不同采样尺度下土壤碱解氮空间变异性研究——以榆树市农田土壤为例

在精准农业的实施过程中,研究如何用较少的样本来反映田间信息的空间变异规律,再用科学的插值方法进行插值和预估是精准农业研究中的一个关键问题。以东北典型黑土区——吉林省榆树市为研究区域,在榆树市弓棚镇13号村内选择相对平整的地块进行土壤采样并测试其土壤养分。在对原始采样格网点按一定的样点间隔和布局进行抽取的基础上,利用克里格插值方法和BP神经网络方法分别进行空间插值,比较不同采样尺度（40m×40m,56m×56m,80m×80m,113m×113m,160m×160m五个尺度）对空间插值精度的影响。结果表明:（1）随着采样尺度的增大,碱解氮的空间结构系数C/（C₀+C）有减小的趋势,表明采样间距以内的不可估计误差逐渐增大,其空间结构的表现能力在逐渐减弱;（2）Kriging插值精度总体优于BP神经网络,随着采样尺度的增加,两种模型的模拟精度都有所下降,BP神经网路的插值精度和Kriging模型的插值精度的差距逐渐减小;（3）两种模型在113m×113m尺度上插值精度都发生了突变,如考虑碱解氮的空间变异规律和经济因素,碱解氮的最佳采样尺度应在80～113m。     

样点密度对土壤有机质空间预测结果的影响——以河南封丘县土壤为例

以河南省封丘县表层土壤有机质含量为例,探讨土壤样点密度对区域化土壤变量描述性统计特征、半方差函数理论模型拟合效果、普通Kriging插值预测结果的精度与表现目标变量空间变异的能力等多方面的影响。研究结果表明,样点数量从5000个大幅减少至20个,研究区表层样品有机质含量均值未发生显著变化。当土壤样点≥625个时,表层土壤有机质含量半方差函数模型具有较好的拟合效果,可以通过Kriging插值手段获得精度较高且对目标变量空间变异特征解释能力较强的预测结果;当土壤样点≤78个时,半方差函数模型理论上无法通过拟合获得,通过普通Kriging插值手段不能获得研究区表层土壤有机质含量理想的预测结果。     

耕地养分空间插值技术与合理采样密度的比较研究

土壤养分连续空间分布数据是土壤信息系统工作的基础,土壤养分空间插值的研究因此变得尤为重要。对湖北省鄂州市进行土壤养分采样调查,以对作物生长作用较为密切的有效氮、有效磷、有效钾、pH为研究对象,运用克里格法(Kriging)、样条函数法(Spline)、距离权重倒数法(IDW)3种插值方法对数据进行栅格化处理,分析比较3种插值方法所得结果的特性以及对耕地养分数据插值的适宜性。通过调整空间采样点密度,比较几种空间采样密度对插值结果的影响,总结3种插值方法在不同空间尺度下的插值精度,并在不同土壤类型内进行不同采样密度的插值分析。     

基于BP神经网络插值的土壤全氮空间变异

大尺度土壤养分空间变异研究可以为土壤改良分区治理提供基础数据。寻求合适的取样数和插值方法是进行土壤养分空间变异研究的关键。以安徽省舒城县为例,共取得0～20cm土壤表层样品523个,土壤全氮的空间变异由BP神经网络插值方法在不同取样数条件下获得,通过与克里格插值法进行比较得出:样本数在100个时,神经网络插值的预测吻合度(G)比克里格插值高7.75%,均方根误差(RMSE)低0.1,总体精度优于克里格;样本数大于200时,神经网络插值和克里格插值精度基本相同,随着采样数量增加,两种方法的插值精度也在提高,并逐步趋于平稳。在大尺度土壤养分空间变异研究中,在小样本情况下,神经网络插值具有优势。     

