Street‐level Spatial Interpolation Using Network‐based IDW and Ordinary Kriging

This study proposes network‐based spatial interpolation methods to help predict unknown spatial values along networks more accurately. It expands on two of the commonly used spatial interpolation methods, IDW (inverse distance weighting) and OK (ordinary kriging), and applies them to analyze spatial data observed on a network. The study first provides the methodological framework, and it then examines the validity of the proposed methods by cross‐validating elevations from two contrasting patterns of street network and comparing the MSEs (Mean Squared Errors) of the predicted values measured with the two proposed network‐based methods and their conventional counterparts. The study suggests that both network‐based IDW and network‐based OK are generally more accurate than their existing counterparts, with network‐based OK constantly outperforming the other methods. The network‐based methods also turn out to be more sensitive to the edge effect, and their performance improves after edge correction. Furthermore, the MSEs of standard OK and network‐based OK improve as more sample locations are used, whereas those of standard IDW and network‐based IDW remain stable regardless of the number of sample locations. The two network‐based methods use a similar set of sample locations, and their performance is inherently affected by the difference in their weight distribution among sample locations.     

Evaluation of Air Pollution Trend Using GIS and RS Applications in South West of Iran

In this paper, remote sensing and GIS have been used to assess the status of NO₂ at the south west of Iran. 221 data about concentration of NO₂ was extracted from Ozone Monitoring Instrument. Ordinary kriging and inverse distance weighting interpolation methods was used to interpolate data. Results showed that ordinary kriging method using cross-validation have had less error. North east of the study area has the highest concentration of NO₂ (329 molecule/cm²) and the concentration of NO₂ decreases from north east to South west of the study area. On the other hand, data trend results showed that the data seems to exhibit a fairly strong trend in the east west direction and a weaker one in the north–south direction.     

Assessment of regression kriging for spatial interpolation – comparisons of seven GIS interpolation methods

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.     

Spatial interpolation and image-integrative geostatistical prediction of mosquito vectors for arboviral surveillance

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.     

Increased accuracy of geostatistical prediction of nitrogen dioxide in the United Kingdom with secondary data

Five techniques were used to map nitrogen dioxide (NO₂) concentrations in the United Kingdom. The methods used to predict from point data, collected as part of the UK NO₂ diffusion tube network, were local linear regression (LR), inverse distance weighting (IDW), ordinary kriging (OK), simple kriging with a locally varying mean (SKlm) and kriging with an external drift (KED). These techniques may be divided into two groups: (i) those that use only a single variable in the prediction process (IDW, OK) and (ii) those that make use of additional variables as a part of prediction (LR, SKlm and KED). Nitrous oxides emission data were used as secondary data with LR, SKlm and KED. It was concluded that SKlm provided the most accurate predictions based on the summary statistics of prediction errors from cross-validation.     

Comparison of interpolation models for estimating heavy metals in soils under various spatial characteristics and sampling methods

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.     

Artificial Neural Networks as a Method of Spatial Interpolation for Digital Elevation Models

This paper examines the performance of artificial neural networks (ANNs) as a method of spatial interpolation, when presented with irregular and regular samples of elevation data. The results of the ANN interpolation are compared with results obtained by kriging. Tests of spatial bias in the systematic errors contained in each of the neural network-derived DEMs were conducted using four attributes: slope, aspect, average direction and average distance from the nearest sampled value. Based on RMS and other evaluation measures, the accuracy of estimated DEMs from regular and irregular sample distributions using neural networks is lower than the accuracy level derived from kriging. The accuracy level of the ANN interpolators also decreases as the range of elevation values in DEMs increases. As reported in the literature, ANNs are approximate interpolators, and the pattern of under-prediction and over-prediction of elevation values in this study revealed that all estimated values fell within the range of sample elevations. Neural networks cannot predict values outside the range of elevation values contained in the sample, a property shared by other interpolators such as inverse weighted distance.     

Spatially weighted supervised classification for remote sensing

A simple approach for incorporating a spatial weighting into a supervised classifier for remote sensing applications is presented. The classifier modifies the feature-space distance-based metric with a spatial weighting. This is facilitated by the use of a non-parametric (k-nearest neighbour, k-NN) classifier in which the spatial location of each pixel in the training data set is known and available for analysis. A remotely sensed image was simulated using a combined Boolean and geostatistical unconditional simulation approach. This simulated image comprised four wavebands and represented three classes: Managed Grassland, Woodland and Rough Grassland. This image was then used to evaluate the spatially weighted classifier. The latter resulted in modest increase in the accuracy of classification over the original k-NN approach. Two spatial distance metrics were evaluated: the non-centred covariance and a simple inverse distance weighting. The inverse distance weighting resulted in the greatest increase in accuracy in this case.     

