The Interpretation of Short Climate Records, with Comments on the North Atlantic and Southern Oscillations

Abstract This pedagogical note reminds the reader that the interpretation of climate records is dependent upon understanding the behavior of stochastic processes. In particular, before concluding that one is seeing evidence for trends, shifts in the mean, or changes in oscillation periods, one must rule out the purely random fluctuations expected from stationary time series. The example of the North Atlantic oscillation (NAO) is mainly used here: the spectral density is nearly white (frequency power law ≈ s-0.2) with slight broadband features near 8 and 2.5 yr. By generating synthetic but stationary time series, one can see exhibited many of the features sometimes exciting attention as being of causal climate significance. Such a display does not disprove the hypothesis of climate change, but it provides a simple null hypothesis for what is seen. In addition, it is shown that the linear predictive skill for the NAO index must be very slight (less than 3% of the variance). A brief comparison with the South...

[1]  N. Wiener.  The Wiener RMS (Root Mean Square) Error Criterion in Filter Design and Prediction , 1949 .

[2]  K. Hasselmann.  Stochastic climate models Part I. Theory , 1976 .

[3]  A. Pittock.  A critical look at long-term Sun-weather relationships , 1978 .

[4]  Jon F. Claerbout,et al.  Fundamentals of Geophysical Data Processing: With Applications to Petroleum Prospecting , 1985 .

[5]  K. Hasselmann,et al.  Stochastic climate models , Part I 1 Application to sea-surface temperature anomalies and thermocline variability , 2010 .

[6]  Upmanu Lall,et al.  Anomalous ENSO Occurrences: An Alternate View* , 1997 .

[7]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[8]  P. Schultz,et al.  Fundamentals of geophysical data processing , 1979 .

[9]  Carl Wunsch,et al.  The Vertical Partition of Oceanic Horizontal Kinetic Energy , 1997 .

[10]  P. Imkeller,et al.  Stochastic climate models , 2001 .

[11]  D J Thomson,et al.  Dependence of global temperatures on atmospheric CO2 and solar irradiance. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[12]  R. Ponte.  The statistics of extremes, with application to El Niño , 1986 .

[13]  Timothy J. Hoar,et al.  El Niño and climate change , 1997 .

[14]  R. Grove.  Global impact of the 1789-93 El Niño , 1998, Nature.

[15]  Mojib Latif,et al.  Predictability of a Stochastically Forced Hybrid Coupled Model of El Niño , 1997 .

[16]  P. W. Strike,et al.  Forecasting and control , 1991 .

[17]  Timothy J. Hoar,et al.  The 1990–1995 El Niño‐Southern Oscillation Event: Longest on Record , 1996 .

[18]  N. Levinson.  The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction , 1946 .

[19]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[20]  J. Hurrell,et al.  DECADAL VARIATIONS IN CLIMATE ASSOCIATED WITH THE NORTH ATLANTIC OSCILLATION , 1997 .

[21]  R. Fisher.  The Advanced Theory of Statistics , 1943, Nature.

[22]  C. Wunsch.  Decade-to-Century Changes in the Ocean Circulation , 1992 .

[23]  S. Rice.  Mathematical analysis of random noise , 1944 .

[24]  J. Hurrell.  Decadal Trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation , 1995, Science.

[25]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[26]  D. E. Harrison,et al.  Darwin sea level pressure, 1876–1996: Evidence for climate change? , 1997 .

[27]  David J. Thomson,et al.  The Seasons, Global Temperature, and Precession , 1995, Science.

[28]  Lamont-Doherty Earth Observatory.  Anomalous ENSO Occurrences : An Alternate View * , 1997 .

[29]  David B. Stephenson,et al.  Is the North Atlantic Oscillation a random walk , 2000 .

[30]  Mojib Latif,et al.  A review of the predictability and prediction of ENSO , 1998 .

[31]  A. Walden,et al.  Spectral analysis for physical applications : multitaper and conventional univariate techniques , 1996 .

[32]  L. H. Koopmans.  The spectral analysis of time series , 1974 .

[33]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 1 , 1967 .

[34]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[35]  D. Gutzler,et al.  Estimating the Effect of Stochastic Wind Stress Forcing on ENSO Irregularity , 1997 .