不同采样点数量下土壤有机质含量空间预测方法对比

运用普通克里格、泛克里格、协同克里格和回归克里格4种方法,结合由DEM获取的高程因子以及土壤全氮和阳离子交换量（CEC）,预测了黑龙江省海伦市耕地有机质含量的空间分布。不同样点数量下海伦市土壤有机质含量的空间变异结构分析表明,样点数量多并不一定能够识别土壤有机质含量的结构性连续组分,最优化的布置采样点位置可能比单纯增加...     

Comparison of statistical prediction methods for characterizing the spatial variability of apparent electrical conductivity in coastal salt-affected farmland

Soil salinity has been known to be problematic to land productivity and environment in the lower Yellow River Delta due to the presence of a shallow, saline water table and marine sediments. Spatial information on soil salinity has gained increasing importance for the demand of management and sustainable utilization of arable land in this area. Apparent electrical conductivity, as measured by electromagnetic induction instrument in a fairly quick manner, has succeeded in mapping soil salinity and many other soil physical and chemical properties from field to regional scales. This was done based on the correlation that existed between apparent electrical conductivity and many other soil properties. In this paper, four spatial prediction methods, i.e., local polynomial, inverse distance weighed, ordinary kriging and universal kriging, were employed to estimate field-scale apparent electrical conductivity with the aid of an electromagnetic induction instrument (type EM38). The spatial patterns estimated by the four methods using EM38 survey datasets of various sample sizes were compared with those generated by each method using the entire sample size. Spatial similarity was evaluated using difference index (DI) between the maps created using various sample sizes (i.e., target maps) and the maps generated with the entire sample size (i.e., the reference map). The results indicated that universal kriging had the best performance owing to the inclusion of residuals and spatial detrending in the kriging system. DI showed that spatial similarity between the target and reference maps of apparent electrical conductivity decreased with the reduction in sample size for each prediction method. Under the same reduction in sample size, the method retaining the most spatial similarity was universal kriging, followed by ordinary kriging, inverse distance weighed, and local polynomial. Approximately, 70 % of total survey data essentially met the need for retaining 90 % details of the reference map for universal kriging and ordinary kriging methods. This conclusion was that OK and UK were two most appropriate methods for spatial estimation of apparent electrical conductivity as they were robust with the reduction in sample size.     

Accounting for exhaustive secondary data into the mapping of water table elevation

This paper presents the incorporation of a digital elevation model into the spatial prediction of water table elevation in Mazandaran province (Iran) using a range of interpolation techniques. The multivariate methods used are: linear regression (LR), cokriging (COK), kriging with an external drift (KED) and regression kriging (RK). The analysis is performed on 3 years (1987, 1997 and 2007) of water table elevation data from about 260 monitoring wells. Prediction performances of the different algorithms are compared with two univariate techniques, i.e. inverse distance weighting and ordinary kriging (OK), through cross validation and examination of the consistency of the generated maps with the natural phenomena. Significantly smaller prediction errors are obtained for four multivariate algorithms but, in particular, KED and RK outperform LR and COK for 3 years. The results show the potential for using elevation for a more precise mapping of water table elevation.     

Mapping soil electric conductivity using Bayesian kriging: A case study from Qasur,Pakistan

Quality of soil data is vital to formulate agricultural policies at different scales. Current agricultural applications in Pakistan depend however, on average values of soil estimates over larger areas. In this work, model-based ordinary kriging (OK) and Bayesian kriging (BK) to interpolate soil data is used. The aim is to compare the two different methods for the accuracy of soil data prediction. For this soils were sampled for Electrical Conductivity (EC, dS m ^–1) at 759 different locations in the rural agricultural areas of Qasur Tehsil, Pakistan. Cross validation was used to compare the performance of OK and BK. Our results show strong skewness and spatial dependency of soil EC values in heterogeneous regions. Box-Cox transformation successfully reduced the level of skewness in the soil EC data (from 14.1 to 0.11). Contrary to OK, under-estimation of soil EC values was not evident in the BK interpolation. Mean square prediction error for BK (1.45) was significantly reduced as compared to that for OK (6.1). Considering these findings, BK is a better model to explain the sub-regional soil EC variability and estimating strategies for sustainable agricultural planning in Pakistan.     

