航测数据处理中的空间插值方法比较

航测数据的航线间距与采样点间距差异很大,生成等值线时需要进行空间插值.以云南省江川地区的航测数据为实验数据源,分别采用反距离权重插值(IDW)、规则样条函数插值(Regularized Spline)、张力样条函数(Tension Spline)插值和Kriging插值等4种插值方法,对航测数据进行分析与比较,从中选出...     

Noisy Data Smoothing in DEM Construction Using Least Squares Support Vector Machines

Since spatial datasets are subject to sampling errors, a smoothing interpolation method should be employed to remove noise during DEM construction. Although least squares support vector machines (LSSVM) have been widely accepted as a classifier, their effect on smoothing noisy data is almost unknown. In this article, the smoothness of LSSVM was explored, and its effect on smoothing noisy data in DEM construction was tested. In order to improve the ability to deal with large datasets, a local method of LSSVM has been developed, where only the neighboring sampling points around the one to be estimated are used for computation. A numerical test indicated that LSSVM is more accurate than the classical smoothing methods including TPS and kriging, and its error surfaces are more evenly distributed. The real‐world example of smoothing noise inherent in lidar‐derived DEMs also showed that LSSVM has a positive smoothing effect, which is approximately as accurate as TPS. In short, LSSVM with a high efficiency can be considered as an alternative smoothing method for smoothing noisy data in DEM construction.     

A New GIS-based Solar Radiation Model and Its Application to Photovoltaic Assessments

The solar radiation model r.sun is a flexible and efficient tool for the estimation of solar radiation for clear‐sky and overcast atmospheric conditions. In contrast to other models, r.sun considers all relevant input parameters as spatially distributed entities to enable computations for large areas with complex terrain. Conceptually the model is based on equations published in the European Solar Radiation Atlas (ESRA). The r.sun model was applied to estimate the solar potential for photovoltaic systems in Central and Eastern Europe. The overcast radiation was computed from clear‐sky values and a clear‐sky index. The raster map of the clear‐sky index was computed using a multivariate interpolation method to account for terrain effects, with interpolation parameters optimized using a cross‐validation technique. The incorporation of terrain data improved the radiation estimates in terms of the model's predictive error and the spatial pattern of the model outputs. Comparing the results of r.sun with the ESRA database demonstrates that integration of the solar radiation model and the spatial interpolation tools in a GIS can be especially helpful for data at higher resolutions and in regions with a lack of ground measurements.     

基于ArcEngine的等雨量线绘制

等雨量线的绘制是济南城市防汛预警决策支持系统中最基本的功能之一。等雨量线的绘制最关键的部分为用已有站点的雨量数据进行空间插值,生成连续的雨量栅格图,再将雨量值相等的点连成等雨量线。本文用ESRI提供的ArcEngine组件实现了反距离加权插值（IDW）、样条函数插值（Spline）、克里金插值（Kriging）3种常用的插值方法,结合济南市现有的31个雨量站点的雨量数据,分别绘制出等雨量线,并比较3种插值方法的插值结果。结果表明：3种插值方法的结果都基本上反映了济南降雨的空间分布规律,而克里金插值的效果最好。     

基于RASM的紧支撑径向基函数自适应并行地形插值方法

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。     

亚热带山地丘陵区气象要素空间化方法分析

空间连续的气象要素是区域环境、生态系统模拟的重要参数,空间插值是实现气象观测站点数据空间化的主要方法。由于不同区域气候要素时空分布的复杂性,研究适用于特定区域的空间化方法具有重要意义。本文以湖南省为研究区,分析长江中游亚热带丘陵区气象要素的空间化方法。基于湖南省及其毗邻地区的46个气象站点14年(2000—2013年)的气象观测数据(月降水量、月均温)和DEM数据,对普通克里金法(OK)、反距离加权法(IDW)、样条法(SPLINE)和基于DEM的多元线性回归插值法(MLR)进行比较分析研究。研究结果表明:1)月降水量和月均温的MRE和RMISE值排序分别为:SPLINEIDWMLROK和SPLINOKIDWMLR;年平均降水量和年均温插值的MRE和RMISE值排序分别为:SPLINEIDWOKMLR和SPLINOKIDWMLR;2)MLR法不仅插值误差小,而且能从细节上反映出气象变化的空间变异性;3)对多变量进行数据探索分析表明,MLR插值法中,经度、坡度与年降水量空间分布存在空间的一致性;纬度、高程和坡度对年均温的空间分布具有很强的解释力。     

