The data used for training are the Niño 3 SST index and the
first 4 EOF coefficients of the FSU monthly wind stress data (Goldenberg
and O'Brien 1981). The seasonal cycle, calculated from the 1961-90 data,
has been removed from the Niño 3 data. Before the EOF calculation,
the wind data were first smoothed with one pass of a 1-2-1 filter in 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 inputs of the neural network for a given month consist of the Niño
3 index and the first 4 wind EOF coefficients of the month and the same
5 numbers for the month that is 3 months earlier, amounting to 10 inputs
to the network. These inputs feed into a hidden layer with 4 sigmoidal
neurons, which in turn feed into 5 linear output neurons, giving the Niño
3 and the first 4 wind EOF coefficients for the month that is 3 months
later. Thus, the time step of the neural network is 3 months. By repeatedly
applying the model output as input to the neural network, we can obtain
forecasts for longer lead times. There are 420 training pairs (i.e., sets
of predictors and predictands) in the 1961-95 period.
To estimate the forecast skill, retroactive real time forecasts 1986-1995
were carried out. Figures 1 and 2 of the March 1996 issue of this Bulletin
show the skill in terms of correlation and RMS error for retroactive real
time as well as hindcasts for a longer historical period. Skills are seen
to be competitive with other empirical forecast approaches such as analogs
or linear regression.
The model we use here is the same as the one we used in the last issue
of this Bulletin. However, the initial conditions have been adjusted with
the new data using the same optimization as the model training, in a way
similar to initialization of adjoint data assimilation.
Figure 1 shows the latest forecast using a neural network trained with
data up to July 1996. Six forecasts of lead times of up to 12 months were
initiated from January to June 1996. Our forecast calls for a slightly
cold tropical Pacific condition for the Niño 3 region in the 1996-97
winter.
The forecast of our neural network model is updated monthly in our web
site. In addition, our web site issues forecasts by a POP model (Tang 1995).
The POP model forecasts the continuation of the current cold condition
for the coming season, but has not called for any warm or cold event for
the 1996-97 winter so far.
References
Cane, M.A., S.E. Zebiak and S. Dolan, 1986: Experimental forecasts
of El Nino. 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, 1996: Forecasting the equatorial
Pacific see surface temperatures by neural network models. Climate Dynamics,
in press.
Weigend, A.S, H.G. Zimmermann, and R. Neuneier, 1996: Clearning. In Neural
Networks in Financial Engineering. Refenes, P., Y. Abu-Mostafa, J.E.
Moody and A.S. Weigend, Eds. Proceedings, Neural Networks in the Capital
Markets, October 1995, London, UK. In press.
Figures
Fig. 1. Forecasts of Niño 3 SST based on wind stress and SST
data through July 1996. The thick solid line denotes the observed SST,
and the 6 thinner solid or dashed lines with circles at the beginnings
and ends denote the forecasts up to lead times of 12 months initiating
from February to July 1996.