Towards spatial geochemical modelling: Use of geographically weighted regression for mapping soil organic carbon contents in Ireland

It is challenging to perform spatial geochemical modelling due to the spatial heterogeneity features of geochemical variables. Meanwhile, high quality geochemical maps are needed for better environmental management. Soil organic C (SOC) distribution maps are required for improvements in soil management and for the estimation of C stocks at regional scales. This study investigates the use of a geographically weighted regression (GWR) method for the spatial modelling of SOC in Ireland. A total of 1310 samples of SOC data were extracted from the National Soil Database of Ireland. Environmental factors of rainfall, land cover and soil type were investigated and included as the independent variables to establish the GWR model. The GWR provided comparable and reasonable results with the other chosen methods of ordinary kriging (OK), inverse distance weighted (IDW) and multiple linear regression (MLR). The SOC map produced using the GWR model showed clear spatial patterns influenced by environmental factors and the smoothing effect of spatial interpolation was reduced. This study has demonstrated that GWR provides a promising method for spatial geochemical modelling of SOC and potentially other geochemical parameters.     

GIS and ANN-based spatial prediction of DOC in river networks: a case study in Dongjiang, Southern China

This paper investigates the use of an artificial neural network (ANN) model to predict dissolved organic carbon (DOC) in a river network and evaluates the impacts of watershed characteristics on stream DOC. Samples and relevant environmental variables were obtained from field sampling at 28 hydrological response units (HRUs) and a MODIS/SRTM DEM satellite image. HRUs can provide reliable spatial interpolation for filling data gaps and incorporate potential spatial correlation among observations in each ANN neuron. The process and results of neural network modeling were assessed by deterministic and statistical methods and spatial regression kriging. The spatial prediction results show that ANN, using improved back propagation algorithms of 7-15-1 architecture, was the optimal network, by which predictions maintained most of the original spatial variation and eliminated smoothing effects of RK. The sum of the relative contributions of four sensitive variables, including soil organic carbon density, geographic longitude, surface runoff and Chl a in river water, was >75 %. A minor prediction error of ~6 % was found in HRUs of open shrublands, but HRUs of urban and croplands had an error of 24–30 %. This pattern exemplifies anthropogenic impacts in urban areas on stream DOC and agricultural activities in croplands. The usefulness of ANN modeling-based GIS in this study is demonstrated by depiction of spatial variation of stream DOC and indicates the benefits of understanding sensitive factors for watershed impact assessments.     

考虑块段效应的RBF神经网络在土壤空间插值中的应用

定义了土壤变异中的块段效应,提出了考虑块段效应的RBF神经网络空间插值模型(RBFBE法),以期提高土壤水分和养分的插值精度;并以江苏省扬州市区北部某试区为例,通过A、B两种训练方案,将RBFBE法对土壤含水率与有机质含量的插值结果与常规的RBF神经网络(RBFANN法)空间插值结果及普通克里金法(OK法)插值结果进行了对比分析。结果表明:与OK法相比,RBFBE法能使土壤特性的均方误差M_se缩小19.0%~62.2%,预测吻合度G提高8.9%~28.8%;与输入信息相同的RBFANN法相比,RBFBE法亦能使土壤特性的均方误差M_se缩小10.0%~48.8%,预测吻合度G提高3.4%~22.0%;此外,研究也表明RBFBE法具有较强的泛化能力。考虑块段效应的RBF神经网络方法有利于拓展人工神经网络方法在土壤特性空间插值中的应用范围,具有一定的应用前景。     

Large-scale spatial interpolation of soil pH across the Loess Plateau, China

Soil pH plays an important role in biogeochemical processes in soils. The spatial distribution of soil pH provides basic and useful information relevant to soil management and agricultural production. To obtain an accurate distribution map of soil pH on the Loess Plateau of China, 382 sampling sites were investigated throughout the region and four interpolation methods, i.e., inverse distance weighting (IDW), splines, ordinary kriging, and cokriging, were applied to produce a continuous soil pH surface. In the study region, soil pH values ranged from 6.06 to 10.76, with a mean of 8.49 and a median of 8.48. Land use type had a significant effect (p < 0.01) on soil pH; grassland soils had higher pHs than cropland and forestland soils. From a regional perspective, soil pH showed weak variation and strong spatial dependence, indicated by the low values of the coefficient of variation (0.05) and the nugget-to-sill ratios (<0.25). Indices of cross-validation, i.e., average error, mean absolute error, root mean square error, and model efficiency coefficient were used to compare the performance of the four different interpolation methods. Kriging methods interpolated more accurately than IDW and splines. Cokriging performed better than ordinary kriging and the accuracy was improved using soil organic carbon as an auxiliary variable. Regional distribution maps of soil pH were produced. The southeastern part of the region had relatively low soil pH values, probably due to higher precipitation, leaching, and higher soil organic matter contents. Areas of high soil pH were located in the north of the central part of the region, possibly associated with the salinization of sandy soils under inappropriate irrigation practices in an arid climate. Map accuracy could be further improved using new methods and incorporating other auxiliary variables, such as precipitation, elevation, terrain attributes, and vegetation types.     

