Earth’s climate history is often understood by breaking it down into constituent climatic epochs1. Over the Common Era (the past 2,000 years) these epochs, such as the Little Ice Age2,3,4, have been characterized as having occurred at the same time across extensive spatial scales5. Although the rapid global warming seen in observations over the past 150 years does show nearly global coherence6, the spatiotemporal coherence of climate epochs earlier in the Common Era has yet to be robustly tested. Here we use global palaeoclimate reconstructions for the past 2,000 years, and find no evidence for preindustrial globally coherent cold and warm epochs. In particular, we find that the coldest epoch of the last millennium—the putative Little Ice Age—is most likely to have experienced the coldest temperatures during the fifteenth century in the central and eastern Pacific Ocean, during the seventeenth century in northwestern Europe and southeastern North America, and during the mid-nineteenth century over most of the remaining regions. Furthermore, the spatial coherence that does exist over the preindustrial Common Era is consistent with the spatial coherence of stochastic climatic variability. This lack of spatiotemporal coherence indicates that preindustrial forcing was not sufficient to produce globally synchronous extreme temperatures at multidecadal and centennial timescales. By contrast, we find that the warmest period of the past two millennia occurred during the twentieth century for more than 98 per cent of the globe. This provides strong evidence that anthropogenic global warming is not only unparalleled in terms of absolute temperatures5, but also unprecedented in spatial consistency within the context of the past 2,000 years.
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The PAGES 2k v.2.0.0 dataset is archived at the World Data Service (WDS) for Paleoclimatology (hosted by the National Oceanic and Atmospheric Administration (NOAA)), formatted for both LiPD and WDS ASCII template (https://www.ncdc.noaa.gov/paleo/study/21171). The screened input data matrix and instrumental target grid, as well as the reconstruction outcomes from this study, are available at Figshare (doi:10.6084/m9.figshare.c.4498373.v1) and NOAA WDS Paleoclimatology (www.ncdc.noaa.gov/paleo/study/26850). We strongly recommend using the multimethod ensembles when working with the reconstructions. For analyses of global mean temperatures we recommend using the reconstruction of the PAGES 2k companion project that explicitly targets the global mean61.
The code to generate the figures is available with the output data (see above).
Köppen, W. & Wegener, A. Die Klimate der Geologischen Vorzeit (Gebrüder Borntraeger, 1924).
Matthes, F. E. Report of Committee on Glaciers, April 1939. Eos 20, 518–523 (1939).
Grove, J. M. The Little Ice Age (Methuen, 1988).
Matthews, J. A. & Briffa, K. R. The ‘little ice age’: re-evaluation of an evolving concept. Geogr. Ann. A 87, 17–36 (2005).
Masson-Delmotte, V. et al. 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 (eds Stocker, T. F. et al.) 383–464 (Cambridge Univ. Press, 2013).
Intergovernmental Panel on Climate Change. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2013).
Brückner, E. Klimaschwankungen seit 1700 nebst Bemerkungen über die Klimaschwankungen der Diluvialzeit (E. Hölzel, 1890).
Mann, M. E. et al. Global signatures and dynamical origins of the Little Ice Age and Medieval Climate Anomaly. Science 326, 1256–1260 (2009).
Lamb, H. H. The early medieval warm epoch and its sequel. Palaeogeogr. Palaeoclimatol. Palaeoecol. 1, 13–37 (1965).
Bradley, R. S., Hughes, M. K. & Diaz, H. F. Climate in medieval time. Science 302, 404–405 (2003).
Helama, S., Jones, P. D. & Briffa, K. R. Dark Ages Cold Period: a literature review and directions for future research. Holocene 27, 1600–1606 (2017).
Ljungqvist, F. C. A new reconstruction of temperature variability in the extra-tropical Northern Hemisphere during the last two millennia. Geogr. Ann. A 92, 339–351 (2010).
Büntgen, U. et al. Cooling and societal change during the Late Antique Little Ice Age from 536 to around 660 AD. Nat. Geosci. 9, 231–236 (2016).
Röthlisberger, F. 10,000 Jahre Gletschergeschichte der Erde (Sauerländer, 1986).
Wang, J., Emile-Geay, J., Guillot, D., Smerdon, J. E. & Rajaratnam, B. Evaluating climate field reconstruction techniques using improved emulations of real-world conditions. Clim. Past 10, 1–19 (2014).
