Accounting for spatially varying directional effects in spatial covariance structures

Wind direction plays an important role in the spread of air pollutants over a geographical region. We discuss how to include wind directional information in the covariance function of spatial models. Our models are based on a constructive convolution approach, wherein a spatial process is described as a convolution between a spatially varying smoothing kernel and a white noise process. We describe two different ways of accounting for wind direction: one makes use of a non-stationary version of the Matérn covariance function and the other a kernel function that resembles the exponential correlation function. We fit the models proposed to ground level ozone observed at a monitoring network in north-eastern USA. We compare our wind-based covariance models with three other models: two that make use of standard covariance functions, and one whose kernel function varies across space according to latent spatial processes. The inference procedure is performed under the Bayesian paradigm, and uncertainty about parameter estimation is naturally accounted for when performing spatial interpolation. Samples from the posterior distribution under our proposed models are obtained much faster when compared with the model based on latent spatial processes. Although fitted values that are obtained under our proposed models and those obtained based on latent processes are quite similar, our models provided smaller ranges of the predictive posterior credible intervals.