A quick post today to round off the “static” part of our atmospheric flow analysis.

Now that we’ve satisfied ourselves that the bumps in the spherical PDF in article 8 of this series are significant (in the narrowly defined sense of the word “significant” that we’ve discussed), we might ask what to sort of atmospheric flow regimes these bumps correspond. Since each point on our unit sphere is really a point in the three-dimensional space spanned by the first three $Z_{500}$ PCA eigenpatterns that we calculated earlier, we can construct composite maps to look at the spatial patterns of flow for each bump just by combining the first three PCA eigenpatterns in proportions given by the “$(x, y, z)$” coordinates of points on the unit sphere.

Here’s what these spatial patterns of $Z_{500}$ variation look like for the four bumps we labelled in the spherical PDF . Here, we really aren’t all that interested in the scale of the contours, just their spatial patterns.

Of most interest here are the distinct patterns of flow seen in the first two bump patterns. Pattern 2 appears to be something closer to the “normal” flow regime, with contours of $Z_{500}$ variation running more or less east-west across the Atlantic (representing the prevailing westerly winds there). Pattern 1, on the other hand, is much more like a “blocking” pattern, with contours of $Z_{500}$ variation bulging downwards into the Atlantic from over Greenland (you can compare these to the patterns of $Z_{500}$ in an earlier article. The correspondence between the patterns here and the hand-selected “normal” and “blocking” regimes shown in the earlier figures isn’t perfect, but it’s quite interesting that the analysis here (pre-processing, PCA, truncation to 3 PCA components, projection to the unit sphere, KDE on the unit sphere) has led us to patterns of spatial variation that are similar to what we think of as these archetypal flows.

At this point, we have developed a purely static picture of what’s going on: we’ve established that there are statistically significant patterns of atmospheric flow that occur in our data set that correspond to our ideas of what are “normal” and “blocking” regimes. We’ve not yet said anything about transitions between these regimes. This question of dynamics is what we’ll address next.