Bradley, R. 1000 years of climate change. Science 288, 1353–1355 (2000).
Osborn, T. J. The spatial extent of 20th-century warmth in the context of the past 1200 years. Science 311, 841–844 (2006).
PAGES2k Consortium. Continental-scale temperature variability during the past two millennia. Nat. Geosci. 6, 339–346 (2013); erratum 6, 503 (2013); corrigendum 8, 981–982 (2015).
Wang, J., Emile-Geay, J., Guillot, D., McKay, N. P. & Rajaratnam, B. Fragility of reconstructed temperature patterns over the Common Era: implications for model evaluation. Geophys. Res. Lett. 42, 7162–7170 (2015).
PAGES2k Consortium. A global multiproxy database for temperature reconstructions of the Common Era. Sci. Data 4, 170088 (2017).
McPhaden, M. J., Zebiak, S. E. & Glantz, M. H. ENSO as an integrating concept in Earth science. Science 314, 1740–1745 (2006).
Stenni, B. et al. Antarctic climate variability on regional and continental scales over the last 2000 years. Clim. Past 13, 1609–1634 (2017).
Caesar, L., Rahmstorf, S., Robinson, A., Feulner, G. & Saba, V. Observed fingerprint of a weakening Atlantic Ocean overturning circulation. Nature 556, 191–196 (2018).
Wang, J. et al. Internal and external forcing of multidecadal Atlantic climate variability over the past 1,200 years. Nat. Geosci. 10, 512–517 (2017).
Delworth, T. L. et al. The North Atlantic Oscillation as a driver of rapid climate change in the Northern Hemisphere. Nat. Geosci. 9, 509–512 (2016).
Hegerl, G. C., Brönnimann, S., Schurer, A. & Cowan, T. The early 20th century warming: anomalies, causes, and consequences. Wiley Interdiscip. Rev. Clim. Change 9, e522 (2018).
Abram, N. J. et al. Early onset of industrial-era warming across the oceans and continents. Nature 536, 411–418 (2016); corrigendum 545, 252 (2017).
Bindoff, N. L. et al. in Climate Change 2013: The Physical Science Basis (eds Intergovernmental Panel on Climate Change) 867–952 (Cambridge Univ. Press, 2013).
Collins, M. et al. Challenges and opportunities for improved understanding of regional climate dynamics. Nat. Clim. Chang. 8, 101–108 (2018).
Xie, S.-P. et al. Towards predictive understanding of regional climate change. Nat. Clim. Chang. 5, 921–930 (2015).
Morice, C. P., Kennedy, J. J., Rayner, N. A. & Jones, P. D. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HadCRUT4 data set. J. Geophys. Res. 117, D08101 (2012).
Taylor, M. H., Losch, M., Wenzel, M. & Schröter, J. On the sensitivity of field reconstruction and prediction using empirical orthogonal functions derived from gappy data. J. Clim. 26, 9194–9205 (2013).
Gneiting, T. & Raftery, A. E. Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102, 359–378 (2007).
Werner, J. P. & Tingley, M. P. Technical note: Probabilistically constraining proxy age–depth models within a Bayesian hierarchical reconstruction model. Clim. Past 11, 533–545 (2015).
Cook, E. R., Briffa, K. R. & Jones, P. D. Spatial regression methods in dendroclimatology: a review and comparison of two techniques. Int. J. Climatol. 14, 379–402 (1994).
Tipton, J., Hooten, M., Pederson, N., Tingley, M. & Bishop, D. Reconstruction of late Holocene climate based on tree growth and mechanistic hierarchical models. Environmetrics 27, 42–54 (2016).
Werner, J. P., Divine, D. V., Charpentier Ljungqvist, F., Nilsen, T. & Francus, P. Spatio-temporal variability of Arctic summer temperatures over the past 2 millennia. Clim. Past 14, 527–557 (2018).
Jones, P. et al. High-resolution palaeoclimatology of the last millennium: a review of current status and future prospects. Holocene 19, 3–49 (2009).
Mann, M. E. et al. Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc. Natl Acad. Sci. USA 105, 13252–13257 (2008).
Cook, E. R. et al. Asian monsoon failure and megadrought during the last millennium. Science 328, 486–489 (2010).
