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.     

A comparison of some robust estimators of the variogram for use in soil survey

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.     

The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment

The purpose of this note is to propose a variance estimator under non-measurable designs that exploits the existence of an auxiliary variable well correlated with the survey variable of interest. Under non-measurable designs, the Sen–Yates–Grundy variance estimator generates a downward bias that can be reduced using a calibration weighting based on the auxiliary variable. Conditions of approximate unbiasedness for the resulting calibration estimator are given. The application to systematic sampling is considered. The proposal proves to be effective for estimating the variance of the forest cover estimator in remote sensing-based surveys, owing to the strong correlation between the reference data, available from a systematic sample, and the satellite map data, available for the whole population and hence exploited as an auxiliary variable. Supplementary materials accompanying this paper appear online.     

Estimation and implications of instrumental drift, random measurement error and nugget variance of soil attributes—a case study for soil pH

We propose a general model for soil pH measurement that includes instrumental drift, random measurement error, and random and correlated spatial variation. Methods for estimating these four components are described in detail. For soil pH in water, instrumental drift, random measurement error and random spatial variation (nugget effect) were greater than the corresponding quantities for soil pH in CaCl₂. For both pH measurements, instrumental drift was quite marked. Measurement error and nugget effect were of a similar size. A modified kriging method is presented that takes into account the four-component model proposed here. It is concluded that, for measuring soil chemical attributes, grid layouts should be supplemented by additional sites for the estimation of short-range variation, that laboratory sampling designs should include controls, and that field measurements should be adjusted for instrumental drift prior to being used for spatial contouring or kriging.     

Using a Master Sample to Integrate Stream Monitoring Programs

The need for aquatic resource condition surveys at scales that are too extensive to census has increased in recent years. Statistically designed sample surveys are intended to meet this need. Simple or stratified random sampling or systematic survey designs are often used to obtain a representative set of sites for data collection. However, such designs have limitations when applied to spatially distributed natural resources, like stream networks. Stevens and Olsen proposed a design that overcomes the key limitations of simple, stratified random or systematic designs by selecting a spatially balanced sample. The outcome of a spatially balanced sample is an ordered list of sampling locations with spatial distribution that balances the advantages of simple or stratified random samples or systematic samples. This approach can be used to select a sample of sites for particular studies to meet specific objectives. This approach can also be used to select a “master sample” from which subsamples can be drawn for particular needs. At the same time, these individual samples can be incorporated into a broader design that facilitates integrated monitoring and data sharing.     

基于结构规模的冬小麦种植面积遥感抽样估算

在种植结构复杂地区,由于受到混合像元和同期作物的影响,传统的以规模为分层标志进行冬小麦种植面积遥感估算难以保证抽样效率和精度。该文综合考虑混合像元、同期作物的影响,构建了结构规模指标进行冬小麦种植面积遥感抽样估算。采用TM和QuickBird为研究数据,设计不同的抽样方案估算冬小麦的种植面积,计算标准误差、准确度和变异系数衡量估算精度,与传统简单随机、规模指标分层抽样进行对比分析,验证本文方法的有效性。试验结果表明,以结构规模指标分层抽样的反推结果在各项指标上均明显优于传统简单随机、规模指标分层抽样方式,尤其在小样本量时,标准误差降低2.0×105m2,准确度提升了1%。该研究结果为在大范围种植结构复杂地区进行冬小麦种植面积遥感估算的改进提供了试验依据。     

作物种植面积空间对地抽样方法设计

传统的粮食作物种植面积估算一般采用目录抽样方法，由于缺乏现实、有效的先验知识，抽样过程受精度和效率制约。本文利用地理信息系统、遥感和全球定位系统技术，结合传统的随机、系统和分层抽样方法，设计三种新的粮食作物种植面积空间对地抽样方案，并在此基础上开展试验对比研究，分析它们在抽样精度、最少样本量和稳定性方面的差异。结果表明，本文所设计的空间分层抽样方法所需样本量较小，且具有较高的估算精度和稳定性，可以用于大范围农作物种植面积监测。     

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。     

空间抽样方法估算冬小麦播种面积

为改进现行农作物播种面积空间抽样技术体系,该文以山东省为研究区,以冬小麦播种面积为研究对象,通过"3S"技术(遥感、地理信息及全球定位技术)与传统抽样方法的联合应用,选取4种抽样技术(简单随机抽样、按冬小麦种植区划分层抽样、按耕地类型分层抽样和按分县冬小麦面积大小分层抽样),设计8种样本容量水平(变化范围74～333)进行了冬小麦播种面积空间抽样方法试验研究,结果表明:4种抽样方法中,在外推总体相对误差相近条件下,以分县冬小麦播种面积大小为分层标志的分层抽样方法效率最高;基于8种样本容量下的样本观测值进行研究区冬小麦播种面积总体外推与误差估计时,随着样本容量增加,外推总体总值估计值与真值的相对误差随之减小,但总体总值估计量的变异系数(CV)值仍较大。     

