Hierarchical modeling of count data with application to nuclear fall-out

We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R². We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998).     

Estimating the area affected by phosphorus runoff in an Everglades wetland: a comparison of universal kriging and Bayesian kriging

Phosphorus-enriched agriculture runoff is believed to be the leading cause of ecosystem changes of Everglades wetlands. To study this effect, it is necessary to estimate the area of the affected region. In this study, Bayesian kriging and universal kriging were used to estimate the area by analysing the data collected by Reddy et al. (1991). The background level of the soil's total phosphorus concentration is usedto determine whether the region is affected by the agriculture runoff, through an indicator function. The area of the affected region was represented by the integration of the indicator function over the entire wetland. The expected value of the affected area was calculated using the results derived from Bayesian and universal kriging. The outcome indicates that universal kriging is sensitive to specification of thecovariance model. It was observed that universal kriging and Bayesian kriging yield comparable results, if the specified covariance structures are of similar nature.     

河北省土壤苯并(a)芘含量的空间变异特征

根据实地采样数据,运用地统计学方法分析苯并(a)芘污染的空间变异特征,同时研究各地污染水平与其自然环境、产业布局之间的关系。结果表明:土壤苯并(a)芘含量在研究区存在空间异质性,在240 km空间尺度上尤其明显,块金值(C0)和基台值(C0 C)之比为44%;这说明其空间变异由结构性因子(如土壤有机质)和随机性因子(如污染源分布)共同构成;钢铁工业(包括焦化工)是苯并(a)芘的主要排放源,土壤苯并(a)芘污染也以钢铁工业(包括焦化工)发达的城市及其附近区域为核心。     

Application of geostatistical methods to arsenic data from soil samples of the Cova dos Mouros mine (Vila Verde-Portugal)

A total of 286 soil samples were collected in the Cova dos Mouros area. All samples were dry sieved into the <200 mesh size fraction and analysed for Fe, Cu, Zn, Pb, Co, Ni, Bi and Mn by atomic absorption spectrometry (AAS) and for As, Se, Sb and Te by atomic absorption spectrometry-hydrid generation (AAS-HG). Only the results of arsenic are discussed in this paper although the survey was extended to all analysed chemical elements. The purpose of this study was to make a risk probability mapping for arsenic that would allow better knowledge about the vulnerability of the soil to arsenic contamination. To achieve this purpose, the initial variable was transformed into an indicator variable using as thresholds the risk-based standards (intervention values) for soils, as proposed by [Swartjes 1999. Risk based assessment of soil and groundwater quality in the Netherlands: Standards and remediation. J. Geochem. Explor.73 1–10]. To account for spatial structure, sample variograms were computed for the main directions of the sampling grid and a spherical model was fitted to each sample variogram (arsenic variable and indicator variables). The parameters of the spherical model fitted to the arsenic variable were used to predict arsenic concentrations at unsampled locations. A risk probability mapping was also done to assess the vulnerability of the soil towards the mining works. The parameters of the spherical model fitted to each indicator variable were used to estimate probabilities of exceeding the corresponding threshold. The use of indicator kriging as an alternative to ordinary kriging for the soil data of Cova dos Mouros produced unbiased probability maps that allowed assessment of the quality of the soil.     

地统计学在太湖水质研究中的应用

在采样数据的基础上，应用地统计学的理论与方法，尝试研究太湖水质参数空间的分布特性。结果显示，太湖水质量参数的空间结构变异性是客观存在的，各水质参数都具有块金效应，对太湖参数进行克立格插值。并进行污染水平分类，可以提供更为直观的环境信息，研究结果对太湖的水环境有一定的参考价值。     

黄土高原不同地貌区土壤有机碳空间变异与合理取样数研究

论文运用经典统计学和地统计学相结合的方法,以黄土高原典型地貌丘陵沟壑区(庄浪县)与平原区(武功县)为例,探讨了土壤有机碳空间变异特征及县域尺度土壤有机碳的合理采样数。研究表明,丘陵沟壑区有机碳的变异系数较小,变化范围在0.176 到0.200 之间,平原区较沟壑区大,变化范围在0.24 到0.26 之间,基于经典统计学,在5%的精度要求和95%的置信区间,沟壑区的合理样本数为64 个,平原区为110 个。丘陵沟壑区与平原区两区域都呈现出强烈的空间相关性且变程较小,分别为2 250、900 m,庄浪县土壤有机碳含量高值区斑块较破碎,东部较西部多、北部比南部多;武功县土壤有机碳含量西南与中部地区含量较高,高值区比庄浪县相对集中。根据土壤有机碳的空间相关性和克里格插值的独立验证得出庄浪县与武功县的合理采样数分别为903、1 838 个,合理样本数的确定对合理评价黄土高原地区碳储量的预测精度有重要意义。     

