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1.

Experimental variograms are crucial for most geostatistical studies. In kriging, for example, the variography has a direct influence on the interpolation weights. Despite the great importance of variogram estimators in predicting geostatistical features, they are commonly influenced by outliers in the dataset. The effect of some randomly spatially distributed outliers can mask the pattern of the experimental variogram and produce a destructuration effect, implying that the true data spatial continuity cannot be reproduced. In this paper, an algorithm to detect and remove the effect of outliers in experimental variograms using the Mahalanobis distance is proposed. An example of the algorithm’s application is presented, showing that the developed technique is able to satisfactorily detect and remove outliers from a variogram.

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2.
Several alternative estimation and interpolation methods for making annual precipitation maps of Asturias are analysed. The data series in this study corresponds to the year 2003. There exists an evident relationship between precipitation and altitude, with a high correlation coefficient of 0.70, that reflects the hillside effect; that is, the increase in the amount of precipitation in more mountainous areas. The direct spatial variability of precipitation and of altitude and the cross variability of precipitation–altitude are defined by two exponential variogram models: one with a short-range structure (15–30 km) that reflects the control exerted by the lesser, local mountain ranges over the amount of precipitation; and another with a long-range structure (80 km) that supposes the influence over precipitation of the major mountainous alignments of the inland areas of the Cantabrian Mountain Range (Cordillera Cantábrica) situated between 60 and 90 km from the coastline. These variogram models had to be validated for coregionalization by the Pardo-Igúzquiza and Dowd method so as to be able to make the cokriging map. The geometric estimation methods employed were triangulation and inverse distance. The geostatistical estimation methods developed were simple kriging, ordinary kriging, kriging with a trend model (universal kriging), lognormal kriging, and cokriging. In all of these methods, a 3 × 3 km2 grid was selected with a total of 2580 points to estimate, a circular search window of 60 km, and a relatively small number of samples with the aim of highlighting the local features and variations on isohyet maps. The kriging methods were implemented using the WinGslib software, incorporating two specific programs, Prog2 and Fichsurf, so as to be able then to make isohyet maps using the Surfer software. All the methods employed, apart from triangulation, rendered realistic maps with good fits to the values of the original data (precipitation) of the sample maps. The problem with triangulation lies not in the reliability of the estimates but in the fact that it gives rise to contrived maps because of the tendency of isohyets to present abundant triangular facets. The reliability of the methods was based on cross-validation analysis and on evaluation of the different types of errors, both in their values and in their graphical representations. Substantial differences were not found in the values of the errors that might discriminate some methods from others in an evident way. Bearing the aforesaid in mind, should we have to make an evaluation of the different estimation methods in decreasing order of acceptance, this would be: kriging with a trend model, inverse distance, cokriging, lognormal kriging, ordinary kriging, simple kriging, and triangulation. The application of other estimation methods such as colocated cokriging, kriging with an external drift, and kriging of variable local means (residual kriging) is dependent on the availability of a digital model of the terrain with an altitude grid of the region.  相似文献   

3.
Characterizing spatial and temporal variability of soil salinity is tremendously important for a variety of agronomic and environmental concerns in arid irrigation areas. This paper reviews the characteristics and spatial and temporal variations of soil salinization in the Ili River Irrigation Area by applying a geostatistical approach. Results showed that:(1) the soil salinity varied widely, with maximum value of 28.10 g/kg and minimum value of 0.10 g/kg, and was distributed mainly at the surface soil layer. Anions were mainly SO_4~(2-) and Cl~-, while cations were mainly Na~+ and Ca~(2+);(2) the abundance of salinity of the root zone soil layer for different land use types was in the following order: grassland cropland forestland. The abundance of salinity of root zone soil layers for different periods was in the following order: March June September;(3) the spherical model was the most suitable variogram model to describe the salinity of the 0–3 cm and 3–20 cm soil layers in March and June, and the 3–20 cm soil layer in September, while the exponential model was the most suitable variogram model to describe the salinity of the 0–3 cm soil layer in September. Relatively strong spatial and temporal structure existed for soil salinity due to lower nugget effects; and(4) the maps of kriged soil salinity showed that higher soil salinity was distributed in the central parts of the study area and lower soil salinity was distributed in the marginal parts. Soil salinity tended to increase from the marginal parts to the central parts across the study area. Applying the kriging method is very helpful in detecting the problematic areas and is a good tool for soil resources management. Managing efforts on the appropriate use of soil and water resources in such areas is very important for sustainable agriculture, and more attention should be paid to these areas to prevent future problems.  相似文献   

