Forecasts
of the Indo-Pacific SSTs Using Canonical Correlation Analysis
contributed
by Willem A. Landman and Simon J. Mason
A
canonical correlation analysis (CCA) model is used to predict near-global SST
anomalies for the next 12 months: four 3-month mean near-global SSTs (DJF, MAM,
JJA and SON 2001) are combined and used as predictors; twelve subsequent
1-month near-global SSTs are the predictands (December 2001 to November 2002).
The CCA model suggests that the weakly negative SST anomalies in the eastern
equatorial Pacific Ocean will continue to persist into the first half of 2002,
but will be replaced by weak warm anomalies towards the boreal autumn.
Pre-orthogonalisation
using standard EOF analysis is performed on the predictor and the predictand
field because of the large number of highly correlated variables and few
observations contained in these fields. The predictor and predictand data sets
are first standardised, so that the EOF pre-orthogonalisation is performed
using the correlation matrices. The number of EOF modes to be retained in the
CCA eigenanalysis is determined such that about 60% of the variance of both the
predictand and predictor field is explained. The value of 60% is justified
since 70% is the recommended threshold by the Guttman-Kaiser criterion (Jackson
1991), which normally over-selects the number of modes, and Jolliffe (1972)
suggested a fraction of the number of modes suggested by this criterion. The
truncation for the number of CCA modes retained is determined by again using
the Guttman-Kaiser criterion. The predictand fields, which are a combination of
several 1-month fields, are separated after the prediction to obtain forecasts
for each 1-month period contained in the combined predictand field.
Reconstructed monthly SST fields (Smith et al. 1996) are used to train the
model, and optimum interpolation SST data (Reynolds and Smith 1994) to make
operational SST anomaly forecasts. The model and its performance over an
independent 18-year retroactive forecast period (1982/83 to
1999/2000) are discussed in
detail in Landman and Mason (2001).
Only forecasts and skill of the
equatorial Indo-Pacific Ocean (Figures 1 and 2) are presented here, because tropical Atlantic Ocean
forecast skill has been found to be generally poor and there is little evidence
of forecast skill over the midlatitudes in any of the oceans. Cold eastern
equatorial Pacific Ocean SST anomalies of about 1ºC are forecast for the DJF season
(not shown). Figure 3 shows the SST forecasts for the
three single months of March, June and September 2002 at 3-, 6- and 9-month
lead-times respectively (Figure 3). The cold eastern
equatorial Pacific SST anomalies are expected to gradually weaken towards the
middle of 2002, and are subsequently replaced by weak warm anomalies soon
after. The current warm SST anomalies over the tropical Indian Ocean are
expected to persist throughout the forecast period.
Jackson,
J. E., 1991: A User’s Guide to Principal Components. Wiley, 569 pp.
Jolliffe,
I. T., 1972: Discarding variables in principal component analysis. I:
Artificial data. Appl. Stat., 21, 160-173.
Landman, W. A., and S.
J. Mason, 2001: Forecasts of near-global sea surface temperatures using
canonical correlation analysis. J. Climate, 14, 3819-3833.
Reynolds, R. W., and
T. M. Smith, 1994: Improved global sea surface temperature analyses using
optimum interpolation. J. Climate, 7, 929-948.
Smith, T. M., R. W.
Reynolds, R. E. Livezey, and D. C. Stokes, 1996: Reconstruction of historical
sea surface temperatures using empirical orthogonal functions. J. Climate,
9, 1403-1420.
Figure
captions:
Figure 1. (left panels) Correlations between predicted and
observed (solid line) and persisted and observed (dashed line) eastern
equatorial Pacific Ocean (approximately the Niño3.4 region) SST anomalies over
the 18-year independent period 1982/83-1999/2000 at (a) 3-month, (b) 6-month,
and (d) 9-month lead-times. The horizontal lines indicate the 90%, 95% and 99%
confidence levels.
Figure 2. (right panels) As for Figure 1, but for the
equatorial Indian Ocean (6°N to 6°S; 48°E to 104°).
Figure 3. CCA forecasts of March, June and September 2002 SST anomalies.
