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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 discuss our recent implementation of a procedure called bootstrap aggregating, or
bagging, to increase the skills and the stability of our neural network models.
Bagging (Breiman 1997) works as follows: First training pairs, consisting of the data at the initial
time and the forecast target of certain 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 advantage of bagging is a reduction of the variance, or instability, of the neural network. The
error surface of neural network training is full of local minima; trainings with different initial
weights and training data are usually trapped in different local minima. These local minima reflect
partly the fitting to the regularities of the data and partly the fitting to the noise in the data.
Bagging tends to cancel the noise part as it varies among the ensemble members, and tends to
retain the fitting to the regularities of the data.
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. To show the improvement brought about by bagging, we list in Table 2 the average of
the test skills of the individual members of the ensemble.
Figure 1 plots the model outputs of test periods, collected from the 5 runs of the different test
periods, against the observations. The lead time is 6 months.
The 3 panels in Fig. 2 show the forecasts at 3 lead times. The more reliable 6-month lead model
forecasts a continued but weakened cold condition from February to August 1997, which is in
agreement with our POP model forecast (see http://www.ocgy.ubc.ca/projects/ clim.pred).
Looking at the test performance, the current neural network models generally will not forecast an
event until the April data become available.
Table 1. The test correlation skills for different test periods.
-----------LEAD TIME-----------------
test period 3-month 6-month 9-month 12-month
1963-1969 0.85 0.67 0.56 0.35
1970-1976 0.91 0.78 0.55 0.31
1977-1983 0.81 0.70 0.58 0.47
1984-1990 0.90 0.83 0.69 0.46
1991-1996 0.91 0.81 0.59 0.25
Table 2. The average of the test skills of the individual members of the ensemble.
-----------LEAD TIME-----------------
test period 3-month 6-month 9-month 12-month
1963-1969 0.82 0.61 0.42 0.23
1970-1976 0.89 0.73 0.48 0.23
1977-1983 0.78 0.64 0.43 0.26
1984-1990 0.88 0.78 0.56 0.30
1991-1996 0.88 0.73 0.44 0.18
References
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. Comparison between the observed SST in Niño 3.4 (solid line) and the model output for
the test periods (circles).
Fig. 2. Current forecasts for Niño 3.4 SST using the neural networks at 3, 6, and 9 month lead
times.
