Articles | Volume 17, issue 8
https://doi.org/10.5194/gmd-17-3409-2024
© 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-17-3409-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
30 Apr 2024
Development and technical paper |
| 30 Apr 2024
| 30 Apr 2024
cfr (v2024.1.26): a Python package for climate field reconstruction
Climate and Global Dynamics Laboratory, NSF National Center for Atmospheric Research, Boulder, CO, USA
Julien Emile-Geay
Department of Earth Sciences, University of Southern California, Los Angeles, CA, USA
Gregory J. Hakim
Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA
Dominique Guillot
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA
Deborah Khider
University of Southern California, Information Sciences Institute, Marina Del Rey, CA, USA
Robert Tardif
Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA
Walter A. Perkins
Allen Institute for Artificial Intelligence, Seattle, WA, USA
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Cited articles
Acevedo, W., Fallah, B., Reich, S., and Cubasch, U.: Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model, Clim. Past, 13, 545–557, https://doi.org/10.5194/cp-13-545-2017, 2017. a
Annan, J. D. and Hargreaves, J. C.: A new global reconstruction of temperature changes at the Last Glacial Maximum, Clim. Past, 9, 367–376, https://doi.org/10.5194/cp-9-367-2013, 2013. a
Annan, J. D., Hargreaves, J. C., and Mauritsen, T.: A new global surface temperature reconstruction for the Last Glacial Maximum, Clim. Past, 18, 1883–1896, https://doi.org/10.5194/cp-18-1883-2022, 2022. a
Bova, S., Rosenthal, Y., Liu, Z., Godad, S. P., and Yan, M.: Seasonal origin of the thermal maxima at the Holocene and the last interglacial, Nature, 589, 548–553, https://doi.org/10.1038/s41586-020-03155-x, 2021. a
Brady, E., Stevenson, S., Bailey, D., Liu, Z., Noone, D., Nusbaumer, J., Otto-Bliesner, B. L., Tabor, C., Tomas, R., Wong, T., Zhang, J., and Zhu, J.: The Connected Isotopic Water Cycle in the Community Earth System Model Version 1, J. Adv. Model. Earth Sy., 11, 2547–2566, https://doi.org/10.1029/2019MS001663, 2019. a, b, c, d
Büntgen, U., Allen, K., Anchukaitis, K. J., Arseneault, D., Boucher, É., Bräuning, A., Chatterjee, S., Cherubini, P., Churakova (Sidorova), 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, 3411, https://doi.org/10.1038/s41467-021-23627-6, 2021. a
Bürger, G., Fast, I., and Cubasch, U.: Climate reconstruction by regression – 32 variations on a theme, Tellus A, 58, 227–235, https://doi.org/10.1111/j.1600-0870.2006.00164.x, 2006. a
Christiansen, B. and Ljungqvist, F. C.: Challenges and Perspectives for Large-Scale Temperature Reconstructions of the Past Two Millennia, Rev. Geophys., 55, 40–96, https://doi.org/10.1002/2016RG000521, 2017. a
Cook, E. R., Woodhouse, C. A., Eakin, C. M., Meko, D. M., and Stahle, D. W.: Long-Term Aridity Changes in the Western United States, Science, 306, 1015–1018, https://doi.org/10.1126/science.1102586, 2004. a
Cook, E. R., Anchukaitis, K. J., Buckley, B. M., D'Arrigo, R. D., Jacoby, G. C., and Wright, W. E.: Asian Monsoon Failure and Megadrought During the Last Millennium, Science, 328, 486–489, https://doi.org/10.1126/science.1185188, 2010. a
Dempster, A. P., Laird, N. M., and Rubin, D. B.: Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion), J. Roy. Stat. Soc. B, 39, 1–38, 1977. a
Dirren, S. and Hakim, G. J.: Toward the assimilation of time-averaged observations, Geophys. Res. Lett., 32, L04804, https://doi.org/10.1029/2004GL021444, 2005. a
