Atmospheric model and data analysis in terms of empirical normal modes

The Empirical Orthogonal Function (EOF) analysis technique has proven to be one of the most powerful methods to analyze data in meteorology and many other fields. However, this method is statistical only and has no physical basis. Brunet (1994) has introduced Held's (1985) concept of conservation of wave activity and orthogonal functions into the EOF analysis and called it the "Empirical Normal Mode" (ENM) analysis technique. This new method uses both statistical concepts from the classical EOF analysis method and a dynamical constraint from the generalized Eliassen-Palm theorem to ensure that the functions that we obtained are orthogonal to each other and are the solutions of linearized dynamical equations.; In this thesis, we use the ENM analysis to analyze data from both a (2D) shallow water model integration and from 3-D atmospheric observations, with an emphasis on stratospheric sudden warming events.; For the shallow water model case, the results of the ENM analysis are evaluated by testing against the theoretical (numerical) normal mode solutions provided by Longuet-Higgins (1968). It is shown that the ENM analysis can recover the spatial structures and the frequencies of the normal modes with a great degree of accuracy if the temporal record is sufficiently long. The average errors in the periods for 2000 and 100 day time series are found to be 1% and 4.6%, respectively. From the eigenvalues (percentage of the total variance) and sharp frequency peaks associated with normal modes, the ENM analysis shows that the model generates only a few modes with monochromatic frequencies. The method can be used to test a new or modified shallow water model integration or to study other Hough modes generated by different kinds of forcings.; Having shown the value of the ENM technique in a barotropic context, we advance further by performing an ENM analysis on an 11 year atmospheric data set. In this study, we focus on stratospheric warming events. The winter (DJF) data set is partitioned into warming and non-warming periods in order to characterize the flow differences between the regimes. The stratospheric quasi-potential vorticity or wave activity structure in the warming period is found to be much stronger, as expected, than in the non-warming periods. The ENM analysis clearly shows the tropospheric difference between the two periods, e.g., a higher wave activity in the main tropospheric structure as well as in the tropospheric polar regions in the warming periods. The analysis also reveals that there is a higher level of stratospheric wave activity during the warming periods in the second normal mode of zonal wave number 1 but the tropospheric structures of the quasi-potential vorticity are the same as during non-warming periods. This suggests that there is/are (a) mechanism(s) associated with the stratospheric warming other than the upward wave propagation. All the common features of the stratospheric warming event are captured by the first two normal modes of zonal wave numbers 1 and 2, such as wave-mean flow interaction leading to the deceleration of the zonal mean wind, the polar vortex being displaced by the northward movement of the Aleutian High, as well as wave amplitude enhancement/reduction during the growing/decaying stages.