Professor Myles Allen CBE FRS

Abstract:

Extended empirical orthogonal functions (EEOFs), alternatively known as multi-channel singular systems (or singular spectrum) analysis (MSSA), provide a natural method of extracting oscillatory modes of variability from multivariate data. The eigen-functions of some simple non-oscillatory noise processes are, however, also solutions to the wave equation, so the occurrence of stable, wave-like patterns in EEOF/MSSA is not sufficient grounds for concluding that data exhibits oscillations. We present a generalisation of the "Monte Carlo SSA" algorithm which allows an objective test for the presence of oscillations at low signal-to-noise ratios in multivariate data. The test is similar to those used in standard regression, examining directions in state-space to determine whether they contain more variance than would be expected if the noise null-hypothesis were valid. We demonstrate the application of the test to the analysis of interannual variability in tropical Pacific sea-surface temperatures.

Abstract:

An analysis of the 130‐year record of the Earth's global mean temperature reveals a significant warming trend and a residual consistent with an auto‐correlated (“red”) noise process whose predictability decays with a timescale of two years. Thus global temperatures, in isolation, do not indicate oscillations at 95% confidence against a red noise null hypothesis. Weak signals identified in the global series can, however, be traced to significant sea surface temperature oscillations in the equatorial Atlantic (period ∼10 years) and the El Niño region of the Pacific (3–5 years). No robust evidence is found in this data for interdecadal oscillations, The 10‐year Atlantic oscillation corresponds to a pattern of temperature anomalies which has been associated with interannual variations in West African rainfall and in U.S. hurricane landfall frequency. Copyright 1994 by the American Geophysical Union.