基于地统计学和GIS技术的北京市大兴区礼贤镇土壤养分空间变异性研究

运用地统计学和GIS方法,对北京市大兴区礼贤镇的表层土壤全氮、全磷、全钾、全硼、碱解氮、有效磷、速效钾、有效硼、有机质和pH值等参数的空间变异及分布特征进行了研究。结果表明,研究区内有效磷、速效钾、碱解氮变异系数分别为10599%、10043%、8029%,分异性较强。经过不同趋势阶数指标插值误差的综合比较,初步确定全磷、有效磷、全钾、速效钾、全硼、有效硼应该选择一阶,碱解氮、有机质和pH值应该选择无趋势,而全氮则应该选择二阶。全磷、有效磷、全钾、全硼、pH值的理论模型为指数模型,速效钾、全氮、碱解氮、有效硼、有机质的理论模型为线性模型。全磷、有效磷、全钾、全硼、pH值主要受到结构性因素的影响,全氮、有效硼、有机质受到结构性因素和随机性因素的共同影响,速效钾、碱解氮主要受到随机性因素的影响。通过普通克里格插值图清晰可见,按照含量分布特点土壤中全氮、碱解氮、全磷、有效硼、有机质、有效磷的空间展布相似,全钾和速效钾的空间展布相似,全硼的空间展布特点与其他指标都不相同,这与统计学分析结果具有相似性。通过了解研究区土壤中10项养分指标分布情况,对及时调整肥料用量比,实现有针对性施肥,调整农业结构以及优势农产品规划和布局提供数据支持。     

黑龙江省海伦市农耕区土壤硒分布特征及影响因素

海伦市是黑龙江省耕地面积最大的县市,为了研究海伦市农耕区土壤硒的分布特征及影响因素,在海伦市农耕区采集了15 608件0~20 cm表层土壤样品和976件150~200 cm深层土壤样品,分析了土壤全硒含量、形态等土壤化学指标。结果表明,表层土壤硒元素含量在0.02~0.87 mg·kg^-1之间,平均含量0.29 mg·kg^-1,93.87%的农耕土壤为足硒土壤,4.99%的土壤为富硒土壤,几乎不存在硒潜在不足和缺硒土壤,无硒中毒地区。不同土壤类型的硒元素平均含量由高到低依次为水稻土>黑土>草甸土>风沙土>暗棕壤。相关分析结果表明:影响研究区土壤硒含量的主要因素是土壤pH、有机质和成土母质,土壤中硒元素赋存形式以有机结合态为主,土壤总硒、有机质、pH也是影响硒有效性的主要因素。     

淮南塌陷塘重金属空间分布特征研究

长期地下煤炭开采在地表产生了大面积的塌陷塘,并造成了不同程度的水域污染。为研究塌陷塘重金属的分布特征及成因,选择了8种对环境影响较大的重金属元素（Fe,Mn,Zn,Cu,Cr,Cd,Pb,Ni）为研究对象,以淮南潘集一矿塌陷塘为研究区域,利用ArcGIS地统计模块中的协同克里格算法,通过水体实测光谱反射率作为协变量来估算水体中的重金属含量空间分布特征。结果表明:水体实测光谱与重金属含量有较好的关系,以水体光谱为协变量的协同克里格插值与单变量的普通克里格插值相比,8种重金属元素的预测值与实际值之间的均方根误差明显减少,证明水体实测光谱适合作为协变量来估计水体重金属的空间分布情况。综合分析发现,水体中的Cd,Pb,Cu,Ni主要来自水域西北部的煤矸石堆山,且Cd,Cu,Pb含量均超过了当地的背景值,对环境影响较大;Cr主要来自农业肥料、成土母质和周边道路旁的煤泥灰厂及煤矸石堆;Zn的来源主要是煤矸石、上游生活污水、农业肥料、土壤母质,由于其含量较低,对水环境质量的影响不大。      

