Abstract
This paper provides a concise description of the philosophy, mathematics, and algorithms for estimating, detecting, and attributing climate changes. The estimation follows the spectral method by using empirical orthogonal functions, also called the method of reduced space optimal averaging. The detection follows the linear regression method, which can be found in most textbooks about multivariate statistical techniques. The detection algorithms are described by using the space-time approach to avoid the non-stationarity problem. The paper includes (1) the optimal averaging method for minimizing the uncertainties of the global change estimate, (2) the weighted least square detection of both single and multiple signals, (3) numerical examples, and (4) the limitations of the linear optimal averaging and detection methods.
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Folland, C. K., and Coauthors, 2001: Global temperature change and its uncertainties since 1861. Geophys. Res. Lett., 28, 2621–2624.
Gillett, N. P., M. F. Wehner, S. F. B. Tett, and A. J. Weaver, 2004: Testing the linearity of the response to combined greenhouse gas and sulfate aerosol forcing. Geophys. Res. Lett., 31(14), L14201, doi: 10.1029/2004GL020111.
Grayhill, F. A., and H. K. Iyer, 1994: Regression Analysis: Concepts and Applications. Duxbury Press, California, 701pp.
Hasselmann, K. 1993: Optimal fingerprints for the detection of time-dependent climate change. J. Climate, 6, 1957–1971.
Huang, N. E., M. C. Wu, S. R. Long, S. S. P. Shen, N. H. Hsu, D. Xiong, W. Qu, and P. Gloersen, 2003: On the establishment of a confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc. Roy. Soc. London. Series A., 459, 2317–2345.
IPCC, 2001: Climate Change 2001: The Scientific Basis. Houghton et al., Eds., Cambridge University Press, Cambridge, United kingdom and New York, USA, 881pp.
Johnson, R. A., and D. W. Wichern, 1992: Applied Multivariate Statistical Analysis. Prentice Hall, New Jersey, 642pp.
Lin, Q., 2002: High performance finite element methods. Recent Progress in Computational and Applied PDES. Proc. of the International Symposium on computational and Applied PDES, July 2001, Zhangjiajie, China, Kluwer Academic Publishers, New York, 267–286.
North, G. R., K. Y. Kim, S. S. P. Shen and J. W. Hardin, 1995: Detection of forced climate signals. Part I: Theory. J. Climate, 8, 401–408.
North, G. R., and Q. Wu, 2001: Detecting climate signals using space-time EOFs. J. Climate, 14, 121–145.
Oh, H. S., C. Ammann, P. Naveau, D. Nychka, and B. Otto-Bliesner, 2003: Multi-resolution time series analysis applied to solar irradiance and climate reconstructions. J. Atmospheric and Solar-Terrestrial Phys., 65, 191–201.
Shen, S. S. P., G. R. North, and K. Y. Kim, 1994: Spectral approach to optimal estimation of the global average temperature. J. Climate, 7, 1999–2007.
Shen, S. S. P., T. M. Smith, C. F. Ropelewski, and R.E. Livezey, 1998: An optimal regional averaging method with error estimates and a test using tropical Pacific SST data. J. Climate, 11, 2340–2350.
Zwiers, F. W., 1999: Climate Change Detection: A review of techniques and applications. 1999: Anthropogenic Climate Change, Proc. of the First GKSS Spring School on Environmental Research, von Storch et al., Eds., Springer Verlag, 161-203.
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Shen, S.S.P. Statistical procedures for estimating and detecting climate changes. Adv. Atmos. Sci. 23, 61–68 (2006). https://doi.org/10.1007/s00376-006-0007-4
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DOI: https://doi.org/10.1007/s00376-006-0007-4