On annular modes and zonal jets

Large-scale statistical modes of zonal-mean extratropical atmospheric variability such as the zonal index or the annular mode are generally interpreted in terms of variability of the zonal jet, in particular with fluctuations in jet position. In this talk, an idealised kinematic model of a jet in zonal-mean zonal wind which fluctuates in position, strength, and width is considered. This model is sufficiently simple that in many cases the leading Empirical Orthogonal Function (EOF) modes for both zonal-mean zonal wind and zonal-mean geopotential can be computed analytically. These analytic EOF modes are then compared to standard interpretations of the EOF modes of observed zonal-mean zonal wind and of zonal-mean geopotential, respectively the zonal index and annular modes. It is shown that the idealised model is able to reproduce the observed EOF structures when observed fluctuations in jet position, strength, and width are accounted for. However, it is not possible in general to relate individual EOF modes to individual jet degrees of freedom (position, strength, or width). Furthermore, it is shown analytically that in general there is no one-to-one correspondence between EOF modes of zonal-mean zonal wind and zonal-mean geopotential when the mean jet width is comparable to the width of the analysis domain. It is concluded that the zonal index mode and the annular mode are related but distinct.