Revisited rainfall network design: evaluation of heuristic versus entropy theory methods

Rain gauges are installed to measure pointwise precipitation and provide a comprehensive perspective of its spatiotemporal variations. Selection of an efficient and reliable rainfall monitoring network is a key role to reduce its maintenance and handling cost. The main purpose of the current paper is to compare efficiencies of various network design methods. The applied methods are entropy theory (as probabilistic multi-criteria decision-making) and genetic algorithm (as one of the heuristic methods) with three objective functions. Also, two classical (ordinary kriging; OK) and modern (Bayesian maximum entropy; BME) spatial simulation methods were undertaken to provide a comprehensive spatial simulation of precipitation. The proposed assessment was applied on spatial mean annual precipitation variability in the Namak Lake watershed located in the central part of Iran. The final efficiency of developed network design methods is evaluated in terms of three criteria known as mass estimation error, total error, and spatial bias of estimated rainfall. Based on the results, different network distributions have been proposed by the methods. Despite the reliability of the heuristic approach in nonlinear optimization due to its mathematical principle, the results indicated that the network design based on entropy theory can be used to estimate long-term mean annual precipitation more reliably and accurately. Results of the mass estimation error have shown 78 and 83% superiority of the entropy theory approach from the worst approach obtained from the OK and BME methods, respectively.     

Geostatistical and multi‐elemental analysis of soils to interpret land‐use history in the Hebrides,Scotland

In the absence of documentary evidence about settlement form and agricultural practice in northwest Scotland before the mid‐18th century, a geoarchaeological approach to reconstructing medieval land use and settlement form is presented here. This study applies multielemental analysis to soils previously collected from a settlement site in the Hebrides and highlights the importance of a detailed knowledge of the local soil environment and the cultural context. Geostatistical methods were used to analyze the spatial variability and distribution of a range of soil properties typically associated with geoarchaeological investigations. Semivariograms were produced to determine the spatial dependence of soil properties, and ordinary kriging was undertaken to produce prediction maps of the spatial distribution of these soil properties and enable interpolation over nonsampled locations in an attempt to more fully elucidate former land‐use activity and settlement patterns. The importance of identifying the spatial covariance of elements and the need for several lines of physical and chemical evidence is highlighted. For many townships in the Hebrides, whose precise location and layout prior to extensive land reorganization in the late 18th–early 19th century is not recoverable through plans, multi‐elemental analysis of soils can offer a valuable prospective and diagnostic tool. © 2007 Wiley Periodicals, Inc.     

Spatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China

The present study examines the spatial dependency of soil organic matter and nutrients in paddy fields at three different scales using geostatistics and geographic information system techniques (GIS). The spatial variability of soil organic matter (SOM), total nitrogen (TN) and available phosphorus (AP) has been characterized using a total of 460, 131 and 64 samples that were, respectively, collected from the Hangzhou–Jiaxing–Huzhou (HJH) Plain (10 km), Pinghu county (1,000 m) and a test plot area (100 m) within the Pinghu county, Zhejiang province of the southeast China. Semivariograms showed that the SOM and TN had moderate spatial dependency on the large scale of HJH plain and moderate scale of Pinghu county with long spatial correlation distances. At the moderate scale of Pinghu county and the small scale of a test plot area, the AP data did not show any spatial correlation, but had moderate spatial dependency in HJH plain. Spherical and exponential variogram models were best fitted to all these soil properties. Maps of SOM and TN were generated through interpolation of measured values by ordinary kriging, and AP by lognormal kriging. This study suggests that precision management of SOM and TN is feasible at all scales, and precision management of AP is feasible at large scales.     

