In canonical correlation analysis (CCA), relation-ships between multicomponent predictors and multi-component predictands are linearly modeled. These typically take the form of pattern-to-pattern relation-ships in space and/or time. CCA is designed to minimize squared error in hindcasting linear combinations of predictand elements from linear combinations of the predictor elements.

CCA has been used in the social sciences for many decades, but only in the last 10 years has it begun being used in the atmospheric sciences. For example, Barnett and Preisendorfer (1987) applied CCA to monthly and seasonal prediction of U.S. temperature. Graham et al. (1987a,b) and Barnston and Ropelewski (1992) applied it to predicting aspects of the ENSO phenomenon, and Barnston (1994) forecasted short-term climate anomalies in the Northern Hemisphere. Recently, Barnston and He (1996) explored CCA as a tool for seasonal temperature and precipitation forecasts for Hawaii and Alaska. The skills resulting from the latter two studies, while generally modest, were high enough for the U.S. National Weather Service to use the forecasts on a real-time, operational basis.

Here, CCA is used to predict 3-month total precipitation anomalies in the Pacific Islands out to a year in advance, as described in He and Barnston (1996). It is well known that rainfall in the tropical and subtropical Pacific is strongly related to ENSO (Ropelewski and Halpert 1987, 1996). Therefore it is worthwhile to set up a seasonal prediction system that produces real-time forecasts on a monthly basis for the benefit of agricultural and commercial interests in the Pacific Islands. The quarterly experimental forecasts shown in this Bulletin may be a precursor of future monthly "official" operational forecasts.

The predictor fields used for the forecasts include quasi-global sea surface temperature (SST), Northern Hemisphere 700 mb geopotential height, and the predictand precipitation itself (33 island stations) at an earlier time. Experiments with different subsets of predictors and predictor field weights showed that the most valuable predictor field is SST, with 700 mb heights and prior precipitation somewhat helpful. The SST predictors are therefore given double their natural weight. This helps prevent overfitting to "lucky" relationships with other predictors over the relatively short (1955-present) period of record. Further details about the skills, the underlying relationships, and the need to weight the SST double are provided in He and Barnston (1996). The set of predictors is configured as four consecutive 3-month periods prior to the time of the forecast, followed by a variable lead time, and then a single 3-month predictand period. The predictand includes 3-month total rainfall at 33 Pacific Island stations within 25oN-30oS, including 4 Hawaiian stations. The lead time is defined as the time between the end of the final (fourth) predictor period (i.e., the time of the forecast) and the beginning of the 3-month predictand period. This strict definition contrasts with that in which the shortest lead forecast would be called 3-month lead instead of zero lead.

The expected skill of the forecasts was estimated using cross-validation, in which each year in turn was held out of the model development sample and used as the forecast target. These skill estimates indicated that at 1 month lead time the highest correlation skill across the Pacific Islands occurs in Jan-Feb-Mar at 0.44 (0.29) averaged over all stations north (south) of the equator, and the lowest occurs from September through December at about 0.15 (0.30) for stations north (south) of the equator. At four months lead skills are only slightly lower except for the Jan-Feb-Mar average skill north of the equator which drops significantly to 0.26.

Figure 1a shows standardized precipitation anomaly forecasts for 33 Pacific Island stations for Jan-Feb-Mar 1997 made using data through August 1996 (4 months lead). The geographical distribution of expected skill for this forecast, based on cross-validation, is shown in part (b) in terms of a temporal correlation between forecasts and observations. These precipitation anomaly forecasts for boreal winter are weak in amplitude, even at stations where skill is moderately high (e.g. Yap [0.57] and neighboring stations, or Rapa [0.47]), where the forecasts could have high amplitude if the predictor values were indicative. This makes sense in view of the current ENSO situation. The mild to medium cold episode over the last year has largely neutralized, and the likely phase of ENSO for winter 1996-97 is statistically already somewhat determined as what we have now. If a strong reversal to warm conditions were in the offing, the transition to the warm side of the mean should have taken place by now. The implication of the forecast is that winter 1996-97 will be approximately a neutral year, and thus ENSO impacts on rainfall will be weak.

More detailed forecasts for 9 U.S.-affiliated and 18 non-U.S.-affiliated Pacific Island stations, located as shown in Fig. 2, are provided in Fig. 3. In Fig. 3, long-lead rainfall forecasts from 1 to 13 seasons lead are shown (solid bars), along with their expected skills (lines). The horizontal axis reflects the lead time, whose corresponding actual target period for this forecast is indicated in the legend along the top of the figure (e.g. 1=Oct-Nov-Dec 1996). The same ordinate scale is used for both forecasts and skills (standardized anomaly and correlation, respectively). The skill curve applies to the target season for the associated lead time of the present forecast. Sometimes a "return of skill" occurs as the lead is increased because a more forecastable target season has been reached. For example, at many stations the expected skill for the boreal winter and spring tends to be higher than that for summer and fall regardless of the lead time. The forecasts and their skills differ as a result of both location differences within the Pacific basin and differences in orientation with respect to the local orography (if any) and subsequent exposure to the prevailing low-level wind flow.

