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

Carl WunschProgram in Atmospheres, Oceans, and Climate, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

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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 Southern Oscillation shows a different spectral distribution, but again a simulation has long periods of apparent systematic sign and trends. Application of threshold-crossing statistics (Ricean) shows no contradiction to the assumption that the Darwin pressure record is statistically stationary.

Corresponding author address: Carl Wunsch, Program in Atmospheres, Oceans, and Climate, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139. E-mail: cwunsch@pond.mit.edu

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 Southern Oscillation shows a different spectral distribution, but again a simulation has long periods of apparent systematic sign and trends. Application of threshold-crossing statistics (Ricean) shows no contradiction to the assumption that the Darwin pressure record is statistically stationary.

Corresponding author address: Carl Wunsch, Program in Atmospheres, Oceans, and Climate, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139. E-mail: cwunsch@pond.mit.edu
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