岩溶区土壤有机质空间变异性分析

采用GIS和地统计学研究土壤有机质（SOM）的空间分布、影响因素和预测是指导农业生产、环境治理和土壤碳储计量的重要手段。基于广西马山县北部岩溶区表层土壤 (0~20 cm)的441个SOM数据,建立普通克里格(OK)、回归克里格（RK）,以及结合辅助变量的地理加权回归克里格(GWRK)、残差均值（MM_OK）和中值（MC_OK）均一化克里格的5种模型,并比较其预测精度,旨在探讨岩溶区SOM制图中地统计学方法的适用性。结果表明:（1）SOM的变异系数为37.30%,属于中等空间变异;（2）岩溶区SOM空间变异受土地利用方式、土壤类型和地形因子等因素共同影响,SOM高值区分布在西北部、西部和东部等石灰土分布的岩溶区和水田,低值区位于北部红水河沿岸的冲积土地带;（3）RK、GWRK、MM_OK和 MC_OK对SOM解释能力均较优,可用于岩溶区SOM预测制图。结合辅助变量因子的GWRK预测模型能有效消除空间变异因素的影响,克服岩溶区SOM含量的空间非平稳性,从而提高SOM含量模型的稳定性和精度,同时MC_OK模型能提高预测的准确度。      

泛克里格趋势分析法在异常下限确定中的应用——以夏河—合作地区为例

异常下限的确定是化探工作中核心环节之一。本文应用泛克里格趋势分析法的原理和方法流程,以甘肃夏河—合作地区1∶20万化探数据中Au、Cu、Ag、As、Sb、Hg元素为例,分别利用泛克里格趋势分析法和传统统计法求取它们的异常下限值,并结合地质矿产背景对比分析了两种方法在研究区内的应用效果。趋势分析法其圈定的异常能够反映元素含量在空间上的变化,受背景的干扰较小,指示矿化的能力较强;与传统统计法相比较,趋势分析法圈定的异常不仅与已知矿床(点)的空间分布吻合更好,而且异常强度大,分带性好,浓集中心高;还反映了区域断裂沿NW—SE向展布。泛克里格趋势法还圈定出一些传统统计法未能识别出的异常,为开展下一阶段的地质矿产勘查工作提供了重要参考。     

中国土壤有机质含量变异性与空间尺度的关系

以中国土种志资料为基础，分析了土壤有机质含量变异与空间尺度的关系及土类内和土类间的变异程度，探讨了不同空间尺度单元下，土壤有机质平均含量与土壤性质的相关性。结果表明，以土壤剖面为单元，随着土壤剖面数的增加，土壤有机质含量的变异系数增大；行政区域尺度单元内部土壤有机质变异程度大于单元间土壤有机质含量的变异程度。以土壤分类单元为空间单元，土类内的有机质含量变异程度小于土类间的变异程度。随着统计单元空间尺度的增大，土壤有机质含量与土壤性质之间的相关性减弱。因此，采用网格法或行政区划分空间区域，获得空间区域单元内土壤有机质含量或贮量的精确估算需要较多的剖面，但外推至数据不足的空间区域时，估算的不确定较小；采用土壤分类单元为空间区域单元，结果则相反。     

南疆棉田表层土壤盐分的空间变异特征分析与应用

通过研究土壤盐分的空间变异,快速准确获取土壤盐分的空间分布是精准农业和环境保护的基础。使用土壤电导率仪(PET2000)网格法在50 m×70 m面积的田块内布点(网格边长5 m),测量棉田表层土壤(0~25 cm深度,每5 cm为一层)电导率;应用ArcGIS9.2中地统计学模块构建、筛选和验证模型;利用地统计学方法研究表层土壤盐分的空间变异规律,进行空间分布预测,并针对棉田表层积盐问题提出了相应的解决措施。结果表明:克里格(Kriging)插值方法中的Rational Quadratic模型适宜预测表层土壤电导率,区内棉田表层盐分的空间变异特征明显,变异系数达到0.578,土壤盐分的空间变异性随深度增大逐渐降低;产生空间变异的主要原因是土壤岩性的空间差异和微咸水灌溉;解决棉田局部积盐的措施是根据土壤盐分空间差异特征的分析与预测进行适时定位灌溉,从而合理利用水资源并改善作物生长环境。     

