Nonlinear canonical correlation analysis

forecasts of the tropical Pacific sea surface temperatures

contributed by Aiming Wu and William W. Hsieh

Dept. of Earth and Ocean Sciences, University of British Columbia,

Vancouver, B.C., Canada V6T 1Z4

The nonlinear canonical correlation analysis (NLCCA), developed by Hsieh (2000) using a neural network (NN) approach, has been applied to study the nonlinear relation between the tropical Pacific sea level pressure (SLP) and sea surface temperature (SST) fields (Hsieh, 2001), as well as between the wind stress and SST fields (Wu and Hsieh, 2002). Here the NLCCA model is used for the seasonal forecasts of the tropical Pacific SST from the SLP.

The monthly tropical Pacific SLP data (COADS, Woodruff et al. 1987) and the monthly tropical Pacific SST data (Smith et al. 1996) had their seasonal cycles and linear trends removed, and a 3-month running mean applied. Predictands are the 6 leading principal components (PCs) of the SST anomalies (SSTA). Predictors are the 10 leading PCs from the singular spectrum analysis (i.e. extended EOF) of the SLP anomalies with a 9-month lag window. The predictors and predictands are the inputs to the NLCCA model. For cross-validation, 5 different models were built. The first was built without the data from 1950-1959, which was to be used as independent validation (or testing) data. Similarly, each of the other models had a different decade of data left out for independent validation.

Due to local minima problems in finding nonlinear modes, only the leading NLCCA mode was used. From the residual data, the linear CCA was used to extract additional modes. Hence the NLCCA forecasts actually use the leading NLCCA mode plus 4 CCA modes. Wu and Hsieh (2001, Table 1) compared the forecasts skills from the NLCCA approach and the standard CCA approach.

These five models, plus a sixth one trained with data from 1950 till Sep., 2001, form a 6-member ensemble forecast model. Using data up to the end of August, 2003, forecasts were made with the nonlinear approach. Ensemble-averaged forecasts for the SSTA in the Nino3.4 region at various lead times are shown in Fig.1, showing near-normal conditions for the winter of 2003-2004, with a warming tendency in the SSTA beyond winter. The forecasted SSTA field over the tropical Pacific is shown in Fig.2 at four consecutive seasons.

References:

Hsieh, W.W., 2000. Nonlinear canonical correlation analysis by neural networks. Neural Networks, 13: 1095-1105.

Hsieh, W.W., 2001. Nonlinear canonical correlation analysis of the tropical Pacific climate variability using a neural network approach. J. Clim. 14: 2528-2539.

Smith, T.M., Reynolds, R.W., Livezey, R.E. and Stokes, D.C., 1996. Reconstruction of historical sea surface temperatures using empirical orthogonal functions. J. Clim. 9: 1403-1420.

Woodruff, S.D., Slutz, R.J., Jenne, R.L. and Steurer, P.M., 1987. A comprehensive ocean-atmosphere data set. Bull. Amer. Meteorol. Soc. 6: 1239-1250.

Wu, A. and W.W. Hsieh, 2001. Forecasting the tropical Pacific sea surface temperatures by nonlinear canonical correlation analysis. Experimental Long Lead Forecast Bull., Dec. 2001.

Wu, A. and Hsieh, W.W., 2002. Nonlinear canonical correlation analysis of the tropical Pacific wind stress and sea surface temperature Clim. Dynam. 19: 713-722. DOI 10.1007/s00382-002-0262-8.

Figure captions:

Figure 1. The SST anomalies (SSTA) (in degree Celsius) in the Nino3.4 area (170W-120W,5S-5N) predicted by the ensemble-averaged nonlinear model at 3, 6, 9 and 12 months of lead time (circles), and the observed SSTA (solid line). Tick marks along the abscissa indicate the January of the given years.

Figure 2: SSTA (in degree Celsius) predicted by the ensemble-averaged nonlinear model at 3, 6, 9 and 12 months of lead time, corresponding to the four consecutive seasons starting with OND (October-December) of 2003. Positive SSTA are drawn with solid contours, negative SSTA with dashed contours, and the zero contour is thickened. Contour intervals are 0.3 C.