Because natural analogues are highly unlikely to occur in high degree-of-freedom processes, 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 Mar-Apr-May 1998), a linear combination is made of the first 5 EOFs of global SST from all 41 years (ex-cluding 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 41 X 41 (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. Note that the predictand is not involved in the construction process. The constructed analogue is the same linear combination for all leads, i.e the weights are persisted, and can be applied to predictands other than Nino3.4.

Additional detail about the constructed analogue method (Van den Dool 1994) shows that constructed analogues usually outperform natural analogues (such as they are) 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. A constructed analogue yields a single linear operator derived from data by which the system can be propagated forward in time. This is methodologically related to POP and linear inverse modelling. The skill of the constructed analogue method in forecasting SST is discussed in Van den Dool and Barnston (1995).

The current constructed analogue forecasts for Niño 3.4 out to 1.5 years lead are shown in Fig. 1, using data through May 1998. The expected cross-validated skill is also shown (dashed). The SST anomaly observed during MAM 1998 is plotted as the earliest "forecast" value. For the early leads AMJ and MJJ the observed SST for JFM 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 is 0.6 through the summer (i.e. we left the spring barrier behind us), with an increase of skill later in the year.

The previously very strongly positive Niño 3.4 SST anomaly is disappearing rapidly by early June 1998, as forecast, and a near record cold SSTA is forecast for next winter.

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. On the other hand, the weights show the contribution of each year's pattern to the constructed analogue. The inner products and the weights, while similar, are not proportional, because co-linearity among years is accounted for. This is because, for example, two past years 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 (JJA97 to MAM98) are, in chronological order, 1957(-), 1958(+), 1965(-),1968(-), 1969(+), 1973(+), 1974(-), 1976(-), 1983(++), 1986(-), 1988(+), 1994(-), 1995(+) and 1996(+). An interdecadal variability in this analogue weights time series (e.g. negatives before 1980, positives in 1980s and 1990s) is not as strongly suggested as it has been over the last several years. ENSO clearly dominates the interdecadal variability at this time. 1968 (denoting the JJA67-MAM68 period), 1957 and 1974 are very heavily negatively weighted. Of the years having strong positive weights, 1958, 1969, 1983 and 1988, and 1995 and 1996, several involved previous mature warm ENSO events. Thus, while the ENSO situation definitely enters into the analogue selection (more strongly so at the moment than generally), non-ENSO (remember, global SST EOFs are used) processes also appear to determine the weighting process and the resulting forecast as well. Even within the contructed analogue one can surmise some conflicts as in an ensemble of possibilities. The consensus for a strong cold event appears to increase. The weight for 1983 is so high that to some approximation the contructed analogue system can be reduced to a natural analogue.

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 (currently the string JJA97, SON97,DJF97/98 and MAM98). Years are labeled by the middle month of the last of the four consecutive predictor seasons. 1997 is not yet used as a candidate analogue because long lead foreasts are not possible beyond the latest observations.

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 May 1998. 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 MAM 1998, and this observation also contributes by decreasing amounts to the AMJ and MJJ plotted values (see text).