Using Canonical Correlation Analysis (CCA)

Canonical correlation analysis (CCA) identifies linear relationships between multicomponent predictors and multicomponent predictands, e.g. pattern-to-pattern relationships in space and/or time. Like simpler forms of linear regression, CCA minimizes squared errors in hindcasting the predictands from the predictors. During the last decade, CCA has been used increasingly in the atmospheric sciences (e.g. Barnett and Preisendorfer 1987; Graham et al. 1987a, 1987b; Barnston and Ropelewski 1992; Barnston 1994, Barnston and He 1996). Here, CCA is used to predict 3-month precipitation anomalies in the Pacific Islands out to a year in advance, as described in He and Barnston (1996). Because rainfall in the tropical and subtropical Pacific is strongly related to ENSO (Ropelewski and Halpert 1987, 1996), it is reasonable to expect usable skill in seasonal Pacific rainfall forecasts, and thus worthwhile to establish a real- time prediction system for the benefit of commercial interests in the Pacific Islands. The experimental forecasts shown in this quarterly Bulletin are provided a monthly basis 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. CCA sensitivity experiments indicate that the SST field is the most valuable predictor field, with 700 mb heights and prior precipitation somewhat helpful. Further details about the skill, the underlying relationships, and the predictors 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°N-30°S, including 4 Hawaiian stations (see Fig. 1 of any of the 1997 issues of this Bulletin). 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 set of stations predicted is expected to increase to at least 50 sometime during 1998, and to include stations close to the equator near the date line and eastward (i.e., in Kiribati). The rainfall data and climatology for the larger set of stations has been described in a recently published atlas (He et al. 1998).

The expected skill of the forecasts was estimated using a 1-year-out cross-validation (see He and Barnston 1996). These skill estimates indicate 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, the skill only slightly lower except for the Jan-Feb-Mar average skill north of the equator which drops significantly to 0.26. When skill is averaged only for periods with significant ENSO signals, average skill considerably higher than the above. This would be expected in view of the increase in the signal-to-noise ratio in the rainfalls when ENSO-neutral periods are removed.

Figure 1 shows forecasts of the standardized precipitation anomaly (X100) for 33 Pacific Island stations using data through February 1997. The top panel shows the forecast for Apr-May-Jun 1998 (1 month lead), and the bottom panel for Jul-Aug-Sep 1998 (4 months lead). The expected skill for these forecasts, based on cross-validation, is shown by the size of the numerals (as opposed to their value, which is the forecast itself): Small numerals indicate low skill (correlation below 0.3), medium sized numerals usable but modest skill (correlation between 0.3 and 0.45), and large numerals moderate or better skill (0.45 and higher). Marked dryness at off-equator locations, and enhanced rainfall at the stations closest to the equator near and east of the date line, is being forecast. This pattern, which is accompanied by higher skill in Apr-May-Jun than Jul-Aug-Sep, is associated with the very strong El Niño conditions that developed during mid-1997, which the CCA expects to continue at least moderately through boreal spring and possibly even very early summer of 1998. Skill is mainly modest, but is moderately high at some of the stations having the strongest ENSO influences. As implied above, skill would be higher if the extremes of ENSO occurred more frequently. Given that much of the existent skill comes from ENSO, our confidence in the qualitative pattern shown in Fig.1 would be higher than that reflected in the skills based on all years when we are confident that an ENSO event will be occurring. This appears to be the case for this boreal spring 1998, since it is physically impossible for the currently still strongly positive (although declining) SST anomalies to dissipate in less than 2-3 months.

More detailed forecasts for 9 U.S.-affiliated and 18 non-U.S.-affiliated Pacific Island stations are shown in Fig. 2, in the form of long-lead rainfall forecasts from 1 to 13 seasons lead (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=Apr-May-Jun 1998). The same ordinate scale is used for both forecasts and skill (standardized anomaly and temporal correlation coefficient, respectively). Sometimes skill may increase as the lead is increased because a more forecastable target season has been reached. The forecasts and their skills differ not only due to their differing ENSO-responsiveness caused by general location differences the Pacific basin, but also due to differences in orientation with respect to the local orography (if any).

Dry conditions are forecast at many of the U.S.- affiliated stations for boreal spring 1998, due to the strong (but declining) El Niño that is still dominating the climate. Among the stations shown here, dryness for Apr-May-Jun is especially marked at Johnston, Guam, Koror, Yap, and Chuuk. Skill tends to peak during boreal winter or spring at these locations. South of the equator at the non-U.S.-affiliated islands, dry conditions in Apr-May-Jun 1998 are also generally expected for stations farthest away from the equator, except for those in the eastern Pacific. In particular, dryness is expected in the regions of Luganville, Udu Point, Noumea, Nadi, and Rapa. Most of these locations, and others that normally experience drought with El Niño, have already been drier than normal for several months and will likely have to keep mitigation strategies in place for another 1 or 2 months. Above-normal rainfall is predicted at Funafuti, Atuona, Takaroa and Rikitea where the rainfall excesses will be most noticeable with the onset of their warm season from May to August. Places along the immediate equator from near the date line eastward (e.g. Kiribati, which is not yet included in our forecasts) have been experiencing abnormally heavy rainfall.

As shown in Fig. 2, most of the strong rainfall effects of ENSO are expected to end (or even reverse, as at Johnston) by August or September 1998. This is not always the case, however, as for example, the wetness at Funafuti and the dryness at Noumea and Luganville could persist for an even longer period, perhaps as a result of residual post-ENSO SST anomalies outside the equatorial portion of the tropical Pacific.

The CCA modes (not shown; He and Barnston 1996) emphasize ENSO as the leading influence on tropical Pacific climate, especially 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 strongly reflect warm ENSO rainfall impacts for the first couple of lead times. The current strong warm ENSO condition, which is weakening but by no means finished yet, is virtually assured of having at least moderate strength (and influencing the climate in the normal impact areas) until at least early/mid- May 1998.

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, 7, 1513-1564. 

Barnston, A.G. and C.F. Ropelewski, 1992: Prediction of ENSO episodes using canonical correlation analysis. J. Climate, 5, 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, 2579-2605. 

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

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He, Y. A.G. Barnston and A.C. Hilton, 1998: NCEP/Climate Prediction Center Atlas No. 5: A precipitation climatology for stations in the tropical Pacific basin; effects of ENSO. U.S. Dept. of Commerce, NOAA, 280pp. 

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Fig. 1. CCA-derived precipitation standardized anomaly forecast (X100) for 33 Pacific Islands stations for (1) Apr-May-Jun and (2) Jul-Aug-Sep, 1998. Latest data for these forecasts is February 1998. The cross-validated skill expected for the forecasts is indicated by the size of the numerals (not their value, which shows the forecast itself). Small numeral size indicates correlation skill of less than 0.30, considered unusable; medium size is used for 0.30<skill<0.45 which is modest but usable; large size indicates skill>0.45, considered a relatively more reliable forecast.

Fig 2. 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 (first page) and 18 non-U.S.-affiliated stations (stations 1-9 and stations 10-18). 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 1998) through 13 (Apr-May-Jun 1999); see the legend at top.