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.

While CCA has been used in the social sciences for many decades, only in the last 10 years has it begun being used in the atmospheric sciences. 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. More recently, Barnston and He (1996) explored CCA for forecasting seasonal surface climate in Hawaii and Alaska. The skills resulting from the latter two studies, while generally modest, were good enough for the U.S. National Weather Service to use the forecasts operationally.

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. In fact, a monthly product is now available on the Internet at address: http://nic.fb4.noaa.gov:80/products/predic-tions/experimental/pacific.

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 25^oN-30^oS, 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.

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 November 1996 (1 month 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. There is a tendency for enhanced rainfall at most of the off-equator locations, and near-normal rainfall at the stations closest to the equator in the eastern sector. This pattern is in keeping with the mild cold phase ENSO conditions that have occurred over the last year. Skill is moderately high for this short-lead forecast in some of the northern stations (e.g. Yap [0.74], Andersen [0.57], Lihue [0.55], Koror [0.55]), where the forecasts could have higher amplitude if the predictor values were more indicative (i.e. if the ENSO situation were stronger).

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. Jan-Feb-Mar 1997). 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. 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 winds.

Wetter than normal conditions are forecast at some of the U.S. affiliated stations this boreal winter/ early spring, such as Kwajalein, Johnston, Koror, Wake, and especially Phonpei, Chuuk and Yap. The positive anomalies at most of these islands decrease toward mid-1997. South of the equator at the non-U.S.-affiliated islands wet conditions are also predicted, but to a lesser extent. Dryness is forecast for Funafuti, Nadi, Wallis and Takaroa during the May-Jun-Jul-Aug period. At Rikitea in the southeastern tropical Pacific, rainy weather is forecast during most of the coming 1-year period.

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 rainfall forecasts imply a slightly cool tropical Pacific ENSO condition continuing through the boreal winter 1996-97 and early spring. Weakly implied is also a reversal to warmer ENSO conditions for boreal winter 1997-98. (Note that the rainfall anomaly forecasts for Jan-Feb-Mar 1998 for some of the northern stations with wet Jan-Feb-Mar 1997 forecasts [e.g. Majuro, Yap, Phonpei] are normal to slightly negative.) However, skills for forecasts whose lead time passes through the boreal spring have low confidence.

Looking at the forecasts produced by the numerous dynamical and statistical models shown in this issue of the Bulletin, a general consensus is for cool to near neutral ENSO conditions for boreal winter 1996-97, with some tendency toward warming later in 1997. However, considerable disagreement among models is found, indicating the uncertainty of the outlook.

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Fig. 1. (a): CCA-derived precipitation standardized anomaly forecast (X100) for 33 Pacific Islands stations for Jan-Feb-Mar 1997 made at 1 month lead (latest data November 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 (Jan-Feb-Mar 1997) through 13 (Jan-Feb-Mar 1998); see the legend at top.

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