Of the total 480 possible regression equations, 411 met the first two criterion of 95 percent confidence and 2.5 percent increase in hindcast ability, providing non-negligible forecast ability (i. e. significantly greater than a linear correlation coefficient of zero). These were based on one to four predictors with most equations containing two to three predictors. In the remainder of the paper, we shall focus only on the Niño 3.4 SSTs for detailed examples of the results. An illustrative example of the form of the prediction equations for Niño 3.4 for a 1 January forecast initiation time in a non-normalized format is as follows:
Zero season lead (JFM) = 0.065 + 0.693 (1 m Niño 3.4)
One season lead (AMJ) = 0.121 + 0.492 (1 m trend Niño 3.4) + 0.864 (3 m trend Niño 4)
Two season lead (JAS) = 0.193 - 0.499 (3 m Niño 3.4) + 1.511 (3 m trend Niño 4)
Three season lead (OND) = 0.037 - 0.899 (3 m Niño 3.4) + 2.432 (3 m trend Niño 4)
Four season lead (JFM) = 0.257 - 0.743 (3 m Niño 3.4) + 1.964 (3 m trend Niño 4)
Five season lead (AMJ) = 0.208 - 0.409 (3 m Niño 3) + 0.873 (3 m trend Niño 3.4)
Six season lead (JAS) = 0.099 - 0.503 (3 m Niño 3.4) - 0.381 (3 m SOI)
Seven season lead (OND) = 0.137
The equations were tested in the hindcast made on 1950-1994 data; yielding linear correlation coefficients of r = 0.93, 0.67, 0.56, 0.63, 0.64, 0.47, 0.36, 0.00 and RMSE of 0.28, 0.38, 0.53, 0.73, 0.58, 0.45, 0.59 ° C, respectively. (The seven season lead forecast, for this case, could not provide non-negligible hindcasts so the 1950-1994 average anomaly value for October-December is forecast. This value, while close to zero, is non-zero because of the differences in climatological values for the 1950-1994 period versus the 1950-1979 era that the anomalies were computed from.) Following Davis (1979) and Shapiro (1984), these values would be expected to degrade (in independent forecast tests) to r = 0.93, 0.64, 0.51, 0.59, 0.60, 0.42, 0.30, 0.00 and RMSE of 0.29, 0.39, 0.55, 0.76, 0.61, 0.46, 0.61, 0.59 ° C, respectively.
Hindcast test results for Niño 3.4 SSTs are presented versus observations in the time series in Fig. 2. For simplicity and clarity, only values for spring (March-May), summer (June-August), fall (September-November) and winter (December-February) are plotted. Close correspondence between the hindcasts and observed values occurred in the zero and one season lead results, but degrading with longer leads while remaining non-negligible at seven seasons lead. Forecasts made after 1 December 1992 - designated by the vertical dashed lines in Fig. 2 - indicate independent tests of the ENSO-CLIPER forecast scheme. Somewhat greater than expected performance degradation is noted in this small data set of out-of-sample forecasts. Values for independent forecasts are provided in tabular form in Appendix A and a comparison to other ENSO prediction schemes is shown in the next section. For the remainder of the paper, only the adjusted linear correlations and RMSE will be presented.
Figure 3 presents adjusted hindcast values (the expected variance explained when used to make independent forecasts) for all five predictands at lead times ranging from zero to seven seasons based upon initial forecast for 1 January, 1 April, 1 July and 1 October. These results are presented as adjusted anomaly correlation coefficients. In general, forecast ability declines as the lead time increases though not always. Notably, the 1 January initial time forecasts for October-December Niño 3.4 show higher correlation (r = 0.61) than do the forecasts for the earlier July-September period (r = 0.52). Additionally, it is evident that the ability of the same lead time forecasts for the same predictand are extremely dependent on initial forecast time (of year). Again using the example of Niño 3.4, two season lead forecasts have regression coefficients that vary from a low of r = 0.52 for those verifying in July-September (see Fig. 3a) to a high of r = 0.80 for those verifying in January-March ( Fig. 3c ). This variability confirms the approach which takes advantage of the strong annual cycle of predictability at the expense of reducing the number of data points available for the regression. Where no predictors were available that fit the two primary criteria, no forecast equations were produced and the correlation for these is shown as "0".
Comparisons of the five predictands in Fig. 3 reveal that the Niño 3.4 and Niño 4 regions have, in general, the most proficient hindcasts at all lead times. The lowest hindcast correlations are generally observed at leads of zero to two seasons for the SOI and at leads three to seven seasons for the Niño 1+2 SSTs. Figure 4 shows comparison with the forecast ability available from persistence and the ENSO-CLIPER Niño 3.4 forecast. While persistence comprises essentially all of the forecast ability at lead times of zero and one season, particularly for the SST indices, predictability for the ENSO-CLIPER model provided by the other predictors is crucial during one to four season leads. At leads of five to seven seasons, persistence again becomes a useful predictor but in a negative sense for the Niño 3.4 SSTs. Predictive ability is also much reduced. Whereas persistence quickly drops to negligible levels, the ENSO-CLIPER is able to retain significant forecast ability in some cases out to seven season lead. Of basic interest are the differences between the performance of ENSO-CLIPER versus persistence only in relation to the initial forecast date. While persistence has substantial forecast ability (greater than r = 0.60) for zero, one and two season leads for the 1 July initial point, persistence only achieves this level at the zero season lead for the 1 April initial point, reconfirming earlier results of the variability of persistence depending on the annual cycle. Corresponding RMSE values are shown in Fig. 5. Typically, at times beyond zero season lead, ENSO-CLIPER has RMSE values which are significantly lower than those provided by persistence only. The largest values of RMSE for both forecasts generally occur during October-December with minima during April-June. This annual cycle is due to increased variability of observed SST in the Niño 3.4 region during October-December and decreased variability during April-June.
Table 2 presents a more comprehensive view of the forecast ability (correlation coefficient) for the zero to seven season leads for all five predictands stratified by verification time, maxima/minima and annual average values. Note that for Niño 3.4 SSTs, dependent on the initial date, ENSO-CLIPER has peak maximum forecast ability of 92, 85, 64, 41, 36, 24, 24 and 28 percent of the variance explained (the square of the values shown in Table 2) from leads of zero to seven seasons in advance. Comparable one month persistence forecasts should give 92, 77, 50, 17, 6, 14, 21 and 17 percent, respectively. Averaged over the entire year (i.e., 12 forecast initiation times) ENSO-CLIPER should give 81, 55, 34, 24, 18, 18, 12 and 7 percent for leads of zero to seven seasons in advance whereas persistence alone should provide only 74, 34, 7, 0, 3, 6, 8, and 6 percent. Dramatic forecastability gains are shown over persistence, especially in the two to four season leads. The ENSO-CLIPER model improvement upon persistence entails explaining 7, 21, 27, 24, 15, 12, 10 and 6 percent respectively, more of the variance annually for lead 0 through 7. Thus, both for the most "predictable" time of year and for the year as a whole, significant improvements are realized over persistence alone are available with the use of ENSO-CLIPER.
Table 2: Adjusted
linear correlation coefficients of the ENSO-CLIPER (CLI) model
and persistence (PER) versus observed values for four Niño
SST regions and the SOI are presented. These are stratified by
verification season (Spring - March through May, Summer - June
through August, Fall - September through November, Winter -
December through February), the maxima and minima skill periods,
and the annual average of skill versus zero through seven season