The perturbation in the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) is defined by the difference between the RSM and its outer model, such as the NCEP global model, on the same given coordinate surfaces. This perturbation is dominated by the difference between terrains of the RSM and the global model if model terrain exists over the domain. After being transformed into spectral space, this difference in terrains is characterized by two distinct groups of coefficients i.e., long-wave and short-wave groups. The long-wave group is considerably larger in amplitude than the short-wave group, and considered to be the cause of error in horizontal diffusion of perturbations on sigma surfaces. A higher order of diffusion and diffusion without long waves on sigma surfaces with perturbations are formulated to investigate the possibility of using diffusion on sigma surfaces.

In a typical case, erroneous circulation occurred when fourth-order diffusion on a sigma surface was used; however, reasonable circulation was simulated with second-order diffusion on the pressure surface. Nevertheless, diffusion on a pressure surface is a non-economical method in spectral modeling. The results of sixth- and eighth-order horizontal diffusions of perturbations and no-diffusion on the group of long waves for all orders (second, fourth, sixth, and eighth) on sigma surfaces did not show erroneous circulations. Thus, diffusions greater than and equal to sixth-order diffusions and no-diffusion on a long-wave group can be implemented into NCEP RSM as an economical computation as it leads to an absence of erroneous circulation comparable to diffusion on pressure surfaces.