• Barnett, T. P., and R. W. Preisendorfer, 1987: Origins and levels of monthly and seasonal forecast skill for United States surface air temperatures determined by canonical correlation analysis. Mon. Wea. Rev., 115 , 18251850.

    • Search Google Scholar
    • Export Citation
  • Beltrami, H., 2002: Climate from borehole data: Energy fluxes and temperatures since 1500. Geophys. Res. Lett., 29 , 2111. doi:10.1029/2002GL015702.

    • Search Google Scholar
    • Export Citation
  • Bond, G., and Coauthors, 2001: Persistent solar influence on North Atlantic climate during the Holocene. Science, 294 , 21302136. doi:10.1126/science.1065680.

    • Search Google Scholar
    • Export Citation
  • Bradley, R. S., and P. D. Jones, 1993: “Little Ice Age” summer temperature variations: Their nature and relevance to recent global warming trends. Holocene, 3 , 367376.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., C. Smith, and J. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Briffa, K. R., P. D. Jones, T. M. L. Wigley, J. R. Pilcher, and M. G. L. Baillie, 1986: Climate reconstruction from tree rings: Part 2, spatial reconstructions of summer mean sea-level pressure patterns over Great Britain. J. Climatol., 6 , 115.

    • Search Google Scholar
    • Export Citation
  • Bürger, G., 2007: On the verification of climate reconstructions. Climate Past, 3 , 397409.

  • Bürger, G., and U. Cubasch, 2005: Are multiproxy climate reconstructions robust? Geophys. Res. Lett., 32 , L23711. doi:10.1029/2005GL024155.

    • Search Google Scholar
    • Export Citation
  • Bürger, G., I. Fast, and U. Cubasch, 2006: Climate reconstruction by regression—32 variations on a theme. Tellus, 58A , 227235.

  • Christiansen, B., 2000: A model study of the dynamical connection between the Arctic Oscillation and stratospheric vacillations. J. Geophys. Res., 105 , 2946129474.

    • Search Google Scholar
    • Export Citation
  • Christiansen, B., 2007: Atmospheric circulation regimes: Can cluster analysis provide the number? J. Climate, 20 , 22292250.

  • Cook, E. R., and L. A. Kairukstis, Eds. 1990: Methods of Dendrochronology: Applications in the Environmental Sciences. Kluwer Academic, 394 pp.

    • Search Google Scholar
    • Export Citation
  • Cook, E. R., K. B. Briffa, and P. D. Jones, 1994: Spatial regression methods in dendroclimatology: A review and comparison of two techniques. J. Climatol., 14 , 379402.

    • Search Google Scholar
    • Export Citation
  • Dahl-Jensen, D., K. Mosegaard, N. Gundestrup, G. D. Clow, S. J. Johnsen, A. W. Hansen, and N. Balling, 1998: Past temperatures directly from the Greenland Ice Sheet. Science, 282 , 268271. doi:10.1126/science.282.5387.268.

    • Search Google Scholar
    • Export Citation
  • Dansgaard, W., H. B. Clausen, N. Gundestrup, C. U. Hammer, S. F. Johnsen, P. M. Kristinsdottir, and N. Reeh, 1982: A new Greenland deep ice core. Science, 218 , 12731277. doi:10.1126/science.218.4579.1273.

    • Search Google Scholar
    • Export Citation
  • Esper, J., E. R. Cook, and F. H. Schweingruber, 2002: Low-frequency signals in long tree-ring chronologies for reconstructing past temperature variability. Science, 295 , 22502253.

    • Search Google Scholar
    • Export Citation
  • Fierro, R. D., G. H. Golub, P. C. Hansen, and D. P. O’Leary, 1997: Regularization by truncated total least squares. SIAM J. Sci. Comput., 18 , 12231241.

    • Search Google Scholar
    • Export Citation
  • Fritts, H. C., 1976: Tree Rings and Climate. Academic Press, 567 pp.

  • Fritts, H. C., T. J. Blasing, B. P. Hayden, and J. E. Kutzbach, 1971: Multivariate techniques for specifying tree-growth and climate relationships and for reconstructing anomalies in paleoclimate. J. Appl. Meteor., 10 , 845864.

    • Search Google Scholar
    • Export Citation
  • Groveman, B. S., 1979: Reconstruction of Northern Hemisphere temperature: 1579–1880. Ph.D. thesis, University of Maryland, 78 pp.

  • Groveman, B. S., and H. E. Landsberg, 1979: Simulated Northern Hemisphere temperature departures 1579–1880. Geophys. Res. Lett., 6 , 767770.

