DEM内插方法与可视性分析结果的相似性研究

以实际采样的散点数据为原始数据,利用反距离权、样条函数、克里格、自然邻点内插、TIN内插5种内插方法生成规则格网DEM,并对其可视性分析结果进行对比分析和相关分析,揭示不同内插方法对可视性分析结果的影响规律和可视性分析对内插方法的敏感程度。结果表明,可视性分析对内插方法比较敏感,不同的内插方法会得到不同的可视性分析结果,其中相关程度最强的是样条函数内插和克里格内插、自然邻点内插和TIN内插。     

基于空间索引的规则格网DTM内插算法研究

从离散点内插规则格网数字地形模型(DTM)方法的关键是如何提高待插点周围数据的搜索效率。该文针对离散点的空间分布特性,给出了基于网格分块和KD-Tree两种空间索引技术的规则格网内插方法。实验表明,这两种索引方法能显著提高搜索速度,算法内插效率较高。最后,在算法效率分析的基础上,对两种索引方法所适应的条件进行了讨论。     

基于DEM的地理要素PRISM空间内插研究

利用PRISM模型基于DEM、站点数据和其它空间数据图层内插了气象要素,以便准确表达其空间分布特征。为了比较PRISM空间内插结果,采用GIS常用的Kriging内插、Spline内插等方法分别对降水和气温站点数据进行空间插补,并对内插结果进行精度分析、DEM空间分辨率的影响分析和各个权重因子的影响分析。分析表明,PRISM方法比其它内插方法能够更加精确地表达气象要素的空间分布,更适合于在地形复杂地区地表参数的空间内插。由于气象要素空间分布的复杂性,PRISM内插方法不能完全表达地表参数空间异质性。以后研究中,应在更小的站点影响单元内考虑更多因子利用PRISM方法进行气象要素的空间内插。     

稀疏观测数据的空间内插方法的分析与比较

依靠稀疏样本数据描述空间指标在地理空间上的连续分布是实践中常常遇到的问题,内插是解决问题的基本方法.以云南省为实验区,15年来6-8月的均温为空间描述指标,在90 m×90 m的分辨率水平上,分别应用不同方法进行内插处理,对内插结果进行了分析和比较.结果表明关联函数法内插效果最好,较好地体现了云南北低南高、西高东低的总体气温变化规律,同时又体现了河谷地带的干热特点.如果无法建立关系函数,则使用克里金插值效果较好,反距离内插法次之,趋势面分析和泰森多边形内插法效果最差.趋势面分析中的高阶多项式内插不优于低阶多项式.     

土壤厚度的空间插值方法比较——以青海三江源地区为例

利用青海三江源地区533个土壤剖面中的厚度数据, 在GIS技术的支持下, 采用确定性内插(反距离加权、全局多项式、局部多项式和径向基函数)和地统计内插(普通克里格、简单克里格、泛克里格和协同克里格)两类共八种插值方法对研究区土壤厚度的空间分布进行了预测, 并综合比较了各种插值方法的预测误差、统计特征值和插值结果分布图。结果表明:(1)在地统计内插方法中, 普通克里格方法(一阶)插值效果比普通克里格方法(二阶)要好;在普通克里格方法(一阶)的半方差函数模型中, 球状模型的插值效果优于指数模型和高斯模型;普通克里格方法在四种地统计内插方法中预测误差最小、预测结果准确性最好。(2)确定性内插方法中, 反距离加权(指数为1)法的误差较小, 并且对区域与局部趋势的反映效果最好。(3)从预测误差大小和对区域总体及局部趋势的综合反映效果来看, 有异向性的球状模型普通克里格(一阶)插值方法预测结果最能准确反映青海三江源地区土壤厚度的空间分布。     

中国土地利用程度的区域分异规律模拟研究

在前人提出的土地利用程度地综合指数计算方法和指标体系基础上,应用地统计学方法模拟了我国土地利用程度的区域分异规律,结果表明,我国土地利用程度与经度和海拔之间存在一定的经向区域分异规律,地统计学“Ｋｒｉｇｅ”内插技术模拟的回归优度达９９．９９％,明显优于二元线性回归模型的模拟效果,能更真实反映我国土地利用程度的区域分异规律,从而为我国土地利用程度时空分布的模拟与预测提供可靠方法。     

中国区域SRTM90m数字高程数据空值区域的填补方法比较

本文对中国地区SRTM90m分辨率的数字高程数据的空值区域做了提取和分析,在此基础上尝试了4种内插填补的方法,并对各种处理方法的过程及结果做了比较,从而确定先从SRTM90m数据中直接提取等高线,再内插生成DEM,用内插出来的值填补原始数据的方法在目前较为适用。此外本文还提出了一些后期处理方法以完善数据。     

丘陵地貌区高程内插适宜方法选择——以长春净月潭为例

对不同的地貌区进行空间内插时选择的适宜方法不同,以典型丘陵地貌区长春市净月潭地区的高程为研究对象,用ArcGIS 9.2分别作反距离权重法、最近邻点法、趋势面分析和克里金法做高程内插。应用交叉检验方法对其内插的精度作出分析,检验其科学性和可靠性,得出反距离权重法、最近邻点法、趋势面法、样条函数法和克里金法高程内插的不同精度,并对各种方法的适用性进行讨论。结果表明最近邻点法精度最高,以下依次为普通克里金插值法、样条函数、反距离权重法、趋势面法。为类似于净月潭地区的丘陵地貌区高程内插提供选择参考。     

