基于Kriging的地形高程插值

将地形高程作为区域化变量,根据普通Kriging法由散乱的高程点进行地形高程插值,并采用Matlab软件开发专门的程序,实现研究区高程插值计算与结果可视化分析。以广州市南沙区10 km2范围内的200个高程点数据为例,分别运用球面模型、指数模型和高斯理论变差函数模型进行10 m×10 m格网插值,借助Matlab可视化分析插值结果及其精度,表明采用指数模型效果最好。     

山区地形开阔度的分布式模型

 地形开阔度是影响山地辐射平衡及其分量的重要地形因子,是山区散射辐射、地形反射辐射等计算的重要参数。在复杂的地形条件下,地形开阔度的计算很难用数学公式描述。 利用数字高程模型（DEM）,全面考虑了坡地自身遮蔽和周围地形相互遮蔽的影响,提出了山区地形开阔度的分布式模型和算法。以1 km×1 km分辨率的DEM数据作为地形的综合反映,计算了起伏地形下中国地形开阔度的空间分布。同时,利用100 m和1 km两个分辨率的DEM数据,从不同DEM分辨率和不同地貌类型两个方面探讨了地形开阔度的空间尺度效应,阐明了区域地形开阔度随地形地貌和空间分辨率的变化规律。所提供的山地开阔度的数据可作为基础地理数据供相关研究应用。     

DEM提取黄土高原地面坡度的不确定性

选择陕北黄土高原6个典型地貌类型区为试验样区,采用野外实测及高精度的1:1万比例尺DEM为基准数据,研究栅格分辨率及地形粗糙度对DEM所提取地面平均坡度精度的影响。结果显示,对于1:1万比例尺DEM,5 m是保证该地区地形描述精度的理想分辨率尺度;多要素逐步回归模拟的方法进一步揭示了DEM所提取的地面平均坡度误差E与栅格分辨率X以及地形起伏的代表性因子-沟壑密度S之间存在的量化关系为E = (0.0015S2+0.031S-0.0325)X-0.0045S2-0.155S+0.1625,该结果也为确定适用的DEM分辨率提供了理论依据。     

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。     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

SRTM DEM高程精度评价

为了全面认识SRTM DEM数据精度特征并完善SRTM DEM数据精度评定方法,该文以我国1∶5万比例尺DEM为参考数据,以具有多种地貌类型的陕西省为实验样区,利用高程中误差模型及空间插值方法对SRTMDEM进行高程精度分析。结果表明:陕西省的SRTM DEM高程中误差在3.5~60.7 m,呈现出较为显著的空间分异特征;并且高程中误差与实验样区平均坡度有较强的指数相关性,拟合的指数函数具有较高的模拟精度。     

An orthogonal least-square-based method for DEM generalization

A new method based on orthogonal least square (OLS) of multiquadric algorithm (MOLS) is proposed for digital elevation model (DEM) generalization by the retrieval of critical points from a grid-based DEM to construct a triangulated irregular network surface. The focus is on the method for accurately obtaining the critical points, which maximally retain the important terrain feature lines. The grid-based DEM to be generalized is first approximated in terms of multiquadric method, and then the significances of the grids are assessed based on OLS method with the merit that each selected grid point gives the maximal increment to the explained variance of the desired output. We used six study sites with different terrain complexities to comparatively analyze the generalization accuracies of MOLS and the classical methods including very important method and point-additive method (Latticetin) under different numbers of retrieved significant points. The results indicate that MOLS averagely performs better than the classical methods for the original DEM generalization in terms of root mean square error. The analytical results also show that MOLS has the better ability in maintaining the feature lines inherent in the original DEM than the classical methods in terms of streamline matching rate. The perfect performance of the newly proposed method can be attributed to the high accuracy of multiquadric method for surface approximation and the effectiveness of OLS for point significance assessment.     

薄盘光滑样条插值中三种协变量方法的降水量插值精度比较

在薄盘光滑样条插值中,高相关协变量的选取决定了插值结果的精确性。以2001-2009年全国728个气象站点日降水为数据源,提取年降水量数据,在分析多年平均降水量与两协变量高程（DEM）和距海岸线距离（DCL）的空间相关性基础上,利用ANUSPLIN软件,比较不同协变量下降水量插值结果精度在全国尺度以及区域尺度上的差异。以DEM、DCL及DEM-DCL分别为协变量对降水量数据进行空间插值发现：①在全国尺度上,DEM法的平均绝对误差（MAE）为47.79,略低于DEM-DCL法（48.90）,但显著低于DCL法（55.54）;且DEM法的平均相对误差和均方根误差也明显低于其它两种方法。②在区域尺度上,除西藏地区外的其他7个区域,3种方法的插值误差与全国尺度上相一致。西藏地区降水插值结果以DCL法的精度最高,而DEM法则较差。研究建议除在西藏地区的降水量插值研究中采用DCL法,在全国其他大部分区域采用DEM法。     

