Comparison of several spatial prediction methods for soil pH

A survey of topsoil pH has been designed specifically to compare the performance of several two-dimensional spatial prediction methods. These methods have been classified as global or local, and interpolating or non-interpolating, and smooth or non-smooth predictors. The techniques tested were global means and medians, moving averages, inverse squared distance interpolation, Akima's interpolation, natural neighbour interpolation, quadratic trend surface, Laplacian smoothing splines and ordinary kriging. All methods showed some deficiencies; for example, prediction sums-of-squares were higher than expected for all methods. Interpolating methods either were very poor predictors, or suffered from theoretical drawbacks, or both. Of the non-interpolating methods, Laplacian smoothing splines and kriging generally performed best. Estimates of variance derived from models which assume independent errors were greater than estimates of variance derived from neighbouring pairs of data sites, suggesting that short range correlations definitely exist, and should be taken into account in any predictive modelling.     

Neural network ensemble residual kriging application for spatial variability of soil properties

High quality, agricultural nutrient distribution maps are necessary for precision management, but depend on initial soil sample analyses and interpolation techniques. To examine the methodologies for and explore the capability of interpolating soil properties based on neural network ensemble residual kriging, a silage field at Hayes, Northern Ireland, UK, was selected for this study with all samples being split into independent training and validation data sets. The training data set, comprised of five soil properties: soil pH, soil available P, soil available K, soil available Mg and soil available S,was modeled for spatial variability using 1) neural network ensemble residual kriging, 2) neural network ensemble and 3) kriging with their accuracies being estimated by means of the validation data sets. Ordinary kriging of the residuals provided accurate local estimates, while final estimates were produced as a sum of the artificial neural network (ANN) ensemble estimates and the ordinary kriging estimates of the residuals. Compared to kriging and neural network ensemble,the neural network ensemble residual kriging achieved better or similar accuracy for predicting and estimating contour maps. Thus, the results demonstrated that ANN ensemble residual kriging was an efficient alternative to the conventional geo-statistical models that were usually used for interpolation of a data set in the soil science area.     

Performance of Soil Electrical Conductivity and Different Methods for Mapping Soil Data from a Small Dataset

The performance of different methods for making soil maps from a small dataset was assessed. Soil samples obtained at five different depths were taken from 39 locations within an arable field in Sweden and analysed for clay content, soil organic matter content, pH (H₂O), K-HCl, P-AL, K-AL and Mg-AL. Detailed and densely sampled soil electrical conductivity (EC) data with a distinct border between two different regions was used for dividing the field into two zones. Averages from these zones gave better prediction for most variables than interpolation without respect to the border. With the border taken into account, cokriging with EC as a covariable improved the prediction, whereas the improvement with ordinary kriging and inverse distance weighting (IDW) was insignificant. Direct interpretation of EC by a simple linear regression model gave reasonable predictions for clay content. In general, even the simplest interpolation method improved the prediction compared to field average.     

基于磁感式土壤表观电导率空间变异性的插值方法比较

针对目前黄河三角洲地区存在的土壤盐渍障碍问题,以该地区典型地块为研究对象,运用磁感大地电导率仪(EM38),结合GIS与地统计学研究了不同样点密度下土壤表观电导率的空间变异特征,确定了最佳的空间插值模式,并采用偏差指数对各分布图层的空间相似性进行了评价。结果表明：不同样点密度下的土壤表观电导率均呈中等变异强度,并服从对数正态分布;各样点密度下的土壤表观电导率均表现为强空间相关性,其空间变异主要表现在小于10 m的田间尺度上,且对于预测精度,泛克立格>普通克立格>反距离权重>局部多项式。偏差指数法分析表明,各插值方法分布图的空间相似性均随样点密度的降低而下降;对于相同的样点密度减小比例下的空间信息保留度,泛克立格>普通克立格>反距离权重>局部多项式,采用泛克立格法可以在保证预测精度的基础上合理降低样点密度。该研究为黄河三角洲地区盐渍土地磁感式田间数据采集的合理密度确定以及优化空间插值模式选取提供了理论依据与技术参考。     

