Linear statistical models may not describe the climate system fully since it can be regarded as a nonlinear system. Since artificial neural network model represents a nonlinear statistical technique, it can be combined with multi-model superensemble technique.
To construct a nonlinear multi-model ensemble, feed-forward neural network was constructed with input layer, hidden layer and output layer. Linear transfer function and hyperbolic tangent function were used for output layer and hidden layer, respectively. The final output of neural network is
output layer of jth layer is
In order to normalize input data (-1.0~1.0), data are rescaled divided by standard deviation as follows;
Thus, the final output of neural network changes to
where is standard deviation of observation data.
From above equations, multi-model ensemble using artificial neural network models can be expressed as follows;
where, is the ith model forecast of the tth year at the mth grid point.
Figure 3. The construction of back propagation neural network model.
There is one layer between input layer and output layer.