A new technique is described for identifying time-dependent patterns (i.e., ''principal oscillation patterns,'' or POPs) in a set of geophysical time series. POPs are defined as the normal modes of a linear dynamical representation of the data in terms of a first-order autoregressive vector process with residual noise forcing. POPs associated with real eigenvalues represent nonpropagating, nonoscillatory patterns which decay exponentially. POPs associated with complex eigenvalues occur in complex conjugate pairs and can represent standing wave structures (if one pattern is much stronger than the other), propagating waves (if both patterns are periodic and have the same structure except for a quarter-wavelength shift) or, in general, an arbitrary amphidromal oscillation. After the POPs have been defined for a selected set of primary variables, associated correlation or composite patterns may be derived for additional secondary fields to gain further insight into the structure of the interaction mechanisms. The method is illustrated by analyzing the tropical variability structure of a 10-year numerical simulation with the T21 general circulation model (GCM) of the European Centre for Medium Range Weather Forecasts, Reading, England. The POP analysis is applied to the 200-hPa horizontal divergence field along the equator for time scales shorter than 10 weeks.

The associated patterns are determined for a number of additional fields in the tropical belt between 30¿S and 30¿N. One dominant POP pair is found. Its spatial scale corresponds to zonal wave number 1. The patterns travel eastward, with an average period of 24 days and an e-folding decay time of 10 days. The maximum variance occurs in the area with maximum tropical precipitation, between 100¿E and the dateline. These features correspond rather closely to the characteristics of the observed tropical ''30- to 60-day wave,'' expect for the smaller period. A frequency-wave number analysis confirms that this 30- to 60-day wave is the most dominant regular oscillation in the tropical GCM troposphere. The associated patterns of sea level pressure, precipitation, and other quantities exhibit a number of intriguing aspects, namely (1) the phase velocity of the 30- to 60-day wave varies with longitude from 6 m s-1 in the Indonesian area to more than 30 m s-1 over the eastern Pacific, small phase speeds being associated with large amplitudes and high phase speeds with small amplitudes; (2) in the high-amplitude regions, rainfall and upper air velocity potential are in phase, while ine the low-amplitude regions, rainfall and velocity potential appear uncorrelated; (3) at the surface a pattern strongly resembing Gill's theoretical response to an equatorial heating source is found, with a trough to the east and two off-equatorial cyclonesto the west of the heating. The lack of meridional winds is probably related to the disregard of the seasonal asymmetries. ¿ American Geophysical Union 1988