Spectral Decomposition of Two-Dimensional Atmospheric Fields on Limited-Area Domains Using the Discrete Cosine Transform (DCT)

Abstract

For most atmospheric fields, the larger part of the spatial variance is contained in the planetary scales. When examined over a limited area, these atmospheric fields exhibit an aperiodic structure, with large trends across the domain. Trying to use a standard (periodic) Fourier transform on regional domains results in the aliasing of largescale variance into shorter scales, thus destroying all usefulness of spectra at large wavenumbers. With the objective of solving this particular problem, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT). The DCT is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention. First, it is shown how the DCT can be employed for producing power spectra from two-dimensional atmospheric fields and how this technique compares favorably with the more conventional technique that consists of detrending the data before applying a periodic Fourier transform. Second, it is shown that the DCT can be used advantageously for extracting information at specific spatial scales by spectrally filtering the atmospheric fields. Examples of applications using data produced by a regional climate model are displayed. In particular, it is demonstrated how the 2D-DCT spectral decomposition is successfully used for calculating kinetic energy spectra and for separating mesoscale features from large scales.

High‐resolution surface analysis for extended‐range downscaling with limited‐area atmospheric models

“…For the atmospheric fields, spectral filters are recommended to identify the large-scale field components, as they allow a high degree of control over the separation of scales [see, e.g., Denis et al, 2002]. Spectral filters are, however, difficult to implement in the case of the surface fields with sharp discontinuities, such as soil moisture, due to land-water contrast.…”

“…In order to determine the appropriate radius, the spectral analysis of soil moisture was performed using the Discrete Cosine Transform [Denis et al, 2002]. For 2 km (15 km) SPS experiments in the present study, the filter size of n = 7 (n = 2) is adopted as optimal, as in this case the double application of the filter preserves the spatial variability at scales larger than roughly 120 km, while for scales about 30 km and smaller the spectral variance is reduced by roughly 2 orders of magnitude when compared to the nonfiltered field (not shown).…”

Storm track sensitivity to sea surface temperature resolution in a regional atmosphere model

“…In order to reliably identify the synoptic scale systems the vorticity is smoothed to a similar level as in Hoskins and Hodges, who used a T42 spectral truncation on the globe. Standard spectral methods cannot be applied to the regional model output as the domain is not periodic, so a discrete cosine transform was used to transform the vorticity field, following Denis et al (2002). The filter of Sardeshmukh and Hoskins (1984) was then used to smooth the vorticity, with a power of 0.1 on the 1,000 km wavelength, and the smoothed data were transformed back onto the model grid.…”

Investigation of indiscriminate nudging and predictability in a nested quasi‐geostrophic model

“…LAMs also present specific issues like sensitivity to the size of the domain of simulation, to the boundary conditions, and to the frequency of update of boundary conditions (Bhaskaran et al, 1996;Seth and Giorgi, 1998;Noguer et al, 1998;Denis et al, 2002aDenis et al, , 2003. For longterm simulations, Lo et al(2008) showed that continuous runs can produce a very low score when the simulations are compared to observations and that simulations reinitialized periodically have better results than continuous runs.…”