Measuring the accuracy of contour interpolated digital elevation models

Digital elevation models (DEM) are becoming increasingly important as tools in hydrological research and water resources management. Since error and uncertainty are inherently associated with spatial data, a complete evaluation of a DEM is of utmost importance before it is put into subsequent analysis. The present paper offers an innovative approach for quality assessment of contour interpolated DEMs of different resolutions. Five most frequently cited interpolation methods viz., TIN with linear interpolation, Inverse Distance Weighing, Thin Plate Spline, Ordinary Kriging and TOPOGRID were selected for gridding of contours at five different resolutions i.e., 30m, 45m, 60m, 75m and 90m. In order to compare the quality of interpolated DEMs, a qualitative and quantitative evaluation of inter-polated DEMs for their vertical, horizontal and shape accuracy were carried out. It was found that different interpolation methods produced DEMs with different levels of artifacts. The analyses of vertical accuracy suggested that the variations were not pronounced in nature. However, the quantitative comparisons for horizontal and shape accuracy showed that there was a high level of disparity with significant differences among the interpolated DEMs.     

THE ACCURACY OF DIGITAL ELEVATION MODELS DERIVED FROM DIGITISED CONTOUR DATA

Although accuracy of digital elevation models (DEMs) can be quantified and measured in different ways, each is influenced by three main factors: terrain character, sampling strategy and interpolation method. These parameters, and their interaction, are discussed. The generation of DEMs from digitised contours is emphasised because this is the major source of DEMs, particularly within member countries of OEEPE. Such DEMs often exhibit unwelcome artifacts, depending on the interpolation method employed. The origin and magnitude of these effects and how they can be reduced to improve the accuracy of the DEMs are also discussed.     

Comparison of basin morphometry derived from topographic maps,ASTER and SRTM DEMs: an example from Kerala,India

The drainage network of a sixth-order tropical river basin, viz. Ithikkara river basin, was extracted from different sources such as Survey of India topographic maps (1: 50,000; TOPO) and digital elevation data of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (30 m) and Shuttle Radar Topography Mapping Mission (SRTM) (90 m). Basin morphometric attributes were estimated to evaluate the accuracy of the digital elevation model (DEM)-derived drainage networks for hydrologic applications as well as terrain characterization. The stream networks derived from ASTER and SRTM DEMs show significant agreement (with slight overestimation of lower order streams) with that of TOPO. The study suggests that SRTM (despite the coarser spatial resolution) provides better results, in drainage delineation and basin morphometry, compared to ASTER. Further, the variability of basin morphometry among the data sources might be attributed to spatial variation of elevation, raster grid size and vertical accuracy of the DEMs as well as incapability of the surface hydrologic analysis functions in the GIS platform.     

Modelling and Remote Sensing of Land Surface Temperature in Turkey

This study introduces artificial neural networks (ANNs) for the estimation of land surface temperature (LST) using meteorological and geographical data in Turkey (26?C45°E and 36?C42°N). A generalized regression neural network (GRNN) was used in the network. In order to train the neural network, meteorological and geographical data for the period from January 2002 to December 2002 for 10 stations (Adana, Afyon, Ankara, Eski?ehir, ?stanbul, ?zmir, Konya, Malatya, Rize, Sivas) spread over Turkey were used as training (six stations) and testing (four stations) data. Latitude, longitude, elevation and mean air temperature are used in the input layer of the network. Land surface temperature is the output. However, land surface temperature has been estimated as monthly mean by using NOAA-AVHRR satellite data in the thermal range over 10 stations in Turkey. The RMSE between the estimated and ground values for monthly mean with ANN temperature(LST_ANN) and Becker and Li temperature(LST_B-L) method values have been found as 0.077?K and 0.091?K (training stations), 0.045?K and 0.003?K (testing stations), respectively.     

基于CryoSat-2测高数据的南极局部地区DEM的建立与精度评定

南极数字高程模型(DEM)是南极冰盖变化研究的基础数据,在我国南极重点考察地区Dome A及中山站至Dome A考察断面,利用新一代测高卫星CryoSat-2,对常用的几种插值方法如反距离加权、克里金、径向基函数、局部多项式和最近邻点插值方法的插值精度进行交叉比较,结果显示克里金插值方法的精度最高。利用中国第21次南极科学考察队采集的GPS数据,对克里金插值方法生成的两个区域的DEM精度进行验证。结果表明,坡度较小的Dome A区域DEM精度较高,平均高差为1.248 m,标准差为0.51 m;坡度较大的中山站至Dome A断面区域DEM精度较低,平均高程差达到3.87 m,标准差为9.358 m。     

Interpolation Methods for Scattered Sample Data: Accuracy,Spatial Patterns,Processing Time

Interpolation routines based on polynomials, splines, linear triangulation, proximation, distance weighting, and kriging are tested on their efficacy to visualize spatial patterns. Implementations in commonly available software packages are used in order to yield practical recommendations on the application of current information technology. Two data sets of physical variables containing irregularly distributed sample point values are used as input data. Accuracy of predicted values at unvisited points, preservation of distinct spatial patterns (established from map use tasks), and processing time, are used as criteria to determine the merits of the various interpolation methods. It was found that highly accurate interpolations do not always produce realistic spatial patterns. Effectiveness of distance weighting and kriging methods was found to be largely dependent on the number of neighbors used. For both gradually and abruptly changing data, geographic reality was visualized most satisfactorily with the squared inverse distance weighting (w=d^-2 ) method using respectively few (four to eight) and many (16 to 24) neighbors.     