采样尺度对土壤养分空间变异分析的影响

以高密度土壤养分采样数据为数据源,通过随机抽取生成不同采样尺度的样点数据,分析采样尺度对土壤养分空间变异特征分析的影响。研究结果表明:区域土壤养分预测均值随采样尺度减小呈下降趋势,而变异系数增加;养分空间分布的全局趋势随采样尺度增大而增强,但不影响半方差模型;当采样尺度较大,样点间自相关较弱时,相对较少的样点也能满足区域统计参数估测分析需要,但不能用于空间变异特征和插值分析;当样点数大于最佳采样数时,养分统计参数、空间变异特征和插值分析随着采样尺度减小而精度提高,当采样尺度达到0.2左右时,能够满足中等空间变异的土壤养分空间插值分析需要;样点空间布局对相关距和空间插值分析精度的影响比采样尺度本身更为显著。     

县域土壤有机质空间变异特征及合理采样数的确定

以有机质为例,以高密度土壤养分采样数据为数据源,通过随机抽取生成不同采样密度的样点数据,分析了不同采样密度下土壤有机质的空间变异特征及县域合理采样数。研究结果表明,在一定研究尺度下采样密度对土壤养分的模型拟合、变程和空间相关性没有显著影响,即适当减少样点数可以满足插值分析的需要,充分考虑土壤养分空间变异评价的精度分析,确定县域土壤有机质合理采样数应控制在400个以上。     

吉林省德惠市土壤速效钾的空间分异及不同插值方法的比较

基于地统计学和地理信息系统,采用区变量的半变异理论定量研究了土壤速效钾的空间变异特征,分析比较了不同空间插值方法的插值精度,并利用最优Kriging法插值生成了研究区土壤速效钾的分布格局图。结果表明:研究区土壤速效钾具有中等强度的空间自相关,步长为108.5km;块金效应显著,C0/sill值为0.43。所有插值方法中,球面多项式插值的RMSE最大,平常克吕格的指数模型插值精度最高。IDW虽然也常常被用来进行土壤属性特征的插值分析,但它只与距离有关,对于区域性的较大差异或存在多因子影响时,Kriging方法有其明显的优势;土壤速效钾的分布以中部饮马河为线,东西差异较大,总体自东北向西南呈有规律地逐渐增大的趋势。     

基于GARBF神经网络的土壤有效锌空间插值方法研究

以土壤有效锌为研究对象,构建遗传径向基函数(GARBF)神经网络对该元素属性值进行空间插值,以训练样本集的测定值与预测值之间的决定系数、逼近误差及检验样本的插值误差为评判标准,比较GARBF神经网络、径向基函数(RBF)神经网络、普通克里格(Ordinary Kriging)的拟合能力和空间插值能力。结果表明:同一区域两种抽样方案(a、b)下三种插值方法对训练样本的拟合能力为GARBFRBFOr-dinary Kriging。以平均绝对误差和误差均方根作为插值精度的评价指标,GARBF与RBF神经网络相比,训练样本的逼近误差分别降低0.22～0.25(a方案)和0.10～0.11(b方案),检验样本的插值误差分别降低0.13～0.11(a方案)和0.02～0.13(b方案);GARBF神经网络与Ordinary Kriging相比,训练样本的逼近误差分别降低1.12～1.40(a方案)和1.45～1.88(b方案),检验样本的插值误差分别降低0.20～0.24(a方案)和0.14～0.32(b方案),GARBF神经网络的误差最小,插值精度最高。从GARBF神经网络的插值图可以看出,遗传算法避免了神经网络容易陷入局部最优点,扩大了对土壤中相关空间信息的搜索范围,在一定程度上避免了类似克里格插值的"平滑效应"。     

土壤属性预测中Kriging参数对插值精度的影响研究

为了有效提高土壤属性预测中的Kriging插值精度,研究借助GS+5.1和ArcGIS 9.3等软件来分析河南省西平县宋集乡土壤全磷和有机质在不同参数条件下的Kriging插值精度,结果表明:决定系数R2最大的变异函数模型,插值结果误差不一定最低、平滑效应不一定最弱,需比较分析插值结果以选择合适的模型;近距离实验变异函数值r#(h)的拟合对提高Kriging插值精度具有重要意义,拟合变异函数理论模型时,除综合考虑各个r(h)#的拟合程度外,同时对近距离r(h)#应给予足够的重视;插值的最佳邻域样本量一般在内层和次内层邻域样本权重达到平稳时取得,对于样本点空间分布相同的不同土壤属性,空间相关性较弱(块金系数较大)的土壤属性,其Kriging插值的最佳邻域样本量较大。     

