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
(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 July
1996, 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
forecasts indicate that the presently cooler than normal conditions in
Niño 3 will continue through spring 1997.
Figure 3 shows the SSA-MEM forecast for the SOI from August 1996 through
July 1997. The SOI is expected to remain close to its mean, but above it,
through early 1997. The present SOI forecast thus agrees with the Niño
3 SSTA forecast.
References
Burg, J.P., 1968: Maximum entropy spectral analysis. Modern Spectrum
Analysis, 34-48. IEEE Press.
Ghil, M. and R. Vautard, 1991: Interdecadal oscillations and the warming
trend in global temperature time series. Nature, 350, 324-327.
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.
Figures
Fig. 1. Forecasts of the area-averaged Niño-3 SST anomalies (SSTA) using the SSA-MEM (star) and MSSA-MEM (circle) schemes. The solid line indicates the observed Niño-3 SSTA. The latest forecast starts from July 1996. 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.
Fig. 3. SSA-MEM forecast of the SOI for September 1996 through August
1997. 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.