| An empirical modification of the barotropic dynamics framework is achieved in this work. Using the conservation of potential vorticity, we construct generalized spectral barotropic operators that apply at single isentropic levels. Information about the baroclinic state of the atmosphere is included by using isentropic potential vorticity instead of isobaric absolute vorticity as the conserved quantity of the single level, spectral, global model.; The dynamics of the model are studied using a quasi-geostrophic model of the troposphere and tropopause. It is found that the empirical barotropic operator corresponds, in varied degrees of accuracy, to QG operators applied in the tropospheric interior and on a discontinuous tropopause.; We perform initial value calculations, where ten-day forecasts are made with the model initialized with low-frequency anomalies. The empirical model shows improvement in the skill with respect to the barotropic model, but it does not forecast significantly higher than persistence. Additionally, one-day forecasts are computed for the generalized and barotropic models. The empirically modified model shows a much closer resemblance to the observed streamfunction tendency than the barotropic one. This serves as a validation of the expected more accurate depiction of the state of the atmosphere by the generalized model.; Finally, the generalized model is scrutinized in terms of its normal, adjoint, optimal and singular modes. It is found that the modes of the empirically modified model are more stable than the ones of the barotropic model. Also the modified barotropic optimal modes are more difficult to excite than their barotropic counterparts. These results are in accordance with previous studies that found that barotropic dynamics may not quantitatively describe LFV. The singular modes of the modified operator have very similar patterns but explain less variance than the barotropic ones. This is consistent with the difficulty in detecting optimal patterns in observations. Finally, we find that the modified barotropic operator is more normal than the classic barotropic one, and thus less variable. |
