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Forecast of Pacific-Indian Ocean SSTs Using
Linear Inverse Modeling
contributed by Cecile Penland1, Klaus Weickmann2 and Catherine Smith1
1Climate Diagnostics Center, CIRES, University of Colorado, Boulder, Colorado
2Climate Diagnostics Center, ERL/NOAA/CDC, Boulder, Colorado
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 DJF 1996-97 initial condition for the
following MAM, JJA, SON and DJF are shown in Fig. 1 (contour interval = 0.2oC). Figure 2a
shows the predictions (light solid lines) of the Niño 3 anomaly for initial conditions ASO, SON,
OND 1996, and NDJ, DJF, 1996-97. Light dotted lines indicate the 1 standard deviation expected
error for the prediction assuming a perfect model based on the JFM 1996 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.
Figure 3, which shows the pattern correlations between predicted and observed SSTA in the
IndoPacific basin, indicates that the present situation was accurately predicted. The dip in pattern
correlations during the fall of 1996 was due to our premature forecast of cold conditions which
did not appear until later in the year. The current forecast supports our previous prediction of
warm anomalies developing in the eastern Pacific by mid-1997. Indeed, forecasts of SSTA pattern
based on NDJ initial conditions (not shown) indicate a classic, though fairly weak, warm event
pattern. Unfortunately, Fig. 2b shows that some, possibly important, part of the Niño 4 signal is
not contained in the 20 EOFs upon which our forecast is based.
Penland, C. and T. Magorian, 1993: Prediction of Niño 3 sea-surface temperatures using linear
inverse- modeling. J. Climate, 6, 1067-1076.
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 Dec-Jan-Feb 1996-97 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
ASO, SON, OND 1996, and NDJ, DJF 1996-97. 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 omitting the truncation error (heavy dotted line)
and including the truncation error (heavy solid line). (b): As in (a) except for Niño 4.
Fig. 3. The pattern correlations between predicted and observed IndoPacific SSTA for selected
1996 initial conditions.