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1.
Shu Tao 《Water, air, and soil pollution》1995,83(1-2):161-172
Two-dimensional ordinary block kriging as an optimal interpolation technique was applied to produce regular grids of predicted estimates of copper, lead, and mercury contents in surface soil in the Shenzhen area for mapping purposes. The kriging analysis was based on theoretical variograms calculated from measured data of eighty three top soil samples. The appropriateness of the whole procedure of kriging analysis was evaluated by both cross-validation and kriging standard deviation mapping. The similarity in area variation between the distribution of soil parent material and the mapped results of copper and lead is demonstrated. The possible influence of agricultural contamination on the spatial distribution pattern of mercurcy is also discussed. 相似文献
2.
内蒙古土壤pH值、粘粒和有机质含量的空间结构特征 总被引：13，自引：2，他引：13
采用半方差函数和普通克里格方法分析了内蒙古地区土壤 pH、粘粒和有机质含量的空间结构特征 .结果表明 ,内蒙古土壤 pH、粘粒和有机质含量的空间结构特征可以用线性半方差函数模型加以描述 ,且具有明显的各向异性 .插值结果显示 ,它们的空间变异尺度与土类分布具有较好的一致性 .内蒙古地区土壤 pH值表现为自东向西逐渐升高的趋势 ,而粘粒和有机质含量测沿同一方向逐渐降低 .表生地球化学作用的空间变异是决定内蒙古土壤上述参数分布特征与尺度的主要因素 . 相似文献
3.
The abundances of copper, lead, zinc, nickel, chromium, cobalt, mercury, vanadium, and manganese in eighty three surface soil samples collected from Shenzhen area were determined. The correlation among element contents and the factors affecting the contents were studied using principle component analysis. The factor scores of the first two components were analyzed as regionalized variables using variogram analysis and Kriging. The interpolated factor scores were then mapped to show the common features in spatial distribution of a set of elements with similar geochemical behavior. It was demonstrated that the spatial distribution patterns of parent material in the area are the primary factor governing the spatial variation of the elements. 相似文献
4.
R. M. Lark 《European Journal of Soil Science》2000,51(1):137-157
The standard estimator of the variogram is sensitive to outlying data, a few of which can cause overestimation of the variogram. This will result in incorrect variances when estimating the value of a soil property by kriging or when designing a sampling grid to map the property to a required precision. Several robust estimators of the variogram, based on location and scale estimation, have been proposed as improvements. They seem to be suitable for analysis of soil data in circumstances where the standard estimator is likely to be affected by outliers. Robust estimators are based on assumptions about the distribution of the data which will not always hold and which need not be made in kriging or in estimating the variogram by the standard estimator. The estimators are reviewed. Simulation studies show that the robust estimators vary in their susceptibility to moderate skew in the underlying distribution, but that the effects of outliers are generally greater. The estimators are applied to some soil data, and the resulting variograms used for ordinary kriging at sites in a separate validation data set. In most cases the variograms derived from the standard estimator gave kriging variances which appeared to overestimate the mean squared error of prediction (MSEP). Kriging with variograms based on robust estimators sometimes gave kriging variances which underestimated the MSEP or did not differ significantly from it. Estimates of kriging variance and the MSEP derived from the validation data were generally close to estimates from cross‐validation on the prediction set used to derive the variograms. This indicates that variogram models derived from different estimators could be compared by cross‐validation. 相似文献
5.
Sample adequately to estimate variograms of soil properties 总被引：17，自引：0，他引：17
The variogram is central in the spatial analysis of soil, yet it is often estimated from few data, and its precision is unknown because confidence limits cannot be determined analytically from a single set of data. Approximate confidence intervals for the variogram of a soil property can be found numerically by simulating a large field of values using a plausible model and then taking many samples from it and computing the observed variogram of each sample. A sampling distribution of the variogram and its percentiles can then be obtained. When this is done for situations typical in soil and environmental surveys it seems that variograms computed on fewer than 50 data are of little value and that at least 100 data are needed. Our experiments suggest that for a normally distributed isotropic variable a variogram computed from a sample of 150 data might often be satisfactory, while one derived from 225 data will usually be reliable. 相似文献
6.
Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood 总被引：2，自引：0，他引：2
It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. 相似文献
7.
