Accounting for topography in the calculation of quasigeoidal heights and plumb-line deflections from gravity anomalies

A calculation of quasigeoidal heights and plumb-line deflections according to Molodensky formulae was carried out under elimination of the effect of topography from gravity anomalies. After the masses of topography had been removed a smoothed-out surface passing through astronomical and gravity stations was considered as representing the physical surface of the Earth. Thus it has been practically rendered possible to use the first-approximation formulae of Molodensky, and, in many cases, also the “zero-approximation” formulae analogous to the formulae of Stokes and Vening-Meinesz. The effect of the restored masses of topography was then added to the quantities found; the said effect was expressed as the effect of topography condensed on the normal equipotential surface passing through the point under investigation, plus a correction for condensation. Following some transformations, the resulting formulae (13) and (18) were obtained which formulae differ in their “zero-approximation” (15) and (20) from traditional formulas in that they contain terrait reductions added to free-air anomalies. Moreover, in the calculation of plumb-line deflections directly in mountain regions a correction for differing effects of topography before and after its condensation is to be introduced. A tentative expansion of terrain reduction in terms of spherical harmonics up to the third order is given; it can be seen therefrom that the Stokes series in its usual form is subject to a mean arror about 15–20%. It is also shown that the expansion of free-air anomalies in terms of spherical functions contains a first-order harmonic with a mean values about ±0.3 mgl. The said harmonic practically disappears in the expansion of the sum of free-air anomalies and terrain reductions.     

Methods for computing deflections of the vertical by modifying Vening-Meinesz' function

Summary The application of combined data (satellite and terrestrial data) to the practical computation of height anomalies or the deflections of the vertical was originally suggested by (Molodensky et al. 1962). This idea usually leads to the modification of Stokes' or Vening-Meinesz' functions in the integration procedure. In the recent decade there were various suggestions in this regard especially for the computation of height anomalies. For example, a considerable mathematical insight into the modification of Stokes' function and the truncation of its integral has been provided by (Meissl 1971, Houtze et al. 1979, Rapp 1980, Jekeli 1980). Five different methods for computing deflections of the vertical by modifying Vening-Meinesz' function are studied and compared with each other. The corresponding formulae, the values of the coefficients in each method and the estimations of their corresponding potential coefficient error and truncation error are given in this article. This paper was written at the Institut f. Angewandte Geod?sie, Technische Universit?t Graz, Austria.     

Systematic errors in levelings of mountainous areas

Sources of errors in the precise leveling influencing the results of measurements especially strongly in mountains are considered in this study. Data are given on new error sources, including (1) the difference in temperatures of invar bands of rods and of the air; and (2) displacements of rock bench marks during diurnal variations in temperature of rocks. The ranges of possible total systematic error in leveding are estimated.     

PM2.5浓度插值中不同空间插值方法对比

针对不同插值方法对于重点大气颗粒物污染源PM_(2.5)大区域内整体分布情况的插值效果和精度存在差异性的问题,该文以石家庄市赵县100个点的PM_(2.5)的数据作为样本点,利用反距离权重法、普通克里格插值法和协同克里格插值法,分别进行PM_(2.5)浓度的空间插值。利用研究区内另外20个PM_(2.5)的数据点进行插值精度的检验。研究结果表明:协同克里格插值的精度最高,但可视化效果不如其他两种方法。     

不同卫星定位加权方法的比较与分析

测量值随机误差加权模型是卫星定位的重要组成部分,它能够更加合理地分配各卫星在解算中所起的作用大小,并获得更高的定位精度。该文对目前基于卫星仰角与载噪比或信噪比两大影响因素的多种主流定权方法进行了系统阐述与讨论。通过GPS实测定位实验,对9种不同定权模型的效果进行了综合比较与分析。实验结果表明,各加权模型基本均能够在不同程度上提高定位精度,其中综合考虑仰角与载噪比或信噪比的加权模型具有最优的性能表现。另外,当定位条件较差时,由于测量值误差构成更为复杂,因此期待更加有效的加权模型与方法。     

