Using landscape characteristics to define an adjusted distance metric for improving kriging interpolations

Interpolation of point measurements using geostatistical techniques such as kriging can be used to estimate values at non-sampled locations in space. Traditional geostatistics are based on the spatial autocorrelation concept that nearby things are more related than distant things. In this study, additional information was used to modify the traditional Euclidean concept of distance into an adjusted distance metric that incorporates similarity in terms of quantifiable landscape characteristics such as topography or land use. This new approach was tested by interpolating soil moisture content, pH and carbon-to-nitrogen (C:N) ratio measured in both the mineral and the organic soil layers at a field site in central Sweden. Semivariograms were created using both the traditional distance metrics and the proposed adjusted distance metrics to carry out ordinary kriging (OK) interpolations between sampling points. In addition, kriging with external drift (KED) was used to interpolate soil properties to evaluate the ability of the adjusted distance metric to incorporate secondary data into interpolations. The new adjusted distance metric typically lowered the nugget associated with the semivariogram, thereby better representing small-scale variability in the measured data compared to semivariograms based on the traditional distance metric. The pattern of the resulting kriging interpolations using KED and OK based on the adjusted distance metric were similar because they represented secondary data and, thus, enhanced small-scale variability compared to traditional distance OK. This created interpolations that agreed better with what is expected for the real-world spatial variation of the measured properties. Based on cross-validation error, OK interpolations using the adjusted distance metric better fit observed data than either OK interpolations using traditional distance or KED.     

Comparison Between Kriging Variance and Interpolation Variance as Uncertainty Measurements in the Capanema Iron Mine, State of Minas Gerais—Brazil

The Capanema Mine, an iron ore deposit, is located in the central portion of the Quadrilátero Ferrífero, State of Minas Gerais, southeastern Brazil. Mine development data from approximately 7000 drillholes were used for a comparative study between kriging variance and interpolation variance as uncertainty measurements associated with ordinary kriging estimates. As known, the traditional kriging variance does not depend on local data and, therefore, does not measure the actual dispersion of data. On the other hand, the interpolation variance measures adequately the local dispersion of data used for an ordinary kriging estimate. This paper presents an application of the concept of interpolation variance for measuring uncertainties associated with ordinary kriging estimates of Fe and silica grades. These data were selected for their distinct statistical characteristics with Fe presenting a negatively skewed distribution and, consequently, a low dispersion, and silica a positively skewed distribution and, therefore, a high variability. Comparative studies between the two uncertainty measurements associated with ordinary kriging estimates of Fe and silica proved the superiority of the interpolation variance as a reliable and precise alternative to the kriging variance.     

Spatial variability and pattern analysis of soil properties in Dehui city, Jilin province

1IntroductionSoil nutrient, as the synthetic results under the influence of various anthropogenic activities and the factors such as climate and topography, etc., possesses certain spatial distribution characteristics, and certain structural and stochastic characteristics. The study of the differences existing in different parts of the region lays the foundation for adjusting all management measures and all material input capacities and for gaining the maximal economic benefit. Presently, the …     

Spatial variability and pattern analysis of soil properties in Dehui city, Jilin province

Based on regionalized variable theory, semivariograms of geo-statistics were used to research the spatial variation of soil properties quantitatively. The results showed that the semivariogram of soil organic matter is best described by spherical model, the best model for semivariograms of soil total N and available K is exponential models and that of available P belongs to linear with sill model. Those soil properties have different spatial correlations respectively, the lag of organic matter is the highest and that of available P is the lowest, the spatial correlation of N and available K belongs to moderate degree. Spatial heterogeneities are different too, the degree of organic matter and total N are higher, the degree of available K is in the next place and that of available P is the lowest. Influenced by the shape, topography and soil of the study area, all isotropies of available P are obvious in all directions while anisotropies of others are manifested. According to the analytical results, supported by GIS, Kriging and IDW methods are applied to describe and analyze the spatial distribution of soil properties. The results indicate that soil organic matter, total N and available K are distributed regularly from northeast to southwest, while available P is distributed randomly.     

