A statistical evaluation of non-ergodic variogram estimators

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.     

地统计学在土壤重金属研究中的应用及展望

从采矿学与地质学研究中发展起来的地统计学是应用数理统计学的一个分支。与传统的统计学相比，地统计学可应用于土壤重金属研究中，能探索土壤重金属的空间分布特征及其变异规律。地统计学的基础理论与方法主要包括：区域化变量、半方差函数、克立格空间插值技术。半方差函数可以用来描述研究土壤重金属分布的空间相关性；而克立格插值可以对未采样区土壤重金属的含量进行无偏最优估计。在对地统计学理论进行简要阐述的基础上，回顾了近些年在土壤重金属研究的采样设计、空间结构分析、空间插值等方面的应用，并就其应用前景作了展望。     

混合重金属对硝化颗粒污泥毒性作用的析因实验研究

分别测定了Cu2 、Zn2 和Cd2 对硝化颗粒污泥的单一毒性,采用析因实验研究了二元和三元重金属混合体系对硝化颗粒污泥的联合毒性.结果表明,Cu2 、Zn2 和Cd2 的2 h半抑制浓度EC50分别为95.23、62.11和12.48 mg/L,由析因实验所得的响应曲面模型具有较好的优度(其R2＞0.95),能够对混合体系的联合毒性很好地进行预测,析因实验可以用于环境领域混合体系联合毒性的研究.     

洋山工程影响海洋环境关键因子的分析

分析了洋山工程群可能对近海生态环境产生的影响。结果表明,就目前而言,洋山工程群对近海生态环境的影响主要表现在施工期。主要的影响有大堤修筑、码头和桥桩钻孔、航道疏浚、炸礁清石、爆破挤淤、海底管道铺设和陆域吹填等作业,并由此产生的水下振动、冲击波、高浓度悬浮物、石油烃、有机物和生物填埋等因子。高浓度悬浮物直接或间接地影响浮游生物、鱼卵、仔稚鱼和游泳动物幼体等生长;冲击波直接引起一定范围内鱼类的死亡;水下振动对鱼群有驱赶作用;石油烃和有机物污染水体;填埋导致底栖动物死亡。洋山工程群建设和营运过程中污水排放量较少,有机污染物对海洋环境影响有限。悬浮物和生物填埋是工程影响海洋生态环境的关键因子。施工期结束,洋山海域生态环境可能较快地得以恢复。     

An analytical platform for cumulative impact assessment based on multiple futures: the impact of petroleum drilling and forest harvesting on moose (Alces alces) and marten (Martes americana) habitats in northeastern British Columbia

The combined influence on the environment of all projects occurring in a single area is evaluated through cumulative impact assessments (CIA), which consider the consequences of multiple projects, each insignificant on its own, yet important when evaluated collectively. Traditionally, future human activities are included in CIA using an analytical platform, commonly based on complex models that supply precise predictions but with reduced accuracy. To compensate for the lack of accuracy in current CIA approaches, we propose a shift in the paradigm governing CIA. The paradigm shift involves a change in the focus of CIA investigations from the detailed analysis of one unlikely future to the identification of the patterns describing multiple potential future changes in the environment. To illustrate the approach, a set of 144 possible and equally likely futures were developed that aimed to identify the potential impacts of forest harvesting and petroleum drilling on the habitat suitability of moose and marten in northeast British Columbia, Canada. The evolution of two measures of habitat suitability (average habitat suitability index and surface of the stands with habitat suitability index >0.5) revealed that the human activities could induce cycles in the habitat dynamics of moose and marten. The planning period of 100 years was separated into three distinct periods following a sinusoidal pattern (i.e., increase - constant - decrease in the habitat suitability measures). The attributes that could induce significant changes in the assessment of environment are the choice of harvesting age and species.     

Accounting for rate instability and spatial patterns in the boundary analysis of cancer mortality maps

Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970–1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e., boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e., edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test.

Mapping the Spatial Variability of Plant Diversity in a Tropical Forest: Comparison of Spatial Interpolation Methods

Knowledge of the spatial distribution of plant species is essential to conservation and forest managers in order to identify high priority areas such as vulnerable species and habitats, and designate areas for reserves, refuges and other protected areas. A reliable map of the diversity of plant species over the landscape is an invaluable tool for such purposes. In this study, the number of species, the exponent Shannon and the reciprocal Simpson indices, calculated from 141 quadrat sites sampled in a tropical forest were used to compare the performance of several spatial interpolation techniques used to prepare a map of plant diversity, starting from sample (point) data over the landscape. Means of mapped classes, inverse distance functions, kriging and co-kriging, both, applied over the entire studied landscape and also applied within vegetation classes, were the procedures compared. Significant differences in plant diversity indices between classes demonstrated the usefulness of boundaries between vegetation types, mapped through satellite image classification, in stratifying the variability of plant diversity over the landscape. These mapped classes, improved the accuracy of the interpolation methods when they were used as prior information for stratification of the area. Spatial interpolation by co-kriging performed among the poorest interpolators due to the poor correlation between the plant diversity variables and vegetation indices computed by remote sensing and used as covariables. This indicated that the latter are not suitable covariates of plant diversity indices. Finally, a within-class kriging interpolator yielded the most accurate estimates of plant diversity values. This interpolator not only provided the most accurate estimates by accounting for the indices' intra-class variability, but also provided additional useful interpretations of the structure of spatial variability of diversity values through the interpretation of their semi-variograms. This additional role was found very useful in aiding decisions in conservation planning.     