A Comparison of Thiessen Polygon,Kriging, and Spline Models of Potential UV Exposure

The performance accuracy of Thiessen-polygon and kriging interpolation methods available in the standard GIS packages was evaluated based on magnitude of errors in predicting potential UV exposure across the continental U.S., and the results were compared with those of the ANUSPLIN routine that runs outside typical GIS through a series of C++ and FORTRAN commands. Input data consisted of global radiation measures recorded at 215 stations, latitude, longitude, and elevation from a 30 arc-second Digital Elevation Model. The objective was to identify the most accurate prediction method for facilitating measurement of potential UV exposure at local (e.g.1km² grid cell) and county levels. The ANUSPLIN method produced the smallest prediction errors in estimating values of potential UV exposure at 1 km² resolution; these measurements were aggregated to the county level. We examined how much variation was lost through aggregation, as well as the potential bias associated with the possibility that some counties have predominantly north or south facing slopes. The impact of using inferior procedures on the estimates and geographic patterns of potential UV exposure was also examined. ANUSPLIN generated results that are reproducible and for which uncertainty is known. These measurements will be used in subsequent analysis of the role of UV exposure in melanoma etiology.     

Zonation of coastal sediments based on the effective properties on the accumulation of heavy metals using the IDW and kriging method (case study: SW Iran)

Abstract

This study investigated the effects of some physicochemical properties of sediments on the accumulation of heavy metals in portions of the Musa creek coasts (Jafari and Petrochemical creeks). Effective properties such as pH, EC, texture, G_S, γ_d, n, CaCO₃ and OM were determined. All variables showed a normal distribution and general trends of NW–SE and NE–SW. After detrending the variables, ordinary kriging was used for modelling. The C₀/σ₂, C₀/σ_2, and search radius criteria were used to select the best semivariogram. All the variables displayed a spatial structure with different intensities. The IDW method was also used for estimation. The cross-validation showed that the results of both IDW and kriging methods are almost similar. Distribution of the sand particle, G_S, n and OM decreases with distance from the waterways, whilst clay–silt deposits. In the center of the studied area, CaCO₃ has the highest value and EC has the lowest value.     

一种基于场论的空间异常探测方法

从空间数据场的角度,借鉴高斯势函数发展了一种新的空间异常度度量指标。进而,提出了一种基于场论的空间异常探测方法。该方法通过空间聚类获得局部相关性较强的空间簇,并构建合理、稳定的空间邻近域。在此基础上,采用专题属性变化梯度修复策略减弱空间邻近域中潜在异常的影响,并利用空间异常度度量指标计算实体的异常度,从而探测空间异常。实验结果及实例证明了此方法的正确性。     

Mapping of Soil Micronutrients in Kashmir Agricultural Landscape Using Ordinary Kriging and Indicator Approach

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.     

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

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.     

Upscaling plot-scale soil respiration in winter wheat and summer maize rotation croplands in Julu County,North China

Soil respiration (R_s) data from 45 plots were used to estimate the spatial patterns of R_s during the peak growing seasons of winter wheat and summer maize in Julu County, North China, by combining satellite remote sensing data, field-measured data, and a support vector regression (SVR) model. The observed R_s values were well reproduced by the model at the plot scale, with a root-mean-square error (RMSE) of 0.31 μmol CO₂ m⁻² s⁻¹ and a coefficient of determination (R²) of 0.73. No significant difference was detected between the prediction accuracy of the SVR model for winter wheat and summer maize. With forcing from satellite remote sensing data and gridded soil property data, we used the SVR model to predict the spatial distributions of R_s during the peak growing seasons of winter wheat and summer maize rotation croplands in Julu County. The SVR model captured the spatial variations of R_s at the county scale. The satellite-derived enhanced vegetation index was found to be the most important input used to predict R_s. Removal of this variable caused an RMSE increase from 0.31 μmol CO₂ m⁻² s⁻¹ to 0.42 μmol CO₂ m⁻² s⁻¹. Soil properties such as soil organic carbon (SOC) content and soil bulk density (SBD) were the second most important factors. Their removal led to an RMSE increase from 0.31 μmol CO₂ m⁻² s⁻¹ to 0.37 μmol CO₂ m⁻² s⁻¹. The SVR model performed better than multiple regression in predicting spatial variations of R_s in winter wheat and summer maize rotation croplands, as shown by the comparison of the R² and RMSE values of the two algorithms. The spatial patterns of R_s are better captured using the SVR model than performing multiple regression, particularly for the relatively high and relatively low R_s values at the center and northeast study areas. Therefore, SVR shows promise for predicting spatial variations of R_s values on the basis of remotely sensed data and gridded soil property data at the county scale.     

