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 (1997), the pattern of IndoPacific sea-surface temperature anomalies (SSTAs; Fig. 1), as well as SSTA in the Niño 3 region (6^oN-6^oS, 90 -150^oW; Fig. 2a), the SSTA in the Niño 4 region (6^oN-6^oS, 150^oW-160^oE; Fig. 2b), the tropical North Atlantic (Fig. 1 and Fig. 2), and the Caribbean (Fig. 1 and Fig. 3) 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). 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 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 SSTAs uses tropical SSTAs in the region 30^oN-30^oS, 30^oE-70^oW 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 0.7^oC; the inverse modeling prediction method has an RMS error of about 0.5^oC at a lead time of nine months and approaches the RMS Niño value at lead times of 18 months. The predicted IndoPacific SSTA patterns based on the DJF 1998-99 initial condition for the following MAM, JJA, SON and DJF are shown in Fig. 1. Fig. 2a shows the predictions (light solid lines) of the Niño 3 anomaly for initial conditions AMJ, MJJ, JJA, JAS, ASO, SON, OND, NDJ and DJF 1998-99. Light dotted lines indicate the one standard deviation (67%) confidence interval for the prediction assuming a perfect model based on the AMJ 1998. Fig. 2b is the same, but for Niño 4 region. Verifications including the truncation error (heavy dashed line) and omitting the truncation error (heavy solid line) are also shown. Fig. 2a shows that the prediction of cold Niño 3 SSTA was somewhat overestimated although verifications do fall within the AMJ 1998 confidence interval. The prediction of Niño 4 SSTA has been very good since AMJ 1998; the predictions and verifications made since then are form a tight bundle, mostly within the one standard deviation confidence interval for the AMJ 1998 prediction.

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 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, 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.

Fig. 2: a) Predictions (light blue solid lines) of the Niño 3 anomaly for initial conditions. AMJ, MJJ, JJA, JAS, ASO, SON, OND, NDJ, and DJF 1998-99. Light black dotted lines indicate the one standard deviation (67%) confidence interval for the prediction assuming a perfect model based on AMJ 1998. 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 red dahed line) and omitting the truncation error (heavy red solid 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 the average SST anomaly 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. Also shown are the verification series (red solid lines) and the one standard deviation confidence interval appropriate to the LIM forecast (black dotted lines).

Fig. 5: As in Fig. 4, but for CAR SST anomaly.