珠三角区域PM2.5时空变异特征

珠三角区域PM_2.5污染严重,以 2012年9月─2013年8月62个大气监测站的PM_2.5联网数据为基础,采用地统计学方法定性、定量分析了该区域ρ(PM_2.5)的时空变异特征. 定性分析结果表明,基底效应在0.12~0.30之间,相应ρ(PM_2.5)变异属于以结构性变异为主的Ⅰ、Ⅱ类,对应的空间自相关程度为强、较强,说明珠三角区域的ρ(PM_2.5)分布差异主要由区域结构所致. 定量分析结果表明:①空间自相关距离受气象因素影响,随方向和时间在51~85 km之间变化,东西方向的影响距离(75~85 km)最大. ②ρ(PM_2.5)在南北方向的变异幅度指数(0.34~0.70)和变异速度指数〔0.14~0.38 μg/(m3·km)〕在各方向中均为最大;而东北─西南方向的2个指标则均为最小,其中变异幅度指数为0.25~0.42,变异速度指数在0.13~0.34 μg/(m3·km)之间,即南北方向的ρ(PM_2.5)变化大于其他方向.③综合异质指数介于0.14~0.54之间,说明ρ(PM_2.5)总体保持在中等异质水平. 鉴于珠三角区域ρ(PM_2.5)的空间变异特征,在进行监测站布设时,矩形网格相较于方形网格更适合于对该区域地理空间进行划分,其中网格的长为东西方向平均空间自相关距离(78 km)的2倍,宽为南北方向平均空间自相关距离(56 km)的2倍.      

关中盆地县域农田土壤碱解氮空间分异及变化研究

论文以陕西省兴平市为例,采用2009年实测的耕层土壤碱解氮数据,运用地统计学结合GIS技术,建立其最佳半方差函数模型,分析关中盆地农田土壤碱解氮的空间特征、丰缺状况及其含量变化,为土壤培肥和农业生产提供理论基础。结果表明:研究区土壤碱解氮含量介于7.70~82.60 mg·kg^-1,多集中在30~40 mg·kg^-1,平均37.76 mg·kg^-1,较第二次土壤普查下降28.62%。在间距约300 m的采样尺度下,最优理论模型为指数模型,表现为弱的空间相关性,施肥管理、种植制度等随机因素起主导作用。含量高低区域分布明显,大致呈中间高四周低格局。72.67%的农田氮素缺乏,27.33%的农田氮素含量中等。近30 a,原土壤碱解氮1~3级农田区含量显著下降,原5、6级区有所改善,整体集中于4级水平。应进一步实地考察分析具体障碍因素,积极采取分区"补氮"措施。     

土壤-水稻系统重金属空间异质性研究——以浙江省嵊州市为例

在嵊州农产品产地共采集94对土壤-水稻样品,研究重金属在土壤-水稻系统的污染特征及空间异质性.结果表明,土壤重金属Cd、Cu、Ni、Pb和Zn的平均含量分别为0.20、28.64、27.03、38.51和98.74mg/kg,与背景值相比较,这些重金属在研究区均有不同程度的累积,局部污染严重,但是水稻重金属没有超过国家规定的食品安全标准,仍处于安全水平.土壤重金属Cd、Cu、Ni、Pb和Zn都属于中等程度变异,其变异系数分别为45.00%、46.65%、81.54%、18.07%、32.47%.地统计学和局部Moran's I指数结果可识别出这五个重金属的污染分布情况.土壤Cd、Cu、Ni和Zn的空间分布较为相似,基本为东西部含量较低,中部较高,这与工业活动和其他的人为活动有关.土壤-水稻系统重金属的迁移、吸收主要受土壤重金属含量和土壤理化性状的影响.从长远来看,重金属污染对当地生态和居民健康仍有潜在的威胁.     

沙地退化植被恢复过程中植被的空间异质性

通过野外取样和室内分析,应用地统计学分析方法研究了科尔沁沙地退化植被恢复过程中不同封育年限（0、11和20年）的流动沙丘的植被盖度和丰富度特征及其空间异质性规律。结果表明,随着流动沙丘的固定和封育年限的增加,植被盖度和丰富度逐渐增加。在流动沙丘植被恢复过程中,植被盖度和丰富度具有明显的空间自相关性,其空间自相关范围从封育0年的流动沙丘（46.05m和33.63m）、封育11的流动沙丘（21.63m和17.25m）到封育20年的流动沙丘（26.12m和24.18m）先减小后增加,但均未超出我们的研究尺度50m,表现出不同大小的斑块形式分布的小尺度分布格局。由半方差函数及其参数和空间分布格局图分析得出,随着沙丘植被的恢复,植被特征的空间异质性在所研究的尺度上表现出先增大（封育0年到封育11年）后减小（封育11年到封育20年）的变化特点。