首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
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   

2.
Geostatistical estimates of a soil property by kriging are equivalent to the best linear unbiased predictions (BLUPs). Universal kriging is BLUP with a fixed‐effect model that is some linear function of spatial co‐ordinates, or more generally a linear function of some other secondary predictor variable when it is called kriging with external drift. A problem in universal kriging is to find a spatial variance model for the random variation, since empirical variograms estimated from the data by method‐of‐moments will be affected by both the random variation and that variation represented by the fixed effects. The geostatistical model of spatial variation is a special case of the linear mixed model where our data are modelled as the additive combination of fixed effects (e.g. the unknown mean, coefficients of a trend model), random effects (the spatially dependent random variation in the geostatistical context) and independent random error (nugget variation in geostatistics). Statisticians use residual maximum likelihood (REML) to estimate variance parameters, i.e. to obtain the variogram in a geostatistical context. REML estimates are consistent (they converge in probability to the parameters that are estimated) with less bias than both maximum likelihood estimates and method‐of‐moment estimates obtained from residuals of a fitted trend. If the estimate of the random effects variance model is inserted into the BLUP we have the empirical BLUP or E‐BLUP. Despite representing the state of the art for prediction from a linear mixed model in statistics, the REML–E‐BLUP has not been widely used in soil science, and in most studies reported in the soils literature the variogram is estimated with methods that are seriously biased if the fixed‐effect structure is more complex than just an unknown constant mean (ordinary kriging). In this paper we describe the REML–E‐BLUP and illustrate the method with some data on soil water content that exhibit a pronounced spatial trend.  相似文献   

3.
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   

4.
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   

5.
R. Kerry  M.A. Oliver 《Geoderma》2007,140(4):383-396
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   

6.
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   

7.
Kriging is a means of spatial prediction that can be used for soil properties. It is a form of weighted local averaging. It is optimal in the sense that it provides estimates of values at unrecorded places without bias and with minimum and known variance. Isarithmic maps made by kriging are alternatives to conventional soil maps where properties can be measured at close spacings. Kriging depends on first computing an accurate semi‐variogram, which measures the nature of spatial dependence for the property. Estimates of semi‐variance are then used to determine the weights applied to the data when computing the averages, and are presented in the kriging equations. The method is applied to three sets of data from detailed soil surveys in Central Wales and Norfolk. Sodium content at Plas Gogerddan was shown to vary isotropically with a linear semi‐variogram. Ordinary punctual kriging produced a map with intricate isarithms and fairly large estimation variance, attributed to a large nugget effect. Stoniness on the same land varied anisotropically with a linear semi‐variogram, and again the estimation error of punctual kriging was fairly large. At Hole Farm, Norfolk, the thickness of cover loam varied isotropically, but with a spherical semi‐variogram. Its parameters were estimated and used to krige point values and produce a map showing substantial short‐range variation.  相似文献   

8.
The general linear model encompasses statistical methods such as regression and analysis of variance (anova ) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design‐based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model‐based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova ‐type models using data from two systematic surveys of soil. We compare an efficient, gradient‐based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.  相似文献   

9.
The pseudo cross‐variogram can be used for cokriging two or more soil properties when few or none of the sampling locations have values recorded for all of them. The usual estimator of the pseudo cross‐variogram is susceptible to the effects of extreme data (outliers). This will lead to overestimation of the error variance of predictions obtained by cokriging. A solution to this problem is to use robust estimators of the pseudo cross‐variogram, and three such estimators are proposed in this paper. The robust estimators were demonstrated on simulated data in the presence of different numbers of outlying data drawn from different contaminating distributions. The robust estimators were less sensitive to the outliers than the non‐robust one, but they had larger variances. Outliers tend to obscure the spatial structure of the cross‐correlation of the simulated variables as described by the non‐robust estimator. The several estimators of the pseudo cross‐variogram were applied to a multitemporal data set on soil water content. Since these were obtained non‐destructively, direct measurements of temporal change can be made. A prediction subset of the data was subsampled as if obtained by destructive analysis and the remainder used for validation. Estimators of the auto‐variogram and pseudo cross‐variogram were applied to the prediction data, then used to predict the change in water content at the validation sites by cokriging. The estimation variances of these predictions were best calculated with a robustly estimated model of coregionalization, although the validation set was too small to conclude that the non‐robust estimators were unsuitable in this instance.  相似文献   

10.
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  
徐尚平  陶澍  曹军 《土壤通报》2001,32(4):145-148
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   

