Editorial Type:
Article
Article Type:
Research Article

Testing for Deterministic Trends in Global Sea Surface Temperature

Susana M. Barbosa University of Lisbon, IDL, Lisbon, Portugal

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Print Publication:
15 May 2011
DOI:
https://doi.org/10.1175/2010JCLI3877.1
Page(s):
2516–2522
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Abstract

Long-term variability in global sea surface temperature (SST) is often quantified by the slope from a linear regression fit. Attention is then focused on assessing the statistical significance of the derived slope parameter, but the adequacy of the linear model itself, and the inherent assumption of a deterministic linear trend, is seldom tested. Here, a parametric statistical test is applied to test the hypothesis of a linear deterministic trend in global sea surface temperature. The results show that a linear slope is not adequate for describing the long-term variability of sea surface temperature over most of the earth’s surface. This does not mean that sea surface temperature is not increasing, rather that the increase should not be characterized by the slope from a linear fit. Therefore, describing the long-term variability of sea surface temperature by implicitly assuming a deterministic linear trend can give misleading results, particularly in terms of uncertainty, since the actual increase could be considerably larger than the one predicted by a deterministic linear model.

Corresponding author address: Susana Barbosa, IDL, Campo Grande, Ed C8, 1749-016 Lisbon, Portugal. E-mail: sabarbosa@fc.ul.pt

Abstract

Long-term variability in global sea surface temperature (SST) is often quantified by the slope from a linear regression fit. Attention is then focused on assessing the statistical significance of the derived slope parameter, but the adequacy of the linear model itself, and the inherent assumption of a deterministic linear trend, is seldom tested. Here, a parametric statistical test is applied to test the hypothesis of a linear deterministic trend in global sea surface temperature. The results show that a linear slope is not adequate for describing the long-term variability of sea surface temperature over most of the earth’s surface. This does not mean that sea surface temperature is not increasing, rather that the increase should not be characterized by the slope from a linear fit. Therefore, describing the long-term variability of sea surface temperature by implicitly assuming a deterministic linear trend can give misleading results, particularly in terms of uncertainty, since the actual increase could be considerably larger than the one predicted by a deterministic linear model.

Corresponding author address: Susana Barbosa, IDL, Campo Grande, Ed C8, 1749-016 Lisbon, Portugal. E-mail: sabarbosa@fc.ul.pt
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  • Andersen, O. B., and P. Knudsen, B. Beckley, 2002: Monitoring sea level and sea surface temperature trends from ERS satellites. Phys. Chem. Earth, 27, 1413–1417.

    • Search Google Scholar
    • Export Citation

  • Barbosa, S. M., and O. B. Andersen, 2009: Trend patterns in global sea surface temperature. Int. J. Climatol., 29, 2049–2055.

  • Barbosa, S. M., M. E. Silva, and M. J. Fernandes, 2008: Time series analysis of sea-level records: Characterising long-term variability. Lecture Notes Earth Sci., 112, 157–173, doi:10.1007/978-3-540-78938-3_8.

    • Search Google Scholar
    • Export Citation

  • Beran, J., 1994: Statistics for Long-Memory Processes. Chapman & Hall, 315 pp.

  • Casey, K. S., and P. Cornillon, 2001: Global and regional sea surface temperature trends. J. Climate, 14, 3801–3818.

  • Cohn, T. A., and H. F. Lins, 2005: Nature’s style: Naturally trendy. Geophys. Res. Lett., 32, L23402, doi:10.1029/2005GL02447.

  • Dickey, D. A., and W. A. Fuller, 1979: Distribution of the estimators for autoregressive time series with a unit root. J. Amer. Stat. Assoc., 74, 427–431.

    • Search Google Scholar
    • Export Citation

  • Fatichi, S., S. M. Barbosa, E. Caporali, and M. E. Silva, 2009: Deterministic versus stochastic trends: Detection and challenges. J. Geophys. Res., 114, D18121, doi:10.1029/2009JD011960.

    • Search Google Scholar
    • Export Citation

  • Fomby, T. B., and T. J. Vogelsand, 2002: The application of size-robust trend statistics to global-warming temperature series. J. Climate, 15, 117–123.

    • Search Google Scholar
    • Export Citation

  • Fraedrich, K., and R. Blender, 2003: Scaling of atmosphere and ocean temperature correlations in observations and climate models. Phys. Rev. Lett., 90, 108501, doi:10.1103/PhysRevLett.90.108501.

    • Search Google Scholar
    • Export Citation

  • Fraedrich, K., U. Luksch, and R. Blender, 2004: 1/f model for long-time memory of the ocean surface temperature. Phys. Rev. E, 70, 037301, doi:10.1103/PhysRevE.70.037301.