复杂地形条件下风速插值研究——以吉林省为例

以ARCGIS为平台,利用吉林省1∶25万DEM数据,土地利用数据和气象台站资料,在Kriging插值的基础上,综合考虑下垫面、海拔高度、坡度、坡向和坡位等地形要素对风速的影响,对吉林省的冬季风风速分布进行模拟。研究结果表明,基于地形因子的风速校正有效提高了风速插值的精度,可以作为风速插值方法的有效补充,实现复杂地形条件下风速的精确模拟。     

顾及风向和风速的气温空间插值方法

当前气温插值方法多将高程、经纬度等作为影响因素,无法解决风向、风速对气温空间分布的影响问题。该文提出一种顾及风向和风速的气温空间插值方法:1)根据气象观测站点的风向、风速数据进行插值,生成连续的风场表面;2)基于该风场数据利用高斯扩散模型构建成本表面;3)利用Dijkstra最短路径算法计算观测点与待求点的累计移动成本最短路径(SPOCMC);4)将SPOCMC作为协变量进行薄盘光滑样条插值以实现气温插值。为验证该方法的有效性和可靠性,选取山东省109个气象观测点样本数据,以SPOCMC、DEM和SPOCMC-DEM分别作为协变量对气温数据进行薄盘光滑样条插值,结果显示:SPOCMC-DEM法的MAE和RMSE均值(分别为0.517、0.779)略低于SPOCMC法(0.583、1.016),显著低于DEM法(0.809、1.231),表明添加SPOCMC作为协变量可有效提高气温空间插值的准确性。在江苏省与贵州省的插值实验结果证明了该方法的普适性。     

起伏地形下黄河流域太阳直接辐射分布式模拟

基于数字高程模型(DEM)数据和气象站观测资料建立了起伏地形下太阳直接辐射分布式计算模型,模型充分考虑了地形因子(坡向、坡度、地形相互遮蔽)对起伏地形下太阳直接辐射空间分布的影响;以1km×1km分辨率的DEM数据作为地形的综合反映,计算了起伏地形下黄河流域1km×1km分辨率太阳直接辐射的空间分布;深入分析了起伏地形下太阳直接辐射受地理、地形因子影响的变化规律。结果表明:受地形起伏和坡向、坡度等局地地形因子的影响,山区年太阳直接辐射量的空间差异比较明显,向阳山坡(偏南坡)的年直接辐射量明显高于背阴山坡(偏北坡)     

基于站点观测数据的气温空间化方法评述

基于统计学的插值方法是地理学、生态学领域研究气温空间化的主要方法之一,对获取精细化气温数据进行生态模拟具有重要意义。结合国内外气温空间插值的主要研究成果,对常用气温空间化方法进行了归纳、对比,探讨各种方法的适用性和不足之处,从而为涉及气温空间化的具体研究提供一定的参考,并探讨了各类方法优化的方向。不同方法的对比分析结果表明:各种气温空间化方法各有所长,在具体的应用中都取得过较好的效果,但并不存在普适性的方法,在实际应用时必须针对研究区域具体的地理特征进行方法适用性验证或对各类方法中的具体参数进行改进,才能实现区域气温的空间最优化模拟。根据气温场的物理分布特征,结合GIS技术,考虑地形等更多的相关因子以提高气温分布微观细节的模拟精度是未来重要的发展趋势。     

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.     

Extended hybrid meshing algorithm for multiresolution terrain models

Hybrid terrains are a convenient approach for the representation of digital terrain models, integrating heterogeneous data from different sources. In this article, we present a general, efficient scheme for achieving interactive level-of-detail rendering of hybrid terrain models, without the need for a costly preprocessing or resampling of the original data. The presented method works with hybrid digital terrains combining regular grid data and local high-resolution triangulated irregular networks. Since grid and triangulated irregular network data may belong to different datasets, a straightforward combination of both geometries would lead to meshes with holes and overlapping triangles. Our method generates a single multiresolution model integrating the different parts in a coherent way, by performing an adaptive tessellation of the region between their boundaries. Hence, our solution is one of the few existing approaches for integrating different multiresolution algorithms within the same terrain model, achieving a simple interactive rendering of complex hybrid terrains.     

