Variograms of Ancillary Data to Aid Sampling for Soil Surveys

To provide reliable estimates for mapping soil properties for precision agriculture requires intensive sampling and costly laboratory analyses. If the spatial structure of ancillary data, such as yield, digital information from aerial photographs, and soil electrical conductivity (EC) measurements, relates to that of soil properties they could be used to guide the sampling intensity for soil surveys. Variograms of permanent soil properties at two study sites on different parent materials were compared with each other and with those for ancillary data. The ranges of spatial dependence identified by the variograms of both sets of properties are of similar orders of magnitude for each study site. Maps of the ancillary data appear to show similar patterns of variation and these seem to relate to those of the permanent properties of the soil. Correlation analysis has confirmed these relations. Maps of kriged estimates from sub-sampled data and the original variograms showed that the main patterns of variation were preserved when a sampling interval of less than half the average variogram range of ancillary data was used. Digital data from aerial photographs for different years and EC appear to show a more consistent relation with the soil properties than does yield. Aerial photographs, in particular those of bare soil, seem to be the most useful ancillary data and they are often cheaper to obtain than yield and EC data.     

不同样本数量下土壤属性空间预测比较

【目的】通过不同样本数量情形下土壤属性空间预测精度的对比,探讨样本数对预测精度的影响。【方法】以土壤有机质、土壤质量含水量、土壤速效钾和土壤有效锰4个土壤属性作为研究对象,采用矩量法（MoM）和有限最大似然法（REML）两种变异函数计算方法,对比分析在不同样本数情形下各土壤属性空间预测精度。【结果】（1）不论是利用MoM法还是REML法计算变异函数,样本点数从50增加到70,各土壤变量预测精度都有了明显提高;样本数从70逐步增加到150过程中,预测精度没有明显提高;（2）在不同样本数情形下,REML法相对于MoM法的预测精度的提高率具有明显的变化,而且在有些情况下,REML法的预测精度比MoM低,而且对于不同土壤变量,表现结果也不相同。【结论】样本数对土壤空间预测准确性具有显著影响,在本研究区域尺度下,当样本数小于70个时,无论用哪种变异函数计算方法进行预测,预测结果的可信度都比较低。     

Estimating Average and Proportional Variograms of Soil Properties and Their Potential Use in Precision Agriculture

Precision Agriculture requires a method of gathering information about the spatial variability of soil that reduces the need for expensive and intensive sampling. This can be achieved through the use of what we term average and proportional variograms. A literature search has enabled the gathering of variograms for multiple soil properties, allowing comparison of the magnitude of variability and the construction of averages. For soil properties that display proportionality between their mean squared and variance, the variogram can be predicted from a mean value. These average and proportional variograms are potentially beneficial to implementers of Precision Agriculture as they can be used to plan optimal soil sampling and management schemes. It was found that if wishing to implement site-specific management to a resolution of 20×20 m then grid soil sampling will generally have to be performed at 20–30 m intervals depending on the attribute of interest. A decision-support chart for differential soil management based on a variogram's comparative magnitude to the average is presented. Further work needs to be done on increasing the data base these results are based on and refining the proportional variogram parameters to site-specificity.     

Precision Farming Protocols: Part 1. Grid Distance and Soil Nutrient Impact on the Reproducibility of Spatial Variability Measurements

To determine temporal changes in soil nutrient status, reproducible results must be obtained at each time step. The objective of this paper was to determine the impact of grid distance on the reproducibility of spatial variability measurements. Soil samples from the 0 to 15 cm depth were collected from a 30 by 30 m grid in May 1995 in a 65 ha notill corn (Zea mays L.) field. Each bulk sample contained 15 individual cores, collected at sample points located every 11.4 cm along a transect that transversed 3 corn rows (57 cm). At each sampling point latitude, longitude, elevation, landscape position, and soil series were determined. The 30 m grid was used to develop 4 and 9 independent data sets having a 60 and 90 m, grids, respectively. Semivariograms, nugget to sill ratios, and mean squared errors were calculated for each data set. At 60 m: (i) the total N, total C, and pH semivariograms, of different start points, were similar, while semivariograms for Olsen P, K, and Zn were different; (ii) the spatial dependence ratings, based on the nugget to sill ratio, for total N, total C, and pH semivariograms were consistent and suggested moderate spatial dependence; (iii) the spatial dependence rating for Olsen P, K, and Zn for the 4 semivariograms were not consistent and ranged from weak to moderate spatial dependence. At 90 m all soil nutrients had different semivariograms for each start point, while the spatial dependence rating for each total N, total C, and pH start point were consistent and showed moderate spatial dependence. The total C, P, K, Zn, and pH MSE values at 60 m, were 30, 30, 41, 28, and 72% lower than the variance, respectively. This study showed that semivariogram, semivariance, MSE, and nugget to sill ratios reproducibility were dependent on soil nutrient and grid distance.     

