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

contributed by Amira Saunders, Michael Ghil and J. David Neelin

Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics,

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 to present.

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, and on those of N. Jiang, M. Ghil and J. D. Neelin for Nino-3 SST anomalies, starting with the March 1995 issue. Detailed information on the forecast method is given by 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 times of 3, 6, 9 and 12 months, from 1996 to the present. The forecast for each point utilizes only the appropriate part of the record that precedes the initial forecast time. The long-lead forecasts for last winter and spring were too warm, suggesting a caveat on current forecasts, but the forecasts for recent months at leads of up to 9-months have been reasonably accurate.

Nino-3 SST anomalies as predicted by the SSA-MEM method (Fig. 2) will transition from the current near-normal conditions into a mild warm event this coming winter season. This is consistent with previous forecasts. The forecast SOI index (Fig. 3) is negative during this fall and winter, consistent with a 20 warming. The consistency of the two indices increases our confidence in the forecast warming (Ghil and Jiang, 1998). The twelve-month forecasts for both indices suggest that the warm event will be decreasing by spring.

References:

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

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.

Fig. 1 . Forecasts of the area-averaged Nino-3 SST anomalies (SSTAs) using the SSA-MEM scheme. Forecasts from 1996 are for lead times of (a) 3 months,(b) 6 months, (c) 9 months, and (d) 12 months. The dashed 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 1990-2000 time span.

Fig. 2. Forecast Nino-3 SSTAs for the upcoming four seasons using the SSA-MEM scheme. The cyan dots are the observed Nino-3 SSTAs through May 2001 20 while the (blue) thick line is the observations after SSA-filteration. The red 20 dots indicate the SSA-MEM forecasts for the next 4 seasons, together with the 20 respective error bars (vertical (brown) lines).

Fig. 3. SSA-MEM forecast of the SOI from June 2001 through May 2002. The cyan dots are the monthly SOI values based on a 5-month running mean. The solid line is the SSA-filtered SOI. The red dots indicate the forecast for the next 12 months.