Non-homogeneity of variance components from spatially nested sampling of the soil

Spatially nested sampling and the associated nested analysis of variance by spatial scale is a well-established methodology for the exploratory investigation of soil variation over multiple, disparate scales. The variance components that can be estimated this way can be accumulated to approximate the variogram. This allows us to identify the important scales of variation, and the general form of the spatial dependence, in order to plan more detailed sampling by design-based or model-based methods. Implicit in the standard analyses of nested sample data is the assumption of homogeneity in the variance, i.e. that all variations from sub-station means at some scale represent a random variable of uniform variance. If this assumption fails then the comparable assumption of stationarity in the variance, which is an important assumption in geostatistics, will also be implausible. However, data from nested sampling may be analysed with a linear mixed model in which the variance components are parameters which can be estimated by residual maximum likelihood (REML). Within this framework it is possible to propose an alternative variance parameterization in which the variance depends on some auxiliary variable, and so is not generally homogeneous. In this paper we demonstrate this approach, using data from nested sampling of chemical and biogeochemical soil properties across a region in central England, and use land use as our auxiliary variable to model non-homogeneous variance components. We show how the REML analysis allows us to make inferences about the need for a non-homogeneous model. Variances of soil pH and cation exchange capacity at different scales differ between these land uses, but a homogeneous variance model is preferable to such non-homogeneous models for the variance of soil urease activity at standard concentrations of urea.     

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.     

Capability of a XRF Method for Monitoring the Content of the Macronutrients Mg, P, S, K and Ca in Agricultural Crops

To examine the concentration of Mg, P, S, K and Ca in agricultural crops growing under changing conditions, plant material was collected from an adequate number of cultivated targets (lysimeter trial) and finally analysed by means of wavelength dispersive X-ray fluorescence spectrometry. The investigations were focused on the evaluation of each 16 grassland and 16 arable land used lysimeters on the other hand. The measurement uncertainty of the method used (including the analytical and sampling components) was estimated by means of the duplicate method. Based on the evaluation of the accumulated data pool, the minimum detectable concentration difference for the individual analytes was estimated. In the framework of the fitness for purpose concept, the present study particularly aimed at the estimation of minimum sample size in consideration of a commonly accepted decision limit and detection capability, given by an error I probability α?=?0.05 and an error II probability β?=?0.05, respectively.     

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。     

Model‐based analysis using REML for inference from systematically sampled data on soil

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.     

SOIL VARIABILITY AND RECONNAISSANCE SOIL MAPPING. A STATISTICAL STUDY IN NORFOLK

The incorporation of measures of soil variability at the reconnaissance stage of soil survey is considered as a possible alternative to, or additional feature of, present procedures. A straightforward hierarchical sampling design based upon the major parent materials of the upland section of the study area and associated analysis of variance model are described. This allowed the estimation of scale components for five levels of the sampling design at separation distances from over two kilometers down to five meters. Principal components analysis is used to economise on the number of variables for further analysis. Analysis of the pattern of principal component scores shows the first six components to have distinctive variability patterns both within and between strata. It is concluded that present soil survey procedures take too little account of soil variability patterns, and that inclusions of such information at the reconnaissance stage would greatly improve the detailed survey.     

Spatial variation of nitrate–N and related soil properties at the plot-scale

Neglecting the spatial variation in soil nutrient status may result in unused yield potential and in environmental damage. Site-specific management has been suggested to reduce inappropriate fertilization that can adversely affect soil, ground and surface water. Decision criteria for determining variable-rate nitrogen fertilization are, however, lacking. This paper analyses the spatial variation of nitrate nitrogen (NO₃–N) and soil properties related to the N cycle at the plot-scale. Three 50×50 m plots were sampled in nested sampling designs of varying complexities. Classical statistics revealed a characteristic ranking in the variability of soil properties. Geostatistical analysis of the NO₃–N data from two plots showed that the small-scale variation found in one small subgrid was not typical for the small-scale variation in the entire plot, indicating bias in the sampling design. A trend component was found in the NO₃–N data and, consequently, the minimal requirement for the regionalized variable theory was not fulfilled. Problems due to design were overcome with a more complex nested sampling at the third plot. However, the spherical model fitted to the NO₃–N data of the first year explained only 21% of the total variance, whereas a pure nugget effect was observed in the second year. The water content data also showed a low structural variance, which was different in the two years. In contrast, two thirds of the variance of total carbon (C_t) and total nitrogen (N_t) could be explained by the fitted models. Seasonal variations, such as varying duration of snow cover, and extrinsic management effects, such as growing of a cover crop, may have contributed to the observed differences in variability between the years. Due to the low proportion of structural variance and the observation that spatial distribution was not stable with time, geostatistical analysis of NO₃–N and water contents data added only little information to classical statistical analysis. However, geostatistical analysis of total C and N contents provided a useful means to calculate spatial distribution patterns of these properties.     