A GIS-based approach to spatio-temporal analysis of environmental pollution in urban areas: A case study of Prague's environment extended by LIDAR data

Environmental pollution of urban areas is one of key factors that state authorities and local agencies have to consider in the decision-making process. To find a compromise among many criteria, spatial analysis extended by geostatistical methods and dynamic models has to be carried out. In this case, spatial analysis includes processing of a wide range of air, water and soil pollution data and possibly noise assessment and waste management data. Other spatial inputs consist of data from remote sensing and GPS field measurements. Integration and spatial data management are carried out within the framework of a geographic information system (GIS). From a modeling point of view, GIS is used mainly for the preprocessing and postprocessing of data to be displayed in digital map layers and visualized in 3D scenes. Moreover, for preprocessing and postprocessing, deterministic and geostatistical methods (IDW, ordinary kriging) are used for spatial interpolation; geoprocessing and raster algebra are used in multi-criteria evaluation and risk assessment methods. GIS is also used as a platform for spatio-temporal analyses or for building relationships between the GIS database and stand-alone modeling tools. A case study is presented illustrating the application of spatial analysis to the urban areas of Prague. This involved incorporating environmental data from monitoring networks and field measurements into digital map layers. Extra data inputs were used to represent the 3D concentration fields of air pollutants (ozone, NO₂) measured by differential absorption LIDAR. ArcGIS was used to provide spatial data management and analysis, extended by modeling tools developed internally in the ArcObjects environment and external modules developed with MapObjects. Ordinary kriging methods were employed to predict ozone concentrations in selected 3D locations together with estimates of variability. Higher ozone concentrations were found above crossroads with their heavy traffic than above the surrounding areas. Ozone concentrations also varied with height above the digital elevation model. Processed data, spatial analysis and models are integrated within the framework of the GIS project, providing an approach that state and local authorities can use to address environmental protection issues.     

Assessing the risk of soil contamination in the Swiss Jura using indicator geostatistics

The probability that the concentrations of toxic substances in soil or other medium exceed tolerablemaxima at any unsampled place can be estimated by indicator geostatistics. The method is developed and used to estimate and map the risk of contamination by cadmium, copper and lead in the topsoil of a 14.5 km 2 region in the Swiss Jura. It combines both direct measurements of metal concentrations and thecalibration of a geological map, and it shows that the risk of toxicity is least on Argovian rocks. Two approaches are proposed to divide a region into safe' and 'hazardous' zones on the basis of probability maps. The first declares as contaminated all places where the risk of contamination exceeds a given threshold. The second approach first evaluates the financial costs that might result from a wrongdeclaration, after which the site is allocated to a class so as to minimize that cost. The risk of exposure for humans and animals is generally greater for contaminated agricultural land than for forest soil, and so land use is taken into account in both procedures.     

Remote sensing: Using the spatial domain

Objects in the terrestrial environment interact differentially with electromagnetic radiation according to their essential physical, chemical and biological properties. This differential interaction is manifest as variability in scattered radiation according to wavelength, location, time, geometries of illumination and observation and polarization. If the population of scattered radiation could be measured, then estimation of these essential properties would be straightforward. The only problem would be linking such estimates to environmental variables of interest. This review paper is divided into three parts. Part 1 is an overview of the attempts that have been made to sample the five domains of scattered radiation (spectral, spatial, temporal, geometrical, polarization) and then to use the results of this sampling to estimate environmental variables of interest. Part one highlights three issues: first, that relationships between remotely sensed data and environmental variables of interest are indirect; second, our ability to estimate these environmental variables is dependent upon our ability to capture a sound representation of variability in scattered radiation and third, a considerable portion of the useful information in remotely sensed images resides in the spatial domain (within the relations between the pixels in the image). This final point is developed in Part 2 that explores ways in which the spatial domain is utilized to describe spatial variation in remotely sensed and ground data; to design optimum sampling schemes for image data and ground data and to increase the accuracy with which remotely sensed data can be used to estimate both discontinuous and continuous variables. Part 3 outlines two specific uses of information in the spatial domain; first, to select an optimum spatial resolution and second, to inform an image classification.