A few years ago, Keppenne and Ghil (1992a,b; see also issues of this Bulletin before December 1995) introduced a methodology to forecast the Southern Oscillation Index (SOI) by applying the maximum entropy method (MEM) to produce autoregressive forecasts of a set of adaptively filtered time series resulting from the application of singular spectrum analysis (SSA) to the raw monthly mean SOI. The success of this methodology has led to the development of a multivariate prediction scheme based on the same concepts, but with the substitution of multivariate SSA for univariate SSA (Keppenne and Ghil 1993, Jiang et al. 1995). The technique used now contains improvements to the linear prediction scheme used to issue the SSA/MEM predictions presented previously.

First, the data base used to compute the forecasts now extends backward to 1881, thanks to our new variation of SSA capable of handling the occasional missing values. Most data adaptive statistical prediction methods are best understood in terms of an Aanalog forecast@ (e.g. Toth 1991, Huang et al. 1993, Livezey et al. 1994). Thus, the extension of the data base increases the likelihood of identifying a suitable Aanalog@ that help determine the forecast=s basis functions. This process forecasts the real and imaginary parts of the SOI=s leading four complex principal components (CPCs) using a variation of multivariate adaptive regression splines (MARS: Friedman 1991, Lewis and Stevens 1991, Lall et al. 1996), a nonlinear data­adaptive statistical method.

Second, in contrast with our earlier work (Keppenne and Ghil 1992a,b) in which SSA was applied to the difference between the Tahiti and Darwin normalized SLP time series, we apply CSSA to the complex time series whose real and imaginary parts consist in the Darwin and Tahiti SLP, forecast the real and imaginary parts of the resulting CPCs separately, and then take their differences to construct a forecast for the filtered SOI. This procedural modification enhances the forecast skill, because taking the difference between two separately CSSA-filtered time series increases the noise­to­signal ratio.

Third, we have replaced the linear autoregressive MEM system by the skill-preserving, analog-like nonlinear MARS methodology. MARS has advantages discussed in earlier issues of this Bulletin. In our variation of MARS, appropriate Aneighbors@ of the prevailing climate conditions are identified in the phase space; regression­splines are then used to develop the predictions. More detail about this procedure is provided in Keppenne and Lall (1995, 1996).

The evaluation of the algorithm=s forecast skill uses a Aretroactive real-time@ simulation in which only forward-looking hindcasts are developed. As detailed in the December 1995 and March 1996 issues of this Bulletin, the MARS model dramatically outperforms the MEM models at leads of less than 2.5 years.

The latest CSSA-MARS forecast is shown in Fig. 1. The CSSA­filtered SOI appears to have peaked and the MARS models applied to the corresponding complex principal components predict a return to normal conditions followed by an El Nino in mid-1998. This differs somewhat from the forecast issued 3 months ago in that further strengthening of the La Nina conditions into 1997 is no longer forecast. This forecast change is in good continuity with that noted from December 1995 to March 1996.

Friedman, J.H., 1991: Multivariate adaptive regression splines. Ann Stat, 19, 1­50.

Huang, J.P., Y.H. Yi, S.W. Wang and J.F. Chou, 1993: An analog­dynamic long­range numerical weather prediction system incorporating historical evolution. Q J R Met. Soc., 119, 547­565.

Jiang, N., M. Ghil and D. Neelin, 1995: Forecasts of equatorial Pacific SST using an autoregressive process using singular spectrum analysis. Exp. Long­Lead Forcst. Bull., 4, No. 1, 24­27.

Keppenne, C.L. and M. Ghil, 1992a: Forecasting extreme weather events. Nature, 358, 547.

Keppenne, C.L. and M. Ghil, 1992b: Adaptive Spectral Analysis and Prediction of the Southern Oscillation Index. J. Geophys. Res., 97, 20449­20554.

Keppenne, C.L. and M. Ghil, 1993: Adaptive filtering and prediction of noisy multi­variate signals: an application to atmospheric angular momentum. Intl. J. Bifurcations and Chaos, 3, 625­634.

Keppenne, C.L. and U. Lall, 1995: A new methodology to forecast paleoclimate time series with application to the Southern Oscillation index. EOS Trans AGU. 1995 Fall Meeting Supplement, 76, F327.

Keppenne, C.L. and U. Lall, 1996: Complex singular spectrum analysis and multivariate adaptive regression splines applied to forecasting the Southern Oscillation. J. Clim., 9, submitted.

Lall, U., T. Sangoyomi and H.D. Abarbanel, 1996: Nonlinear dynamics of the Great Salt Lake: nonparametric short term forecasting. Water Resources Res., in press.

Lewis, P.A.W. and J.G. Stevens, 1991: Nonlinear modeling of time series using multivariate adaptive regression splines (MARS). J. Amer. Stat. Assoc., 86, 864­877.

Livezey, R.E., A.G. Barnston, G.V. Gruza and E.Y. Rankova, 1994: Comparative skill of 2 analog seasonal temperature prediction systems: Objective selection of predictors. J. Clim., 7, 608­615.

Toth, Z., 1991: Estimation of atmospheric predictability by circulation analogs. Mon. Wea. Rev., 119, 65­72.

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