区域土壤质地层次三维空间分布的地统计模拟方法比较 总被引：1，自引：0，他引：1
为了定量化描述冲积平原区土壤剖面质地层次的复杂变异性,本研究根据华北冲积平原一块面积约15 km2区域内的139个土壤剖面（0 ~ 2 m）观测数据,分别应用顺序指示模拟和多点地统计学模拟方法分析了区域内土壤质地层次的三维空间分布特征。前者的结果显示土壤质地层在水平方向上的分布具有很强的随机特性,而后者的结果表明土壤质地层在水平方向上的分布具有一定的规律性。将转移概率函数得到的各向同性分布比例和各向异性平均长度（厚度）用来生成三维训练图像,然后将生成的训练图像用于多点地统计学模拟,并与传统的顺序指示模拟结果进行了对比。结果表明,多点地统计学模拟在估计精度以及垂直方向上土壤质地层次连贯性的再现性上优于传统顺序指示模拟,所得结果能更好地反映土壤质地层次的空间分布特征。 相似文献
8.
R. M. Lark 《European Journal of Soil Science》2009,60(4):706-719
Stochastic models of soil variation are used in geostatistical analysis, but in general they bear no relation to our mechanistic understanding of the processes in soil that cause its properties to vary spatially. It is proposed that we require a suitable stochastic model in which space is partitioned into discrete domains as a first step towards random spatial models that incorporate our understanding of processes in soil. Even though the soil is essentially continuous in its spatial variation, there are components of soil variation (e.g. differences between parent materials) which are discontinuous. This paper shows how variogram models can be derived directly from the Poisson Voronoi Tessellation (PVT), a stochastic-geometric partition of d -dimensional space. The PVT variogram models, for d = 2 and 3, were fitted to variograms estimated from data over disparate scales, including computerized tomographic images of soil aggregates (pixels of a few tens of micrometres long) and the land systems of Swaziland. In all cases, PVT variogram models fitted better than the conventional geostatistical ones. The good performance of PVT variogram models at these disparate scales encourages further work on tessellation models for soil variation. In principle such models could incorporate information on underlying factors of soil formation such as the spatial distribution of individual plants, the origin and growth of microbial colonies, spatial processes in soil chemistry (such as reaction–diffusion processes) and geometrical information on boundaries between geological strata or contrasting plant communities. PVT models may therefore be one component of a random model of soil variation which reflects our understanding of soil-forming processes, and so have a stronger scientific basis than the models that are now in standard use. 相似文献
9.
R. M. Lark 《European Journal of Soil Science》2003,54(1):187-202
If we wish to describe the coregionalization of two or more soil properties for estimation by cokriging then we must estimate and model their auto‐ and cross‐variogram(s). The conventional estimates of these variograms, obtained by the method‐of‐moments, are unduly affected by outlying data which inflate the variograms and so also the estimates of the error variance of cokriging predictions. Robust estimators are less affected. Robust estimators of the auto‐variogram and the pseudo cross‐variogram have previously been proposed and used successfully, but the multivariate problem of estimating the cross‐variogram robustly has not yet been tackled. Two robust estimators of the cross‐variogram are proposed. These use covariance estimators with good robustness properties. The robust estimators of the cross‐variogram proved more resistant to outliers than did the method‐of‐moments estimator when applied to simulated fields which were then contaminated. Organic carbon and water content of the soil was measured at 256 sites on a transect and the method‐of‐moments estimator, and the two robust estimators, were used to estimate the auto‐variograms and cross‐variogram from a prediction subset of 156 sites. The data on organic carbon included a few outliers. The method‐of‐moments estimator returned larger values of the auto‐ and cross‐variograms than did either robust estimator. The organic carbon content at the 100 validation sites on the transect was estimated by cokriging from the prediction data plus a set of variograms fitted to the method‐of‐moments estimates and two sets of variograms fitted to the robust estimates. The ratio of the actual squared prediction error to the cokriging estimate of the error variance was computed at each validation site. These results showed that cokriging using variograms obtained by the method‐of‐moments estimator overestimated the error variance of the predictions. By contrast, cokriging with the robustly estimated variograms gave reliable estimates of the error variance of the predictions. 相似文献
10.