A numerical investigation on height anomaly prediction in mountainous areas

This paper provides numerical examples for the prediction of height anomalies by the solution of Molodensky's boundary value problem. Computations are done within two areas in the Canadian Rockies. The data used are on a grid with various grid spacings from 100 m to 5 arc-minutes. Numerical results indicate that the Bouguer or the topographicisostatic gravity anomalies should be used in gravity interpolation. It is feasible to predict height anomalies in mountainous areas with an accuracy of 10 cm (1) if sufficiently dense data grids are used. After removing the systematic bias, the differences between the geoid undulations converted from height anomalies and those derived from GPS/levelling on 50 benchmarks is 12 cm (1) when the grid spacing is 1km, and 50 cm (1) when the grid spacing is 5. It is not necessary, in most cases, to require a grid spacing finer than 1 km, because the height anomaly changes only by 3 cm (1) when the grid spacing is increased from 100 m to 1000 m. Numerical results also indicate that, only the first two terms of the Molodensky series have to be evaluated in all but the extreme cases, since the contributions of the higher order terms are negligible compared to the objective accuracy.     

机载激光雷达在密林山区测绘中的应用

机载激光雷达是近年来发展迅速的高新测绘技术,具有机动性高、数据覆盖量大、作业效率高和精度可靠等特点。针对当前山区沟壑且有大量植被覆盖区域进行传统测量作业较为困难,危险性大的问题,采用机载激光雷达技术获取研究区原始点云数据,在此基础上,对比分析四种滤波算法的点云分类效果,得到适用于密林沟壑区的点云滤波方法,进而通过人机交互和地面点内插实现了测区高精度数字高程模型（digital elevation model,DEM）的构建,最终获得的DEM高程中误差为0.09 m,满足实际测绘生产需求,生产效率大大提高。研究结果表明,机载激光雷达技术应用于复杂危险地形测绘具有极大优势。     

Analysis of different methods for monitoring the urbanization process

The monitoring of urban sprawl in agricultural and natural areas requires the frequent acquisition of information relative to land cover changes. The loss of high capability agricultural lands is a major problem. The sound management of resources requires the knowledge of the nature and orientation of the urban dynamics.

Remote sensing is a useful tool for highlighting areas where changes have occured,for determining the type of change and for quantifying these changes. A spatial‐temporal analysis of the urban processes is carried out for the urban area of Montreal, Canada. Different sources of information are used: three Landsat MSS satellite images acquired in 1972, 1979 and 1982, planimetric data from the Department of Municipal Affairs of Quebec and statistics compiled by Environment Canada.

The satellite data shows a sharp increase, in the order of 65%, in urban areas during the period under consideration. These results are compared with governmental data derived from classical photo‐interpretation techniques.

On one hand, we observe that the results obtained by automatic classification of the satellite data are superior in the order of between 5% to 30%, depending on the year and the different governmental sources. On the other hand, we discuss problems of homogeneity in the use of terms related to land cover between the various governmental organizations.     

Iterative vector methods for computing geodetic latitude and height from rectangular coordinates

 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −10⁶ to +10⁹ m. Received: 13 December 2000 / Accepted: 13 July 2001     

Improving operational measurement of precipitation using radar in mountainous terrain-Part I: methods

Four major rainfall events that affected the Western Alps between autumn 1994 and autumn 2000 are analyzed to assess the bias between the radar rainfall estimates at rain gauge locations and the gauge amounts. The aim of this study is to demonstrate the importance of: 1) bias adjustment; 2) the training procedure used to train various adjustment methods by means of independent data; and 3) a quality check of the radar-gauge couples that were used for the training itself. A first adjustment method is simply based on a single "bias-correction" coefficient. A weighted multiple regression (WMR) is well worth the additional effort of determining three additional coefficients, which give a spatial distribution of the adjustment factor rather than a constant one for the whole domain as the output. The independent dataset that was used to train the gauge-adjustment techniques consists of daily radar/gauge amounts accumulated during the first day of each event. The following days are used for an independent verification that is dealt with in a companion letter, which will validate the methods and illustrate the improvements and the feasibility of a real-time application during intense events. The WMR technique tries to correct not only the overall bias but also the beam-broadening, visibility, and orography influences. The training procedure of both the bulk- and WMR-adjustment methods highlighted a considerable radar underestimation, which is certainly not surprising in mountainous terrain. The WMR-derived coefficients also clearly show that the radar underestimates precipitation for higher sampling volumes and longer distances. Since the WMR is fast and simple to use, it represents an alternative to more sophisticated methods and seems to be particularly useful for operational services.     