4.
ABSTRACT

Recently developed urban air quality sensor networks are used to monitor air pollutant concentrations at a fine spatial and temporal resolution. The measurements are however limited to point support. To obtain areal coverage in space and time, interpolation is required. A spatio-temporal regression kriging approach was applied to predict nitrogen dioxide (NO2) concentrations at unobserved space-time locations in the city of Eindhoven, the Netherlands. Prediction maps were created at 25 m spatial resolution and hourly temporal resolution. In regression kriging, the trend is separately modelled from autocorrelation in the residuals. The trend part of the model, consisting of a set of spatial and temporal covariates, was able to explain 49.2% of the spatio-temporal variability in NO2 concentrations in Eindhoven in November 2016. Spatio-temporal autocorrelation in the residuals was modelled by fitting a sum-metric spatio-temporal variogram model, adding smoothness to the prediction maps. The accuracy of the predictions was assessed using leave-one-out cross-validation, resulting in a Root Mean Square Error of 9.91 μg m?3, a Mean Error of ?0.03 μg m?3 and a Mean Absolute Error of 7.29 μg m?3. The method allows for easy prediction and visualization of air pollutant concentrations and can be extended to a near real-time procedure.  相似文献   

5.
Most forest fires in Korea are spatially concentrated in certain areas and are highly related to human activities. These site-specific characteristics of forest fires are analyzed by spatial regression analysis using the R-module generalized linear mixed model (GLMM), which can consider spatial autocorrelation. We examined the quantitative effect of topology, human accessibility, and forest cover without and with spatial autocorrelation. Under the assumption that slope, elevation, aspect, population density, distance from road, and forest cover are related to forest fire occurrence, the explanatory variables of each of these factors were prepared using a Geographic Information System-based process. First, we tried to test the influence of fixed effects on the occurrence of forest fires using a generalized linear model (GLM) with Poisson distribution. In addition, the overdispersion of the response data was also detected, and variogram analysis was performed using the standardized residuals of GLM. Second, GLMM was applied to consider the obvious residual autocorrelation structure. The fitted models were validated and compared using the multiple correlation and root mean square error (RMSE). Results showed that slope, elevation, aspect index, population density, and distance from road were significant factors capable of explaining the forest fire occurrence. Positive spatial autocorrelation was estimated up to a distance of 32 km. The kriging predictions based on GLMM were smoother than those of the GLM. Finally, a forest fire occurrence map was prepared using the results from both models. The fire risk decreases with increasing distance to areas with high population densities, and increasing elevation showed a suppressing effect on fire occurrence. Both variables are in accordance with the significance tests.  相似文献   

6.
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。  相似文献   

7.
This article describes a proposed work-sequence to generate accurate reservoir-architecture models, describing the geometry of bounding surfaces (i.e., fault locations and extents), of a structurally complex geologic setting in the Jeffara Basin (South East Tunisia) by means of geostatistical modeling. This uses the variogram as the main tool to measure the spatial variability of the studied geologic medium before making any estimation or simulation. However, it is not always easy to fit complex experimental variograms to theoretical models. Thus, our primary purpose was to establish a relationship between the geology and the components of the variograms to fit a mathematically consistent and geologically interpretable variogram model for improved predictions of surface geometries. We used a three-step approach based on available well data and seismic information. First, we determined the structural framework: a seismo-tectonic data analysis was carried out, and we showed that the study area is cut mainly by NW–SE-trending normal faults, which were classified according to geometric criteria (strike, throw magnitude, dip, and dip direction). We showed that these normal faults are at the origin of a large-scale trend structure (surfaces tilted toward the north-east). At a smaller scale, the normal faults create a distinct compartmentalization of the reservoirs. Then, a model of the reservoir system architecture was built by geostatistical methods. An efficient methodology was developed, to estimate the bounding faulted surfaces of the reservoir units. Emphasis was placed on (i) elaborating a methodology for variogram interpretation and modeling, whereby the importance of each variogram component is assessed in terms of probably geologic factor controlling the behavior of each structure; (ii) integrating the relevant fault characteristics, which were deduced from the previous fault classification analysis, as constraints in the kriging estimation of bounding surfaces to best reflect the geologic structure of the study area. Finally, the estimated bounding surfaces together with seismic data and variogram interpretations were used to obtain further insights into the tectonic evolution of the study area that has induced the current reservoirs configuration.  相似文献   