Dubinkina, S. and Goosse, H.: An assessment of particle filtering methods and nudging for climate state reconstructions, Clim. Past, 9, 1141–1152, https://doi.org/10.5194/cp-9-1141-2013, 2013. a
Dubinkina, S., Goosse, H., Sallaz-Damaz, Y., Crespin, E., and Crucifix, M.: Testing a particle filter to reconstruct climate changes over the past centuries, Int. J. Bifurcat. Chaos, 21, 3611–3618, https://doi.org/10.1142/S0218127411030763, 2011. a
Emile-Geay, J., Cobb, K., Mann, M., and Wittenberg, A. T.: Estimating Central Equatorial Pacific SST variability over the Past Millennium. Part 1: Methodology and Validation, J. Climate, 26, 2302–2328, https://doi.org/10.1175/JCLI-D-11-00510.1, 2013a. a
Emile-Geay, J., Cobb, K., Mann, M., and Wittenberg, A. T.: Estimating Central Equatorial Pacific SST variability over the Past Millennium. Part 2: Reconstructions and Implications, J. Climate, 26, 2329–2352, https://doi.org/10.1175/JCLI-D-11-00511.1, 2013b. a
Evans, M. N., Kaplan, A., and Cane, M. A.: Pacific sea surface temperature field reconstruction from coral δ18O data using reduced space objective analysis, Paleoceanography, 17, 7-1–7-13, https://doi.org/10.1029/2000PA000590, 2002. a
Evans, M. N., Tolwinski-Ward, S. E., Thompson, D. M., and Anchukaitis, K. J.: Applications of proxy system modeling in high resolution paleoclimatology, Quaternary Sci. Rev., 76, 16–28, https://doi.org/10.1016/j.quascirev.2013.05.024, 2013. a, b, c
Evensen, G.: Data Assimilation: The Ensemble Kalman Filter, 2nd Edn., Springer, ISBN 978-3-642-03710-8, 2009. a
Fang, M., Li, X., Chen, H. W., and Chen, D.: Arctic Amplification Modulated by Atlantic Multidecadal Oscillation and Greenhouse Forcing on Multidecadal to Century Scales, Nat. Commun., 13, 1865, https://doi.org/10.1038/s41467-022-29523-x, 2022. a
Franke, J., Brönnimann, S., Bhend, J., and Brugnara, Y.: A Monthly Global Paleo-Reanalysis of the Atmosphere from 1600 to 2005 for Studying Past Climatic Variations, Scientific Data, 4, 170076, https://doi.org/10.1038/sdata.2017.76, 2017. a
Friedman, J., Hastie, T., and Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso, Biostat, 9, 432–441, https://doi.org/10.1093/biostatistics/kxm045, 2008. a
Gebhardt, C., Kühl, N., Hense, A., and Litt, T.: Reconstruction of Quaternary Temperature Fields by Dynamically Consistent Smoothing, Clim. Dynam., 30, 421–437, https://doi.org/10.1007/s00382-007-0299-9, 2008. a
GISTEMP Team: The GISS Surface Temperature Analysis (GISTEMP), version 4, GISTEMP Team [data set], https://data.giss.nasa.gov/pub/gistemp/gistemp1200_GHCNv4_ERSSTv5.nc.gz, last access: 23 April 2024. a
Goosse, H., Renssen, H., Timmermann, A., Bradley, R. S., and Mann, M. E.: Using paleoclimate proxy-data to select optimal realisations in an ensemble of simulations of the climate of the past millennium, Clim. Dynam., 27, 165–184, https://doi.org/10.1007/s00382-006-0128-6, 2006. a, b
Goosse, H., Crespin, E., de Montety, A., Mann, M. E., Renssen, H., and Timmermann, A.: Reconstructing Surface Temperature Changes over the Past 600 Years Using Climate Model Simulations with Data Assimilation, J. Geophys. Res.-Atmos., 115, D09108, https://doi.org/10.1029/2009JD012737, 2010. a, b
Hakim, G. J., Emile-Geay, J., Steig, E. J., Noone, D., Anderson, D. M., Tardif, R., Steiger, N., and Perkins, W. A.: The Last Millennium Climate Reanalysis Project: Framework and First Results, J. Geophys. Res.-Atmos., 121, 6745–6764, https://doi.org/10.1002/2016JD024751, 2016. a, b, c, d, e, f, g, h, i, j, k