单基站GPS差分系统在山区线路测量中的应用探讨

RTK技术的出现,使得野外实时测量精度达到厘米级,RTK测量具有实时性好、精度高、速度快等优点,是常规测量所无法比拟的,RTK已经作为快速采集数据与定位的有效工具。本文比较分析了常规RTK系统和网络RTK的优缺点,并详细介绍了单基站GPS差分系统的特点,并在实际工程应用中对其精度和有效距离进行了探讨。     

Modelling position dependent errors in gravimetric deflections of the vertical

Comparisons of gravimetric and astrogeodetic deflections of the vertical in the Australian region indicate that the former are affected by position dependent systematic errors, even after orientation onto the Australian Geodetic Datum. These are probably due to errors in the predicted mean anomalies for gravimetrically unsurveyed oceanic regions to the east, south and west of the continent. Deflection component residuals (astrogeodetic minus oriented gravimetric) at 83 control stations are made the observables in a set of observation equations, based on the Vening Meinesz equations, from which pseudocorrections to the mean anomalies for a set of arbitrarily selected surface elements are computed. These pseudocorrections compensate for prediction errors in much larger unsurveyed regions. Their effects on individual deflection components are calculated using the Vening Meinesz equations. Statistical tests indicate that pseudocorrections computed for four large offshore elements and six smaller elements in unsurveyed areas produce corrections to the gravimetric deflections which make the ξ and η components in seconds of arc consistent with normally distributed populations N (0.00, 0.70²).     

CAD数据向GIS数据转换的方法比较

针对传统的CAD地形图数据向ArcGIS数据转换的需求越来越高的现状,该文以某市的计算机辅助设计地形图为实例,讨论了ArcGIS工具模块、FME软件、C/S转换平台、编程这4种数据转换方法的优缺点和适用范围。利用这几种方法对计算机辅助设计地形图数据进行转换,并将转换结果进行对比分析。实验结果表明,基于FME软件的转换方法最为简便、可行,在一定的条件下转换的结果精度更高、更可靠。     

Evaluation of different topographic correction methods for Landsat imagery

The recent free availability of Landsat historical data provides new potentials for land-cover change studies. Multi-temporal studies require a previous radiometric and geometric homogenization of input images, to better identify true changes. Topographic normalization is one of the key steps to create consistent and radiometricly stable multi-temporal time series, since terrain shadows change throughout time. This paper aims to evaluate different methods for topographic correction of Landsat TM-ETM+ data. They were assessed for 15 ETM+ images taken under different illumination conditions, using two criteria: (a) reduction of the standard deviation (SD) for different land-covers and (b) increase in temporal stability of a time series for individual pixels. We observed that results improve when land-cover classes where processed independently when applying the more advanced correction algorithms such as the C-correction and the Minnaert correction. Best results were obtaining for the C-correction and the empiric–statistic correction. Decreases of the SD for bare soil pixels were larger than 100% for the C-correction and the empiric–statistic correction method compared to the other correction methods in the visible spectrum and larger than 50% in the IR region. In almost all tests the empiric–statistic method provided better results than the C-correction. When analyzing the multi-temporal stability, pixels under bad illumination conditions (northern orientation) improved after correction, while a deterioration was observed for pixels under good illumination conditions (southern orientation). Taken this observation into account, a simple but robust method for topographic correction of Landsat imagery is proposed.     

GPS高程拟合的方法比较

GPS高程拟合的方法有很多,各有其优点和适用范围。本文在最小二乘估计算法的基础上,讨论主成分估计法和半参数模型估计法及各自的优点,并利用六参数模型的最小二乘估计、主成分估计和半参数模型三种拟合方法对GPS高程进行拟合,通过实例计算结果比较分析,得出半参数估计方法优于其他方法,在一定条件下精度高的优点。最后得出半参数估计方法精度达毫米级,论证了其在实际应用中的优越性。     

ON THE EVALUATION OF DEFLECTIONS OF THE VERTICAL USING FFT TECHNIQUE

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