Spatial Analysis of Soil Fertility Parameters

Databases identifying spatial distributions of soil properties are needed to implement site-specific management practices. This study examined spatial patterns for nine soil chemical properties in two adjacent fields, one in a corn (Zea mays L.)-soybean [Glycine max (L.) Merr.] rotation with inorganic fertilizer and the other in a 5-yr corn-soybean-corn-oat (Avena sativa L.)-meadow rotation with organic nutrient sources. We established sampling grids in both fields and collected soil cores to a depth of 30 cm. Soil properties with strong spatial correlations (low nugget variance/total variance ratio) and the maximum distance to which those properties were correlated (range) differed for the two fields. Soil pH, exchangeable Ca, total organic C, and total N were strongly correlated and had range values greater than 182 m in the conventional field. Bray P and exchangeable Mg were strongly correlated with range values of less than 100 m within the other. Low nugget/total variance ratios and small range values for P and Mg suggest patchy distributions, probably from long-term animal manure and municipal sludge application. Since most variance was structural in the organic field, placing sampling points closer together would improve data precision. In contrast, a relatively coarse sampling grid with fewer sampling points spaced further apart appears adequate for the conventional field. To develop accurate sampling strategies for precision agriculture, long-term field management histories should be documented since the practices appear to affect both the properties that are strongly correlated and the range to which the correlation exists.     

Three dimensional spatial distribution modeling of soil texture under agricultural systems using a sequence indicator simulation algorithm

Understanding the distribution of alluvial soil textures on a large scale is crucial for agricultural and environmental management. In our study an indicator variogram and a sequence indicator simulation (SIS) algorithm were used to analyze and simulate the spatial distribution of soil textures based on observations of 139 soil profiles in a 15 km² region in the Huabei alluvial plain in China. The nugget-to-sill ratio value (SH) of the indicator variograms for all textures in a vertical direction (Z) was equal to 1. This suggests that spatial auto-correlation dominates in the direction of sedimentary deposition with 0.05 m sampling intervals. In contrast, SH ratios from 0.48 to 0.81 show that the soil textures have a degree of randomness in the horizontal direction (X, Y) where the sampling distance was about 300 m. Using the indicator variograms in 3 directions (X, Y and Z) as outlined above, a 3D SIS algorithm was used to simulate textures. Finally, the simulation results were evaluated by the reproduction of a histogram, variogram and the mean absolute error (MAE) of prediction. The mean absolute percentage error (MAPE) of the histogram reproduction showed that the main textures (sand, sandy loam and clay) were described well, whereas the less prevalent textures were underestimated. The MAPE of the indicator variograms reproduction were reasonable although some deviation existed as less prevalent textures in the vertical direction. The mean absolute error (MAE) of the SIS prediction was 0.47. This result is considered acceptable for a category variable because of the stochastic nature of soil textures in a horizontal direction, and hence may provide useful data for other agricultural research.     

西昌市耕地土壤有效钼空间变异特征及影响因素分析

采用GIS和地统计相结合的方法,对西昌市耕地土壤耕层有效钼含量的空间分布特征及影响因素进行分析.结果表明:该区域内耕层土壤有效钼含量为( 0.27±0.15 )mg/kg,其空间分布呈带状,土壤有效钼含量变异函数曲线的理论模型能较好地符合指数模型;块金值与基台值之比为6.1％,具有强烈的空间相关性,表明受母质、地形、土壤类型等结构性因素影响较大;不同海拔高度对土壤有效钼含量的影响存在显著差异;不同地貌类型中土壤有效钼含量为平原＞丘陵＞山地,平原与山地之间土壤有效钼含量存在显著差异,但平原与丘陵、丘陵与山地之间无显著差异;成土母质也是影响土壤有效钼空间分布的主要因素.     

