Phased sampling for soil remediation

In phased sampling, data obtained in one phase is used to design the sampling network for the next phase. GivenN total observations, 1, ...,N phases are possible. Experiments were conducted with one-phase, two-phase, andN-phase design algorithms on surrogate models of sites with contaminated soils. The sampling objective was to identify through interpolation, subunits of the site that required remediation. The cost-effectiveness of alternate methods was compared by using a loss function. More phases are better, but in economic terms, the improvement is marginal. The optimal total number of samples is essentially independent of the number of phases. For two phase designs, 75% of samples in the first phase is near optimal; 20% or less is actually counterproductive.The U.S. Environmental Protection Agency (EPA) through its Office of Research and Development (ORD), partially funded and collaborated in the research described here. It has been subjected to the Agency's peer review and has been approved as an EPA publication. The U.S. Government has a non-exclusive, royalty-free licence in and to any copyright covering this article.     

Hierarchical spatial modeling for estimation of population size

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.     

Spatial analysis of semi-arid patchy vegetation by the cumulative distribution of patch boundary spacings and transition probabilities

The vegetative cover in semi-arid lands typically occurs as patches of individual species more or less separated from one another by bare ground. We have adapted two methods to quantify the spatial pattern of such cover from measurements across patches on transects.Transects were laid in several directions across digital maps of the land surface or across the land itself, and the distances between successive patch boundaries were measured. The distances were ranked in order, and their cumulative distributions were computed and modeled with gamma functions. The parameters of the model provided estimates of the mean distance across patches. The means for different directions were further tested for anisotropy. Transitions between classes on the transects estimate the probabilities with which the different species occur next to others (and to bare ground) and so describe the arrangement of the patches occupied by the different species.The methods were tested with data from mosaic patterns at three semi-arid sites dominated by the tussock grass Stipa tenacissima. The differences in the estimated mean boundary spacings from site to site accorded with prior qualitative assessment, as did the estimated anisotropy. The transition matrices and the estimated proportions of cover showed the dominance of the bare soil with which all the individual species are intimately associated. The transitions also suggest the presence of both positive and negative relations among the main species. Those between Stipa tenacissima and Brachypodium retusum seem to be facilitative, as do those between this grass and the shrub Anthyllis cytisoides. In contrast, Globularia alypum seems to inhibit the other species.We also estimated transition probabilities geostatistically by summing the indicator variograms of the individual species. Standard variogram models were then fitted to describe the ordered series of values, and these again produced results that accorded with visual impressions.     

GIS and geostatistics: Essential partners for spatial analysis

Initially, geographical information systems (GIS) concentrated on two issues: automated map making, and facilitating the comparison of data on thematic maps. The first required high quality graphics, vector data models and powerful data bases, the second is based on grid cells that can be manipulated by suites of mathematical operators collectively termed map algebra. Both kinds of GIS are widely available and are taught in many universities and technical colleges. After more than 20 years of development, most standard GIS provide both kinds of functionality and good quality graphic display, but until recently they have not included the methods of statistics and geostatistics as tools for spatial analysis. Recently, standard statistical packages have been linked to GIS for both exploratory data analysis and statistical analysis and hypothesis testing. Standard statistical packages include methods for the analysis of random samples of cases or objects that are not necessarily co-located in space—if the results of statistical analysis display a spatial pattern then that is because the underlying data also share that pattern. Geostatistics addresses the need to make predictions of sampled attributes (i.e., maps) at unsampled locations from sparse, often expensive data. To make up for lack of hard data geostatistics has concentrated on the development of powerful methods based on stochastic theory. Though there have been recent moves to incorporate ancillary data in geostatistical analyses, insufficient attention has been paid to using modern methods of data display for the visualization of results. GIS can serve geostatistics by aiding geo-registration of data, facilitating spatial exploratory data analysis, providing a spatial context for interpolation and conditional simulation, as well as providing easy-to-use and effective tools for data display and visualization. The value of geostatistics for GIS lies in the provision of reliable interpolation methods with known errors, methods of upscaling and generalization, and for supplying multiple realizations of spatial patterns that can be used in environmental modeling. These stochastic methods are improving understanding of how errors in models of spatial processes accrue from errors in data or incompleteness in the structure of the models. New developments in GIS, based on ideas taken from map algebra, cellular automata and image analysis are providing high level programming languages for modeling dynamic processes such as erosion or the development of alluvial fans and deltas. Research has demonstrated that these models need stochastic inputs to yield realistic results. Non-stochastic tools such as fuzzy subsets have been shown to be useful for spatial analysis when probabilistic approaches are inappropriate or impossible. The conclusion is that in spite of differences in history and approach, the linkage of GIS, statistics and geostatistics provides a powerful, and complementary suite of tools for spatial analysis in the agricultural, earth and environmental sciences.     