县域农田土壤养分空间变异及合理样点数确定

以武功县为例,应用地统计学和GIS相结合的方法,对土壤有机质、速效磷、速效钾、碱解氮等土壤养分空间变异特征进行研究,并对不同采样密度下有机质的空间插值结果进行分析比较,用均方根误差和相关系数检验不同密度下的插值精度,以确定县域有机质合理采样数。研究结果表明:各土壤养分均存在中等强度空间变异,土壤养分变异系数的顺序是速效磷速效钾有机质碱解氮。各土壤养分均存在正的基底效应,其中,有机质和速效钾的空间变异性受人为因素影响较小,控制其空间变异性的主要因素与成土母质、土壤类型、气候条件等有关。而碱解氮和速效磷的空间变异性受人为因素影响较大,控制其空间变异性的主要因素与耕作方式及农业生产中施肥等有关。随着采样点密度的增加,克里格插值精度提高,适当减少样点数可以满足插值分析的需要,充分考虑土壤养分空间变异评价的精度分析,确定县域土壤有机质合理采样数应控制在2213个以上,即最大以17.8 hm2为一个采样单元。     

Continuous Spatial Process Models for Spatial Extreme Values

We propose a hierarchical modeling approach for explaining a collection of point-referenced extreme values. In particular, annual maxima over space and time are assumed to follow generalized extreme value (GEV) distributions, with parameters μ, σ, and ξ specified in the latent stage to reflect underlying spatio-temporal structure. The novelty here is that we relax the conditionally independence assumption in the first stage of the hierarchial model, an assumption which has been adopted in previous work. This assumption implies that realizations of the the surface of spatial maxima will be everywhere discontinuous. For many phenomena including, e.g., temperature and precipitation, this behavior is inappropriate. Instead, we offer a spatial process model for extreme values that provides mean square continuous realizations, where the behavior of the surface is driven by the spatial dependence which is unexplained under the latent spatio-temporal specification for the GEV parameters. In this sense, the first stage smoothing is viewed as fine scale or short range smoothing while the larger scale smoothing will be captured in the second stage of the modeling. In addition, as would be desired, we are able to implement spatial interpolation for extreme values based on this model. A simulation study and a study on actual annual maximum rainfall for a region in South Africa are used to illustrate the performance of the model.     

Spatial prediction with left-censored observations

Environmental monitoring of contaminants often involves left-censored observations falling below the minimum detection limits (MDLs) of the instruments used to assay their concentrations. Statistical procedures for handling left-censored observations generally assume that the observations are independently distributed. However, data collected over a spatial network of sample sites are likely to be spatially correlated. This correlation structure can be exploited to obtain improved imputations of left-censored observations, and hence improved estimates of environmental parameters. This article applies a Robbins-Monro algorithm for estimating the parameters of a spatial regression model. This algorithm uses importance sampling to obtain conditional simulations of left-censored observations. A predictor for data at unsampled sites is obtained by taking the weighted mean of kriging predictors computed from independent importance samples. The proposed methods are illustrated using data from the South Florida Ecosystem Assessment Project.     

西安市水土流失空间分布特征与管控空间划分

城镇规模的快速发展是引发城市水土流失的关键因素。以西安市为研究区域,计算了各区县土壤侵蚀面积并进行了强度等级划分,分析了水土流失在空间上的分布特征并进行预测,识别出需要重点监管的区域。结果表明:西安市年均土壤侵蚀量为278.49万t,年均土壤侵蚀模数为176.74 t/(km^2·a),微度侵蚀和轻度侵蚀占总侵蚀面积的99.76%,中度侵蚀以上面积仅占0.24%;未来情景下西安市各区域土壤侵蚀模数主要分布在0~200 t/(km^2·a),其中建成区和发展区土壤侵蚀面积分别为65.37,302.19 km^2;水土流失空间管控与重点区域主要分布在高陵区、鄠邑区、长安区和临潼区等地区。随着城市建设与发展的完善,西安市重点管控区的面积也在发生变化。     

Spatial Regression Using Kernel Averaged Predictors

Traditional spatial linear regression models assume that the mean of the response is a linear combination of predictors measured at the same location as the response. In spatial applications, however, it seems plausible that neighboring predictors can also inform about the response. This article proposes using unobserved kernel averaged predictors in such regressions. The kernels are parametric introducing additional parameters that are estimated with the data. Properties and challenges of using kernel averaged predictors within a regression model are detailed in the simple case of a univariate response and a single predictor. Additionally, extensions to multiple predictors and generalized linear models are discussed. The methods are demonstrated using a data set of dew duration and shrub density. Supplemental materials are available online.     