Limited Spatial Transferability of the Relationships Between Kriging Variance and Soil Sampling Spacing in Some Grasslands of Ireland: Implications for Sampling Design

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.     

Application of nested analysis of variance in mapping procedures for land evaluation

Abstract. Assuming that other sources of error can be neglected, the reliability of a land suitability classification depends on the homogeneity of physiographically delineated map units with regard to land qualities. The map unit homogeneity of a small area in France was estimated using 64 observation points, arranged according to a nested sampling scheme, followed by nested analysis of variance.
The analysis shows that in this area map units are too heterogeneous to accept the suitability classification as being completely reliable. However, alternative procedures using methods of optimal interpolation to map gradual change within the physiographic units are too expensive at a mapping scale of 1:25000 or smaller. It is not possible to produce completely accurate suitability maps at smaller scales. However, incorporating nested sampling and analysis of variance as standard procedures in land evaluation surveys costs little effort and yields at least an estimate of map accuracy and reliability of the suitability classification.     

基于方差四叉树法的滨海盐土电导率采样布局研究

利用土壤空间变异特性和空间分布特征进行采样设计是当前土壤采样研究的重要内容。采用方差四叉树法（Variance quad-tree method，简称VQT），结合半方差函数，设计滨海盐土采样的最优布局。并利用普通克立格法对传统网格采样法与方差四叉树采样法所得到的不同的样点数目进行插值，计算估值误差并进行精度比较。结果发现，同样的样本数目，利用方差四叉树法得到的克立格估值误差明显地较利用网格采样法得到的克立格估值误差小，其采样效率提高约16％一25％。该方法的优势在于，可设计在土壤特性变异大的区域密集采样而在变异较小的区域稀疏地采样，从而在有效表达土壤空间变异性的同时，提高了采样效率，减少了采样成本。     

The behaviour of soil process models of ammonia volatilization at contrasting spatial scales

Process models are commonly used in soil science to obtain predictions at a spatial scale that is different from the scale at which the model was developed, or the scale at which information on model inputs is available. When this happens, the model and its inputs require aggregation or disaggregation to the application scale, and this is a complex problem. Furthermore, the validity of the aggregated model predictions depends on whether the model describes the key processes that determine the process outcome at the target scale. Different models may therefore be required at different spatial scales. In this paper we develop a diagnostic framework which allows us to judge whether a model is appropriate for use at one or more spatial scales both with respect to the prediction of variations at those scale and in the requirement for disaggregation of the inputs. We show that spatially nested analysis of the covariance of predictions with measured process outcomes is an efficient way to do this. This is applied to models of the processes that lead to ammonia volatilization from soil after the application of urea. We identify the component correlations at different scales of a nested scheme as the diagnostic with which to evaluate model behaviour. These correlations show how well the model emulates components of spatial variation of the target process at the scales of the sampling scheme. Aggregate correlations were identified as the most pertinent to evaluate models for prediction at particular scales since they measure how well aggregated predictions at some scale correlate with aggregated values of the measured outcome. There are two circumstances under which models are used to make predictions. In the first case only the model is used to predict, and the most useful diagnostic is the concordance aggregate correlation. In the second case model predictions are assimilated with observations which should correct bias in the prediction, and errors in the variance; the aggregate correlations would be the most suitable diagnostic.     

How geostatistics can help you

Abstract. Geostatistics is basically a technology for estimating the local values of properties that vary in space from sample data. Research and development in the last 15 years has shown it to be eminently suited for soil and ripe for application in soil survey and land management. The basic technique, ordinary kriging, provides unbiased estimates with minimum and known variance. Data for related variables can be incorporated to improve estimates using cokriging. By more elaborate analysis using disjunctive kriging the probabilities of deficiency and excess can be estimated to aid decision.
The variogram is crucial in all geostatistics; it must be estimated reliably from sufficient data at a sensible scale and modelled properly. Once obtained it can be used not only in the estimation itself but also to choose additional sampling sites, improve a monitoring network or design an optimal sampling scheme for a survey. It may also be used to control a multivariate classification so that the resulting classes are not too fragmented spatially to manage.     