不同尺度下低山茶园土壤阳离子交换量空间变异性研究

 【目的】研究茶园土壤阳离子交换量（CEC）的空间变异性特征，可以为茶园生态建设以及茶园土壤肥力管理提供理论依据。【方法】本文利用地统计学方法探讨了两个取样尺度下四川蒙顶山茶园土壤CEC的空间变异性特征。【结果】（1）小尺度下，茶园土壤CEC具有强烈的空间相关性（C0/（C0+C）值为18.84%），相关距离高达1 818 m，结构性因子是影响其空间变异的主要因素；（2）微尺度下，茶园土壤CEC仍具有强烈的空间相关性（C0/（C0+C）值为16.52%），空间相关距离达311 m，结构性因子是影响其空间变异的主要因素。【结论】小尺度下土壤CEC在坡度方向变异明显，横坡方向变异最弱；普通Kriging插值分析表明其在东北至西南方向呈明显的条带状分布，并在垂直方向随海拔高度的上升而增加；微尺度下土壤CEC的变异方向与小尺度下不同，在接近坡度的方向空间变异明显，接近横坡方向变异最弱；土壤CEC沿横坡方向呈条带状分布并伴随部分斑块状分布，从坡面至上而下，呈先增加后减少再增加的趋势。     

基于GIS和FCM的宁乡植烟土壤养分管理分区

采用GPS、地统计学和模糊c均值聚类相结合的方法,对湖南省宁乡植烟土壤主要养分的空间变异特征和管理分区进行研究。结果表明,宁乡植烟土壤主要养分指标均为中等程度变异,有机质、有效磷和速效钾3项指标的块金效应在25%~75%之间,表明研究区域该3项养分指标是由结构性因素和随机因素共同作用的结果;碱解氮的块金效应75%,表明研究区土壤碱解氮主要由随机性因素决定。土壤有机质为高水平,碱解氮和速效钾均为中等水平,有效磷为极高水平,研究区大部分区域有机质、碱解氮、有效磷为中等至极高,但约有40%的面积土壤速效钾缺乏。宁乡烟区可划分为3个养分管理分区,分区间有机质、全氮、碱解氮和速效钾含量差异极显著。     

豫中典型烟田土壤养分空间变异特征分析

利用地统计学方法研究了豫中植烟土壤有机质、全氮、速效磷和速效钾的空间变异规律。结果表明:4种土壤养分的空间结构模型均符合球状模型;土壤全氮的块金值/基台值25%,表现出强烈的空间相关性;有机质、速效磷和速效钾的块金值/基台值在30%~46%,表现出中等强度的空间相关性,空间自相关距离在274~556 m。利用Kriging法生成土壤有机质、全氮、速效磷和速效钾的空间分布图,为研究区域开展精准施肥提供了决策参考。     

湘南紫色丘陵耕作区土壤肥力质量空间变异研究

本文在分析土壤各单项肥力要素空间变异基础上,结合Fuzzy综合评价法和GIS技术研究了湘南紫色丘陵耕作区土壤肥力质量空间变异,为该区合理规划、开发土壤资源,科学培肥提供依据。研究结果表明:选取的8种肥力指标具有一定空间相关性,有机质、全氮、有效磷、速效磷值的空间异质比(块金值与基台值的比值)分别为100.0%、100.0%、87.9%和99.9%,属于空间弱相关,而pH、碱解氮、全磷、全钾的空间异质比分别为33.8%、63.3%、66.1%、73.7%,属中等空间相关;各单项肥力要素空间分布随土地利用变化呈不同的规律性变化。研究区土壤肥力质量偏低,为Ⅱ、Ⅲ和Ⅳ等,分别占整个区域面积的46.2%、19.6%和34.2%;不同土地利用类型表现为:水田土壤肥力质量较优,主要为Ⅱ等;丘陵下部梯田和地势较低的坡耕地土壤肥力质量为Ⅲ等;地势较高的地块和荒地均为Ⅳ等。     

沈阳城市土壤pH和养分的空间变异性研究

采用地统计学和地理信息系统（G IS）相结合的方法研究了沈阳城市土壤pH、全磷和速效钾的空间变异特征。结果表明：pH、全磷、速效钾的最佳拟合模型为指数模型。全磷、速效钾的C0/（C0＋C）分别为10.62%、9.94%,说明沈阳城市土壤全磷和速效钾的空间相关性较强,其空间变异主要是结构性因素引起的;pH的C0/（C0＋C）为44.25%,说明土壤pH具有中度的空间相关性,其空间变异是由随机性因素和结构性因素共同引起的。最后通过克里格插值分析沈阳城市土壤pH、全磷和速效钾的空间分布特征。     

