Abstract
Bayesian regularized back-propagation neural network (BRBPNN) was developed for trend analysis, acidity and chemical composition of precipitation in North Carolina using precipitation chemistry data in NADP. This study included two BRBPNN application problems: (i) the relationship between precipitation acidity (pH) and other ions (NH4 +, NO3 −, SO4 2−, Ca2+, Mg2+, K+, Cl− and Na+) was performed by BRBPNN and the achieved optimal network structure was 8-15-1. Then the relative importance index, obtained through the sum of square weights between each input neuron and the hidden layer of BRBPNN(8-15-1), indicated that the ions' contribution to the acidity declined in the order of NH4 + > SO4 2− > NO3 −; and (ii) investigations were also carried out using BRBPNN with respect to temporal variation of monthly mean NH4 +, SO4 2− and NO3 − concentrations and their optimal architectures for the 1990–2003 data were 4-6-1, 4-6-1 and 4-4-1, respectively. All the estimated results of the optimal BRBPNNs showed that the relationship between the acidity and other ions or that between NH4 +, SO4 2−, NO3 − concentrations with regard to precipitation amount and time variable was obviously nonlinear, since in contrast to multiple linear regression (MLR), BRBPNN was clearly better with less error in prediction and of higher correlation coefficients. Meanwhile, results also exhibited that BRBPNN was of automated regularization parameter selection capability and may ensure the excellent fitting and robustness. Thus, this study laid the foundation for the application of BRBPNN in the analysis of acid precipitation.
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Xu, M., Zeng, G., Xu, X. et al. Application of Bayesian Regularized BP Neural Network Model for Trend Analysis, Acidity and Chemical Composition of Precipitation in North Carolina. Water Air Soil Pollut 172, 167–184 (2006). https://doi.org/10.1007/s11270-005-9068-8
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DOI: https://doi.org/10.1007/s11270-005-9068-8