MJO Metrics Combined EOF

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MJO MetricsCombined EOFs using 20-100 day
filtered OLR, u850, and u200 averaged between
15N-15S
Prior to computing EOFs, each equatorially-average
d field is normalized by the square-root of the
zonal mean of the temporal variance at each
longitudinal point. The normalizations are (OLR,
u850, u200) 8.64 Wm-2, 1.18 ms-1, 3.34 ms-1
(all seasons) 9.67 Wm-2, 1.26 ms-1, 3.58 ms-1
(southern summer) 7.51 Wm-2, 1.09 ms-1, 3.09
ms-1 (northern summer). Data used was January
1980 to December 2002. Winds were NCEP/NCAR
Reanalysis. Southern Summer November to April
Northern Summer May to October
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note that eof2 and eof1 swapped for n. summer to
be consistent with other seasons
Variance explained by each EOF
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Coherence squared and phase between PC1 and PC2
from each EOF calculation (The input data was
band-pass filtered for 20-100 days, so the
cross-spectrum outside this range is meaningless.)
All Seasons
S. Summer
N. Summer
Cross-spectra of the all-season PCs computed
separately for southern summer and northern
summer.
Note These cross-spectra were computed by
applying FFTs to a long time-series composed of
stringing-together all the 6-month segments.
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Project the anomaly data onto the EOFs computed
with the band-pass filtered data. The anomalies
have the long-term mean and 3 harmonics of the
seasonal cycle removed. Compute spectra for ALL
SEASONS. That is, project all seasons of data
onto the season-specific EOFs, and compute
spectra using all months of the year. Spectra
computed on 6-month segments of data, padded with
zeroes to 256 days.
Projection onto All Season EOFs
Projection onto S. Summer EOFs
Projection onto N. Summer EOFs
The EOFs act as a highly selective filter for the
frequencies of the MJO
Note that the projected PCs will no longer have
unit standard deviation. In fact, the variance of
the PCs computed from the projection onto the
northern summer EOFs is greater because the
normalization factors used for northern summer
are less.
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Project the anomaly data onto the EOFs computed
with the band-pass filtered data. The anomalies
have the long-term mean and 3 harmonics of the
seasonal cycle removed. Compute spectra for
SOUTHERN SUMMER only. Spectra computed on 6-month
segments of data, padded with zeroes to 256 days.
Projection onto All Season EOFs
Projection onto S. Summer EOFs
Note that the projected PCs will no longer have
unit standard deviation, and the different
normalization factors cause the projected PCs to
have different amplitudes.
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Project the anomaly data onto the EOFs computed
with the band-pass fitlered data. The anomalies
have the long-term mean and 3 harmonics of the
seasonal cycle removed. Compute spectra for
NORTHERN SUMMER only. Spectra computed on 6-month
segments of data, padded with zeroes to 256 days.
Projection onto All Season EOFs
Projection onto N. Summer EOFs
Note that the projected PCs will no longer have
unit standard deviation, and the different
normalization factors cause the projected PCs to
have different amplitudes.
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Create a synthesized MJO OLR field through 3-d
regression with the projected PCs. That is,
compute the 3-d regression between (20-100 day
filtered) OLR at each grid point and PC1 and PC2
from the different EOF analyses. This regression
is seasonally-varying, that is, a different
regression is formed for each month of the year.
There is little difference in the MJO-OLR
variance in JJAS associated with the all season
EOF analysis compared to the northern summer only
EOFs.
a) Variance of synthesized MJO OLR field (from
All Season EOFs) - JJAS
b) Variance of synthesized MJO OLR field (from N.
Summer EOFs) - JJAS
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Create a synthesized MJO OLR field through 3-d
regression with the projected PCs. That is,
compute the 3-d regression between (20-100 day
filtered) OLR at each grid point and PC1 and PC2
from the different EOF analyses. This regression
is seasonally-varying, that is, a different
regression is formed for each month of the year.
There is little difference in the MJO-OLR
variance in DJFM associated with the all season
EOF analysis compared to the southern summer only
EOFs All season EOFs are adequate.
a) Variance of synthesized MJO OLR field (from
All Season EOFs) - DJFM
b) Variance of synthesized MJO OLR field (from S.
Summer EOFs) - JJAS
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Conclusion Even though the spatial structure of
the seasonally-specific EOFs differ slightly from
the all-season EOFs (especially over the E.
Pacific), virtually the same variability is
captured by the all-season EOFs. Furthermore, the
all season EOFs resolve the distinct behavior of
the MJO off of the equator in N. Summer and S.
Summer via regression or composites for the two
seasons separately (see attached composites of
OLR and for DJFM and MJ from Wheeler and Hendon
2004). Hence, for ease of understanding and
simplicity, we recommend computation of combined
EOFs using all seasons of data. That is, we
recommend using the all season EOFs for this MJO
metric. We also see no good reason for varying
the latitudinal averaging for different seasons.
Even though the OLR signal of the MJO shifts into
the summer hemisphere, the strongest zonal wind
signal tends to shift into the winter hemisphere.
Hence, if your intent is to capture variability
associated with the MJO, we recommend averaging
15S to 15N.
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Projected PCs computed when anomaly data is
projected onto the EOFs of the filtered data
PCs from the all season EOF calculation on 20-100
day filtered data
Lag correlations between PC1 and itself, and with
PC2.
Cross-spectra between PC1 and PC2. Note that
they are identical in the 20-100 day band.
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Fig. 8 from Wheeler and Hendon. Composite OLR and
850HPa winds for DJF based on all season EOFs
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Fig. 9 from Wheeler and Hendon. Composite OLR and
850HPa winds for MJ based on all season EOFs