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1.
When measurements of values that are less than the limit of detection are reported as not detected, the data are referred to as censored. The non-recording of values below the limit of detection is common in soil science research although modelling data affected by censoring can be problematic. This paper develops and tests a modified version of Spatial Simulated Annealing, called Simulated Annealing by Variogram and Histogram form, for drawing values for censored points given a mixed set of observed and censored data. The algorithm aims to maximise the goodness of fitting between the experimental and theoretical variograms (by allowing variation in its parameters) while the imputed values are constrained to a target histogram form. In practice, the experimental histogram is estimated by transforming the available data (interval and exact observations) to quantiles and fitting a plausible distribution. The theoretical distribution of the data is used to constrain the variogram fitting. The proposed simulated annealing method is designed to find the optimal spatial arrangement of values, given by the lowest errors in variogram and histogram fitting and kriging prediction. The accuracy of the method proposed is assessed on a simulated data set in which the censored point values are known and compared with the Spatial Simulated Annealing algorithm. According to the results obtained, the Simulated Annealing by Variogram and Histogram form (SAVH) approach can be recommended as a useful tool for the analysis of spatially distributed data with censoring.  相似文献   

2.
Soil nutrient maps based on intensive soil sampling are useful to adopt site-specific management practices. Geostatistical methods have been widely used to determine the spatial correlation and the range of spatial dependence at different sampling scales. If spatial dependence is detected, the modeled semivariograms can then be used to map the interested variable by kriging, an interpolation method that produces unbiased estimates with minimal estimation variance. The objectives of this paper were to examine and map the spatial distribution of the soil micronutrients Cu, Zn, Fe and Mn on an agricultural area in Kupwara, J&K, under temperate climatic conditions. The ordinary kriging was first used to determine the values for the non-sampled locations, and then the indicator approach was used to transform the micronutrient content values into binary values having the mean values of each nutrient as the threshold content. All four elements analyzed showed spatial dependence using the indicator semivariograms. The strength of spatial dependence was assessed using the values of nugget effect and range from the semivariogram, the fitted range values decreased in the order Zn > Cu > Mn > Fe. The spatial dependence of the combination of two or more of the studied micronutrients was also examined using indicator semivariograms. In opposition to spatial analysis of individual microelements, indicator semivariograms obtained for the binary coding of the variables showed a great nugget effect value or a low proportion of sill. The maps for each nutrient obtained using indicator kriging showed some similarity in the spatial distribution, suggesting the delimitation of uniform management areas.  相似文献   

3.
Geostatistical characterization of local DEM error is usually based on the assumption of a stationary variogram model which requires the mean and variance to be finite and constant in the area under investigation. However, in practice this assumption is appropriate only in a restricted spatial location, where the local experimental variograms vary slowly. Therefore, an adaptive method is developed in this article to model non‐stationary variograms, for which the estimator and the indicator for characterization of spatial variation are a Voronoi map and the standard deviation of mean values displayed in the Voronoi map, respectively. For the adaptive method, the global domain is divided into different meshes with various sizes according to the variability of local variograms. The adaptive method of non‐stationary variogram modeling is applied to simulating error surfaces of a LiDAR derived DEM located in Sichuan province, China. Results indicate that the locally adaptive variogram model is more accurate than the global one for capturing the characterization of spatial variation in DEM errors. The adaptive model can be considered as an alternative approach to modeling non‐stationary variograms for DEM error surface simulation.  相似文献   

4.
Traditional methods of recording fire burned areas and fire severity involve expensive and time-consuming field surveys. Available remote sensing technologies may allow us to develop standardized burn-severity maps for evaluating fire effects and addressing post fire management activities. This paper focuses on multiscale characterization of fire severity using multisensor satellite data. To this aim, both MODIS (Moderate Resolution Imaging Spectroradiometer) and ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) data have been processed using geo-statistic analyses to capture pattern features of burned areas.Even if in last decades different authors tried to integrate geo-statistics and remote sensing image processing, methods used since now are only variograms, semivariograms and kriging. In this paper, we propose an approach based on the use of spatial indicators of global and local autocorrelation. Spatial autocorrelation statistics, such as Moran's I and Getis–Ord Local Gi index, were used to measure and analyze dependency degree among spectral features of burned areas. This approach enables the characterization of pattern features of a burned area and improves the estimation of fire severity.  相似文献   