Hoyer, S. and Hamman, J.: xarray: N-D labeled arrays and datasets in Python, Journal of Open Research Software, 5, 10, https://doi.org/10.5334/jors.148, 2017. a
Huang, B., Thorne, P. W., Banzon, V. F., Boyer, T., Chepurin, G., Lawrimore, J. H., Menne, M. J., Smith, T. M., Vose, R. S., and Zhang, H.-M.: Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5): Upgrades, Validations, and Intercomparisons, J. Climate, 30, 8179–8205, https://doi.org/10.1175/JCLI-D-16-0836.1, 2017. a, b
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, J. and Widmann, M.: Reconstructing Large-scale Variability from Palaeoclimatic Evidence by Means of Data Assimilation Through Upscaling and Nudging (DATUN), in: The KIHZ project: Towards a Synthesis of Holocene Proxy Data and Climate Models, edited by: Fischer, H., Kumke, T., Lohmann, G., Flösser, G., Miller, H., von Storch, H., and Negendank, J., Springer, Heidelberg, Berlin, New York, 171–193, ISBN 978-3-642-05826-4, 2004. a
Kalman, R. E.: A New Approach to Linear Filtering and Prediction Problems, J. Fluid. Eng.-T. ASME, 82, 35–45, https://doi.org/10.1115/1.3662552, 1960. a
Khider, D., Emile-Geay, J., Zhu, F., James, A., Landers, J., Ratnakar, V., and Gil, Y.: Pyleoclim: Paleoclimate Timeseries Analysis and Visualization With Python, Paleoceanography and Paleoclimatology, 37, e2022PA004509, https://doi.org/10.1029/2022PA004509, 2022. a
King, J., Tierney, J., Osman, M., Judd, E. J., and Anchukaitis, K. J.: DASH: a MATLAB toolbox for paleoclimate data assimilation, Geosci. Model Dev., 16, 5653–5683, https://doi.org/10.5194/gmd-16-5653-2023, 2023. a
King, J. M., Anchukaitis, K. J., Tierney, J. E., Hakim, G. J., Emile-Geay, J., Zhu, F., and Wilson, R.: A data assimilation approach to last millennium temperature field reconstruction using a limited high-sensitivity proxy network, J. Climate, 1, 1–64, https://doi.org/10.1175/JCLI-D-20-0661.1, 2021. a, b
Kluyver, T., Ragan-Kelley, B., Pérez, F., Granger, B., Bussonnier, M., Frederic, J., Kelley, K., Hamrick, J., Grout, J., Corlay, S., Ivanov, P., Avila, D., Abdalla, S., and Willing, C.: Jupyter Notebooks – a publishing format for reproducible computational workflows, in: Positioning and Power in Academic Publishing: Players, Agents and Agendas, edited by: Loizides, F. and Schmidt, B., IOS Press, 87–90, https://doi.org/10.3233/978-1-61499-649-1-87, 2016. a
Lauritzen, S. L.: Graphical Models, Clarendon Press, Oxford, ISBN 9780198522195, 1996. a
Lenssen, N. J. L., Schmidt, G. A., Hansen, J. E., Menne, M. J., Persin, A., Ruedy, R., and Zyss, D.: Improvements in the GISTEMP Uncertainty Model, J. Geophys. Res.-Atmos., 124, 6307–6326, https://doi.org/10.1029/2018JD029522, 2019. a, b, c, d
Liu, H., Liu, Z., and Lu, F.: A Systematic Comparison of Particle Filter and EnKF in Assimilating Time-Averaged Observations, J. Geophys. Res.-Atmos., 122, 13155–13173, https://doi.org/10.1002/2017JD026798, 2017. a
Lough, J. M.: Climate records from corals, WIRes Clim. Change, 1, 318–331, https://doi.org/10.1002/wcc.39, 2010. a
Lyu, Z., Goosse, H., Dalaiden, Q., Klein, F., Shi, F., Wagner, S., and Braconnot, P.: Spatial Patterns of Multi–Centennial Surface Air Temperature Trends in Antarctica over 1–1000 CE: Insights from Ice Core Records and Modeling, Quaternary Sci. Rev., 271, 107205, https://doi.org/10.1016/j.quascirev.2021.107205, 2021. a, b