    • Search Google Scholar
    • Export Citation
  • Halpert, M. S., and C. F. Ropelewski, 1992: Surface temperature patterns associated with the Southern Oscillation. J. Climate, 5 , 577593.

    • Search Google Scholar
    • Export Citation
  • Harris, R. N., and D. S. Chapman, 2001: Mid-latitude (30°–60°N) climatic warming inferred by combining borehole temperatures with surface air temperatures. Geophys. Res. Lett., 28 , 747750.

    • Search Google Scholar
    • Export Citation
  • Hegerl, G. C., T. J. Crowley, M. Allen, W. T. Hyde, H. N. Pollack, J. Smerdon, and E. Zorita, 2007: Detection of human influence on a new, validated 1500-year temperature reconstruction. J. Climate, 20 , 650666.

    • Search Google Scholar
    • Export Citation
  • Huang, S., H. N. Pollack, and P-Y. Shen, 2000: Temperature trends over the last five centuries reconstructed from borehole temperatures. Nature, 403 , 756758.

    • Search Google Scholar
    • Export Citation
  • Jones, P. D., and K. R. Briffa, 1992: Global surface air temperature variations during the twentieth century: Part 1, Spatial, temporal and seasonal details. Holocene, 2 , 165179.

    • Search Google Scholar
    • Export Citation
  • Jones, P. D., and M. E. Mann, 2004: Climate over past millennia. Rev. Geophys., 42 , RG2002. doi:10.1029/2003RG000143.

  • Klein, W. H., B. M. Lewis, and I. Enger, 1959: Objective prediction of five-day mean temperatures during winter. J. Meteor., 16 , 672682.

    • Search Google Scholar
    • Export Citation
  • Manley, G., 1953: The mean temperature of Central England, 1698 to 1952. Quart. J. Roy. Meteor. Soc., 79 , 242261.

  • Mann, M. E., and S. Rutherford, 2002: Climate reconstruction using ‘pseudoproxies.’. Geophys. Res. Lett., 29 , 1501. doi:10.1029/2001GL014554.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., R. S. Bradley, and M. K. Hughes, 1998: Global-scale temperature patterns and climate forcing over the past six centuries. Nature, 392 , 779787.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., R. S. Bradley, and M. K. Hughes, 2004: Corrigendum: Global-scale temperature patterns and climate forcing over the past six centuries. Nature, 430 , 105. doi:10.1038/nature02478.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., S. Rutherford, E. Wahl, and C. Ammann, 2005: Testing the fidelity of methods used in proxy-based reconstructions of past climate. J. Climate, 18 , 40974107.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., S. Rutherford, E. Wahl, and C. Ammann, 2007a: Reply. J. Climate, 20 , 36993703.

  • Mann, M. E., S. Rutherford, E. Wahl, and C. Ammann, 2007b: Robustness of proxy-based climate field reconstruction methods. J. Geophys. Res., 112 , D12109. doi:10.1029/2006JD008272.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., S. Rutherford, E. Wahl, and C. Ammann, 2007c: Reply. J. Climate, 20 , 56715674.

  • McIntyre, S., and R. McKitrick, 2005: Hockey sticks, principal components, and spurious significance. Geophys. Res. Lett., 32 , L03710. doi:10.1029/2004GL021750.

    • Search Google Scholar
    • Export Citation
  • Moberg, A., D. M. Sonechkin, K. Holmgren, N. M. Datsenko, and W. Karlén, 2005: Highly variable northern hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature, 433 , 613617.

    • Search Google Scholar
    • Export Citation
  • National Research Council, 2006: Surface Temperature Reconstructions for the Last 2,000 Years. National Academies Press, 196 pp.

  • Ogilvie, A. E. J., 1996: Sea-ice conditions off the coasts of Iceland A.D. 1601–1850 with special reference to part of the Maunder Minimum period (1675–1715). North European Climate Data in the Latter Part of the Maunder Minimum Period A.D. 1675–1715, E. S. Pedersen, Ed., Museum of Archaeology, 9–12.

    • Search Google Scholar
    • Export Citation
  • Parker, D. E., and E. B. Horton, 2005: Uncertainties in central England temperature 1878–2003 and some improvements to the maximum and minimum series. Int. J. Climatol., 25 , 11731188.

    • Search Google Scholar
    • Export Citation
  • Pfister, C., 1995: Monthly temperature and precipitation in central Europe from 1525–1979: Quantifying documentary evidence on weather and its effects. Climate Since A.D. 1500, R. S. Bradley and P. D. Jones, Eds., Routledge, 118–142.

