Forecasts of Nino-3 SST Anomalies and SOI Based on Singular Spectrum Analysis Combined with the Maximum Entropy Method

contributed by Dmitri Kondrashov, Michael Ghil and J. David Neelin

Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California

Singular spectrum analysis (SSA: Vautard and Ghil 1989) and the maximum entropy method (MEM: Penland et al.1991) are combined to produce long-lead forecasts of sea-surface temperature (SST) anomalies averaged over the Nino-3 area and of the Southern Oscillation Index (SOI). The forecast is for up to one year ahead based on data from January 1950 through February 2006.

This forecast follows up on earlier forecasts using combined SSA-MEM methodology for the SOI index by C. Keppenne and M. Ghil, starting in the March 1992 issue of this Bulletin, on those of N. Jiang, M. Ghil and J. D. Neelin for Nino-3 SST anomalies, starting from March 1995, and on those of A. Saunders, M. Ghil and J. D. Neelin from September 1997. Detailed information on the forecast method can be found in Keppenne and Ghil (1992) and in the March 1995 issue of this Bulletin (also Jiang et al. 1995). Briefly, the time series is filtered by SSA so that only the statistically significant low-frequency components are retained. Next, MEM is applied to advance these components in time. The extended components are then used in the SSA reconstruction to produce the forecast values.

Figure 1 shows the method's Nino-3 SSTA forecasts for lead time of 6 months, from 1990 to the present.  The forecast for each point utilizes only the appropriate part of the record that precedes the initial forecast time.

The current SSA-MEM forecast for Nino-3 SSTA (Fig. 2) is for a warming trend in through 2006. The forecast SOI index (Fig. 3) is for a weak cooling phase, and it is generally consistent with the SSTA forecast.

References:

Ghil, M., and N. Jiang, 1998: Recent forecast skill for the El Nino/Southern Oscillation. Geophys. Res. Lett.,25, 171-174.

Ghil, M., M. R. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. W. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou, 2002: Advanced spectral methods for climatic time series, Rev. Geophys., 40(1), pp. 3.1-3.41, 10.1029/2000RG000092.

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.

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, 22, 659-22, 671.

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

Figure 1 shows observed area-averaged Nino 3 SSTAs and it's forecast for lead time of 6 months since 1990, using the SSA-MEM scheme. The forecast for each point utilizes only the appropriate part of the record that precedes the initial forecast time. The solid blue line gives the observed SSTAs, data-adaptively filtered by SSA; the solid red line is the forecast; and the red lines are situated each at a distance of one standard deviation from the SSA-MEM forecasts. The standard deviation value is based on forecast verification over the 1990-2005 time span.

Fig. 2. Forecast Nino-3 SSTAs for the next 12 months using the SSA-MEM scheme. The black line is  Nino-3 SSTAs, data-adaptively filtered by SSA,  and it's prediction through January 2007;  the solid blue line is raw SST data. The red line indicate forecast error bars (see caption to Fig. 1). 

Fig.3. SSA-MEM forecast of the SOI for the next 12 months. The black line is the SSA-filtered observed SOI index and it's prediction, the blue line is the raw data. The red lines are forecast error bars.