Section 6.3: Characteristic Patterns of Global Sea Surface Temperature 99
ing values for season t at the m = 297 10° lat x 10° lang grid-boxes. For
each year, the four seasons DJF, MAM, JJA and SON are formed.
• pk is the k th EOF of X, i.e., it is the k th eigenvector of the estimated
covariance matrix of X. The EOFs are normalized so that (pk)T pk = l.
The EOFs have been derived from seasonal time series (4 values per year)
for 1901-1980.
• CXk contains the time coefficients (which form a time-series) for the k th
EOF pattern. The coefficient CXk(t) can be viewed as measuring the
strength of EOF pattern k in the observed SST anomaly field for season
t.
• After the EOFs pk have been determined, time coefficients CXk can be
calculated, by means of (6.3), for any dataset of 10° x 10° SST anomalies
X. SO for study ofthe boreal summer season in this chapter, a dataset of
1949-90 JAS SST anomalies has been used to yield CXk time coefficients
for JAS 1949-90.
6.3.4 EOFs fl_f3
The weights inpl are all the same sign, so the EOF time-coefficient represents
a weighted average of SST anomalies across the analysis domain. The timecoefficients contain an upward trend, describing the pattern of global warming
through the historical period. This is not the subject of this chapter, so pI
is not discussed further .
The weights of p2 describe the SST covariance associated with ENSOThe
weights in the EOF have been plotted on a map and contoured to show
the pattern of p2 (Figure 6.1a). The pattern suggests that warm events
in the central/eastern Pacific usually accompany cold SST anomalies in the
extratropical Pacific and warm anomalies in the Indian Ocean. The EOF
suggests that the reverse pattern of anomalies occurs in cold events. Note
that the two opposite phases of a mode described by an EOF may have
some asymmetry, but this cannot be deduced from an EOF analysis like
that reported here. The JAS p2 time coefficients CX2(t) (Figure 6.1a) clearly
describe the known major warm and cold events.
EOF p3 (Figure 6.1b) has negative weights in the North Atlantic and
North Pacific and positive weights in the South Atlantic, Indian Ocean and
southwestern Pacific. The time coefficients CX3(t) for p3 (Figure 6.1b) have
strong variability on decadal to multidecadal timescales. In particular, they
describe a large climate fluctuation that has occurred over the last 45 years,
with the re cent 25 years marked by a warmer Southern Hemisphere (including
all the Indian Ocean) and cooler Northern Hemisphere.
ing values for season t at the m = 297 10° lat x 10° lang grid-boxes. For
each year, the four seasons DJF, MAM, JJA and SON are formed.
• pk is the k th EOF of X, i.e., it is the k th eigenvector of the estimated
covariance matrix of X. The EOFs are normalized so that (pk)T pk = l.
The EOFs have been derived from seasonal time series (4 values per year)
for 1901-1980.
• CXk contains the time coefficients (which form a time-series) for the k th
EOF pattern. The coefficient CXk(t) can be viewed as measuring the
strength of EOF pattern k in the observed SST anomaly field for season
t.
• After the EOFs pk have been determined, time coefficients CXk can be
calculated, by means of (6.3), for any dataset of 10° x 10° SST anomalies
X. SO for study ofthe boreal summer season in this chapter, a dataset of
1949-90 JAS SST anomalies has been used to yield CXk time coefficients
for JAS 1949-90.
6.3.4 EOFs fl_f3
The weights inpl are all the same sign, so the EOF time-coefficient represents
a weighted average of SST anomalies across the analysis domain. The timecoefficients contain an upward trend, describing the pattern of global warming
through the historical period. This is not the subject of this chapter, so pI
is not discussed further .
The weights of p2 describe the SST covariance associated with ENSOThe
weights in the EOF have been plotted on a map and contoured to show
the pattern of p2 (Figure 6.1a). The pattern suggests that warm events
in the central/eastern Pacific usually accompany cold SST anomalies in the
extratropical Pacific and warm anomalies in the Indian Ocean. The EOF
suggests that the reverse pattern of anomalies occurs in cold events. Note
that the two opposite phases of a mode described by an EOF may have
some asymmetry, but this cannot be deduced from an EOF analysis like
that reported here. The JAS p2 time coefficients CX2(t) (Figure 6.1a) clearly
describe the known major warm and cold events.
EOF p3 (Figure 6.1b) has negative weights in the North Atlantic and
North Pacific and positive weights in the South Atlantic, Indian Ocean and
southwestern Pacific. The time coefficients CX3(t) for p3 (Figure 6.1b) have
strong variability on decadal to multidecadal timescales. In particular, they
describe a large climate fluctuation that has occurred over the last 45 years,
with the re cent 25 years marked by a warmer Southern Hemisphere (including
all the Indian Ocean) and cooler Northern Hemisphere.