基于温度梯度修正的山东省年均温资料插值方法比较研究

对研究区气象站点的年均温与其他地理要素进行相关分析,发现温度与高程具有较高的相关系数。在此基础上,设计了使用空间内插方法分别获得研究区气温与高程,再根据内插得到的高程与实际DEM之差对内插得到的气温进行温度梯度修正,以得到实地气温的方法。这种方法可以有效的消除对气温进行内插时,高程要素对其产生的干扰。分别运用IDW、Kriging、Spline3种方法进行插值,比较结果发现IDW法得到的结果最能反映温度随空间位置变化的趋势,较其他两种内插方法具有较大的优势。     

人口统计数据的空间转换

在经济和社会研究中,所要研究的区域之上经常没有数据,而这些数据需要由已知区域的数据求得,即统计数据需要空间转换,这就通常涉及到面积内插。本文从GIS的角度研究如何解决人口内插问题,认为面积内插和GIS中的叠加分析是一致的。在传统的面积内插方法的基础上是提出了基于人口真实分布的面积内插方法,并推导出了公式。同时提出了人口密度的递归算法,即把居住区分为人口稀疏地区和人口稠密地区,估计出人口稀疏地区的人口密度,就可以求出人口密集地区的人口密度;再把人口密集区分为新的人口稀疏区和密集区,此过程反复直至求出接近于人口真实分布的人口模型。     

Using Mahalanobis Distance to Detect and Remove Outliers in Experimental Covariograms

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.

     

Spatial interpolation of marine environment data using P-MSN

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.     

Evaluation of Diverse Geometric and Geostatistical Estimation Methods Applied to Annual Precipitation in Asturias (NW Spain)

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.     

地统计法支持的北部湾东部海域沉积物粒径趋势分析

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。     

Estimating Population Attribute Values in a Table: “Get Me Started in” Iterative Proportional Fitting

Iterative proportional fitting (IPF) is a technique that can be used to adjust a distribution reported in one data set by totals reported in others. IPF is used to revise tables of data where the information is incomplete, inaccurate, outdated, or a sample. Although widely applied, the IPF methodology is rarely presented in a way that is accessible to nonexpert users. This article fills that gap through discussion of how to operationalize the method and argues that IPF is an accessible and transparent tool that can be applied to a range of data situations in population geography and demography. It offers three case study examples where IPF has been applied to geographical data problems; the data and algorithms are made available to users as supplementary material.     

Spatio-temporal regression kriging for modelling urban NO2 concentrations

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.     

SRTM resample with short distance‐low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60° north latitude and 56° south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc‐second (～30 m) for areas within the USA and at 3 arc‐second (～90 m) resolution for the rest of the world. A resolution of 90 m can be considered suitable for the small or medium‐scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3” to 1”. We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1” model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1” NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1” surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline‐interpolated surface still presented some noise and linear artifacts, which were removed by kriging.     

Variogram Identification Aided by a Structural Framework for Improved Geometric Modeling of Faulted Reservoirs: Jeffara Basin, Southeastern Tunisia

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.     

Modeling Short-Term Spatial and Temporal Variability of Groundwater Level Using Geostatistics and GIS

Continuous depletion of groundwater levels from deliberate and uncontrolled exploitation of groundwater resources lead to the severe problems in arid and semi-arid hard-rock regions of the world. Geostatistics and geographic information system (GIS) have been proved as successful tools for efficient planning and management of the groundwater resources. The present study demonstrated applicability of geostatistics and GIS to understand spatial and temporal behavior of groundwater levels in a semi-arid hard-rock aquifer of Western India. Monthly groundwater levels of 50 sites in the study area for 36-month period (May 2006 to June 2009; excluding 3 months) were analyzed to find spatial autocorrelation and variances in the groundwater levels. Experimental variogram of the observed groundwater levels was computed at 750-m lag distance interval and the four most-widely used geostatistical models were fitted to the experimental variogram. The best-fit geostatistical model was selected by using two goodness-of-fit criteria, i.e., root mean square error (RMSE) and correlation coefficient (r). Then spatial maps of the groundwater levels were prepared through kriging technique by means of the best-fit geostatistical model. Results of two spatial statistics (Geary’s C and Moran’s I) indicated a strong positive autocorrelation in the groundwater levels within 3-km lag distance. It is emphasized that the spatial statistics are promising tools for geostatistical modeling, which help choose appropriate values of model parameters. Nugget-sill ratio (<0.25) revealed that the groundwater levels have strong spatial dependence in the area. The statistical indicators (RMSE and r) suggested that any of the three geostatistical models, i.e., spherical, circular, and exponential, can be selected as the best-fit model for reliable and accurate spatial interpolation. However, exponential model is used as the best-fit model in the present study. Selection of the exponential model as the best-fit was further supported by very high values of coefficient of determination (r ² ranging from 0.927 to 0.994). Spatial distribution maps of groundwater levels indicated that the groundwater levels are strongly affected by surface topography and the presence of surface water bodies in the study area. Temporal pattern of the groundwater levels is mainly controlled by the rainy-season recharge and amount of groundwater extraction. Furthermore, it was found that the kriging technique is helpful in identifying critical locations over the study area where water saving and groundwater augmentation techniques need to be implemented to protect depleting groundwater resources.     

The comap as a diagnostic tool for non-stationary kriging models

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.