Using Matching Pursuit to Assess Atmospheric Circulation Changes over the North Pacific

Matching pursuit was originally formulated as a technique for identifying the time/frequency content of a time series whose spectral properties evolve over time. The basic idea was to construct a large ‘dictionary’ of explanatory vectors that are localized both in time and in frequency and then to analyze a time series by projecting it against the vectors in the dictionary. Matching pursuit can be adapted to explore other properties of a time series besides its time/frequency content. In this paper the technique is described in detail and then used to investigate the notion that North Pacific climate time series exhibit sudden changes in levels (regime-like shifts). In particular matching pursuit is used to explore a hypothesis by Minobe (1999) that there are pentaand bi-decadal oscillations in a North Pacific (NP) index of sea level pressures, with sharp transitions between high and low states that cannot be easily modeled by sinusoidal oscillations. When the NP index is analyzed using a dictionary containing square wave oscillations, sinusoidal oscillations and descriptors of isolated events (Haar wavelet and scaling vectors), matching pursuit selects square wave oscillations with periods and phases that agree closely with Minobe’s analysis and penta-decadal hypothesis; however, the results call into question the existence of an independent bi-decadal oscillation. Matching pursuit was adjusted to handle a time series of winter air temperature measurements from Sitka, Alaska, which have been recorded since 1829, but with 22 missing values scattered throughout the 1800s. For this series, matching pursuit again picks out a square wave oscillation that is quite similar to the one identified for the NP index, with zero crossings during 1840–1, 1867–8, 1894–5, 1921–2, 1948–9 and 1975–6.