Malevich, S. B., Vetter, L., and Tierney, J. E.: Global Core Top Calibration of δ18O in Planktic Foraminifera to Sea Surface Temperature, Paleoceanography and Paleoclimatology, 34, 1292–1315, https://doi.org/10.1029/2019PA003576, 2019. a
Mann, M. E., Bradley, R. S., and Hughes, M. K.: Global-scale temperature patterns and climate forcing over the past six centuries, Nature, 392, 779–787, https://doi.org/10.1038/33859, 1998. a
Mann, M. E., Bradley, R. S., and Hughes, M. K.: Northern hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations, Geophys. Res. Lett., 26, 759–762, https://doi.org/10.1029/1999GL900070, 1999. a
Mann, M. E., Rutherford, S., Wahl, E., and Ammann, C.: Robustness of proxy-based climate field reconstruction methods, J. Geophys. Res.-Atmos., 112, D12109, https://doi.org/10.1029/2006JD008272, 2007. 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., Zhang, Z., Rutherford, S., Bradley, R. S., Hughes, M. K., Shindell, D., Ammann, C., Faluvegi, G., and Ni, F.: Global Signatures and Dynamical Origins of the Little Ice Age and Medieval Climate Anomaly, Science, 326, 1256–1260, https://doi.org/10.1126/science.1177303, 2009. a
Marcott, S. A., Shakun, J. D., Clark, P. U., and Mix, A. C.: A Reconstruction of Regional and Global Temperature for the Past 11 300 Years, Science, 339, 1198–1201, https://doi.org/10.1126/science.1228026, 2013. a
Masson-Delmotte, V., Schulz, M., Abe-Ouchi, A., Beer, J., Ganopolski, A., Rouco, J. G., Jansen, E., Lambeck, K., Luterbacher, J., Naish, T., Osborn, T., Otto-Bliesner, B., Quinn, T., Ramesh, R., Rojas, M., Shao, X., and Timmermann, A.: Information from Paleoclimate Archives, in: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 383–464, https://doi.org/10.1017/CBO9781107415324.013, 2013. a
McKinney, W.: Data Structures for Statistical Computing in Python, in: Proceedings of the 9th Python in Science Conference, edited by: van der Walt, S. and Millman, J., 51–56, https://doi.org/10.25080/Majora-92bf1922-00a, 2010. a
Menne, M. J., Williams, C. N., Gleason, B. E., Rennie, J. J., and Lawrimore, J. H.: The Global Historical Climatology Network Monthly Temperature Dataset, Version 4, J. Climate, 31, 9835–9854, https://doi.org/10.1175/JCLI-D-18-0094.1, 2018. a, b
Met Office: Cartopy: a cartographic python library with a Matplotlib interface, Exeter, Devon, Met Office [code], https://scitools.org.uk/cartopy (last access: 23 April 2024), 2010. a
Morice, C. P., Kennedy, J. J., Rayner, N. A., and Jones, P. D.: Quantifying Uncertainties in Global and Regional Temperature Change Using an Ensemble of Observational Estimates: The HadCRUT4 Data Set, J. Geophys. Res.-Atmos., 117, D08101, https://doi.org/10.1029/2011JD017187, 2012. a, b, c
Neukom, R., Barboza, L. A., Erb, M. P., Shi, F., Emile-Geay, J., Evans, M. N., Franke, J., Kaufman, D. S., Lücke, L., Rehfeld, K., Schurer, A., Zhu, F., Brönnimann, S., Hakim, G. J., Henley, B. J., Ljungqvist, F. C., McKay, N., Valler, V., and von Gunten, L.: Consistent multidecadal variability in global temperature reconstructions and simulations over the Common Era, Nat. Geosci., 12, 643–649, https://doi.org/10.1038/s41561-019-0400-0, 2019a. a
Neukom, R., Steiger, N., Gómez-Navarro, J. J., Wang, J., and Werner, J. P.: No evidence for globally coherent warm and cold periods over the preindustrial Common Era, Nature, 571, 550–554, https://doi.org/10.1038/s41586-019-1401-2, 2019b. a