Neukom, R. et al. Inter-hemispheric temperature variability over the past millennium. Nat. Clim. Chang. 4, 362–367 (2014).
Luterbacher, J. et al. Reconstruction of sea level pressure fields over the Eastern North Atlantic and Europe back to 1500. Clim. Dyn. 18, 545–561 (2002).
Luterbacher, J., Dietrich, D., Xoplaki, E., Grosjean, M. & Wanner, H. European seasonal and annual temperature variability, trends, and extremes since 1500. Science 303, 1499–1503 (2004).
Neukom, R. et al. Multi-centennial summer and winter precipitation variability in southern South America. Geophys. Res. Lett. 37, L14708 (2010).
Neukom, R. et al. Multiproxy summer and winter surface air temperature field reconstructions for southern South America covering the past centuries. Clim. Dyn. 37, 35–51 (2011).
Smerdon, J. E. & Pollack, H. N. Reconstructing Earth’s surface temperature over the past 2000 years: the science behind the headlines. Wiley Interdiscip. Rev. Clim. Change 7, 746–771 (2016).
Christiansen, B., Schmith, T. & Thejll, P. A surrogate ensemble study of climate reconstruction methods: stochasticity and robustness. J. Clim. 22, 951–976 (2009).
Smerdon, J. E., Kaplan, A., Chang, D. & Evans, M. N. A pseudoproxy evaluation of the CCA and RegEM methods for reconstructing climate fields of the last millennium. J. Clim. 23, 4856–4880 (2010).
Guillot, D., Rajaratnam, B. & Emile-Geay, J. Statistical paleoclimate reconstructions via Markov random fields. Ann. Appl. Stat. 9, 324–352 (2015).
Friedman, J., Hastie, T. & Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432–441 (2008).
Steiger, N. J., Hakim, G. J., Steig, E. J., Battisti, D. S. & Roe, G. H. Assimilation of time-averaged pseudoproxies for climate reconstruction. J. Clim. 27, 426–441 (2014).
Hakim, G. J. et al. The last millennium climate reanalysis project: framework and first results. J. Geophys. Res. D 121, 6745–6764 (2016).
Steiger, N. J., Smerdon, J. E., Cook, E. R. & Cook, B. I. A reconstruction of global hydroclimate and dynamical variables over the Common Era. Sci. Data 5, 180086 (2018).
Otto-Bliesner, B. L. et al. Climate variability and change since 850 CE: an ensemble approach with the Community Earth System Model. Bull. Am. Meteorol. Soc. 97, 735–754 (2016).
Gómez-Navarro, J. J., Zorita, E., Raible, C. C. & Neukom, R. Pseudoproxy tests of the analogue method to reconstruct spatially resolved global temperature during the Common Era. Clim. Past 13, 629–648 (2017).
Proakis, J. G. & Manolakis, D. G. Digital Signal Processing Principles, Algorithms, and Applications (Macmillan, 1992).
Hosking, J. R. M. Modeling persistence in hydrological time series using fractional differencing. Wat. Resour. Res. 20, 1898–1908 (1984).
Wahl, E. R. & Smerdon, J. E. Comparative performance of paleoclimate field and index reconstructions derived from climate proxies and noiseonly predictors. Geophys. Res. Lett. 39, L06703 (2012).
Higham, N. J. Cholesky factorization. Wiley Interdiscip. Rev. Comput. Stat. 1, 251–254 (2009).
Neukom, R., Schurer, A. P., Steiger, N. J. & Hegerl, G. C. Possible causes of data model discrepancy in the temperature history of the last millennium. Sci. Rep. 8, 7572 (2018).
PAGES 2k Consortium Consistent multi-decadal variability in global temperature reconstructions and simulations over the Common Era. Nature Geosci. (in the press).
Christiansen, B. & Ljungqvist, F. C. Challenges and perspectives for large-scale temperature reconstructions of the past two millennia. Rev. Geophys. 55, 40–96 (2017).
Ammann, C. M. & Wahl, E. R. The importance of the geophysical context in statistical evaluations of climate reconstruction procedures. Clim. Change 85, 71–88 (2007).
Gergis, J., Neukom, R., Gallant, A. J. E. & Karoly, D. J. Australasian temperature reconstructions spanning the last millennium. J. Clim. 29, 5365–5392 (2016).
