DPTIMAL INTERPOLATION AND ISARITHMIC MAPPING OF SOIL PROPERTIES. IV SAMPLING STRATEGY

A sampling strategy is presented for soil survey in which an individual soil property is of interest and can be measured. It depends on first determining accurately the semi-variogram for the property, and this must be done in a prior reconnaissance stage of a survey. Then from the semi-variogram estimation variances can be found for any combination of block size and sampling density by the methods of kriging. Alternatively for a given block size the sampling density needed to achieve a predetermined precision (maximum estimation variance) can be determined. The strategy is optimal in the sense that the sampling effort is the least possible to achieve the precision desired. An equilateral triangular configuration of sampling points is best where variation is isotropic, but a square grid at the same density is very nearly as good, and will usually be preferred for convenience. Where there is simple anisotropic variation optimal sampling is achieved by choosing a rectangular grid with sides in the same proportion to one another as the slopes of the semi-variogram in the directions of maximum and minimum variation.     

Optimal interpolation and isarithmic mapping of soil properties

The principle of optimal estimation using regionalized variable theory is extended from that of a single soil property to situations where there are two or more spatially interdependent ones. Auto and cross semi-variograms express the spatial relations among the properties concerned. They can be estimated from data and can then be used to interpolate the values of a variable by co-kriging from measurements of it plus data on one or more other properties that have been more intensively sampled. The technique of co-kriging is described and illustrated by a case study of the particle size distribution at Woburn experimental farm. There was a strong co-regionalization with common anisotropy between topsoil silt, subsoil silt and subsoil sand. This allowed topsoil silt to be estimated and mapped by co-kriging more precisely than by kriging from data on topsoil silt alone. When the auto and cross semi-variograms for a set of variables are known in advance or estimated from reconnaissance they can be used to plan an optimal sampling scheme. The main variable is sampled on a rectangular grid with finer grids for subsidiary variables. The maximum kriging variances are calculated for a range of sample spacings and relative sampling intensities. Those that match the maximum tolerable variance are potentially useful. The optimum scheme is the one that achieves the desired precision for least cost. For Woburn it is shown that measuring a main variable would need to cost at least 5 times that of a subsidiary variable to make a design for co-kriging economically sound. Such differences are unlikely for particle size fractions. Nevertheless there are many other instances in soil research where there are large differences in cost. If there is also a strong co-regionalization then savings should be possible by designing a sampling scheme that takes advantage of co-kriging.     

Choosing functions for semi-variograms of soil properties and fitting them to sampling estimates

The semi-variogram is central to geostatistics and the single most important tool in geo-statistical applications to soil. Mathematical functions for semi-variograms must be conditional negative semi-definite, and there are only a few families of simple function that meet this demand. These include the transitive models with finite a priori variance deriving from moving average processes. The spherical and exponential schemes are the most often encountered members. The other major group is that of unbounded models in which the variance appears to increase without limit. The linear model is the most common in this group. If more complex models are needed they can be formed by combining two or more simple models. The usual estimator of the semi-variance is often considered inefficient and to be sensitive to departures from normality in the data. It is compared with a robust estimator and shown to be generally preferable in being unbiased and having confidence intervals that are no wider. For routine analysis, fitting models to sample semi-variograms by weighted least squares approximation, with weights proportional to the expected semi-variance, is preferred to the more elaborate and computationally demanding statistical procedures of generalized least squares and maximum likelihood. The Akaike information criterion is recommended for selecting the best model from several plausible ones to describe the observed variation in soil, though for kriging it may be desirable to validate the chosen model. Examples of models fitted to soil semi-variograms are shown and compared.     

OPTIMAL INTERPOLATION AND ISAR1THMIC MAPPING OF SOIL PROPERTIES

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. Simple punctual kriging produced a map with intricate isarithms and fairly large estimation variance, attributed to a large nugget effect. Sloniness 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.     

