Prediction of tropospheric ozone concentrations: Application of a methodology based on the Darwin’s Theory of Evolution

Abstract

This study aims to predict the next day hourly average tropospheric ozone (O₃) concentrations using genetic programming (GP). Due to the complexity of this problem, GP is an adequate methodology as it can optimize, simultaneously, the structure of the model and its parameters. It is an artificial intelligence methodology that uses the same principles of the Darwinian Theory of Evolution. GP enables the automatic generation of mathematical expressions that are modified following an iterative process applying genetic operations.

The inputs of the models were the hourly average concentrations of carbon monoxide (CO), nitrogen oxide (NO), nitrogen dioxide (NO₂) and O₃, and some meteorological variables (temperature – T; solar radiation – SR; relative humidity – RH; and wind speed – WS) measured 24 h before. GP was also applied to the principal components (PC) obtained from these variables. The analysed period was from May to July 2004 divided in training and test periods.

GP was able to select the most relevant variables for prediction of O₃ concentrations. The original variables, T, RH and O₃ measured 24 h before were considered significant inputs for prediction. The selected PC had also important contributions of the same variables and of NO₂. GP models using the original variables presented better performance in training period and worse performance in test period when compared with the models obtained using PC. The results achieved using the GP methodology demonstrated that it can be very useful to solve several environmental complex problems.

Introduction

Ozone (O₃) is a strong photochemical oxidant present in different layers of the atmosphere. In the troposphere, this irritating and reactive gas has negative impacts on human health, climate, vegetation and materials (Bytnerowicz et al., 2006, Pires et al., 2008). Tropospheric ozone is the result of three basic processes: (i) photochemical production by the interaction of hydrocarbons and nitrogen oxides under the action of suitable ambient meteorological conditions (Guerra et al., 2004, Zolghadri et al., 2004); (ii) vertical transport of stratospheric air, rich in ozone, into the troposphere (Dueñas, Fernández, Cañete, Carretero, & Liger, 2002); and (iii) horizontal transport due to the wind that brings O₃ produced in other regions.

The formation of O₃ is a complex, nonlinear, time and space varying process. Accordingly, several studies presented different statistical approaches to predict O₃ concentrations (Al-Alawi et al., 2008, Coman et al., 2008, Omidvari et al., 2008, Pires et al., 2008a, Sousa et al., 2007, Sousa et al., 2006, Sousa et al., 2009), including linear and nonlinear models. The applied linear models found in the literature were: (i) multiple linear regression (MLR); (ii) principal component regression (PCR); (iii) quantile regression; and (iv) time series. On the other hand, the most common nonlinear model was the artificial neural network (ANN). The selection of a model must consider some features, such as, complexity, flexibility, accuracy and speed of computation (Pires, Martins, Sousa, Alvim-Ferraz, & Pereira, 2008b). ANN models usually presented better performance than the linear ones (Al-Alawi et al., 2008, Sousa et al., 2006, Sousa et al., 2007) due to the nonlinearity behaviour associated to the O₃ formation. However, they are included in a group called black box models, having limited interpretation. Moreover, the selection of the optimal network architecture and the computation time are the main disadvantages of these models.

Besides the structure, the success of a statistical model depends of several factors: (i) the data size; (ii) the method to optimize their parameters; (iii) the input variables; and (iv) the collinearity between the input variables. The collinearity between the input variables can be eliminated through the application of principal component analysis (PCA). It is mathematically defined as an orthogonal linear transformation that modifies the original data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on (Pires, Sousa, et al., 2008). Thus, the principal components (PC) are orthogonal and uncorrelated to each other, being determined by linear combinations of the original variables. The directions of the new coordinate axes are given by the eigenvectors of the covariance matrix of the original variables. The magnitude of the eigenvalues corresponds to the variance of the data along the eigenvector direction. Varimax rotation is the most widely employed orthogonal rotation in PCA, because it tends to produce simplification of the unrotated loadings to easier interpretation of the results. It simplifies the loadings by rigidly rotating the PC axes such that the variable projections (loadings) on each PC tend to be high or low. After the rotation, the loadings show the relative contributions of the original variables on each PC.

As many factors could influence the performance of models, their development should have more degrees of freedom. For the models referred above, their structure is fixed in advance and only the parameters are optimized. In stochastic processes, such as the prediction of O₃ concentrations, the structure of the models should be more flexible. In this context, genetic programming (GP) could be a successful methodology, as it does not assume in advance any structure for the model. GP can optimize both the structure of the model and its parameters, simultaneously. As far as it is known, no study was published applying GP for predicting air pollutant concentrations. This study aims to predict the next day hourly average O₃ concentrations applying GP to the original input variables and their correspondent principal components.