Statistical Science

Sir Gilbert Walker and a Connection between El Niño and Statistics

Richard W. Katz

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Abstract

The eponym “Walker Circulation” refers to a concept used by atmospheric scientists and oceanographers in providing a physical explanation for the El Niño–Southern Oscillation phenomenon, whereas the eponym “Yule–Walker equations” refers to properties satisfied by the autocorrelations of an autoregressive process. But how many statisticians (or, for that matter, atmospheric scientists) are aware that the “Walker” in both terms refers to the same individual, Sir Gilbert Thomas Walker, and that these two appellations arose in conjunction with the same research on the statistical prediction of climate? Like George Udny Yule (the “Yule” in Yule– Walker), Walker’s motivation was to devise a statistical model that exhibited quasiperiodic behavior. The original assessments of Walker’s work, both in the meteorology and in statistics, were somewhat negative. With hindsight, it is argued that his research should be viewed as quite successful.

Article information

Source
Statist. Sci., Volume 17, Number 1 (2002), 97-112.

Dates
First available in Project Euclid: 11 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.ss/1023799000

Digital Object Identifier
doi:10.1214/ss/1023799000

Mathematical Reviews number (MathSciNet)
MR1917900

Zentralblatt MATH identifier
1032.01521

Keywords
Autoregressive process quasiperiodic behavior Southern Oscillation teleconnections Yule–Walker equations

Citation

Katz, Richard W. Sir Gilbert Walker and a Connection between El Niño and Statistics. Statist. Sci. 17 (2002), no. 1, 97--112. doi:10.1214/ss/1023799000. https://projecteuclid.org/euclid.ss/1023799000


