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Probabilistic Predictions of ENSO Indices Using Statistical Models

Predictions of monthly NIÑO1&2, NIÑO3, NIÑO3.4, and NIÑO4 sea-surface temperature anomalies with lead-times of up to 11 months are produced using predictive discriminant analysis, canonical variate analysis, four forms of generalized linear models, and multiple linear regression with posterior probabilities derived by integration of the prediction intervals. Full details of the models are provided by Mason and Mimmack (2002). The predictions presented here represent an average of the probabilities from these statistical models. The first four unrotated principal components of gridded monthly sea-surface temperatures over the tropical Pacific (25ºN—25ºS, 110ºE—70ºW), and the respective NIÑO index are used as the only predictors. The NIÑO index is regressed out of the sea-surface temperatures before the principal components are calculated to ensure that the index remains orthogonal to the components. Skilful predictions of tropical Pacific sea-surface temperature anomalies can be developed relatively simply using only prior temperatures in the region as predictors (Barnston and Ropelewski 1992; Penland and Sardeshmukh 1995; Latif et al. 1998), and so the relatively simple sets of predictors used here can provide predictions with high levels of skill.

Careful assessments of the operational levels of predictive skill have been made by using a retroactive forecast procedure: the models were trained over an initial 30-year training period, and were then used to produce 22 years of retroactive predictions. Three categories of anomalies were defined ranging from "cool", through "neutral", to "warm". Probabilities for each of the categories over the 22-year retroactive period January 1981 to December 2002 were calculated. The training period was initially set as 30 years (1951—80), and retroactive predictions for the following three years were then made using the optimal model. After this 3-year period the models were retrained over the period 1951—83, possibly selecting different variables and a different number of retained variables, and predictions for 1984—86 were made. This procedure was repeated until the set of 22 years of retroactive predictions had been made. At each stage, the definitions of the three categories were reset to ensure that the categories remained equi-probable a priori. While the categories are defined as equi-probable over the training periods, this is not necessarily the cases for the verifications over the independent period. For 1981—83, the verifications were categorized on the basis of the 1951—80 training period; the verifications for 1984—86 were categorized on the basis of the 1951—83 training period, etc.. For the predictions presented here, the training period was from 1951 to the end of the latest year available, and anomalies are defined with reference to this same period.

The combined prediction is calculated by averaging the posterior probabilities from the various models. No attempt is made to weight the probabilities from the different models by a measure of model skill, since ranked model performance is sensitive to the precise skill measure used, and can be conditional upon the actual outcome. Good reliability is demonstrated for predictions for all categories (Fig. 1). Ranked probability skill scores (RPSS's) for the combined probabilities compared to a strategy of climatology were calculated for each month separately. The skill scores are shown in Fig. 2, where they are compared to the skill of forecasts of damped persistence. The seasonal dependence of skill is clearly apparent for both the model and the damped persistence forecasts.

Fig. 1. Reliability diagram for retroactive combined predictions at increasing lead-times of "cool" (line), "neutral" (green line), and "warm" (red line) conditions for the 22-year period Jan 1981—Dec 2002. Predictions at all lead-times and for all months are pooled. The histograms indicate the frequency of predictions with probabilities in the ranges 0.00—0.05, 0.05—0.15, 0.15—0.25, ..., 0.95—1.00. The y-axes range to 1500. The top histogram is for "warm" conditions, the middle for "neutral" conditions, and bottom for "cool" conditions.

Fig. 2. Ranked probability skill scores for retroactive combined NIÑO1&2, NIÑO3, NIÑO3.4, and NIÑO4 sea-surface temperature anomaly categories for the 22-year period Jan 1981—Dec 2002. The skill scores are calculated with reference to a strategy of forecasting climatology. The red bars represent the scores for the models, and the blue gray bars are for forecasts of persisted anomaly categories damped toward climatology.

REFERENCES

Barnston, A. G., and C. F. Ropelewski, 1992: Prediction of ENSO using canonical correlation analysis. J. Climate, 5, 1316—1345.

Latif, M., D. L. T. Anderson, T. P. Barnett, M. A. Cane, R. Kleeman, A. Leetmaa, J. O'Brien, A. Rosati, and E. Schneider, 1998: A review of the predictability and prediction of ENSO. J. Geophys. Res., 103, 14 375—14 393.

Mason, S. J., and G. M. Mimmack, 2002: Comparison of some statistical methods of probabilistic forecasting of ENSO. J. Climate, 15, 8—29.

Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea-surface temperature anomalies. J. Climate, 8, 1999—2024.