吉林省德惠市土壤特性空间变异特征与格局

Based on regionalized variable theory, semivariograms of geo-statistics were used to research the spatial variation of soil properties quantitatively. The results showed that the semivariogram of soil organic matter is best described by spherical model, the best model for semivariograms of soil total N and available K is exponential models and that of available P belongs to linear with sill model. Those soil properties have different spatial correlations respectively, the lag of organic matter is the highest and that of available P is the lowest, the spatial correlation of N and available K belongs to moderate degree. Spatial heterogeneities are different too, the degree of organic matter and total N are higher, the degree of available K is in the next place and that of available P is the lowest. Influenced by the shape, topography and soil of the study area, all isotropies of available P are obvious in all directions while anisotropies of others are manifested. According to the analytical results, supported by GIS, Kriging and IDW methods are applied to describe and analyze the spatial distribution of soil properties. The results indicate that soil organic matter, total N and available K are distributed regularly from northeast to southwest, while available P is distributed randomly.     

A HIGH-RESOLUTION, GRIDDED DATASET FOR MONTHLY TEMPERATURE NORMALS (1971-2000) IN SWEDEN

A baseline climatology is required in evaluating climate variability and changes on regional and local scales. Gridded climate normals, i.e. averages over a 30‐year period, are of special interest since they can be readily used for validation of climate models. This study is aimed at creating an updated gridded dataset for Swedish monthly temperature normals over the period 1971–2000, based on standard 2‐m air temperature records at 510 stations in mainland Sweden. Spatial trends of the normal temperatures were modelled as functions of latitude, longitude and elevation by multiple linear regression. The study shows that the temperature normals are strongly correlated with latitude throughout the year and especially in cold months, while elevation was a more important factor in June and July. Longitude played a minor role and was only significant in April and May. Regression equations linking temperature to latitude, longitude and elevation were set up for each month. Monthly temperature normals were detrended by subtracting spatial trends given by the regressions. Ordinary kriging was then applied to both original data (simple method) and de‐trended data (composite method) to model the spatial variability and to perform spatial gridding. The multiple regressions showed that between 82% (summer) and 96% (winter) of the variance in monthly temperature normals could be explained by latitude and elevation. Unexplained variances, i.e. the residuals, were modelled with ordinary kriging with exponential semivariograms. The composite grid estimates were calculated by adding the multiple linear trends back to the interpolated residuals at each grid point. Kriged original temperature normals provided a performance benchmark. The cross–validation shows that the interpolation errors of the normals are significantly reduced if the composite method rather than the simple one was used. A gridded monthly dataset with 30‐arcsecond spacing was created using the established trends, the kriging model and a digital topographic dataset.     

福州晋安河沿岸区域地表径流中氮磷污染物的空间分布特征及来源分析

以福州市晋安河沿线区域为研究对象,采集区内地表径流样品,通过分析径流水样中全氮、全磷浓度,采用普通克里格法分析了地表径流中全氮、全磷的空间分布特征.结果表明,全氮是地表径流的主要污染物质,全磷除少部分地段超标外,总体上不构成污染;全氮、全磷的半方差函数用球状模型拟合的最好,其空间分布表现为各向同性;地表径流中全氮污染主要集中于管理条件落后的居民区、餐饮业集中的娱乐场所以及非城市主干道路.地表径流中的全磷主要分布在餐饮业集中区域及管理落后的住宅小区.福州城市地表径流的氮磷污染主要来自于居民的日常生活排污.     

A treatise on the use of geostatistics for the characterization of nonrenewable resources

Five decades of geostatistical development are reviewed to summarize the state of the art for spatial interpolation vis-à-vis kriging or a form thereof. Although a search of the literature reveals a variety of kriging methods, there are but two infrastructures for geostatistical interpolation: simple cokriging, for estimating a single variable using two variables, and generalized cokriging, for estimating one or more variables using the same number of variables that are estimated. The many forms of kriging are varieties of these two interpolation infrastructures. This notion is emphasized to aid the selection of an appropriate interpolation model for a nonrenewable resource. These models are discussed, and literature for the models and for applicable software is cited. Additionally, all aspects of spatial interpolation are discussed, including the adequacy of spatial sampling, distribution characteristics of spatial samples, semivariograms, search parameters, and selection of interpolation models in conformance with spatial data characteristics. Finally, the relationship between interpolation and raster-based geographic information systems is emphasized.     