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References

  • ACHUTARAO, K., SPERBER, K. R. and 13 OTHERS (2000). El Niño Southern Oscillation in coupled GCMs. PCMDI Report 61, Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Univ. California.
  • ALLAN, R., LINDESAY, J. and PARKER, D. (1996). El Niño Southern Oscillation and Climate Variability. CSIRO Publishing, Melbourne.
  • ANDERSON, T. W. (1971). The Statistical Analy sis of Time Series. Wiley, New York.
  • BJERKNES, J. (1969). Atmospheric teleconnections from the equatorial Pacific. Monthly Weather Review 97 163-172.
  • BOX, G. E. P. and JENKINS, G. M. (1976). Time Series Analy sis: Forecasting and Control, rev. ed. Holden-Day, San Francisco.
  • BRAUN, H. I., ed. (1994). The Collected Works of John W. Tukey, V. VIII, Multiple Comparisons: 1948-1983. Wadsworth, Belmont, CA.
  • BROWN, B. G. and KATZ, R. W. (1991). Use of statistical methods in the search for teleconnections: past, present, and future. In Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact (M. H. Glantz, R. W. Katz and N. Nicholls, eds.) 371-400. Cambridge Univ. Press.
  • CAVE-BROWNE-CAVE, F. E. (1904). On the influence of the time factor in the correlation between the barometric heights at stations more than 1,000 miles apart. Proc. Roy. Soc. London Ser. A 74 403-413.
  • CHANGNON, S. A., ed. (2000). El Niño, 1997-1998: The Climate Event of the Century. Oxford Univ. Press.
  • CHAPMAN, S. (1934). Sy mons Memorial Medal, 1934. Quarterly Journal of the Roy al Meteorological Society 60 184-185.
  • CHELTON, D. B. (1994). physical oceanography: a brief overview for statisticians. Statist. Sci. 9 150-166.
  • CHU, P.-S. and KATZ, R. W. (1989). Spectral estimation from time series models with relevance to the Southern Oscillation. Journal of Climate 2 86-90.
  • CLAy TON, H. H. (1917). Effect of short period variations of solar radiation on the Earth's atmosphere. Smithsonian Miscellaneous Collections 68 1-18.
  • CLAy TON, H. H., ed. (1934). World weather records. Part IV. (Errata in Volume 79.) Smithsonian Miscellaneous Collections 90 573-589.
  • CRUTZEN, P. J. and RAMANATHAN, V. (2000). The ascent of atmospheric sciences. Science 290 299-304.
  • DAVIS, H. T. (1941). The Analy sis of Economic Time Series. Principia Press, Bloomington, IN.
  • DAVIS, M. (2001). Late Victorian Holocausts: El Niño Famines and the Making of the Third World. Verso, London.
  • DIAZ, H. F. and MARKGRAF, V., eds. (1992). El Niño: Historical and Paleoclimatic Aspects of the Southern Oscillation. Cambridge Univ. Press.
  • DIAZ, H. F. and MARKGRAF, V., eds. (2000). El Niño and the Southern Oscillation: Multiscale Variability and Global and Regional Impacts. Cambridge Univ. Press.
  • DINES, W. H. (1916). Review of "Correlation in seasonal variations of weather, I-VI." Memoirs of the Indian Meteorological Department by G. T. Walker. Quarterly Journal of the Roy al Meteorological Society 42 129-132.
  • DURBIN, J. (1960). The fitting of time-series models. Internat. Statist. Rev. 28 233-244.
  • FISHER, R. A. (1929). Tests of significance in harmonic analysis. Proc. Roy. Soc. London Ser. A 125 54-59.
  • FISHER, R. A. and MACKENZIE, W. A. (1922). The correlation of weekly rainfall (with discussion). Quarterly Journal of the Roy al Meteorological Society 48 234-245.
  • GERSHUNOV, A., SCHNEIDER, N. and BARNETT, T. (2001). Low-frequency modulation of the ENSO-Indian monsoon rainfall relationship: signal or noise? Journal of Climate 14 2486-2492.
  • GLANTZ, M. H. (2001). Currents of Change: Impacts of El Niño and La Niña on Climate and Society, 2nd ed. Cambridge Univ. Press.
  • GLANTZ, M. H., KATZ, R. W. and NICHOLLS, N., eds. (1991). Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact. Cambridge Univ. Press.
  • GRAHAM, N. E. and WHITE, W. B. (1988). The El Niño cy cle: a natural oscillator of the Pacific ocean-atmosphere sy stem. Science 240 1293-1302.
  • GRANT, A. M. (1956). The application of correlation and regression to forecasting. Meteorological Study 7, Bureau of Meteorology, Melbourne, Australia.
  • HUERTA, G. and WEST, M. (1999). Priors and component structures in autoregressive time series models. J. Roy. Statist. Soc. Ser. B 61 881-899.
  • HURRELL, J. W. (1995). Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science 269 676-679.
  • HURRELL, J. W. (1996). Influence of variations in extratropical wintertime teleconnections on Northern Hemisphere temperature. Geophy s. Res. Lett. 23 665-668.
  • JENKINS, G. M. and WATTS, D. G. (1968). Spectral Analy sis and Its Applications. Holden-Day, San Francisco.
  • KATZ, R. W. and BROWN, B. G. (1991). The problem of multiplicity in research on teleconnections. International Journal of Climatology 11 505-513.
  • KENDALL, M. G. (1945). On the analysis of oscillatory time-series (with discussion). J. Roy. Statist. Soc. 108 93-141.
  • KENDALL, M. G. (1949). The estimators of parameters in linear autoregressive time series. Econometrica 17 (supplement) 44- 57.
  • KENDALL, M. G. (1952). George Udny Yule, C.B.E., F.R.S. J. Roy. Statist. Soc. Ser. A 115 156-161.
  • KLEIN, J. L. (1997). Statistical Visions in Time: A History of Time Series Analy sis, 1662-1938. Cambridge Univ. Press.
  • LAMB, P. J. and PEPPLER, R. A. (1987). North Atlantic Oscillation: concept and an application. Bulletin of the American Meteorological Society 68 1218-1225.
  • LOCKy ER, N. and LOCKy ER, W. J. S. (1904). The behavior of the short-period atmospheric pressure variation over the Earth's surface. Proc. Roy. Soc. London 73 457-470.
  • MEEHL, G. A. and ARBLASTER, J. M. (1998). The Asian- Australian monsoon and El Niño-Southern Oscillation in the NCAR Climate Sy stem Model. Journal of Climate 11 1356- 1385.
