REDUCTION OF THE GIBBS OSCILLATION IN SPECTRAL MODEL SIMULATIONS

Spectral atmospheric general circulation models (GCMs) have been used for many years for the simulation and prediction of the atmospheric ci rculation, and their value has been widely recognized. Over the years, however, some deficiencies have been noticed. One of the major drawba cks is the inability of the spectral spherical harmonics transform to represent discontinuous features, resulting in Gibbs oscillations. In particular, precipitation and cloud fields present annoying ripple pat terns, 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 i n this paper to alleviate this problem by changing the spectral repres entation of the fields in the GCM. The technique is to apply various f ilters to reduce the Gibbs oscillations. Lanczos and Cesaro filters ar e tested for both one and two dimensions. In addition, for two-dimensi onal applications an isotropic filter is tested. This filter is based on the Cesaro summation principle with a constraint on the total waven umber. 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 discontinui ties. 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 t he second application, a Gibbs reduction technique is applied to the c ondensation process. In this paper the moist-adiabatic adjustment sche me is used for the cumulus parameterization, in addition to large-scal e condensation. Numerical results with this method to reduce Gibbs osc illations due to condensation show some improvement in the distributio n of rainfall, and the procedure significantly reduces the need for ne gative filling of moisture. Currently, however, this approach is only partially successful. The negative moisture areas at high latitudes ca n be, to some extent, controlled by an empirical procedure, but the fi lter approach is not sophisticated enough to satisfactorily remove the complex Gibbs oscillations present in the condensation field.