On baroclinic instability in filtered and non-filtered numerical prediction models

The criterion for baroclinic instability in a two level model of the large-scale motion in the atmosphere is computed and compared for the following cases: (1) A quasigeostrophic model with constant static stability. (2) A quasi-geostrophic model with a horizontal variation of static stability. (3) A primitive equation model with constant static stability. (4) A primitive equation model with horizontal variation of static stability.

It is found that the models containiig a horizontal variation of the static stability have a maximum instability at shorter wavelengths than the models with constant static Stability; that only small differences are observed in the amplification rate of baroclinic disturbances in models with the aame variation of static stability but with different basic equations 88 long as the variation of the meteorological parameters are in the observed range; but that large differences in the amplification rate occur when the Richardson number is small, i.e. for smell mean static stabilities and/or large vertical wind shears.

The structure of the baroclinically unstable disturbances are computed and compared for the four models mentioned above. The variation of the ageostrophic wind and the static stability through the wave is of special importance. It tuns out that the maximum ageostrophic wind at the upper level is about 15 % of the maximum wind, while the corresponding number at the lower level is 20 %. The distribution of the ageostrophic wind at the upper level is such that the wind is supergeostrophic around the ridge in the geopotential with a maximum close to the maximum geopotential and subgeostrophic around the trough in the geopotential. The distribution of static stability in the developing baroclinic wave is such that the air becomes more stable than the average between the ridge and trough (looking downstream), but more unstable between the trough and the ridge.