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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 January 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 forecasts
indicate a slow, gradual warming trend during the next few seasons.
Figure 3 shows the SSA-MEM forecast for the SOI from February 1997 through January 1998.
The SOI is expected to regress toward and remain above its mean through the year 1997. The
present SOI forecast agrees well with the previous one (December 1996 issue of this Bulletin),
and our Niño 3 SSTA forecast also agrees with those of Penland and Magorian's (1993) linear
inverse model and those of the Cane/Zebiak model (Cane it al. 1986, Zebiak and Cane 1987). Our
confidence in the current--albeit not spectacular--forecast is further enhanced by the fact that over
the last few months the coupled ocean-atmosphere system in the tropical Pacific shows signs of
resuming its usual behavior, with the SOI and Niño 3 SSTs being anticorrelated (Ghil and Jiang
1997).
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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 January 1997. Shown for: (a) 3-month, (b) 6-month, © 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 February 1997 through January 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.