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Precipitation Forecasts for the Tropical Pacific Islands
Using Canonical Correlation Analysis (CCA)
contributed by Yuxiang He and Anthony Barnston
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
May-Jun-Jul 1997 made using data through February 1997 (2 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 weak tendency
for enhanced rainfall at off-equator locations, and a clearer tendency toward below normal rainfall
at the stations closest to the equator near and east of the date line. This pattern is in keeping with
the cool phase ENSO conditions that have prevailed during the last year, even if they end before
the target period (Barnston and He 1996). Skill is moderately high for this forecast at some
locations (e.g. Guam [0.50], Wake [0.47], Funafuti [0.70]), where the forecasts could have higher
amplitude if the predictor values were more indicative (i.e. if the ENSO situation were stronger).
Skill for the Hawaiian islands is unusably low.
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=Apr-May-Jun 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
spring and early summer, such as Guam, Johnston, and Majuro, and more briefly at Wake, Yap
and Chuuk. The positive anomalies at most of these islands decrease by the end of boreal summer
1997, and may become negative by the end of 1997. South of the equator at the
non-U.S.-affiliated islands, dry conditions are predicted during this austral fall and winter
at stations closest to the equator, such as Funafuti, Atuona and Takaroa. Normal to slightly wet
conditions are predicted at many of the other southern islands.
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 continue to show the aftereffects
of the cool tropical Pacific ENSO condition that has persisted over the last 1 to 2 years. A return
to warmer ENSO conditions for boreal winter 1997-98 is suggested by the reversals in forecast
rainfall anomalies from early 1997 to late 1997 at some of the more ENSO-sensitive stations such
as Johnston, Yap, Funafuti and Atuona. However, skills for these longer lead forecasts are low,
particularly as we have not yet progressed through the majority of the boreal spring 1997 forecast
"barrier". By late June, the ENSO situation for the rest of 1997 and boreal winter 1997-98 will be
noticeably clearer.
Looking at the forecasts produced by the numerous dynamical and statistical models shown in this
issue of the Bulletin, the consensus shows some tilt toward warming over the coming months of
middle and late 1997. However, considerable disagreement among models is found (including
cool forecasts from one or more highly respected models), indicating the uncertainty of the
outlook.
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.
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Oscillation cycle with statistical models. 1. Predictor field characteristics. J. Geophys. Res., 92,
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Oscillation cycle with statistical models. 2. Model results. J. Geophys. Res., 92, 14271-14289.
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Pacific islands Using CCA. J. Climate, 9, 2020-2035.
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associated with the El Nino/Southern Oscillation. Mon. Wea. Rev., 115, 1606-1626.
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Fig. 1. (a): CCA-derived precipitation standardized anomaly forecast (X100) for 33 Pacific
Islands stations for May-Jun-Jul 1997 made at 2 months lead (latest data February 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. 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 (Apr-May-Jun 1997) through 13 (Apr-May-Jun 1998); see the legend at top.
Fig. 3 (continued) ----for 2nd sheet of Fig. 3
Fig. 3 (continued) ----for 3rd sheet of Fig. 3