Site‐specific management requires accurate knowledge of the spatial variation in a range of soil properties within fields. This involves considerable sampling effort, which is costly. Ancillary data, such as crop yield, elevation and apparent electrical conductivity (ECa) of the soil, can provide insight into the spatial variation of some soil properties. A multivariate classification with spatial constraint imposed by the variogram was used to classify data from two arable crop fields. The yield data comprised 5 years of crop yield, and the ancillary data 3 years of yield data, elevation and ECa. Information on soil chemical and physical properties was provided by intensive surveys of the soil. Multivariate variograms computed from these data were used to constrain sites spatially within classes to increase their contiguity. The constrained classifications resulted in coherent classes, and those based on the ancillary data were similar to those from the soil properties. The ancillary data seemed to identify areas in the field where the soil is reasonably homogeneous. The results of targeted sampling showed that these classes could be used as a basis for management and to guide future sampling of the soil. 相似文献
11.
Spatial distribution maps depicting the concentrations of antimony, lead, tin, copper and zinc, and the presence of land-use
units were generated for Mühlburg, a district of the City of Karlsruhe, Germany. The influence of the spatial land-use structure
on the distributions of the element concentrations is statistically evaluated and discussed. The variography for Mühlburg
shows an average range of 200-400 m for the spatial correlations of Sb, Pb, Sn and Zn. The variograms of Pb and Zn are characterised
by hole effects at 300 m distances, i.e. the result of repeated stronger spatial correlations for certain distances between
the sample sites. Most probably, this is an effect of the typical urban structure of streets, buildings, green spaces, and
industry. Kriging method was used for the interpolation of Sb, Pb, Sn and Zn concentrations. Only Cu does not show a spatial
correlation. In this case, the interpolation was carried out with a smoothed triangulation routine. Pollution plumes of point
sources such as lead works, a bell foundry and a coal-fired thermal power station superimpose the more diffuse pollution from
traffic, household heating processes, waste material disposal, etc. The trace element concentrations in soils of housing areas
increase with the age of the developed area. Industrial areas show the highest level of pollution, followed by housing areas
developed before 1920, traffic areas, allotments, housing areas developed between 1920 and 1980, parks and sports areas, cemetery
and housing areas developed after 1980.
It is demonstrated that spatial distribution maps of element concentrations indicate potential emission sources of harmful
substances, even if the emission itself or the direct surrounding soil have not been analysed. The analytical tools presented
enable town planners to discern areas of higher soil pollution. Detailed investigations can be focussed on these areas to
evaluate the possibilities of soil usage and transfer. These methods enable one to manage urban soil in an adequate manner.
For these reasons, the methods demonstrated support an urban environmental impact assessment and are a part of a sustainable
urban soil management. 相似文献
12.
Estimating variograms of soil properties by the method-of-moments and maximum likelihood 总被引：6，自引：0，他引：6
R. M. Lark 《European Journal of Soil Science》2000,51(4):717-728
Variograms of soil properties are usually obtained by estimating the variogram for distinct lag classes by the method‐of‐moments and fitting an appropriate model to the estimates. An alternative is to fit a model by maximum likelihood to data on the assumption that they are a realization of a multivariate Gaussian process. This paper compares the two using both simulation and real data. The method‐of‐moments and maximum likelihood were used to estimate the variograms of data simulated from stationary Gaussian processes. In one example, where the simulated field was sampled at different intensities, maximum likelihood estimation was consistently more efficient than the method‐of‐moments, but this result was not general and the relative performance of the methods depends on the form of the variogram. Where the nugget variance was relatively small and the correlation range of the data was large the method‐of‐moments was at an advantage and likewise in the presence of data from a contaminating distribution. When fields were simulated with positive skew this affected the results of both the method‐of‐moments and maximum likelihood. The two methods were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variograms were used for kriging. Both estimators were susceptible to sampling problems which resulted in over‐ or underestimation of the variance of three of the metals by kriging. For four other metals the results for kriging using the variogram obtained by maximum likelihood were consistently closer to the theoretical expectation than the results for kriging with the variogram obtained by the method‐of‐moments, although the differences between the results using the two approaches were not significantly different from each other or from expectation. Soil scientists should use both procedures in their analysis and compare the results. 相似文献
13.