5.
It is well known that terrain may vary markedly over small areas and that statistics used to characterise spatial variation in terrain may be valid only over small areas. In geostatistical terminology, a non-stationary approach may be considered more appropriate than a stationary approach. In many applications, local variation is not accounted for sufficiently. This paper assesses potential benefits in using non-stationary geostatistical approaches for interpolation and for the assessment of uncertainty in predictions with implications for sampling design. Two main non-stationary approaches are employed in this paper dealing with (1) change in the mean and (2) change in the variogram across the region of interest. The relevant approaches are (1) kriging with a trend model (KT) using the variogram of residuals from local drift and (2) locally-adaptive variogram KT, both applied to a sampled photogrammetrically derived digital terrain model (DTM). The fractal dimension estimated locally from the double-log variogram is also mapped to illustrate how spatial variation changes across the data set. It is demonstrated that estimation of the variogram of residuals from local drift is worthwhile in this case for the characterisation of spatial variation. In addition, KT is shown to be useful for the assessment of uncertainty in predictions. This is shown to be true even when the sample grid is dense as is usually the case for remotely-sensed data. In addition, both ordinary kriging (OK) and KT are shown to provide more accurate predictions than inverse distance weighted (IDW) interpolation, used for comparative purposes.  相似文献   

6.
Multiscale Terrain and Topographic Modelling with the Implicit TIN   总被引：1，自引：0，他引：1  
It is often assumed that real land surfaces demonstrate the statistically self-affine scaling behaviour of fractional Brownian surfaces. Tests of this assumption against empirical data, however, show many deviations. Estimates of fractal properties vary between methods and over different scale ranges. So far, this empirical evidence has come from the analysis of variograms for DEMs representing areas up to tens of kilometres in diameter. Here we report results obtained by using variograms to analyse land surface DEMs at the continental scale, with a grid resolution of 30 arc seconds. Results reveal variogram curvature and breaks of slope, but also linear sections over distance lags of hundreds of kilometres. The estimated mean fractal dimension calculated from these sections is 2.66, substantially higher for all continents at these broad scales (around 200 km) than values calculated at the erosional landscape scale (around 200 m). Thus the land surface is not self-affine, and it is not clear that it follows any simple multifractal model. At the longest wavelengths, patterns found in the variograms appear to be related to broad tectonic features of the Earth's surface. For the reader to assess their quality and generality, estimates of fractal dimension should always be accompanied by statements of the scale range covered and the goodness of fit to a log-linear relationship.  相似文献   

7.
Area-to-point (ATP) kriging is a common geostatistical framework to address the problem of spatial disaggregation or downscaling from block support observations (BSO) to point support (PoS) predictions for continuous variables. This approach requires that the PoS variogram is known. Without PoS observations, the parameters of the PoS variogram cannot be deterministically estimated from BSO, and as a result, the PoS variogram parameters are uncertain. In this research, we used Bayesian ATP conditional simulation to estimate the PoS variogram parameters from expert knowledge and BSO, and quantify uncertainty of the PoS variogram parameters and disaggregation outcomes. We first clarified that the nugget parameter of the PoS variogram cannot be estimated from only BSO. Next, we used statistical expert elicitation techniques to elicit the PoS variogram parameters from expert knowledge. These were used as informative priors in a Bayesian inference of the PoS variogram from BSO and implemented using a Markov chain Monte Carlo algorithm. ATP conditional simulation was done to obtain stochastic simulations at point support. MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric temperature profile data were used in an illustrative example. The outcomes from the Bayesian ATP inference for the Matérn variogram model parameters confirmed that the posterior distribution of the nugget parameter was effectively the same as its prior distribution; for the other parameters, the uncertainty was substantially decreased when BSO were introduced to the Bayesian ATP estimator. This confirmed that expert knowledge brought new information to infer the nugget effect at PoS while BSO only brought new information to infer the other parameters. Bayesian ATP conditional simulations provided a satisfactory way to quantify parameters and model uncertainty propagation through spatial disaggregation.  相似文献   