Analysis of the volatile components in vanilla extracts and flavorings by solid-phase microextraction and gas chromatography

The development and application of a solid-phase microextraction (SPME) method in the analysis of vanilla extracts and vanilla flavorings was studied. The SPME method was developed to be used in conjunction with gas chromatography mass spectrometry (GC-MS). The optimized SPME sampling parameters for the determination of the volatile components included a poly(acrylate) fiber, a 40-min sampling time at room temperature, and a 2-min desorption time. The reproducibility of the method was good, with a percent relative standard deviation between 2.5 and 6.4% for the target compounds. The data suggest that the origin of natural extracts can be readily determined from the GC profile and that differences exist between nature-identical and synthetic flavorings and the natural extracts. The method also has potential for identifying the type of vanilla extract/flavoring used to flavor food.     

基于多源数据的盐碱地精确农作管理分区研究

为了便于对盐碱地实施变量管理和精确农作，以海涂围垦区盐碱土为研究对象，以NDVI数据、盐分数据以及作物产量数据作为分区变量，对一面积为15 hm²的盐碱地农田进行了基于多个数据源的精确农作管理分区研究。利用模糊c均值聚类方法进行分类分区，引入了模糊聚类指数(FPI)和归一化分类熵(NCE)作为最佳分区数目的判断标准，通过单项方差分析对分区结果进行比较和评价。研究发现，对本研究区，最佳的分区数目为三个。不同管理分区之间土壤化学性质(EC1:5,有机质，速效磷，速效钾，全氮，碱解氮以及阳离子交换量)的均值都存在着统计意义上的显著差异性，其中子区3具有最高的肥力水平和作物生产能力而子区1最低。利用所选取的三个变量，模糊c均值聚类算法可以较好地进行精确农作管理分区划分。分区结果不但可以指导采样, 而且可以作为变量管理的决策单元用于田间变量管理作业中,为精确农业变量投入的实施提供有效手段和决策依据。     

Surface and profile soil moisture spatio-temporal analysis during an excessive rainfall period in the Southern Great Plains,USA

In this work we analyze the temporal stability of soil moisture at the field and watershed scales in the Little Washita River Experimental Watershed (LWREW), as part of the remote sensing Cloud and Land Surface Interaction Campaign (CLASIC07) during June 2007 in south-central Oklahoma. Temporal stability of surface and profile soil moisture data were investigated for 20 LWREW soil moisture measurement stations. In addition, daily surface and profile soil moisture measurements were obtained in four 800 m by 800 m fields (remote sensing footprint), including two rangeland sites and two winter wheat fields. The work aimed to analyze the temporal stability of soil moisture at the watershed and field scale and to identify stations within the watershed, as well as locations within each field, that were representative of the mean areal soil moisture content. We also determined the relationship between sites found to be temporally stable for surface soil moisture versus those determined stable for average profile soil moisture content. For the unusually wet experimental period, results at the watershed scale show that LWREW stations 133 and 134 provided stable underestimates, while stations 132 and 154 provided stable overestimates of the watershed mean at all depths. In addition, station 136 had very high non-zero temporal stability at the 25 cm and 45 cm depths indicating that it could be used as representative watershed site provided a constant offset value is used to acquire a watershed mean soil water content value. In general, the deeper depths exhibited higher soil moisture spatial variability, as indicated by the higher standard deviations. At the field scale, measured average profile soil moisture was higher in the winter wheat fields than the rangeland fields with the majority of the winter wheat depth intervals having high non-zero temporal stability. Field scale temporal stability analysis revealed that 4 of the 16 sampling sites in the rangeland fields and 3 of the 16 sampling sites in the winter wheat fields either under or overestimated the field means in the 0–5 and 0–60 cm depth intervals. Field sites considered temporally stable for the surface soil moisture were not stable for the profile soil moisture, except for the LW45 field where two sites were stable at both the surface and profile soil moisture. This finding is significant in terms of soil moisture ground-truth sampling for calibrating and validating airborne remotely sensed soil moisture products under extremely wet conditions. In addition, identification of temporally stable sites at the watershed and field scales in the LWREW provide insight in determining future measurement station locations and field scale ground sampling protocol, as well as providing data sets for hydrologic modeling.     

