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 "analog 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 "analog" 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 data-adaptive 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 noise-to-signal 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 "neighbors" of the prevailing climate conditions are identified in the phase space; regression-splines 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 "retroactive 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 system predicts a return to normal conditions by winter 1996-97, followed by another weak La Nina beginning in winter 1997-98 and lasting through much of 1998. Then a return to El Niño-like conditions is predicted for late 1999 to 2000. This differs from the forecast issued 3 months ago, in which a trend toward lower SOI was to occur in late 1996 and during 1997 without a second weak La Nina beforehand.

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Fig. 1. The application of a variant of multivariate adaptive regression splines (MARS) to the real and imaginary parts of the leading four complex principal components (CPCs) resulting from a CSSA yields this forecast for the SOI for the remainder of 1996 through early 2001.