Climatic Change

, Volume 47, Issue 4, pp 411–438 | Cite as

Detecting a Global Warming Signal in Hemispheric Temperature Series: AStructural Time Series Analysis

  • David I. Stern
  • Robert K. Kaufmann
Article

Abstract

Non-stationary time series such as global andhemispheric temperatures, greenhouse gasconcentrations, solar irradiance, and anthropogenicsulfate aerosols, may contain stochastic trends (thesimplest stochastic trend is a random walk) which, dueto their unique patterns, can act as a signal of theinfluence of other variables on the series inquestion. Two or more series may share a commonstochastic trend, which indicates that either oneseries causes the behavior of the other or that thereis a common driving variable. Recent developments ineconometrics allow analysts to detect and classifysuch trends and analyze relationships among seriesthat contain stochastic trends. We apply someunivariate autoregression based tests to evaluate thepresence of stochastic trends in several time seriesfor temperature and radiative forcing. The temperatureand radiative forcing series are found to be ofdifferent orders of integration which would cast doubton the anthropogenic global warming hypothesis.However, these tests can suffer from size distortionswhen applied to noisy series such as hemispherictemperatures. We, therefore, use multivariatestructural time series techniques to decomposeNorthern and Southern Hemisphere temperatures intostochastic trends and autoregressive noise processes. These results show that there are two independentstochastic trends in the data. We investigate thepossible origins of these trends using a regressionmethod. Radiative forcing due to greenhouse gases andsolar irradiance can largely explain the common trend.The second trend, which represents the non-scalarnon-stationary differences between the hemispheres,reflects radiative forcing due to tropospheric sulfateaerosols. We find similar results when we use the sametechniques to analyze temperature data generated bythe Hadley Centre GCM SUL experiment.

