In this Bulletin we find a fairly large number of forecasts for the east-central tropical Pacific SST for the coming year. Some predict continuation of the current cold episode throughout 1996. Others forecast a rapid dissipation, followed by varying degrees of warming as boreal winter 1996-97 approaches. The direction of the forecast is not related to the type of model--either statistical or dynamical models may go either way. Which models are we to believe this time, or any time?
One approach to the problem is to combine, or consolidate, the forecasts of several models into a single forecast. This could be done on the basis of the past behavior of each contributing model, as well as the overlap of information among the models. There are several methods by which this can be done. A common method, and the one used here, is linear multiple regression. In effect, a statistical scheme is used to combine outputs of entire models whose natures themselves may be statistical, dynamical, or a mixture of the two. In this case we use four input models. Two are dynamical: the Lamont-Doherty Earth Observatory's simple coupled model (the improved LDEO2; Chen et al. 1995; Cane and Zebiak 1986), and the NCEP coupled model (Ji et al. 1994). The other two models are statistical: the NCEP constructed analogue (CA) model (Van den Dool 1994; Van den Dool and Barnston 1995), and the NCEP canonical correlation analysis (CCA) model (Barnston 1994). The individual forecasts of each model are shown elsewhere in this Bulletin issue.
To derive the multiple regression equations for each target season for each lead time, histories of the forecasts of each model were obtained. The CCA and CA models have histories covering 1956-1995. The Lamont coupled model has a 1972-95 history, and the NCEP coupled model 1982-95. To circumvent the problem of the differing units and climatologies used, all forecasts were converted to actual C forecasts. The observations were expressed likewise. The regressions are based on forecasts for the Niño 3.4 region (5N-5S, 120-170W), except for the Lamont model, from which we receive forecasts for the Niño 3 region. The Niño 3 forecast histories from the Lamont model were used as a predictor for Niño 3.4 in the equation development. The regression coefficients compensate for the slight differences between Niño 3 and Niño 3.4 to obtain the least squares fit for Niño 3.4. We expect to begin receiving gridded forecast fields from Lamont shortly, and will then be able to use Lamont's Niño 3.4 forecasts directly.
The desired lead times of the consolidated forecasts range from 0.5 months to 12.5 months by 1 month increments, where lead time is defined as the time skipped between the time of the forecast and the beginning of the forecasted (target) period. For example, the forecasts shown here, which are issued in the middle of March 1996, have target periods including Apr-May-Jun 1996, May-Jun-Jul 1996, ..., Apr-May-Jun 1997. Three of the four individual models have forecast histories whose leads range to 12.5 months or greater, while one (the NCEP coupled model) has a maximum lead of only 7.5 months. Consolidated forecasts for lead times higher than 7.5 months, therefore, are based only on the other three models; a slight discontinuity in the forecast time series may thus be expected between the Nov-Dec-Jan and the Dec-Jan-Feb 1996-97 forecasts.
Because the NCEP coupled model forecast only has a 1982-95 history, the training period for the regression is limited to that period and thus results in greater uncertainty in the coefficients than would be the case if a longer history could be used. When that model is not included in the consolidation process for the longer lead times, the 1972-95 period is used to derive the regression equations, making for a more favorable training sample.
The consolidated forecast for Niño 3.4 resulting from the multiple regression run in mid-March 1996, expressed as a standardized anomaly, is shown in Fig. 1. The box and whisker intervals for the forecasts at each time indicate the one and two error standard deviation, based on estimated skill following shrinkage of the dependent sample skill results in accordance with the sample size and number of predictors. The SST is expected to remain cold through fall 1996 before returning to normal in early spring 1997 and then switching to a weak positive anomaly.
Examination of the regression coefficients reveals that the statistical models are relatively heavily weighted in boreal winter. The Lamont model is the most heavily weighted input for target periods in and around boreal summer. The CCA and CA models, whose forecasts are fairly highly positively correlated (>0.8 during the cold season when their skills are highest), often create some instability in the coefficients such that one of them (usually CA) is positively weighted while the other (CCA) is negatively weighted by roughly the same magnitude. This instability could be alleviated by (1) eliminating one of the two statistical models, (2) forming a simple combination (e.g. an average) of the CCA and CA forecasts prior to the regression, or (3) keeping both models but "ridging" the diagonal of the variance-covariance matrix (increasing the diagonal elements) to make for a more stable matrix inversion. Presently we do not entirely understand the problem or its solution, and are studying these. We do know that the amount of colinearity between CA and CCA is not enormous.
In the present forecast, intuition is lacking in the sense that as CCA predicts rising SST between spring and fall of 1996, its negative regression weight contributes to the decrease in the consolidated forecast in that time interval (Fig. 1). In the coming months the consolidation procedure will be further developed and, it is hoped, made more trustworthy as well as intuitively reasonable.
Acknowledgments: We are grateful to Stephen Zebiak and Mark Cane of Lamont Doherty Earth Observatory, and Ming Ji and Ants Leetmaa from the National Centers for Environmental Prediction, for providing the forecast histories from their respective dynamical models, as well as their current real-time forecasts.
Barnston, A.G., 1994: Linear statistical short-term climate predictive skill in the Northern Hemisphere. J. Climate, 5, 1514-1564.
Cane, M., S.E. Zebiak and S.C. Dolan, 1986: Experimental forecasts of El Nino. Nature, 321, 827-832.
Chen, D., S.E. Zebiak, A.J. Busalacchi and M.A. Cane, 1995:An improved procedure for El Nino forecasting: Implications for predictability. Science, 269, 1699-1702.
Ji, M., A. Kumar and A. Leetmaa, 1994: An experimental coupled forecast system at the National Meteorological Center: Some early results. Tellus, 46A, 398-418.
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.
Figure 1. Consolidated forecast
for the standardized anomaly of the SST in the Ni¤o 3.4 region
(5øN-5øS, 120-170øW) for the next 13 running 3-month period. Month
labels on the abscissa denote the middle month of the 3-month
predictand periods. Box and whiskers for each point forecast indicate
the one and two error standard deviation intervals, based on estimated
cross-validated skill.