Data Noise and Spectral Differencing in Geophysical Modeling

Abstract

This paper discusses the impact of data noise on the accuracy of derivatives obtained by differentiating a Fourier series of an observed dataset. It is first brought to the fore that the kth component of the energy density of the mth derivative of a Fourier series is proportional to k2m. It is then argued that since the energy density of atmospheric parameters resolvable by the current observing network decreases at a rate of no less than k?2, it is desirable to apply a low-pass filter to the spectrally computed derivatives to arrest the rapid growth of noise-induced errors at the smaller scales. Based on the analysis of a sample set of atmospheric data, it is also recommended that to avoid noise-induced spurious growth of short-wave energy at the onset of a time integration, in geophysical modeling where the model grid is finer than the observational resolution, model initial conditions should contain only those scales that are resolvable by the observing network.