Precipitation Forecasts for the Tropical Pacific Islands Using Canonical Correlation Analysis (CCA)

In canonical correlation analysis (CCA), relation-ships between multicomponent predictors and multicom-ponent predictands are linearly modeled. These typically take the form of pattern-to-pattern relationships 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 known from past work that rainfall in the tropical and subtropical Pacific is strongly related to ENSO (Ropelewski and Halpert 1987). 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 predictor fields used for the forecasts include quasi-global sea surface temperature (SST), Northern Hemisphere 700 mb geopotential height, and the precipitation itself over the 33 stations used as the predictand. 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. 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 Jul-Aug-Sep 1996 made using data through Feb 1996 (3 months lead). The geographical distribution of expected skill for this forecast, based on cross-validation, is shown in part (b) in terms of a correlation between forecasts and observations. The forecasts are fairly weak in amplitude. However, a tendency toward positive rainfall anomalies is noted north of 10N. While this response agrees with the findings of Ropelewski and Halpert (1987) for the cold phase of ENSO, that response was found to be limited to the cold half of the Northern Hemisphere year. However, Barnston and He (1996) showed that the expected effects from either phase of ENSO may continue for several additional seasons in Hawaii. This delay may be caused partly by lingering SST anomalies off the equator at higher tropical latitudes. Presently the east-west band of negative SST anomalies along the equator in the central and eastern Pacific has not expanded north of 10N, except near Central America.

More detailed forecasts for 9 U.S.-affiliated Pacific Island stations, located as shown in Fig. 2, are provided in Fig. 3. In the latter figure, 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=AMJ 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. 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 stations no substantial anomalies in either direction are predicted in the next few months. It should also be noted that the expected skill for the boreal warm half of the year is generally relatively low. However, enhanced rainfall is predicted with modest but usable skill at Johnston Island this summer. At longer lead, a tendency for dryness is noted for boreal winter 1996-97 at Wake, Yap and Johnston Islands. While the associated skills are not high enough to react with concern at this point, expected skill will slowly rise as the lead time decreases.

The CCA modes (not shown) emphasize ENSO as the leading influence on tropical Pacific climate, but 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). Mild to moderate cold episode conditions have now prevailed for about 9 months. Their effect on the forecasts has begun overshadowing that of the long warmish period that ended in spring 1995, although the forecast magnitudes are weak. Another important mode is a long-term trend related to a warming of the global tropical SST. This mode can cause the forecasts to repeat from one year to the next at given times of the year, and may govern the forecasts by a higher proportion in the northern summer when ENSO's influence is diminished at many of the off-equator stations.

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, submitted..

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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.

Figures

Figure 1. (a): CCA-derived precipitation standardized anomaly forecast (X100) for 33 Pacific Islands stations for Jun-Jul-Aug 1996 made at 3 months lead (latest data February 1996). (b): The cross-validated skill expected for the forecast shown in (a), expressed as a correlation X100.

Figure 2. Locations of the 9 U.S.-affiliated Pacific Island stations whose long-lead precipitation forecasts are shown in detail in Figure 3.

Figure 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 (see Figure 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 (Apr-May-Jun 1996) through 13 (Apr-May-Jun 1997); see the legend at top.