Historic reconstruction of reservoir topography using contour line interpolation and structure from motion photogrammetry

The geometry of impounded surfaces is a key tool to reservoir storage management and projection. Yet topographic data and bathymetric surveys of average-aged reservoirs may be absent for many regions worldwide. This paper examines the potential of contour line interpolation (TOPO) and Structure from Motion (SfM) photogrammetry to reconstruct the topography of existing reservoirs prior to dam closure. The study centres on the Paso de las Piedras reservoir, Argentina, and assesses the accuracy and reliability of TOPO- and SfM- derived digital elevation models (DEMs) using different grid resolutions. All DEMs were of acceptable quality. However, different interpolation techniques produced different types of error, which increased (or decreased) with increasing (or decreasing) grid resolution as a function of their nature, and relative to the terrain complexity. In terms of DEM reliability to reproduce area–elevation relationships, processing-related disagreements between DEMs were markedly influenced by topography. Even though they produce intrinsic errors, it is concluded that both TOPO and SfM techniques hold great potential to reconstruct the bathymetry of existing reservoirs. For areas exhibiting similar terrain complexity, the implementation of one or another technique will depend ultimately on the need for preserving accurate elevation (TOPO) or topographic detail (SfM).     

Topodata: Brazilian full coverage refinement of SRTM data

This work presents the selection of a set of geostatistical coefficients suitable for a unified SRTM data refinement from 3″ to 1″ through kriging over the entire Brazilian territory. This selection aimed at data potential for geomorphometric derivations, given by the preservation of detailed geometric characteristics of the resulting digital elevation models (DEM), which are sensitive to refining procedures. The development contained a long-term experimentation stage, when data refinement through kriging was locally developed to support distinct regional projects, followed by a unified selection stage, where the acquired experience was applied to select a single and unified interpolation scheme. In this stage, the selected geostatistical models with promising performances were tested for unified refinement on 40 Brazilian areas with distinct geological settings. Tested areas encompass reliefs varying from mountainous to plain. The effects of data preparation were observed on the perception of patterns (texture and roughness), as well as of singularities (edges, peaks, thalwegs etc.). Results were evaluated mainly through the examination of shaded reliefs, transects and perspectives observed in different scales. Terrains with low slopes and small amplitudes had their DEM promptly affected by the refining methods, as opposed to mountainous terrains. The evaluation, unambiguously confirmed by all consulted interpreters, converged into a refining model with outstanding performance in all tested conditions.     

基于DEM的黄河流域天文辐射空间分布

基于1 km×1 km分辨率的数字高程模型(DEM) 数据,利用建立的起伏地形下天文辐射分布式计算模型,计算了黄河流域1 km×1 km分辨率各月天文辐射的空间分布。结果表明:局部地形对黄河流域年和四季天文辐射的空间分布影响明显;在太阳高度角较低的冬季,地理和地形因子对天文辐射的影响相当强烈,山区天文辐射的空间差异大,1月份向阳山坡(偏南坡) 天文辐射可为背阴山坡(偏北坡) 的2~3倍,极端天文辐射的差异可达10倍以上;而在太阳高度角较高的夏季,天文辐射空间差异较小,7月份不同地形极端天文辐射的差异仅在16%左右;四季中,地形对天文辐射影响的程度为冬季>秋季>春季>夏季。     

数字地形模型在濒危动物生境研究中的应用

本文建立了卧龙自然保护区２０００ｋｍ２范围的数字地形模型,并将其应用在濒危珍稀动物大熊猫的生境研究上。通过计算机叠加大熊猫可分布的高度、坡度及竹子分布区域,获得了大熊猫在卧龙自然保护区内的潜在生境区,其比实际的熊猫分布范围大出近一倍,文章还对潜在生境的适宜性进行了划分。     

中国中部六省预期寿命时序加密估算研究

年龄组死亡率是利用年龄分组人口数据计算预期寿命的关键参数,而非采样年份的统计年鉴中年龄分组死亡率缺失导致无法计算预期寿命。针对该问题,本文将人口普查数据与统计年鉴数据融合,首次提出一种基于拉格朗日插值的中国省级预期寿命时间序列加强密集度（时序加密）的算法,以解决非采样（即未进行人口普查或1%人口抽样调查）年份省级预期寿命的估算问题。以中国中部六省为例,在所选取年份省级预期寿命估算实验中,绝对精度表明年龄分组人口比例线性插值计算的精度明显高于人口比例抛物线插值和直接插值算法的精度,故为推荐算法。本研究为高时间分辨率下省级预期寿命值的获取提供了一个新的可行思路,为分省较精确地进行预期寿命趋势分析奠定基础。     

一种基于坡度分析的DEM数字水印算法

提出一种新的基于坡度分析的DEM数字水印算法.该算法以DEM坡度为主要研究对象,由于坡度误差主要集中在平坦地区,而经小波变换后的DEM低频系数信息可反映DEM区域的地形复杂度,因此,通过对DEM低频系数进行分析,可自适应地确定水印的嵌入位置;然后以加性法则将水印信息嵌入低频系数,再经小波逆变换,即可得到含水印信息的DEM数据.实验结果表明,该算法能完全满足水印的不可见性,对DEM数据的高程精度、坡度精度及等高线的提取精度影响都很小,能够满足一定的应用要求,且具有良好的抗噪能力.