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 IndoPacific sea-surface temperature anomalies (SSTA; Fig. 1), as well as SSTA in the Niño 3 region (6N-6S, 150W-90W; Fig. 2a), and the Niño 4 region (6N-6S, 160 E-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 SSTA 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 SST 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 and consolidated into COADS-compatible monthly statistics at CDC. [Two sets of predictors/predictands are used, one for the IndoPacific and tropical Atlantic.] 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 SSTA uses tropical SSTA in the region (30N-30S, 30E-70W) as predictors. The COADS 1950-79 climatological annual cycle has been removed, and the leading 20 EOFs explain about 70% of the remaining 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 0.5C at a lead time of nine months and approaches the RMS Niño 3 value at lead times of 18 months. The predicted IndoPacific SSTA patterns based on the MAM 1999 initial condition for the following JJA,SON,DJF and MAM are shown in Fig. 1. This initial condition represents the strongest negative projection (-0.38) onto the optimal initial condition for growth (Penland and Sardeshmukh 1995) since we began real-time forecasting in 1991. Fig. 2a shows the predictions (light solid lines) of the Niño 3 anomaly for initial conditions JAS, ASO, SON, OND, NDJ, DJF 1998-99, JFM, FMA and MAM 1999. Light dotted lines indicate the one-standard-deviation (67%) confidence interval for the prediction assuming a perfect model based on JAS 1998. That is, these confidence intervals do not increase as the model does worse. Fig, 2b is the same, but for the Niño 4 region. Verifications based on all EOFs (heavy solid line) and those based on EOFs 1-20 (heavy dashed line) are also shown.

Fig. 2a shows that the prediction of cold Niño 3 SST was somewhat overestimated as verifications are falling out of the JAS 1998 confidence interval. The current forecast continues to predict a rapid cooling consistent with the strong projection onto the optimal structure. On the other hand, the prediction of Niño 4 SSTA (Fig. 2b) had been very good, at least until fall 1998. Since then the predictions have also called for a rapid cooling, which has not yet materialized. In fact, the observed curve (Fig. 2b) still seems to be tracking the long range predictions from early fall 1998.

The prediction of tropical Atlantic SSTA is confined to the north tropical Atlantic (NTA) and Caribbean (CAR) sectors (Fig. 3) since persistence on the timescales shown is a remarkably good predictor of SSTA 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 the Pacific, so SSTA 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 discussed in the March 1997 issue of this Bulletin. According to the current forecasts, the predicted decay of SSTA in those regions can be expected to continue.

References

Penland, C., 1989: Random forcing and forecasting 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, 1998: Prediction of tropical Atlantic sea surface temperatures using Linear Inverse Modeling. J. Climate, 11, 483-496.





Fig. 1: Forecasts of IndoPacific SST anomalies projected onto 20 leading EOFs, based on DJF 1998-99 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 0.3C. This initial condition represents the strongest negative projection (-).38) onto the optimal structure since 1991.

Fig. 2: a) Predictions (light blue solid lines) of the Niño 3 SSTA for initial conditions. JAS, ASO, SON, OND, NDJ, and DJF 1998-99, JFM, FMA, MAM 1999. Light black dotted lines indicate the one-standard-deviation (67%) confidence interval appropriate to a perfect model based on JAS 1998 conditions. That is, about one in three predictions could be expected to lie outside this interval even with a perfect model. Verifications based on all EOFs (heavy solid line) and those based on EOFs 1-20 (heavy dashed line) are also 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 average SSTA is predicted.

Fig. 4 Time series of linear inverse modeling (LIM) predictions (green solid lines) of NTA SSTA for lead times of 3, 6, 9 and 12 months. Anomalies are calculated relative to the 1950-1993 climatology. Also shown are the verification series (red solid line) and the one-standard-deviation (67%) confidence interval appropriate to the LIM forecast (black dotted lines).

Fig. 5: As in Fig. 4, but for CAR SSTA