Combining neural network models to predict spatial patterns of airborne pollutant accumulation in soils around an industrial point emission source

Neural networks (NNs) have the ability to model a wide range of complex nonlinearities. A major disadvantage of NNs, however, is their instability, especially under conditions of sparse, noisy, and limited data sets. In this paper, different combining network methods are used to benefit from the existence of local minima and from the instabilities of NNs. A nonlinear k-fold cross-validation method is used to test the performance of the various networks and also to develop and select a set of networks that exhibits a low correlation of errors. The various NN models are applied to estimate the spatial patterns of atmospherically transported and deposited lead (Pb) in soils around an historical industrial air emission point source. It is shown that the resulting ensemble networks consistently give superior predictions compared with the individual networks because, for the ensemble networks, R2 values were found to be higher than 0.9 while, for the contributing individual networks, values for R2 ranged between 0.35 and 0.85. It is concluded that combining networks can be adopted as an important component in the application of artificial NN techniques in applied air quality studies.