利用数字高程模型改进高山灰岩坑土壤pH值预测

Among spatial interpolation techniques,geostatistics is generally preferred because it takes into account the spatial correlation between neighbouring observations in order to predict attribute values at unsampled locations.A doline of approximately 15 000 m 2 at 1 900 m above sea level (North Italy) was selected as the study area to estimate a digital elevation model (DEM) using geostatistics,to provide a realistic distribution of the errors and to demonstrate whether using widely available secondary data provided more accurate estimates of soil pH than those obtained by univariate kriging.Elevation was measured at 467 randomly distributed points that were converted into a regular DEM using ordinary kriging.Further,110 pits were located using spatial simulated annealing (SSA) method.The interpolation techniques were multi-linear regression analysis (MLR),ordinary kriging (OK),regression kriging (RK),kriging with external drift (KED) and multi-collocated ordinary cokriging (CKmc).A cross-validation test was used to assess the prediction performances of the different algorithms and then evaluate which methods performed best.RK and KED yielded better results than the more complex CKmc and OK.The choice of the most appropriate interpolation method accounting for redundant auxiliary information was strongly conditioned by site specific situations.     

Integrating properties of soil map delineations into ordinary kriging

Stratification of a region based on soil map delineations followed by within-stratum interpolation is sometimes used to combine soil maps and spatial interpolation. However, not all delineations are equally suitable to subdivide an area into precisely located mutually exclusive strata. This paper proposes a flow-path to characterize the nature of soil map delineations and a methodology to integrate the properties of map delineations into ordinary kriging.Four types of delineations were distinguished based on three criteria: the nature of transition (discontinuous or gradual), the mapping accuracy, and the structure of the within-unit spatial variation. For each type of delineation the ordinary kriging algorithm was modified to integrate its properties in the interpolation.As a test case, the sand content of the topsoil in the province of West-Flanders (Belgium) was mapped, using independent test data for validation. Inside the mapping units and at delineations identified as gradual transitions, our procedure, termed ordinary kriging integrating properties of map delineations (OKPD) , performed similarly to stratified ordinary kriging (SOK). However, close to the delineations identified as inaccurately mapped discontinuities the mean square prediction error of OKPD was 0.64 times that of SOK. Moreover, near these delineations, the prediction variance was largely underestimated by SOK (relative variance = 5.1), whereas OKPD produced a more realistic value (relative variance = 1.5).     

地统计软件包的开发及在土壤空间变异中的应用

Geo-STATer是一个用来进行半方差分析、地统计估值和模拟的工具软件。它除了具备传统统计学的基本统计分析功能外，还集成了地统计学的几项主要功能：单变量半方差分析、交互变量半方差分析、半方差函数模型拟合、空间插值方法（包括普通克立格法、协同克立格法和逆距离加权法）。本文介绍了该软件的总体设计思路、主要功能模块和开发实现，并用实例土壤数据演示了软件的操作计算过程并将计算结果与其它的地统计软件进行了比较。结果表明．Geo-STATer软件具有较好的运算效率和精度．可以运用于土壤特性的空间变异性研究和插值制图，并能与其他专业模型进行集成开发．服务于田间精确施肥管理系统的开发。     

Comparison of spatial interpolation techniques for mapping soil pH and salinity in agricultural coastal areas,northern Iran

This study attempted to characterize the spatial distributions of soil pH and electrical conductivity (EC_e) of coastal fields in the Miyandoroud region, northern Iran, for three soil layer depths by assessing spatial variability and comparing different interpolation techniques such as inverse distance weighting (IDW), ordinary kriging (OK), and conditional simulations (CS). Three soil composite samples were collected from 0–50, 50–100, and 100–150 cm depths at 105 sampling sites. At all three soil depths, pH and EC_e were best fitted by exponential and spherical models, respectively. Nugget effects were higher for soil EC_e data sets compared with soil pH at all three soil depths showing soil EC_e had a spatial variability in small distances. The prediction accuracy of the interpolation methods indicated that the minimum error for all data sets was achieved with the OK method, except for pH at 50–100 cm depth, and the CS technique revealed the largest error. The effect of different numbers of simulations (100, 500 and 1000) in the CS interpolation method resulted not in a realistic mapping for the soil EC_e and pH. Considering the high importance of irrigated agriculture in the Caspian Sea coastal areas, more subsoil salinity build-up and groundwater salinity monitoring plans are needed as a prerequisite for sustainable agricultural production systems of the future.     

