A least squares method for spectral analysis of space-time series

Common methods in spectral analyses of satellite data are the discrete Fourier transform (DFT) type of approaches, which generally require regular sampling and uniform spacing. These conditions sometimes cannot be met in the satellite applications, for example, such as one made by the High Resolution Doppler Imager (HRDI) on board the Upper Atmosphere Research Satellite (UARS). To be able to handle irregular sampling cases, a least squares fitting method is established here for a space-time Fourier analysis and has been applied to the HRDI sampling as well as other regular sampling cases. This method can resolve space-time spectra as robustly and accurately as DFT-type methods for the regular cases. In the same fashion, given an appropriate sampling pattern, it can also handle the irregular cases in which there exist large data gaps, frequent mode changes, and varying weight samples. Various sampling schemes and the associated aliasing spectra are examined. A better sampling plan than those currently used by the UARS instruments to reduce spectral aliasing is proposed, which leads to the question of how to optimize satellite sampling in the future.