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Constructed Analogue Prediction of the East Central
Tropical Pacific SST through Early Summer 1999
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 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 Sep-Oct-Nov 1997), a linear combination is made of the first 5 EOFs of global SST from all
40 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 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 forecasts for Niño 3.4 out to 1.5 years lead are shown in Fig. 1,
using data through November 1997. The expected cross-val-idated skill is also shown. The SST
anomaly observed during Sep-Oct-Nov 1997 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, 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 very strongly positive Niño 3.4 SST anomaly is forecast to begin weakening, and to
decline rapidly to normal by late spring and below normal for fall 1998 and winter 1998-99.
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 (DJF 1996-97 to SON 1997) are, in chronological order, 1957(+),
1964(-), 1973(-), 1975(-), 1981(+), 1982(+) and 1987(+). An interdecadal variability in this
analogue 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 seasons. 1973 (denoting the Dec 1972 to Nov 1973
period) and 1975 are 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. The scenario two years later, while similar in the
direction and timing of changes, completely lacked a warm event in 1974. 1964 behaved similarly
to 1973, but less strongly. Of the four years having strongest positive weights, 1957, 1982 and
1987 clearly involved warm ENSO development (with different timings and strengths), but 1981
had only a very weak ENSO signal. Thus, while the ENSO situation definitely enters into the
analogue selection, non-ENSO processes also appear to determine the weighting process and the
resulting forecast.
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 (DJF 1996-97, MAM, JJA and SON 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 | -3 | -6 | 67 | -3 | -5 | 78 | -2 | -7 | 89 | 0 | 7 |
57 | 2 | 12 | 68 | 0 | 4 | 79 | 8 | 4 | 90 | 4 | 4 |
58 | 1 | 6 | 69 | 3 | 4 | 80 | 4 | 7 | 91 | 3 | 0 |
59 | 0 | -7 | 70 | -3 | -2 | 81 | 2 | 12 | 92 | 2 | 0 |
60 | -2 | -1 | 71 | -5 | -9 | 82 | 4 | 12 | 93 | 4 | 1 |
61 | -2 | -4 | 72 | 1 | 5 | 83 | 2 | 1 | 94 | 3 | 0 |
62 | -1 | 7 | 73 | -4 | -18 | 84 | 1 | -2 | 95 | 2 | 6 |
63 | 2 | 9 | 74 | -3 | -5 | 85 | 0 | 1 | |||
64 | -6 | -14 | 75 | -5 | -19 | 86 | 4 | 5 | |||
65 | 1 | 2 | 76 | -1 | 1 | 87 | 3 | 16 | |||
66 | 0 | -8 | 77 | 2 | -2 | 88 | 0 | -4 |
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 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
Sep-Oct-Nov 1997, and this observation also contributes by decreasing amounts to the
Oct-Nov-Dec and Nov-Dec-Jan plotted values (see text).