The zonal winds at several levels between 70 and 10 hPa (roughly 20--30 km) measured at near-equatorial stations during 1956--2000 were analyzed to produce a one-dimensional approximation. The neural network-based technique applied was the circular nonlinear principal component analysis (NLPCA.cir) designed to characterize quasiperiodic phenomena. The reconstructed height-time series of wind based on the one-dimensional NLPCA.cir captures many of the characteristic features of the observed quasi-biennial oscillation (QBO). The nonlinear results were evaluated relative to comparable linear principal component analysis and found to produce a superior one-dimensional representation of the data. The NLPCA.cir analysis produces a single time series of QBO phase based on data at all levels. This phase was then applied to demonstrate a strong correlation of the state of the tropical QBO and boreal winter high-latitude stratospheric temperatures.