Wahl, E. R., Ritson, D. M. & Ammann, C. M. Comment on “Reconstructing past climate from noisy data”. Science 312, 529 (2006).
von Storch, H. Reconstructing past climate from noisy data. Science 306, 679–682 (2004).
Bürger, G. & Cubasch, U. Are multiproxy climate reconstructions robust? Geophys. Res. Lett. 32, L23711 (2005).
Taylor, K. E., Stouffer, R. J. & Meehl, G. A. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93, 485–498 (2012).
Xiao-Ge, X., Tong-Wen, W. & Jie, Z. Introduction of CMIP5 experiments carried out with the climate system models of Beijing Climate Center. Adv. Clim. Chang. Res. 4, 41–49 (2013).
Landrum, L. et al. Last millennium climate and its variability in CCSM4. J. Clim. 26, 1085–1111 (2013).
Phipps, S. J. et al. The CSIRO Mk3L climate system model version 1.0 – Part 2: response to external forcings. Geosci. Model Dev. 5, 649–682 (2012).
Schmidt, G. A. et al. Present-day atmospheric simulations using GISS ModelE: comparison to in situ, satellite, and reanalysis data. J. Clim. 19, 153–192 (2006).
Schurer, A. P., Hegerl, G. C., Mann, M. E., Tett, S. F. B. & Phipps, S. J. Separating forced from chaotic climate variability over the past millennium. J. Clim. 26, 6954–6973 (2013).
Dufresne, J.-L. et al. Climate change projections using the IPSL-CM5 Earth System Model: from CMIP3 to CMIP5. Clim. Dyn. 40, 2123–2165 (2013).
Jungclaus, J. H. et al. Characteristics of the ocean simulations in the Max Planck Institute Ocean Model (MPIOM) the ocean component of the MPI-Earth system model. J. Adv. Model. Earth Syst. 5, 422–446 (2013).
Cowtan, K. & Way, R. G. Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends. Q. J. R. Meteorol. Soc. 140, 1935–1944 (2014).
Mann, M. E., Rutherford, S., Wahl, E. & Ammann, C. Robustness of proxy-based climate field reconstruction methods. J. Geophys. Res. 112, D12109 (2007).
Gallant, A. J. E. & Gergis, J. An experimental streamflow reconstruction for the River Murray, Australia, 1783–1988. Wat. Resour. Res. 47, W00G04 (2011).
Gergis, J. et al. On the long-term context of the 1997–2009 ‘Big Dry’ in South-Eastern Australia: insights from a 206-year multi-proxy rainfall reconstruction. Clim. Change 111, 923–944 (2012).
Frank, D. C. et al. Ensemble reconstruction constraints on the global carbon cycle sensitivity to climate. Nature 463, 527–530 (2010).
This is a contribution to the PAGES 2k initiative. PAGES 2k network members are acknowledged for providing input proxy data. J. Emile-Geay provided the graphEM-infilled temperature target grid. Some calculations were run on the Ubelix cluster of the University of Bern. R.N. is supported by the Swiss National Science Foundation (NSF; grant PZ00P2_154802). N.S. was supported by the NOAA Climate and Global Change Postdoctoral Fellowship Program, administered by the University Corporation for Atmospheric Research (UCAR)’s Visiting Scientist Programs, and by US NSF grants OISE-1743738 and AGS-1805490. This is the Lamont-Doherty Earth Observatory (LDEO) contribution number 8324. J.J.G.-N. acknowledges the Juan de la Cierva-Incorporación program (grant IJCI-2015-26914), as well as the Autonomous Community of the Region de Murcia for funding provided through the Seneca Foundation (projects 20022/SF/16 and 20640/JLI/18).