Osman, M. B., Tierney, J. E., Zhu, J., Tardif, R., Hakim, G. J., King, J., and Poulsen, C. J.: Globally resolved surface temperatures since the Last Glacial Maximum, Nature, 599, 239–244, https://doi.org/10.1038/s41586-021-03984-4, 2021. a, b, c, d
Otto-Bliesner, B. L., Brady, E. C., Fasullo, J., Jahn, A., Landrum, L., Stevenson, S., Rosenbloom, N., Mai, A., and Strand, G.: Climate Variability and Change since 850 CE: An Ensemble Approach with the Community Earth System Model, B. Am. Meteorol. Soc., 97, 735–754, https://doi.org/10.1175/BAMS-D-14-00233.1, 2016. a
PAGES2k Consortium: PAGES2k Global 2,000 Year Multiproxy Database, PAGES2k Consortium [data set], https://doi.org/10.25921/ycr3-7588, last access: 23 April 2024. a
Perkins, W. A. and Hakim, G. J.: Reconstructing paleoclimate fields using online data assimilation with a linear inverse model, Clim. Past, 13, 421–436, https://doi.org/10.5194/cp-13-421-2017, 2017. a
Perkins, W. A. and Hakim, G. J.: Coupled Atmosphere–Ocean Reconstruction of the Last Millennium Using Online Data Assimilation, Paleoceanography and Paleoclimatology, 36, e2020PA003959, https://doi.org/10.1029/2020PA003959, 2021. a
Plotly Technologies Inc.: Collaborative data science, https://plot.ly (last access: 23 April 2024), 2015. a
Rew, R. and Davis, G.: NetCDF: An Interface for Scientific Data Access, IEEE Comput. Graph., 10, 76–82, https://doi.org/10.1109/38.56302, 1990. a
Ridgwell, A., Hargreaves, J. C., Edwards, N. R., Annan, J. D., Lenton, T. M., Marsh, R., Yool, A., and Watson, A.: Marine geochemical data assimilation in an efficient Earth System Model of global biogeochemical cycling, Biogeosciences, 4, 87–104, https://doi.org/10.5194/bg-4-87-2007, 2007. a
Rutherford, S., Mann, M. E., Osborn, T. J., Bradley, R. S., Briffa, K. R., Hughes, M. K., and Jones, P. D.: Proxy-Based Northern Hemisphere Surface Temperature Reconstructions: Sensitivity to Method, Predictor Network, Target Season, and Target Domain, J. Climate, 18, 2308–2329, 2005. a
Schneider, T.: Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values, J. Climate, 14, 853–871, https://doi.org/10.1175/1520-0442(2001)014<0853:AOICDE>2.0.CO;2, 2001. a
Seabold, S. and Perktold, J.: statsmodels: Econometric and statistical modeling with python, in: 9th Python in Science Conference, https://doi.org/10.25080/Majora-92bf1922-011, 2010. a
Shakun, J. D., Clark, P. U., He, F., Marcott, S. A., Mix, A. C., Liu, Z., Otto-Bliesner, B., Schmittner, A., and Bard, E.: Global Warming Preceded by Increasing Carbon Dioxide Concentrations during the Last Deglaciation, Nature, 484, 49–54, https://doi.org/10.1038/nature10915, 2012. a
Shi, F., Zhao, S., Guo, Z., Goosse, H., and Yin, Q.: Multi-proxy reconstructions of May–September precipitation field in China over the past 500 years, Clim. Past, 13, 1919–1938, https://doi.org/10.5194/cp-13-1919-2017, 2017. a
Shi, F., Goosse, H., Klein, F., Zhao, S., Liu, T., and Guo, Z.: Monopole Mode of Precipitation in East Asia Modulated by the South China Sea Over the Last Four Centuries, Geophys. Res. Lett., 46, 14713–14722, https://doi.org/10.1029/2019GL085320, 2019. a, b
Smerdon, J. E. and Pollack, H. N.: Reconstructing Earth's surface temperature over the past 2000 years: the science behind the headlines, WIREs Clim. Change, 7, 746–771, https://doi.org/10.1002/wcc.418, 2016. a
Steiger, N. and Hakim, G.: Multi-timescale data assimilation for atmosphere–ocean state estimates, Clim. Past, 12, 1375–1388, https://doi.org/10.5194/cp-12-1375-2016, 2016. a