Spatial scan statistics using elliptic windows

The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in Sat Scan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic windows and propose a new way to present the information when a spatial point process is considered. This method gives smooth changes for smooth expansions of the set of clusters. A simulation study is used to show how the elliptic windows outperforms the usual circular windows. The proposed method for graphical representation of the information in a set of clusters contain more information than just presenting nonoverlapping clusters. We suggest that more than one graphical representation of a set of clusters should be used to easily extract more information and to avoid pitfalls of the selected method.     

Non-Stationary Dependence Structures for Spatial Extremes

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.     

Spatial stochastic volatility for lattice data

Spatial heteroscedasticity may arise jointly with spatial autocorrelation in lattice data collected from agricultural trials and environmental studies. This leads to spatial clustering not only in the level but also in the variation of the data, the latter of which may be very important, for example, in constructing prediction intervals. This article introduces a spatial stochastic volatility (SSV) component into the widely used conditional autoregressive (CAR) model to capture the spatial clustering in heteroscedasticity. The SSV component is a mean zero, conditionally independent Gaussian process given a latent spatial process of the variances. The logarithm of the latent variance process is specified by an intrinsic Gaussian Markov random field. The SSV model relaxes the traditional homoscedasticity assumption for spatial heterogeneity and brings greater flexibility to the popular spatial statistical models. The Bayesian method is used for inference. The full conditional distribution of the heteroscedasticity components can be shown to be log-concave, which facilitates an adaptive rejection sampling algorithm. Application to the well-known wheat yield data illustrates that incorporating spatial stochastic volatility may reveal the spatial heteroscedasticity hidden from existing analyses.     

Spatial models for line transect sampling

This article develops methods for fitting spatial models to line transect data. These allow animal density to be related to topographical, environmental, habitat, and other spatial variables, helping wildlife managers to identify the factors that affect abundance. They also enable estimation of abundance for any subarea of interest within the surveyed region, and potentially yield estimates of abundance from sightings surveys for which the survey design could not be randomized, such as surveys conducted from platforms of opportunity. The methods are illustrated through analyses of data from a shipboard sightings survey of minke whales in the Antarctic.     

Spatial prediction on a river network

This article develops methods for spatially predicting daily change of dissolved oxygen (Dochange) at both sampled locations (134 freshwater sites in 2002 and 2003) and other locations of interest throughout a river network in South East Queensland, Australia. In order to deal with the relative sparseness of the monitoring locations in comparison to the number of locations where one might want to make predictions, we make a classification of the river and stream locations. We then implement optimal spatial prediction (ordinary and constrained kriging) from geostatistics. Because of their directed-tree structure, rivers and streams offer special challenges. A complete approach to spatial prediction on a river network is given, with special attention paid to environmental exceedances. The methodology is used to produce a map of Dochange predictions for 2003. Dochange is one of the variables measured as part of the Ecosystem Health Monitoring Program conducted within the Moreton Bay Waterways and Catchments Partnership.     

土壤空间变异研究中的半方差问题

简要回顾了土壤空间变异的研究。根据地质统计学理论和多年从事土壤空间变异研究的经验,对土壤空间变异研究的关键问题——半方差函数的基本假设、取样、模型选取及模型的检验进行了讨论,并对确定半方差函数模型应注意的问题提出建议。在保证取样样本容量的前提下,检查测定数据是否服从内蕴假设;注意提高每一个估算值的置信水平;尽量选择安全型模型作为半方差函数模型;对确定的半方差模型进行统计检验。由此可以求得较为客观合理的半方差模型。