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Constructed Analogue Prediction of the East Central
Tropical Pacific SST through Fall 1998
contributed by Huug van den Dool
Climate Prediction Center, NOAA, Camp Springs, Maryland
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 February 1997), a linear combination is made of the global SST patterns
(using the first 5 EOFs) from all 40 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 40 X 40 (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 February 1997. The expected cross-validated skill is also shown. In Fig.
1 the SST anomaly observed during Dec-Jan-Feb 1996-97 is plotted as the earliest "forecast"
value. For Jan-Feb-Mar and Feb-Mar-Apr the observed SST for Dec-Jan-Feb 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 spring
1997, becoming slightly warm by summer and reaching a still warmer maximum around 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 (MAM 1996 to DJF 1996-97) are, in chronological order, 1973(-), 1985(+),
1989(+), 1990(+), and 1991(+). Some interdecadal variability in this analogue time series is
suggested by a tendency for temporal grouping of like-signs. More negative than positive weights
are found in the earlier three-quarters of the record, and vice versa from 1985 onward.
The result of the process is a forecast for a warming trend beginning with slightly cool SST early
this spring followed by increasing positive anomalies beginning in late spring 1997. The SST
becomes moderately warm from fall 1997 to spring 1998, subsiding by mid-1998. Looking at
some of the strongly weighted years, we note that the most strongly weighted year is negatively
weighted (i.e. 1973, which denotes the period of March 1972 to February 1973). A warm event
developed in the early half of 1972 and lasted through early 1973, turning to cold by late summer
1973. Of the four years having strong positive weights (1985, 89, 90 and 91), 1985, 1989 and
1990 had been preceded by cold in the east-central tropical Pacific in somewhat similar fashion to
the present ENSO situation. The 1991 scenario was quite different, however, in that the entire
1-year period contained mildly to moderately warm tropical Pacific SST. Thus, while there is a
tendency for positive weights to be assigned to cool episode years that were returning to normal
or beginning to warm, (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
the existence of phenomena that vary on decadal or even longer time scales.
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 (MAM, JJA and SON 1996, and DJF 1996-97).
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 -2 69 1 8 82 5 7
57 -2 -3 70 0 -1 83 0 -7
58 -2 -2 71 2 3 84 1 -2
59 -1 -4 72 -2 -2 85 6 10
60 -1 1 73 -4 -15 86 6 7
61 -2 0 74 0 -2 87 3 8
62 0 -2 75 -2 -2 88 1 -2
63 0 1 76 -2 -8 89 4 12
64 -1 -1 77 -4 -8 90 7 12
65 -1 1 78 -8 -6 91 6 12
66 -5 -8 79 -3 -2 92 2 4
67 -3 -2 80 -3 -2 93 1 4
68 -1 1 81 0 3 94 1 -1
95 2 4
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 February 1997. The dashed line indicates
the expected skill (correlation) based on historical performance for 1956-96. The x-axis represents
the target period. The verifying observation is shown instead of the constructed analogue
specification for Dec-Jan-Feb 1996-97, and this observation also contributes by decreasing
amounts to the Jan-Feb-Mar and Feb-Mar-Apr plotted values (see text).