Statistical data fusion of multi-sensor AOD over the Continental United States

This article illustrates two techniques for merging daily aerosol optical depth (AOD) measurements from satellite and ground-based data sources to achieve optimal data quality and spatial coverage. The first technique is a traditional Universal Kriging (UK) approach employed to predict AOD from multi-sensor aerosol products that are aggregated on a reference grid with AERONET as ground truth. The second technique is spatial statistical data fusion (SSDF); a method designed for massive satellite data interpolation. Traditional kriging has computational complexity O(N³), making it impractical for large datasets. Our version of UK accommodates massive data inputs by performing kriging locally, while SSDF accommodates massive data inputs by modelling their covariance structure with a low-rank linear model. In this study, we use aerosol data products from two satellite instruments: the moderate resolution imaging spectrometer and the geostationary operational environmental satellite, covering the Continental United States.     

波形反演震源机制中的权重优化:应用于2013年芦山地震

对剪切-粘贴方法（cut and paste,CAP）和地震软件包（computer programs in seismology,CPS）两个较常用的震源机制格点搜索反演方法的加权策略进行分析,发现二者权重分别仅单独考虑了波形数据信噪比或振幅差异,且权重数值大小随震中距的变化趋势相互冲突。为了解决此数值矛盾并保留二者权重的优势,将两种加权策略进行联合,综合考虑波形信噪比和振幅差异对反演的影响。此外,考虑到震中距定权的粗糙性,提出了针对各波形本身的数据信息精化计算权重方案。为了检验联合定权的优越性,以2013-04-20的芦山地震为例,利用CPS程序分别用联合及单独定权进行多次反演,比较发现联合加权方法反演结果最优。最终的震源机制解为（走向211°±3°,倾角41°±1°,滑动角94°±2°）,震源深度17 km,与其他研究者的研究成果有很好的一致性,且与震源区的应力及地质构造情况均相互吻合,表明所提出的权重方法优化效果明显。     

Comparison of extrapolation and interpolation methods for estimating daily photosynthetically active radiation (PAR)

Measurements of photosynthetically active radiation (PAR), which are indispensable for simulating plant growth and productivity, are generally very scarce. This study aimed to compare two extrapolation and one interpolation methods for estimating daily PAR reaching the earth surface within the Poyang Lake national nature reserve, China. The daily global solar radiation records at Nanchang meteorological station and daily sunshine duration measurements at nine meteorological stations around Poyang Lake were obtained to achieve the objective. Two extrapolation methods of PARs using recorded and estimated global solar radiation at Nanchang station and three stations (Yongxiu, Xingzi and Duchang) near the nature reserve were carried out, respectively, and a spatial interpolation method combining triangulated irregular network (TIN) and inverse distance weighting (IDW) was implemented to estimate daily PAR. The performance evaluation of the three methods using the PARs measured at Dahuchi Conservation Station (day number of measurement = 105 days) revealed that: (1) the spatial interpolation method achieved the best PAR estimation (R ₂ = 0.89, s.e. = 0.99, F = 830.02, P < 0.001); (2) the extrapolation method from Nanchang station obtained an unbiased result (R ₂ = 0.88, s.e. = 0.99, F = 745.29, P < 0.001); however, (3) the extrapolation methods from Yongxiu, Xingzi and Duchang stations were not suitable for this specific site for their biased estimations. Considering the assumptions and principles supporting the extrapolation and interpolation methods, the authors conclude that the spatial interpolation method produces more reliable results than the extrapolation methods and holds the greatest potential in all tested methods, and more PAR measurements should be recorded to evaluate the seasonal, yearly and spatial stabilities of these models for their application to the whole nature reserve of Poyang Lake.     

