Near-Global Forecasts of Sea-Surface Temperatures Using Canonical Correlation Analysis
contributed by Willem A. Landman
South African Weather Bureau, South Africa
The statistically based model used to predict the near-global sea-surface temperature anomalies is based on canonical correlation analysis (CCA) (Barnston and Ropelewski, 1992). Four combined 3-month mean near-global sea-surface temperatures (Reynolds and Smith, 1994; Smith et al., 1996) are used as predictors. A combination of successive 1-month mean near-global sea-surface temperatures are the predictands. Pre-orthogonalisation using standard EOF analysis (Barnston, 1994) has been performed on the predictor and the predictand field, because of the large number of highly correlated variables and few observations (about 50 years) contained in these fields. The predictor and predictand data sets have been standardised, resulting in correlation matrices on which the EOF analysis has been performed.
The number of EOF modes to be retained in the CCA eigenanalysis has been determined such that about 60% of the variance of both the predictand and predictor field are explained. This value of 60% is justified because 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 the Guttman-Kaiser criterion. The truncation for the number of CCA modes retained has been determined by using the Guttman-Kaiser criterion.
Forecasts have been variance adjusted (Ward and Folland, 1991) using the correlations at each grid-point obtained from cross-validation, because linear statistical models will underestimate extreme El Niño events (Burgers and Stephenson, 1999). Forecasts where the grid-point cross-validation correlations are not significant at the 95% level of confidence have been replaced by climatology. The predictand field, which is a combination of several 1-month fields, have been separated after the prediction to obtain forecasts for each 1-month period contained in the combined predictand field. The predicted fields subsequently have been filtered to reduce the noise associated with the CCA forecasts. The filter structure is a general tapped delay-line filter described by a difference equation (Press et al., 1992).
The following schematic illustrates the lead-times involved in making forecasts during early December for 9 consecutive 1-month periods for the 1999/2000 season:
| 1998 1999 | 1999 2000 |
| S O N D J F M A M J J A S O N => | D, J, F, M, ... |
After separation of the predicted fields into 1-month periods, 3-month means have been calculated to produce forecasts for December-January-February, March-April-May and June-July-August. The forecasts (Figure 1) are for a La Niña event to persist into the boreal spring, with weak negative anomalies over the tropical Indian and Atlantic Oceans.
References:
Barnston, A. G. 1994. 'Linear statistical short-term climate predictive skill in the Northern Hemisphere', Journal of Climate, 7, 1513-1564.
Barnston, A. G. and Ropelewski, C. F. 1992. 'Prediction of ENSO using canonical correlation analysis', Journal of Climate, 5, 1316-1345.
Burgers, G. and Stephenson, D. B. 1999. 'The "normality" of El Niño', Geophysical Research Letters, 26, 1027-1030.
Jackson, J. E. 1991. A User's Guide to Principal Components, Wiley, New York, p. 569.
Jolliffe, I. T. 1972. 'Discarding variables in principal component analysis. I: Artificial data', Applied Statistics, 21, 160-173.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. 1992. Numerical Recipes in Fortran. The Art of Scientific Computing. Second Edition, Cambridge University Press, p.963.
Reynolds, R. W. and Smith, T. M. 1994. 'Improved global sea surface temperatures analyses using optimum interpolation', Journal of Climate, 7, 929-948.
Smith, T. M., Reynolds, R. W., Livezey, R. E. and Stokes, D. C. 1996. 'Reconstruction of historical sea surface temperatures using empirical orthogonal functions', Journal of Climate, 9, 1403-1420.
Ward, M. N. and Folland, C. K. 1991. 'Prediction of seasonal rainfall in the north Nordeste of Brazil using eigenvectors of sea-surface temperature', International Journal of Climatology, 11, 711-743.
FIGURE CAPTION
Figure 1: Forecasts of sea-surface temperature anomalies using CCA for December 1999 to February 2000 (DJF; top panel), March to May 2000 (MAM; middle panel) and June to August 2000 (JJA; bottom panel).