An Experimental Comparison of Ordinary and Universal Kriging and Inverse Distance Weighting

A factorial, computational experiment was conducted to compare the spatial interpolation accuracy of ordinary and universal kriging and two types of inverse squared-distance weighting. The experiment considered, in addition to these four interpolation methods, the effects of four data and sampling characteristics: surface type, sampling pattern, noise level, and strength of small-scale spatial correlation. Interpolation accuracy was measured by the natural logarithm of the mean squared interpolation error. Main effects of all five factors, all two-factor interactions, and several three-factor interactions were highly statistically significant. Among numerous findings, the most striking was that the two kriging methods were substantially superior to the inverse distance weighting methods over all levels of surface type, sampling pattern, noise, and correlation.     

Geostatistical method to delineate anomalies of multi-scale spatial variation in hydrogeological changes due to the ChiChi earthquake in the ChouShui River alluvial fan in Taiwan

This study uses Ordinary Kriging (OK), Sequential Gaussian Simulation (SGS) and Simulated Annealing Simulation (SAS) to relocate the completely heterotopic dataset from the locations of the Standardized Satellite Oriented Control Point System (SSOCPS) stations to the Groundwater Monitoring Networks (GMNS) stations and factorial kriging to analyze and map relationships among seven variables, including the hydraulic conductivities of three aquifers, the vertical displacements of the ground and groundwater level changes in the wells of three aquifers, and also to delineate the anomalies of multi-scale spatial variation of hydrogeological properties associated with the ChiChi earthquake, measuring 7.3 on the Richter scale, in the ChouShui River alluvial fan in Taiwan. In this study, the anomalies of spatial variation of hydrogeological properties associated with the earthquake are illustrated at micro, local and regional scales of 9, 12 and 36 km, respectively. In the study area, regionalization components associated with variation at local and regional scales are obtained and mapped by factorial kriging. Factorial Kriging Analysis (FKA) also demonstrated that the main effects of the ChiChi earthquake on the spatial variations of groundwater hydrological changes include porous media compression at micro scale, hydrogeological heterogeneousness of the sediments within the aquifer at local scale and the cyclic loading of deviatoric stress at regional scale. Finally, maps of spatial variations of regional components fully depicted all of the anomalies of spatial variation of hydrogeological changes due to the ChiChi earthquake and can be used to identify, confirm and monitor the hydrogeological properties in this study area.     

Combining Areal and Point Data in Geostatistical Interpolation: Applications to Soil Science and Medical Geography

A common issue in spatial interpolation is the combination of data measured over different spatial supports. For example, information available for mapping disease risk typically includes point data (e.g. patients’ and controls’ residence) and aggregated data (e.g. socio-demographic and economic attributes recorded at the census track level). Similarly, soil measurements at discrete locations in the field are often supplemented with 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 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. The procedure is illustrated using two data sets: (1) geological map and heavy metal concentrations recorded in the topsoil of the Swiss Jura, and (2) incidence rates of late-stage breast cancer diagnosis per census tract and location of patient residences for three counties in Michigan. In the second case, the kriging system includes an error variance term derived according to the binomial distribution to account for varying degree of reliability of incidence rates depending on the total number of cases recorded in those tracts. Except under the binomial kriging framework, area-and-point (AAP) kriging ensures the coherence of the prediction so that the average of interpolated values within each mapping unit is equal to the original areal datum. The relationships between binomial kriging, Poisson kriging, and indicator kriging are discussed under different scenarios for the population size and spatial support. Sensitivity analysis demonstrates the smaller smoothing and greater prediction accuracy of the new procedure over ordinary and traditional residual kriging based on the assumption that the local mean is constant within each mapping unit.     

