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 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, 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 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.
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, 10.1029/2000GR000092.
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 dot-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 magenta line connects the smoothed observed Nino-3 SSTAs through August 2003, and the blue line is SSA filtered SST. The red line indicates the SSA-MEM forecasts for the next 4 seasons, together with the respective error bars (vertical black lines).
Fig.3. SSA-MEM forecast of the SOI for the upcoming four seasons. The magenta line is the smoothed observed SOI index, the blue line is the SSA-filtered SOI. The red line indicates the forecast for the next 4 seasons, together with the respective error bars (vertical black lines).