Estimating Long-Term Trends in Tropospheric Ozone Levels

This paper estimates the long-term trends in the daily maxima of tropospheric ozone at six sites around the state of Texas. The statistical methodology we use controls for the effects of meteorological variables because it is known that variables such as temperature, wind speed and humidity substantially affect the formation of tropospheric ozone. A nonparametric regression model is estimated in which a general trivariate surface is used to model the relationship between ozone and these meteorological variables because there is little, or no, theory to specify the functional dependence of ozone on these variables. The model also allows for the effects of wind direction and seasonality. Each function in the model is represented as a linear combination of basis functions located at all of the design points. A trivariate basis is used for the function representing the combined effect of temperature, wind speed and humidity, while univariate bases are used to represent the other functions in the model. To estimate the functions nonparametrically we use a Bayesian hierarchical framework with a fractional prior. Due to the high dimensional representation of the signal, a Markov chain Monte Carlo sampling scheme employing Gibbs sub-chains that 'focus' on the basis terms that are most likely to contribute to the signal is used to carry out the computations. We also estimate an appropriate data transformation simultaneously with the function estimates. The empirical results indicate that key meteorological variables explain most of the variation in daily ozone maxima through a nonlinear interaction and that their effects are consistent across the six sites. However, the estimated trends vary considerably from site to site, even within the same city. A simulation based on the design of the data indicates that the Bayesian approach is substantially more efficient than MARS (Friedman, 1991).