Variation in Soil Nitrate Concentrations in Two N-Saturated Norway Spruce Forests (Picea abies (L.) Karst.) in Southern Bavaria

Persistently high Nitrogen (N) deposition may have caused widespread N saturation in Central Europe’s forests. Simple and inexpensive methods are required for estimating the N status. This study suggests that the current N status of forest ecosystems can be estimated by measuring CaCl₂-extractable nitrate concentrations in the soil below the main rooting zone. We tested this possibility using a large number of samples (135 in total) in a nested sampling design in two homogeneous Norway spruce forests in southern Bavaria. This approach was accompanied by a small scale survey with suction cups (N = 54) in one forest. Nitrate concentrations determined by soil extracts varied widely (coefficients of variance 95 and 125%) and were well comparable with those of the simultaneous investigation of seepage water. Site and stand conditions explained only a small portion (<10%) of the total variation. Mineral soil nitrate concentrations were not spatially dependent at the medium and large scales (about 10 m to several km) in both forests. Therefore the reliability of estimates at these scales depends mainly on the sample size. At the small scale (<about 10 m) large variation in nitrate concentrations and a considerable spatial dependency could be observed. Therefore intensive sampling is necessary at short distances in order to estimate the mean adequately. From our results, we deduct possibilities and limitations of nitrate inventories as a tool for regional assessment of the N status of forests.     

A DGGE-cloning method to characterize arbuscular mycorrhizal community structure in soil

Although arbuscular mycorrhizal fungi (AMF) are crucial for ecosystem functioning, characterizing AMF community structure in soil is challenging. In this study, nested polymerase chain reaction (PCR) and denaturing gradient gel electrophoresis (DGGE) were combined with cloning of fungal 18S ribosomal gene fragments for the rapid comparison of AMF community structure in soil. Reference AMF isolates, representing four major genera of AMF, were used to develop the method. Sequential amplification of 18S rDNA fragments by nested PCR using primer pairs AM1-NS31 and Glo1-NS31GC followed by DGGE analysis yielded a high-resolution band profile. In parallel, 18S rDNA fragment clone libraries were constructed and clones screened by DGGE. Sequence identity was inferred by matching the electrophoretic mobility of the sample fingerprint bands to that of bands from individual clones. The effectiveness of this approach was tested on soil samples from different ecosystems, yielding reproducible, complex DGGE band patterns specific to each site. The coupling of PCR–DGGE with clone library analysis provides a robust, reliable, and precise means to characterize AMF community structure in soils.     

Spatial variation of ammonia volatilization from soil and its scale‐dependent correlation with soil properties

Quantitative predictions of ammonia volatilization from soil are useful to environmental managers and policy makers and empirical models have been used with some success. Spatial analysis of the soil properties and their relationship to the ammonia volatilization process is important as predictions will be required at disparate scales from the field to the catchment and beyond. These relationships are known to change across scales and this may affect the performance of an empirical model. This study is concerned with the variation of ammonia volatilization and some controlling soil properties: bulk density, volumetric water content, pH, CEC, soil pH buffer power, and urease activity, over distances of 2, 50, 500, and >2000 m. We sampled a 16 km × 16 km region in eastern England and analyzed the results by a nested analysis of (co)variance, from which variance components and correlations for each scale were obtained. The overall correlations between ammonia volatilization and the soil properties were generally weak: –0.09 for bulk density, 0.04 for volumetric water content, –0.22 for CEC, –0.08 for urease activity, –0.22 for pH and 0.18 for the soil pH buffer power. Variation in ammonia volatilization was scale‐dependent, with substantial variance components at the 2‐ and 500‐m scales. The results from the analysis of covariance show that the relationships between ammonia volatilization and soil properties are complex. At the >2000 m scale, ammonia volatilization was strongly correlated with pH (–0.82) and CEC (–0.55), which is probably the result of differences in parent material. We also observed weaker correlations at the 500‐m scale with bulk density (–0.61), volumetric water content (0.48), urease activity (–0.42), pH (–0.55) and soil pH buffer power (0.38). Nested analysis showed that overall correlations may mask relationships at scales of interest and the effect of soil variables on these soil processes is scale‐dependent.