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Coloured areas show global area fractions (as percentages) with warm (red shading) and cold (blue shading) temperature anomalies with respect to the reference period 1–2000 ad (see Methods). a, Annual unfiltered data; b, 51-year butterworth filtered data, over the full ensemble. (Whereas Fig. 2 shows the mean area fractions of the six reconstruction ensemble medians, this figure displays the fraction over all ensemble members and locations.) Like the weak spatial coherence seen in Figs. 3, 4, this ensemble-based illustration shows much weaker spatial coherence (lower percentages) than does Fig. 2. c, As for Fig. 2b, but for 101-year filtered data instead of 51-year filterd data.
a–e, Uncertainties in the century in which peak warming or cooling (Fig. 3) occurred at each location and for each epoch, quantified by bootstrapping. The maps display the standard deviation of 1,000 recalculations of the century that has the largest ensemble probability of peak 51-year warming/cooling on the basis of bootstrap resampling of the 600 ensemble members (Methods). The maps show that the identified cold and warm peaks are generally robust across epochs. The largest uncertainties are found for the DACP epoch and for tropical and Southern Hemisphere regions. The uncertainty in the CWP warming is also very large in the (mainly Antarctic) regions in which peak warming is not identified in the late twentieth century (Fig. 3). f–j, As for panels a–e, but showing the 90% range instead of the standard deviation. Numbers on the y axis and upper x axis are degrees latitude and longitude.
The figure shows peak warming/cooling for each epoch in the proxy records. a–e, All proxies that have full coverage of the respective epoch are shown. f–i, As for panels a–e, but also showing proxies with only partial coverage of the respective epoch. In contrast to Fig. 3, here colours are coded by century, using a differential colour scheme for better visibility. The relative fraction of proxy records with peak warming/cooling in each century is indicated with barplots under the maps. We note that for this figure we use the full, unscreened PAGES2 k v2.0.0 proxy database (the screened network yields a consistent picture). This analysis shows that the heterogeneity in the timing of maxima and minima is an inherent property of the input proxy data themselves, which show a similar lack of global coherence in the timing of each putative preindustrial climate epoch. However, the proxy maps are not directly comparable to the reconstruction maps because the reconstructions are an objectively weighted, statistically optimal fit between all available proxy values using covariance information from a spatial temperature field.
a–e, As for Fig. 3 but using the full unscreened PAGES 2k temperature proxy database. Note that the methods used herein do not incorporate low-frequency records (with resolutions of less than 1 year); therefore, only 559 of the 692 records from the PAGES 2k database were used to generate this figure. Colours in maps indicate the century with the largest ensemble-based probability of containing the warmest (a–c) and coldest (d, e) 51-year period within each climatic epoch (see Methods). f, As for Fig. 4, but using the full unscreened PAGES 2k temperature proxy database. The figure shows the fraction of Earth’s surface (y axis) that simultaneously experienced the warmest (top panels) or coldest (bottom panels) multidecadal period (51 years) during each of five different epochs (see Methods). Each solid circle represents an ensemble member, plotted according to the year in which the largest area experienced peak warm/cold conditions. Horizontal grey shading represents the distribution from the same analysis based on multivariate AR1 noise fields, with darker shading indicating a higher probability. Boxplots on the right show area fractions integrated over time. The centre line is the median; the ends of the boxes represent the interquartile range; and whiskers represent the 90% range. Bold text in panel f represents epochs with reconstructed area fractions that are significantly larger than from the noise fields (Mann–Whitney U-test; α = 0.05). Recall that we searched for CWP maxima within the full 2,000-year reconstruction period. Unlike in Fig. 4, which used the screened proxy matrix, in this figure the period of largest warming within the 2,000-year range falls in the second century ad for one single CCA ensemble member, thus overlapping with the search windows of the RWP period. Therefore, circles representing the CWP have a black border to distinguish them from other epochs.
a–e, As for Fig. 3, but for 101-year instead of 51-year periods. Colours in maps indicate the century that has the largest ensemble-based probability of containing the warmest (a–c) and coldest (d, e) 51-year period within each climatic epoch (see Methods). f, As for Fig. 4, but for 101-year periods. The figure shows the fraction of Earth’s surface (y axis) that simultaneously experienced the warmest (top panels) or coldest (bottom panels) multidecadal period (51 years) during each of five different epochs (see Methods). Each solid circle represents an ensemble member, plotted according to the year in which the largest area experienced peak warm/cold conditions. Horizontal grey shading represents the distributions from the same analysis based on multivariate noise fields from an AR1 analysis, with darker colours indicating higher probabilities. Boxplots on the right show area fractions integrated over time. The centre line is the median; the ends of the boxes represent the interquartile range; and whiskers represent the 90% range. Bold text represents epochs with reconstructed area fractions significantly higher than those from the noise fields (Mann–Whitney U-test; α = 0.05). Recall that we searched for CWP maxima within the full 2,000-year reconstruction period. Unlike the 51-year maxima displayed in Fig. 4, some of the 101-year maxima within this 2,000-year range fall within the pre-1350 period, thus overlapping with the search windows of the RWP and MCA periods. Therefore, circles representing the CWP have a black border to distinguish them from other epochs.
