**(looking for coherence and stability
of the modes)**

**Data. **The
primary sea surface temperature (SST) data set for this analysis is the
Hadley sea ice and SSTs from the Hadley Centre for Climate (1870-2002,
version 1.1). The data set is extrapolated from the original 1x1 grid to
a 5x2 grid, and cut to the shorter 1945-2002 period. In what is to follow
the main interest is on the decadal variability of the Pacific basin so
special attention will be paid on those modes that capture such variability.

**Methodology.** Before
doing anything, anomalies are calculated with respect to the monthly/season
means (i.e. annual cycle removed), and then an area weighting of the anomalies
is done in order to avoid bias due to unequal areas of a latitude-longitude
grid. Finally, the weighted anomalies are normalized dividing them by the
square root of the spatially integrated temporal variance. Modes of SST
variability are extracted from a regular Rotated EOF analysis and from
an Extended Rotated EOF analysis. In both cases a covariance based Rotated
Principal Component Analysis of monthly SST anomalies for the mostly Pacific
domain (120E-60W,20S-60N) is carried out. EOFs of the covariance matrix
are obtained from the Singular Value Decomposition analysis of SST anomalies
in the regular analysis, and of combined lagged SST anomalies for the extended
analysis. The eigenvectors are then rotated using the VARIMAX technique.

**Basic Experiments. **It
is possible to identify five main patterns from de rotated EOF analysis
performed for the 1950-1993
period, namely, ENSO, Pacific Decadal, North
Pacific, Western Pacific, and a "less-than-shape" equatorial pattern. However,
when the analysis is performed for the 1945-2002 period two additional
patterns emerge, one of which is trend related; the five patterns mentioned
before are now in the first 7 patterns: ENSO,
"less-than-shape",
Pacific
Decadal, North
Pacific, Western
Pacific. As for the 1950-1993 period, 9 eigenvectors
are rotated explaining 66% of the variance (and about the same variance
than for the shorter period). Those results impose some basic questions
about the coherence and sensitivity of the modes to a number of things
like to the length of the period, and the number of EOFs to be rotated.
An extension of those questions may be the dependence of the identified
modes on the type of analysis
performed.

An alternative approach in identifying the main modes of variability in the Pacific basin, is to use the extended rotated EOF analysis (EREOF). The EREOF method identifies the dominant spatial and temporal structures of lagged sequences of covariances. This procedure is able to extract time evolving patterns because phase information is retained in the decomposition of the combined lagged data.

An EREOF analysis is done for monthly
SST anomalies in the 1945-2002 period using 5 "lags" of three months centered
around the period July 1945-June 2002 (i.e. 2 "lags" before this central
period, the central period, plus 2 "lags" after the central period so that
every lagged SST field contains 684 months). After rotating the first 9
eigenvectors, which explain a combined variance close to 52%, it is possible
to identify the main named modes from the regular analysis, however, some
of the patterns seem to be split in two "modes" lagged in time. ENSO occupies
the first
and second
modes (with the first
lagging the second by 9 months** **); a linear
trend is evident in third place; the Pacific Decadal pattern is seen in
fourth
place; the equatorial "less-than-shape" pattern occupies the fifth
andsixth
places (with the fifth
leading the sixth by 9 months); the Western and North Pacific patterns
take the seventh
andeighth
places respectively (with the seventh
lagging the eighth by 9 months too). Correlation between time series
of both analyses confirm their association. Spectrum
analysis of the PCs of the EREOF indicates
the ENSO patterns have a main/secondary peak at ~3.5/5.7 years while the
Pacific Decadal pattern has a main/secondary peak at ~28.5/5.7 years. There
are two equatorial "less-than-shape" patterns from which the first of those
has comparable peaks at ~8 and ~11.4 years, while the second pattern has
peaks at ~11.4/28.5 years, however interannual and higher variability is
relatively important in those modes. In turn, the Western Pacific pattern
has a main/secondary peak at 57/5.7 years while the North Pacific pattern
has a main/secondary peak at 57/3.8 years; however, similarities in spatial
patterns and time series of these two modes make difficult to separate
one from the other in this analysis and that will be postponed to a sensitivity
analysis later.

In order to minimize intraseasonal variability the EREOF analysis is repeated but for the seasons of the whole 1945-2002 period. In this case, similarly to the monthly case, 5 "lags" of 1 season are considered. Rotation of the first 9 eigenvectors explain now 61% of the variance (9% more than the monthly case!!) with some changes in the order of the patterns but not in their structure. ENSO patterns are still the same and first and second; Pacific Decadal pattern is now third, displacing the trend to fourth place; the equatorial "less-than-shape" patterns are not consecutive patterns and occupy fifthandseventhplaces. The most significant change is for the duality of midlatitude Pacific patterns that now are merged as one and located in sixth place.

For reference purposes the previous
analyses are labeled as follows:

EXPERIMENT ID |
ANALYSIS |
PERIOD/UNIT |
FIELD |
DETRENDED? |

EXP1 | REOF | 1945-2002 / MONTHLY | SST | NO |

EXP2 | EREOF: 5 lags of 3 months | 1945-2002 / MONTHLY | SST | NO |

EXP3 | EREOF: 5 lags of 1 season | 1945-2002 / SEASONAL | SST | NO |

It is apparent from the previous
analyses that the appearance of the equatorial "less-than-shape" pattern
complicate matters in the identification of a clear separation of the Pacific
Decadal pattern and decadal variability along the equator and along the
west coasts of Mexico and the US. Comparison of the already shown patterns
with regressed SST anomalies on the well known Mantua
and NINO3.4indices
does not provide any insight because the similarities between the regressed
fields and several patterns of the extended analyses. Correlations
between Mantua index and PCs of the midlatitudes
Pacific patterns are between 0.55-0.65, and those with ENSO patterns are
not low at all (~0.5) while correlations with the Pacific Decadal pattern
is low (~0.35). Correlations
between NINO3.4 index and PCs of ENSO patterns
are the highest (~0.8), however those with the equatorial "less-than-shape"
patterns are not low neither (0.55-0.6).

This EREOF analysis is done in a
number of ways: 1) for the 1945-2002 period; 2) for the 1900-2002 period;
3) rotating 6 EOFs, 4) for the