We note that at most of the U.S. affiliated stations no substantial anomalies in either direction are predicted in the next 6 months, but that the forecast for spring and/or summer 1997 shows a tendency for below normal precipitation at Wake and Yap Islands. South of the equator at the non-U.S.-affiliated islands the forecast calls for dryness in boreal spring and/or summer 1997 near the dateline (e.g. Hihifo, Funafuti, Udu Point, Rotuma, Luganville), while excess rainfall is indicated for near-equator stations (e.g. Funafuti, Atuona) near or east of the dateline for late boreal summer/autumn.

The CCA modes (not shown; He and Barnston 1996) emphasize ENSO as the leading influence on tropical Pacific climate. This is the case most strongly during the months of Nov-Dec-Jan-Feb-Mar-Apr-May (and even earlier than Nov along the immediate equator near and somewhat east of the dateline). The current forecast indicates that the predicted mainly near-normal rainfall for spring 1997 reflects the expectation of a roughly neutral tropical Pacific ENSO condition continuing through the boreal winter 1996-97 and early spring. It also predicts, with marginal skill, warming in late spring to early summer, continuing for the remainder of 1997. This is consistent with the tendency for wetness near the equator near the dateline and eastward by late spring, and some dryness off the equatorial band at this time. Looking at the forecasts produced by the numerous dynamical and statistical models shown in this issue of the Bulletin, a general consensus is for near neutral ENSO conditions for the coming winter, with some tendency toward warming later in 1997. Considerable disagreement among models is found, however, indicating the uncertainty of the outlook. With the boreal summer-to-winter SST "persistence period" upon us and a current absence of warm conditions, it appears unlikely that a significant warm event will begin before summer 1997.

Barnett, T.P. and R. Preisendorfer, 1987: Origins and levels of monthly and seasonal forecast skill for United States surface air temperatures determined by canonical correlation analysis. Mon. Wea. Rev., 115, 1825-1850.

Barnston, A.G., 1994: Linear statistical short-term climate predictive skill in the Northern Hemisphere. J. Climate, 5, 1514-1564.

Barnston, A.G. and C.F. Ropelewski, 1992: Prediction of ENSO episodes using canonical correlation analysis. J. Climate, 7, 1316-1345.

Barnston, A.G. and Y. He, 1996: Skill of CCA forecasts of 3-month mean surface climate in Hawaii and Alaska. J. Climate, 9, accepted.

Graham, N.E., J. Michaelsen and T. Barnett, 1987a: An investigation of the El Nino-Southern Oscillation cycle with statistical models. 1. Predictor field characteristics. J. Geophys. Res., 92, 14251-14270.

Graham, N.E., J. Machaelsen and T. Barnett, 1987b: An investigation of the El Nino-Southern Oscillation cycle with statistical models. 2. Model results. J. Geophys. Res., 92, 14271-14289.

He, Y. and A.G. Barnston, 1996: Long-lead forecasts of seasonal precipitation in the tropical Pacific islands Using CCA. J. Climate, 9, in press.

Ropelewski, C.F. and M.S. Halpert, 1987: Global and regional scale precipitation patterns associated with the El Nino/Southern Oscillation. Mon. Wea. Rev., 115, 1606-1626.

Ropelewski, C.F., and M.S. Halpert, 1996: Quantifying Southern Oscillation-precipitation relationships. J. Climate, 9, 1043-1059.

Fig. 1. (a): CCA-derived precipitation standardized anomaly forecast (X100) for 33 Pacific Islands stations for Jan-Feb-Mar 1997 made at 4 months lead (latest data August 1996). (b): The cross-validated skill expected for the forecast shown in (a), expressed as a correlation X100.

Fig. 2. Locations of 14 U.S.-affiliated Pacific Island stations (including 4 in Hawaii) and 19 non-U.S.-affiliated stations (south of the equator), most (27) of whose long-lead precipitation forecasts are shown in detail in Fig. 3.

Fig. 3. Time series of CCA-based long-lead precipitation anomaly forecasts, and their expected skills, out to one year into the future for 9 U.S.-affiliated Pacific Island stations and 18 non-U.S.-affiliated stations (see Fig. 2). The bars indicate the forecast values (as standardized anomalies) and the lines indicate the associated skills (as correlation coefficients). Both forecasts and skills use the same ordinate scale. The target season is indicated on the abscissa, ranging from 1 (Oct-Nov-Dec 1996) through 13 (Oct-Nov-Dec 1997); see the legend at top.