Spatial interpolation of severely skewed data with several peak values by the approach integrating kriging and triangular irregular network interpolation

It was not unusual in soil and environmental studies that the distribution of data is severely skewed with several high peak values, which causes the difficulty for Kriging with data transformation to make a satisfied prediction. This paper tested an approach that integrates kriging and triangular irregular network interpolation to make predictions. A data set consisting of total Copper (Cu) concentrations of 147 soil samples, with a skewness of 4.64 and several high peak values, from a copper smelting contaminated site in Zhejiang Province, China. The original data were partitioned into two parts. One represented the holistic spatial variability, followed by lognormal distribution, and then was interpolated by lognormal ordinary kriging. The other assumed to show the local variability of the area that near to high peak values, and triangular irregular network interpolation was applied. These two predictions were integrated into one map. This map was assessed by comparing with rank-order ordinary kriging and normal score ordinary kriging using another data set consisting of 54 soil samples of Cu in the same region. According to the mean error and root mean square error, the approach integrating lognormal ordinary kriging and triangular irregular network interpolation could make improved predictions over rank-order ordinary kriging and normal score ordinary kriging for the severely skewed data with several high peak values.     

Predictive geochemical mapping using environmental correlation

The distribution of chemical elements at and near the Earth's surface, the so-called critical zone, is complex and reflects the geochemistry and mineralogy of the original substrate modified by environmental factors that include physical, chemical and biological processes over time.Geochemical data typically is illustrated in the form of plan view maps or vertical cross-sections, where the composition of regolith, soil, bedrock or any other material is represented. These are primarily point observations that frequently are interpolated to produce rasters of element distributions. Here we propose the application of environmental or covariate regression modelling to predict and better understand the controls on major and trace element geochemistry within the regolith. Available environmental covariate datasets (raster or vector) representing factors influencing regolith or soil composition are intersected with the geochemical point data in a spatial statistical correlation model to develop a system of multiple linear correlations. The spatial resolution of the environmental covariates, which typically is much finer (e.g. ∼90 m pixel) than that of geochemical surveys (e.g. 1 sample per 10-10,000 km²), carries over to the predictions. Therefore the derived predictive models of element concentrations take the form of continuous geochemical landscape representations that are potentially much more informative than geostatistical interpolations.Environmental correlation is applied to the Sir Samuel 1:250,000 scale map sheet in Western Australia to produce distribution models of individual elements describing the geochemical composition of the regolith and exposed bedrock. As an example we model the distribution of two elements – chromium and sodium. We show that the environmental correlation approach generates high resolution predictive maps that are statistically more accurate and effective than ordinary kriging and inverse distance weighting interpolation methods. Furthermore, insights can be gained into the landscape processes controlling element concentration, distribution and mobility from analysis of the covariates used in the model. This modelling approach can be extended to groups of elements (indices), element ratios, isotopes or mineralogy over a range of scales and in a variety of environments.     

On the equivalence of kriging and maximum entropy estimators

This study compares kriging and maximum entropy estimators for spatial estimation and monitoring network design. For second-order stationary random fields (a subset of Gaussian fields) the estimators and their associated interpolation error variances are identical. Simple lognormal kriging differs from the lognormal maximum entropy estimator, however, in both mathematical formulation and estimation error variances. Two numerical examples are described that compare the two estimators. Simple lognormal kriging yields systematically higher estimates and smoother interpolation surfaces compared to those produced by the lognormal maximum entropy estimator. The second empirical comparison applies kriging and entropy-based models to the problem of optimizing groundwater monitoring network design, using six alternative objective functions. The maximum entropy-based sampling design approach is shown to be the more computationally efficient of the two.     

Spatial analysis of land use and shallow groundwater vulnerability in the watershed adjacent to Assateague Island National Seashore,Maryland and Virginia,USA

Spatial relations between land use and groundwater quality in the watershed adjacent to Assateague Island National Seashore, Maryland and Virginia, USA were analyzed by the use of two spatial models. One model used a logit analysis and the other was based on geostatistics. The models were developed and compared on the basis of existing concentrations of nitrate as nitrogen in samples from 529 domestic wells. The models were applied to produce spatial probability maps that show areas in the watershed where concentrations of nitrate in groundwater are likely to exceed a predetermined management threshold value. Maps of the watershed generated by logistic regression and probability kriging analysis showing where the probability of nitrate concentrations would exceed 3 mg/L (>0.50) compared favorably. Logistic regression was less dependent on the spatial distribution of sampled wells, and identified an additional high probability area within the watershed that was missed by probability kriging. The spatial probability maps could be used to determine the natural or anthropogenic factors that best explain the occurrence and distribution of elevated concentrations of nitrate (or other constituents) in shallow groundwater. This information can be used by local land-use planners, ecologists, and managers to protect water supplies and identify land-use planning solutions and monitoring programs in vulnerable areas.