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Forecasts of NiZo 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 long­lead forecasts of the sea­surface temperature (SST) anomalies averaged over the NiZo 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 single­channel SSA combined with MEM is given by Keppenne and Ghil (1992), while multi­channel SSA (M­SSA: 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 M­SSA (if multivariate), so that the statistically significant components are retained, specifically the quasiquadren-nial (QQ) and the quasi­biennial (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 area­averaged NiZo 3 SSTAs, forecast and observed, since 1990, using the SSA- and MSSA­MEM schemes for a 3­, 6­, 9­ and 12­month lead. The last forecast, for the next 1-4 seasons, using data through April 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 NiZo 3 will gradually return toward normal through early 1997.

Figure 3 shows the SSA­MEM forecast for the SOI from May 1996 through April 1997. The SOI is expected to remain close to its mean, but above it, over the remainder of this year. The present SOI forecast thus agrees with the NiZo 3 SSTA forecast; this was not the case for our last two quarterly forecasts. The time evolution during a 12­year period (from 1984 to 1995) of the forecast skill of our SSA­MEM SSTA prediction and of the correlation between NiZo­3 SSTA and SOI show a modest correlation (Figure 4): a high forecast skill tends to correspond to a high (anti)correlation between these two ENSO signals (NiZo­3 SSTA and SOI). This suggests a Arecovery@ of ENSO from its relatively unpre-dictable state over the last few years or so, and better prospects for our current 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: Quasi­quadrennial and quasi­biennial variability in the equatorial Pacific. Clim. Dyn., 12, 101-112.

Jiang, N., M. Ghil and D. Neelin, 1995: Forecasts of Equatorial Pacific SST anomalies using an autoregressive process using singular spectrum analysis. Experimental Long-Lead Forecast Bulletin, 4, 1, 24-27.

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, 625­634.

Kimoto, M., M. Ghil and K.C. Mo, 1991: Spatial structure of the 40­day oscillation in the Northern Hemisphere extratropics. Proc. 8th Conf. Atmos. & Oceanic Waves & Stability. Amer. Met. Soc., Boston, 115­116.

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 area­averaged NiZo­3 SST anomalies (SSTA) by the SSA­MEM (star) and MSSA­MEM (circle) schemes. The solid line indicates the observed NiZo­3 SSTA. The latest forecast starts from April 1996. Shown for: (a) 3­month, (b) 6­month, (c) 9­month and (d) 12­month lead.

Fig. 2. The forecasts of the NiZo­3 SSTA for the upcoming 4 seasons using the SSA­MEM scheme. The solid line indicates the observed NiZo­3 SSTA.

Fig. 3. SSA­MEM forecast of the SOI for May 1996 through April 1997. The circles are the monthly SOI values based on a 5­month running mean without the seasonal cycle and the solid line is the SSA­filtered SOI. The dashed line indicates the forecast for the next 12 months.

Fig. 4. The correlation between the NiZo­3 SSTA and (­SOI) (solid line), and the forecast skill of SSTA using the SSA­MEM scheme for 3­month lead forecasts (dashed line) during 1984­1995. Both the correlation and the forecast skill are calculated for nonoverlapping one­year intervals (from January to December), where the means over the 12 months are removed in calculating the correlation (i.e. it is a standard correlation coefficient).

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