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 the IndoPacific sea-surface temperature anomalies (SSTA; Fig. 1), 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 table 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 leading empirical orthogonal functions (EOFs), 17 for the Indo-Pacific prediction and 20 for the Atlantic prediction.

The prediction of IndoPacific SSTA uses tropical SSTA in the region (30N-30S, 30E-70W) as predictors. We have removed the 1951-2000 average annual cycle and projected onto the leading 17 EOFs, which explain about 2/3 of the anomaly variance in this region. The training period is also 1951-2000.

The predicted IndoPacific SSTA patterns based on the SON 2003 initial condition for the following four seasons are shown in Fig. 1. Fig. 2 shows the prediction error (verification minus prediction) of the Nino 3.4 SSTA forecast standardized by one standard deviation of the expected forecast error (Penland and Sardeshmukh 1995; Penland 1996, Penland and Matrosova 2001). This expected error includes contributions from the annually-varying stochastic forcing, as well as uncertainties in the initial condition and in the empirically-estimated Green function. The vertical line in Fig. 2 separates the training period from the verification period. The forecast indicates a persistence of warm SSTs in the tropical Pacific, with the current warmth in the Indian Ocean and west tropical Pacific persisting or even increasing in the near future.

One result of Penland and Sardeshmukh (1995) was the identification of an optimal initial structure for growth, an SST anomaly pattern which precedes a mature El Nino pattern by 6 to 9 months. This pattern, and more detail about the analysis, may be viewed at the site http://www.cdc.noaa.gov/forecasts/optstr.html). In Fig. 3a we see the time series of the Nino3.4 SSTA and that of the pattern correlation between this structure and the IndoPacific SSTA field eight months earlier. Fig. 3b shows a scatter plot of the two time series. The arrow shows the current projection of 0.48. What is remarkable is that projections this high have been followed by positive or neutral Nino 3.4 SST anomalies in every case since 1950.

Global tropical SSTs are used as predictors for the tropical Atlantic. 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, which is why SSTA in the global tropical strip (30N-30S) are used as predictors. The leading 20 EOFs in this case also contain about 2/3 of the variance. Forecasts suggest a continuation of positive SST anomalies in the NTA region and near-neutral SSTA in the CAR region. Please note, however, that the recent NTA predictions have basically been persistence forecasts.

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.

Penland, C., and Matrosova, 2001: Expected and Actual Errors of Linear Inverse Model Forecasts. Mon. Wea. Rev., 129, 1740-1745.

Figure captions:

Fig. 1: Forecasts of IndoPacific SST anomalies projected onto 17 leading EOFs, based on SON 2003 initial conditions. Anomalies were calculated relative to the 1951-2000 climatology. SST data were provided by NCEP and summarized onto COADS-compatible monthly statistics at CDC. The contour interval is 0.3C.

Fig. 2: Prediction errors, normalized by one standard deviation of the expected error. The vertical line separates latter part of training period from verification period.

Fig. 3: (a) Time series of Nino 3.4 SSTA (light blue line) and projection of IndoPacific SSTA field onto the optimal structure eight months earlier (heavy red line). (b) Scatter plot of these time series. Arrow indicates current value of projection. Best fit straight line, flanked by one standard deviation error bars, is also shown. Red asterisk indicates current value of Nino 3.4 SSTA anomaly and projection value eight months ago.

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 (blue solid line) of NTA SSTA for lead times of 3, 6, 9 and 12 months. Anomalies are calculated relative to the 1951-2000 climatology. Also shown are the verification series (red solid line) and the one-standard-deviation confidence interval appropriate to the LIM forecast (black dotted lines). The vertical line separates latter part of training period from verification period.

Fig. 6: As in Fig. 5, but for CAR SSTA.