    • Search Google Scholar
    • Export Citation

  • Ghil, M., and R. Vautard, 1991: Interdecadal oscillations and the warming trend in global temperature time series. Nature, 350, 324–327.

    • Search Google Scholar
    • Export Citation

  • Hamilton, D. J., 1994: Time Series Analysis. Princeton University Press, 820 pp.

  • Hasselmann, K., 1976: Stochastic climate models I: Theory. Tellus, 28, 473–485.

  • Kallache, M., H. W. Rust, and J. Kroop, 2005: Trend assessement: Applications for hydrology and climate research. Nonlinear Processes Geophys., 12, 201–210.

    • Search Google Scholar
    • Export Citation

  • Koutsoyiannis, D., 2006: Nonstationarity versus scaling in hydrology. J. Hydrol., 324, 239–254, doi:10.1016/j.jhydrol.2005.09.022.

  • Koutsoyiannis, D., and A. Montanari, 2007: Statistical analysis of hydroclimatic time series: Uncertainty and insights. Water Resour. Res., 43, W05429, doi:10.1029/2006WR005592.

    • Search Google Scholar
    • Export Citation

  • Kwiatkowski, D., P. Phillips, P. Schmidt, and Y. Shin, 1992: Testing the null hypothesis of stationarity against the alternative of a unit root. J. Econom., 54, 159–178.

    • Search Google Scholar
    • Export Citation

  • Lee, J., and R. Lund, 2004: Revisiting simple linear regression with autocorrelated errors. Biometrika, 91, 240–245.

  • Lennartz, S., and A. Bunde, 2009: Trend evaluation in records with long-term memory: Application to global warming. Geophys. Res. Lett., 36, L16706, doi:10.1029/2009GL039516.

    • Search Google Scholar
    • Export Citation

  • Miranda, P. M. A., and A. R. Tomé, 2009: Spatial structure of the evolution of surface temperature (1951–2004). Climatic Change, 93, 269–284, doi:10.1007/s10584-008-9540-8.

    • Search Google Scholar
    • Export Citation

  • Phillips, P. C. B., and P. Perron, 1988: Testing for a unit root in time series regression. Biometrika, 75, 335–346.

  • Rybski, D., and A. Bunde, 2009: On the detection of trends in long-term correlated records. Physica A, 388, 1687–1695.

  • Rybski, D., A. Bunde, S. Havlin, and H. von Storch, 2006: Long-term persistence in climate and the detection problem. Geophys. Res. Lett., 33, L06718, doi:10.1029/2005GL025591.

    • Search Google Scholar
    • Export Citation

  • Said, S. E., and D. A. Dickey, 1984: Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71, 599–607.

    • Search Google Scholar
    • Export Citation

  • Smith, T. M., and R. W. Reynolds, 2005: A global merged land–air–sea surface temperature reconstruction based on historical observations (1880–1997). J. Climate, 18, 2021–2036.

    • Search Google Scholar
    • Export Citation

  • Smith, T. M., R. W. Reynolds, T. C. Peterson, and J. Lawrimore, 2008: Improvements to NOAA’s historical merged land-ocean surface temperature analysis (1880–2006). J. Climate, 21, 2283–2296.

    • Search Google Scholar
    • Export Citation

  • Thompson, D. W. J., J. M. Wallace, J. J. Kennedy, and P. D. Jones, 2010: An abrupt drop in northern hemisphere sea surface temperature around 1970. Nature, 467, 444–447.

    • Search Google Scholar
    • Export Citation

  • Trapletti, A., and K. Hornik, 2009: tseries: Time Series Analysis and Computational Finance. R package version 0.10–22. [Available online at http://CRAN.R-project.org/package=tseries.]

    • Search Google Scholar
    • Export Citation

  • Vinod, H. D., and J. L. de Lacalle, 2009: Maximum entropy bootstrap for time series: The meboot R package. J. Stat. Software, 29. [Available online at http://www.jstatsoft.org/v29/i05/paper.]

    • Search Google Scholar
    • Export Citation

  • Woodward, W. A., and H. L. Gray, 1995: Selecting a model for detecting the presence of a trend. J. Climate, 8, 1929–1937.

  • Wunsch, C., 1999: The interpretation of short climatic records. Bull. Amer. Meteor. Soc., 80, 245–255.

  • Zheng, X., and R. E. Basher, 1999: Structural time series models and trend detection in global and regional temperature series. J. Climate, 12, 2347–2358.

    • Search Google Scholar
    • Export Citation
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