Keywords

Global Warming Solar Irradiance Stochastic Trend Series Technique Hemisphere Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H.: 1973, 'Information Theory and an Extension of the Maximum Likelihood Principle', in Petrov, B. N. and Csaki, F. (eds.), 2nd International Symposium on Information Theory, Akademini Kiado, Budapest, pp. 267-281.Google Scholar
  2. Andrews, D. W. K.: 1991, 'Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation', Econometrica 59, 817-858.Google Scholar
  3. A.S.L. and Associates: 1997, Sulfur Emissions by Country and Year, Report No. DE96014790, U.S. Department of Energy, Washington D.C.Google Scholar
  4. Battle, M., Bender, M., Sowers, T., Tans, P. P., Butler, J. H., Elkins, J. W., Ellis, J. T., Conway, T., Zhang, N., Lang, P., and Clarke, A. D.: 1996, 'Atmospheric Gas Concentrations over the Past Century Measured in Air from Firn at the South Pole', Nature 383, 231-235.Google Scholar
  5. Berndt, E., Hall, B., Hall, R. E., and Hausman, J. A.: 1974, 'Estimation and Inference in Non-Linear Structural Models', Ann. Econ. Soc. Measure. 55, 653-665.Google Scholar
  6. Chernoff, H.: 1954, 'On the Distribution of the Likelihood Ratio', Ann. Math. Stat. 25, 573-578.Google Scholar
  7. Cunnold, D., Fraser, P., Weiss, R., Prinn, R., Simmonds, P., Miller, B., Alyea, F., and Crawford, A.: 1994, 'Global Trends and Annual Releases of CCl3F and CCl2F2 Estimated from ALE/GAGE and Other Measurements from July 1978 to June 1991', J. Geophys. Res. 99 (D1), 1107-1126.Google Scholar
  8. De Jong, P.: 1988, 'The Likelihood for a State Space Model', Biometrika 75, 165-169.Google Scholar
  9. De Jong, P.: 1991a, 'Stable Algorithms for the State Space Model', J. Time Ser. Anal. 12 (2), 143-157.Google Scholar
  10. De Jong, P.: 1991b, 'The Diffuse Kalman Filter', Ann. Stat. 19, 1073-1083.Google Scholar
  11. Dickey, D. A. and Fuller, W. A.: 1979, 'Distribution of the Estimators for Autoregressive Time Series with a Unit Root', J. Amer. Stat. Assoc. 74, 427-431.Google Scholar
  12. Dickey, D. A. and Fuller, W. A.: 1981, 'Likelihood Ratio Statistics for Autoregressive Processes', Econometrica 49, 1057-1072.Google Scholar
  13. Dlugokenchy, E. J., Lang, P. M., Masarie, K. A., and Steele, L. P.: 1994, 'Global CH4 Record from the NOAA/CMDL Air Sampling Network', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 262-266.Google Scholar
  14. Enders, W.: 1995, Applied Econometric Time Series, John Wiley, New York.Google Scholar
  15. Engle, R. E. and Granger, C. W. J.: 1987, 'Cointegration and Error-Correction: Representation, Estimation, and Testing', Econometrica 55, 251-276.Google Scholar
  16. Etheridge, D.M., Pearman, G. I., and Fraser, P. J.: 1994, 'Historical CH4 Record from the “DE08” Ice Core at Law Dome', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 256-260.Google Scholar
  17. Etheridge, D. M., Steele, L. P., Langenfelds, R. L., Francey, R. J., Barnola, J.-M., and Morgan, V. I.: 1996, 'Natural and Anthropogenic Changes in Atmospheric CO2 over the Last 1000 Years from Air in Antarctic Ice and Firn', J. Geophys. Res. 101, 4115-4128.Google Scholar
  18. Fletcher, R. and Powell, M. J. D.: 1963, 'A Rapidly Convergent Descent Method for Minimization', Computer J. 6, 163-168.Google Scholar
  19. Folland, C. K., Karl, T. R., Nicholls, N., Nyenzi, B. S., Parker, D. E., and Vinnikov, K. Y.: 1992, 'Observed Climate Variability and Change', in Houghton, J. T., Callander, B. A., and Varney, S. K. (eds.), Climate Change 1992: The Supplementary Report to the IPCC Scientific Assessment, Cambridge University Press, Cambridge, pp. 139-170.Google Scholar
  20. Granger C. W. J. and Newbold, P.: 1974, 'Spurious Regressions in Econometrics', J. Econometrics 35, 143-159.Google Scholar
  21. Haldrup, N.: 1997, A Review of the Econometric Analysis of I(2) Variables, Working Paper No. 1997-12, Centre for Non-linear Modelling in Economics, University of Aarhus, Aarhus, Denmark.Google Scholar
  22. Hamilton, J. D.: 1994, Time Series Analysis, Princeton University Press, Princeton, NJ.Google Scholar
  23. Hansen, H. and Juselius, K.: 1995, CATS in RATS: Cointegration Analysis of Time Series, Estima, Evanston IL.Google Scholar