As for Fig. 4, but overlaid with results from PCR AR noise-proxy reconstructions (see also Extended Data Fig. 7) instead of the grey bars that are based on AR(1) noise fields. Shown is the global area fraction that simultaneously experienced the warmest (top) or coldest (bottom) multidecadal period (of 51 years) during each of five different epochs (see Methods). Each solid circle represents an ensemble member plotted according to the year in which the largest area experienced peak warm/cold conditions. The result from each noise-proxy reconstruction ensemble member is shown as a grey circle. Noise-proxy reconstruction circles for the CWP epoch have a black border to distinguish them from the RWP and MCA epochs, because the AR noise-proxy results are scattered through time. Boxplots on the right integrate the area fractions of all ensemble members independently of the timing. The centre line is the median; the ends of the boxes represent the interquartile range; and whiskers represent the 90% range. Note that the area fractions for the noise-proxy reconstructions are lower than for the AR noise fields in Fig. 4, but still only the CWP epoch stands out as having significantly larger fractions than the noise benchmark. Dotted horizontal black lines indicate the area fractions expected from within a spatiotemporally uncorrelated field. In this case, the expected area fraction is modelled with a binomial distribution, with M = 2,592 trials (the number of grid cells), and with the probability of success on each trial being 51/N, where N is the number of years, within which the 51-year peak is searched for each epoch. The dotted lines represent the 95th percentile of this distribution divided by M.
a, As for the CWP panel in Fig. 3, but with reconstructions using noise proxies. Colours in maps indicate the century with the largest ensemble-based probability of containing the warmest 51-year period within the Common Era (see Methods). Maps show the 25 reconstruction realizations, each consisting of six 100-member ensemble reconstructions, for the R-FDR-screened (n = 66) noise-proxy networks (see Methods). b, The global area fraction of peak warmth in each century for each reconstruction method. Top, real proxies (screened); middle, average values across the 25 screened (n = 66) noise-proxy reconstruction ensembles; bottom, average values across the 25 force-screened (n = 210) noise-proxy reconstruction ensembles. c, Fraction of global area having the CWP warm peak within the twentieth century for all three noise-proxy types described in the Methods. Large grey boxplots represent noise-proxy reconstructions across all methods. Grey filled circles show individual noise-proxy reconstructions across all methods. Coloured boxplots show noise-proxy results for the individual reconstruction methods (with colours as in b). Vertical red lines show real proxy reconstructions for both unscreened and screened networks. Boxplots are across 25 reconstruction experiments; centre lines represent median; boxes represent the interquartile range; whiskers show the 95% range. All noise-proxy experiments across all methods yield a weaker spatial agreement of maximum-century 51-year warming compared with the real data reconstructions. The more ‘traditional’ statistical reconstruction methods (CPS, PCR and CCA) mostly exhibit smaller areas of twentieth-century warming in the noise reconstructions than do the other methods (GraphEM, AM and DA; see Methods). A possible explanation for this difference is that the traditional methods are designed to yield reconstructions with as little variance loss as possible independently of data uncertainty (see, for example, ref. 62). Reconstructed temperatures over the full Common Era thus exhibit fluctuations with a magnitude comparable to the calibration period in all noise experiments. By contrast, the newer methods usually generate reconstructed variance that is inversely proportional to the errors in the input data. Thus they converge towards zero with increasing data uncertainty and decreasing coherence among the input data, as is the case in the noise-proxy experiments. For these methods, this results in noise-proxy reconstructions with little temperature variance before the calibration period, and thus a higher probability that the twentieth-century warming exceeds earlier warm periods in magnitude. For a general discussion of the results, see Methods.
Extended Data Fig. 8 Timing of peak warm and cold periods in detrended calibration reconstructions and model data.
