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1.
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
2.
As an important GIS function, spatial interpolation is one of the most often used geographic techniques for spatial query, spatial data visualization, and spatial decision-making processes in GIS and environmental science. However, less attention has been paid on the comparisons of available spatial interpolation methods, although a number of GIS models including inverse distance weighting, spline, radial basis functions, and the typical geostatistical models (i.e. ordinary kriging, universal kriging, and cokriging) are already incorporated in GIS software packages. In this research, the conceptual and methodological aspects of regression kriging and GIS built-in interpolation models and their interpolation performance are compared and evaluated. Regression kriging is the combination of multivariate regression and kriging. It takes into consideration the spatial autocorrelation of the variable of interest, the correlation between the variable of interest and auxiliary variables (e.g., remotely sensed images are often relatively easy to obtain as auxiliary variables), and the unbiased spatial estimation with minimized variance. To assess the efficiency of regression kriging and the difference between stochastic and deterministic interpolation methods, three case studies with strong, medium, and weak correlation between the response and auxiliary variables are compared to assess interpolation performances. Results indicate that regression kriging has the potential to significantly improve spatial prediction accuracy even when using a weakly correlated auxiliary variable. 相似文献
3.
Average variograms to guide soil sampling 总被引：4，自引：0，他引：4
R. Kerry M.A. Oliver 《International Journal of Applied Earth Observation and Geoinformation》2004,5(4):307-325
To manage land in a site-specific way for agriculture requires detailed maps of the variation in the soil properties of interest. To predict accurately for mapping, the interval at which the soil is sampled should relate to the scale of spatial variation. A variogram can be used to guide sampling in two ways. A sampling interval of less than half the range of spatial dependence can be used, or the variogram can be used with the kriging equations to determine an optimal sampling interval to achieve a given tolerable error. A variogram might not be available for the site, but if the variograms of several soil properties were available on a similar parent material and or particular topographic positions an average variogram could be calculated from these. Averages of the variogram ranges and standardized average variograms from four different parent materials in southern England were used to suggest suitable sampling intervals for future surveys in similar pedological settings based on half the variogram range. The standardized average variograms were also used to determine optimal sampling intervals using the kriging equations. Similar sampling intervals were suggested by each method and the maps of predictions based on data at different grid spacings were evaluated for the different parent materials. Variograms of loss on ignition (LOI) taken from the literature for other sites in southern England with similar parent materials had ranges close to the average for a given parent material showing the possible wider application of such averages to guide sampling. 相似文献
4.
In practical applications of area-to-point spatial interpolation, inequality constraints, such as non-negativity or more general constraints on the maximum and/or minimum attribute value, should be taken into account. The geostatistical framework proposed in this paper deals with the spatial interpolation problem of downscaling areal data under such constraints, while: (1) explicitly accounting for support differences between sample data and unknown values, (2) guaranteeing coherent (mass-preserving) predictions, and (3) providing a measure of reliability (uncertainty) for the resulting predictions. The formal equivalence between Kriging and spline interpolation allows solving constrained area-to-point interpolation problems via quadratic programming (QP) algorithms, after accounting for the support differences between various constraints involved in the problem formulation. In addition, if inequality constraints are enforced on the entire set of points discretizing the study domain, the numerical algorithms for QP problems are applied only to selected locations where the corresponding predictions violate such constraints. The application of the proposed method of area-to-point spatial interpolation with inequality constraints in one and two dimension is demonstrated using realistically simulated data. 相似文献
5.
Remote sensing can augment traditional methods of mosquito species surveillance for arboviruses. Abundance and patterns of mosquito vectors of West Nile virus in Chesapeake, Virginia, USA, were studied using light trap collection data and a Landsat-7 Enhanced Thematic Mapper+ digital image for spatial interpolation and geostatistical mapping of the abundance of 24 species of mosquitoes capable of transmitting West Nile virus to humans. We evaluated spatial interpolation techniques including inverse distance weighting, ordinary kriging, co-kriging geostatistics using combined Landsat-7 tasselled cap transform indices (brightness, greenness, and wetness) to characterize habitats and breeding conditions. Results highlight gaps in surveillance coverage, geostatistical improvement of vector patterns and abundance, and spatial patterns of error. Constraints and opportunities for adoption of remote sensing and spatial analysis for mosquito control are identified and discussed. 相似文献
6.
Qingmin Meng Chris Cieszewski Marguerite Madden 《ISPRS Journal of Photogrammetry and Remote Sensing》2009,64(1):27-36
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
7.
