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Forecast of Pacific-Indian Ocean SSTs Using
Linear Inverse Modeling
contributed by Cécile Penland, Klaus Weickmann and Catherine Smith
NOAA-CIRES/Climate Diagnostics Center, Boulder, Colorado 80309-0449
Using the methods previously described in issues of the Experimental Long-Lead Forecast
Bulletin, and in Penland and Magorian (1993), the pattern of IndoPacific sea-surface temperature
anomalies (SSTAs), the SSTA in the Niño 3 region (6oN-6oS, 90 -150 oW), as well as the SSTA
in the Niño 4 region (6oN-6oS, 150 oW-160 oE), are predicted. A prediction at lead time is made
by applying a statistically-obtained Green function G() to an observed initial condition consisting
of SSTAs in the IndoPacific basin. Three-month running means of the temperature anomalies are
used, the seasonal cycle has been removed, and the data have been projected onto the 20 leading
empirical orthogonal functions (EOFs) explaining about 70% of the variance. The Niño 3 region
has an RMS temperature anomaly of about 0.7 oC; the inverse modeling prediction method has an
RMS error of about 0.5oC at a lead time of nine months and approaches the RMS value at lead
times of 18 months to two years. Data have been provided by NCEP, courtesy of R.W. Reynolds.
The COADS 1950-79 climatological annual cycle has been removed.
The predicted IndoPacific SSTA patterns based on the MAM 1997 initial condition for the
following JJA, SON, DJF and MAM are shown in Fig. 1 (contour interval = 0.2oC). A mature El
Niño is predicted, with anomalies to begin weakening around the first part of 1998. Figure 2a
shows the predictions (light solid lines) of the Niño 3 anomaly for initial conditions JFM, FAM
and MAM 1997. Light dotted lines indicate the 1 standard deviation expected error for the
prediction assuming a perfect model based on the JFM 1997 initial conditions. Figure 2b is the
same, but for the Niño 4 region. Verifications including the truncation error (heavy solid line) and
omitting the truncation error (heavy dotted line) are also shown.
It is clear from Fig. 2 that Pacific SST anomalies are increasing much more rapidly than was
predicted. It is also clear that much of the Niño 4 SSTA variability is not included in the 20
retained EOFs. The COADS data record is not observed with sufficient density to allow
expanding the number of retained EOFs; however, it is clear that the truncation is too severe. This
conclusion is corroborated by Fig. 3, which shows the Niño 3 and Niño 4 SSTA time series, along
with the projection of the optimal initial structure for growth (Penland and Sardeshmukh 1995)
onto the IndoPacific SSTA field seven months earlier. In only two previous cases since 1950
(asterisks in Fig. 3: 1991-92 and 1994-95) have the Niño 3 and Niño 4 SSTA indices exceeded
their one standard deviation (+1) levels (0.7C and 0.6C, respectively) without a preceding rise in
projection of the optimal structure onto the SSTA field. In both of those cases, the difference
between the Niño 4 SSTA index and the contribution to that index from the leading 20 EOFs was
more than 25%. This observation suggests that east Pacific dynamics played a more important
role in the development of a mature El Niño pattern previous to 1990 than it did after that. Also
from Fig. 3, one notes that the projection of the optimal initial structure for growth onto the
IndoPacific SSTA currently exceeds 0.5 by about 20%. A projection of this size has been
accompanied by Niño 3 and Niño 4 anomalies in excess of their +1 levels in every case in the
1950-97 record, with most cases represented by strong El Niño events. Therefore we would not
be at all surprised if the currently developing El Niño were to be stronger and of longer duration
than is suggested by Fig. 1.
Penland, C. and T. Magorian, 1993: Prediction of Niño 3 sea-surface temperatures using linear
inverse- modeling. J. Climate, 6, 1067-1076.
Penland, C. And P Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature
anomalies. J. Climate, 8, 1999-2024.
Fig. 1. Linear inverse modeling forecasts of SST anomalies, relative to the standard 1950-79
COADS climatology both for the training period (1950-84) and for these forecasts. Forecast
anomalies are projected onto 20 leading EOFs, based on Mar-Apr-May 1997 initial conditions
(top panel). Contour interval is 0.2oC. Positive anomalies are represented by heavy solid lines,
negative anomalies by dashed lines. SST data have been provided by NCEP. Prediction by linear
inverse modeling is described in Penland and Magorian (1993).
Fig. 2. (a): Inverse modeling predictions (light solid lines) of Niño 3 SSTA for initial conditions
Jan-Feb-Mar, Feb-Mar-Apr and Mar-Apr-May 1997. Light dotted lines indicate the 1 standard
deviation expected error bars for the prediction assuming a perfect model based on the JFM 1996
initial condition. Anomalies are defined as explained in Fig. 1 caption, and projected onto 20
leading EOFs. Also shown are the verification contributed by the 20 leading EOFs (heavy dashed
lines) and including the truncation error (heavy solid lines). (b): As in (a) except for Niño 4.
Fig. 3. Time series of the pattern correlation between the optimal initial structure for growth (light
solid line) and a) the Niño 3 SST anomaly time series (heavy dotted line). b) As in a), but for the
Niño 4 SST anomaly time series. Solid horizontal lines denote projections of the IndoPacific
SSTA field onto the optimal structure equal to +0.5, 0., and -0.5.
