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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 5oN-5oS, 120-170oW). 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 November 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 November 1996. The expected cross-validated skill is also shown. In Fig. 1 the SST anomaly observed during
Sep-Oct-Nov 1996 is plotted as the earliest "forecast" value. For Oct-Nov-Dec and Nov-Dec-Jan the observed SST for
Sep-Oct-Nov 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 somewhat below normal SST conditions are forecast to return to normal by late winter 1996-97,
becoming slightly warm into spring-summer 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
(DJF 1995-96 to SON 1996) are, in chronological order, 1965(-), 1972(-), 1975(-), 1976(-), 1977(-), 1984(+), 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 warming trend beginning with cool SST this early winter followed by
increasing positive anomalies 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 (i.e. 1989, which denotes the period of December 1988 to
November 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, one was fairly cold (1975), two were cool but becoming warm (1965 and 1976), one was neutral (1977), and one
was quite warm (1972). There is a tendency for positive weights to be assigned to cool episode years that were beginning
to warm, and vice versa. However, the occurrence 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 time
scales. While ENSO may have some very low frequency in its power spectrum, most of its variance is intradecadal.
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.
Yr IP Wt Yr IP Wt Yr IP Wt
56 -1 0 69 0 -1 82 1 2
57 -2 1 70 3 7 83 0 -7
58 -1 -3 71 -1 1 84 6 10
59 -1 0 72 -5 -15 85 5 6
60 -2 1 73 0 -7 86 4 9
61 -1 -3 74 -1 0 87 1 -1
62 0 3 75 -2 -10 88 4 12
63 0 2 76 -3 -10 89 6 15
64 -1 1 77 -8 -12 90 7 12
65 -4 -10 78 -4 -4 91 3 6
66 -5 -9 79 -8 -5 92 1 3
67 -2 -2 80 0 0 93 0 -3
68 0 6 81 2 8 94 2 3
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. Proceedings of the 19th Annual Climate Diagnostics Workshop, November 14-18, 1994,
College Park, Maryland, 416-419.
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 November 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 Sep-Oct-Nov 1996, and this observation also contributes by
decreasing amounts to the Oct-Nov-Dec and Nov-Dec-Jan plotted values (see text).