  • MONTGOMERY, R. B. (1937). Verification of three of Walker's seasonal forecasting formulae for India monsoon rain. Bulletin of the American Meteorological Society 18 287-290.
  • MORETTIN, P. A. (1984). The Levinson algorithm and its applications in time series analysis. Internat. Statist. Rev. 52 83-92.
  • NORMAND, C. (1953). Monsoon seasonal forecasting. Quarterly Journal of the Roy al Meteorological Society 79 463-473.
  • NORMAND, C. (1958). Sir Gilbert Walker, C.S.I., F.R.S. Nature 182 1706.
  • Ny CHKA, D. (2000). Challenges in understanding the atmosphere. J. Amer. Statist. Assoc. 95 972-975.
  • PHILANDER, S. G. (1990). El Niño, La Niña, and the Southern Oscillation. Academic Press, San Diego.
  • PIEGORSCH, W. W., SMITH, E. P., EDWARDS, D. and SMITH,
  • R. L. (1998). Statistical advances in environmental science. Statist. Sci. 13 186-208.
  • PITTOCK, A. B. (1978). Critical look at long-term sun-weather relationships. Reviews of Geophysics and Space physics 16 400-420.
  • RASMUSSON, E. M. (1991). Observational aspects of ENSO cy cle teleconnections. In Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact (M. H. Glantz, R. W. Katz and N. Nicholls, eds.) 309-343. Cambridge Univ. Press.
  • SCHUSTER, A. (1898). On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena. Terrestrial Magnetism 3 13-41.
  • SHEPPARD, P. A. (1959). Sir Gilbert Walker, C.S.I., F.R.S. Quarterly Journal of the Roy al Meteorological Society 85 186.
  • SIMPSON, G. C. (1959). Sir Gilbert T. Walker, C.S.I., F.R.S. Weather 14 67-68.
  • SUAREZ, M. J. and SCHOPF, P. S. (1988). A delay ed action oscillator for ENSO. J. Atmospheric Sci. 45 3283-3287.
  • TAy LOR, G. I. (1962). Gilbert Thomas Walker, 1868-1958. Biographical Memoirs of Fellows of the Roy al Society 8 166- 174.
  • TRENBERTH, K. E. (1991). General characteristics of El Niño- Southern Oscillation. In Teleconnections Linking Worldwide Climate Anomalies: Scientific Basis and Societal Impact (M. H. Glantz, R. W. Katz and N. Nicholls, eds.) 13-42. Cambridge Univ. Press.
  • TRENBERTH, K. E. and CARON, J. M. (2000). The Southern Oscillation revisited: sea level pressures, surface temperatures, and precipitation. Journal of Climate 13 4358-4365.
  • TRENBERTH, K. E. and HOAR, T. J. (1996). The 1990-1995 El Niño-Southern Oscillation event: longest on record. Geophy s. Res. Lett. 23 57-60.
  • WALKER, G. T. (1910). Correlation in seasonal variations of weather. II. Memoirs of the Indian Meteorological Department 21(Part 2) 22-45.
  • WALKER, G. T. (1914). Correlation in seasonal variations of weather. III. On the criterion for the reality of relationships or periodicities. Memoirs of the Indian Meteorological Department 21(Part 9) 13-15.
  • WALKER, G. T. (1918). Correlation in seasonal variations of weather. Quarterly Journal of the Roy al Meteorological Society 44 223-224.
  • WALKER, G. T. (1923). Correlation in seasonal variations of weather. VIII. A preliminary study of world-weather. Memoirs of the Indian Meteorological Department 24(Part 4) 75-131.
  • WALKER, G. T. (1924). Correlation in seasonal variations of weather. IX. A further study of world weather. Memoirs of the Indian Meteorological Department 24(Part 9) 275-332.
  • WALKER, G. T. (1925). On periodicity (with discussion). Quarterly Journal of the Roy al Meteorological Society 51 337-346.
  • WALKER, G. T. (1927a). The Atlantic Ocean. Quarterly Journal of the Roy al Meteorological Society 53 97-113.
  • WALKER, G. T. (1927b). Review of "Climate through the Ages. A Study of Climatic Factors and Climatic Variations" by C. E. P. Brooks. Quarterly Journal of the Roy al Meteorological Society 53 321-323.
  • WALKER, G. T. (1930). On periodicity III-criteria for reality. Memoirs of the Roy al Meteorological Society 3 97-101.
  • WALKER, G. T. (1931). On periodicity in series of related terms. Proc. Roy. Soc. London Ser. A 131 518-532.
  • WALKER, G. T. (1936a). Editorial. Quarterly Journal of the Roy al Meteorological Society 62 1-2.
  • WALKER, G. T. (1936b). Seasonal weather and its prediction. Smithsonian Institution Annual Report for 1935 117-138.
  • WALKER, G. T. and BLISS, E. W. (1926). On correlation coefficients, their calculation use (with discussion). Quarterly Journal of the Roy al Meteorological Society 52 73-84.
  • WALKER, J. M. (1997). Pen portraits of presidents-Sir Gilbert Walker, CSI, ScD, MA, FRS. Weather 52 217-220.
  • WALLACE, J. M. and GUTZLER, D. S. (1981). Teleconnections in the geopotential height field during the Northern Hemisphere winter. Monthly Weather Review 109 784-812.
  • WANG, C. (2001). A unified oscillator model for the El Niño- Southern Oscillation. Journal of Climate 14 98-115.
  • WHITTLE, P. (1954a). The statistical analysis of a seiche record. Journal of Marine Research 13 76-100.
  • WHITTLE, P. (1954b). A statistical investigation of sunspot observations with special reference to H. Alfvén's sunspot model. Astrophysical Journal 120 251-260.
  • WHITTLE, P. (1963). Prediction and Regulation. Van Nostrand, Princeton.
  • WISHART, J. (1928). On errors in the multiple correlation coefficient due to random sampling. Memoirs of the Roy al Meteorological Society 2 29-37.
  • WOLD, H. (1938). A Study in the Analy sis of Stationary Time Series. Almqvist and Wiksell, Stockholm.
  • YULE, G. U. (1926). Why do we sometimes get nonsensecorrelations between time-series?-A study in sampling and the nature of time-series. J. Roy. Statist. Soc. 89 1-64.
  • YULE, G. U. (1927). On a method of investigating periodicities in disturbed series, with special reference to Wolfer's sunspot numbers. Philos. Trans. Roy. Soc. London Ser. A 226 267-298.