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Precipitation Forecasts for the Tropical Pacific Islands
Using Canonical Correlation Analysis (CCA)
contributed by Yuxiang He
Climate Prediction Center, NOAA, Camp Springs, Maryland
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 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.
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 1998 made using data through May 1997 (7 months lead). The geographical
distribution of expected skill for this forecast, based on cross-validation, is shown in part (b) in
terms of the temporal correlation between forecasts and observations. There is a tendency for
dryness at off-equator locations, and for enhanced rainfall at the stations closest to the equator
near and east of the date line. This pattern is in keeping with the warm phase ENSO conditions
that have developed during the past few months, which the CCA impicitly expects to continue
through JFM 1998. Skill is very modest for this long-lead forecast; the skill meets the minimum
"usability" requirement of 0.30 at only three stations. It should be noted, however, that the little
skill that does exist comes largely from ENSO effects, and thus is dependent on the certainty of
the expected ENSO state 7 to 10 months later than the time of the forecast. If we are sure there
will be a warm ENSO event in early 1998, then our confidence in the qualitative pattern shown in
this forecast should be higher than that reflected in the overall skills in Fig. 1b.
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. Jul-Aug-Sep 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.
Dry conditions are forecast at many of the U.S. affiliated stations for boreal winter 1997-98
through spring 1998, due to the expected warm tropical Pacific episode already in progress.
This dryness is especially marked at Johnston, Guam, Koror and Yap. Skill tends to peak during
early spring at these locations. South of the equator at the non-U.S.-affiliated islands, dry
conditions in late 1997 and early 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 region of Henderson, Luganville, Udu Point, Rarotonga and Rapa, while enhanced rainfall is
predicted at Funafuti, Atuona and Rikitea.
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 have swung noticeably toward
warm ENSO-like rainfall impacts compared with the forecasts issued 3 months ago. Now that we
have progressed through much of the boreal spring 1997 forecast "barrier", the ENSO situation
for the rest of 1997 and boreal winter 1997-98 has become clearer. With each month between
June and August that the ENSO clues do not change from what they are presently, the more
certain will a persistence of the current ENSO state into at least the early portion of the coming
boreal winter become.
Looking at the forecasts produced by the numerous dynamical and statistical models shown in this
issue of the Bulletin, the consensus strongly tilts toward continuing or increasing positive SST
anomalies in the tropical Pacific over the coming months of middle and late 1997. Not all models
agree with this outlook, however.
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 Niño-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 Niño-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, 2020-2035.
Ropelewski, C.F. and M.S. Halpert, 1987: Global and regional scale precipitation patterns
associated with the El Niño/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 1998 made at 7 months lead (latest data May 1997). (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. 3a, b, c (three separate links). 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 (this page) and 18 non-U.S.-affiliated stations (next two pages). 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 (Jul-Aug-Sep 1997) through 13 (Jul-Aug-Sep 1998);
see the legend at top.
