Spatial Modeling, Analysis and Prediction of Nonstationary Environmental Processess

摘要：非平稳环境过程的空间建模、分析和预测北卡罗来纳州立大学蒙特塞拉特·富恩特斯，北卡罗来纳大学教堂山分校理查德·L·史密斯空间统计学是环境统计学的主要方法之一；它的应用包括产生空气污染场的空间平滑或内插表示，基于有限数量监测站的数据计算区域平均或区域平均趋势，以及使用空间相关误差进行回归分析，以评估观测数据与某些数值模式的预测之间的一致性。然而，最常用的空间统计方法，也称为地统计学或克里格法，基本上是基于平稳和各向同性随机场的假设。不能指望这样的假设在大型非均质油田中成立。这里描述的研究集中在非平稳空间模型上。介绍了一些新的模型，以及基于谱分析的新的拟合方法。这些应用包括三组实际数据集：(1)硝酸盐数据与作为评估1990年《清洁空气法修正案》遵守情况的进程一部分而产出的模型3的比较；(2)建立颗粒物场的空间分布模型，作为改进对颗粒物对人体健康影响的风险评估所需的组成部分之一；(3)开发空间温度场统计模型，并将其应用于气候模型产生的各种“信号”的归属--特别是，这一方法将有助于改进对所观察到的全球气候变化在多大程度上可归因于人为影响的评估。更详细地说，新的统计方法集中在两种非平稳模型的方法上：一种是由Guttorp和Sampson引起的空间变形方法，另一种是将场局部表示为平稳的各向同性随机场，但允许平稳随机场的参数在空间上连续变化。核函数用于确保字段定义良好，但也是连续的。对于既不是平稳的也不是各向同性的场，可能需要这两种方法的某种组合。新的拟合算法被开发出来，使用空间域和谱方法；在数据精确或近似分布在一个格子上的情况下，与最大似然法相比，谱方法具有潜在的巨大计算优势。使用近似贝叶斯方法将该方法扩展到预测/内插问题，以考虑参数的不确定性。我们开发的应用程序用于获得不同地缘政治边界上的污染物浓度和通量的总负荷，颗粒物随机场的风险评估，以及将观测到的气候记录归因于数值气候模式产生的各种分量，后者形成了气候学家开发的指纹估计技术的新方法。这项计划由数学科学部和数学和物理科学局的多学科活动办公室联合资助。

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.