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), the tropical North Atlantic (Figs. 3 and 4), and the Caribbean (Figs. 3 and 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 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 17 leading empirical orthogonal functions (EOFs).
PLEASE NOTE THAT WE HAVE UPDATED OUR MODEL!
The prediction of IndoPacific SSTA uses tropical SSTA in the region (30N-30S, 30E-70W) as predictors. In keeping with guidelines recently put out by NCEP, we have removed the 1951-2000 average annual cycle.
EOFs were newly calculated in this region, with the leading 17 EOFs explaining about 2/3 of the anomaly variance using 1951-2000 to train the new data, we find that warm and cold events predicted by this model are more equatorially confined than the previous version. Further, had we used this newer version during 2001-2002, the persisting Indian Ocean warm anomalies would have been correctly predicted. The new version did not predict well the amplitude of the recent 2002-2003 El Nino, but it did not corroborate the spurious cold event forecast by the older model version, either. For a history of forecasts by our newer version model, please see http://www.cdc.noaa.gov/forecasts/IndoPacific.frcst.html.
The predicted IndoPacific SSTA patterns based on the DJF 2002-2003 initial condition for the following MAM, JJA, SON and DJF 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 forecasts shown in Fig. 1 suggest an imminent demise of the current warm conditions in the equatorial Pacific. Unlike earlier forecasts made by the previous model, the warmth in the Indian Ocean is expected to persist, and the cooling in the Pacific is closely confined to the equator.
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 also contain about 67% of the variance. Forecasts suggest a continuation of positive SST anomalies in the NTA and Car regions.
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 20 leading EOFs, based on DJF 2002-2003 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: 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 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.