Steiger, N. J., Hakim, G. J., Steig, E. J., Battisti, D. S., and Roe, G. H.: Assimilation of Time-Averaged Pseudoproxies for Climate Reconstruction, J. Climate, 27, 426–441, https://doi.org/10.1175/JCLI-D-12-00693.1, 2014. a, b
Steiger, N. J., Smerdon, J. E., Cook, E. R., and Cook, B. I.: A Reconstruction of Global Hydroclimate and Dynamical Variables over the Common Era, Scientific Data, 5, 1–15, https://doi.org/10.1038/sdata.2018.86, 2018. a
Tardif, R.: The post-processed “iCESM1” last millennium simulation, https://atmos.washington.edu/~rtardif/LMR/prior, last access: 23 April 2024. a
Tardif, R., Hakim, G. J., Perkins, W. A., Horlick, K. A., Erb, M. P., Emile-Geay, J., Anderson, D. M., Steig, E. J., and Noone, D.: Last Millennium Reanalysis with an expanded proxy database and seasonal proxy modeling, Clim. Past, 15, 1251–1273, https://doi.org/10.5194/cp-15-1251-2019, 2019. a, b, c, d, e, f, g, h, i, j, k
Tierney, J. E. and Tingley, M. P.: A Bayesian, Spatially-Varying Calibration Model for the TEX86 Proxy, Geochim. Cosmochim. Ac., 127, 83–106, https://doi.org/10.1016/j.gca.2013.11.026, 2014. a
Tierney, J. E. and Tingley, M. P.: BAYSPLINE: A New Calibration for the Alkenone Paleothermometer, Paleoceanography and Paleoclimatology, 33, 281–301, https://doi.org/10.1002/2017PA003201, 2018. a
Tierney, J. E., Abram, N. J., Anchukaitis, K. J., Evans, M. N., Giry, C., Kilbourne, K. H., Saenger, C. P., Wu, H. C., and Zinke, J.: Tropical sea surface temperatures for the past four centuries reconstructed from coral archives, Paleoceanography, 30, 226–252, https://doi.org/10.1002/2014PA002717, 2015. a
Tierney, J. E., Malevich, S. B., Gray, W., Vetter, L., and Thirumalai, K.: Bayesian Calibration of the
Tierney, J. E., Zhu, J., King, J., Malevich, S. B., Hakim, G. J., and Poulsen, C. J.: Glacial Cooling and Climate Sensitivity Revisited, Nature, 584, 569–573, https://doi.org/10.1038/s41586-020-2617-x, 2020. a, b, c
Tingley, M. P. and Huybers, P.: Recent temperature extremes at high northern latitudes unprecedented in the past 600 years, Nature, 496, 201–205, https://doi.org/10.1038/nature11969, 2013. a, b
Tingley, M. P. and Huybers, P. J.: A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part 1: Development and Applications to Paleoclimate Reconstruction Problems, J. Climate, 23, 2759–2781, https://doi.org/10.1175/2009JCLI3015.1, 2010a. a
Tingley, M. P. and Huybers, P. J.: A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part 2: Comparison with the Regularized Expectation-Maximization Algorithm, J. Climate, 23, 2782–2800, https://doi.org/10.1175/2009JCLI3016.1, 2010b. a
Tingley, M. P. and Li, B.: Comments on “Reconstructing the NH Mean Temperature: Can Underestimation of Trends and Variability Be Avoided?”, J. Climate, 25, 3441–3446, https://doi.org/10.1175/JCLI-D-11-00005.1, 2012. a
Tingley, M. P., Craigmile, P. F., Haran, M., Li, B., Mannshardt, E., and Rajaratnam, B.: Piecing together the past: statistical insights into paleoclimatic reconstructions, Quaternary Sci. Rev., 35, 1–22, https://doi.org/10.1016/j.quascirev.2012.01.012, 2012. a, b
Tolwinski-Ward, S. E., Evans, M. N., Hughes, M. K., and Anchukaitis, K. J.: An efficient forward model of the climate controls on interannual variation in tree-ring width, Clim. Dynam., 36, 2419–2439, https://doi.org/10.1007/s00382-010-0945-5, 2011. a, b
Tolwinski-Ward, S. E., Anchukaitis, K. J., and Evans, M. N.: Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width, Clim. Past, 9, 1481–1493, https://doi.org/10.5194/cp-9-1481-2013, 2013. a, b
