Forecast of Tropical SSTs using Linear Inverse Modeling (LIM)

Cecile Penland, Ludmila Matrosova, Klaus Weickmann and Catherine Smith

NOAA-CIRES/Climate Diagnostics Center, Boulder, Colorado

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 Nino 3 region (6N-6S, 150W-90W; Fig. 2a) and the Nino 4 region (6N-6S, 160E-150W; Fig. 2b), the tropical North Atlantic (Fig. 3 and Fig. 4), and the Caribbean (Fig. 3 and Fig. 5) are predicted. A prediction at lead time tau is made by applying a statistically-estimated Green function G(tau) 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 SSTA 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 were provided by NCEP and consolidated into COADS-compatible monthly statistics at CDC. Two sets of predictors/predictands are used, one for the Indo-Pacific 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 SSTA uses tropical SSTA in the region (30N-30S, 30E-70W) as predictors. The COADS 1950-1979 climatological annual cycle has been removed, and the leading 20 EOFs explain about 70% of the remaining variance. The Nino 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 Nino 3 value at lead times of about 18 months. The predicted IndoPacific SSTA patterns based on the SON 2000 initial condition for the following DJF, MAM, JJA, and SON are shown in Fig. 1. Fig. 2a shows the predictions (light solid lines) of the Nino 3 anomaly for DJF 1999-2000, JFM, FMA, MAM, AMJ, MJJ, JJA, JAS, ASO and SON 2000 initial conditions. Light dotted lines indicate the one-standard-deviation (67%) confidence interval for the prediction based on DJF 1999-2000. Fig. 2b is the same, but for the Nino 4 region. Verifications including the truncation error (heavy dashed line) and omitting the truncation error (heavy solid line) are also shown. Confidence intervals include estimations of the uncertainty due to seasonally-varying stochastic forcing (Penland and Sardeshmukh 1995; Penland 1996), as well as uncertainties in the initial condition and in the empirically--estimated Green function.

Current forecasts call for cool to normal SST anomalies until well into next year. The enhanced trades associated with a recent Madden-Julian Oscillation (MJO) have acted to further cool the SST's in the central equatorial Pacific, thus supporting the prediction. Previously, we speculated that this broadband phenomenon along with positive SST anomalies extending to 150E could eventually result in further eastward shift of the warm west Pacific, a shift which Linear Inverse Modeling is not designed to predict. The cooling effects from the recent MJO suggest the eastward shift of warm SST's may be delayed.

The prediction of tropical Atlantic SSTA is confined to the north tropical Atlantic (NTA) and Caribbean (CAR) sectors (Fig. 3) since persistence on the time scales 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. Current forecasts call for cool to normal anomalies in the tropical Atlantic. However, recent forecasts have been too cold by about 0.2C at a lead time of six months.

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 Nino 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., 1996: A stochastic model of IndoPacific sea surface temperature anomalies. Physica D, 98, 534-558.

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 SON 2000 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 black solid lines) of the Nino 3 SSTA for initial conditions DJF 1999-2000, JFM, FMA, MAM, AMJ, MJJ, JJA, JAS, ASO and SON 2000. Light blue dotted lines indicate the one-standard-deviation (67%) confidence interval appropriate to a forecast based on DJF 1999-2000 initial conditions. 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 dashed line) and omitting the truncation error (heavy red solid line) are also shown. b) As is a), but for the Nino 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 (blue solid line) 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.