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：北卡罗来纳州立大学Richard L. Smith，北卡罗来纳大学的非组织环境过程的空间建模，分析和预测，北卡罗来纳州立大学，教堂山空间统计是环境统计学的主要方法之一；它的应用包括生产空气污染场的空间平滑或插值表示，根据数据以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，并执行具有空间相关误差的回归分析，以评估观察到的数据和某些数字模型的预测之间的一致性。 但是，最常用的空间统计方法（也称为地统计学或克里格）基本上是基于固定和各向同性随机场的假设。不能期望这种假设在大型异质领域中持有。此处描述的研究集中在非组织空间模型上。引入了一些新模型，以及基于光谱分析的新拟合方法。这些应用程序包括三个实际数据集：（i）与模型3输出相比，监视硝酸盐场的数据，这是评估1990年《清洁空气法》修正案的过程的一部分； （ii）对颗粒物领域的空间分布进行建模，这是改善颗粒物质人类健康影响风险评估所需的组成部分之一； （iii）开发用于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”的归因 - 特别是，这种方法将允许改进评估观察到的全球气候变化的程度可能归因于人为影响。 更详细地，新的统计方法集中在非组织模型的两种方法上：由于Guttorp和Sampson引起的空间变形方法，以及该方法在本地表示为固定的各向异性随机场，但是允许平稳随机场的参数在整个空间之间连续不断地变化。内核函数用于确保字段定义明确但也连续。可能需要两种方法的某种组合，而具有既不静止也不是各向同性的。使用空间域和光谱方法开发了新的拟合算法。如果数据精确或大致在晶格上分布，则认为光谱方法与最大似然相比具有巨大的计算益处。该方法使用近似贝叶斯方法扩展到预测/插值问题，以说明参数不确定性。 我们开发了用于在不同的地缘政治边界上获得污染物浓度和通量的总负荷，对颗粒物随机场的风险评估，以及观察到的气候记录归因于数值气候模型产生的各种组件的归因，后者形成了一种新的方法，以通过质地学技术形成了一种新方法。 该计划由数学科学划分以及数学和物理科学局的多学科活动办公室共同资助。