8.
遥感数据为土地利用/覆盖变化提供了海量数据来源,如何选择合适空间分辨率的遥感影像进行特定地区的土地利用/覆盖变化研究,成为土地利用/覆盖变化研究的一个重要内容。地统计学方法已经广泛应用与遥感图像处理以及土地覆盖分类研究中,但应用于土地利用/覆盖变化的研究还比较缺乏。北京地区为研究区,运用遥感和地统计分析方法对该区土地利用/覆盖变化的空间结构的变异特征和合理的遥感影像数据源的选取问题做了初步探讨。研究表明地统计学方法能够揭示土地利用/覆盖变化的空间变异特征,有助于选择有效的遥感影像数据进行不同地区的土地利用/覆盖变化分析。  相似文献   

9.
Evaluation and prediction of groundwater levels through specific model(s) helps in forecasting of groundwater resources. Among the different robust tools available, the Integrated Time Series (ITS) and Back-Propagation Artificial Neural Network (BPANN) models are commonly used to empirically forecast hydrological variables. Here, we discuss the modeling process and accuracy of these two methods in assessing their relative advantages and disadvantages based on Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and coefficient of efficiency (CE). The arid and semi-arid areas of western Jilin province of China were chosen as study area owing to the decline of groundwater levels during the past decade mainly due to overexploitation. The simulation results indicated that both ITS and BPANN are accurate in reproducing (fitting) the groundwater levels and the CE are 0.98 and 0.97, respectively. In the validation phase, the comparison of the prediction accuracy of the BPANN and ITS models indicated that the BPANN models is superior to the ITS in forecasting the groundwater levels time series in term of the RMSE, MAE and CE.  相似文献   

10.

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.  相似文献   

11.
In this study, we demonstrate a novel use of comaps to explore spatially the performance, specification and parameterisation of a non-stationary geostatistical predictor. The comap allows the spatial investigation of the relationship between two geographically referenced variables via conditional distributions. Rather than investigating bivariate relationships in the study data, we use comaps to investigate bivariate relationships in the key outputs of a spatial predictor. In particular, we calibrate moving window kriging (MWK) models, where a local variogram is found at every target location. This predictor has often proved worthy for processes that are heterogeneous, and most standard (global variogram) kriging algorithms can be adapted in this manner. We show that the use of comaps enables a better understanding of our chosen MWK models, which in turn allows a more informed choice when selecting one MWK specification over another. As case studies, we apply four variants of MWK to two heterogeneous example data sets: (i) freshwater acidification critical load data for Great Britain and (ii) London house price data. As both of these data sets are strewn with local anomalies, three of our chosen models are robust (and novel) extensions of MWK, where at least one of which is shown to perform better than a non-robust counterpart.  相似文献   

12.
Spatial interpolation of marine environment data using P-MSN   总被引：1，自引：0，他引：1  
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.  相似文献   

13.
Evaluation of recharge and groundwater dynamics of an aquifer is an important step for finding a proper groundwater management scenario. This has been performed on the basis of statistical Kendall Tau test to find a relationship between groundwater levels and hydro-meteorological parameters (e.g., precipitation, temperature, evaporation). Recharge to the aquifer was estimated for identification of critical areas/locations based on the analytical Soil and Water Assessment Tool. Moreover, spatiotemporal variability of groundwater levels has been quantified using space–time variogram. The overall characterization method has been applied to the shallow alluvial aquifer of Kanpur city in India. The analysis was performed using groundwater level data from 56 monitoring piezometer locations in Kanpur from March 2006 to June 2011. Groundwater level shows relatively higher correlation with temperature. Performance of the geostatistical model was evaluated by comparing with the observed values of groundwater level from January 2011 to June 2011 for two scenarios: “with limited spatiotemporal data” and “without spatiotemporal data.” It is evident that spatiotemporal prediction of groundwater level can be performed even for the unmonitored/missing data. This analysis demonstrates the potential applicability of the method for a general aquifer system.  相似文献   

14.
“Krige”空间内插技术在地理学中的应用   总被引：24，自引：1，他引：24  
称为“Krige”技术的内插稀疏观测资料的随机方法是Matheron(1970年)提出的,D.R.Krige首先将这一方法应用于找矿上,因而命名于“Krige”技术。本文首先定义和说明了空间协方差曲线,基于无偏估计和最优原理导出了“Krige”内插权重系数的代数方程组,最后给出实例说明该方法如何应用到地理学和水文学中。  相似文献   