8.
刘殿锋  刘耀林  赵翔 《测绘学报》2013,42(5):722-728
提出一种基于多目标微观邻域粒子群的土壤空间优化抽样方法。方法面向土壤空间调查的多目标特征,构建了基于最小克里金方差（MKV）和极大熵准则（ME）的粒子群多目标适应度函数,设计了最小样本量限制、样点可达性、采样成本限制和最小空间关联性四类粒子微观邻域操作策略,能高效协调土壤空间抽样精度、代表性、成本、样本量与样点布局等多目标冲突。实验结果表明,相比单目标粒子群算法和模拟退火算法,该方法的目标冲突协同能力强、收敛效率高,所设计抽样方案最优,为土壤质量精确调查与高效监测提供了技术支持。  相似文献   

9.
For obtaining maps of good precision by the spatial inference method, the distribution of sampling sites in geographical and feature space is very important. For a regional variable with trends, the predicting error comes from trend estimation, variogram estimation and spatial interpolation. Based on the cLHS (conditioned Latin hypercube Sampling) method, a sampling method called scLHS (spatial cLHS) considering all these three aspects with the help of ancillary data is proposed in this article. Its advantage lies in simultaneously improving trend estimation, variogram estimation and spatial interpolation. MODIS data and simulated data were used as sampling fields to draw sample sets using scLHS, cLHS, cLHS with x and y coordinates as covariates, simple random and spatial even sampling methods, and the distribution and prediction errors of sample sets from different methods were evaluated. The results showed that scLHS performed well in balancing spreading in geographic and feature space, and can generate points pairs with small distances, and the sample sets drawn by scLHS produced smaller mapping error, especially when there were trends in the target variable.  相似文献   

10.
Forest canopy cover (CC) and above-ground biomass (AGB) are important ecological indicators for forest monitoring and geoscience applications. This study aimed to estimate temperate forest CC and AGB by integrating airborne LiDAR data with wall-to-wall space-borne SPOT-6 data through geostatistical modeling. Our study involved the following approach: (1) reference maps of CC and AGB were derived from wall-to-wall LiDAR data and calibrated by field measurements; (2) twelve discrete LiDAR flights were simulated by assuming that LiDAR data were only available beneath these flights; (3) training/testing samples of CC and AGB were extracted from the reference maps inside and outside the simulated flights using stratified random sampling; (4) The simple linear regression, ordinary kriging and regression kriging model were used to extend the sparsely sampled CC/AGB data to the entire study area by incorporating a selection of SPOT-6 variables, including vegetation indices and texture variables. The regression kriging model was superior at estimating and mapping the spatial distribution of CC and AGB, as it featured the lowest mean absolute error (MAE; 11.295% and 18.929 t/ha for CC and AGB, respectively) and root mean squared error (RMSE; 17.361% and 21.351 t/ha for CC and AGB, respectively). The predicted and reference values of both CC and AGB were highly correlated for the entire study area based on the estimation histograms and error maps. Finally, we concluded that the regression kriging model was superior and more effective at estimating LiDAR-derived CC and AGB values using the spatially-reduced samples and the SPOT-6 variables. The presented modeling workflow will greatly facilitate future forest growth monitoring and carbon stock assessments for large areas of temperate forest in northeast China. It also provides guidance on how to take full advantage of future sparsely collected LiDAR data in cases where wall-to-wall LiDAR coverage is not available from the perspective of geostatistics.  相似文献   

11.
最小二乘配置法和Kriging法进行高程转换时均兼顾考虑高程异常的系统部分和随机部分,为对比分析两种方法在GPS高程转化时的优劣性,根据最小二乘配置法的协方差函数（或kriging法的变异函数）的不同,采用五种方案对实测数据进行处理。结果分析证明了以距离作为协方差函数的最小二乘配置法在算法和推估结果可靠性要优于其他方案。  相似文献   

