Many physical space-time processes are nonstationary in either space or time. While there are existing strategies to cope with these problems---like various methods of assuming piecewise-stationarity---they often require difficult ad-hoc decisions about the time or spatial scale on which an observed process is reasonably close to being stationary. Moreover, space-time covariance functions are difficult to characterize flexibly even without further requirements of smooth, parametric variation in space or time. In this presentation, we extend the spectral-in-time framework of Stein (2005) to processes that are nonstationary in space and cyclostationary in time, providing a new method to flexibly and naturally characterize the evolving covariance structure of a broad class of nonstationary space-time processes. We then apply this method to a very large dataset of Doppler LIDAR vertical wind speed profiles, demonstrating both its flexibility and its computational scalability.