Directional or vector time-dependent observations, such as the flow at a river branch, streamflow, lake flow, ocean currents, or wind data, are commonly observed in the environment. Traditionally, a rose diagram can be used to summarize the possible main orientation using all the data in the time domain. However, it cannot indicate the significant variation in the specific frequency bands that may show dominant periodic fluctuations. Assessment of directional time series often requires the identification of significant components in the specific frequency bands for not only the magnitude but also the orientation. The rotary pattern, main orientation, and magnitude of directional time series in the frequency domain for five sets of seasonal wind velocity observed at the northern, southern, eastern, and western coast of the subtropical island Taiwan and Taiwan Strait have been demonstrated. It shows that the representative pattern is clockwise, counterclockwise, or near rectilinear, and semidiurnal and diurnal components are significant in the frequency domain for most stations. The most important research innovation suggests that the use of rotary spectral analysis in the frequency domain to effectively assess the orientation and magnitude of directional time series, such as hydrological, coastal, or environmental observations, has become feasible.