土壤调查数据地域统计的最佳估值研究-彰武县表层土全氮量的半方差图和块状Kriging估值

近年来国际土壤应用数学和土壤信息系统的研究趋势之一,是引用地质统计(Geostatistics)的最佳估值法处理土壤调查的数据.地质统计是目前地质部门在探矿与采矿应用的一种先进空间分析方法,它的要点是根据地面不同选点钻井所获得的不同深度的数据资料、寻求数据信息与采样点的位置和采样深度的统计相关性来对矿产进行空间结构分析与数量估计.     

OPTIMAL INTERPOLATION AND ISARITHMIC MAPPING OF SOIL PROPERTIES

Soil properties mapped in two intensive surveys had large nugget variances, leading to large estimation variances and erratic isarithms when mapped by punctual kriging. It is likely that both surveyors and survey clients are interested in average values of soil properties over areas rather than point values, and such values can be obtained by block kriging. Estimation variances are very much smaller, and maps of sodium and stone content at Plas Gogerddan, Central Wales, kriged over blocks 920m², and thickness of cover loam at Hole Farm, Norfolk, kriged over blocks of 400m², are much smoother than the punctually kriged maps. The map of Hole Farm has a distinct and meaningful regional pattern.     

A case study on the estimation accuracy of soil properties and fertilizer rates for different soil‐sampling grids

Soil testing is used to help make fertilizer recommendations for greater yields and profits. But the increase of soil‐sampling density raises costs of sample collection and analyses. The aim of this study was to compare grid‐cell sampling densities (1, 2, and 4 ha) in terms of the estimation accuracy of macronutrients (P, K, Mg) availability and pH and to investigate how sampling density affects the amount of fertilizers and lime recommended and correctly applied to winter wheat (Triticum aestivum L.). The distribution of liming requirements and available nutrients were quite similar for the 1‐ and 2‐ha grids but notably different for the 4‐ha grid. However, the whole‐field average values of pH and P, K, and Mg concentrations in soil obtained for different sampling densities were very similar, thus placing, respectively, the soil of the studied area in the same class of liming needs and nutrient availability. The range and estimation errors of these parameters decreased with sampling‐grid size increase. The amount of lime and fertilizers to be applied on the field and the portion of a field correctly limed or fertilized depended on the soil chemical property considered. If one treats the 1‐ha grid as the reference and the most correct soil‐sampling approach, 2‐ha grid offered the greatest part of the field to be adequately fertilized with lime, P, and K. However, fertilization with Mg was much more appropriate if the recommendation was based on 4‐ha, than on a 2‐ha soil‐sampling grid. To gain an insight into soil variation and soil process occurring at small scale, laboratory and geostatistical analyses on individual soil samples may be necessary in some cases. Possibly, such costly research can deliver relevant information which could be then applied into farmer's practice.     

基于Kriging估计误差的县域耕地等级监测布样方法

为了监测耕地的质量等级,通常采取抽样调查的方法.由于空间样本间存在不独立性等原因,传统抽样方法效率低、精度不高.为此,该文提出基于Kriging估计误差的布样方法,定义了反映Kriging估计情况的统计量作为评估监测网的标准,通过分析样本量与抽样精度的变化趋势确定最优样本容量,将调整过的方形格网作为监测网的基础,在泰森多边形限制下对监测网优化增密,并选用部分标准样地作为监测点.以北京市大兴区为例对该方法进行验证,结果表明,当监测点数同为48时,该文方法均方根误差小于简单随机抽样、分层抽样以及单一使用格网布样的方法,预测总体均值的相对误差为0.07%.因此,该文方法使用较少的监测点反映县域耕地等级的分布状况和变化趋势,能够满足县域耕地等级监测的需求.     

The elucidation of soil pattern in the Wyre Forest of the West Midlands, England. II. Spatial distribution

The spatial distribution of soil in the Wyre Forest of England was analysed in two phases. In the first the soil was examined at sites chosen using a five-stage nested design with spacings increasing geometrically from 6 m to 600 m. Some 80% of the variance was contributed by components for the spacings between 6 m and 60 m. Measurements were then made on transects at 5 m intervals and semi-variograms estimated to 70 m. Except for those of pH the semi-variograms of the soil properties had the same general transitive form and a common effective range of about 40 m. This short range meant that very intensive sampling, approximately one point per 400 m², is needed to map the soil variation. A survey was made of a small portion of the forest on a 20m × 25 m grid to test the inference. Maps of clay and sand content were made successfully by kriging from the data. The mutual correlations between soil properties and the common range of their semi-variograms enabled a general purpose and spatially coherent soil classification to be created from the data. Its mapping confirmed the intricacy of the soil pattern in the Forest.     

