Robert J. Foxall

Modelling SO2 concentration at a point with statistical approaches

In this paper, the results obtained by inter-comparing several statistical techniques for modelling SO2 concentration at a point such as neural networks, fuzzy logic, generalised additive techniques and other recently proposed statistical approaches are reported. The results of the inter-comparison are the fruits of collaboration between some of the partners of the APPETISE project funded under the Framework V Information Societies and Technologies (IST) programme. Two different cases for study were selected: the Siracusa industrial area, in Italy, where the pollution is dominated by industrial emissions and the Belfast urban area, in the UK, where domestic heating makes an important contribution. The different kinds of pollution (industrial/urban) and different locations of the areas considered make the results more general and interesting. In order to make the inter-comparison more objective, all the modellers considered the same datasets. Missing data in the original time series was filled by using appropriate techniques. The inter-comparison work was carried out on a rigorous basis according to the performance indices recommended by the European Topic Centre on Air and Climate Change (ETC/ACC). The targets for the implemented prediction models were defined according to the EC normative relating to limit values for sulphur dioxide. According to this normative, three different kinds of targets were considered namely daily mean values, daily maximum values and hourly mean values. The inter-compared models were tested on real cases of poor air quality. In the paper, the inter-compared techniques are ranked in terms of their capability to predict critical episodes. A ranking in terms of their predictability of the three different targets considered is also proposed. Several key issues are illustrated and discussed such as the role of input variable selection, the use of meteorological data, and the use of interpolated time series. Moreover, a novel approach referred to as the technique of balancing the training pattern set, which was successfully applied to improve the capability of ANN models to predict exceedences is introduced. The results show that there is no single modelling approach, which generates optimum results in terms of the full range of performance indices considered. In view of the implementation of a warning system for air quality control, approaches that are able to work better in the prediction of critical episodes must be preferred. Therefore, the artificial neural network prediction models can be recommended for this purpose. The best forecasts were achieved for daily averages of SO2 while daily maximum and hourly mean values are difficult to predict with acceptable accuracy.

Heteroscedastic kernel ridge regression

In this paper we extend a form of kernel ridge regression (KRR) for data characterised by a heteroscedastic (i.e. input dependent variance) Gaussian noise process, introduced in Foxall et al. (in: Proceedings of the European Symposium on Artificial Neural Networks (ESANN-2002), Bruges, Belgium, April 2002, pp. 19–24). It is shown that the proposed heteroscedastic kernel ridge regression model can give a more accurate estimate of the conditional mean of the target distribution than conventional KRR and also provides an indication of the spread of the target distribution (i.e. predictive error bars). The leave-one-out cross-validation estimate of the conditional mean is used in fitting the model of the conditional variance in order to overcome the inherent bias in maximum likelihood estimates of the variance. The benefits of the proposed model are demonstrated on synthetic and real-world benchmark data sets and for the task of predicting episodes of poor air quality in an urban environment.

Error Functions for Prediction of Episodes of Poor Air Quality

Prediction of episodes of poor air quality using artificial neural networks is investigated. Logistic regression,con ventional sumof-squares regression and heteroscedastic sum-of-squares regression are employed for the task of predicting real-life episodes of poor air quality in urban Belfast due to SO2. In each case,a Bayesian regularisation scheme is used to prevent over-fitting of the training data and to provide pruning of redundant model parameters. Non-linear models assuming a heteroscedastic Gaussian noise process are shown to provide the best predictors of pollutant concentration of the methods investigated.

Nonlinear modelling of air pollution time series

An analysis of predictability of a nonlinear and nonstationary ozone time series is provided. For rigour, the deterministic versus stochastic (DVS) analysis is first undertaken to detect and measure inherent nonlinearity of the data. Based upon this, neural and linear adaptive predictors are compared on this time series for various filter orders, hence indicating the embedding dimension. Simulation results confirm the analysis and show that for this class of air pollution data, neural, especially recurrent neural predictors, perform best.

Estimating the Costs Associated with Worthwhile Predictions of Poor Air Quality

In this study we investigate the effect of varying the ratio of false-positive and false-negative misclassification costs on the sensitivity and selectivity of binary predictions of exceedences of atmospheric pollutants. This allows us to determine a window of values far this ratio far which it is worthwhile making definite rather than probabilistic predictions. The support vector machine provides a suitable statistical pattern recognition method for this work.

On Predictability of Atmospheric Pollution Time Series

Atmospheric pollution is a health hazard. Thus, an accurate prediction of atmospheric pollution time series is almost a necessity nowdays. The existence of missing data further complicates this challenging problem. The cubic spline interpolation method is applied on the hourly measurements of nitrogen oxide (NO), nitrogen dioxide (NO 2), ozone (O 3), and dust partides (PM10). In order to asses predictability of an air pollution time series, a class of gradient-descent based neural adaptive filters is employed. Results indicate that, yet simple, this class of neural adaptive filters is a suitable solution.