Abstract
Timeseries of estimated temperature have been combined to create global or hemispheric climate series over periods exceeding 1000 yr. The data used in these studies, however, may be subject to dating errors. It is shown that when timeseries with dating error are combined, the noise in the data smoothes periodic signals but leaves linear trends intact. This means that the effect of dating error of sample data in a timeseries reconstruction is to smooth out any signals (waves, cycles) that may be present. The purpose of this study was to develop signal extraction methods that will work for this type of historical data. The method used was nonlinear estimation of sample series where dating error has been added by Monte Carlo sampling. Several algorithms were tested for handling the dating error problem. Results were that using nonlinear model fitting, the periods of signals can be identified even from the averaged data. In a second stage of the estimation procedure, the cycle magnitudes can be estimated. Very good fits were achieved for two example cases. Temperature estimation error (white noise due to the use of proxies) was also considered and the method was extended to cover this case with quite good results. Using the new estimation methods, the information inherent in multiple series can be used to overcome the problem of dating error.
Similar content being viewed by others
References
Anderson, N. J., 2000, Diatoms, temperature and climate change: Eur. J. Phycol., v. 35, p. 307–314.
Bradley, R. S., Hughes, M. K., and Diaz, H. F., 2003, Climate in medieval time: Science, v. 302, p. 404–405.
Crowley, T. J., 2000, Causes of climate change over the past 1000 years: Science, v. 289, p. 270–277.
Crowley, T. J., and Lowery, T. S., 2000, How warm was the Medieval warm period?: Ambio, v. 29, p. 51.
Damon, P. E., and Jirikowic, J. L., 1992, The sun as a low-frequency harmonic oscillator: Radiocarbon 34, p. 199–205.
Efrom, B., and Tibshirani, R. J., 1993, An introduction to the bootstrap: Chapman & Hall, New York, 436 p.
Ferraz-Mello, S., 1981. Estimation of periods from unequally spaced observations: Astronom. J., v. 86 p. 619–624.
Goslar, T., Arnold, M., Tisnerat-Laborde, N., Czernik, J., and Wickowski, K., 2000, Variations of Younger Dryas atmospheric radiocarbon explicable without ocean circulation changes: Nature, v. 403, p. 877–880.
Grewal, M. S., and Andrews, A. P., 1993, Kalman filtering: Theory and practice: Prentice-Hall, Englewood Cliffs, New Jersey. 381 p.
Hu, F. S., Kaufman, D., Yoneji, S., Nelson, D., Shemesh, A., Huang, Y., Tian, J., Bond, G., Clegg, B., and Brown, T., 2003, Cyclic variation and solar forcing of holocene climate in the Alaskan subarctic: Science, v. 301, p. 1890–1893.
Jones, P., 1998, It was the best of times, it was the worst of times: Science, v. 280, p. 544–545.
Karner, D. B., and Muller, R. A., 2000, A causality problem for Milankovitch: Science, v. 288, p. 2143–2144.
Kullman, L., 1998, Holocene history of the forest-alpine tundra ecotone in the Scandes Mountains (central Sweden): The New Phytologist, v. 108, p. 101–110.
Loehle, C., 2004, Climate change: detection and attribution of trends from long-term geologic data: Ecol. Model., v. 171, p. 433–450.
Mann, M. E., and Lees, J. M., 1996, Robust estimation of background noise and signal detection in climatic timeseries: Clim. Change, v. 33, p. 409–445.
Mann, M. E., Bradley, R. S., and Hughes, M. K., 1998, Global-scale temperature patterns and climate forcing over the past six centuries: Nature, v. 392, p. 779–787.
Mann, M. E., Bradley, R. S., and Hughes, M. K., 1999, Northern hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations: Geophys. Res. Lett., v. 26, p. 759–762.
Mann, M. E., Park, J., and Bradley, R. S., 1995, Global interdecadal and century-scale climate oscillations during the past five centuries: Nature, v. 378, p. 266–270.
Overpeck, J., Hughen, K., Hardy, D., Bradley, R., Case, R., Douglas, M., Finney, B., Gajewski, K., Jacoby, G., Jennings, A., Lamoureux, S., Lasca, A., MacDonald, G., Moore, J., Retelle, M., Smith, S., Wolfe, A., and Zielinski, G., 1997, Arctic environmental change of the last four centuries: Science, v. 278, p. 1251–1256.
Pienitz, R., Smol, J. P., and MacDonald, G. M., 1999, Paleolimnological reconstruction of Holocene climatic trends from two boreal tree-line lakes, Northwest Territories, Canada: Arctic, Antarctic Alpine Res., v. 31, p. 82–93.
Rempel, A. W., Waddington, E. D., Wettlaufer, J. S., and Worster, M. G., 2001, Possible displacement of the climate signal in ancient ice by premelting and anomalous diffusion: Nature, v. 411, p. 568–571.
Seppä, H., and Weckström, J., 1999, Holocene vegetational and limnological changes in the Fennoscandian tree-line area as documented by pollen and diatom records from Lake Tsulbmajavri, Finland: Ecoscience, v. 6, p. 621–635.
Soon, W. H., and Baliunas, S., 2003, Proxy climatic and environmental changes of the past 1000 years: Clim. Res. v. 23, p. 89–110.
Vogel, J. C., 2002, Secular variations in carbon-14 and their geophysical implications: South African J. Sci., v. 98, p. 154–160.
Von Storch, H., and Zwiers, F. W., 1999, Statistical analysis in climate research: Cambridge University Press, Cambridge, 484 p.
Wilks, D. S., 1995, Statistical methods in the atmospheric sciences: Academic Press, New York. 467 p.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Loehle, C. Estimating Climatic Timeseries From Multi-Site Data Afflicted With Dating Error. Math Geol 37, 127–140 (2005). https://doi.org/10.1007/s11004-005-1305-6
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11004-005-1305-6