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Forecast of Tropical SSTs Using Linear Inverse Modeling (LIM)
contributed by Cécile Penland, Klaus Weickmann,
Catherine Smith and Ludmila Matrosova
NOAA-CIRES/Climate Diagnostics Center, Boulder, Colorado 80309-0449
Using the methods previously described in issues of the Experimental Long-Lead Forecast
Bulletin, in Penland and Magorian (1993), and in Penland and Matrosova (1997), the pattern of
IndoPacific sea-surface temperature anomalies (SSTAs; Fig. 1), as well as SSTA in the Niño 3
region (6oN-6oS, 90 -150 oW; Fig. 2a), the SSTA in the Niño 4 region (6oN-6oS, 150oW-160oE;
Fig. 2b), the tropical North Atlantic (Figs. 3 and 4), and the Caribbean (Figs. 3 and 5) 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 an appropriate domain. Although the
parameters of the model are obtained statistically, the dynamical assump-tion of stable linearity
implicit in the method (an assumption that in the case of tropical SSTs is largely corroborated by
data) requires a fixed-point attractor in phase space. The technique, therefore, cannot be
considered a purely statistical prediction method (Penland 1989; Penland and Sardeshmukh 1995).
Data have been provided by NCEP, courtesy of R.W. Reynolds. Two sets of
predictor/predictands are used, one for the IndoPacific and one for the tropical Atlan-tic. In both
cases, 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).
The prediction of IndoPacific SSTAs uses tropical SSTAs in the region 30oN-30oS, 30oE-70oW as
predic-tors. The COADS 1950-79 climatological annual cycle has been removed, and the leading
20 EOFs explain about 70% of the variance. The Niño 3 region has an RMS temperature anomaly
of about 0.7oC; 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. The
predicted IndoPacific SSTA patterns based on the SON 1997 initial condition for the following
DJF, MAM, JJA and SON 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 JJA, JAS, ASO, and
SON, 1997. Light dotted lines indicate the 1 standard deviation expected error for the prediction
assuming a perfect model based on the MAM 1997 initial conditions. Figure 2b is the same, but
for the Niño 4 region. Verifications including the truncation error (heavy dotted line) and omitting
the truncation error (heavy solid line) are also shown. Nearly all the SSTA variability in Niño 3
has been contained in the leading 20 EOFs until recently. Lately, however, the contribution to the
Niño 3 anomaly from the leading 20 EOFs has dropped while the full Niño 3 SST anomaly has
continued to rise. Our forecasts are based on the truncated field and predict a significant cold
event to develop by fall of 1998. The contribution to the Niño 4 SST anomaly from the leading 20
EOFs has continued to rise, as has the full anomaly, with the truncated value being slightly larger.
The prediction of tropical Atlantic SSTAs is confined to the north tropical Atlantic (NTA) and
Caribbean (Car) sectors (Fig. 3) since persistence is a remarkably good predictor of SSTA in the
equatorial and south tropical Atlantic (Penland and Matrosova 1997). The added predictability in
the northern tropical Atlantic is primarily due to the effect of El Niño, so SSTAs in the global
tropical strip (30oN-30oS) are used as predictors. Forecast skill is indicated in the March 1997
issue of this Bulletin. The COADS annual cycle has been removed from three-month running
means of SSTs and anomalies were projected onto the leading 20 EOFs containing about 67% of
the variance. The predictions are characterized by an upturn of SSTA in those regions (Figs. 4
and 5), possibly due to the influence of the current warm event in the Pacific.
Penland, C., 1989: Random forcing and forecast-ing using Principal Oscillation Pattern Analysis.
Mon. Wea. Rev., 117, 2165-2185.
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.D. Sardeshmukh, 1995: The optimal growth of tropical sea surface
temperature anomalies. J. Climate, 8, 1999-2024.
Penland, C. and L. Matrosova, 1997: Prediction of tropical Atlantic sea surface temperatures
using Linear Inverse Modeling. J. Climate, 10, in press.
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 Sep-Oct-Nov 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, courtesy of R.W. Reynolds,
and summarized onto COADS-compatible monthly statistics at CDC. Prediction by linear inverse
modeling is described in Penland and Magorian (1993: J. Climate, 6, 1067-1076).
Fig. 2. (a): Linear Inverse modeling predictions (light solid lines) and verifications (heavy solid
lines) of Niño 3 SSTA. Light dotted lines indicate 1 standard deviation error bars appropriate to a
stable linear system driven by stochastic forcing, based on the Jun-Jul-Aug 1997 initial condition.
Anomalies were calculated as described in the Fig. 1 caption, using 20 EOFs. The contribution to
the verification by the 20 leading EOFs (heavy dashed lines) and the verification including the
truncation error (heavy solid lines) are shown. (b): As in (a) but for the Niño 4 region.
Fig. 3. Map showing the North Tropical Atlantic (NTA) and Caribbean (CAR) regions, within
which the average SSTA is predicted.
Fig. 4. Time series of linear inverse modeling (LIM) predictions (light solid line) of NTA SSTA
for lead times of 3, 6, 9 and 12 months. Also shown are the verification series (heavy solid line)
and the one standard deviation confidence interval appropriate to the LIM forecasts (dotted lines).
Fig. 5. As in Fig. 4, but for the Caribbean region.
