50mb Geopotential Height

Figure 4.7 shows the first two principal components of Trial A at the 50mb geopotential height. The structure is simpler than that at the 500mb geopotential height. The first PC is an oscillation similar to the tropospheric Arctic Oscillation. This is a symptom of an oversimplified representation of the stratosphere. The second PC is the dipole oscillation. Figure 4.8 shows the score of the first three PCs.

The CNLPCA output of the scores (figure 4.9) reveals a loop that lies on the PC1-PC2 plane. This is similar to the tropospheric case, which supports the idea of an oversimplified stratosphere [16]. The penalty factor used to obtain an optimal solution is only 0.1, compared to 1.0 at the 500mb level. This shows that there is less non-linearity involved in the stratosphere of the model.

The angular distribution, shown in figure 4.10, has a similar structure as that in the 500mb geopotential height. This shows that even though the spatial patterns are oversimplified, the model successfully captured the evolution of the score.

Figure 4.7: First two PCs for the Trial A at 50mb between $20^{\circ}$N and $90^{\circ}$N. ``Exp'' is the percentage of variance.

Figure 4.8: The scores of the first three PCs for the Trial A at 50mb.

Figure 4.9: CNLPCA results for Trial A at 50mb in PC space are the overlapping circles. The dots are the input data into the CNLPCA neural network. The dashed line represents the linear PCA results.

Figure 4.10: Angular distribution of the results at 50mb. The horizontal axis is the angle obtained from taking $\arctan(\frac{PC2}{PC1})$ for each point on the CNLPCA output. Each bin is $6^{\circ}$ in size, for 60 bins in total.

The spatial patterns of the regimes, figure (4.11), show that the stratosphere changes between oscillating as a monopole (top left and bottom left) and a dipole (top right and bottom right). The patterns at the extrema (figure 4.12), however, show more wavelike structures than the regimes.

Figure 4.11: The average spatial patterns around each regime at 50mb. The angles are determined by the well-separated peaks in the angular distribution, figure 4.10.

Figure 4.12: The spatial patterns at the points on figure 4.9 with (top left) Maximum PC1, (top right) Minimum PC1, (lower left) Maximum PC2, and (lower right) Minimum PC2.