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Modeling and Prediction of Monthly Total Ozone Concentrations by Use of an Artificial Neural Network Based on Principal Component Analysis

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Abstract

In the work discussed in this paper we considered total ozone time series over Kolkata (22°34′10.92″N, 88°22′10.92″E), an urban area in eastern India. Using cloud cover, average temperature, and rainfall as the predictors, we developed an artificial neural network, in the form of a multilayer perceptron with sigmoid non-linearity, for prediction of monthly total ozone concentrations from values of the predictors in previous months. We also estimated total ozone from values of the predictors in the same month. Before development of the neural network model we removed multicollinearity by means of principal component analysis. On the basis of the variables extracted by principal component analysis, we developed three artificial neural network models. By rigorous statistical assessment it was found that cloud cover and rainfall can act as good predictors for monthly total ozone when they are considered as the set of input variables for the neural network model constructed in the form of a multilayer perceptron. In general, the artificial neural network has good potential for predicting and estimating monthly total ozone on the basis of the meteorological predictors. It was further observed that during pre-monsoon and winter seasons, the proposed models perform better than during and after the monsoon.

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The authors wish to express their sincere thanks to the anonymous reviewers for providing constructive comments and suggestions to enhance the quality of the manuscript.

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Correspondence to Surajit Chattopadhyay.

Annexure I

Annexure I

It sometimes happens that the size N of the available sample is small compared with the number of weights of the neural network. The resulting neural model is considered overparameterized. When the number of training examples is finite, the generalization error is different from the empirical risk function. Thus the network parameters converge to a biased solution. This is known as overfitting or overtraining (Amari et al., 1997). Association between overparameterization and overfitting has been discussed by Duprat et al. (1998). However, significant theoretical studies of overparameterized multilayer perceptron models have been conducted. De Veaux et al. (1998) worked on a one-hidden-layer perceptron with more than 200 weights trained with 61 data units comprising measurements taken from a polymer pilot plant. Lawrence et al. (1996, 1997) provided many simulations with overparameterized MLPs, concluding that oversized networks can result in low training and generalization errors. Bartlett (1998) showed that the generalization performance of a multilayer perceptron depends more on the \( L_{1} \) norm \( \left\| c \right\|_{1} \)of the weights between the hidden layer and the output layer than on the total number of weights. Based on the results of Bartlett (1998), Ingrassia and Morlini (2005) investigated the role of the weights of a neural network. With a suitable choice of mapping function they proved that the two levels of weights have quite different effects; the input-to hidden weights concern just a (nonlinear) projection from \( R^{\text{m} } \) to \( R^{\text{p} } \), whereas the hidden-to-output weights fit the projected data and perform the regression or the classification, according to the problem at hand. Ingrassia and Morlini (2005) further proved that both the projection and the fit are optimized according to the target values and, on the basis of this point of view, they concluded that the complexity of the network depends more on the number of hidden units than on the whole set of weights. On the basis of this theoretical view, in our work we generated ANN models with a limited dataset and the hold out method was adopted to support the generalization ability of the network.

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Chattopadhyay, S., Chattopadhyay, G. Modeling and Prediction of Monthly Total Ozone Concentrations by Use of an Artificial Neural Network Based on Principal Component Analysis. Pure Appl. Geophys. 169, 1891–1908 (2012). https://doi.org/10.1007/s00024-011-0437-5

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