Spatial Analysis of 1991 Gulf War Troop Locations in Relationship with Postwar Health Symptom Reports Using GIS Techniques

Spatial autocorrelation analysis was used to identify spatial patterns of 1991 Gulf War (GW) troop locations in relationship to subsequent postwar diagnosis of chronic multisymptom illness (CMI). Criteria for the diagnosis of CMI include reporting from at least two of three symptom clusters: fatigue, musculoskeletal pain, and mood and cognition. A GIS‐based methodology was used to examine associations between potential hazardous exposures or deployment situations and postwar health outcomes using troop location data as a surrogate. GW veterans from the Devens Cohort Study were queried about specific symptoms approximately four years after the 1991 deployment to the Persian Gulf. Global and local statistics were calculated using the Moran's I and G statistics for six selected date periods chosen a priori to mark important GW‐service events or exposure scenarios among 173 members of the cohort. Global Moran's I statistics did not detect global spatial patterns at any of the six specified data periods, thus, indicating there is no significant spatial autocorrelation of locations over the entire Gulf region for veterans meeting criteria for severe postwar CMI. However, when applying local G* and local Moran's I statistics, significant spatial clusters (primarily in the coastal Dammam/Dharhan and the central inland areas of Saudi Arabia) were identified for several of the selected time periods. Further study using GIS techniques, coupled with epidemiological methods, to examine spatial and temporal patterns with larger sample sizes of GW veterans is warranted to ascertain if the observed spatial patterns can be confirmed.     

利用Sentinel-2影像超分辨率重建的红树林冠层氮含量反演

氮素是植被整个生命周期的必要元素,红树林冠层氮素含量（CNC）遥感估算对红树林健康监测具有重要意义。以广东湛江高桥红树林保护区为研究区,本文旨在基于Sentinel-2影像超分辨率重建技术进行红树林CNC估算和空间制图。研究首先基于三次卷积重采样、Sen2Res和SupReMe算法实现Sentinel-2影像从20 m分辨率到10 m的重建;然后以重建后的影像和原始20 m影像为数据源构建40个相关植被指数,采用递归特征消除法（SVM-RFE）确定CNC估算的最优变量组合,进而构建CNC反演的核岭回归（KRR）模型;最后选取最优模型实现CNC制图。研究结果表明：基于Sen2Res和SupReMe超分辨率算法的重建影像不仅与原始影像具有很高的光谱一致性,且明显提高了影像的清晰度和空间细节。红树林CNC反演波段主要集中在红（B4）、红边（B5）、近红外波段（B8a）以及短波红外波段（B11和B12）,与“红边波段”相关的植被指数（RSSI和TCARIre1/OSAVI）也是红树林CNC反演的有效变量。基于3种方法重建后10 m的影像构建的模型反演精度（R²val>0.579）均优于原始20 m的影像（R²val=0.504）;基于Sen2Res算法重建影像构建的反演模型拟合精度（R²val=0.630,RMSE_val=5.133,RE_val=0.179）与基于三次卷积重采样重建影像的模型拟合精度（R²val=0.640,RMSE_val=5.064,RE_val=0.179）基本相当,前者模型验证精度（R²cv=0.497,RMSE_cv=5.985,RE_cv=0.214）较高且模型变量选择数量最为合理。综合重建影像光谱细节及模型精度,基于Sen2Res算法重建的Sentinel-2影像在红树林CNC估算中具有良好的应用潜力,能为区域尺度红树林冠层健康状况的精细监测提供有效的方法借鉴和数据支撑。     

一种空间交叉异常显著性判别的非参数检验方法

空间异常探测旨在从海量空间数据中挖掘不符合普适性规律、表现出“与众不同”特性的空间实体集合,对于揭示地理现象的特殊发展规律具有重要价值。现有研究在空间异常度量方面取得了重要进展,但多缺乏对空间异常模式显著性的统计判别,且是针对单一类别数据,没有顾及多类别数据间的相互影响。为此,本文基于空间随机过程的思想,针对两种类别空间点数据,提出了一种空间交叉异常显著性判别的非参数检验方法。首先,针对基本数据集实体,采用约束Delaunay三角网,构建合理、稳定的空间邻近域;然后,统计落在基本数据集实体空间参考邻域半径范围内的参考数据集实体的数目,度量初始异常度;进而,采用α-Shape法构建支撑域,以空间随机过程为基础构建零模型,采用蒙特卡洛模拟检验空间异常的显著性;最后,采用生存距离对异常模式的稳定性进行评价分析。通过试验分析与比较发现,该方法能够有效识别具有统计显著性的空间交叉异常。