沈阳市土壤铅的空间分布及风险评价研究

经测定,沈阳市土壤铅含量范围为22～2910.600mg/kg,平均值是270.297mg/kg。铅污染比较严重且空间变化大,局地污染非常严重。利用地统计方法研究了沈阳市土壤铅的空间结构和分布特征。结果显示,沈阳市土壤铅具有较好的空间结构性,利用半方差函数的结果进行克里格插值得到土壤铅含量的分布图。沈阳市有6个土壤铅污染中心,其中以铁西区和太原街的污染比较突出。工业排放、汽车尾气和污灌是沈阳市铅污染的三大污染源。风险评价结果表明,铁西区属于极高风险区,儿童铅中毒的潜在风险非常大。     

承德市土壤重金属空间结构与分布特征

基于地统计学和GIS相结合的方法，对承德全域表层土壤重金属As、Cd、Cr、Cu、Hg、Ni、Pb、Zn、微量元素Se正态分布特征、主导分布趋势及相互作用规律进行了分析，确定了不同元素最适宜的地统计插值模型并厘定出其空间分布规律。结果表明:As、Cd、Cr、Cu、Hg、Ni、Pb、Zn的质量含量平均值分别为8.28，0.200，60.85，24.37，0.034，27.76，26.65，77.10 mg/kg，Cd、Cu、Hg和Pb变异系数分别为385%、143%、350%、118%，分异性强。Zn含量均值受土壤类型影响显著，Cr、Cu、Ni含量均值则受土地利用类型影响显著。经过不同趋势阶数元素插值误差的综合对比，确定As、Cr、Pb、Zn、Ni、Se适宜选择无趋势参数，Hg和Cu适宜选择一阶趋势参数，而Cd适宜选择二阶趋势参数。As的理论模型为指数模型，主要受到结构性因素的影响；Cd、Cr、Cu、Hg、Ni、Pb、Zn、Se的理论模型为线性模型，主要受到随机性因素的影响。通过普通克里格插值图可见区内9种元素具有北低南高的特点，中部地区形成了一条较宽的Pb高值带，与Cd相似。按照含量分布特点，土壤中Cr和Ni、Cu和Hg、Zn和Pb、Se和Cd之间的高值空间展布区具有相似性且来源相同，仅As具有个性，分析结果与传统统计学结果数据保持部分一致性。     

多维分形克里格方法

时间序列与空间场信号往往是非规则分布的，经常需要将非规则分布的时空信号插值为规则分布的信号或估计某些未知点的值。如油气田、煤田以及金属矿山储量估算，工程地质参数估计，病虫害区域分布调查等都要求根据少量不规则数据点进行插值估算。估值方法中应用最为广泛的地质统计学方法（或(Krige)克里格方法）是一种低通滤波器，无法重建原始信号中的高频、局部与弱信号。开发的多维分形克里格方法可以将不规则分布的时间—空间（时空）信号插值为规则分布的信号；可以提取时空信号中高频、局部与弱信号，估计过程参数可以作为特征参数用于模式识别。利用褶积滤波理论定量导出了地质统计学的低通滤波特性，它在插值过程中丢失了高频、局部和弱信号。在定义了时空信号的度量尺度与测度后，实现了多维分形插值，多维分形插值保留了系统中更多的高频信息。将克里格方法与多维分形方法有机的结合起来产生了多维分形克里格方法，它具有克里格方法和多维分形插值的共同优点。用大洋钻探(ODP)184航次1143A孔的岩芯密度分析进行了插值试验，对比了插值结果及其功率谱。多维分形克里格插值比克里格插值、多维分形插值更为接近已知点值并保留更多的高频信息。还定量分析、对比了影响多维分形克里格插值的因素、厘清了估值问题中固有的测不准关系。 另外，多维分形克里格插值过程得到的局部奇异性、相关性和回归方差能有效地刻划高频、局部与弱信号。这样，多维分形克里格插值过程可以用于提取（非规则或规则网格）时空信号中的局部、高频与弱信号，用于信息提取、模式识别、找矿预测与信号增强等领域。     

Spatial prediction of soil properties in a watershed scale through maximum likelihood approach