Vaccaro, A., Emile-Geay, J., Guillot, D., Verna, R., Morice, C., Kennedy, J., and Rajaratnam, B.: Climate field completion via Markov random fields – Application to the HadCRUT4.6 temperature dataset, J. Climate, 1, 1–66, https://doi.org/10.1175/JCLI-D-19-0814.1, 2021a. a, b, c, d, e, f, g, h, i, j, k
Vaccaro, A. D., Emile-Geay, J., Guillot, D., Verna, R., Morice, C., Kennedy, J., and Rajaratnam, B.: GraphEM-infilled HadCRUT4.6.0.0 January 1850 – December 2017, Zenodo [data set], https://doi.org/10.5281/zenodo.4601616, 2021b. a
Valler, V., Franke, J., Brugnara, Y., and Brönnimann, S.: An Updated Global Atmospheric Paleo-Reanalysis Covering the Last 400 Years, Geosci. Data J., 9, 89–107, https://doi.org/10.1002/gdj3.121, 2022. a
van der Walt, S., Colbert, S. C., and Varoquaux, G.: The NumPy Array: A Structure for Efficient Numerical Computation, Comput. Sci. Eng., 13, 22–30, https://doi.org/10.1109/MCSE.2011.37, 2011. a
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nat. Methods, 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020. a
Wang, J., Emile-Geay, J., Guillot, D., McKay, N. P., and Rajaratnam, B.: Fragility of reconstructed temperature patterns over the Common Era: Implications for model evaluation., Geophys. Res. Lett., 42, 7162–7170, https://doi.org/10.1002/2015GL065265, 2015. a, b
Waskom, M. L.: seaborn: statistical data visualization, Journal of Open Source Software, 6, 3021, https://doi.org/10.21105/joss.03021, 2021. a
Widmann, M., Goosse, H., van der Schrier, G., Schnur, R., and Barkmeijer, J.: Using data assimilation to study extratropical Northern Hemisphere climate over the last millennium, Clim. Past, 6, 627–644, https://doi.org/10.5194/cp-6-627-2010, 2010. a
Wikle, C. K. and Berliner, L. M.: A Bayesian tutorial for data assimilation, Physica D, 230, 1–16, https://doi.org/10.1016/j.physd.2006.09.017, 2007. a
Zhu, F. and Emile-Geay, J.: The GitHub repository for cfr, GitHub [code], https://github.com/fzhu2e/cfr, last access: 23 April 2024. a
Zhu, F. and Tolwinski-Ward, S.: PyVSL v0.4.0, Zenodo [code], https://doi.org/10.5281/zenodo.7967103, 2023. a
Zhu, F., Emile-Geay, J., Hakim, G. J., King, J., and Anchukaitis, K. J.: Resolving the Differences in the Simulated and Reconstructed Temperature Response to Volcanism, Geophys. Res. Lett., 47, e2019GL086908, https://doi.org/10.1029/2019GL086908, 2020. a
Zhu, F., Emile-Geay, J., Anchukaitis, K. J., Hakim, G. J., Wittenberg, A. T., Morales, M. S., Toohey, M., and King, J.: A re-appraisal of the ENSO response to volcanism with paleoclimate data assimilation, Nat. Commun., 13, 747, https://doi.org/10.1038/s41467-022-28210-1, 2022. a, b
Zhu, F., Emile-Geay, J., Anchukaitis, K. J., McKay, N. P., Stevenson, S., and Meng, Z.: The pseudoPAGES2k Dataset v1.4, Zenodo [data set], https://doi.org/10.5281/zenodo.8173256, 2023b. a, b, c
Short summary
Climate field reconstruction encompasses methods that estimate the evolution of climate in space and time based on natural archives. It is useful to investigate climate variations and validate climate models, but its implementation and use can be difficult for non-experts. This paper introduces a user-friendly Python package called cfr to make these methods more accessible, thanks to the computational and visualization tools that facilitate efficient and reproducible research on past climates.
Climate field reconstruction encompasses methods that estimate the evolution of climate in space...
