Forecast of Tropical SSTs using Linear Inverse Modeling (LIM)
contributed by 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 Niño 3 region (6N-6S, 150W-90W; Fig. 2a) and the Niño 4 region (6N-6S, 160E-150W; Fig. 2b), the tropical North Atlantic (Figs. 4 and 5), and the Caribbean (Figs. 4 and 6) 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 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 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 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 Niño 3 value at lead times of about 18 months. The predicted IndoPacific SSTA patterns based on the DJF 1999-2000 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 SON, OND, NDJ and DJF 1999-2000 initial conditions. Light dotted lines indicate the one-standard-deviation (67%) confidence interval for the prediction assuming a perfect model based on SON1999. Fig. 2b is the same, but for the Niño 4 region. Verifications including the truncation error (heavy dashed line) and omitting the truncation error (heavy solid line) are also shown.
The predictions show continued cold anomalies persisting throughout most of 2000, peaking out sometime around the beginning of that year. Predictions during 1999 overestimated the magnitude of the cold anomalies during the first part of the year, although the present Niño 3 SSTA lies within the expected error intervals of the prediction based on SON 1999 conditions. The persisting SSTA cold event pattern has been very well predicted (Fig. 3), with pattern correlations between the prediction and verification remaining above 0.7 for most of the year, and even the DJF 1998-1999 prediction verifying with anomaly correlations greater than 0.6 for nearly an entire year.
The prediction of tropical Atlantic SSTA is confined to the north tropical Atlantic (NTA) and Caribbean (CAR) sectors (Fig. 4) 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 general decaying trend of SSTA in the Caribbean and north tropical Atlantic 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.
Hardcopy version:
Fig. 1: Forecasts of IndoPacific SST anomalies projected onto 20 leading EOFs, based on DJF 1999-2000 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 0.2C. Positive anomalies are represented by heavy solid lines, negative anomalies by dashed lines.
Fig. 2: a) Predictions (light solid lines) of the Niño 3 SSTA for initial conditions SON, OND, NDJ and DJF 1999-2000. Light dotted lines indicate the one-standard-deviation (67%) confidence interval appropriate to a perfect model based on SON 1999 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 dashed line) and omitting the truncation error (heavy solid line) are also shown. b) As in a), but for the Niño 4 region.
Fig. 3: Pattern correlations between predicted and verified SST anomaly field in the tropical Pacific, beginning with DJF 1998-1999 initial conditions.
Fig. 4: Map showing the North Tropical Atlantic (NTA) and Caribbean (CAR) regions within which average SSTA is predicted.
Fig. 5: Time series of linear inverse modeling (LIM) predictions (light 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 (heavy solid line) and the one-standard-deviation (67%) confidence interval appropriate to the LIM forecast (dotted lines).
Fig. 6: As in Fig. 4, but for CAR SSTA.
Netscape version:
Fig. 1 : Forecasts of IndoPacific SST anomalies projected onto 20 leading EOFs, based on DJF 1999-2000 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 blue solid lines) of the Niño 3 SSTA for initial conditions SON, OND, NDJ and DJF 1999-2000. Light black dotted lines indicate the one-standard-deviation (67%) confidence interval appropriate to a perfect model based on MAM 1999 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 in a), but for the Niño 4 region.
Fig. 3: Pattern correlations between predicted and verified SST anomaly field in the tropical Pacific, beginning with DJF 1998-1999 initial conditions. Fig. 4: Map showing the North Tropical Atlantic (NTA) and Caribbean (CAR) regions within which average SSTA is predicted.
Fig. 5: Time series of linear inverse modeling (LIM) predictions (green 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).