12.
The spatial distribution of some soil chemical properties and trace element contents of a plot affected by the Aznalcóllar mine spill were investigated using statistical and geostatistical methods to assess the extent of soil contamination. Total and EDTA-extractable soil trace element concentrations and total S content showed great variability and high coefficients of variation in the three examined depths. Soil in the plot was found to be significantly contaminated by As, Cd, Cu, Pb and Zn within a wide range of pH. Total trace element concentrations at all depths (0–60 cm) were much higher than background values of non-affected soil, indicating that despite the clean-up operations, the concentration of trace elements in the experimental plot was still high. The spatial distribution of the different variables was estimated by kriging to design contour maps. These maps allowed the identification of specific zones with high metal concentrations and low pH values corresponding to spots of residual sludge. Moreover, kriged maps showed distinct spatial distribution and hence different behaviour for the elements considered. This information may be applied to optimise remediation strategies in highly and moderately contaminated areas.  相似文献   

13.
Optimized land resource management depends on reliable and detailed information describing the spatial distribution of soils, geology, topography, and land use. Soil–landscapes are three–dimensional (3D) systems commonly represented using 2D maps utilizing geographic information systems. Addressing 3D soil–landscape reality is crucial for land resource management in terms of crop growth and transport processes (e.g. nitrate leaching) that are driving soil and water quality. Our objective was to investigate the usefulness of 3D geographic information technology (GIT) applied to land resource management. Our approach is based on 2D and 3D ordinary kriging interpolating surface and subsurface attributes to reconstruct soil–landscapes. We used Virtual Reality Modeling Language, which is a web–based 3D graphics language, to visualize objects (e.g. voxels, polyhedrons) representing soil and landscape attributes. We produced a 3D block model showing the spatial distribution of bulk densities and relief for a site in southern Wisconsin and a 3D stratigraphic model showing the spatial distribution of soil horizons and relief for a site in northern Florida. Emerging GIT was used to develop 3D soil–landscape models describing continuous changes of soil and landscape attributes. Combining multimedia elements (e.g. WWW, 3D visualization, and interactivity) can produce insight that would not arise from use of the elements alone. Three–dimensional scientific visualization is a powerful tool to help us see what is invisible from above the ground.  相似文献   

14.
Large area forest inventory is important for understanding and managing forest resources and ecosystems. Remote sensing, the Global Positioning System (GPS), and geographic information systems (GIS) provide new opportunities for forest inventory. This paper develops a new systematic geostatistical approach for predicting forest parameters, using integrated Landsat 7 Enhanced Thematic Mapper Plus (ETM+) images, GPS, and GIS. Forest parameters, such as basal area, height, health conditions, biomass, or carbon, can be incorporated as a response variable, and the geostatistical approach can be used to predict parameter values for uninventoried points. Using basal area as the response and Landsat ETM+ images of pine stands in Georgia as auxiliary data, this approach includes univariate kriging (ordinary kriging and universal kriging) and multivariable kriging (co-kriging and regression kriging). The combination of bands 4, 3, and 2, as well as the combination of bands 5, 4, and 3, normalized difference vegetation index (NDVI), and principal components (PCs) were used in this study with co-kriging and regression kriging. Validation based on 200 randomly sampling points withheld field inventory was computed to evaluate the kriging performance and demonstrated that band combination 543 performed better than band combination 432, NDVI, and PCs. Regression kriging resulted in the smallest errors and the highest R-squared indicating the best geostatistical method for spatial predictions of pine basal area.  相似文献   

15.
Abstract

During the Second World War, the German army developed the largest organization of any nation ever to contribute military applications of earth science in wartime. In the summer of 1940, its military geologists assisted planning for potentially the greatest amphibious assault to that time in history by preparing maps which analysed the terrain of southeast England in terms of coastal geomorphology, groundwater supply, quarry sites for construction materials and off-road trafficability. These specialist maps were generated at scales of 1:50 000, 1:100 000 or 1:250 000 by annotating topographical base maps, derived from the then current Ordnance Survey maps at most similar scale, with data derived from maps and memoirs published by the Geological Survey of Great Britain or larger-scale Ordnance Survey maps. They represent an early example of geotechnical mapping skills developed more fully in the German armed forces for operations elsewhere later in the war.  相似文献   

