Robust estimation of background noise and signal detection in climatic time series

Abstract

We present a new technique for isolating climate signals in time series with a characteristic ‘red’ noise background which arises from temporal persistence. This background is estimated by a ‘robust’ procedure that, unlike conventional techniques, is largely unbiased by the presence of signals immersed in the noise. Making use of multiple-taper spectral analysis methods, the technique further provides for a distinction between purely harmonic (periodic) signals, and broader-band (‘quasiperiodic’) signals. The effectiveness of our signal detection procedure is demonstrated with synthetic examples that simulate a variety of possible periodic and quasiperiodic signals immersed in red noise. We apply our methodology to historical climate and paleoclimate time series examples. Analysis of a ≈ 3 million year sediment core reveals significant periodic components at known astronomical forcing periodicities and a significant quasiperiodic 100 year peak. Analysis of a roughly 1500 year tree-ring reconstruction of Scandinavian summer temperatures suggests significant quasiperiodic signals on a near-century timescale, an interdecadal 16–18 year timescale, within the interannual El Niño/Southern Oscillation (ENSO) band, and on a quasibiennial timescale. Analysis of the 144 year record of Great Salt Lake monthly volume change reveals a significant broad band of significant interdecadal variability, ENSO-timescale peaks, an annual cycle and its harmonics. Focusing in detail on the historical estimated global-average surface temperature record, we find a highly significant secular trend relative to the estimated red noise background, and weakly significant quasiperiodic signals within the ENSO band. Decadal and quasibiennial signals are marginally significant in this series.

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Mann, M.E., Lees, J.M. Robust estimation of background noise and signal detection in climatic time series. Climatic Change 33, 409–445 (1996). https://doi.org/10.1007/BF00142586

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Keywords

  • Interdecadal Variability
  • Great Salt Lake
  • Spectral Analysis Method
  • Climatic Time Series
  • Temporal Persistence