松嫩平原玉米带土壤有机质和全氮的时空变异特征

采用地统计学和GIS相结合的方法,研究了松嫩平原玉米带1980～2005年间土壤有机质和全氮的时空变异特征.结果表明:去除异常值后,土壤有机质和全氮均符合对数正态分布,两个时期土壤有机质的平均含量分别为2.14%和2.54%,土壤全氮的平均含量均为0.12%.通过变异函数分析,两个时期土壤有机质和全氮均符合高斯模型,1...     

吉林省鼠密度的三明治空间抽样模型制图（英文）

Rodents are the main host animals that spread plague, and Spermophilus dauricus(S. dauricus) is the most common rodent in North China. In this study, a rodent density survey was carried out in China's Jilin Province from April to August 2005. Moran's I and semivariogram curves were used to investigate the spatial distribution characteristics of the sampling data. We found that the spatial auto-correlation index was low and failed to generate a meaningful semivariogram curve. In this case, commonly used interpolators, such as kriging, were not suitable for mapping density over the study area. However, the Sandwich model, which is based on spatial stratified heterogeneity, could be applied to our data. Our results showed that the type of soil and land use significantly influenced the distribution of rodent density, and the interactive effect of these variables was much stronger than that of each variable alone. The Sandwich-estimated rodent density map showed that rodent density increased from the southeast to the northwest in Jilin Province. Finally, a framework of a rodent density survey using the Sandwich model was introduced.     

Sandwich mapping of rodent density in Jilin Province,China

Rodents are the main host animals that spread plague, and Spermophilus dauricus (S. dauricus) is the most common rodent in North China. In this study, a rodent density survey was carried out in China’s Jilin Province from April to August 2005. Moran’s I and semivariogram curves were used to investigate the spatial distribution characteristics of the sampling data. We found that the spatial auto-correlation index was low and failed to generate a meaningful semivariogram curve. In this case, commonly used interpolators, such as kriging, were not suitable for mapping density over the study area. However, the Sandwich model, which is based on spatial stratified heterogeneity, could be applied to our data. Our results showed that the type of soil and land use significantly influenced the distribution of rodent density, and the interactive effect of these variables was much stronger than that of each variable alone. The Sandwich-estimated rodent density map showed that rodent density increased from the southeast to the northwest in Jilin Province. Finally, a framework of a rodent density survey using the Sandwich model was introduced.     

中国土壤温度的空间插值方法比较

利用中国698个气象站点1971~2000年的地面气候资料,采用三种不同方法预测中国0cm、20cm和40cm深度年均土壤温度的空间分布,其中普通克里格和泛克里格法直接以年均土壤温度数据为源数据、回归克里格法以中国年均气温数据和中国DEM数据为源数据进行预测。预测结果的准确性通过平均绝对误差(MAE)和均方根误差(RMSE)值来评价。结果表明回归克里格法预测的MAE值和RMSE值均为最小,说明其预测结果的准确性最好、预测的极端误差也最小;其次为泛克里格法;普通克里格法预测的效果最差。回归克里格法预测结果由于采用了中国DEM数据进行修正,在空间特征表达方面能够更好地表达复杂地形地区的局部变异,其平滑效应明显小于泛克里格法和普通克里格法的预测结果。     

喀斯特地区春季土壤水分空间插值方法对比

以杨眉河小流域为研究区,通过土壤水分采样,选取辅助变量,采用普通克里金、协同克里金、回归克里金3种地统计学方法对土壤水分数据进行空间插值。结果表明：1）回归克里金对研究区土壤水分估算误差最小,其次为协克里金,普通克里金的误差最大;2）普通克里金生成的土壤水分表面最为平滑,而回归克里金最大程度反映了研究区实际的土壤水分空间变化;3）对于协同克里金,以湿度指数（WI）样点数据作为辅助变量的估算误差小于将WI栅格数据作为辅助变量的估算误差。总之,在可获得有效辅助变量的条件下,回归克里金对研究区土壤水分估算的效果优于协同克里金与普通克里金。     

