117
Figure 14: 500hPa stream function of dominant barotropic day-8 singular vector at day
8 for (a) cluster 2 and (b) cluster 5 of Molteni et al (1990). From Molteni and Palmer
(1993) .
winters.
Evidence of variations in the instability characteristics of positive and
negative PNA states was discussed in Palmer (1988), who found that the
growth of linear perturbations in a barotropic model depended strongly
on the sign of the PNA index of the basic-state flow. However, it was
noted that the difference in these growth rates could not be explained
in terms of differences in the eigenmode growth associated with the basic states. Molteni and Palmer (1993) compared the growth rates of the
fastest-growing eigenmodes and the optimal singular vectors for the cluster 2 and cluster 5 flow in the barotropic model. For the most unstable
eigenmode (which is stationary in both cases) there is little difference in
growth rates for the two basic states. On the other hand, the dominant
singular values are quite different. In particular, for 8-day optimisation,
the dominant singular value for the cluster 2 flow is almost a factor of 2
smaller than that of the cluster 5 flow. The streamfunction of the final
dominant singular vector for an 8-day optimisation is shown in Fig 13 for
the cluster 2 and cluster 5 basic states.
There are two important approximations that have been made in these
calculations. The first is the use of a barotropic model. The second relates to the fact that we have chosen stationary basic states which are not
Figure 14: 500hPa stream function of dominant barotropic day-8 singular vector at day
8 for (a) cluster 2 and (b) cluster 5 of Molteni et al (1990). From Molteni and Palmer
(1993) .
winters.
Evidence of variations in the instability characteristics of positive and
negative PNA states was discussed in Palmer (1988), who found that the
growth of linear perturbations in a barotropic model depended strongly
on the sign of the PNA index of the basic-state flow. However, it was
noted that the difference in these growth rates could not be explained
in terms of differences in the eigenmode growth associated with the basic states. Molteni and Palmer (1993) compared the growth rates of the
fastest-growing eigenmodes and the optimal singular vectors for the cluster 2 and cluster 5 flow in the barotropic model. For the most unstable
eigenmode (which is stationary in both cases) there is little difference in
growth rates for the two basic states. On the other hand, the dominant
singular values are quite different. In particular, for 8-day optimisation,
the dominant singular value for the cluster 2 flow is almost a factor of 2
smaller than that of the cluster 5 flow. The streamfunction of the final
dominant singular vector for an 8-day optimisation is shown in Fig 13 for
the cluster 2 and cluster 5 basic states.
There are two important approximations that have been made in these
calculations. The first is the use of a barotropic model. The second relates to the fact that we have chosen stationary basic states which are not