空间自相关性对冬小麦种植面积空间抽样效率的影响

空间抽样是实现区域农作物面积高效估算的重要手段,农作物分布受自然条件等因素影响普遍存在空间自相关性,但以往针对空间相关性对农作物面积抽样效率的影响研究明显不足。该研究选取安徽省凤台县为研究区,通过2017年4月4景GF-1全色多光谱影像(Panchromatic and Multispectral, PMS)与Google Earth高空间分辨率影像相结合提取研究区冬小麦。设计10种抽样单元尺度、3种抽样外推方法、2种相对允许误差和5种样本布局方式,构建多种冬小麦面积空间抽样方案。利用全局莫兰指数(global Moran’s index)评价不种尺度下抽样单元内冬小麦面积比的空间自相关强度,分析空间自相关性对冬小麦面积抽样效率(抽样误差、样本容量和空间布局)的影响。研究结果表明,抽样单元内冬小麦面积比的空间自相关强度随单元尺度的增大而减小,全局莫兰指数相应地由0.75降至0.50。无论在何种尺度下抽样单元内冬小麦面积比都呈显著的空间正相关性;抽样外推冬小麦面积总体的误差随空间自相关强度的减小呈先减小后明显增大的趋势。在10种抽样单元尺度中,当抽样单元尺度为2000m且抽样比为5%时,无论采用何种抽样方法外推总体的误差均为最小(简单随机抽样、系统和分层抽样外推总体的相对误差分别为17.94%、9.48%和1.82%);当相对允许误差设计为5%时,简单随机抽样外推总体所需样本容量随空间自相关强度的降低从660降至56。而分层抽样的样本容量不受空间自相关性的影响;5种样本布局方式中,采用分层随机抽样方式外推冬小麦面积总体的平均相对误差、平均变异系数和均方根误差最小,分别为1.82%、3.19%和0.11×108 m2。该研究可为有空间自相关存在下的农作物面积空间抽样方案合理设计提供参考依据。     

Robust estimation of the pseudo cross‐variogram for cokriging soil properties

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.     

A three-phase sampling strategy for large-scale multiresource forest inventories

This article considers a two-phase estimation for the areal extent of K land categories partitioning a study region and a three-phase estimation for the biomass of W forest categories out of the K. In the first phase, a sample of N points is selected according to the unaligned systematic sampling. In the second phase, the selected points are partitioned into L strata on the basis of aerial photos. Then, a total sample of n < N points is selected by stratified sampling and the selected points are visited on the ground and correctly classified into one of K categories. The information achieved in the second phase is sufficient for obtaining an unbiased estimator of the areal extent vector together with a conservative estimator of its variance-covariance matrix. As to the estimation of the biomass of the W forest categories, in the third phase the second-phase sample is further partitioned into substrata on the basis of ground information. Finally, a total sample of m < n points is selected by stratified sampling. Then a plot of adequate radius centered at each point is considered and the biomass is recorded within. An unbiased estimator of the biomass vector is derived together with a conservative estimator of its variance-covariance matrix. The proposed strategy also makes it possible to obtain the calibrated estimator of the areal extent vector as well as estimators for the sums or ratios of the areal extents and biomasses. The application of the strategy in the Italian National Forest Inventory is considered.     

Soil salinity characteristics using moderate resolution imaging spectroradiometer (MODIS) images and statistical analysis

Remote sensing is currently a tremendous asset in controlling and monitoring soil salinity. Moderate resolution imaging spectroradiometer (MODIS) images can be obtained daily, are free, offer more opportunities to acquire cloud-free images and may be preferred over high-resolution spatial data. The main objective of this study was to evaluate the capability of MODIS imagery to assess soil properties when coupled with field soil sampling. The study area was ～95,000 ha, located in the south-east of Fars Province, Iran. In total, 240 soil samples were selected from 60 georeferenced soil pits, following a stratified random sampling approach. Sixteen spectral indices were calculated from a nadir-viewed MODIS scene to establish statistical correlation models between measured soil properties and MODIS band values. A precise map of the soil properties was produced using geostatistical techniques. A paired-sample t-test indicates that there are no significant differences between values estimated using MODIS data statistical modeling and laboratory-measured soil properties of samples collected through fieldwork. The results also indicate that image transformation (salinity index (SI) to radiance) reduces estimation errors and increases both model efficiency and the R ² of the models. The results also indicate that MODIS imagery provides useful information on soil properties.     

Exploring scale‐dependent correlation of soil properties by nested sampling

The value of nested sampling for exploring the spatial structure of univariate variation of the soil has been demonstrated in several studies and applied to practical problems. This paper shows how the method can be extended to the multivariate case. While the extension is simple in theory, in practice the direct estimation of covariance components by equating mean‐square matrices with their expectation will often lead to estimates that are not positive semidefinite. This paper discusses solutions to this problem for balanced and unbalanced sample designs. In the balanced case there is a residual maximum likelihood (REML) estimator that will find estimates of covariance components that maximize an overall likelihood on the condition that all components are positive semidefinite (p.s.d.). This is possible because the condition is met if the differences of successive mean‐square matrices are positive semidefinite, and this constraint can be incorporated into an algorithm. This does not hold for unbalanced designs. In this paper the problem was solved for unbalanced designs by scaling covariance components that were not p.s.d. to the nearest p.s.d. matrix according to a Euclidean distance. These methods were applied to data from three surveys, two with balanced and one with unbalanced sampling. Different patterns of scale‐dependence of the correlation of soil properties were found. For example, at Ginninderra Experimental Station in Australia the soil water content and bulk density were correlated significantly, with the correlation increasing with distance to 56 m, but at longer distances the properties were not significantly correlated. By contrast, the pH of the soil and the available P content showed correlation that increased with distance. The implications of these results for planning more detailed sampling, both for prediction and for investigation of processes, are discussed.     

