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.     

Estimating temporal change in soil monitoring: I. Statistical theory

Detecting small temporal change of spatially varying soil properties demands precise estimation. Design– and model–based methods are compared for estimating temporal change of soil properties over finite areas. Analytical expressions for the estimators and their variances arc derived for the two approaches, and formulae for the expectations of the variances under the random–process model are developed. Among the randomized designs simple, stratified, and systematic random sampling using the arithmetic mean as estimator have been studied. Pairing the sampling positions on the different occasions increases the precision of design–based estimation if the observations are positively cross–correlated. The relative precisions of the means of stratified and systematic samples depends on the spatial correlation. Neither is more precise than the other in all circumstances. The stratified design provides an unbiased estimator for the sampling error, which is not available from systematic samples. Theoretically, the geostatistical global estimator is more precise than the estimates derived from any of the classical designs when many realizations arc repeatedly sampled at random. In practice, with only a single realization of the process, this is no longer relevant. Moreover, errors in estimating the variograms add to the total error of the method. It seems that only by sampling from large auto–correlated random fields can the precisions of the methods be compared in practice.     

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。     

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。     

土壤制图中多等级代表性采样与分层随机采样的对比研究

采样设计是土壤地理研究中备受关注的重要问题。本文以区域尺度土壤属性制图为例,将多等级代表性采样与经典采样中的分层随机采样进行对比研究。以安徽宣城研究区的表层砂粒含量为目标要素,采集数量均为59个的两套样点,设计不同数量(46、58和59)的样点分组,采用两种制图方法进行制图并利用独立验证点进行评价。结果表明:1)无论是采用多元线性回归方法还是基于环境相似度的制图方法,在同等样点数量下,利用代表性样点所得土壤图精度均高于利用随机样点所得精度,并且利用少量代表性样点(46个)所得土壤图精度也高于利用多量随机样点(59个)所得精度;2)随着代表性较低样点的增加,土壤制图精度基本有一个提高的趋势,而采用随机样点所得土壤图的精度波动较大。因此,可认为多等级代表性采样方法是一种可用于区域尺度土壤调查的有效采样方法,且比分层随机采样高效、稳定。     

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。     

Evaluating soil maps for prediction of soil water properties

Conventional soil survey stratifies a region into mapping classes and characterizes each by a representative soil profile within it. The efficacy of the procedure for predicting particle-size fractions, bulk density, water retention, and available water capacity (AWC) of the soil at previously unvisited sites on the Plain of Languedoc in southern France is evaluated for three scales of survey (1/10 000, 1/25 000 and 1/100 000) and is compared to that of prediction from stratified random and simple random samples. Data from 85 soil profiles on a random transect were used for evaluation. Classification partitioned the variation of the measured properties, except for AWC, well at the 1/10 000 and 1/25 000 scales, whereas classification at the 1/100 000 scale was less effective. At the 1/10 000 and 1/25 000 scales both classification and stratified random sampling were better for prediction than simple random sampling for the same total sample. On average the representative profiles proved substantially better predictors than the stratified random samples, but in most situations where soil stratification performed well efficiencies of the two predictors were similar. In essence, the more successful the classification was the more difficult it was to improve prediction by selecting representatives instead of sampling randomly within classes. These results confirmed statistically that the soil surveyor can exercise intuition and judgement to classify and select representatives.     

数据驱动的农作物遥感分类地面样本点布设

地面样本点是农作物遥感分类模型训练的基础，样本点数量和质量是影响模型分类精度的2个主要因素。该研究构建了数据驱动的样本点布设方法，利用待分类影像的光谱、植被指数等特征构造分层抽样底图，结合分层随机抽样方法进行地面样本点布设，并分析不同抽样策略对农作物遥感分类结果的影响。采取基于k-means聚类分析的数据驱动方法，考虑6景哨兵2号影像提取的共78个分类特征，生成同一个最优k的聚类结果图；设计等量分配和按面积比分配2种样本量分配方式，样本点数量为25、49、100、169、225的5个总样本量；基于不同抽样策略获取地面样本点信息，利用同一个支持向量机模型对待分类影像进行监督分类，并通过与139个样本点的理论总样本量和400个样本点的传统方式总样本量对比分析，定量解析不同抽样策略对分类精度的影响。结果表明：1）在数据驱动非监督聚类生成的底图上进行抽样（按面积比分层抽样法、等量分层抽样法）获得的样本点质量和分类精度明显优于没有该底图的抽样策略（简单随机抽样法、系统抽样法）；2）当总样本量低于理论总样本量时，等量分层抽样法能获取比按面积比分层抽样法更高的分类精度。例如，当理论样本量为139时，...     

Repeated measurements on permanent plots using local variability sampling for monitoring soil cover

On US military installations, training activities such as vehicle use disturb ground and vegetation cover of landscapes, and increase potential rainfall runoff and soil erosion. In order to sustain training lands, soil erosion is of major concern. Thus there is a need for sampling designs to monitor degradation and recovery of land conditions. Traditionally, permanent plots are used to obtain the change of land conditions. However, the permanent plots often provide less information over time in characterizing the land conditions because of the fixed number and locations of plots. In this paper, we analyzed the sufficiency of a permanent plot sample and developed a method to improve the re-measurements of the permanent plots over time for a monitoring system of soil erosion based on spatial and temporal variability of a random function. We first applied a local variability based sampling method to generate reference samples that have sampling distances varying spatially and temporally to monitor a soil erosion relevant cover factor for an installation, Fort Riley, USA. Then, we compared a permanent sample with the reference samples annually over 13 years to determine additional sampling in the areas with high variability and temporarily suspending measurements of the permanent plots in the areas with low variability. The local variability based sampling provides estimates of local variability of the cover factor and thus is more cost-efficient than random sampling. By comparison with a reference samples, the re-measurements obtained should more accurately characterize the dynamics of the land conditions.     

