Spectral distributions of the pressure gradient force errors in σ-coordinate spectral and grid-point models in an idealized case

Summary

The spectral distributions of the pressure gradient force errors of the spectral and the finite-difference techniques used in combination with the σ vertical coordinate were examined in an idealized case of an atmosphere at rest and in hydrostatic equilibrium. The vertical temperature profile was piece-wise linear in lnp, with an inversion at the bottom. Trapezoidal mountains of different widths were used. The same amounts of input information were given to both the spectral and the finite-difference methods. In the rms sense, the spectral errors were generally much larger than those of the finite-difference method. However, on the larger and medium scales, a remarkable similarity of the error spectra of the two methods was found. The build up of the error of the spectral method occurs at the smallest scales. This may explain difficulties in documenting the error in higher resolution spectral models where the contribution to the total error in this part of the spectrum may be removed as the small-scale noise by the horizontal smoothing and/or filtering. In order to reduce the small-scale noise generation, the finite-difference pressure gradient force may be used in spectral models.