插值方法对GIS土壤养分插值结果的影响

精准农业技术的应用越来越受到大家的关注,通过对一个地块土壤养分进行详细栅格采样化验分析,利用反距离法和克里格(Kriging)两种不同计算机插值方法对土壤中各种营养元素进行了分析研究。在采样栅格大小不同的条件下,随机选择5个采样点插值,分析对比了5个采样点在不同栅格采样条件下利用两种插值方法的插值结果。通过插值计算得到土壤中全氮、速效氮和速效磷在采样栅格较小的情况下,由于反距离法考虑的周围点数较多,插值点处的插值误差要较克里格插值总体上来讲误差小,而随着采样栅格距离的加大,克里格插值的误差要小于反距离法插值的误差。     

土地混合使用制度下土壤硝态氮分布的地理空间制图研究

Mapping the spatial distribution of soil nitrate-nitrogen (NO₃-N) is important to guide nitrogen application as well as to assess environmental risk of NO₃-N leaching into the groundwater. We employed univariate and hybrid geostatistical methods to map the spatial distribution of soil NO₃-N across a landscape in northeast Florida. Soil samples were collected from four depth increments (0-30, 30-60, 60-120 and 120-180 cm) from 147 sampling locations identified using a stratified random and nested sampling design based on soil, land use and elevation strata. Soil NO₃-N distributions in the top two layers were spatially autocorrelated and mapped using lognormal kriging. Environmental correlation models for NO₃-N prediction were derived using linear and non-linear regression methods, and employed to develop NO₃-N trend maps. Land use and its related variables derived from satellite imagery were identified as important variables to predict NO₃-N using environmental correlation models. While lognormal kriging produced smoothly varying maps, trend maps derived from environmental correlation models generated spatially heterogeneous maps. Trend maps were combined with ordinary kriging predictions of trend model residuals to develop regression kriging prediction maps, which gave the best NO₃-N predictions. As land use and remotely sensed data are readily available and have much finer spatial resolution compared to field sampled soils, our findings suggested the effcacy of environmental correlation models based on land use and remotely sensed data for landscape scale mapping of soil NO₃-N. The methodologies implemented are transferable for mapping of soil NO₃-N in other landscapes.     

A coherent geostatistical approach for combining choropleth map and field data in the spatial interpolation of soil properties

Information available for mapping continuous soil attributes often includes point field data and choropleth maps (e.g. soil or geological maps) that model the spatial distribution of soil attributes as the juxtaposition of polygons (areas) with constant values. This paper presents two approaches to incorporate both point and areal data in the spatial interpolation of continuous soil attributes. In the first instance, area-to-point kriging is used to map the variability within soil units while ensuring the coherence of the prediction so that the average of disaggregated estimates is equal to the original areal datum. The resulting estimates are then used as local means in residual kriging. The second approach proceeds in one step and capitalizes on: 1) a general formulation of kriging that allows the combination of both point and areal data through the use of area-to-area, area-to-point, and point-to-point covariances in the kriging system, 2) the availability of GIS to discretize polygons of irregular shape and size, and 3) knowledge of the point-support variogram model that can be inferred directly from point measurements, thereby eliminating the need for deconvolution procedures. The two approaches are illustrated using the geological map and heavy metal concentrations recorded in the topsoil of the Swiss Jura. Sensitivity analysis indicates that the new procedures improve prediction over ordinary kriging and traditional residual kriging based on the assumption that the local mean is constant within each mapping unit.     