    • Search Google Scholar
    • Export Citation
  • Pfister, C., J. Luterbacher, G. Schwarz-Zanetti, and M. Wegmann, 1998: Winter air temperature variations in Central Europe during the early and high Middle Ages (A.D. 750–1300). Holocene, 8 , 547564.

    • Search Google Scholar
    • Export Citation
  • Pollack, H. N., and S. Huang, 2000: Climate reconstruction from subsurface temperatures. Annu. Rev. Earth Planet. Sci., 28 , 339365.

  • Pollack, H. N., and J. E. Smerdon, 2004: Borehole climate reconstructions: Spatial structure and hemispheric averages. J. Geophys. Res., 109 , D11106. doi:10.1029/2003JD004163.

    • Search Google Scholar
    • Export Citation
  • Preisendorfer, R. W., and C. D. Mobley, 1988: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 426 pp.

  • Rahmstorf, S., 2006: Testing climate reconstructions. Science, 312 , 18721873.

  • Rutherford, S., M. E. Mann, T. L. Delworth, and R. J. Stouffer, 2003: Climate field reconstruction under stationary and nonstationary forcing. J. Climate, 16 , 462479.

    • Search Google Scholar
    • Export Citation
  • Rutherford, S., M. E. Mann, T. J. Osborn, R. S. Bradley, K. R. Briffa, M. K. Hughes, and P. D. Jones, 2005: Proxy-based Northern Hemisphere surface temperature reconstructions: Sensitivity to method, predictor network, target season, and target domain. J. Climate, 18 , 23082329.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., 2001: Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. J. Climate, 14 , 853871.

    • Search Google Scholar
    • Export Citation
  • Sen, A. K., and M. Srivastava, 1990: Regression Analysis: Theory, Methods, and Applications. Springer-Verlag, 372 pp.

  • Smerdon, J. E., and A. Kaplan, 2007: Comments on “Testing the fidelity of methods used in proxy-based reconstructions of past climate”: The role of the standardization interval. J. Climate, 20 , 56665670.

    • Search Google Scholar
    • Export Citation
  • Smerdon, J. E., A. Kaplan, and D. Chang, 2008: On the origin of the standardization sensitivity in RegEM climate field reconstructions. J. Climate, 21 , 67106723.

    • Search Google Scholar
    • Export Citation
  • Stendel, M., I. A. Mogensen, and J. H. Christensen, 2006: Influence of various forcings on global climate in historical times using a coupled atmosphere-ocean general circulation model. Climate Dyn., 26 , 115.

    • Search Google Scholar
    • Export Citation
  • van Huffel, S., and J. Vandewalle, 1991: The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, 314 pp.

  • von Storch, H., E. Zorita, J. M. Jones, Y. Dimitriev, F. Gonzalez-Rouco, and S. F. B. Tett, 2004: Reconstructing past climate from noisy data. Science, 306 , 679682.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., E. Zorita, J. M. Jones, F. Gonzalez-Rouco, and S. F. B. Tett, 2006a: Response to comment on “Reconstruction past climate from noisy data.”. Science, 312 , 529. doi:10.1126/science.1121571.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., E. Zorita, J. M. Jones, F. Gonzalez-Rouco, and S. F. B. Tett, 2006b: Response to “Testing climate reconstructions.”. Science, 312 , 18721873.

    • Search Google Scholar
    • Export Citation
  • Wahl, E. R., D. M. Ritson, and C. M. Ammann, 2006: Comment on “Reconstructing past climate from noisy data.”. Science, 312 , 529530. doi:10.1126/science.112086.

    • Search Google Scholar
    • Export Citation
  • Wolfe, A. P., G. H. Miller, C. A. Olsen, S. L. Forman, P. T. Doran, and S. U. Holmgren, 2004: Geochronology of high latitude lake sediments. Long-Term Environmental Change in Arctic and Antarctic Lakes, R. Pienitz, M. S. V. Douglas, and J. P. Smol, Eds., Kluwer Academic, 1–32.

    • Search Google Scholar
    • Export Citation
  • Zorita, E., F. Gonzales-Rouco, and S. Legutke, 2003: Testing the Mann et al. (1998) approach to paleoclimate reconstructions in the context of a 1000-year control simulation with the ECHO-G coupled climate model. J. Climate, 16 , 13781390.

    • Search Google Scholar
    • Export Citation
  • Zorita, E., F. Gonzales-Rouco, and H. von Storch, 2007: Comments on “Testing the fidelity of methods used in proxy-based reconstructions of past climate.”. J. Climate, 20 , 36933698.

