Data Noise and Spectral Differencing in Geophysical Modeling

View More View Less
  • 1 Phillips Laboratory, Hanscom Air Force Base, Bedford, Massachusetts
© Get Permissions
Restricted access

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.

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.

Save