Accuracy Assessments of Stochastic and Deterministic Interpolation Methods in Estimating Soil Attributes Spatial Variability

ABSTRACT

Spatial interpolation methods are frequently used to characterize soil attributes’ spatial variability. However, inconclusive results, about the comparative performance of these methods, have been reported in the literature. Therefore, the present study aimed to analyze the efficiency of ordinary kriging (OK) and inverse distance weighting (IDW) methods in estimating the soil penetration resistance (SPR), soil bulk density (SBD), and soil moisture content (SM) using two distinct sampling grids. The soil sampling was performed on a 5.7 ha area in Southeast Brazil. For data collection, a regular grid with 145 points (20 x 20 m) was created. Soil samples were taken at a 0.20 m layer depth. In order to compare the accuracy of OK and IDW, another grid was created from the initial grid (A), by eliminating one interspersed line, which resulted in a grid with 41 sampled points (40 x 40 m). Results showed that sampling grid A presented less errors than B, proving that the more sampling points, the lower the errors that are associated with both methods will be. Overall, the OK was less biased than IDW only for SBD (A) and SM (B) maps, whereas IDW outperformed OK for the other attributes for both sampling grids.     

绿洲土壤表层含盐量空间变异分析的插值方法研究

为了比较土壤表层含盐量空间变异性研究的各种空间插值方法的优劣,以渭库绿洲为例,运用基于ArcGIS的4种空间插值方法（反距离加权、样条函数、克里格、协同克里格空间插值方法）,分析了土壤表层含盐量的空间变异性。并通过分析各个交叉检验统计量来验证评估数据的误差,从而选取最优的空间插值方法。结果表明:4种插值方法的插值结果基本能反映含盐量的空间分布特征,简单克里格法更适合绿洲表层土壤含盐量的空间插值;通过空间插值可以发现表层土壤含盐量呈现出东南高、西北低的态势。对渭库绿洲土壤盐分空间分布特征及空间变异进行了解,有利于土壤盐渍化的快速诊断,是盐渍化土壤治理和改良的重要基础。     

山区县域尺度降水量空间插值方法比较

随着空间降水信息需求的日益增加,降水的空间插值已被广泛应用,而不同的插值方法因不同的地区和研究目的产生不同的效果。该文以浙江省淳安县为例,选取17个站点1959～2000年多年平均和月均降水资料,在地统计学和地理信息系统(GIS)支持下,结合一些地形地理因子,采用多种插值方法对研究区降水量进行了空间插值研究,分析不同插值方法对研究区的适用性和精度,并对模拟的空间降水量图像进行了比较。通过3个检验站点的插值误差的比较,混合插值法,即回归克里金插值法误差最小,效果最好。     

基于地形属性使用回归, 克里格和人工神经网络方法估算饱和导水率空间分布

Several methods,including stepwise regression,ordinary kriging,cokriging,kriging with external drift,kriging with varying local means,regression-kriging,ordinary artificial neural networks,and kriging combined with artificial neural networks,were compared to predict spatial variation of saturated hydraulic conductivity from environmental covariates.All methods except ordinary kriging allow for inclusion of secondary variables.The secondary spatial information used was terrain attributes including elevation,slope gradient,slope aspect,profile curvature and contour curvature.A multiple jackknifing procedure was used as a validation method.Root mean square error (RMSE) and mean absolute error (MAE) were used as the validation indices,with the mean RMSE and mean MAE used to judge the prediction quality.Prediction performance by ordinary kriging was poor,indicating that prediction of saturated hydraulic conductivity can be improved by incorporating ancillary data such as terrain variables.Kriging combined with artificial neural networks performed best.These prediction models made better use of ancillary information in predicting saturated hydraulic conductivity compared with the competing models.The combination of geostatistical predictors with neural computing techniques offers more capability for incorporating ancillary information in predictive soil mapping.There is great potential for further research and development of hybrid methods for digital soil mapping.     

Geostatistics-based spatial distribution of soil moisture and temperature regime classes in Mazandaran province,northern Iran

