Atmospheric Stability in a Generalized Barotropic Model

Abstract An empirical modification of conventional barotropic dynamics is implemented to study the low-frequency variability (LFV) of the upper troposphere. Using the conservation of potential vorticity, generalized spectral barotropic operators that apply at single isentropic levels are constructed. In initial value calculations the empirical model shows improvement in skill compared to the conventional barotropic model, but it does not do significantly better than persistence. For short times, however, the empirically modified model shows a much closer resemblance to the observed streamfunction tendency. Overall, it is a significantly more accurate representation of the atmosphere than the conventional barotropic model. Normal, optimal, and singular modes of the modified model are calculated. The modes of the empirically modified model are more stable and more difficult to excite than those of the barotropic model. These results are consistent with previous studies that found barotropic dynamics deficient for the quantitative description of LFV. The singular modes of the modified operator have very similar patterns but explain less variance than those of the barotropic operator, which is consistent with the difficulty in detecting optimal patterns in observations. The modified barotropic operator is also more normal than the barotropic operator, and thus less variable.