A spectral model for investigation of amplifying baroclinic waves

A spectral quasi-geostrophic model with vertical derivatives approximated by finite differences is used to study the effect of different vertical resolutions on the behaviour of baroclinic waves. The effect of the small terms in the complete vorticity and thermodynamic equations is also investigated. These terms are treated separately and modify a first order growing wave and the induced zonal field. The baroclinic instability with respect to first order perturbations is computed for different x- and y-wave numbers. Numerical experiments indicate that a low vertical resolution is most serious when the horizontal scale is small. High resolution models have a significantly higher instability in the short wave interval 1 000–2 000 km and the instability is split into two separate maxima. The secondary maximum at the shortest wavelengths is very sensitive to changes in the static stability and is also present in a linearized primitive model. A necessary spacing needed to resolve this instability is of the order of 5 vertical levels and 150 km horizontal gridlength. The effect of the vertical resolution on the induced zonal and second order field was found to be very small. The contribution from the small terms in the complete equations is mainly a deepening of the cyclones and a weakening of the anticyclones and an increased cyclonic circulation in the eastern parts of the upper troughs and ridges. The relative importance of each of the small terms is studied and it is concluded that it is important to keep them all.