OPTIMAL INTERPOLATION AND ISARITHMIC MAPPING OF SOIL PROPERTIES III CHANGING DRIFT AND UNIVERSAL KRIGING

Universal kriging is a form of interpolation that takes account of local trends in data when minimizing the error associated with estimation. The presence of such trends, or drifts as they are known, is identified qualitatively, and their form found quantitatively by structural analysis, which simultaneously estimates semi-variances of the differences between the drift and actual data. The resulting semi-variograms are then used for the interpolation. The method was applied to measurements of electrical resistivity made in the soil at 1 m intervals at Bekesbourne, Kent. Analysis showed that the data could be adequately represented as a series of linear drifts over distances of 4 m to 8 m and with negligible nugget variance. Semi-variances of residuals from the drift were computed, and used to krige missing values and so complete an isarithmic map of the site. The method is by no means universally applicable in soil survey, mainly because of the large nugget variances usually encountered. These effectively prevent any distinction between constant and changing drift. They arise in part because measurements are made on small widely separated volumes of soil. Universal kriging is likely to be profitable only where measurements are made on contiguous volumes of soil or after substantial bulking.     

Estimating temporal change in soil monitoring: II. Sampling from simulated fields

Design-based and model-based methods of estimating temporal change of soil properties over a finite area have been compared. Two large fields of auto- and cross-correlated data were simulated, each representing the spatial distribution of a variable at one time. The fields were then sampled repeatedly. The means of stratified and systematic random samples and geostatistical global estimates were used to infer the mean difference between the fields. All estimators were unbiased, but their variances differed. Pairing the positions on the two occasions increased the precision of the design–based estimates. Systematic sampling was slightly more precise than stratified sampling. Kriging was less precise than both because some of the sample information must be used to estimate the variograms at short lags. Neither balanced differences nor the normal formula for simple random sampling predicted the estimation variances of small (n< 50) systematic samples accurately. For larger samples the method of balanced differences performed well. If the spatial variation is unknown in advance and only small samples can be taken then stratified random sampling with two observations per stratum is the preferred design. It resulted in the best combination of precision and accuracy in predicting the sampling error.     

短距离样点对土壤呼吸空间变异预测精度的影响

不同采样设计会对土壤呼吸空间变异特征的预测精度产生重要影响。本研究选取黄淮海平原北部潮土区1 km×1 km夏玉米样地,在7×7单元规则格网(样点间距167 m)、完全随机(样点平均间距433 m)以及3×3单元规则格网+完全随机(样点平均间距405m)3种布点方式的基础上,保持样本总量(49)不变,以占总样点2%～14%的短距离样点(样点间距4m)随机替换原方案相应样点个数的方法优化布点方式,应用普通克里金法插值,以均方根误差(RMSE)和确定系数(R2)作为验证指标,检验基于3种布点方式设置的短距离样点对土壤呼吸空间变异预测精度的影响。结果表明:研究区土壤呼吸平均速率为2.65μmol·m?2·s?1,空间分布均呈西高东低,表现出中等程度变异。采样设计对土壤呼吸空间分布的预测精度影响显著,基于3种布点方式设置短距离样点可提高预测精度7%～13%。无短距离样点替换时,规则格网+完全随机的布点方式最优,比完全随机布点和规则格网布点的空间插值预测精度分别提高10%和22%;设置短距离样点替换后,在最优布点方式(规则格网+完全随机)中,对土壤呼吸空间变异的预测精度可再提高4%～7%,其中短距离样点个数占样本总量10%对土壤呼吸空间变异预测精度的提高最为明显。研究发现,基于相同的样本数量设置短距离样点可增加区域范围内样点密度,提高土壤呼吸空间变异预测精度及试验结果的可靠性。因此,在黄淮海平原北部潮土区100 hm2尺度的夏玉米样地中,规则格网+完全随机+10%短距离样点的布点方式是预测土壤呼吸空间变异最适宜的采样布点方式。     

