An analogue selection procedure, based on the non­linear time series forecasting technique of Sugihara and May (1990), is applied to the Southern Oscillation Index (Drosdowsky 1994).

The time series to be forecast x_i is "embedded" in an E dimensional space defined by a sequence of lagged coordinates (x_t, x_t­g, x _t­2g,..., x _t­(e­1)g), where g is the lag interval, usually taken as one time step. The E+1 closest neighbors (analogues) to the current state, defined by the vector x_t, x _t­g, x _t­2g,..., x _t­(e­1)g, are found and used to construct the smallest simplex containing the current state. Future states of the system are found by projecting each analogue forward nT, where n=1,2,..., time steps and taking a suitably weighted average of the analogues. The optimal embedding dimension E is determined by a trial and error procedure, using the library of patterns formed by the first half of the time series to predict the evolution at each point of the last half of the time series. This effectively determines the window over which the analogue is selected.

The forecast system has been tested on time series with known properties. For the SOI, the optimal embedding dimension is found to be of order 9 to 12. The operational scheme has been used in the monthly Seasonal Climate Outlook issued by the National Climate Centre of the Australian Bureau of Meteorology since mid­1991. Analogues are selected from the entire available SOI time series from 1876 to the present time. An element of persistence is included in the forecast by adjusting the weighted analogue so that the t=0 value agrees with the current observed base value.

The skill of the analogue system has been examined in hindcast experiments (Drosdowsky 1994), and is shown in Fig. 9-1 in the September 1994 issue of this Bulletin. For RMSE the one time step forecasts are approximately equal to persistence while the two or more time step forecasts are more skillful than persistence within the appropriate range of embedding dimension. The spread of the analogues during the forecast period can provide a measure of the confidence level of the forecast.

Beginning with the forecast that appeared in the December 1994 issue, an improved SOI data set has been used. It covers the same Jan. 1876-present period as before, but periods of missing data have been filled. Information on the new data set can be obtained from Rob Allan (rja@dar.csiro.au).

Figure 1 shows the analogue forecast starting from May 1996 and extending through August 1996. The SOI has remained at small positive values over the past three months. The spread of the analogs over both the selection period (September to May) and the forecast period (June to August) has increased over the past three months. This is a result of the Apredictability barrier@ and the currently weak ENSO signal. Forecast values for the next three months (in SD units X 10) are:

Verification of the previous 3 months= forecasts:

The forecast issued in early March failed to predict the maintenance of positive SOI, although forecasts based on March and April data (as discussed below) are performing better.

Figure 2 shows the analogue forecast starting from April 1996 (one month earlier than for Fig. 1), and Fig. 3 starting from March 1996. While the forecasts from these three start times are somewhat similar (in fact, some of the same years are seen to have been selected for all three starting months), short-term forecasts for a falling SOI has tended to change to one of a rising SOI as the observed starting point has decreased from what it was in March. The forecasts beginning from March and May have considerable internal spread among the five best picks. The verifications of the two previous months' forecasts (Figs. 2, 3) are good.

Drosdowsky, W., 1994: Analogue (non­linear) forecasts of the Southern Oscillation Index time series. Wea. Forecasting, 9, 78­84.

Sugihara, G. and R.M. May, 1990: Nonlinear forecasting as a way of distinguishing chaos from mea-surement error in time series. Nature, 344, 734­741.

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