Surface map of soil properties plays an important role in various applications in a watershed. Ordinary kriging (OK) and regression kriging (RK) are conventionally used to prepare these surface maps but generally need large number of regularly girded soil samples. In this context, REML-EBLUP (REsidual Maximum Likelihood estimation of semivariogram parameters followed by Empirical Best Linear Unbiased Prediction) shown capable but not fully tested in a watershed scale. In this study, REML-EBLUP approach was applied to prepare surface maps of several soil properties in a hilly watershed of Eastern India and the performance was compared with conventionally used spatial interpolation methods: OK and RK. Evaluation of these three spatial interpolation methods through root-mean-squared residuals (RMSR) and mean squared deviation ratio (MSDR) showed better performance of REML-EBLUP over the other methods. Reduction in sample size through random selection of sampling points from full dataset also resulted in better performance of REML-EBLUP over OK and RK approach. The detailed investigation on effect of sample number on performance of spatial interpolation methods concluded that a minimum sampling density of 4/km² may successfully be adopted for spatial prediction of soil properties in a watershed scale using the REML-EBLUP approach.     

Spatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China

The present study examines the spatial dependency of soil organic matter and nutrients in paddy fields at three different scales using geostatistics and geographic information system techniques (GIS). The spatial variability of soil organic matter (SOM), total nitrogen (TN) and available phosphorus (AP) has been characterized using a total of 460, 131 and 64 samples that were, respectively, collected from the Hangzhou–Jiaxing–Huzhou (HJH) Plain (10 km), Pinghu county (1,000 m) and a test plot area (100 m) within the Pinghu county, Zhejiang province of the southeast China. Semivariograms showed that the SOM and TN had moderate spatial dependency on the large scale of HJH plain and moderate scale of Pinghu county with long spatial correlation distances. At the moderate scale of Pinghu county and the small scale of a test plot area, the AP data did not show any spatial correlation, but had moderate spatial dependency in HJH plain. Spherical and exponential variogram models were best fitted to all these soil properties. Maps of SOM and TN were generated through interpolation of measured values by ordinary kriging, and AP by lognormal kriging. This study suggests that precision management of SOM and TN is feasible at all scales, and precision management of AP is feasible at large scales.     

Accounting for exhaustive secondary data into the mapping of water table elevation

This paper presents the incorporation of a digital elevation model into the spatial prediction of water table elevation in Mazandaran province (Iran) using a range of interpolation techniques. The multivariate methods used are: linear regression (LR), cokriging (COK), kriging with an external drift (KED) and regression kriging (RK). The analysis is performed on 3 years (1987, 1997 and 2007) of water table elevation data from about 260 monitoring wells. Prediction performances of the different algorithms are compared with two univariate techniques, i.e. inverse distance weighting and ordinary kriging (OK), through cross validation and examination of the consistency of the generated maps with the natural phenomena. Significantly smaller prediction errors are obtained for four multivariate algorithms but, in particular, KED and RK outperform LR and COK for 3 years. The results show the potential for using elevation for a more precise mapping of water table elevation.     

Comparison of statistical prediction methods for characterizing the spatial variability of apparent electrical conductivity in coastal salt-affected farmland

Soil salinity has been known to be problematic to land productivity and environment in the lower Yellow River Delta due to the presence of a shallow, saline water table and marine sediments. Spatial information on soil salinity has gained increasing importance for the demand of management and sustainable utilization of arable land in this area. Apparent electrical conductivity, as measured by electromagnetic induction instrument in a fairly quick manner, has succeeded in mapping soil salinity and many other soil physical and chemical properties from field to regional scales. This was done based on the correlation that existed between apparent electrical conductivity and many other soil properties. In this paper, four spatial prediction methods, i.e., local polynomial, inverse distance weighed, ordinary kriging and universal kriging, were employed to estimate field-scale apparent electrical conductivity with the aid of an electromagnetic induction instrument (type EM38). The spatial patterns estimated by the four methods using EM38 survey datasets of various sample sizes were compared with those generated by each method using the entire sample size. Spatial similarity was evaluated using difference index (DI) between the maps created using various sample sizes (i.e., target maps) and the maps generated with the entire sample size (i.e., the reference map). The results indicated that universal kriging had the best performance owing to the inclusion of residuals and spatial detrending in the kriging system. DI showed that spatial similarity between the target and reference maps of apparent electrical conductivity decreased with the reduction in sample size for each prediction method. Under the same reduction in sample size, the method retaining the most spatial similarity was universal kriging, followed by ordinary kriging, inverse distance weighed, and local polynomial. Approximately, 70 % of total survey data essentially met the need for retaining 90 % details of the reference map for universal kriging and ordinary kriging methods. This conclusion was that OK and UK were two most appropriate methods for spatial estimation of apparent electrical conductivity as they were robust with the reduction in sample size.     

