RPCA Technique for Calculating Monthly Teleconnection Indices

The procedure used to calculate the Northern Hemisphere teleconnection indices is based on the Rotated Principal Component Analysis (RPCA) used by Barnston and Livezey (1987, Mon. Wea. Rev., 115, 1083-1126). This procedure isolates the primary teleconnection patterns for all months and allows time series of the patterns to be constructed. For our monitoring purposes, we apply the RPCA technique to monthly mean standardized 500-mb height anomalies obtained from the CDAS in the analysis region 20°N-90°N between January 1950 and December 2000. The anomalies are standardized by the 1950-2000 base period monthly means and standard deviations.

The calculation procedure is a follows. For each of the twelve calendar months, the ten leading unrotated EOFs are first determined from the standardized monthly height anomaly fields in the three-month period centered on that month: [i.e., The July patterns are calculated based on the June through August monthly standardized anomaly fields]. A Varimax rotation is then applied to these ten leading un-rotated modes, yielding the ten leading rotated modes and their time series for that calendar month. Therefore, these ten leading rotated modes for each calendar month are based on 153 (51 x 3) monthly standardized anomaly maps. In the Varimax rotation technique, the indices for the ten leading rotated modes are calculated simultaneously for each month in the record using a Least Squares solution. These indices are the solution to the Least Squares system of equations, and reflect the combination of modes which explains the most spatial variance of the observed standardized height anomaly field in that month.

An examination of all twelve sets of rotated modes revealed ten dominant teleconnection patterns, of which eight to nine appear in each of the twelve calendar months. These patterns are referred to as the North Atlantic Oscillation, the Pacific/North American teleconnection pattern, the East Atlantic pattern, the West Pacific pattern, the East Pacific -- North Pacific pattern, the East Atlantic/ Western Russia pattern, the Tropical/ Northern Hemisphere pattern, the Polar-Eurasian pattern, the Scandinavia pattern, and the Pacific Transition pattern. Click here for additional discussion on how the teleconnection patterns are displayed]. The remaining 1-2 spurious modes in each month have no apparent physical meaning.

To calculate the teleconnection indices, these spurious modes are omitted from the Least Squares equations. The solution to this system of equations yields the resulting teleconnection indices, which represent the combination of teleconnection patterns (instead of the combination of the ten leading rotated modes) that accounts for the most spatial variance of the observed standardized anomaly map in the month.

Other Links:

Historical Archive of all Indices: Monthly Tabulated Indices for all teleconnection pattern amplitudes dating back to 1950.

Monthly Tabulated Indices: Last 12 months of indices for selected teleconnection patterns, as appears in the Climate Diagnostics Bulletin.

Monthly Plotted Time series: Time series of pattern amplitudes for the last few years for selected teleconnection patterns, from the Climate Diagnostics Bulletin.

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