干热河谷冲沟DEM插值误差的空间分布研究

为了分析云南元谋干热河谷典型冲沟插值误差的空间分布特征,采用反距离加权（inverse distance weighting,IDW）、局部多项式（local polynomial interpolation,LPI）、张力样条（spline with tension,ST）、析取克里格（disjunctive Kriging,DK）以及不规则三角网（triangulated irregular network,TIN）模型方法对高程采样点进行插值,用交叉验证法、相对差系数及沟谷线差异衡量其插值精度。遴选高程误差大于1 m的误差点,用变异系数（coefficient of variation,CV）、全局Moran指数和Getis-Ord G_i*指数分析其空间格局特征。结果表明:TIN和DK精度较高,IDW精度最低;高程误差均呈聚集分布,聚集程度TIN > LPI > DK > ST > IDW;高程误差均呈空间正自相关,TIN模型插值误差的自相关程度最高;误差热点位于坡度大的区域。     

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.     

Efficient collection of training data for sub-pixel land cover classification using neural networks

Artificial neural networks (ANNs) are a popular class of techniques for performing soft classifications of satellite images. They have successfully been applied for estimating crop areas through sub-pixel classification of medium to low resolution images. Before a network can be used for classification and estimation, however, it has to be trained. The collection of the reference area fractions needed to train an ANN is often both time-consuming and expensive. This study focuses on strategies for decreasing the efforts needed to collect the necessary reference data, without compromising the accuracy of the resulting area estimates. Two aspects were studied: the spatial sampling scheme (i) and the possibility for reusing trained networks in multiple consecutive seasons (ii). Belgium was chosen as the study area because of the vast amount of reference data available. Time series of monthly NDVI composites for both SPOT-VGT and MODIS were used as the network inputs. The results showed that accurate regional crop area estimation (R² > 80%) is possible using only 1% of the entire area for network training, provided that the training samples used are representative for the land use variability present in the study area. Limiting the training samples to a specific subset of the population, either geographically or thematically, significantly decreased the accuracy of the estimates. The results also indicate that the use of ANNs trained with data from one season to estimate area fractions in another season is not to be recommended. The interannual variability observed in the endmembers’ spectral signatures underlines the importance of using up-to-date training samples. It can thus be concluded that the representativeness of the training samples, both regarding the spatial and the temporal aspects, is an important issue in crop area estimation using ANNs that should not easily be ignored.     

Topographic correction of ALOS-PALSAR images using InSAR-derived DEM

Topographic corrections of synthetic aperture radar (SAR) images over hilly regions are vital for retrieval of correct backscatter values associated with natural targets. The coarse resolution external digital elevation models (DEM) available for topographic corrections of high resolution SAR images often result into degradation of spatial resolution or improper estimation of backscatter values in SAR images. Also, many a times the external DEMs do not spatially co-register well with the SAR data. The present study showcases the methodology and results of topographic correction of ALOS-PALSAR image using high resolution DEM generated from the same data. High resolution DEMs of Jaipur region, India were generated using multiple pair SAR images acquired from ALOS-PALSAR using interferometric (InSAR) techniques. The DEMs were validated using differential global positioning system measured elevation values as ground control points and were compared with photogrammetric DEM (advanced spaceborne thermal emission and reflection radiometer – ASTER) and SRTM (Shuttle Radar Topography Mission) DEM. It was observed that ALOS-PALSAR images with optimum baseline parameters produced high resolution DEM with better height accuracy. Finally, the validated DEM was used for topographic correction of ALOS-PALSAR images of the same region and were found to produce better result as compared with ASTER and SRTM-DEM.     

DEM Fusion using a modified k-means clustering algorithm

Digital elevation models (DEMs) are a necessary dataset for modelling the Earth’s surface; however, all DEMs contain error. Researchers can reduce this error using DEM fusion techniques since numerous DEMs can be available for a region. However, the use of a clustering algorithm in DEM fusion has not been previously reported. In this study a new DEM fusion algorithm based on a clustering approach that works on multiple DEMs to exploit consistency in the estimates as indicators of accuracy and precision is presented. The fusion approach includes slope and elevation thresholding, k-means clustering of the elevation estimates at each cell location, as well as filtering and smoothing of the fusion product. Corroboration of the input DEMs, and the products of each step of the fusion algorithm, with a higher accuracy reference DEM enabled a detailed analysis of the effectiveness of the DEM fusion algorithm. The main findings of the research were: the k-means clustering of the elevations reduced the precision which also impacted the overall accuracy of the estimates; the number of final cluster members and the standard deviation of elevations before clustering both had a strong relationship to the error in the k-means estimates.     

