Singular spectrum analysis (SSA: Vautard and Ghil 1989) and the maximum entropy method (MEM: Penland et al. 1991) are used here for long-lead forecasts of the sea-surface temperature (SST) anomalies averaged over the Nino 3 area and the Southern Oscillation Index (SOI). The forecast is for up to one year ahead, based on the last 47 years of observed data.

This forecast follows up on earlier forecasts using combined SSA-MEM methodology by C. Keppenne and M. Ghil for the SOI index, starting in the March 1992 issue of this Bulletin, and on those of N. Jiang, M. Ghil and J.D. Neelin for Nino-3 SST anomalies, starting with the March 1995 issue. More detailed information on the forecast method based on single-channel SSA combined with MEM is given by Keppenne and Ghil (1992), while multi-channel SSA (M-SSA: Keppenne and Ghil 1993) combined with MEM is documented in the March 1995 issue of this Bulletin (see also Jiang et al. 1995). Briefly, the time series is filtered first by SSA (if univariate) or M-SSA (if multivariate), so that the statistically significant components are retained, specifically the quasi-quadrennial (QQ) and the quasi-biennial (QB) components of ENSO variability (Rasmusson et al. 1990; Keppenne and Ghil 1992; Jiang et al. 1995). Then MEM is applied to advance these components in time.

Figure 1 shows area-averaged Nino 3 SSTA, forecast and observed, since 1990, using the SSA- and MSSA-MEM schemes for 3-, 6-, 9- and 12-month lead. The latest forecasts, for the next 1-4 seasons, using data through March 1998, are shown in Fig. 2. The vertical bars are one standard deviation in length, based on forecast verification over the 1984-93 time span. The current forecast indicates a gradual decline in the warm event throughout the coming year. The observed SST anomalies are actually declining at a faster rate than the model is able to do, since it tends to capture low-frequency components. Thus, the 3-month forecast is probably not as low as it should be. The MSSA forecast at 3 and 6 months lead is slightly cooler than the single-channel SSA. 

Figure 3 shows the SSA-MEM forecast for the SOI from April 1998 through March 1999. The SOI is predicted to rise through the year, roughly consistent with the forecast colder SSTA. However the observed SOI has not yet began to rise. This is of concern because the anticorrelation between the present SOI and Nino-3 SSTA tends to indicate higher predictability (Ghil and Jiang 1997).

References:

Ghil, M. And N. Jiang, 1997: Recent forecast skill for the El Nino/Southern Oscillation. Geophys. Res. Lett., 102, in press.

Jiang, N., D. Neelin and M. Ghil, 1995: Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific. Clim. Dyn., 12, 101-112.

Keppenne, C. L. and M. Ghil, 1992: Adaptive filtering and prediction of the Southern Oscillation Index. J. Geophys. Res., 97: 20449-20454.

Keppenne, C. L. and M. Ghil, 1993: Adaptive filtering and prediction of noisy multivariate signals: An application to subannual variability in atmospheric angular momentum. Intl. J. Bif. & Chaos, 3, 625-634. 

Penland, C., M. Ghil and K. M. Weickmann, 1991: Adaptive filtering and maximum entropy spectra, with application to changes in atmospheric angular momentum. J. Geophys. Res., 96, 659-671. 

Rasmusson E. M., X. Wang and C. F. Ropelewski, 1990: The biennial component of ENSO variability. J. Mar. Sys., 1, 71-96.

Vautard, R., and M. Ghil, 1989: Singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series. Physica D, 35, 395-424.

Fig. 1. Forecasts of the area-averaged Nino-3 SST anomalies (SSTA) using the SSA-MEM (star) and MSSA-MEM (open circle) schemes. The solid line indicates the observed Nino-3 SSTA. The latest forecast starts from December 1997 shown for (a) 3-month lead and (b) 6-month lead (c) 9-month lead (d) 12-month lead.

Fig. 2. The forecasts of the Nino-3 SSTA for the upcoming 4 seasons using the SSA-MEM scheme. The solid line indicates the observed Nino-3 SSTA through March 1998. The vertical bars are one standard deviation in length, based on forecast verification over the 1984-93 time span.

Fig. 3. SSA-MEM forecast of the SOI for April 1998 through March 1999. The circles are the monthly SOI values based on a 5-month running mean without the seasonal cycle and the solid line is the SSA-filtered SOI. The dashed line indicates the forecast for the next 12 months.