《制图学和地理信息科学》2013,40(4):209-216
Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with "rips" and "tears" throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood. 相似文献
8.
Nitrogen dioxide (NO2) is known to act as an environmental trigger for many respiratory illnesses. As a pollutant it is difficult to map accurately, as concentrations can vary greatly over small distances. In this study three geostatistical techniques were compared, producing maps of NO2 concentrations in the United Kingdom (UK). The primary data source for each technique was NO2 point data, generated from background automatic monitoring and background diffusion tubes, which are analysed by different laboratories on behalf of local councils and authorities in the UK. The techniques used were simple kriging (SK), ordinary kriging (OK) and simple kriging with a locally varying mean (SKlm). SK and OK make use of the primary variable only. SKlm differs in that it utilises additional data to inform prediction, and hence potentially reduces uncertainty. The secondary data source was oxides of nitrogen (NOx) derived from dispersion modelling outputs, at 1 km × 1 km resolution for the UK. These data were used to define the locally varying mean in SKlm, using two regression approaches: (i) global regression (GR) and (ii) geographically weighted regression (GWR). Based upon summary statistics and cross-validation prediction errors, SKlm using GWR derived local means produced the most accurate predictions. Therefore, using GWR to inform SKlm was beneficial in this study. 相似文献
9.
Comparison of interpolation models for estimating heavy metals in soils under various spatial characteristics and sampling methods 总被引：2，自引：0，他引：2 
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下载免费PDF全文 Heavy metal pollution in soils has become increasingly challenging, especially in developing countries. Estimating the spatial distribution of heavy metals in soils is essential to preventing their build‐up. This article aims to identify the effects of spatial scales, spatial autocorrelation, sampling methods, and proportion on interpolation models in estimating the distribution of heavy metals in soils. Six interpolation models (area‐and‐point kriging, AAPK; inverse distance weighting, IDW; local polynomial interpolation, LP; ordinary kriging, OK; simple kriging, SK; and thin plate spline, TPS), three sampling methods (random, stratified, and systematic sampling), and five sampling proportions (1, 5, 10, 15, and 20%) are considered in this study using sets of simulated data, and the real situation was tested for verification. The results show that, in general, with the increase of spatial autocorrelation or the sampling percentage, the accuracy and stability of different interpolation models gradually increase; however, the various interpolation models have their own specific characteristics and application conditions. The best application conditions of the interpolation models compared with other models under the same situation are summarized and explained in theory. These conclusions have implications for future work. 相似文献
10.
Discriminant Models of Uncertainty in Nominal Fields 总被引：3，自引：0，他引：3
Despite developments in error modeling in discrete objects and continuous fields, there exist substantial and largely unsolved conceptual problems in the domain of nominal fields. This article explores a novel strategy for uncertainty characterization in spatial categorical information. The proposed strategy is based on discriminant space, which is defined with essential properties or driving processes underlying spatial class occurrences, leading to discriminant models of uncertainty in area classes. This strategy reinforces consistency in categorical mapping by imposing class-specific mean structures that can be regressed against discriminant variables, and facilitates scale-dependent error modeling that can effectively emulate the variation found between observers in terms of classes, boundary positions, numbers of polygons, and boundary network topology. Based on simulated data, comparisons with stochastic simulation based on indicator kriging confirmed the replicability of the discriminant models, which work by determining the mean area classes based on discriminant variables and projecting spatially correlated residuals in discriminant space to uncertainty in area classes. 相似文献
11.
Bayesian and Geostatistical Approaches to Combining Categorical Data Derived from Visual and Digital Processing of Remotely Sensed Images 总被引：1，自引：0，他引：1
ZHANGJingxiong LIDeren 《地球空间信息科学学报》2005,8(2):90-97
This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification. By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated. It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly. Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy. Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique. 相似文献
12.
This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification. By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated. It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly. Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy. Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique. 相似文献
13.
快速、准确地对地形进行重建以生成数字高程模型是地理信息表达的重要研究内容,径向基函数（radial basis function,RBF）作为一种插值性能较优的空间插值方法,特别适合于重建复杂的地形模型,但随着已知地形采样点数量的增加,RBF插值模型求解速度变慢,同时插值矩阵过于庞大而导致插值模型求解困难甚至求解失败。针对这个问题,本文基于区域分解和施瓦兹并行原理进行地形插值,以紧支撑径向基函数（compact support RBF,CSRBF）构建基于所有地形采样数据的全局插值矩阵,并自适应求解子区域CSRBF插值节点紧支撑半径,基于限制性加性施瓦兹方法（restricted additive Schwarz method,RASM）采用多核并行架构对各局部子区域的插值矩阵进行求解。以某地区数字高程模型（DEM）数据进行插值实验,结果表明,本文方法能够对大规模地形数据进行准确重建,并且具有较高的求解效率。 相似文献
14.