  24. Harman, H. H.: 1976, Modern Factor Analysis, University of Chicago Press, Chicago, IL.Google Scholar
  25. Harvey, A. C.: 1989, Forecasting, Structural Time Series Models, and the Kalman Filter, Cambridge University Press, Cambridge.Google Scholar
  26. Harvey, A. C.: 1993, Time Series Models, 2nd edn., Harvester Wheatsheaf, London.Google Scholar
  27. Johansen, S.: 1988, 'Statistical Analysis of Cointegration Vectors', J. Econ. Dyn. Control 12, 231-254.Google Scholar
  28. Jones, P. D., Wigley, T. M. L., and Biffa, K. R.: 1994, 'Global and Hemispheric Temperature Anomalies-Land and Marine Instrumental Records', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., and Stoss, F. S. (eds.), Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 603-608.Google Scholar
  29. Kattenberg, A., Giorgi, F., Grassl, H., Meehl, G. A., Mitchell, J. F. B., Stouffer, R. J., Tokioka, T., Weaver, A. J., and Wigley, T. M. L.: 1996, 'Climate Models-Projections of Future Climate', in Houghton, J. T., Meira Filho, L. G., Callander, B. A., Harris, N., Kattenberg, A., and Maskell, K. (eds.), Climate Change 1995: The Science of Climate Change, Cambridge University Press, Cambridge, pp. 285-357.Google Scholar
  30. Kaufmann, R. K. and Stern, D. I.: 1997, 'Evidence for Human Influence on Climate from Hemispheric Temperature Relations', Nature 388, 39-44.Google Scholar
  31. Keeling, C. D. and Whorf, T. P.: 1994, 'Atmospheric CO2 Records from Sites in the SIO Air Sampling Network', in Boden, T. A., Kaiser, D. P., Sepanski, R. J., Stoss, F. S. (eds.) Trends '93: A Compendium of Data on Global Change, ORNL/CDIAC-65, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, pp. 16-26.Google Scholar
  32. Kiehl, J. T. and Briegleb, B. P.: 1993, 'The Relative Roles of Sulfate Aerosols and Greenhouse Gases in Climate Forcing', Science 260, 311-314.Google Scholar
  33. Kim, K. and Schmidt, P.: 1990, 'Some Evidence on the Accuracy of Phillips-Perron Tests Using Alternative Estimates of Nuisance Parameters', Econ. Lett. 34, 345-350.Google Scholar
  34. Kitamura, Y.: 1995, 'Estimation of Cointegrated Systems with I(2) Processes', Econometric Theory 11, 1-24.Google Scholar
  35. Kuo, C., Lindberg, C., and Thomson D. J.: 1990, 'Coherence Established between Atmospheric Carbon Dioxide and Global Temperature', Nature 343, 709-714.Google Scholar
  36. Kwiatowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y.: 1992, 'Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root: How Sure Are We that Economic Time Series Have a Unit Root', J. Econometrics 54, 159-178.Google Scholar
  37. Lean, J., Beer, J., and Bradley, R.: 1995, 'Reconstruction of Solar Irradiance since 1610: Implications for Climate Change', Geophys. Res. Lett. 22, 3195-3198.Google Scholar
  38. Ljung, G. M. and Box, G. E. P.: 1978, 'On a Measure of Lack of Fit in Time Series Models', Biometrika 65, 297-303.Google Scholar
  39. Machida, T., Nakazawa, T., Fujii, Y., Aoki, S., and Watanabe, O.: 1995, 'Increase in the Atmospheric Nitrous Oxide Concentration during the Last 250 Years', Geophys. Res. Lett. 22, 2921-2924.Google Scholar
  40. Mitchell, J. F. B., Johns, T. C., Gregory, J. M., and Tett, S. F. B.: 1995, Climate Response to Increasing Levels of Greenhouse Gases and Sulfate Aerosols, Nature 376, 501-504.Google Scholar
  41. Newey, W. K. and West, K. D.: 1987: 'A Simple Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix', Econometrica 55, 1029-1054.Google Scholar
  42. Pantula, S.: 1991, 'Asymptotic Distributions of Unit-Root Tests when the Process is Nearly Stationary', J. Busin. Econ. Stat. 9, 63-71.Google Scholar
  43. Phillips, P. C. B.: 1991, 'Optimal Inference in Cointegrated Systems', Econometrica 59, 283-306.Google Scholar
  44. Phillips, P. C. B. and Ouliaris, S.: 1990, 'Asymptotic Properties of Residual Based Test for Cointegration', Econometrica 58, 190.Google Scholar
  45. Phillips, P. C. B. and Perron, P.: 1988, 'Testing for a Unit Root in Time Series Regression', Biometrika 75, 335-346.Google Scholar
  46. Prather, M., McElroy, M., Wofsy, S., Russel, G., and Rind, D.: 1987, 'Chemistry of the Global Troposphere: Fluorocarbons as Tracers of Air Motion', J. Geophys. Res. 92D, 6579-6613.Google Scholar