田间尺度下测定土壤有效K、P的采样方法

Field nutrient distribution maps obtained from the sutdy on soil variations within fields are the basis of precision agriculture,The quality of these maps for maagement depends on the accuracy of the predicted values,which depends on the initial sampling.to Produce reliable predictions efficently the minimal sampling size and combination should be decided firstly,which could avoid the misspent funds for field sampling work.A 7.9 hectare silage field close to the Agricultural Research Institute at Hillaborough,Northern Irealnd,was selected for the study,Soil samples were collected from the field at 25m intervals in a rectangular grid to provide a database of selected soil propoerties.Different data combinations were subsequently abstracted from this database for comparison purposes,and ordinary krging used to produce interpolated soil maps.These prediced data groups were compared using least significant difference(LSD) test method.The results showed that the 62 sampling sizes of triangle arrangement for soil available K were sufficient to reach the required accuracy.The triangular sample combination proved to be superior to a rectangular one of similar sample size.     

西南丘陵区坡地土壤水分的时空变异

利用地统计学方法研究了我国西南丘陵区坡地土壤水分特性的时空变异特性。土壤水分含量在不同季节和不同层次具有一定的空间结构,可用纯块金效应模型、指数模型和球状模型进行拟合;土壤平均含水量、剖面各层含水量和半方差参数除变程外均随季节表现出明显的变化,但随土壤层次无明显的变化规律;土壤含水量的空间相关性随季节呈波动变化,块金值的变化趋势与基台值相似。克立格插值结果显示不同季节土壤平均含水量的空间分布格局不同。     

土壤硝态氮含量检测和分布图生成中的最优样本量

土壤参数的时空变异是实施精细农业时要考虑的重要因素，在土壤检测的栅格采样中有必要确定最优样本量。本研究的试验田是一块生长中的玉米地块，试验区的面积为4.2 m×4.2 m，该试验区被假定为土壤采样中的一个栅格，该栅格又被细分为49个0.6 m×0.6 m的子栅格。采样时，所分析的土壤参数为土壤硝态氮含量，从播种到收获共进行了7次采样。通过对土壤样本土壤硝态氮时空变异的分析，揭示了样本量和土壤硝态氮含量预测误差之间的相关关系。土壤硝态氮含量呈非正态分布，通过对玉米各个生长期获得的数据分析表明：含量水平的预测误差随深度的增加而增大；当从一个栅格只采集1个土壤样本时(样本量为1)，预测误差基本在50％左右(显著水平：α≈0.10)，而当从一个栅格采集5个土壤样本时(样本量为5)，预测误差将降至25％左右。另一方面，当要求预测误差低于30％时，对于普通生长条件下的土壤需要从1个栅格至少采集3个样本，而对于追肥后的土壤则至少需采集15个样本。     

COMPUTER-BASED SOIL MAPPING OF SMALL AREAS FROM SAMPLE DATA

A 1400 m × 600 m rectangular area of north Berkshire had been sampled at the intersections of a 100 m square grid, and seventeen properties of the soil profile measured. The eighty-four sampling sites were classified numerically to produce a hierarchy, and the classes of the upper part of the hierarchy mapped. The mapped classes became increasingly fragmented as the number of classes increased. At the 3-class level, the classes corresponded to character space clusters and class fragmentation was not serious. Principal-component analysis of the sample data yielded a first component that accounted for 40 per cent of the total variance and well represented the field characters used for soil classification. An isarithm map of the first component shows how the soil changes gradually over the landscape in good agreement with a soil-series map made by free survey.     