Colours in the maps indicate the century with the largest ensemble-based probability of containing the warmest (a–c, e) and coldest (d) 51-year period within each climatic epoch (see Methods). a, As for the CWP panel in Fig. 3, but including barplots below the maps to show the relative occurrence of peak warming in each century for each reconstruction method. b, As for panel a but using only the CPS reconstruction, with calibration based on linearly detrended proxy and instrumental target data. Detrending calibration data partly removes the variance associated with physical processes63, leading to reduced reconstruction skill (discussed in refs 64,65,66,67). Nevertheless, the reconstruction based on detrended data shows warm peaks in the twentieth century over much of the globe, with the exception of the Eurasian land masses and the Southern Hemisphere extratropics. c–e, As for Fig. 3a–e, but using climate-model simulations. We use CMIP568 last-millennium runs from the models BCC-CSM69, CCSM470, CESM-LME54 (member 10), CSIROMk3L-1-271, GISS-E2-R72 (member 127), HadCM373, IPSL-CM5A-LR74 and MPI_ESM_P75. From models with more than one ensemble member, only one member is used, to avoid biases towards single models. Note that because the shortest simulations extend back to the year 851 ad, no results are available for the RWP and DACP periods, and the MCA peak is only searched within the period 851 ad to 1350 ad.
a, Validation metrics (see Methods) for the different reconstruction methods. Boxplots integrate over all grid cells; centre lines are medians; the ends of the boxes represent the interquartile range; and whiskers represent the 90% range. Horizontal axes are adjusted so that better skill is always on the right-hand side. Dotted vertical lines represent the median across all grid cells and methods. Dashed grey lines indicate the value of zero (except for RMSE). Note that over the validation period 1881–1910 ad, the spatial coverage of instrumental data is already very sparse31,76, strongly limiting the validity of verification experiments at the grid-cell level. In addition, the limited number of years available for validation can strongly affect the outcome of skill estimates77,78,79,80. We note that the short validation period does not allow for a robust assessment of reconstruction skill on decadal and lower frequencies. The validation statistics are representative of the most-replicated proxy nest. Extending these estimates back in time requires a nested reconstruction approach, which is not implemented in all methods used herein. Extended Data Fig. 10 shows the corresponding values for the years 1 ad and 1000 ad for the PCR method. The width of the uncertainty intervals shown in Fig. 1 (red line) provides an illustration of the continuously increasing reconstruction errors as we move further back in time. b–e, Maps showing the spatial distribution of skill scores. The mean of all methods is shown. Darker red denotes higher skill in all maps. Proxy locations are indicated with grey circles. In general, the reconstruction skill is lowest in the high southern latitudes, tropical South America and Africa and over some oceanic regions, where coverage by proxy data, but also availability of instrumental data, is sparse.
a, Density of CRPS_RE values in PCR reconstructions based on: the full proxy network (dark yellow, the same as the PCR boxplot in Extended Data Fig. 9); proxy records extending at least to 1000 ad (green); and the records covering the full Common Era (blue). Numbers besides the curves indicate the percentage of grid cells with positive values. b, c, Maps showing the spatial distribution of CRPS_RE for the years 1000 ad (b) and 1 ad (c). Proxy locations are indicated with grey circles. d–f, As for a–c but for the CRPS_CE. g–i, As for a–c but for the RMSE. j–l, As for a–c but for the correlation coefficient. In general the spatial patterns between the time periods we analysed remain similar over time, but with areas of lower skill naturally extending backwards in time (see also the red line in Fig. 1). The largest decrease in skill generally occurs in the first millennium ad. m–o, Average correlation of ensemble median reconstructions accross all methods over the periods 1900–1999 ad (m), 1000–1099 ad (n) and 1–99 ad (o). More than 99% of correlations are positive in all three periods. Respectively 97%, 76% and 73% of correlations in the twentieth, eleventh and first centuries ad are above 0.28, which is the average α = 0.05 significance level given the autocorrelation in the reconstructions. In all periods the method agreement is larger in the Northern Hemisphere, particularly in the North Pacific and European domains, than in the Southern Hemisphere. Lowest agreement is found over tropical South America and Africa and over the Southern Ocean, the same areas that also exhibit the largest errors in the reconstructions.
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Neukom, R., Steiger, N., Gómez-Navarro, J.J. et al. No evidence for globally coherent warm and cold periods over the preindustrial Common Era. Nature 571, 550–554 (2019). https://doi.org/10.1038/s41586-019-1401-2
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