  47. Prinn, R. G., Cunnold, D., Fraser, P., Weiss, R., Simmonds, P., Alyea, F., Steele, L. P., and Hartley, D.: 1997, CDIAC World Data Center Dataset No. DB-1001/R3 (anonymous ftp from cdiac.esd@ornl.gov).Google Scholar
  48. Prinn, R. G., Cunnold, D., Rasmussen, R., Simmonds, P., Alyea, F., Crawford, A., Fraser, P., and Rosen, R.: 1990, 'Atmospheric Emissions and Trends of Nitrous Oxide Deduced from Ten Years of ALE/GAGE Data', J. Geophys. Res. 95, 18369-18385.Google Scholar
  49. Richards, G. R.: 1993, 'Change in Global Temperature: a Statistical Analysis', J. Climate 6, 546-559.Google Scholar
  50. Sato, M., Hansen, J. E., McCormick, M. P., and Pollack, J. B.: 1993, 'Stratospheric Aerosol Optical Depths, 1850-1990', J. Geophys. Res. 98, 22987-22994.Google Scholar
  51. Schmidt, P. and Phillips, P. C. B.: 1992, 'LM Tests for a Unit Root in the Presence of Deterministic Trends', Oxford Bull. Econ. Stat. 54, 257-287.Google Scholar
  52. Schönwiese, C.-D.: 1994, 'Analysis and Prediction of Global Climate Temperature Change Based on Multiforced Observational Statistics', Environ. Pollut. 83, 149-154.Google Scholar
  53. Schweppe, F.: 1965, 'Evaluation of Likelihood Functions for Gaussian Signals', IEEE Trans. Information Theory 11, 61-70.Google Scholar
  54. Schwert, G. W.: 1989, 'Tests for Unit Roots: a Monte Carlo Investigation', J. Busin. Econ. Stat. 7, 147-159.Google Scholar
  55. Shine, K. P. R. G., Derwent, D. J., Wuebbles, D. J., and Mocrette, J. J.: 1991, 'Radiative Forcing of Climate', in Houghton, J. T., Jenkins, G. J., and Ephramus, J. J. (eds.), Climate Change: The IPCC Scientific Assessment, Cambridge University Press, Cambridge, pp. 47-68.Google Scholar
  56. Stern, D. I. and Kaufmann, R. K.: 1996, Estimates of Global Anthropogenic Sulfate Emissions 1860-1993, CEES Working Papers 9601, Center for Energy and Environmental Studies, Boston University (available on WWWat: http://cres.anu.edu.au/ dstern/mirror.html).Google Scholar
  57. Stern, D. I. and Kaufmann, R. K: 1999, 'Econometric Analysis of Global Climate Change', Environ. Model. Software 14, 597-605.Google Scholar
  58. Stock, J. H. and Watson, M. W.: 1993, 'A Simple Estimator of the Cointegrating Vectors in Higher Order Integrated Systems', Econometrica 61, 783-820.Google Scholar
  59. Thomson, D. J.: 1995, 'The Seasons, Global Temperature, and Precession', Science 268, 59-68.Google Scholar
  60. Thomson, D. J.: 1997, 'Dependence of Global Temperatures on Atmospheric CO2 and Solar Irradiance', Proc. Natl. Acad. Sci. 94, 8370-8377.Google Scholar
  61. Tol, R. S. J.: 1994, 'Greenhouse Statistics-Time Series Analysis: Part II', Theor. Appl. Climatol. 49, 91-102.Google Scholar
  62. Tol, R. S. J. and de Vos, A. F.: 1993, 'Greenhouse Statistics-Time Series Analysis', Theor. Appl. Climatol. 48, 63-74.Google Scholar
  63. Tol, R. S. J. and de Vos, A. F.: 1998, 'A Bayesian Statistical Analysis of the Enhanced Greenhouse Effect', Clim. Change 38, 87-112.Google Scholar
  64. Wigley, T.M. L.: 1989, 'Possible Climate Change Due to SO2-Derived Cloud Condensation Nuclei', Nature 339, 356-367.Google Scholar
  65. Wigley, T.M. L. and Raper, S. C. B.: 1992, 'Implications for Climate and Sea Level of Revised IPCC Emissions Scenarios', Nature 357, 293-300.Google Scholar
  66. Wigley, T. M. L., Smith, R. L., and Santer, B. D.: 1998, 'Anthropogenic Influence on the Autocorrelation Structure of Hemispheric-Mean Temperatures', Science 282, 1676-1679.Google Scholar
  67. Woodward, W. A. and Gray, H. L.: 1993, 'Global Warming and the Problem of Testing for Trend in Time Series Data', J. Climate 6, 953-962.Google Scholar
  68. Woodward, W. A. and Gray, H. L.: 1995, 'Selecting a Model for Detecting the Presence of a Trend', J. Climate 8, 1929-1937.Google Scholar
  69. Yoo, B. S.: 1986, Multi-Cointegrated Time Series and a Generalized Error-Correction Model, University of California at San Diego Department of Economics Discussion Paper.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • David I. Stern
    • 1
  • Robert K. Kaufmann
    • 2
  1. 1.Centre for Resource and Environmental StudiesAustralian NationalUniversityCanberraAustralia
  2. 2.Center for Energy and Environmental StudiesBoston UniversityBostonU.S.A.

Personalised recommendations