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Forecasts of Niño 3.4 SST Using Neural Network Models

contributed by Benyang Tang, William Hsieh and Fred Tangang

Department of Earth and Ocean Sciences, University of British Columbia, Vancouver, B.C., Canada

Web site of the UBC Climate Prediction Group: http://www.ocgy.ubc.ca/projects/clim.pred

Throughout 1996, forecasts for the tropical Pacific SST in the Niño 3 region were presented in this Bulletin using a neural network model with features such as an additional continuity term and a "clearning" term in the cost function (Tang et al. 1994; Tangang et al. 1997). However, attempts to improve the forecasts made by the neural network models continue, because we believe that higher skills and/or better model behavior may be possible. In the December 1996 issue, for example, we discussed how greater forecast stability could be achieved by pruning the networks using Optimal Brain Damage (OBD), so that fewer weights were included.

In this issue we continue to use the procedure called bootstrap aggregating, or bagging. As described in the previous (March 1997) issue of this Bulletin, the primary goals of bagging are to increase the skills and the stability of the neural network models.

Bagging (Breiman 1997) works as follows: First training pairs, consisting of the data at the initial time and the data at the forecast target time of a certain number of months (lead time) later, are formed. The available training pairs are separated into a training set and a test set. The test set is reserved for testing only and not used for training. The training set is used to generate an ensemble of neural network models; each member of the ensemble is trained by only a subset of the training set. The subset is drawn at random with replacement from the training set. The subset has the same number of training pairs as the training set; some pairs in the training set appear more than once in the subset, and about 37% of the training pairs in the training set are absent in the subset. The final model output is the average of the outputs from all members of the ensemble. The way in which bagging increases the stability of the neural network was discussed in more detail in the March 1997 issue of the Bulletin.

The neural networks in this forecast have 11 inputs and 3 hidden neurons. The Niño 3.4 index (from http://nic.fb4.noaa.gov/data/cddb), and the 2nd and 3rd EOF coefficients of the FSU monthly wind stress (Goldenberg and O'Brien 1981, from ftp://coaps.fsu. edu/pub/wind/pac) of the initial month, form the first 3 inputs. The same 3 variables of 2 months and 4 months before the initial month are also used as inputs. The last 2 inputs are the sine and cosine of a 12-month period to simulate the annual cycle.

Before the EOF calculation, the wind data were first smoothed with one pass of a 1-2-1 filter in the zonal and meridional directions and in time, and detrended and de-seasoned by subtracting from a given month the average of the same calendar months of the previous four years. This pre-EOF processing is the same as that used in Lamont's coupled model (Cane et al. 1986) and in Tang (1995).

The ensemble in the bagging procedure has 30 members. For each lead time, we produced 5 bagging neural networks, with 5 different test periods: 1963-1969, 1970-1977, 1978-1984, 1984-1990, and 1991-1996. Table 1 lists the skills for lead times of 3 to 12 months, for the 5 test periods. As shown in the March 1997 issue of this Bulletin, a noticeable im-provement in skill was achieved by bagging as compared with the individual members of the ensemble.

The 3 panels in Fig. 1 show the forecasts at 3 lead times using data up to May 1997. Forecasts at all lead times indicate an El Niño is under way, in agreement with our POP model forecast (see http://www.ocgy .ubc.ca/projects/clim.pred). The signal of a coming El Niño event was carried in the wind data of April and May 1997, and was not seen in the data older than April 1997. In the 9-month lead time forecasts, the March 1997 initial condition produced a warm Niño 3.4 SST due to the influence of the April data through the 1-2-1 filtering. We are compiling a real-time sea level pressure data set, which we will use in our future forecasts.

Table 1. The test correlation skills for 4 lead times, for 5 different test periods.

Breiman, L., 1997: Bagging predictions. Machine Learning, in press. Available at ftp://stat.berkeley.edu/ users/pub/breiman.

Cane, M.A., S.E. Zebiak and S. Dolan, 1986: Experimental forecasts of El Niño. Nature, 321, 827-832.

Goldenberg, S.B., and J.J. O'Brien, 1981: Time and space variability of tropical Pacific wind stress. Mon. Wea. Rev., 109, 1190-1207.

Tang, B., 1995: Periods of linear development of the ENSO cycle and POP forecast experiments.J. Climate, 8, 682-691.

Tang, B.,G. Flato and G. Holloway, 1994: A study of Arctic sea ice and sea level pressure using POP and neural network methods. Atmos.-Ocean, 32, 507-529.

Tangang, F.T., W.W. Hsieh and B. Tang, 1997: Forecasting the equatorial Pacific sea surface temperatures by neural network models. Climate Dynamics, accepted.

Fig. 1. Current forecasts for Niño 3.4 SST using the neural networks at 3, 6, and 9 month lead times.

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