复杂地形景区三维导览图的设计与实现

为满足复杂地形景区对三维地图导览的需求,构建更为清晰的三维地图模型,提供良好的三维导览地图设计方案显得尤为重要。为了更好地与卫星影像进行贴合,DEM数据的采样密度要与卫星影像的分辨率一致。本文通过对比当下常用的四种空间插值方法的适用范围与运用特点,设置相关阈值及权重,直观比较了四种插值方法产生的插值结果,选择更适合复杂景区DEM插值的插值方法并对其进行精度提升,以此得到符合精度要求的DEM数据。最后利用相应地区的卫星影像进行地图投影及影像贴图,两种数据结合构建复杂景区的三维地图模型,给游客带来更为精确直观的定位信息和空间要素信息。     

基于空间变异修正普通克里金的矿区复杂地形高精度建模

普通克里金法是构建矿区三维地形模型并揭示地表沉陷形变场动态变化规律的有效方法。但普通克里金法存在平滑效应的问题,导致估计值的空间变异程度小于实际,无法真实反映矿区复杂地表形态的空间变化特征。本文结合矿区实际地形采样数据,提出了一种空间变异修正的普通克里金法,并将其应用于矿区复杂地形的高精度建模,并与已有方法在建模精度和空间变异性复现方面进行了对比分析。研究结果表明,空间变异修正的普通克里金法能够很好地处理平滑效应对建模的影响,具有更高的建模精度和空间变异性复现能力,在矿区复杂地形高精度建模应用中具有较强的适用性,可以作为一种可靠的建模工具用于矿区复杂地形沉陷形变场动态变化规律分析。     

时序变差函数特征驱动下的月平均降水空间分布模拟

高精度降水场是水文、气象以及环境分析的重要数据支撑,直接影响相关服务的准确性。传统降水分布模拟大多依赖站点空间维的驱动因素,而忽略了降水时序变化特征对其空间分布的影响。使用2015—2017年中国湖北省83个国家气象观测站点和28个省级观测站点近3 a月平均累积降水资料,通过相关性分析,引入站点降水时序理论变差函数模型的拱高值(C)和块金值(C₀)作为影响因素,使用地理加权回归(geographically weighted regression, GWR)建立湖北省月平均降水分布模型。结果表明:（1）各站点降水的时序变差函数曲线与降水的季节性基本吻合。站点时序理论变差函数模型中,有25.3%能够在4个月内达到平稳,36.14%在6个月内达到平稳。（2）站点降水时序理论变差函数模型的C和C₀与逐年12月平均累积降水在0.01水平（双侧）上显著相关,平均相关系数分别为0.745和0.526,大于地理位置和高程对降水的影响。（3）引入C和C₀ 有助于提升GWR模型的整体拟合优度和插值精度。对比仅使用经纬度的GWR模型和引入时序理论变差函数特征的GWR模型,3 a平均整体拟合优度从0.852提升至0.912。验证集站点插值精度评价显示,3 a绝对误差、均方根误差和平均绝对百分误差下降幅度均大于60%。因此,引入时序理论变差函数特征的时空GWR模型能够获得较高精度的降水模拟结果,更适合具有丰富历史降水资料地区的降水空间分布估算。     

A new machine learning paradigm for terrain reconstruction

Terrain models that permit multiresolution access are essential for model predictive control of unmanned aerial vehicles in low-level flights. The authors present the extreme learning machine (ELM), a recently proposed learning paradigm, as a mechanism for learning the stored digital elevation information to allow multiresolution access. We give results of simulations designed to compare the performance of our approach with two other approaches for multiresolution access, namely: 1) linear interpolation on Delaunay triangles of the sampled terrain data points and 2) terrain learning using support vector machines (SVMs). The results show that to achieve the same mean square error during access, the memory needed in our approach is significantly lower. Additionally, the offline training time for the ELM network is much less than that for the SVM.     