Soil moisture regime (SMR) and soil temperature regime (STR) classes as soil classification criterions are required by US Soil Taxonomy because they affect genesis, use, and management of soils. The lack of sufficient soil moisture and temperature data requires the characterization of the pedoclimate on the basis of climatic data processed by simulation models. This research was conducted to consider the new approach for SMR and STR mapping. The objectives of this study were to compare the four interpolation schemes including ordinary kriging (OK), cokriging (Co-K), inverse distance weighting, and conditional simulation for interpolating the monthly mean total precipitation (MMTP) and monthly mean air temperature (MMAT) and to apply the Java Newhall simulation model for the MMTP and MMAT predictive values at each node of 1 km² grids across the Mazandaran province, northern Iran, for delineating the SMR and STR classes. The semivariogram analyses showed moderate to strong spatial dependence of data sets. The accuracy of interpolators varied within months for both MMTP and MMAT data sets. In most cases, OK and Co-K methods had the highest accuracy with lower mean error, root mean square error, and higher concordance correlation coefficient. The predictive maps show high diversity of SMR classes including Aridic, Ustic, Udic, and Xeric. The STR classes comprise Mesic, Thermic, and Cryic regimes. Results herein indicated that geostatistical approaches can potentially provide the opportunity for mapping of SMR and STR classes in data scarce regions.     

A topographic geostatistical approach for mapping monthly mean values of daily global solar radiation: A case study in southern Spain

Local topography influences total incoming solar radiation at ground surface in mountainous areas, and so it becomes a key factor for the spatial distribution of plants. However, radiometric stations are often clustered only around farmland or populated areas, usually throughout valleys and flat regions. In this work, we use residual kriging methods to account for cloud- and terrain-related effects, especially when availability of measurements in mountains is scarce. Terrain-related effects have been considered through the terrain elevation and a topographic clear-sky solar radiation model that, additionally, also allow us to consider local clouds effects. Mesoscale-level phenomena were considered through the distance to the coast and the geographical longitude, that partially explain the atmospheric circulation in the studied region. The study has been conducted in the region of Andalusia, in southern Spain, using a target grid support of 1 km of grid-spacing and based on a 10-year length experimental dataset of 63 stations. Two different residual kriging approaches were evaluated and compared against ordinary kriging estimates. Overall, all kriging methods showed good skills in predicting the spatial regionalization of the monthly averages of daily solar radiation. The use of the distance to the coast and the geographical longitude enhanced the performance of residual kriging methods. Elevation proved to be important during summer months, while clear-sky solar radiation estimates were helpful especially during winter months. Overall, the RMSE value for ordinary kriging at the validation sites was about 3%. The residual kriging methods were able to outperform ordinary kriging around a 5% in winter and up to a 18% in summer, in relative terms.     

县域土壤质量数字制图方法比较

土壤质量研究几乎涵盖土壤研究的所有领域,土壤质量制图理论与方法是土壤质量研究的一项重要研究内容。该研究以北京市密云县为研究区,基于土壤质量评价最小数据集和指数和法计算的土壤质量指数,探究了在地学模型支持下区域土壤质量数字制图方法。研究设计了5种区域土壤质量数字制图方法,并比较了不同方法的空间数字制图精度。结果显示,目前广泛使用的基于参评指标空间插值结果的土壤质量数字制图方法精度最低、工序较繁琐,且无法反映研究区景观高度异质的特点;而基于计算后的土壤质量指数（soil quality index,SQI）,借助于地统计学方法的土壤质量数字制图方法相对比较科学合理,其中又以基于计算后的SQI和回归克里格法预测效果最好,均方根误差最小,仅为0.01897,相对于基于参评指标空间插值结果的土壤质量数字制图方法,精度相对提高率最大,达到50%以上。综合考虑空间制图精度、工序的繁简程度,在该研究设计的5种方法中基于计算的SQI和回归克里格法最佳,该法避免了地统计插值在景观高度异质区的应用局限性,预测结果与实际最为相符。     

普通克里格评估土壤污染物空间分布精度控制研究

从数据的统计特征分析、异常值筛选及处理、实验半变异函数计算及拟合等方面对普通克里格计算过程中的精度控制问题进行了初步研究,并以天津市东南郊区土壤砷（As）空间分布评估为例,分析了在多步骤精度控制下普通克里格法估计土壤污染物空间分布的可靠性。结果表明,研究区土壤As表现出了明显的累积特征,且监测值为正态分布,异常值较少且为局部异常值,实验半变异函数表现出明显的各向异性。在较严格的精度控制下,普通克里格估值的最优无偏特性可以得到较好的体现,其对土壤As的空间分布的估计精度可以达到较高的水平。