土壤多环芳烃污染的地统计学研究进展

土壤中的多环芳烃对人体健康具有潜在的危害。应用地统计学的方法研究土壤多环芳烃的空间特性,以及在此基础上开展风险评价、污染源识别、土壤修复等工作,是土壤多环芳烃研究的重要方向之一。文章介绍了国内外在这个领域的研究成果,并提出了此领域的发展方向展望。     

基于条件模拟的污染场地土壤修复量的确定研究

针对一般空间插值方法的局限性,以某铁合金厂污染场地为例,利用基于地统计的条件模拟法对研究区待修复的范围及土方量进行评估,定量评价土壤修复量估算结果的不确定性所带来的风险大小,并引入传递函数量化决策结果与风险损失之间的关系,提出一种以风险损失最小化为原则的修复范围划定方法.同时,将结果与利用反距离权重法、径向基函数法和普通克里格法得到的评估结果进行对比分析.研究结果显示,利用条件模拟法可以得到超过修复目标的污染概率的空间分布,进而得到确定不同土壤修复量时所面对的风险大小.研究区大部分面积的土壤中Mn的超标概率在20%~70%,超标概率较高的区域集中在场区北部和西南部.如果分别将超标概率在30%和50%以上的区域作为修复范围,所面对的相对风险值将分别为4.1%和56.5%.此外,通过与传递函数相结合,利用条件模拟法可以得到基于风险损失的修复范围,按照本研究所设定的风险损失条件,得到风险损失最小的待修复土方量为32.4×104m3.该方法将有助于决策者从风险损失出发对污染场地修复范围进行合理划定.     

基于GIS下的太湖水质富营养化模糊综合评价

在地理信息系统和地统计学的支持下,探讨了模糊数学与层次分析法相结合的方法在水体富营养化评价中的应用.以太湖为研究对象,选取总磷、总氮、叶绿素、化学需氧量、5日生化需氧量、溶解氧和透明度7项指标进行评价.在对研究区域采样数据进行地统计分析后估算出整个区域评价指标的值,在此基础上建立不同指标的隶属度函数,并计算其隶属度;同时根据层次分析法的原理,确定了各项评价指标的权重,最终得到研究区域的综合结果,绘制出富营养化评价图.结果表明:北部、西北部湖区营养水平最高,属重富营养;中部湖区营养程度为中富营养;东南部湖区营养水平最低,属中营养.     

白洋淀及周边土壤重金属的分布特征及生态风险评估

为了解白洋淀土壤重金属污染现状和潜在生态风险,采集白洋淀区域表层土壤样本55个并检测锰（Mn）、铬（Cr）、铜（Cu）、锌（Zn）、砷（As）、镉（Cd）、铅（Pb）和镍（Ni）等8种重金属的含量.采用地统计学方法（莫兰指数和半方差函数）分析其空间变异结构和分布格局,运用地累积指数（I_geo）和潜在生态风险指数（E_rⁱ和RI）评估了重金属污染的程度及其风险.结果表明,研究区土壤重金属ω（Mn）、ω（Cr）、ω（Cu）、ω（Zn）、ω（As）、ω（Cd）、ω（Pb）和ω（Ni）平均值分别为467.75、43.59、28.57、89.04、12.32、0.18、19.26和30.56 mg ·kg^-1,均低于农用地土壤污染风险筛选值,但Cu、Zn和Cd明显高于背景值,其中,Cu （48.65%）和Cd （37.52%）为高度变异元素.莫兰指数显示Mn、Cu、Cd和Pb空间自相关不显著,半方差函数模型拟合显示Cd和Pb的块金系数均为100%,说明其空间变异由随机变异主导,受人为因素影响较大.重金属高值区主要分布在白洋淀的西南部地区,并且元素之间均有显著的相关性,表现为复合污染.重金属污染程度I_geo从高到低依次为：Cd>Cu>Zn>Ni>As>Pb>Mn>Cr,其中,Cd污染最为普遍,67.27%的样本为轻度污染.风险评估（E_rⁱ）显示,Cd的E_rⁱ平均值为58.81,属于中等程度生态风险;其他重金属均为轻微生态风险.研究区土壤重金属污染RI为轻微生态风险（87.81）,其中,Cd对RI的贡献率最高（66.39%）.因此,未来需要加强对白洋淀西南部重点区域重金属Cd污染的监测和治理.     

