Spatial Modeling, Analysis and Prediction of Nonstationary Environmental Processes

非平稳环境过程的空间建模、分析和预测

• 批准号: 0002790
• 负责人: Montserrat Fuentes
• 金额: $ 14.98万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0002790&HistoricalAwards=false
• 关键词: Spatial; Modeling; Analysis; Prediction; Nonstationary

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.

摘要：非平稳环境过程的空间建模、分析和预测蒙特塞拉特·富恩特斯，北卡罗来纳州立大学理查德·史密斯，北卡罗来纳大学教堂山分校空间统计是环境统计的主要方法之一；其应用包括生成空气污染场的空间平滑或插值表示，根据有限数量的监测站的数据计算区域平均平均值或区域平均趋势，以及使用空间相关误差进行回归分析以评估观测数据与实际数据之间的一致性。一些数值模型的预测。 然而，最常用的空间统计方法，也称为地统计学或克里金法，本质上是基于平稳和各向同性随机场的假设。这种假设不能指望在大型异质领域中成立。这里描述的研究集中于非平稳空间模型。引入了一些新模型以及基于谱分析的新拟合方法。这些应用程序包括三个真实数据集：(i) 与 Models-3 输出相比的硝酸盐田监测数据，作为评估 1990 年《清洁空气法修正案》遵守情况过程的一部分； ㈡ 对颗粒物场的空间分布进行建模，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； ㈢ 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"的归因，特别是，这种方法将有助于改进对观测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，新的统计方法集中于非平稳模型的两种方法：Guttorp 和 Sampson 提出的空间变形方法，以及将场局部表示为平稳各向同性随机场的方法，但平稳随机场的参数允许在空间上连续变化。核函数用于确保该字段定义明确且连续。对于既不平稳也不各向同性的场，可能需要两种方法的某种组合。使用空间域和谱方法开发了新的拟合算法；在数据精确或近似分布在格子上的情况下，有人认为，与最大似然相比，谱方法具有潜在的巨大计算优势。这些方法扩展到使用近似贝叶斯方法来解释参数不确定性的预测/插值问题。 我们开发的应用程序可以获取不同地缘政治边界上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型产生的各种组成部分，后者形成气候学家开发的一种新的指纹估计技术方法。 该计划由数学科学部和数学与物理科学局多学科活动办公室共同资助。