基于遥感与地统计的森林生物量时空变异分析

大兴安岭林区是我国最大的天然林区,估算该区域的森林生物量,并研究该区域的森林生物量的空间格局特征具有重要意义。以20世纪末至21世纪10年代期间(1994—1997、2006—2007、2010—2011)的Landsat5系列TM遥感影像为基础数据,建立遥感信息模型,估算黑龙江省大兴安岭地区3个时期的森林生物量。采用0°、45°、90°、135°方向以及全局Morans I系数和半变异函数块金值、基台值、变程、块金值与基台值比值、拱高与基台值比值5个参数,对20世纪末至21世纪10年代研究区域3个时期的森林生物量进行异质性和空间自相关性分析。结果表明:研究区3个时期的森林生物量的整体性良好,均成连片化分布,没有出现破碎情况。森林生物量的半变异函数模型均为线性模型,3个时期的森林生物量的块金值与基台值比值都接近1。通过遥感反演方法获得森林生物量且估算精度均达到75%以上,为地统计分析提供了可靠的数据源。采用地统计分析方法对森林生物量进行空间异质性和自相关性分析,是对单独使用GIS工具对森林生物量进行空间分析的有益补充。因此,基于遥感与地统计学相结合的方法能够更好地实现森林生物量的时空变异分析。      

Spatial variation in tree characteristics and yield in a pear orchard

We examined the spatial structure of fruit yield, tree size, vigor, and soil properties for an established pear orchard using Moran’s I, geographically weighted regression (GWR) and variogram analysis to determine potential scales of the factors affecting spatial variation. The spatial structure differed somewhat between the tree-based measurements (yield, size and vigor) and the soil properties. Yield, trunk cross-sectional area (TCSA) and normalized difference vegetation index (NDVI, used as a surrogate for vigor) were strongly spatially clustered as indicated by the global Moran’s I for these measurements. The autocorrelation between trees (determined by applying a localized Moran’s I) was greater in some areas than others, suggesting possible management by zones. The variogram ranges for TCSA and yield were 30–45 m, respectively, but large nugget variances indicated considerable variability from tree to tree. The variogram ranges of NDVI varied from about 14–27 m. The soil properties copper, iron, organic matter and total exchange capacity (TEC) were spatially structured, with longer variogram ranges than those of the tree characteristics: 31–95 m. Boron, pH and zinc were not spatially correlated. The GWR analyses supported the results from the other analyses indicating that assumptions of strict stationarity might be violated, so regression models fitted to the entire dataset might not be fitted optimally to spatial clusters of the data.     

Spatial Variability of Soil Cation Exchange Capacity in Hilly Tea Plantation Soils Under Different Sampling Scales

Studies on the spatial variability of the soil cation exchange capacity （CEC） were made to provide a theoretical basis for an ecological tea plantation and management of soil fertilizer in the tea plantation. Geostatistics were used to analyze the spatial variability of soil CEC in the tea plantation site on Mengding Mountain in Sichuan Province of China on two sampling scales. It was found that, （1） on the small scale, the soil CEC was intensively spatially correlative, the rate of nugget to sill was 18.84% and the spatially dependent range was 1 818 m, and structural factors were the main factors that affected the spatial variability of the soil CEC; （2） on the microscale, the soil CEC was also consumingly spatially dependent, and the rate of nugget to sill was 16.52%, the spatially dependent range was 311 m, and the main factors affecting the spatial variability were just the same as mentioned earlier. On the small scale, soil CEC had a stronger anisotropic structure on the slope aspect, and a weaker one on the lateral side. According to the ordinary Kriging method, the equivalence of soil CEC distributed along the lateral aspect of the slope from northeast to southwest, and the soil CEC reduced as the elevation went down. On the microscale, the anisotropic structure was different from that measured on the small scale. It had a stronger anisotropic structure on the aspect that was near the aspect of the slope, and a weaker one near the lateral aspect of the slope. The soil CEC distributed along the lateral aspect of the slope and some distributed in the form of plots. From the top to the bottom of the slope, the soil CEC increased initially, and then reduced, and finally increased.     

Outlier identification of soil phosphorus and its implication for spatial structure modeling

Outliers are classified as global outliers and spatial outliers. Up to now, there is little information about the outliers especially the spatial outliers and their influence on the spatial structure modeling of soil properties. A total of 537 soil samples were collected based on a 30 × 30 m grid in a permanent dairy farm in southeast Ireland. Graphic methods of histogram and box plot combined with Moran’s I were applied to detect the outliers of soil phosphorus (P). Sixteen outliers (5 global outliers and 11 spatial outliers) of soil P were found in the study area. Compared to the raw data, the data with global outliers excluded always had the larger global Moran’s I value indicating a stronger spatial autocorrelation. Clear spatial clusters (High–High and Low–Low clusters) were observed based on local Moran’s I. The High–High spatial clusters were located around the main farm yard and near the traffic route due to more intensive management by farmers. The Low–Low spatial clusters were mainly close to the river. For these areas, P fertilizer or slurry should be applied for healthy grass growth. The dataset with outliers excluded had a reliable semi-variogram model with a low nugget/sill ratio (32.4 %), which was closed to its corresponding transformed data (30.5 %). The cross-validation results revealed that the dataset without outliers had the strongest linear regression model (r = 0.768), indicating that the outliers played an important role in the spatial structure modeling.     