基于地统计学分析的太湖颗粒态和溶解态氮、磷营养盐时空分布特征及来源分析

研究水体氮、磷营养盐的空间变异性及时空动态变化,有助于人们深入认识和了解氮、磷营养盐的变化对藻类生长繁殖的影响,对于治理富营养化水体中藻类的暴发性增长具有重要意义.基于地统计学分析方法,以太湖2014年8月～2015年5月夏、秋、冬、春四季为研究时段,分析了草、藻型等不同生态类型湖区颗粒态和溶解态氮、磷营养盐的来源以及赋存形态,营养盐限制类型的时空分布特征,并探寻其时空变化原因.结果表明:(1)时空分布上,水体中氮、磷含量整体表现为冬季高于其他季节,呈现由西北湖区向东南湖区递减的特征;颗粒态氮、磷与叶绿素a含量则表现为夏季高于其他季节,冬季高值区均位于南部湖区,其余季节高值区集中在西北湖区.(2)随季节变化,太湖草、藻型湖区氮磷营养盐形态组成发生了大的变化;藻型湖区由冬季以硝酸盐氮和有机磷为主,转变为其余季节以颗粒态氮磷为主,而草型湖区由冬季以颗粒态氮磷为主,转变为其余季节以氨氮和有机氮磷为主.(3)营养结构上,藻型湖区总氮/总磷比值由秋冬季节大于16,降低为夏春季节的小于16;而草型湖区却由秋冬季节小于16,升高为夏春季节大于16.溶解态氮磷比在藻型湖区的空间变化规律与总氮/总磷比值一致,而在草型湖区溶解态氮磷比由秋季小于16,升高为夏、冬、春季节大于16.颗粒态氮磷比时空变化均不显著(P 0. 05),各季节藻型湖区颗粒态氮磷比值均小于16,草型湖区均大于16.     

亚高山草甸土壤呼吸的空间异质性研究

运用传统和地统计学的方法,对山西云顶山亚高山草甸的土壤呼吸、土壤温度、土壤水分和土壤有机碳的空间异质性以及它们的关系进行了分析.传统统计分析表明,土壤呼吸及环境因子均呈正态分布,变异系数在12%~24%之间,属于中等变异;土壤呼吸和土壤有机碳的相关系数(r=0.61)大于和温度(r=0.27)、水分(r=0.26)的相关系数,表明土壤有机碳对土壤呼吸空间分布的影响要远大于土壤温度和水分的影响.地统计学分析结果表明,线性模型能很好地反映土壤呼吸以及环境因子的空间结构特征.土壤呼吸、土壤温度、土壤水分及土壤有机碳的C0/(C0+C)值分别为41%、3%、77%、57%,表明土壤温度具有高度的空间自相关性,土壤呼吸和土壤有机碳具有中等程度的空间自相关性,土壤水分表现出较弱的空间自相关性,结构因素对土壤温度和土壤呼吸的空间分布起着主导作用,而随机因素对土壤水分和土壤有机碳的空间变异则起着主导作用;土壤呼吸、温度和水分的变程均为53.2 m,有机碳的变程为52.1 m;土壤呼吸和土壤温度具有较好的分形特征,存在尺度上的依赖性.分维数从大到小依次为:土壤水分(1.96)>土壤有机碳(1.95)>土壤呼吸(1.85)>土壤温度(1.60),表明土壤水分依赖于尺度的变异最小,空间分布结构最复杂,而土壤温度的空间分布格局最简单;土壤呼吸的空间分布表现出与土壤水分和有机碳相似的特点,并表现出自己的规律性.随着置信水平和估计精度的降低,土壤呼吸及其影响因子所要求的采样数量均出现较大幅度的下降.