Spatio‐temporal change of soil organic matter content of Jiangsu Province,China, based on digital soil maps

Estimation of spatio‐temporal change of soil is needed for various purposes. Commonly used methods for the estimation have some shortcomings. To estimate spatio‐temporal change of soil organic matter (SOM) in Jiangsu province, China, this study explored benefits of digital soil maps (DSM) by handling mapping uncertainty using stochastic simulation. First, SOM maps on different dates, the 1980s and 2006–2007, were constructed using robust geostatistical methods. Then, sequential Gaussian simulation (SGS) was used to generate 500 realizations of SOM in the area for the two dates. Finally, E‐type (i.e. conditional mean) temporal change of SOM and its associated uncertainty, probability and confidence interval were computed. Results showed that SOM increased in 70% of Jiangsu province and decreased in the remaining 30% during the past decades. As a whole, SOM increased by 0.22% on average. Spatial variance of SOM diminished, but the major spatial pattern was retained. The maps of probability and confidence intervals for SOM change gave more detailed information and credibility about this change. Comparatively, variance of spatio‐temporal change of SOM derived using SGS was much smaller than sum of separate kriging variances for the two dates, because of lower mapping variances derived using SGS. This suggests an advantage of the method based on digital soil maps with uncertainty dealt with using SGS for deriving spatio‐temporal change in soil.     

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.     

基于空间平衡法的县域耕地质量监测布样方法

县域监测样点布局是反映耕地质量等级变化的基础,样本点布设的质量直接影响到耕地质量监测的结果和精度。因此,该文提出了基于空间平衡法的县域耕地质量监测布样方法,对影响耕地质量监测成本和精度的主要因素进行分析,选取样本点距离道路远近、样本点所在位置坡度高低和自然质量各等别样本容量3个方面综合生成包含概率栅格图层,图层中的像元值指总体单元中一个单元相对于其他单元被抽中的相对概率,在此基础上,运用空间平衡算法对包含概率栅格层进行空间改造,抽样选取监测样点,以平均Kriging预测标准差和监测样本点距县级主要道路的平均距离作为优化评价准则,将该方法与传统抽样方法进行比较分析。以江西省吉安县为例,全县布设78个监测样点,结果表明,当样点数量相同时,该方法相较传统布样方法在抽样精度和抽样成本方面均有一定的优势,能有效地监测耕地质量变化,满足县域耕地质量监测的需求。     

玉米种植面积空间抽样调查方案优化设计

抽样比、样本空间布局及抽样单元尺度是组成空间抽样调查方案的基础要素。为进一步改善现行农作物种植面积空间抽样调查效率,该文以吉林省德惠市为研究区,以玉米种植面积为研究对象,选取正方形网格作为抽样单元,通过空间分析、"3S"技术与传统抽样方法相结合进行农作物种植面积空间抽样方案优化设计试验研究。结果表明,抽样单元间空间自相关性随单元尺度的增大而增大,两者间呈线性正相关关系。当抽样单元尺度为500 m×500 m时,抽样单元间空间自相关性几乎不存在。遵循传统抽样理论要求样本间相互独立原则,选取500 m×500 m作为最优抽样单元尺度;对抽样单元内玉米种植面积与耕地面积进行相关分析发现,两者间存在极显著线性正相关关系。为提高玉米种植面积空间分层抽样效率,可选取耕地面积作为分层标志;以抽样外推总体相对误差(r)和变异系数(coefficient of variation,CV)为空间抽样效率评价指标,在4种(简单随机、系统等距、分层随机及分层系统等距)样本空间布局方式中,选取分层系统等距抽样作为最优样本布局方式;在7种抽样比(0.5%、1.0%、1.5%、2.0%、2.5%、3.0%、3.5%)设计水平中,选取1%作为最优抽样比。该文可为提高农作物面积空间抽样调查效率提供试验依据。     

Employing elevation data for efficient mapping of soil pollution on floodplains

Abstract The co-regionalization between relative elevation and zinc concentration was used to map zinc concentration in the soil of the Geul floodplain in the southern Netherlands by co-kriging from 154 observations. Point co-kriging and point kriging for estimating zinc content in the soil were compared in terms of kriging variances. Another 45 samples were used to compare the precision of the estimated values in terms of squared and absolute estimation errors. Point co-kriging produced better estimates of zinc concentration than either simple point kriging or linear regression from the relative elevation data alone. Moreover, the estimation variances for co-kriging are substantially smaller than those for kriging. The results suggest that knowledge of geomorphological processes can often improve the quality of interpolation maps of properties that are expensive to measure.