Spatial Modeling, Analysis and Prediction of Nonstationary Environmental Processes

摘要： 空间模拟、分析和预测 非固定式环境探测器蒙特塞拉特富恩特斯，北卡罗来纳州州立大学理查德L。Smith，北卡罗来纳州，Chapel Hill空间统计是环境统计的主要方法之一;其应用包括产生空气污染场的空间平滑或插值表示，根据有限数量监测站的数据计算区域平均值或区域平均趋势，以及利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型的预测之间的一致性。 然而，最常用的空间统计方法，也称为地质统计学或克里金法，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异质油气田中成立。这里描述的研究集中在非平稳空间模型。介绍了一些新的模型，以及基于谱分析的新的拟合方法。这些应用包括三个真实的数据集：（i）硝酸盐场的监测数据与模型-3输出的比较，作为评估遵守1990年清洁空气法修正案过程的一部分;（ii）模拟颗粒物场的空间分布，作为改进颗粒物对人类健康影响的风险评估所需的组成部分之一;开发空间温度场的统计模型，并将其应用于气候模型产生的各种"信号"的归属-特别是，这一方法将有助于更好地评估观测到的全球气候变化在多大程度上可归因于人类活动的影响。 更详细地说，新的统计方法集中在两种方法的非平稳模型：由于Guttorp和Sampson的空间变形方法，以及一种方法，其中该字段被局部表示为一个平稳的各向同性随机场，但平稳随机场的参数被允许在空间上连续变化。核函数用于确保该字段是定义良好的，但也是连续的。这两种方法的某些组合可能需要既不是平稳的，也不是各向同性的字段。新的拟合算法的开发，使用空间域和频谱的方法;在数据分布的情况下，精确或近似的晶格上，有人认为，频谱的方法有潜在的巨大的计算效益相比，最大似然。该方法扩展到预测/插值问题，使用近似贝叶斯方法来考虑参数的不确定性。 我们开发的应用程序，以获得不同的地缘政治边界的污染物浓度和通量的总负荷，颗粒物随机场的风险评估，并将观测到的气候记录归因于数值气候模式产生的各种组件，后者形成了一种新的方法，气候学家开发的指纹估计技术。 该计划由数学科学部和数学和物理科学局多学科活动办公室共同资助。

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.