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Forecasts of Niño 3 SST Anomalies and SOI Based on Singular
Spectrum Analysis Combined with the Maximum Entropy Method
Ning Jiang, 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; Ghil and Vautard 1991; Plaut et al.
1995) and the maximum entropy method (MEM: Burg 1968; Penland et al. 1991) are used here
for long-lead forecasts of the sea-surface temperature (SST) anomalies averaged over the Niño 3
area and the Southern Oscillation Index (SOI). The forecast is for up to one year ahead, based on
the last 45 years of observed data. 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: Kimoto et al. 1991; Keppenne and Ghil 1993; Plaut and Vautard
1994) 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
quasiquadrennial (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 Niño 3 SSTAs, forecast and observed, since 1990, using the SSA-
and MSSA-MEM schemes for a 3-, 6-, 9- and 12-month lead. The last forecast, for the next 1-4
seasons, using data through April 1997, is shown in Fig. 2. The vertical bars are one standard
deviation in length, based on forecast verification over the 1984-93 time span. The forecast
indicates a continuous warm anomaly during the next few seasons, peaking in late 1997.
Figure 3 shows the SSA-MEM forecast for the SOI from May 1997 through April 1998. The SOI
is expected to be below its mean through early 1998. The present SOI forecast does agree with
the Niño-3 SSTA forecast inasmuch as the two indices are anticorrelated, the way they usually
are; this enhances our confidence in the forecast (Ghil and Jiang 1997). The present forecast
agrees, furthermore, with the National Centers for Environmental Prediction (NCEP) statistical
CCA forecast (Barnston and Ropelewski 1992), and the NCEP coupled model forecast (Ji et al.
1996) as they appear in the March 1997 Climate Diagnostics Bulletin, although the magnitude of
the peak warm anomaly prediction here is smaller than theirs.
Barnston, A.G., C. F. Ropelewski, 1992: Predic-tion of ENSO episodes using canonical
correlation analysis. J. Climate, 5, 1316-1345.
Burg, J.P., 1968: Maximum entropy spectral analysis. Modern Spectrum Analysis, 34-48. IEEE
Press.
Ghil, M. And N. Jiang, 1997: Recent forecast skill for the El Niño/Southern Oscillation. Geophys.
Res. Lett., 102, submitted.
Ghil, M. and R. Vautard, 1991: Interdecadal oscillations and the warming trend in global
temperature time series. Nature, 350, 324-327.
Ji , M., A. Leetmaa and V.E. Kousky, 1996: Coupled model forecasts of ENSO during the 1980s
and 1990s at the National Meteorological Center. J. Climate, 9, 3105-3120
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
Adaptive filtering and prediction of noisy multivariate signals: An application to subannual
variability in atmospheric angular momentum. Intl. J. Bif. & Chaos, 3, 625-634.
Kimoto, M., M. Ghil and K.C. Mo, 1991: Spatial structure of the 40-day oscillation in the
Northern Hemisphere extratropics. Proc. 8th Conf. Atmos. & Oceanic Waves & Stability. Amer.
Met. Soc., Boston, 115-116.
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.
Plaut, G.R. and R. Vautard, 1994: Spells of oscillations and weather regimes in the low-frequency
dynamics of the Northern Hemisphere. J. Atmos. Sci., 51, 210-236.
Plaut, G.R., M. Ghil and R. Vautard, 1995: Interannual and interdecadal variability in 335 years of
central England temperature. Science, 268, 710-713.
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 Niño-3 SST anomalies (SSTA) using the SSA-MEM (star)
and MSSA-MEM (open circle) schemes. The solid line indicates the observed Niño-3 SSTA.
The latest forecast starts from April 1997. Shown for: (a) 3-month, (b) 6-month, (c) 9-month and
(d) 12-month lead.
Fig. 2. The forecasts of the Niño-3 SSTA for the upcoming 4 seasons using the SSA-MEM
scheme. The solid line indicates the observed Niño-3 SSTA through April 1997.
Fig. 3. SSA-MEM forecast of the SOI for May 1997 through April 1998. 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.