基于空间模拟退火算法的耕地质量布样及优化方法

耕地质量监测是保障耕地资源的永续利用,实现耕地产能提升、加强耕地资源的管理、保护、合理利用的重要措施,对实现持续粮食安全具有重要意义。该文提出了基于空间模拟退火算法的耕地质量布样优化方法,以空间模拟退火算法为基础生成一组最优样本,构成基础监测网络,在此基础上,通过多期耕地等级成果数据提取属性发生变化的分等因素和对应发生变化的区域,生成潜在变化区,并结合研究区实际情况辅以专家知识和异常监测点,对基础样本点进行增加、删除、替换等优化操作,生成最终监测样点。以北京市大兴区为例,最终确定布设55个监测样点,结果表明,该方法布设的样点在耕地质量预测方面的精度高于传统的随机抽样和分层抽样方法,能有效地预测县域耕地质量并监控耕地质量的变化情况。     

Developing effective sampling designs for monitoring natural resources in Alaskan national parks: An example using simulations and vegetation data

Monitoring natural resources in Alaskan national parks is challenging because of their remoteness, limited accessibility, and high sampling costs. We describe an iterative, three-phased process for developing sampling designs based on our efforts to establish a vegetation monitoring program in southwest Alaska. In the first phase, we defined a sampling frame based on land ownership and specific vegetated habitats within the park boundaries and used Path Distance analysis tools to create a GIS layer that delineated portions of each park that could be feasibly accessed for ground sampling. In the second phase, we used simulations based on landcover maps to identify size and configuration of the ground sampling units (single plots or grids of plots) and to refine areas to be potentially sampled. In the third phase, we used a second set of simulations to estimate sample size and sampling frequency required to have a reasonable chance of detecting a minimum trend in vegetation cover for a specified time period and level of statistical confidence. Results of the first set of simulations indicated that a spatially balanced random sample of single plots from the most common landcover types yielded the most efficient sampling scheme. Results of the second set of simulations were compared with field data and indicated that we should be able to detect at least a 25% change in vegetation attributes over 31 years by sampling 8 or more plots per year every five years in focal landcover types. This approach would be especially useful in situations where ground sampling is restricted by access.     

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.     

Analysing spatially intermittent variation of nitrous oxide emissions from soil with wavelets and the implications for sampling

Emissions of gases from the soil are known to vary spatially in a complex way. In this paper we show how such data can be analysed with the wavelet transform. We analysed data on rates of N₂O emission from soil cores collected at 4‐m intervals on a 1024‐m transect across arable land at Silsoe in England. We used a thresholding procedure to represent intermittent variation in N₂O emission from the soil as a sparse wavelet process, i.e. one in which most of the wavelet coefficients are not significantly different from zero. This analysis made clear that the rate of N₂O emission varied more intermittently on this transect than did soil pH, for which many more of the wavelet coefficients had to be retained. This account of intermittent variation motivated us to consider a class of random functions, which we call wavelet random functions, for the simulation of spatially intermittent variation. A wavelet random function (WRF) is an inverse wavelet transform of a set of random wavelet coefficients with specified variance at each scale. We generated intermittent variation at a particular scale in the WRF by specifying a binormal process for the wavelet coefficients at this scale. We showed by simulation that adaptive sampling schemes are more efficient than ordinary stratified random sampling to estimate the mean of a spatial variable that is intermittent at a particular scale. This is because the sampling can be concentrated in the more variable regions. When we simulated values that emulate the intermittency of our data on N₂O we found that the gains in efficiency from simple adaptive sampling schemes were small. This was because the emission of N₂O is intermittent over several disparate scales. More sophisticated adaptive sampling is needed for these conditions, and it should embody knowledge of the relevant soil processes.     

A Model-Based Approach to Designing a Fishery-Independent Survey

This paper uses Generalized Additive Models to evaluate model-based designs for wildlife abundance surveys where substantial pre-existing data are available. This is often the case in fisheries with historical catch and effort data. Compared to conventional stratified design or design-based designs, our model-based designs can be both efficient and flexible, for example in allowing uneven sampling due to survey logistics, and providing a general framework to answer specific design questions. As an example, we describe the design and preliminary implementation of a trawl survey for eleven fish species along the continental slope off South-East Australia.     

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。     

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。     

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.     

基于分融策略的土壤采样设计方法

采样设计方法在地理要素空间分布推测中起着关键作用。采集的样点数量尽可能少且推测精度较高通常是采样设计的目标。此外,高效合理的采样方案应保证较高的推测可信度,同时尽可能避免冗余样点。传统的采样方法大多依靠增加样点个数来提高推测精度,且对样点集内部的冗余情况考虑较少。为获取更加高效合理的样点集,在环境条件越相似、地理要素越相似的假设下,通过环境相似度分析计算,得到样点的推测可信度和样点集内部的冗余度,并提出一种基于分融策略的样点设计方法。该方法在分化阶段将推测可信度低的样点进行分化,增加样点以降低推测不确定性,在融合阶段将环境条件过于相似的样点进行融合以降低冗余,通过多次分化融合最终使得推测可信度和冗余度均达到一定的预设标准,得到最佳样点方案。将该方法应用于美国Raffelson研究区的土壤采样,结果表明,该方法在分化阶段可以有效提高样点的推测可信度,在融合阶段能够有效去除冗余样点,最终可得到用于推测的高效样点。将本方法与传统的规则采样和分层随机采样进行对比,结果反映本方法获得的样点在同等数量下推测可信度更高,冗余度更低,更高效。