11.
B.P. Marchant  R.M. Lark   《Geoderma》2007,140(4):337-345
The Matérn variogram model has been advocated because it is flexible and can represent varied behaviour at small lags. We show how the constraints on the spherical and exponential variogram at short lags ignore a possible source of uncertainty in the variogram and so in kriging surveys, that the Matérn model can describe. Matérn, spherical and exponential variogram models were fitted by maximum likelihood to a set of log10(K) observations made on a regular grid at Broom's Barn Farm, Suffolk, England. The likelihood profiles of the Matérn parameter estimates were asymmetric. Thus the uncertainty of these estimates could only be adequately assessed by a Bayesian approach. The uncertainty of estimated parameters of the Matérn variogram was larger than for the exponential variogram. This is an indication that the assumption of an exponential model limits the behaviour that may be described by the variogram. Thus uncertainty analyses where an exponential variogram is assumed may underestimate the uncertainty of kriged estimates. Bayesian analysis of the kriged estimates of log10(K) at Broom's Barn Farm using the Matérn variogram revealed an observable component of uncertainty due to variogram uncertainty. When an exponential variogram model was used, the estimate of this component of uncertainty was negligible. The Matérn variogram should therefore be used rather than the exponential model when assessing the adequacy of a variogram estimate. A method of designing sample schemes which is suitable for both estimating a Matérn variogram and interpolation is suggested.  相似文献   

12.
The German soil protection regulation (BBodSchV) requires the investigation and evaluation of sites with known, or suspected contamination. The purpose of this study is the application of geostatistical methods to locate hazardous zones within such a site and to estimate the amount and uncertainty of the contaminant load in these zones. The study site is an area around a metal smelter in the city of Nordenham, Germany, where among other heavy metals, Cd was released to the environment by dust emissions for many decades. In an earlier study soil cores were taken in the area and analyzed for Cd using various extraction methods. After translation of data to results corresponding to a single extraction method using linear regression analysis, Cd concentrations were mapped by ordinary and lognormal kriging. Crossvalidation showed that both methods perform similarly. However, neither ordinary nor lognormal kriging were able to account for the uncertainty of the kriged estimates. We repeated ordinary kriging with a relative variogram having a unit sill. The estimated relative kriging variance was scaled locally. This method considerably improved the estimation of uncertainty. Subsequently, we estimated Cd contents for the land use dependent size of support as specified in the BBodSchV. The kriged Cd estimates as well as their uncertainty were evaluated with regard to limits set by the BBodSchV. Parts of the area which may be declared safe based on merely the kriged estimates, can actually exceed a sanction or test limit by a chance of up to 50 % when uncertainty is also considered. Within the BBodSchV a recommended limit should therefore always be accompanied by a tolerable uncertainty that it may be exceeded on a given support (e.g. 5 %).  相似文献   

13.
Soil scientists often use prediction models to obtain values at unsampled locations. The spatial variation in the soil is best captured by using the empirical best linear unbiased predictor (EBLUP) based on a restricted maximum likelihood (REML) approach that efficiently exploits available data on both mean trends and correlation structures. We proposed a practical two‐step implementation of the REML approach for model‐based kriging, exemplified by predicting soil organic carbon (SOC) concentrations in mineral soils in Estonia from the large‐scale digital soil map information and a previously established prediction model. The prediction model was a linear mixed model with soil type, physical clay content (particle size < 0.01 mm) and A‐horizon thickness as fixed effects and site, transect, plot, year, year‐transect random intercepts and site‐specific random slopes for clay content. We used only the site‐specific intercept EBLUPs for estimating spatial correlation parameters as they described most of the variation in the random effects (86.8%). Fitting an exponential correlation model to these EBLUPs resulted in an estimated range of 10.5 km and the estimated proportion of the variance from the nugget effect was 0.23. The results of a simulation study showed a downwards bias that decreased with sample size. The results were validated through an external dataset, resulting in root mean square errors (RMSE) of 1.06 and 1.07% for the two‐step approach for kriging and the model with only fixed effects (no kriging), respectively. These results indicate that using the two‐step approach for kriging may improve prediction.  相似文献   

14.
《Geoderma》2002,105(1-2):49-80
Recent studies have attempted to optimize the configuration of sample sites for estimation of the variogram by the usual method-of-moments. This paper shows that objective functions can readily be defined for estimation by the method of maximum likelihood. In both cases an objective function can only be defined for a specified variogram so some prior knowledge about the spatial variation of the property of interest is necessary.This paper describes the principles of the method, using Spatial Simulated Annealing for optimization, and applies optimized sample designs to simulated data. For practical applications it seems that the most fruitful way of using the technique is for supplementing simple systematic designs that provide an initial estimate of the variogram.  相似文献   