16.
Environmental modelling usually requires spatially distributed inputs for model operation. We propose that such inputs are best obtained from field measured data. Geographic information systems (GIS) provide a logical framework to distribute measured inputs spatially, to manipulate ensuing data fields during analysis, and to display the results. This paper describes a study conducted on a 123 km2 catchment in Pennsylvania. The purpose was to evaluate how spatial variability of macroporosity affects distribution of other infiltration-related parameters. We measured sorptivity, conductivity and macroporosity at specific points within a catchment, and interpolated their spatial distributions by kriging. The measurements were made with ring and disk infiltrometers, sampling locations were geo-referenced with a global positioning system (GPS), and data were analysed using geostatistical techniques in a GIS context. Field values ( hard data ) were supplemented by soft data derived from cumulative distribution functions (cdfs) and available soil maps. Results showed that, when spatial variability associated with macroporosity was removed, infiltration parameters became less variable. Observed correlation among measured parameters suggested a form of potential transfer functions. We conclude that infiltration can be modelled at either the farm or catchment scale if macroporosity and spatial variability of infiltration parameters are adequately defined, and we suggest approaches which can be used in a GIS context to attain that goal.  相似文献   

17.
Mapmaking has become widespread through the Internet, resulting in a wide range of cartographic quality. To achieve better quality, mapmaking needs tools and online services for intuitive and efficient on-demand mapping. A project team at IGN, the French National Mapping Agency, is working on producing a digital cartographic model (DCM) from various existing databases and maps on which such tools and services are based. This DCM ranges from detailed topographic maps to small general road maps. GeoServer Web Map Service capabilities were used extensively to produce quality maps with various legends. Special care was taken to make a default legend suitable for customer data overlays, both on-screen and on paper. Web-based interface prototypes were built to guide users in choosing colors and creating their own original map legends. Users can also rely on a growing catalog of harmonious color palettes and map samples as sources of inspiration.  相似文献   

18.
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19.
Coseismic displacements play a significant role in characterizing earthquake causative faults and understanding earthquake dynamics. They are typically measured from InSAR using pre- and post-earthquake images. The displacement map produced by InSAR may contain missing coseismic values due to the decorrelation of ASAR images. This study focused on interpolating missing values in the coseismic displacement map of the 2003 Bam earthquake using geostatistics with the aim of running a slip distribution model. The gaps were grouped into 23 patches. Variograms of the patches showed that the displacement data were spatially correlated. The variogram prepared for ordinary kriging (OK) indicated the presence of a trend and thus justified the use of universal kriging (UK). Accuracy assessment was performed in 3 ways. First, 11 patches of equal size and with an equal number of missing values generated artificially, were kriged and validated. Second, the four selected patches results were validated after shifting them to new locations without missing values and comparing them with the observed values. Finally, cross validation was performed for both types of patch at the original and shifted locations. UK results were better than OK in terms of kriging variance, mean error (ME) and root mean square error (RMSE). For both OK and UK, only 4 out of 23 patches (1, 5, 11 and 21) showed ME and RMSE values that were substantially larger than for the other patches. The accuracy assessment results were found to be satisfactory with ME and RMSE values close to zero. InSAR data inversion demonstrated the usefulness of interpolation of the missing coseismic values by improving a slip distribution model. It is therefore concluded that kriging serves as an effective tool for interpolating the missing values on a coseismic displacement map.  相似文献   

20.
Mapping the spatial distribution of soil nutrient contents from sample data has received much attention in the recent decade. Accurately mapping soil nutrients purely based on sample data, however, is difficult due to the sparsity and high cost of samples. Land use types usually influence the contents of soil nutrients at the local level and it is desirable to integrate such information into predictive mapping. The area-and-point kriging (AAPK) method, which was proposed recently, may provide an interpolation technique for such purposes. This study mapped the soil total nitrogen (TN) distribution of Hanchuan County, China, using AAPK with sample data (consisting of 402 points) and land use information. Ordinary kriging (OK) and residual kriging (RK) were compared to evaluate the performance of AAPK. Results showed that: (1) land use types had important impacts on the spatial distribution of soil TN; (2) measured data at 135 validation locations had stronger correlation with the data predicted by AAPK than by RK and OK, and the mean error and root mean square error with AAPK were lower than with RK and OK; and (3) AAPK generated smaller error variances than RK and OK did. This suggests that AAPK represents an effective method for increasing the interpolation accuracy of soil TN. It should be pointed out that some of the land use polygons used in this study are very large and complex, which might impact the effectiveness of AAPK in improving the prediction accuracy. Segmenting them into simple smaller areas might be helpful.  相似文献   

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