Constructed Analogue Prediction of the East Central Tropical Pacific SST through remainder of 1998 and 1999
contributed by Huug van den Dool
Climate Prediction Center, NOAA, Camp Springs, Maryland
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 past 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 SON 1998), a linear combination is made of the first 5 EOFs of global SST from all 41 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 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 past, 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 Nov 1998. The expected cross-validated skill is also shown (dashed;right-hand scale). The SST anomaly observed during SON 1998 is plotted as the earliest "forecast" value. For the early leads OND and NDJ the observed SST for SON enters into the plotted forecast with a 2/3 and 1/3 weight, respectively, providing continuity with the known initial condition (SON).
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). An evaluation over 1996-98 (Barnston et al 1999) shows CA, CCA and CLIPER to be the clear frontrunners among the empirical methods and continuing to be competitive with dynamical methods NCEP and COLA models. 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 dependence on the target season is sometimes a stronger factor. Currently, correlation skill is 0.9 for the early leads and 0.6 through the end of next spring.
The currently moderately cold La Niña is forecast to peak in NDJ and DJF98/9 at -1.8oC (or 2.2 stand.dev). The cold event should finish by AMJ99, but no transition to positve Nino3.4 anomalies is forecast for any time in 1999. Values between -0.5 and 0oC persist from JJA99 till winter 99/00.
Although the forecast is for negative Nino3.4 it is too simplistic to say that the forecast is for the opposite of last winter when record positive values for Nino3.4 (+3 stand deviations) occurred. Inspection of the forecast in terms of SST-EOFs shows that last winter was extreme in EOF#1, while winter 98/99 appears to peak in EOF#2, 3 and even 4. Put another way: Nino3.4 is a compromise index that does justice to warm events with SST anomalies from the dataline to the S. American coast (last year) as well as cold events that have SST anomalies both east and west of the dateline, as is currently the case. Nino3 (farther east) is a poor index for the current quite strong cold conditions.
Table 1 provides information about the role of each of the past years in the construction process for the current forecasts. The inner product (IP) shows the degree of similarity (or, if negative, dissimilarity) of this year's predictor periods to those of the other years on the global domain. On the other hand, the weights (Wt) shows 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 weights have changed little from 3 months ago, see Spetember issue, as they should if CA is to be skillful in making forecasts. Indeed, CA has been above average in accuracy on both the onset and maturing of the current cold event.
The most important positive (+) and negative (-) contributors to the description of the global SST over the last 4 seasons (DJF97/8 to JJA98; denoted as 1998) are, in chronological order, 1965(-), 1968(-), 1983(+), 1987(+), 1988(+), 1989(+) and 1995(+). An interdecadal variability in this analogue weights time series (e.g. negatives before 1980, positives in 1980s and 1990s) is suggested, but not as strong as it had been until 1997. ENSO clearly dominates the interdecadal variability at this time. 1968 (denoting the DJF67/8-SON68 period), 1965 and 1994 are very heavily negatively weighted. Of the years having strong positive weights 1983 and 1988, and 1995 and 1996, several involve the aftermath of previous mature warm ENSO. 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 determine the weighting process and the resulting forecast as well. The weights for 1983 and 1988 are so high that to some approximation the CA system can be reduced to a natural analogue.
References
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-here do we stand? Bull. Amer. Meteor. Soc., 75, 2097-2114.
Barnston, A. G., M. H. Glantz and Yuxiang He, 1999: Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997/98 El Nino episode and the 1998 La Nina onset. Bull. Amer. Meteor. Soc., Feb 1999 issue
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 DJF97/98 , MAM98, JJA98 and SON98). 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 forecasts are not possible beyond the latest observations.
| Year | IP | Wt | Year | IP | Wt | Year | IP | Wt | Year | IP | Wt |
| 56 | -2 | -5 | 67 | -6 | -15 | 78 | 1 | -1 | 89 | 2 | 15 |
| 57 | -3 | -7 | 68 | -6 | -25 | 79 | 4 | 4 | 90 | 4 | 7 |
| 58 | 1 | 15 | 69 | 4 | 12 | 80 | 3 | 1 | 91 | 1 | -3 |
| 59 | -1 | -4 | 70 | 3 | 4 | 81 | 2 | 6 | 92 | 1 | 5 |
| 60 | -1 | 5 | 71 | -2 | 0 | 82 | -1 | -13 | 93 | 1 | -15 |
| 61 | 0 | -3 | 72 | -3 | -9 | 83 | 3 | 35 | 94 | 0 | -19 |
| 62 | 1 | 19 | 73 | 4 | 14 | 84 | 2 | -9 | 95 | 5 | 27 |
| 63 | -1 | 1 | 74 | -4 | -15 | 85 | -1 | -5 | 96 | 5 | 15 |
| 64 | -1 | 3 | 75 | -2 | -8 | 86 | -1 | -16 | |||
| 65 | -6 | -22 | 76 | -4 | -6 | 87 | 3 | 21 | |||
| 66 | -1 | -10 | 77 | -4 | -10 | 88 | 5 | 23 |
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 NOV 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 observation is shown instead of the constructed analogue specification for the initial state SON 1998, and this observation also contributes by decreasing amounts to the OND and NDJ plotted values (see text).