县域农田土壤有机质空间变异及其影响因素分析 总被引：8，自引：1，他引：7
研究县域农田空间变异特征可以为培肥地力,增加作物产量提供指导。本文运用地统计学和 GIS相结合的方法,研究了四川省双流县土壤有机质的空间变异特征及其影响因素。结果表明： ①研究区域土壤有机质含量处于中等偏高水平,平均值为 29.72 g/kg,变异系数为 30.11%,属中等变异强度。②有机质变异函数的理论最佳模型为球状模型,块金值与基台值之比为12.67%,表明有机质含量具有强烈的空间相关性,空间相关距离为 91.10 km,普通Kriging插值表明土壤有机质含量呈现北部向东南部减少的趋势。③影响有机质空间变异的主要因素为土壤类型、地貌类型等结构性因子,而土地利用方式、施肥等随机性因子也对有机质空间变异产生重要影响,其中秸秆还田是有机质含量普遍升高的原因。 相似文献
14.
The effort required to survey a soil variable depends upon the acceptable uncertainty of estimates and the variogram of the variable. The variogram is unknown prior to sampling, so it must be inferred from a reconnaissance survey before an efficient survey can be designed. The results of reconnaissance surveys are subject to uncertainty, which depends upon the variogram and the number and location of observations. Here, we develop an adaptive approach for optimizing reconnaissance surveys. The observations within these reconnaissance surveys are collected in distinct phases. After each phase, a probability density function of the required sampling density of the main survey is calculated within a Bayesian framework. The number and location of observations within further phases are selected to reduce efficiently the uncertainty of the estimate of the required sampling density. In simulation studies, the number and location of observations in Bayesian adaptive reconnaissance surveys vary according to the variogram of the property of interest. For variograms with a short range, the reconnaissance surveys are intensive with a large proportion of clustered locations. Fewer, more evenly spread locations are required for variables with a long range. Bayesian adaptive reconnaissance surveys lead to more efficient surveys than conventional approaches because the reconnaissance survey is specifically designed for the variable of interest. A hand‐held field system is implemented and tested in a survey of soil moisture content over a field. 相似文献
15.
Scale-dependent correlation between topsoil copper and cobalt concentrations in Scotland 总被引：14，自引：0，他引：14
The soil of south-east Scotland is locally deficient in copper and cobalt. Measurements from nearly 3000 fields for which the soil association is known were analysed to study the coregionalization of the two elements and to assess the influence of parent material on the metals' concentrations. The experimental auto- and cross-variograms revealed distinct local (1.5 km) and regional (20 km) scales of spatial variation. A combination of indicator variograms of the soil associations had the same spatial structures, suggesting that parent material influences the concentrations of the metals. The coregionalization between copper and cobalt was modelled as a linear combination of three spatial structures. The resulting structural correlation coefficients showed the two elements to be fairly strongly positively correlated at the regional scale. Kriging allowed determination and mapping of each spatial component; these maps were then compared with the spatial distribution of soil associations in the region. An analysis of variance was performed before and after filtering out the nugget and short-range spatial components. Classification by soil association (parent material) accounted for a large proportion of the variance at the regional scale, suggesting that the parent material contributes substantially more to the trace element content of the soil than had been thought earlier. 相似文献
16.
SUN Xiaolin WANG Huili Dermot FORRISTAL FU Weijun Hubert TUNNEY Chaosheng ZHANG 《土壤圈》2019,29(5):577-589
Sampling plays an important role in acquiring precise soil information required in modern agricultural production worldwide, which determines both the cost and quality of final soil mapping products. For sampling design, it has been proposed possibile to transfer the relationships between kriging variance and sampling grid spacing from an area with existing information to other areas with similar soil-forming environments. However, this approach is challenged in practice because of two problems:i) different population variograms among similar areas and ii) sampling errors in estimated variograms. This study evaluated the effects of these two problems on the transferability of the relationships between kriging variance and sampling grid spacing, by using spatial data simulated with three variograms and soil samples collected from four grasslands in Ireland with similar soil-forming environments. Results showed that the variograms suggested by different samples collected with the same grid spacing in the same or similar areas were different, leading to a range of mean kriging variance (MKV) for each grid spacing. With increasing grid spacing, the variation of MKV for a specific grid spacing increased and deviated more from the MKV generated using the population variograms. As a result, the spatial transferability of the relationships between kriging variance and grid spacing for sampling design was limited. 相似文献
17.
