Navarra, A., W. F. Stern, and K. Miyakoda, 1994: Reduction of the Gibbs oscillation in spectral model simulations. Journal of Climate, 7(8), 1169-1183.

Abstract: Spectral atmospheric general circulation models (GCMs) have been used for many years for the simulation and prediction of the atmospheric circulation, and their value has been widely recognized. Over the years, however, some deficiencies have been noticed. One of the major drawbacks is the instability of the spectral spherical harmonics transform to represent discontinuous features, resulting in Gibbs oscillations. In particular, precipitation and cloud fields present annoying ripple patterns which may obscure true drought episodes in climate runs. Other fields, such as the surface winds along the Andes, are also plagued by the fictitious oscillations. On the other hand, it is not certain to what extent the large-scale flow may be affected. An attempt is made in this paper to alleviate this problem by changing the spectral representations of the fields in the GCM. The technique is to apply various filters to reduce the Gibbs oscillations. Lanczos and Cesaro filters are tested for both one and two dimensions. In addition, for two-dimensional applications an isotropic filter is tested. This filter is based on the Cesaro summation principle with a constraint on the total wavenumber. At the end, two-dimensional physical space filters are proposed that can retain high-mountain peak values. Two applications of these filters are presented. In the first application, the method is applied to the orography field by filtering out sharp gradients or discontinuities. The numerical results with this method show some improvement in the cloud and precipitation fields, along with some improvement of the surface wind pattern, resulting in an overall better simulation.

In the second application, a Gibbs reduction technique is applied to the condensation process. In this paper the moist-adiabatic adjustment scheme is used for the cumulus parameterization, in addition to large-scale condensation. Numerical results with this method to reduce Gibbs oscillations due to condensation show some improvement in the distribution of rainfall, and the procedure significantly reduces the need for negative filling of moisture. Currently, however, this approach is only partially successful. The negative moisture areas at high latitudes can be, to some extent, controlled by an empirical procedure, but the filter approach is not sophisticated enough to satisfactorily remove the complex Gibbs oscillations present in the condensation field.