Because excellent naturally occurring analogues are highly unlikely to occur, we may benefit from constructing an analogue having greater similarity than the best natural analogue. As described in Van den Dool (1994), the construction is a linear combination of observed anomaly patterns in the predictor fields such that the combination is as close as desired to the base. Here, we forecast the future SST anomaly in the ENSO-related east-central tropical Pacific ("Niño 3.4", or 5^oN-5^oS, 120-170^oW). We use as our predictor (the analogue selection criterion) the first 5 EOFs of the global SST field at four consecutive 3-month periods prior to forecast time. Predictor and predictand data extending from 1955 to the present are used for a priori skill evaluation.

For any given base time (i.e. previous ones extending back to 1955, or the current "operational forecast" ending with August 1996), a linear combination is made of the global SST patterns (using the first 5 EOFs) from all 39 years (excluding the base year), so as to match the SST pattern of the base time as closely as possible. This is done by classical least-squares multiple regression, with each year's SST state as a predictor to which a weight is assigned, determined by inverting the 39 X 39 (available years) covariance matrix. The weights assigned each year to reconstruct the base SST state are then applied to the subsequently occurring Niño 3.4 SST in the predictand period for these years, thereby constructing the forecast for the base year's predictand period.

Additional detail about the constructed analogue method is found in the September 1994 issue of this Bulletin and in Van den Dool (1994). In the latter paper it is shown that constructed analogues outperform natural analogues in specification mode (i.e. "forecasting" one meteorological variable from another, contemporaneously). This advantage may be expected to occur in actual forecasting also, as long as the (linear) construction does not compromise the physics of the system too much. Brief discussion of the skill of the constructed analogue method in forecasting SST is given in Van den Dool and Barnston (1995).

The forecasts for Niño 3.4 for 0 to about 1.5 years lead using constructed analogues are shown in Fig. 1, using data through August 1996. The expected cross-validated skill is also shown. In Fig. 1 the SST anomaly observed during Jun-Jul-Aug 1996 is plotted as the earliest "forecast" value. For Jul-Aug-Sep and Aug-Sep-Oct the observed SST for Jun-Jul-Aug enters into the plotted forecast with a 2/3 and 1/3 weight, respectively, providing continuity with the known initial condition.

A closer look at the skill of the constructed analogue method is provided by Fig. 2 in the June 1996 issue of this Bulletin (p. 73). The skill is competitive with those of other empirical as well as dynamical methods (Barnston et al. 1994). Forecasts for late fall through winter tend to be most skillful at short as well as long lead times, while summer forecasts have relatively lower skill. While skill (dashed line in Fig. 1) generally decreases with lead time, the dependence on the target season can sometimes be a stronger factor.

The presently still slightly below normal SST conditions are forecast to return to normal by late fall/early winter 1996-97, becoming slightly warm by spring 1997 and still warmer for winter 1997-98.

Table 1 provides information about the role of each of the past years in the construction process for the current forecasts. The inner product shows the degree of similarity (or, if negative, dissimilarity) of this year's predictor periods to those of the other years. The weight shows the contribution of each year's pattern to the constructed analogue. The inner products and the weights, while similar, are not proportional. This is because, for example, two analogues having the same kind of similarity are unnecessary; only one of them may have been assigned the appropriately high weight, leaving the other with little to contribute.

The important positive (+) and negative (-) contributors to the description of the global SST over the last 4 seasons (SON 1995 to JJA 1996) are, in chronological order, 1966(-), 1973(-), 1976(-), 1983(-), 1984(+), 1986(+), 1988(+), 1989(+), and 1990(+). An interdecadal variability in this analogue time series is suggested by the temporal grouping of like-signs. The weights have been mainly positive from 1984 to the present, suggesting that the present SST configuration is typical for the last 11 years and atypical for certain groups of years before 1984 such as the mid-1960s and most of the 1970s.

The result of the process is a forecast for a continued trend toward warming but still near normal SST followed by weak warmth from spring 1997 onward. The SST reaches moderately warm levels late in 1997 and into the following winter. Looking at some of the strongly weighted years, we note that the most strongly positively weighted year had been strongly cold and was returning to normal (e.g. 1989, which denotes the period of September 1988 to August 1989). Another year with positive weight was somewhat cold (1984), or cool but about to become very warm (1986). However, 1988 had been warm and was beginning to cool rapidly. Among the four strongly negatively weighted years, three had been warm and were in the process of cooling (1966, 1973 and 1983), but 1976 had been warm and was cooling. Thus, there is a tendency for negative weights to be assigned to warm episode years that were beginning to cool, and vice versa. This is quite reasonable in view of the cool episode that has now all but concluded. However, the appearance of strong positive or negative weights for years that do not follow this simple pattern indicates that phenomena other than ENSO are determining the weighting process and the resulting forecast. The weights shown in Table 1 suggest the existence of phenomena that vary on decadal or even longer-term time scales. While ENSO may "piggy-back" on these lower frequency oscillations to some extent, its variance is largely separate from theirs.



Table 1. Inner products (IP; scaled such that sum of absolute values is 100) and weights (Wt; from multiple regression) of each of the years to construct an analogue to the sequence of 4 consecutive 3-month periods defined as the base (SON '95, DJF '95-96, MAM '96, and JJA '96). Years are labeled by the middle month of the last of the four predictor seasons.

Fig. 1. Time series of constructed analogue forecasts (solid line) for Niño 3.4 SST based on the sequence of four consecutive 3-month periods ending in August 1996. The dashed line indicates the expected skill (correlation) based on historical performance for 1956-95. The x-axis represents the target period. The verifying observation is shown instead of the constructed analogue specification for Jun-Jul-Aug 1996, and this observation also contributes by decreasing amounts to the Jul-Aug-Sep and Aug-Sep-Oct plotted values (see text).