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Quantifying Persistence in ENSO

John P. WeissProgram in Atmospheric and Oceanic Science, University of Colorado, Boulder, Colorado

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Jeffrey B. WeissProgram in Atmospheric and Oceanic Science, University of Colorado, Boulder, Colorado

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Abstract

The seasonal dependence of predictability in ENSO manifests itself in the so-called spring barrier found in the cyclostationary lag autocorrelations, or persistence. This work examines the statistics of persistence, with particular focus on the phase-of-year-dependent pattern found in ENSO data, the barrier. Simple time series of one sine wave produce a barrier if the frequency is a biennial cycle or one of its harmonics. Time series of two sine waves produce a barrier if one frequency is a biennial cycle or a harmonic thereof. They additionally produce a barrier if their frequencies sum to unity. Time series with continuous but narrow spectral peaks at barrier-producing frequencies produce barriers only if the phase angles vary slowly or coherently across the peaks. The shape of the barrier seen in these simple time series is used to construct a model persistence map, which is a combination of an idealized barrier and the persistence of a red-noise process. A nonlinear least squares fit of the persistence of a time series to the model persistence provides a quantitative measure of the properties of the persistence barrier in any time series. Application of the measure to the Southern Oscillation index and sea surface temperature in the NINO3 region of the equatorial Pacific indicates that the ENSO persistence barrier is a feature that is statistically distinguishable from the theoretical persistence of a red-noise process. The ENSO barrier results from phase coherency of the continuum of interannual modes near the biennial frequency. Measuring the barrier on windowed data shows that there was a weak persistence barrier from approximately 1915 to 1945, a strong barrier during the 1960s and early 1970s, and a weakening barrier in the late 1970s.

Corresponding author address: Dr. Jeffrey B. Weiss, Program in Atmospheric and Oceanic Sciences, Campus Box 311, University of Colorado, Boulder, CO 80309-0311.

Email: jweiss@colorado.edu

Abstract

The seasonal dependence of predictability in ENSO manifests itself in the so-called spring barrier found in the cyclostationary lag autocorrelations, or persistence. This work examines the statistics of persistence, with particular focus on the phase-of-year-dependent pattern found in ENSO data, the barrier. Simple time series of one sine wave produce a barrier if the frequency is a biennial cycle or one of its harmonics. Time series of two sine waves produce a barrier if one frequency is a biennial cycle or a harmonic thereof. They additionally produce a barrier if their frequencies sum to unity. Time series with continuous but narrow spectral peaks at barrier-producing frequencies produce barriers only if the phase angles vary slowly or coherently across the peaks. The shape of the barrier seen in these simple time series is used to construct a model persistence map, which is a combination of an idealized barrier and the persistence of a red-noise process. A nonlinear least squares fit of the persistence of a time series to the model persistence provides a quantitative measure of the properties of the persistence barrier in any time series. Application of the measure to the Southern Oscillation index and sea surface temperature in the NINO3 region of the equatorial Pacific indicates that the ENSO persistence barrier is a feature that is statistically distinguishable from the theoretical persistence of a red-noise process. The ENSO barrier results from phase coherency of the continuum of interannual modes near the biennial frequency. Measuring the barrier on windowed data shows that there was a weak persistence barrier from approximately 1915 to 1945, a strong barrier during the 1960s and early 1970s, and a weakening barrier in the late 1970s.

Corresponding author address: Dr. Jeffrey B. Weiss, Program in Atmospheric and Oceanic Sciences, Campus Box 311, University of Colorado, Boulder, CO 80309-0311.

Email: jweiss@colorado.edu

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