Limited-Area Fourier Spectral Models and Data Analysis Schemes: Windows, Fourier Extension, Davies Relaxation, and All That

Regional spectral models have previously periodized and blended limited-area data through ad hoc low-order schemes justified by intuition and empiricism. By using infinitely differentiable “window functions” or “bells” borrowed from wavelet theory, one can periodize with preservation of spectral accuracy. Similarly, it is shown through a mixture of theory and numerical examples that Davies relaxation for blending limited-area and global data in one-way nested forecasting can be performed using the same C∞ bells as employed for the Fourier blending.“The relative success of empirical methods . . . may be used as partial justification to allow us to make the daring approximation that the data on a limited area domain may be decomposed into a trend and a periodic perturbation, and to proceed with Fourier transformation of the latter.” Laprise (2003, p. 775)