Abstract
The results of numerical weather prediction based on the quasi-geostrophic equations with vanishing p-velocities both at the top and bottom of the troposphere appear to indicate that the propagation speeds of waves in the upper troposphere are too large and the east-ward speeds of waves (of medium length) in the lower troposphere are too small in com-parison with those observed. In this paper, perturbation analyses for the two-level geos-trophic equations are made for the following two sets of boundary conditions, (i) ωT (=p- velocity at the top of the troposphere) is proportional to the height-change at the upper level and ωs (=p-velocity at the bottom of the troposphere) vanishes, (ii) ωT vanishes, whereas ωs is proportional to the height-change at the lower level. The result indicates that the phase speed of waves at the upper level in case (i) is smaller than that in case of vanishing ωT, whereas the phase speed of waves at the lower level in case (ii) is smaller than that in case of vanishing ωs.