亚热带红壤丘陵典型区土壤全氮的空间变异特征 总被引：18，自引：3，他引：18
在GIS支持下,运用地统计学方法分析了耕层土壤全氮的空间变异特征,并在此基础上利用Kriging插值方法绘制了土壤全氮的空间分布图。结果表明,在步长间隔60 m下,土壤全氮具有较强的空间相关性,其相关距离为208 m。在NE30°、NE120°两个方向上具有典型的几何异向性结构特点;在NE60°、NE150°两个方向上具有典型的带状异向性结构特点。Kriging插值结果表明,研究区土壤全氮的空间分布表现为条带状和斑块状分布。土壤全氮高值斑块区的分布与地势相对低洼的地形部位相吻合。地形是影响土壤全氮空间变化的主要因素。 相似文献
18.
黑龙江省肇源县土壤汞的空间分异研究 总被引：1，自引：0，他引：1
研究土壤汞的空间分异,可以探明影响汞分布的因素,从而有助于解决汞污染等重大生态环境问题。以肇源县的表层和深层土壤为研究对象,利用统计指标、GS+软件中的半方差函数模型和ArcGIS软件支持下的克里格插值法,对258个深层土壤样品和1 030个表层土壤样品进行分析,探讨了研究区重金属汞的积累特征。结果表明:样本点之间具有一定的空间相关性。表层土壤汞分布较深层更为不均匀,表层差异更大主要是受人为因素影响,与灌溉、施肥、工农业活动密切相关。深层土壤汞分布状况主要受自然因素影响。 相似文献
19.
Abstract. In response to the European Community Nitrate Directive (91/676) a catchment scale Geographical Information System (GIS) model of nitrate leaching has been developed to map nitrate vulnerability and predict average weekly fluxes of nitrate from agricultural land units to surface water. This paper presents a pilot study which investigated the spatial variability of soil nitrates in order to: (1) define an appropriate pixel size for modelling N leaching; (2) quantify the within-unit variability of soil nitrate concentrations for pasture and arable fields; and (3) assist in the design of an efficient sampling strategy for estimating mean nitrate concentrations. Soil samples, taken from two 800 m transects in early September 1994, were analysed for water soluble nitrate. The arable soils had a mean nitrate-nitrogen concentration of 0.693 μg/g (S.E. 0.054 μg/g) and the pasture soils had a higher mean nitrate-nitrogen concentration of 0.86 μg/g (S.E. 0.085 μg/g). Spatial variability was investigated using variograms. The pasture data had a weak spatial relationship, whereas the arable data exhibited a strong spatial relationship which fitted a spherical variogram model (r2 0.87), with a range of 40 m. A pixel size of 40 m is suggested for nitrate modelling within the GIS based on the arable variogram and an improved sampling strategy for model validation is suggested, involving bulking sub-samples over a 40 m grid for estimating mean nitrate concentrations in combined land use and soil units. 相似文献
20.
Soil data accumulated in national and regional archives derive from many sources and tend to be concentrated in zones of particular interest. Experimental variograms computed from such data by the usual method of moments can appear highly erratic, and therefore models fitted to them are likely to be unreliable. We have explored two methods of avoiding the effects, one by computing declustering weights and incorporating them into the method of moments, the other using residual maximum likelihood. The methods are illustrated with data on bulk density, exchangeable magnesium, cation exchange capacity and organic carbon of 4182 samples of soil from numerous soil surveys in the whole of Australia and stored in the CSIRO's national archive. The experimental variograms of all four variables are erratic. Cell declustering produced much smoother sequences of estimates to which plausible models could be fitted with confidence. The residual maximum likelihood models closely matched those models over several hundred km. Finally values were simulated at the same sampling points from the residual maximum likelihood models, reproducing ‘spiky’ experimental variograms such as those computed from the data. The simulation showed that clustered design of sampling causes spiky artefacts. We conclude that where data are clustered experimental variograms should be computed with declustered weighting or variogram models be fitted by residual maximum likelihood. 相似文献