Exploitation of spatial information in high resolution digital imagery to map leaf area index

Crop responses to management practices and the environment, as quantified by leaf area index (LAI), provide decision-making criteria for the delineation of crop management zones. The objective of this work was to investigate whether spatial correlations inferred from remotely sensed imagery can be used to interpolate and map LAI using a relatively small number of ground-based LAI measurements. Airborne imagery was recorded with the Airborne Imaging Spectrometer for Applications (AISA) radiometer over a 3.2 ha corn field. Spectral vegetation indexes (SVI) were derived from the image and aggregated to cells of 2 × 2 m², 4 × 4 m², and 8 × 8 m² resolution. The residual maximum likelihood method was used to estimate the LAI variogram parameters. A generalized least squares regression was used to relate ground truth LAI data and collocated image pixels. This regression result was then used to convert variograms from the imagery to LAI units as well as to interpolate and map LAI. The decrease in resolution by merging pixels led to an increase in the value of the r ² and to a decrease in root mean-squared error (RMSE) values. The accuracy of kriged estimates from the variogram of the measured LAI and that from the image derived variograms was estimated by cross-validation. There was no difference in the accuracy of the estimates using either variograms from measured LAI values or from those of converted SVIs. Maps of LAI from ground-based measurements made by kriging the data with image-derived variogram parameters were similar to those obtained by with kriging with the variogram of measured LAI. Similar coarse spatial trends of high, medium and low LAI were evident for both maps. Variogram parameters from ground-based measurements of LAI compared favorably with those derived from remotely sensed imagery and could be used to provide reasonable results for the interpolation of LAI measurements.     

农业用地土壤重金属样本点数据精化方法——以北京市顺义区为例

样本点空间分布是样点数据检测评价和挖掘分析的关键因素。以北京市顺义区为例,研发了一种农业用地土壤重金属样本点数据精化方法：首先构建样本点均匀变异指数和均匀因子离散图来共同检测样本点数据均匀性,进一步将样本点类型划分为均匀样本点、聚集样本点和稀疏样本点并确定其数量;其次删除聚集样本点,基于研究区历史数据加密稀疏样本点;最后基于地理空间样本点均匀变异指数、特征空间偏离指数和插值误差共同评价数据精化效果。结果表明,研究区样本点的均匀变异指数为0.429,存在一个聚集样本点和一个稀疏样本点,空间偏离指数为0.327,空间属性插值误差为6.538;冗余数据精化后进行均匀性检测没有发现聚集样本点和稀疏样本点,均匀变异指数下降到0.406,特征空间偏离指数微弱下降,空间属性插值误差下降到6.357。研究表明该方法可以对提高采样数据的均匀性和代表性提供理论指导,可以服务于土壤污染防治行动计划（土十条）、土壤污染状况详查等,为更加精确研究土壤空间信息变化提供一定的基础条件。     

Exploring the Spatial Relationships Between Some Soil Properties and Wheat Yields in Two Soil Types

A field study was conducted to quantify spatial soil variability and to analyze correlations among soil properties at different spatial scales. Soil samples from 0 to 30 cm depth were collected from two adjacent fields in the southwestern Beauce Plain (France) which consisted of Haplic Calcisols and Rendzic Leptosols. Factorial kriging analysis (FKA) was used to describe the co-regionalization of nine soil properties. A linear model of co-regionalization including a nugget effect, and two spherical models were fitted to the experimental data direct and cross-variograms of the topsoil layer properties which were previously estimated. Co-kriged regionalized factors, related to short and long-range variation, were then mapped to characterize soil variation across the two fields. The potential value of ancillary sampled variables, such as yield data, to provide information on soil properties was tested. The relation between yield and measured soil properties appeared to be weak in general. However, the structures of the variation in yield appeared to be relatively stable for two years and showed similar patterns as the co-kriged soil factors. This suggests that information on the scale of variation of soil properties can be derived from yield maps, which can also be used as a guide to suitable sampling interval for soil properties and as a basis for managing fields in a precise way.