geophys. Res. Lett., 41, 463–469, https://doi.org/10.1002/2013GL058084, 2014. a
Otto-Bliesner, B.: CCSM4 coupled simulation for CMIP5 past 1000 years (850–1850) with natural forcings, World Data Center for Climate (WDCC) at DKRZ [data set], https://doi.org/10.1594/WDCC/CMIP5.NRS4pk, 2014. a, b
PAGES2k: A global multiproxy database for temperature reconstructions of the Common Era, Sci. Data, 4, 170088, https://doi.org/10.1038/sdata.2017.88, 2017. a, b
PAGES2k: Consistent multi-decadal variability in global temperature reconstructions and simulations over the Common Era, Nat. Geosci., 12, 643, https://doi.org/10.1038/s41561-019-0400-0, 2019. a
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E.: Scikit-learn: Machine learning in Python, J. Mach. Learn. Res., 12, 2825–2830, 2011. a
Saenger, C., Cohen, A. L., Oppo, D. W., Halley, R. B., and Carilli, J. E.: Surface-temperature trends and variability in the low-latitude North Atlantic since 1552, Nat. Geosci., 2, 492–495, https://doi.org/10.1038/ngeo552, 2009. a
Särkkä, S.: Bayesian filtering and smoothing, 3, Cambridge University Press, https://doi.org/10.1017/CBO9781139344203, 2013. a
Singh, H. K. A., Hakim, G. J., Tardif, R., Emile-Geay, J., and Noone, D. C.: Insights into Atlantic multidecadal variability using the Last Millennium Reanalysis framework, Clim. Past, 14, 157–174, https://doi.org/10.5194/cp-14-157-2018, 2018. a, b
Smerdon, J. E.: Climate models as a test bed for climate reconstruction methods: pseudoproxy experiments, Wires Clim. Change, 3, 63–77, https://doi.org/10.1002/wcc.149, 2012. a, b
Smerdon, J. E., Kaplan, A., Zorita, E., González-Rouco, J. F., and Evans, M.: Spatial performance of four climate field reconstruction methods targeting the Common Era, Geophys. Res. Lett., 38, L11705, https://doi.org/10.1029/2011GL047372, 2011. a
Svendsen, L., Hetzinger, S., Keenlyside, N., and Gao, Y.: Marine-based multiproxy reconstruction of Atlantic multidecadal variability, Geophys. Res. Lett., 41, 1295–1300, https://doi.org/10.1002/2013GL059076, 2014. a
Von Storch, H., Zorita, E., Jones, J. M., Dimitriev, Y., González-Rouco, F., and Tett, S. F.: Reconstructing past climate from noisy data, Science, 306, 679–682, https://doi.org/10.1126/science.1096109, 2004. a
von Storch, H., Zorita, E., and González-Rouco, F.: Assessment of three temperature reconstruction methods in the virtual reality of a climate simulation, Int. J. Earth Sci., 98, 67–82, https://doi.org/10.1007/s00531-008-0349-5, 2009. a
Wang, J., Yang, B., Ljungqvist, F. C., Luterbacher, J., Osborn, T. J., Briffa, K. R., and Zorita, E.: Internal and external forcing of multidecadal Atlantic climate variability over the past 1,200 years, Nat. Geosci., 10, 512–517, https://doi.org/10.1038/ngeo2962, 2017. a, b, c, d
Wegmann, M. and Jaume-Santero, F.: Artificial intelligence achieves easy-to-adapt nonlinear global temperature reconstructions using minimal local data, Commun. Earth Environ., 4, 217, https://doi.org/10.1038/s43247-023-00872-9, 2023. a
Yan, X., Zhang, R., and Knutson, T. R.: A multivariate AMV index and associated discrepancies between observed and CMIP5 externally forced AMV, Geophys. Res. Lett., 46, 4421–4431, https://doi.org/10.1029/2019GL082787, 2019. a
Zhang, R. and Delworth, T. L.: Impact of Atlantic multidecadal oscillations on India/Sahel rainfall and Atlantic hurricanes, Geophys. Res. Lett., 33, L17712, https://doi.org/10.1029/2006GL026267, 2006. a
Zhang, R., Delworth, T. L., and Held, I. M.: Can the Atlantic Ocean drive the observed multidecadal variability in Northern Hemisphere mean temperature?, Geophys. Res. Lett., 34, L02709, https://doi.org/10.1029/2006GL028683, 2007. a
Zhang, R., Sutton, R., Danabasoglu, G., Kwon, Y.-O., Marsh, R., Yeager, S. G., Amrhein, D. E., and Little, C. M.: A review of the role of the Atlantic meridional overturning circulation in Atlantic multidecadal variability and associated climate impacts, Rev. Geophys., 57, 316–375, https://doi.org/10.1029/2019RG000644, 2019. a, b
Zhang, Z., Wagner, S., Klockmann, M., and Zorita, E.: Evaluation of statistical climate reconstruction methods based on pseudoproxy experiments using linear and machine-learning methods, Clim. Past, 18, 2643–2668, https://doi.org/10.5194/cp-18-2643-2022, 2022. a, b
Zorita, E., González-Rouco, F., and Legutke, S.: Testing the approach to paleoclimate reconstructions in the context of a 1000-yr control simulation with the ECHO-G coupled climate model, J. Climate, 16, 1378–1390, https://doi.org/10.1175/1520-0442(2003)16<1378:TTMEAA>2.0.CO;2, 2003. a
Short summary
Reconstructions of climate variability before the observational period rely on climate proxies and sophisticated statistical models to link the proxy information and climate variability. Existing models tend to underestimate the true magnitude of variability, especially if the proxies contain non-climatic noise. We present and test a promising new framework for climate-index reconstructions, based on Gaussian processes, which reconstructs robust variability estimates from noisy and sparse data.
Reconstructions of climate variability before the observational period rely on climate proxies...