分形模拟在DEM内插中的应用

为提高DEM的空间分辨率,避免线性插值方法的平滑和低通滤波作用,本文依据地形的分数布朗运动(FBM)特性,提取地形的分形参数,利用分形模拟方法进行插值,并将不同地形的试验结果与线性插值方法进行比较和分析。结果表明该方法能较好保持地形的随机性、不规则性和丰富的细节信息,同时也具有一定的插值精度。     

顾及邻近关系的NPP/VIIRS序列影像时空插值方法

针对可见红外成像辐射仪(visible infrared imaging radiometer suite,VIIRS)月度夜光遥感影像的数据缺失问题,提出一种利用地物邻近关系相关性的像元时空插值方法,以时、空关系互相作为约束条件,将时序变化一致性较好的像元数据作为空间插值的参考,将空间关系一致性较好的月度数据作为时序插值的参考,通过构建不同的卷积核, 在时序和空间维度分别对初步插值结果进行卷积运算,求得待插值像元的时空插值。以2015年江苏省月度夜光遥感影像修复为例,对不同维度时空插值方法进行对比分析,结果表明, 空间维度插值虽然顾及到像元的空间关联性,仍无法满足数据大范围缺失的插值要求,插值结果整体偏低;时间维度插值考虑到像元的时间趋势性,插值精度较空间维度插值有一定提高,但部分月份插值结果有较大偏差;相对于三次Hermit插值,时空插值方法获得的月度影像灯光亮度总和的最大相对误差、年度影像灯光亮度总和相对误差以及逐像元差值均显著降低。总的来看,所提时空插值方法在插值过程中同时顾及到VIIRS数据的时间趋势平稳性和空间结构稳定性,影像插值精度提高明显,且对待插值月份前后时序数据没有严格要求,更具有广泛性。     

京津冀地区GNSS对流层延迟空间插值研究

对流层延迟差异影响合成孔径雷达干涉测量技术(InSAR)形变测量精度;水汽的变化影响天气变化．对流层延迟与水汽具有较好的对应,因此有必要开展全球导航卫星系统(GNSS)对流层延迟的插值研究．以京津冀地区为例,针对GNSS对流层延迟,开展对流层延迟的空间插值研究．首先开展了GNSS对流层延迟与水汽的比较分析,两者存在显著正相关特性,相关性超过91.7％,论证了对流层延迟取代水汽的可行性．然后利用反距离权重法对京津冀地区2016年9月至2017年8月的12组GNSS测站对流层延迟进行空间插值,通过提取插值点对流层延迟与GNSS站点对流层延迟比较验证空间插值精度．全年数据平均偏差最大为1.12 cm,均方根误差最大为0.89 cm;未发生降水过程平均偏差最大为1.25 cm,均方根误差最大为0.82 cm;发生降水过程平均偏差最大为1.08 cm,均方根误差最大为1.38 cm．京津冀平原区域的GNSS对流层延迟空间插值结果精度满足气象等应用要求,可为气象预报和InSAR大气校正提供参考.      

土壤重金属的空间插值方法比较分析——以阳谷县为例

空间插值通过采集少量的数据点,利用其中的空间关联,推求该区域内其他位置的属性值。本文以山东省阳谷县土壤重金属Cu采样数据为例进行空间探索性分析,分别采用了反距离权重插值和普通克里金插值两种方法进行空间分布插值模拟。结果表明,针对研究区采样数据,反距离权重插值方法生成的模型平均误差为1.97 mg/kg,总体精度为92%;普通克里金插值模型的平均误差为1.91 mg/kg,总体精度为92.35%,普通克里金插值方法更优。     

基于LROC NAC影像的高分辨率连续DEM数据制作

具有高分辨率和连续表面的DEM数据是获取月球形貌特征并进行数字地形分析的主要数据源。本文选择嫦娥五号候选着陆区中的一个区域作为试验区,首先,基于LROC NAC立体影像、ISIS3和Stereo Pipeline软件生成高分辨率DOM影像及对应DEM数据,并将其与日本SELENE数据进行对比;然后,利用反距离权重、径向基函数和经验贝叶斯克里金3种插值方法对DEM数据的空洞区域进行修复,并对不同修复方法进行交叉验证分析。结果表明：生成的DOM和DEM分辨率约3.5 m,明显比7.4 m分辨率的日本SELENE数据清晰,并具有更强的地形表达能力;径向基函数插值法的空洞修复效果最好,交叉验证均方根误差为0.26 m。本文对准确获取月球形貌特征、探测器选址等具有一定作用,并能够为其他区域的高分辨率连续DEM数据生成提供参考。     

顾及垂直递减率的中国区域Tm格点产品空间插值

大气加权平均温度(T_m)是全球导航卫星系统(global navigation satellite system, GNSS)反演大气水汽(precipitation water vapor, PWV)的关键参数。当前已有T_m模型提供的T_m信息难以捕获其日周期变化,因此限制了其在高时间分辨率GNSS PWV估计中的精度。大气再分析资料可提供高时空分辨率的T_m格点产品,但是在使用时需要对其进行空间插值,且T_m在高程上的变化远大于其在水平方向上变化。同时,针对中国区域地形起伏大等特点,提出顾及垂直递减率的中国区域T_m格点产品空间插值方法,以分布于中国区域的2015年89个探空站资料为参考值,验证了提出的方法在全球大地测量观测系统大气中心T_m格点产品和美国国家航空和太空管理局提供的MERRA-2的T_m格点产品中的空间插值精度。结果表明：(1)在顾及垂直递减率的T_m格点产品空间插值中,反距离加权法的...     