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.     

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.     

Effect of the SRTM global DEM on the determination of a high-resolution geoid model: a case study in Iran

Any errors in digital elevation models (DEMs) will introduce errors directly in gravity anomalies and geoid models when used in interpolating Bouguer gravity anomalies. Errors are also propagated into the geoid model by the topographic and downward continuation (DWC) corrections in the application of Stokes’s formula. The effects of these errors are assessed by the evaluation of the absolute accuracy of nine independent DEMs for the Iran region. It is shown that the improvement in using the high-resolution Shuttle Radar Topography Mission (SRTM) data versus previously available DEMs in gridding of gravity anomalies, terrain corrections and DWC effects for the geoid model are significant. Based on the Iranian GPS/levelling network data, we estimate the absolute vertical accuracy of the SRTM in Iran to be 6.5 m, which is much better than the estimated global accuracy of the SRTM (say 16 m). Hence, this DEM has a comparable accuracy to a current photogrammetric high-resolution DEM of Iran under development. We also found very large differences between the GLOBE and SRTM models on the range of −750 to 550 m. This difference causes an error in the range of −160 to 140 mGal in interpolating surface gravity anomalies and −60 to 60 mGal in simple Bouguer anomaly correction terms. In the view of geoid heights, we found large differences between the use of GLOBE and SRTM DEMs, in the range of −1.1 to 1 m for the study area. The terrain correction of the geoid model at selected GPS/levelling points only differs by 3 cm for these two DEMs.     

The isotropic organization of DEM structure and extraction of valley lines using hexagonal grid

The automatic extraction of valley lines (VLs) from digital elevation models (DEMs) has had a long history in the GIS and hydrology fields. The quality of the extracted results relies on the geometrical shape, spatial tessellation, and placement of the grids in the DEM structure. The traditional DEM structure consists of square grids with an eight‐neighborhood relationship, where there is an inconsistent distance measurement between orthogonal neighborhoods and diagonal neighborhoods. The directional difference results in the extracted VLs by the D8 algorithm not guaranteeing isotropy characteristics. Alternatively, hexagonal grids have been proved to be advantageous over square grids due to their consistent connectivity, isotropy of local neighborhoods, higher symmetry, increased compactness, and more. Considering the merits above, this study develops an approach to VL extraction from DEMs based on hexagonal grids. First, the pre‐process phase contains the depression filling, flow direction calculation, and flow accumulation calculation based on the six‐neighborhood relationship. Then, the flow arcs are connected, followed by estimating the flow direction. Finally, the connected paths are organized into a tree structure. To explore the effectiveness of hexagonal grids, comparative experiments are implemented against traditional DEMs with square grids using three sample regions. By analyzing the results between these two grid structures via visual and quantitative comparison, we conclude that the hexagonal grid structure has an outstanding ability in maintaining the location accuracy and bending characteristics of extracted valley networks. That is to say, the DEM‐derived VLs based on hexagonal grids have better spatial agreement with mapped river systems and lower shape diversion under the same resolution representation. Therefore, the DEMs with hexagonal grids can extract finer valley networks with the same data volume relative to traditional DEM.     

多目标微观邻域粒子群算法及其在土壤空间优化抽样中的应用

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。     

QUALITY CONTROL OF PHOTOGRAMMETRICALLY SAMPLED DIGITAL ELEVATION MODELS

The object of this paper is to study the geometric accuracy of photogrammetrically sampled digital elevation models (DEMs)obtained by using an on line graphical DEM editor. As a reference, DEMs obtained by regular grid measurements have been used. Three different test areas are used in the study, each representing different ground types and degrees of homogeneity. The DEMs have been evaluated with respect to their standard errors in elevation, slope and curvature. The results show that the standard errors are not improved by using the on line DEM editor. It is also demonstrated that an increased point density decreases the standard error in elevation while its effect on the standard error in slope is limited. The standard error in curvature is almost independent of the point density.     

A total error-based multiquadric method for surface modeling of digital elevation models

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that MQ-T performs better than the classical MQ in terms of root mean square error. The real-world example of DEM construction with sample points derived from a total station instrument demonstrates that regardless of the sample interval and DEM resolution, MQ-T is more accurate than classical interpolation methods including inverse distance weighting, ordinary kriging, and Australian National University DEM. Therefore, MQ-T can be considered as an alternative interpolator for surface modeling with sample points subject to both horizontal and vertical errors.     

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.     

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.