It is common for spatial-temporal data to be collected by a number of monitors at fixed locations in space, with each monitor recording data at regular intervals in time. A weather station network is a canonical example. For modeling and computational purposes, it is useful to view these data as multiple time series. This presentation considers half-spectral spatial-temporal models, in which the time series are modeled in the frequency (spectral) domain, with spatial correlation induced by allowing the Fourier coefficients to be spatially correlated. This regime allows for flexible semiparametric and nonstationary modeling, and computationally efficient inference and interpolations. Applications to weather station data and climate model output are presented.