Forecasts of Niño 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 Niño 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 Niño-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 SSA-reconstruction to produce the forecasted values.

Figure 1 shows the methods Niño-3 SSTA forecasts for lead times of 3, 6, 9 and 12 months, from 1994 to present. The forecast for each point utilizes only appropriate "past" part of the record.

The SSA-MEM method predicts a slow warming of Niño-3 SST anomalies throughout the year, remaining negative in the next six months and crossing over mild warm conditions afterwards, yet still within error bars of normal conditions. The forecasted SOI index shows a gradual decline as it reaches toward zero in February 2001. The agreement between these forecasts suggests that cold anomalies will weaken in the next 12 months but it is unlikely that strong warm anomalies will develop.

References:

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 Niño 3 SST anomalies (SSTA) using the SSA-MEM scheme. The blue line connects the observed Niño 3 SSTA (diamonds). The latest forecast starts from March 2000 and is shown for (a) 3-month (b) 6-month (c) 9-month and (d) 12-month lead times. In each figure the (red) line connects the individual forecasts (circles). 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 1984-93 time span.

Fig. 2. Forecast Niño 3 SSTA for the upcoming four seasons using the SSA-MEM scheme. The solid (blue) line connects the observed Niño 3 SSTA through February 2000. The (red) circles indicate the SSA-MEM forecasts for the next 4 seasons, together with the respective error bars (vertical brown lines).

Fig. 3. SSA-MEM forecast of the SOI from March 2000 through February 2001. The black circles are the monthly SOI values based on a 5-month running mean without the seasonal cycle. The solid (blue) line is the SSA-filtered

SOI. The (red) circles indicate the forecast for the next 12 months.