Forecast of Tropical SSTs using Linear Inverse Modeling (LIM)
contributed by Cécile Penland, Ludmila Matrosova, 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, in Penland and Magorian (1993), and in Penland and Matrosova (1998), the pattern of Indo-Pacific sea-surface temperature anomalies (SSTAs; Fig. 1), as well as SSTA in the Niño 3 region (6N-6S; 150W-90W; Fig. 2a), the Niño 4 region (6N-6S; 160E-150W; 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 assumption 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). SST data have been provided by NCEP, courtesy of R. W. Reynolds. Two sets of predictor/predictands are used, one for the Indo-Pacific and one for the tropical Atlantic. In both cases, three-month running mean 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 Indo-Pacific SSTAs uses tropical SSTAs in the region (30N-30S; 30E-70W as the predictors. The COADS 1950-1979 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 0.7C; the inverse modeling prediction method has an RMS error of about 0.5C at a lead time of nine months and approaches the RMS value at lead times of 18 months to two years. The predicted Indo-Pacific SSTA patterns based on the JJA 1998 initial condition for the following SON, DJF, MAM and JJA are shown in Fig. 1. Fig. 2a shows the predictions (light solid lines) of the Niño 3 anomaly for initial conditions DJF, FMA, MAM, AMJ, MJJ and JJA 1997-98. Light dotted lines indicate the 1 standard deviation (67%) confidence interval for the prediction assuming a perfect model based on NDJ 1997-98. Fig. 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. Fig. 2a shows predictions of a premature decay of the Niño 3 anomaly, which, as stated in our previous ELLFB contribution, is typical for predictions initialized during the warmest phase of the warm event. However, the dramatic decrease of SST anomalies in the east-central equatorial Pacific recently is consistent with this forecast. The forecast of Niño 4 anomalies has been much better; current and previous predictions of the Niño 4 anomalies (Fig. 2b, c) have been verified by the observed decay of SST anomaly there.
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 SSTAs in the equatorial and south tropical Atlantic (Penland and Matrosova 1998). The added predictability in the northern tropical Atlantic is primarily due to the effect of El Niño, so SSTAs in the global tropical strip (30N-30S) are used as predictors. The leading 20 EOFs in this case contain about 67% of the variance. Forecast skill is indicated in the March 1997 issue of this Bulletin. Our predictions indicate an end to rising SSTAs in those regions (Figs. 4 and 5).
Penland, C., 1989: Random forcing and forecasting using Principal Oscillation Pattern Analysis. Mon. Wea. Rev., 117, 2165-2185.
Penland, C., and Theresa 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, 9, 1999-2024
Penland, C., and L. Matrosova, 1998: Prediction of tropical Atlantic sea surface temperatures using Linear Inverse Modeling. J. Climate, 11, 483-496.
Figure. 1: Forecasts of Indo-Pacific SST anomalies projected onto 20 leading EOFs, based on JJA 1998 initial conditions. Anomalies were calculated relative to the 1950-1979 COADS climatology. SST data were provided by NCEP, courtesy of R.W. Reynolds, and summarized onto COADS-compatible monthly statistics at CDC. The contour interval is 0.2C. Positive anomalies are represented by heavy solid lines, negative anomalies by dashed lines.
Figure. 2: a) Predictions (light solid lines) of the Niño 3 anomaly for initial conditions DJF, JFM, FMA, MAM, AMJ, MJJ and JJA 1997-98, 1997-98. Light dotted lines indicate the one standard deviation (67%) confidence interval for the prediction assuming a perfect model based on DJF 1997-98. That is, about one in three predictions could be expected to lie outside this interval even with a perfect model. Verifications including the truncation error (heavy dashed line) and omitting the truncation error (heavy solid line) are also shown. B) As in a), but for the Niño 4 region. C) As in b), but for the single forecast from JAS 1997 initial conditions.
Figure. 3: Map showing the North Tropical Atlantic (NTA) and Caribbean (CAR) regions within which the average SST anomaly is predicted.
Figure. 4: Time series of linear inverse modeling (LIM) predictions (light solid lines) 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 forecast (dotted lines).
