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 Niño 3.4 region (5N-5S, 120-170W) of the tropical Pacific. 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 a given base time (previous ones extending back to 1956, or the current real forecast ending with Jun-Jul-Aug 1997), a linear combination is made of the first 5 EOFs of global SST from all 40 years (excluding the base year), so as to match the SST pattern of the base time. This is done using multiple regression, with each year's SST state as a predictor to which a weight is assigned, determined by inverting the 40 X 40 (available years) covariance matrix. These weights are then applied to the subsequently occurring Niño 3.4 SST in the predictand period for these years, forming the forecast for the base year's predictand period.

Additional detail about the constructed analogue method (Van den Dool 1994) shows that constructed analogues outperform natural analogues in specification mode (i.e. "forecasting" one meteorological variable from another, contemporaneously). This advantage may also be expected to occur in real forecasting, as long as the (linear) construction does not compromise the physics of the system too much. The skill of the constructed analogue method in forecasting SST is discussed in Van den Dool and Barnston (1995).

The current constructed analogue forecast for Niño 3.4 out to 1.5 years lead are shown in Fig. 1, using data through August 1997. The expected cross-valid-ated skill is also shown. The SST anomaly observed during Jun-Jul-Aug 1997 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, while summer forecasts have lower skill. While skill (dashed line in Fig. 1) generally decreases with lead time, the depend-ence on the target season is sometimes a stronger factor. Currently, correlation skill 0.8 through Jan-Feb-Mar.

The presently strongly positive Niño 3.4 SST anomaly is forecast to persist through boreal winter 1997-98, after which a rapid decline to normal is expected by summer 1998.

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 most important positive (+) and negative (-) contributors to the description of the global SST over the last 4 seasons (SON 1996 to JJA 1997) are, in chronological order, 1964(-), 1973(-), 1975(-), 1983(+), 1987(+), and 1989(+). Some interdecadal variability in this analogue time series is suggested by a tendency for temporal grouping of like-signs (e.g. negatives in the 1970s, positives in 1980s and 1990s). 1973 (denoting the Sep 1972 to Aug 1973 period) is very heavily negatively weighted. A strong warm event peaked during middle to late 1972 and reversed to a cold event by summer 1973, in opposite fashion to what has happened over the last 12 months presently. While 1964 showed similar behavior but less strongly, 1975 had been below normal during the entire relevant 12-month period. Of the three years having strongest positive weights 1983 had a very strong positive anomaly peaking during Feb and Mar, and 1987 was also very warm with a peak near midyear. 1989, on the other hand, was very cold with a minimum in the latter part of 1988. Thus, while there is a tendency for positive weights to be assigned to years when the SST anomaly was rising (and vice versa for negative weights), processes other than ENSO also determine the weighting process and the resulting forecast. The weights shown in Table 1 suggest phenomena that vary on decadal or even longer time scales.

Barnston, A.G., H.M. van den Dool, S.E. Zebiak, T.P. Barnett, M. Ji, D.R. Rodenhuis, M.A. Cane, A. Leetmaa, N.E. Graham, C.F. Ropelewski, V.E. Kousky, E.A. O'Lenic and R.E. Livezey, 1994: Long-lead seasonal forecasts--Where do we stand? Bull. Amer. Meteor. Soc., 75, 2097-2114.

van den Dool, H.M., 1994: Searching for analogues, how long must we wait? Tellus, 46A, 314-324.

van den Dool, H.M. and A.G. Barnston, 1995: Forecasts of global sea surface temperature out to a year using the constructed analogue method. Proceed-ings of the 19th Annual Climate Diagnostics Workshop, Nov. 14-18, 1994, College Park, Maryland, 416-419.

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 1996, DJF , MAM and JJA 1997). Years are labeled by the middle month of the last of the four predictor seasons.

Year	IP	Wt	Year	IP	Wt	Year	IP	Wt	Year	IP	Wt
56	-2	-6	67	-2	-2	78	-4	-9	89	2	12
57	2	10	68	-1	-4	79	3	2	90	7	10
58	1	10	69	2	5	80	3	5	91	4	8
59	0	-5	70	-1	1	81	1	10	92	4	7
60	0	3	71	-4	-4	82	7	13	93	4	5
61	0	3	72	-1	1	83	1	-1	94	3	0
62	-1	2	73	-4	-25	84	2	-1	95	3	1
63	1	7	74	-2	0	85	2	5
64	-5	-14	75	-5	-15	86	5	6
65	0	3	76	-2	-4	87	3	12
66	-2	-11	77	-2	-4	88	1	-3

 
 
 

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 1997. The dashed line indicates the expected skill (correlation) based on historical performance for 1956-96. The x-axis represents the target period. The left y-axis shows the SST forecast; the right y-axis shows the skill. The verifying observation is shown instead of the constructed analogue specification for Jun-Jul-Aug 1997, and this observation also contributes by decreasing amounts to the Jul-Aug-Sep and Aug-Sep-Oct plotted values (see text).