祁连山青海云杉林动态监测样地土壤pH和养分的空间异质性

为了探讨青海云杉林对土壤pH和养分的影响,选择祁连山青海云杉林动态监测样地(340 m×300 m)为试验样地采集土样,利用经典统计学和地统计学方法对其空间异质性进行了研究。结果表明:(1)pH、水解氮和全磷为弱变异性,有机碳、全氮、速效磷、全钾和速效钾为中等变异性,它们的大小依次为速效钾 >有机碳 >速效磷 >全氮 >全钾 >水解氮 >全磷 >pH。(2)半方差最优模型拟合分析表明,pH、全氮、水解氮、全磷、速效磷和速效钾均符合球状模型,有机碳和全钾均符合指数模型;pH、有机碳、全氮、水解氮、全磷、速效磷、全钾和速效钾的变程依次为108.8 m、88.5 m、112.8 m、131.9 m、143.3 m、73.3 m、73.3 m和134.7 m。从空间结构特征看,pH具有中等强度的空间自相关,而养分表现出强烈的空间自相关。(3)pH和养分均呈斑块状分布,有机碳和氮素具有相似的空间分布格局,全磷和速效钾分布变化较为明显,速效磷和全钾分布变化较为平缓。上述研究结果可为祁连山青海云杉林土壤pH和养分的取样设计和空间分布图制作等提供参考,也可为青海云杉林的土壤环境恢复与重建提供科学依据。     

Spatial interpolation of marine environment data using P-MSN

ABSTRACT

When a marine study area is large, the environmental variables often present spatially stratified non-homogeneity, violating the spatial second-order stationary assumption. The stratified non-homogeneous surface can be divided into several stationary strata with different means or variances, but still with close relationships between neighboring strata. To give the best linear-unbiased estimator for those environmental variables, an interpolated version of the mean of the surface with stratified non-homogeneity (MSN) method called point mean of the surface with stratified non-homogeneity (P-MSN) was derived. P-MSN distinguishes the spatial mean and variogram in different strata and borrows information from neighboring strata to improve the interpolation precision near the strata boundary. This paper also introduces the implementation of this method, and its performance is demonstrated in two case studies, one using ocean color remote sensing data, and the other using marine environment monitoring data. The predictions of P-MSN were compared with ordinary kriging, stratified kriging, kriging with an external drift, and empirical Bayesian kriging, the most frequently used methods that can handle some extent of spatial non-homogeneity. The results illustrated that for spatially stratified non-homogeneous environmental variables, P-MSN outperforms other methods by simultaneously improving interpolation precision and avoiding artificially abrupt changes along the strata boundaries.     

Spatial Prediction of Lateral Variability of a Laterite-Type Bauxite Horizon Using Ancillary Ground-Penetrating Radar Data

Tropical laterite-type bauxite deposits often pose a unique challenge for resource modelling and mine planning due to the extreme lateral variability at the base of the bauxite ore unit within the regolith profile. An economically viable drilling grid is often rather sparse for traditional prediction techniques to precisely account for the lateral variability in the lower contact of a bauxite ore unit. However, ground-penetrating radar (GPR) offers an inexpensive and rapid method for delineating laterite profiles by acquiring fine-scale data from the ground. These numerous data (secondary variable) can be merged with sparsely spaced borehole data (primary variable) through various statistical and geostatistical techniques, provided that there is a linear relation between the primary and secondary variables. Four prediction techniques, including standard linear regression, simple kriging with varying local means, co-located cokriging and kriging with an external drift, were used in this study to incorporate exhaustive GPR data in predictive estimation the base of a bauxite ore unit within a lateritic bauxite deposit in Australia. Cross-validation was used to assess the performance of each technique. The most robust estimates are produced using ordinary co-located cokriging in accordance with the cross-validation analysis. Comparison of the estimates against the actual mine floor indicates that the inclusion of ancillary GPR data substantially improves the quality of the estimates representing the bauxite base surface.     

