Modeling complex environmental data.

Artificial neural networks (ANNs) are used to model the interactions that occur between ozone pollution, climatic conditions, and the sensitivity of crops and other plants to ozone. A number of generic methods for analysis and modeling are presented. These methods are applicable to the modeling and analysis of any data where an effect (in this case damage to plants) is caused by a number of variables that have a nonlinear influence. Multilayer perceptron ANNs are used to model data from a number of sources and analysis of the trained optimized models determines the accuracy of the model's predictions. The models are sufficiently general and accurate to be employed as decision support systems by United Nations Economic Commission for Europe (UNECE) in determining the critical acceptable levels of ozone in Europe. Comparison is made of the accuracy of predictions for a number of modeling approaches. It is shown that the ANN approach is more accurate than other methods and that the use of principal components analysis on the inputs can improve the model. The validation of the models relies on more than simply an error measure on the test data. The relative importance of the causal agents in the model is established in the first instance by summing absolute weight values. This indicates whether the model is consistent with domain knowledge. The application of a range of conditions to the model then allows predictions to be made about the nonlinear influences of the individual principal inputs and of combinations of two inputs viewed as a three-dimensional graph. Equations are synthesized from the ANN to represent the model in an explicit mathematical form. Models are formed with essential parameters and other inputs are added as necessary, in order of decreasing priority, until an acceptable error level is reached. Secondary indicators substituting for primary indicators with which they are strongly correlated can be removed. From the synthesized equations both known and novel aspects of the process modeled can be identified. Known effects validate the model. Novel effects form the basis of hypotheses which can then be tested.