Local disjunctive kriging of soil properties with change of support

Disjunctive kriging estimates from a set of measurements the conditional probability that true values of a regionalized variable such as a soil property exceed, or are less than critical thresholds. Estimates can be for sites equal in size to the supports of the samples and, by changing the support of the variogram, for larger blocks. The method also estimates the block averages and their associated variances. The underlying theory and steps in the analysis are described. They are illustrated using a case study from south-east Scotland where the aim is to estimate the likelihood of copper and cobalt deficiency over whole farms or 1 km² blocks of land using data from individual fields of 5 to 10 ha only. Maps show the conditional probabilities for 1 km² squares that the available copper in the soil is less than 1 mg kg^?1 and that cobalt is less than 0.25 mg kg^?1.     

Spatial structures of soil organic carbon in tropical forests—A case study of Southeastern Tanzania

Southeastern Tanzania serves as a typical example of soil degradation and soil organic carbon (SOC) losses on the African continent. Although sequestration of SOC through aforestation or reforestation proved favorable, these measures are restricted by the ability to produce rapid, cost-effective and precise sampling schemes. The aim of this study is to contribute to a better knowledge of the spatial distribution of soil C in tropical natural and plantation forest. This paper presents sampling strategies for estimating mean SOC values as well as for SOC mapping, based on different methods for SOC determination and on different precision levels. To do so we conducted a carbon variability study in five common forest types of Southeastern Tanzania (coastal dry forest, Miombo woodland, teak plantation, pine plantation and cashew plantation) using conventional statistical methods, as well as geostatistics. In the 5 forest types of this study, SOC stocks in the upper 5 cm ranges between 5 (in the cashew plantation) and 13 (in the coastal forest) t ha^− 1. The optimal sampling distance for measuring mean SOC stocks varies between 36 m (in the patchy miombo woodland) and 422 m (in the homogenized cashew plantation). Sample sizes fluctuate between 6 and 72 (1 t ha^− 1 precision) for respectively cashew plantation and coastal forest. A rectangular grid with a sample interval of 25 m can be used for SOC mapping with a point kriging estimation error of 3.0 t ha^− 1 in the coastal forest, 2.6 t ha^− 1 in miombo woodland, 2.2 t ha^− 1 in the teak plantation and 1.1 t ha^− 1 in the cashew plantation. Since the pine plantation has no spatial structure; samples can be arranged randomly and its best soil map has an average C content attributed over the whole field. Refining the sampling strategy with a new spatial variability study in other forest types can be based on a regular grid with sampling distances of half the range identified in this study. This paper proves that the optimal sampling scheme varies strongly as a result of the different spatial behavior of SOC in forests and depends on the required precision and research question. Only when the right strategy is followed, high standards of precision can be met without economic loss or risk of statistical misinterpretation.     

类别辅助变量参与下的土壤无偏采样布局优化方法

为了提高采样点在地理空间和辅助变量特征空间中的代表性,该文提出特征空间偏离指数用以测度采样点在特征空间中的无偏性,采用类别型辅助变量参与下的多维特征空间构建方法,融合地理空间和特征空间均匀分布的多目标优化目标函数,并利用空间模拟退火的方法实现采样点布局优化。以北京顺义区农田土壤重金属采样为例,选取土地利用类型、土壤质地和母质为辅助变量进行样点布局优化,并与特征空间均匀和地理空间均匀采样方法比较,结果表明:用于区域变量总体估计时,地理空间均匀采样估计精度最低,在采样尺度大于0.275时以特征空间均匀采样估计精度最好,而在采样尺度小于0.275时,无偏采样能获得更好的估计结果;在特征空间代表性方面,采样尺度较大时特征空间均匀采样样点代表性最好,采样尺度小于0.302时,无偏采样与特征空间均匀采样的代表性基本一致,地理空间采样点的代表性最差;用于空间制图时,无偏采样总体上比其他2种方法具有更好的制图精度。可见,在辅助变量支持的采样优化中,当采样尺度大且样点数较少时,适合采用特征空间均匀方法,且只能用于总体估计;采样尺度较小,样点数多时,适合采用无偏采样方法。该研究为利用辅助变量设计区域采样布局提供参考。