宁夏盐池沙地3种植物群落土壤表层养分的空间异质性

采用经典统计学和地统计学方法,通过半变异函数及其模型、克里格局部插值估计、空间分布图及分形维数等对宁夏盐池沙地3种植物群落(牛枝子、牛枝子-黑沙蒿、黑沙蒿)土壤表层养分的空间异质性进行了研究。结果表明:0~5 cm土壤有机质、全氮、速效磷含量的空间自相关尺度分别是67 m、519 m、143 m;结构方差比分别为0.558、0.882、0.514,说明结构性因素和随机性因素在0~5 cm土壤有机质和速效磷的空间分布中共同发挥作用。全氮表现出较强空间自相关性,在空间分布上具有明显的结构特征,表明结构性因素在其空间总变异中发挥主导作用。空间格局图反映出0~5 cm土壤有机质、全氮含量表现为牛枝子群落较高,经牛枝子-黑沙蒿群落,含量逐渐减少,至黑沙蒿群落含量又有所增加;0~5 cm土壤速效磷含量表现为牛枝子群落和黑沙蒿群落含量较高而牛枝子-黑沙蒿群落含量较低的趋势。反映出研究区从牛枝子群落经牛枝子-黑沙蒿群落至黑沙蒿群落,植被从以草原种为主的群落,逐渐灌木化,植物群落结构组成由复杂到简单的过程,深刻影响了土壤养分的分布格局,导致了土壤“肥力岛”的形成和发展,又反作用引起研究区植物群落的进一步灌丛化,并逐步向沙漠化的方向发展的趋势。     

吉林省德惠市土壤特性空间变异特征与格局

基于区变量理论,通过地统计学的半变异函数定量研究吉林省中部德惠市土壤有机质、全氮、速效钾和速效磷的空间异质性特征。表明土壤有机质的理论模型属于球状模型、全氮和速效钾的理论模型为指数模型、速效磷则属于有基台值的线状模型。空间结构上,有机质具有很强的空间相关性,全氮和速效钾的空间相关性属于中等程度,而速效磷则具有弱相关性。四种土壤养分的空间自相关范围具有明显的差异,有机质和全氮的有效变程最大,速效钾次之,速效磷的有效变程最小。受研究区形状、地形及土壤母质区域性差异的影响,速效磷各向同性显著,其他养分各向带状性比较明显。根据空间分异的分析结果,在GIS支持下,采用Kriging和IDW两种插值方法,分析研究区土壤养分的空间格局,表明土壤有机质、全氮、速效钾均自东北向西南有规律地分布;速效磷分布的随机性较强,较前三者结构性特征不明显。     

Application of Kriging Interpolation for Glacier Mass Balance Computations

In order to compute the specific mass balance of a glacier, point measurements of mass balance need to be integrated and thus interpolated over the entire glacier. In this study kriging was applied as interpolation technique to mass balance data of Storglaciren, a 3 km² valley glacier, focusing on the sensitivity of results to the choice of some kriging parameters. Although the spatial means varied only little in most cases, the spatial distribution of the mass balance quantities was sensitive to the assumption on kriging parameters, suggesting that the kriging parameters need to be carefully optimized for each case if the spatial distribution is of interest.     

某污染场地土壤苯并(a)芘含量的三维估值及不确定性分析

污染场地修复前的准确评估是开展场地修复行动的基础和前提。建立了一套评估污染场地中污染土方量的三维插值方法,采用该方法模拟了某污染场地土壤苯并(a)芘(BaP)含量的空间分布并分析其不确定性。结果表明：场地地下环境中BaP含量数据服从对数正态分布,土壤中污染严重区域分别位于研究区的西南部和北部。通过普通克里格插值得到的BaP浓度超过0.4 mg·kg^-1的污染羽体积为14134 m³,对应的累积概率为0.585。依据给定变差范围值计算,得出现有收集数据对整个场地的描述程度为65%。基于该三维插值方法能准确地反映场地污染物空间分布特征,其不确定性分析可为补充采样布点及精准评估提供参考。