Downscaling has an important role to play in remote sensing. It allows prediction at a finer spatial resolution than that of the input imagery, based on either (i) assumptions or prior knowledge about the character of the target spatial variation coupled with spatial optimisation, (ii) spatial prediction through interpolation or (iii) direct information on the relation between spatial resolutions in the form of a regression model. Two classes of goal can be distinguished based on whether continua are predicted (through downscaling or area-to-point prediction) or categories are predicted (super-resolution mapping), in both cases from continuous input data. This paper reviews a range of techniques for both goals, focusing on area-to-point kriging and downscaling cokriging in the former case and spatial optimisation techniques and multiple point geostatistics in the latter case. Several issues are discussed including the information content of training data, including training images, the need for model-based uncertainty information to accompany downscaling predictions, and the fundamental limits on the representativeness of downscaling predictions. The paper ends with a look towards the grand challenge of downscaling in the context of time-series image stacks. The challenge here is to use all the available information to produce a downscaled series of images that is coherent between images and, thus, which helps to distinguish real changes (signal) from noise. 相似文献
15.
利用时空Kriging进行气温插值研究 总被引：4，自引：0，他引：4
以黑龙江省近37a的月均气温数据为研究对象,介绍了一类积分式时空协方差(变异)函数模型进行时空Kriging插值。针对月均气温呈现出的明显季节变化,对各站点的气温进行去季节项处理,并在此基础上建立时空变异函数。将空间维的普通Kriging插值扩展至时空维,同时考虑空间和时间相关性对研究变量进行时空估计,并将估计结果与空间Kriging插值效果进行了比较。结果表明,时空插值效果理想,插值精度较空间Kriging更高。 相似文献
16.
以地形地貌特征复杂、观测站点分布稀疏不均匀的四川省为研究区,引入地形因子（坡度和坡向）和植被指数,采用顾及空间关系非平稳性的（混合）地理加权回归克里格模型（（mixed）geographically weighted regression Kriging,（m）GWRK）进行月尺度平均气温插值方法及精度分析研究。针对不同季节和不同地区,将（m）GWRK插值结果与基于全局回归的回归克里格（regression Kriging,RK）插值结果进行对比。结果表明,RK、GWRK、mGWRK回归关系的决定系数R2分别为0.795、0.922、0.911,均方根误差分别为0.83℃、0.64℃、0.55℃,表明GWRK、mGWRK对目标变量的解释能力以及插值精度都优于RK;GWRK、mGWRK相对于RK对月平均气温插值的改进具有季节与地区差异,冬半年的改进大于夏半年,在地形地貌变化大的地区改进大于地形地貌变化小的地区。 相似文献
17.
A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling. 相似文献
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19.
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
20.
The hierarchid tessellation model belongs to a class of spatial data models based on the recursive decomposition of space. The quadtree is one such tessellation and is characterized by square cells and a 1:4 decomposition ratio. To relax these constraints in the tessellation, a generalized hierarchical tessellation data model, called Adaptive Recursive Tessellations (ART), has been proposed. ART increases flexibility in the tessellation by the use of rectangular cells and variable decomposition ratios. In ART, users can specify cell sizes which are intuitively meaningful to their applications, or which can reflect the scales of data. ART is implemented in a data structure called Adaptive Recursive Run-Encoding (ARRE), which is a variant of two-dimensional run-encoding whose running path can vary with the different tessellation structures incorporated in an ART model. Given the recognition of the benefits of implementing statistical spatial analysis in GIS, the use of hierarchical tessellation models such as ART in spatial analysis is discussed. Three examples are introduced to show how ART can: (1) be applied to solve the quadrat size problem in quadrat analysis of point patterns; (2) act as the data model in the variable resolution block kriging technique for geostatistical data to reduce variation in kriging error; and (3) facilitate the evaluation of spatial autocorrelation for area data at multiple map resolutions via the construction of a connectivity matrix for calculating spatial autocorrelation indices based on ARRE. 相似文献