In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model non-stationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and discuss methods to assess its dependence on local covariate information by means of a simulation study and the analysis of data observed at ozone-monitoring stations in the Southeast United States.

We explore the ability of a process-based space-time model to decompose 8-hour ozone on a given day and site into parts attributable to local emissions and regional transport, to provide space-time predictions, and to assess the efficacy of past and future emission controls. We model ozone as created plus transported plus an error with seasonally varying spatial covariance parameters. Created ozone is a function of the observed NO x concentration, the latent VOC concentration, and solar radiation surrogates. Transported ozone is a weighted average of the ozone observed at all sites on the previous day, where the weights are a function of wind speed and direction. The latent VOC process mean includes emissions, temperature, and a workday indicator, and the error has seasonally varying spatial covariance parameters. Using likelihood methods, we fit the model and obtain one set of predictions appropriate for prediction backward in time, and another appropriate for predicting under hypothetical emission scenarios.The first set of predictions has a lower root-mean-squared error (RMSE) when compared to point observations than do the 36 km gridcell averages from the Community Mesoscale Air Quality Model (CMAQ) used by the EPA; the second set has the same RMSE as CMAQ, but under-predicts high ozone values.

Climate change is increasing variation in freshwater input and the intensity of this variation in estuarine systems throughout the world. Estuarine salinity responds to dynamic meteorological and hydrological processes with important consequences to physical features, such as vertical stratification, as well as living resources, such as the distribution, abundance and diversity of species. We developed and evaluated two space-time statistical models to predict bottom salinity in Pamlico Sound, NC: (i) process and (ii) time models. Both models used 20-years of observed salinity and contained a deterministic component designed to represent four key processes that affect salinity: (1) recent and long-term fresh water influx (FWI) from four rivers, (2) mixing with the ocean through inlets, (3) hurricane incidence, and (4) interactions among these variables. Freshwater discharge and distance from an inlet to the Atlantic Ocean explained the most variance in dynamic salinity. The final process model explained 89% of spatiotemporal variability in salinity in a withheld dataset, whereas the final time model explained 87% of the variability within the same withheld data set. This study provides a methodological template for modeling salinity and other normally-distributed abiotic variables in this lagoonal estuary.