In this study, recent extreme events over the Northern Hemisphere are quantified in terms of an energy norm of the anomaly of the state variables. Since persistent low-frequency variabilities are characterized, in most cases, by their barotropic structure, the energy norm of the anomaly is measured for the barotropic component of the atmosphere. The norm is then normalized by its climatology to assess the abnormality of the extreme events. In this study the norm is evaluated in the framework of the 3-D spectral primitive equation model to assess the external forcing as well as the state variabiles. According to the analysis of the monthly mean anomaly data for 50 years from 1953 to 2002, the most abnormal months appear to be Apr. 1997, Jan. 1963, Jan. 1977, Mar. 1983, Apr. 1967, Feb. 1989, and Jan. 1989. Those are well known abnormal months in the past studies. In this study, the top 3% of the extreme events are listed as the abnormal months.
The quantification of the abnormality is further extended to the external forcing of the barotropic component of the atmosphere and also to the SST anomaly. It is found that only 3 cases of the abnormal months (Jan. 1963, Feb. 1989 and Jan. 1989) are associated with the abnormal external forcing, and the rest of the abnormal months are associated with the non-abnormal external forcing. Likewise, it is found that most of the abnormal external forcing result in a non-abnormal month. The SST forcing anomaly is not directly related to the external forcing. It is concluded from the result that more than 80% of the abnormal months are induced by the natural variability of the barotropic component of the atmosphere under the non-abnormal external forcing for the last 50 years. For the monthly time scale, the chaotic nonlinear behavior is quantitatively larger than a linear response to the external forcing or that to the SST anomaly.