克里金算法与多重分形理论在岩土参数随机场分析中的应用

岩土参数的空间分布特征由于存在取样数据之间自相关和互相关的特性,未知点的岩土参数属性可通过特定的方法内插或外推,经典的数理统计方法难以确定周围的数据样本点以及相应的插值系数。首先介绍地统计学中基于距离加权的普通克里金（ordinary kriging, OK）算法、泛克里金算法（UK）和协克里金算法（CK）。由于基于滑动距离加权的OK算法无法度量局部空间的奇异性,将引入多重分形理论弥补该缺陷。以2010上海世博会的世博轴区域（长525 m,宽80 m）为工程背景,区域内共有42个取土钻孔,以典型的粉质黏土层3个重要的物理力学指标,即黏聚力、内摩擦角和压缩模量验证以上算法。对于岩土参数黏聚力和内摩擦角,预测精度由高至低为多重分形联合模型（MK）、协克里金模型（CK）、泛克里金模型（UK）、普通克里金模型（OK）;对于岩土参数压缩模量,相应的顺序为泛克里金模型和普通克里金模型位置互换。研究结果证明,在岩土参数空间场的分析中,辅助信息有助于提高数据预测精度,并且多重分形联合模型有助于分析空间局部的奇异性。     

The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets

Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference. Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation (in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based models are useful in that they provide extra information on the spatial processes generating the data that are being predicted.     

Trend removal in spatially correlated datasets

Typically, datasets originated from mining exploration sites, industrially polluted and hazardous waste sites are correlated spatially over the region under investigation. Ordinary kriging (OK) is a well-established geostatistical tool used for predicting variables, such as precious metal contents, biomass, species counts, and environmental pollutants at unsampled spatial locations based on data collected from the neighboring sampled locations at these sites. One of the assumptions required to perform OK is that the mean of the characteristic of concern is constant for the entire region under consideration (e.g., there is no spatial trend present in the contaminant distribution across the site). This assumption may be violated by dalasets obtained from environmental applications. The occurrence of spatial trend in a dataset collected from a polluted site is an indication of the presence of two or more statistical populations (strata) with significantly different mean concentrations. Use of OK in these situations can result in inaccurate kriging estimates with higher SDs which, in turn, can lead to incorrect decisions regarding all subsequent environmental monitoring and remediation activities. A univariate and a multivariate approach have been described to identify spatial trend that may be present at the site. The trend then is removed by subtracting the respective means from the corresponding populations. The results of OK before and after trend removal are being compared. Using a real dataset, it is shown that standard deviations (SDs) of the kriging estimates obtained after trend removal are uniformly smaller than the corresponding SDs of the estimates obtained without the trend removal.     

Restricted kriging for mixture of grade models

A modified type of kriging, referred to as restricted kriging (RK), is proposed in this study. The method incorporates constraints on different grade classes to restrict the influence of the samples having different likelihoods in estimation. RK is motivated by the estimation of mineral reserves when grades have highly skewed distributions. Ordinary kriging tends to produce an overly smoothed interpolated surface by underestimating high grades and overestimating low grades. The fact that ordinary kriging gives a uniform prior treatment to all samples independent of their values is a major factor associated with this smoothing effect. The new approach differentiates each grade portion by preselected cutoffs. RK is developed for a single cutoff and then extended into a general form for any finite number of cutoffs. Restricted cokriging (RCK) is also formulated to simultaneously estimate a set of random functions with restriction conditions. Methods are suggested for determination of the probabilities of occurrence of different grade portions. Finally, the new approach is demonstrated on a case study of an epithermal gold deposit.