    • Search Google Scholar
    • Export Citation
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A Surrogate Ensemble Study of Climate Reconstruction Methods: Stochasticity and Robustness

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  • 1 Danish Meteorological Institute, Copenhagen, Denmark
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Abstract

Reconstruction of the earth’s surface temperature from proxy data is an important task because of the need to compare recent changes with past variability. However, the statistical properties and robustness of climate reconstruction methods are not well known, which has led to a heated discussion about the quality of published reconstructions. In this paper a systematic study of the properties of reconstruction methods is presented. The methods include both direct hemispheric-mean reconstructions and field reconstructions, including reconstructions based on canonical regression and regularized expectation maximization algorithms. The study will be based on temperature fields where the target of the reconstructions is known. In particular, the focus will be on how well the reconstructions reproduce low-frequency variability, biases, and trends.

A climate simulation from an ocean–atmosphere general circulation model of the period a.d. 1500–1999, including both natural and anthropogenic forcings, is used. However, reconstructions include a large element of stochasticity, and to draw robust statistical interferences, reconstructions of a large ensemble of realistic temperature fields are needed. To this end a novel technique has been developed to generate surrogate fields with the same temporal and spatial characteristics as the original surface temperature field from the climate model. Pseudoproxies are generated by degrading a number of gridbox time series. The number of pseudoproxies and the relation between the pseudoproxies and the underlying temperature field are determined realistically from Mann et al.

It is found that all reconstruction methods contain a large element of stochasticity, and it is not possible to compare the methods and draw conclusions from a single or a few realizations. This means that very different results can be obtained using the same reconstruction method on different surrogate fields. This might explain some of the recently published divergent results.

Also found is that the amplitude of the low-frequency variability in general is underestimated. All methods systematically give large biases and underestimate both trends and the amplitude of the low-frequency variability. The underestimation is typically 20%–50%. The shape of the low-frequency variability, however, is well reconstructed in general.

Some potential in validating the methods on independent data is found. However, to gain information about the reconstructions’ ability to capture the preindustrial level it is necessary to consider the average level in the validation period and not the year-to-year correlations. The influence on the reconstructions of the number of proxies, the type of noise used to generate the proxies, the strength of the variability, as well as the effect of detrending the data prior to the calibration is also reported.

Corresponding author address: B. Christiansen, Danish Meteorological Institute, Danish Climate Centre, Lyngbyvej 100, DK-2100 Copenhagen Ø, Denmark. Email: boc@dmi.dk

Abstract

Reconstruction of the earth’s surface temperature from proxy data is an important task because of the need to compare recent changes with past variability. However, the statistical properties and robustness of climate reconstruction methods are not well known, which has led to a heated discussion about the quality of published reconstructions. In this paper a systematic study of the properties of reconstruction methods is presented. The methods include both direct hemispheric-mean reconstructions and field reconstructions, including reconstructions based on canonical regression and regularized expectation maximization algorithms. The study will be based on temperature fields where the target of the reconstructions is known. In particular, the focus will be on how well the reconstructions reproduce low-frequency variability, biases, and trends.

A climate simulation from an ocean–atmosphere general circulation model of the period a.d. 1500–1999, including both natural and anthropogenic forcings, is used. However, reconstructions include a large element of stochasticity, and to draw robust statistical interferences, reconstructions of a large ensemble of realistic temperature fields are needed. To this end a novel technique has been developed to generate surrogate fields with the same temporal and spatial characteristics as the original surface temperature field from the climate model. Pseudoproxies are generated by degrading a number of gridbox time series. The number of pseudoproxies and the relation between the pseudoproxies and the underlying temperature field are determined realistically from Mann et al.

It is found that all reconstruction methods contain a large element of stochasticity, and it is not possible to compare the methods and draw conclusions from a single or a few realizations. This means that very different results can be obtained using the same reconstruction method on different surrogate fields. This might explain some of the recently published divergent results.

Also found is that the amplitude of the low-frequency variability in general is underestimated. All methods systematically give large biases and underestimate both trends and the amplitude of the low-frequency variability. The underestimation is typically 20%–50%. The shape of the low-frequency variability, however, is well reconstructed in general.

Some potential in validating the methods on independent data is found. However, to gain information about the reconstructions’ ability to capture the preindustrial level it is necessary to consider the average level in the validation period and not the year-to-year correlations. The influence on the reconstructions of the number of proxies, the type of noise used to generate the proxies, the strength of the variability, as well as the effect of detrending the data prior to the calibration is also reported.

Corresponding author address: B. Christiansen, Danish Meteorological Institute, Danish Climate Centre, Lyngbyvej 100, DK-2100 Copenhagen Ø, Denmark. Email: boc@dmi.dk

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