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.     

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.     

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。     

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。     

Parameter estimation with egg production surveys to estimate snapper, Pagrus auratus, biomass in Shark Bay, Western Australia

Snapper (Pagrusauratus) stocks found inside Shark Bay, Western Australia, are the basis of important recreational fisheries. An evaluation of the daily egg production method for annual snapper stock assessment commenced in 1997. Initial spawning biomass estimates were inconclusive due to wide confidence intervals around egg production in particular. In 1998, more comprehensive surveys were conducted in an effort to improve the accuracy and precision of the estimated parameters. Egg survey design used information on the location of the main spawning areas and spawning times identified in 1997 and employed a systematic stratified adaptive sampling approach. Further refinements to the daily egg production method included use of nonlinear regression and nonparametric bootstrapping techniques. Results are discussed in relation to the precision of parameter estimates, with reference to egg production in particular, and the appropriateness of analytical methods used.     

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。     

不同取样方式下土壤质地空间插值的精度分析

为研究土壤质地的合理取样方式,进而研究其空间变异情况,为田间施肥及灌溉提供依据,本试验利用地统计学方法和GIS技术,在重庆市彭水县重庆烟草试验站,利用289个表层土样,研究了16 m间距的栅格取样法(对照,253个土样,扣除36个验证样点)、34 m间距的栅格取样法(115个土样)和随机取样法(115个土样)3种取样方式下土壤质地的空间插值精度。3种土壤颗粒指标中粉粒占68.43%,砂粒含量最少,占12.68%,黏粒含量略高于砂粒。砂粒和黏粒具有中等强度的变异性,粉粒具弱变异性,且数据符合正态分布。地统计分析显示,在分析该区域土壤质地时,采用栅格取样方法应适当增大取样间距,而采用随机取样方法可适当缩小取样间距。交叉检验显示,土壤质地成分在3种取样方式下的插值精度均以对照最大,栅格取样次之,随机取样最小。综合考虑插值误差、样品采集和分析成本及时效性等因素,本研究建议在该区域进行土壤质地空间变异规律分析为生产服务时应采用随机取样。     

Environmental and spatial characterisation of bacterial community composition in soil to inform sampling strategies

Soil physicochemical properties and microbial communities are highly heterogeneous and vary widely over spatial scales, necessitating careful consideration of sampling strategies to provide representative and reproducible soil samples across field sites. To achieve this, the study aimed to establish appropriate sampling methodology and to determine links between the variability of parameters, utilising two sampling strategies. The first (design 1) involved extracting 25 cores from random locations throughout the field and pooling them into five sets of five cores. The second (design 2) involved a further 25 cores within five 1 m² sub-plots. Sub-samples from each sub-plot were pooled in order to determine between and within sub-plot variability. All samples were analysed independently and as pooled sub-samples. Results indicate that pooling spatially separated samples significantly reduced the variability in pH, compared to individual samples. Pooling samples from a small area resulted in lower within sub-plot variability than between sub-plots for pH and bacterial community composition assessed by terminal-restriction fragment length polymorphism analysis. Following multivariate statistical analysis, a large amount of variation in community composition was explained by soil pH, which is remarkable given the relatively small size of the sampling area and minor differences in pH. Moisture content was also important in determining bacterial communities in the random design (design 1). In the 1 m² sub-plot design (design 2), the spatial location of the plots explained a large degree of the variation in bacterial community composition between plots, which was due to spatial autocorrelation of pH and possible additional environmental parameters. This study emphasises the importance of sampling design for obtaining representative samples from soil.     

Using regression models in design‐based estimation of spatial means of soil properties

The precision of design‐based sampling strategies can be increased by using regression models at the estimation stage. A general regression estimator is given that can be used for a wide variety of models and any well‐defined sampling design. It equals the π estimator plus an adjustment term that accounts for the differences between the π estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The regression estimator and ratio estimator follow from certain assumptions on the model and the sampling design. These are compared with the π estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple regression estimator to that of the π estimator was approximately 55%. The bias of the simple regression estimator was negligibly small. The confidence interval estimators were valid for all sample sizes except for n = 10. Also the ratio estimator was approximately unbiased, and the confidence interval estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio estimator assumes that the intercept of the regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55% of the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) regression estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) regression estimator was more precise than the π estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the regression estimator was less precise than the π estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.     

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.     

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。     

区域土壤侵蚀遥感抽样调查方法

土壤侵蚀是全球性环境问题,土壤侵蚀调查是水土保持规划和生态文明建设的科学基础。为了完善土壤侵蚀抽样调查方法,快速、精准地估算土壤侵蚀实际速率,对基于高分辨率遥感影像进行目视解译,提取高精度土地利用和水土保持措施信息的方法进行了研究。基于现代地理信息科学,充分利用虚拟地球及其提供的公开高分辨率遥感数据资源,考虑土壤侵蚀及其治理的时空特征,采用分层不等概系统空间抽样方法布设抽样单元,通过对公开高分辨率遥感影像的目视解译,完成泛第三极地区土地利用和水保措施的遥感抽样调查。研究实现了2万个抽样调查单元的解译,提取了土地利用和水土保持措施信息;基于CSLE模型完成了典型抽样调查单元的土壤流失速率计算,并对解译结果进行了精度和实用性分析。结果表明:基于公开高分辨率遥感影像、利用分层不等概系统空间抽样方法,可快速提取土地利用和水土保持措施信息,完成区域土壤侵蚀抽样调查。     

Exploring the spatial relations between cereal yield and soil chemical properties and the implications for sampling

Abstract. In general, agricultural management has focused on differences between fields or on the gross differences within them. Recent developments in agricultural technology, yield mapping, Global Positioning Systems and variable rate applications, have made it possible to consider managing the considerable variation in soil and other properties within fields. This system is known as precision agriculture. More precise management of fields depends on a better understanding of the factors that affect crop input decisions. This paper examines the spatial variation in crop yield, soil nutrient status and soil pH within two agricultural fields using geostatistics. The observed properties vary considerably within each field. The relation between yield and the measured soil properties appears to be weak in general. However, the range of spatial correlation for yield, shown by the variogram, is similar to that of the soil chemical properties. In addition the latter changed little over two years. This suggests that information on the scale of variation of soil chemical properties can be derived from yield maps, which can also be used as a guide to a suitable sampling interval for soil properties.     

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。     

Spatial designs and properties of spatial correlation: Effects on covariance estimation

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.     

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。     

土壤养分空间变异及合理取样数研究

土壤养分存在明显的空间差异，田间土壤养分合理取样数取决于养分要素自身空间变异程度和人们对数据精度的要求。若空间变异大、精度要求高则需要较多采样数，反之需较少样点数。计算结果表明，极大多数养分要素的合理取样数较实际取样数有较大幅度减少，意味着可大幅降低采样及分析成本。据统计学空间自相关和半方差函数方法研究结果，养分要素存在一定的空间自相关性，但不同方向上的自相关性有明显差异，独立间距也因养分要素而异。研究结果可为精准农业土壤养分样点密度设定、养分要素等值线绘制及精准施肥提供支持。