15.
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.  相似文献   

16.
空间自相关的可塑性面积单元问题效应   总被引：13，自引：3，他引：10  
陈江平  张瑶  余远剑 《地理学报》2011,66(12):1597-1606
可塑性面积单元问题(modifiable areal unit problem,MAUP) 效应是对空间数据分析结果产生不确定性影响的主要原因之一,在空间自相关分析中也不例外.本文分别利用网格模拟数据和中国人均GDP实例数据为数据源,以全局Moran's I 系数来探究空间自相关统计中的MAUP效应,分析结果表明,变量的空间自相关程度依赖于空间的粒度大小与单元的划分方法,但空间单元的变化与自相关性并不存在某种函数关系.因此,在进行空间自相关研究时必须选择合适的地理单元的粒度大小和分区.最后本文给出一种基于地统计内插方法来降低MAUP对空间自相关分析影响.  相似文献   

17.
太湖流域典型地区土壤磷素含量的空间变异特征   总被引：43，自引：8，他引：35  
在地统计学和地理信息系统的支持下,以半方差函数为基本工具,分析了太湖流域典型地区土壤耕层全磷含量的空间变异特征,并运用块段克立格法进行线性无偏最优插值,制作了土壤耕层全磷含量的空间分布图。结果表明:研究区域土壤全磷含量具有中等的空间相关性和良好的结构性,其自相关距离在11km左右;土壤磷素含量的空间分布具有明显的斑块状特点,沿江平田区、地势低洼的圩田及低平田区磷素的含量相对较高,应作为农业面源磷污染的重点监控对象。  相似文献   

18.
地统计法支持的北部湾东部海域沉积物粒径趋势分析   总被引：7，自引：0，他引：7  
马菲  汪亚平  李炎  叶长江  徐志伟  张凡 《地理学报》2008,63(11):1207-1217
在北部湾东部海域采集表层沉积物71 个, 通过粒度分析获得其粒度参数(平均粒径、分选系数、偏态), 用克里格插值法将不规则采样站位的粒度参数内插为规则网格分布的相应粒度参数。采用地统计法分析其空间相关性, 计算度量空间相关性范围的参数, 即半方差图中的变程值。结果表明, 使用地统计分析获得的粒度参数变程值物理意义较为明确, 可作为粒径趋势分析模型的特征距离, 其中分选系数变程值作为特征距离的计算结果与前人的海流、沉积物输运信息更为吻合; 这在一定程度上消除了传统方法(试算法或经验估计法) 获取特征 距离可能造成的模型计算误差。采用不同间距插值时得到的粒径趋势矢量具有不同的空间分 辨率, 其中高分辨率的细化图所反映的海底沉积物净输运趋势与余流和环流等所反映的沉积物输运细节特征吻合较好, 低分辨率的概化图可大致反映该区域沉积物的总体输运趋势。地统计分析的结果对未来研究工作中采样间距的选取也具有指导意义。  相似文献   

19.
We studied the relationship between primary productivity and species richness of small mammals at both large and small spatial scales in the arid and semi-arid grasslands of north China. The productivity (x)–species richness (y) pattern at a large spatial scale can be described by a unimodal quadratic regression curve (y=7·41+0·1*x−0·0003*x2,p =0·008, r2=0·788). At a small spatial scale, however, neither linear nor quadratic regression fit the data for 1980 and 1994 (p>0·25). Primary productivity may not be an appropriate predictor of the species richness of small mammals at a small spatial scale. We conclude, therefore, that the primary productivity–species richness pattern of small mammals may be scale-dependent in the arid and semi-arid grasslands of north China. Landscape complexity should be considered in future studies of productivity–richness relationships.  相似文献   

20.
Geographical information systems could be improved by adding procedures for geostatistical spatial analysis to existing facilities. Most traditional methods of interpolation are based on mathematical as distinct from stochastic models of spatial variation. Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analysing them. Kriging is the method of interpolation deriving from regionalized variable theory. It depends on expressing spatial variation of the property in terms of the variogram, and it minimizes the prediction errors which are themselves estimated. We describe the procedures and the way we link them using standard operating systems. We illustrate them using examples from case studies, one involving the mapping and control of soil salinity in the Jordan Valley of Israel, the other in semi-arid Botswana where the herbaceous cover was estimated and mapped from aerial photographic survey.  相似文献   

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