15.
An attempt to improve the representation of a geo statistically mapped soil attribute, clay content of the surface soil, through partitioning of the study area into two new regions was made. A topographic boundary divided the study area into hill and plain regions. Possible global non-stationarity or non-stationarity within the two newly defined regions was dealt with through the use of intrinsic random functions (IRF) of order k. Cross-validation of generalized covariance functions suggested that ordinary kriging might also have been appropriate. Exponential variogram models were subsequently fitted to the experimental variograms for each region. IRF-k block kriging and ordinary block kriging were then used as the primary methods of estimation. Both IRF-k and ordinary kriging performed badly in the vicinity of the topographic boundary when global models were used. This discontinuity was removed, at the expense of the introduction of some additional edge effects, when the hill and plain regions were kriged using models appropriate to each region. Independent zero-order generalized covariance functions with nugget and linear terms and exponential variogram models produced similar representations of clay content within each region, when used with their respective estimators. Splitting the region resulted in a 6% reduction in mean absolute deviation and a 14% reduction in mean squared deviation of predicted clay contents compared with a global model.  相似文献   

16.
The clay content of the topsoil in two regions of contrasting physiography was predicted from sample data using four different procedures. The predictors were the means of mapped classes, the usual kriging estimator, a cubic spline interpolator and a kriging estimator within classes using a pooled within-class variogram. The performances of the procedures were evaluated and compared. In the first region, Sandford St Martin on Jurassic sediments where there were some abrupt changes in soil, the classification predicted best within those classes bounded by sharp change. Elsewhere the usual kriging performed somewhat better, and kriging within classes was still more precise. In the second region, Yenne on the alluvial plain of the Rhone where the soil varied gradually, kriging performed better than classification, though a small improvement resulted from combining kriging with classification. Both prediction by class means and kriging attempt to minimize the estimation variance, and their mean prediction variances were close to the theoretical values overall. Spline interpolation is more empirical, and though it followed the abrupt changes better than kriging, it fluctuated excessively elsewhere, and its overall performance was poorer than that of kriging.  相似文献   

17.
Empirical Bayesian kriging (EBK) is a modern mapping method, which accounts for the uncertainty of parameter estimates in functions describing the changes in property variance with increasing the survey area (variograms). Cartograms plotted using ordinary kriging and EBK have been compared for the data on the content of organic carbon in an isolated land with agrogray soils (Greyzemic Phaeozems (Loamic, Aric)) located in the Bryansk Opol’e region. It is shown that the cartograms of EBK errors reveal the structure of the spatial variability of the property, which cannot be revealed by other methods. Thus, the EBK method can be recommended for revealing heterogeneities in disputable cases.  相似文献   

18.
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   

19.
Eighty-three surface soil samples were collected from the Shenzhen area for determination of copper, lead, and mercury contents. The nature of spatial dependence of the measured results was quantified using variogram analysis. All variograms show well-defined structure with zero nugget and distinct sills and ranges and can be fitted by a spherical model. The range scale and the geometric anisotropy of the variograms suggest that the spatial structures of copper and lead relate closely to the distribution of parent material in the area. The variogram of mercury appears to be isotropic with a relatively small range, indicating significant influence of geographical distribution of paddy soil fields that have been severely polluted by agricultural practice.  相似文献   

20.
以黄土高原寺底沟小流域为研究对象,根据不同土地利用方式采集46个样点的土壤样品,通过地统计方法对土壤有机碳和全氮的空间变异特征进行了分析。采用受限最大似然法(REML)和矩法(MOM)两种方法分别对变异函数进行了估计,通过交叉检验选择克里金预测效果较好的变异函数进行地统计插值。(1)与矩法(MOM)相比,在多数情况下受限最大似然法(REML)估计的变异函数进行克里金插值更加准确。(2)土层深度对土壤全氮空间变异影响较小,对土壤有机碳影响较大,表层土壤有机碳含量及变异程度明显高于下层土壤。(3)土地利用方式对土壤有机碳和全氮的空间分布有重要影响,灌木林和天然草地土壤有机碳和全氮水平最高,弃耕地其次,梯田、果园、人工草地最低,表明退耕还林对提高土壤碳氮水平有重要贡献。  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号