Application of MK-PRISM for interpolation of wind speed and comparison with co-kriging in South Korea

The spatial distribution of wind speed is important information required to understand climate-related regional phenomena. This paper presents the Modified Korean Parameter-elevation Regression on Independent Slopes Model (MK-PRISM) as a method for spatial interpolation of monthly wind speeds. A database of gridded monthly mean wind speeds with a spatial resolution of 1 km for the period of March 2011–February 2014 is constructed by MK-PRISM. Wind speed observation data collected from the 529 to 641 meteorological stations in South Korea were utilized as the input data for interpolation. The wind speed distribution estimated by co-kriging is used for comparison with the MK-PRISM results. Research demonstrates that the efficiency difference between the two models, MK-PRISM and co-kriging, is insignificant. The Kling and Gupta efficiencies of both models were 0.68-0.78 and the root mean square errors (RMSEs) were 0.44-0.68 m/s. The spatial distribution of wind speeds, however, differs between MK-PRISM and co-kriging, which can be considered a reflection of the influence of topographic features such as terrain convexity, aspect, and coastal proximity. MK-PRISM can perform more appropriately to represent the phenomena where similar wind speeds appear continuously along ridges and coastlines. This suggests that a knowledge-based approach that considers topographic features can be successfully applied to the interpolation of monthly or seasonal wind speeds, similar to temperature and precipitation. The wind speed distribution generated by MK-PRISM can be utilized as important data for different geographical studies.     

A Spatial Conditioned Latin Hypercube Sampling Method for Mapping Using Ancillary Data

For obtaining maps of good precision by the spatial inference method, the distribution of sampling sites in geographical and feature space is very important. For a regional variable with trends, the predicting error comes from trend estimation, variogram estimation and spatial interpolation. Based on the cLHS (conditioned Latin hypercube Sampling) method, a sampling method called scLHS (spatial cLHS) considering all these three aspects with the help of ancillary data is proposed in this article. Its advantage lies in simultaneously improving trend estimation, variogram estimation and spatial interpolation. MODIS data and simulated data were used as sampling fields to draw sample sets using scLHS, cLHS, cLHS with x and y coordinates as covariates, simple random and spatial even sampling methods, and the distribution and prediction errors of sample sets from different methods were evaluated. The results showed that scLHS performed well in balancing spreading in geographic and feature space, and can generate points pairs with small distances, and the sample sets drawn by scLHS produced smaller mapping error, especially when there were trends in the target variable.     

克里金插值的多路径误差空间分布特征

针对多路径误差的空间分布特征,该文提出采用克里金插值法构建多路径误差的空间插值模型。通过采用ArcGIS中克里金插值工具构建的多路径误差的空间插值模型,较好地展现出多路径误差与测站位置、反射源距离等因素的空间分布特征。实验结果表明:对比泛克里金插值法、普通克里金插值法、简单克里金插值法3种方法构建的多路径误差插值模型,普通克里金插值法的效果最好。研究成果直观反映出在林区、多层建筑物等环境下多路径误差影响较大,还预测出未采样区域的多路径误差影响范围,该研究成果可应用于GPS观测站选址、GPS测量技术设计等领域。该文从空间分布特征的角度提出了一种新的研究多路径误差特性的思路,实现了对指定测区内的多路径误差的空间分布特征的探究。     

Accuracy of areal interpolation: A comparison of alternative methods

This paper discusses the accuracy of spatial data estimated by areal interpolation, a process of transferring data from one zonal system to another. A stochastic model is proposed which represents areal interpolations in diverse geographic situations. The model is used to examine the relationship between estimation accuracy and the spatial distribution of estimation error from a theoretical viewpoint. The analysis shows that the uniformity in error distribution improves the accuracy of areal interpolation. Four areal interpolation methods are then assessed through numerical examinations. From this it is found that the accuracy of simple interpolation methods heavily depends on the appropriateness of their hypothetical distributions, whereas the accuracy of intelligent methods depends on the fitness of the range of supplementary data for that of true distribution. Received: 19 February 1999/Accepted 17 September 1999