Section 12.1: Objective Teleconnections
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anomaly, namely the horizontal dimension of the patch of fluid that is presumably dynamically coherent. Each basis grid point will have one of these
ellipses because the grid points are not independent of each other but they
tend to be organized in features much larger than a single grid-point.
For most grid points only the local ellipses will be generated, resulting in
rather uninteresting distributions, but for a few others, complicated patterns
show up. Basically there are two broad classes of large scale patterns. There
are patterns that exhibit large negative correlations that together with the
original ellipse form a dipole structure. These patterns are most commonly
found over the oceans and they present a north-south orientation of the axis
of the dipole. There are also more elongated patterns, with multiple centers
of positive and negative high correlation, stretching over the hemisphere.
Figure 12.1 shows an example from the Wallace and Gutzier paper. In this
case the basis point is located in the North Pacific and it is easily recognizable
by the value of 1.0 of the correlation coefficient. The basis point is obviously
perfectly correlated with itself. The correlation drops to -.65 in the next
center of action to the east, meaning that positive anomalies in that location
are often simultaneous to positive anomalies in the basis point.
Testing the statistical significance of the teleconnections is rather difficult,
because it is not known apriori which is the level of correlation coefficient
that is relevant. Apopular, but not mathematically rigorous method, is to
check the reproducibilty of the patterns with sub sets of the original data
or with different data sets. The reproducibility is then taken as a strong
indication of significance for a given teleconnection pattern.
The original analysis of Wallace and Gutzier identified five principal patterns for the 500mb geopotential height field. Three patterns consisted of
multiple centers, the Eastern Atlantic pattern (EA), thePacific/North American pattern (PNA) and the Eurasian pattern (EU) pattern. The remaining
two represented dipole structure, the West Pacific pattern (WP) and the
West Atlantic pattern (WA). Each pattern is identified by the location of
the nodes and antinodes. The antinodes correspond to the centers 0/ action,
namely the geographical locations of the grid point more strongly correlated
with each other. The centers of action can be used to define teleconnections
indices by combining linearly the anomalies at such centers. For instance the
index for the PNA can be defined as
P N A = ~[(200 N, 160 0 W) - (45° N, 165°W) + (55° N, 115°W) - (30° N, 85°W)]
The index is such that very high values of the index indicate an anomaly
field with highs and lows in phase with the PNA and with high amplitude.
Similarly, we can define indices for the other patterns
EA
~(55° N, 20 0 W) - i(25° N, 25°W) - i(50 0 N, 40° E)
W A = ~(55° N, 55°W) - ~(300 N, 55°W)
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anomaly, namely the horizontal dimension of the patch of fluid that is presumably dynamically coherent. Each basis grid point will have one of these
ellipses because the grid points are not independent of each other but they
tend to be organized in features much larger than a single grid-point.
For most grid points only the local ellipses will be generated, resulting in
rather uninteresting distributions, but for a few others, complicated patterns
show up. Basically there are two broad classes of large scale patterns. There
are patterns that exhibit large negative correlations that together with the
original ellipse form a dipole structure. These patterns are most commonly
found over the oceans and they present a north-south orientation of the axis
of the dipole. There are also more elongated patterns, with multiple centers
of positive and negative high correlation, stretching over the hemisphere.
Figure 12.1 shows an example from the Wallace and Gutzier paper. In this
case the basis point is located in the North Pacific and it is easily recognizable
by the value of 1.0 of the correlation coefficient. The basis point is obviously
perfectly correlated with itself. The correlation drops to -.65 in the next
center of action to the east, meaning that positive anomalies in that location
are often simultaneous to positive anomalies in the basis point.
Testing the statistical significance of the teleconnections is rather difficult,
because it is not known apriori which is the level of correlation coefficient
that is relevant. Apopular, but not mathematically rigorous method, is to
check the reproducibilty of the patterns with sub sets of the original data
or with different data sets. The reproducibility is then taken as a strong
indication of significance for a given teleconnection pattern.
The original analysis of Wallace and Gutzier identified five principal patterns for the 500mb geopotential height field. Three patterns consisted of
multiple centers, the Eastern Atlantic pattern (EA), thePacific/North American pattern (PNA) and the Eurasian pattern (EU) pattern. The remaining
two represented dipole structure, the West Pacific pattern (WP) and the
West Atlantic pattern (WA). Each pattern is identified by the location of
the nodes and antinodes. The antinodes correspond to the centers 0/ action,
namely the geographical locations of the grid point more strongly correlated
with each other. The centers of action can be used to define teleconnections
indices by combining linearly the anomalies at such centers. For instance the
index for the PNA can be defined as
P N A = ~[(200 N, 160 0 W) - (45° N, 165°W) + (55° N, 115°W) - (30° N, 85°W)]
The index is such that very high values of the index indicate an anomaly
field with highs and lows in phase with the PNA and with high amplitude.
Similarly, we can define indices for the other patterns
EA
~(55° N, 20 0 W) - i(25° N, 25°W) - i(50 0 N, 40° E)
W A = ~(55° N, 55°W) - ~(300 N, 55°W)