Spatial Modeling, Analysis and Prediction of Nonstationary Environmental Processess

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Abstract: SPATIAL MODELING, ANALYSIS AND PREDICTION OF NONSTATIONARY ENVIRONMENTAL PROCESSESMontserrat Fuentes, North Carolina State UniversityRichard L. Smith, University of North Carolina, Chapel HillSpatial statistics is one of the major methodologies of environmental statistics; its applications include producing spatially smoothed or interpolated representations of air pollution fields, calculating regional average means or regional average trends based on data at a finite number of monitoring stations, and performing regression analyses with spatially correlated errors to assess the agreement between observed data and the predictions of some numerical model. However, the most commonly used spatial statistics methodology, also known as geostatistics or kriging, is essentially based on the assumption of stationary and isotropic random fields. Such assumptions cannot be expected to hold in large heterogeneous fields. The research described here concentrates on nonstationary spatial models. Some new models are introduced, as well as new fitting methods based on spectral analysis. The applications include three real data sets: (i) monitoring data for nitrate fields compared with Models-3 output as part of the process for assessing compliance with the Clean Air Act Amendments of 1990; (ii) modeling the spatial distribution of particulate matter fields, as one of the components needed for an improved risk assessment of human health effects of particulate matter; (iii) developing statistical models for spatial temperature fields and applying them to the attribution of various "signals" produced by climate models - in particular, this methodology will permit improved assessment of the extent to which observed global climate change may be attributed to anthropogenic influences. In more detail, the new statistical methodology concentrates on two approaches to nonstationary models: a spatial deformation approach due to Guttorp and Sampson, and an approach where the field is represented locally as a stationary isotropic random field, but the parameters of the stationary random field are allowed to vary continuously across space. Kernel functions are used to ensure that the field is well-defined but also continuous. Some combination of the two approaches may be needed for fields with are neither stationary nor isotropic. New fitting algorithms are developed, using both space domain and spectral approaches; in cases where the data are distributed exactly or approximately on a lattice, it is argued that spectral approaches have potentially enormous computational benefits compared with maximum likelihood. The methods are extended to prediction/interpolation questions using approximate Bayesian approaches to account for parameter uncertainty. We develop applications to obtaining the total loading of pollutant concentrations and fluxes over different geo-political boundaries, to risk assessment for particulate matter random fields, and to the attribution of an observed climate record to various components produced by numerical climatic model, the latter forming a new approach to the fingerprint estimation technique developed by climatologists. This program is being jointly funded by the Division of Mathematical Sciences and the Office of Multidisciplinary Activities from the Directorate of Mathematical and Physical Sciences.