On the geoid-quasigeoid separation in mountain areas
On the geoid-quasigeoid separation in mountain areas
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DOI：
10.1007/s00190-009-0302-9
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发表时间：
2009-09-01
影响因子：
4.4
通讯作者：
Rummel, Reiner
中科院分区：
文献类型：
--
作者：
Flury, Jakob;Rummel, Reiner
正高和正常高的参考面--大地水准面和似大地水准面--之间的间隔通常在几个分米量级，但在极端情况下可以达到近3米。大地水准面-似大地水准面精度达到厘米级或更高精度的知识，对于实现国家和国际高程参照系，以及大地测量工程中的精密高程测量至关重要。大地水准面-似大地水准面分离的最大贡献是地形质量的分布。我们发展了一个用于严格处理地形质量的紧凑公式，并将其应用于阿尔卑斯山地形非常粗糙的两个试验区的大地水准面-似大地水准面分离，使用100m的非常精细的网格分辨率，分析了大地水准面-似大地水准面分离的大小及其精度、斜率、粗糙度和与高度的相关性。结果表明，对地形质量的严格处理导致了相当小的大地水准面-准大地水准面分离-在最高山顶只有30厘米-而基于近似值的结果往往大几个分米。对于地形极端的地区，地形对大地水准面-似大地水准面分离的贡献精度估计为2-3厘米。大地水准面-似大地水准面分离的粗糙度分析表明，要达到这些精度，建模网格的分辨率需要小于或等于200m。模拟了地形块体内部的重力和垂直重力梯度以及垂线上的平均重力，这是确定大地水准面-似大地水准面分离的重要中间量。我们的结论是，在几厘米的精度范围内一致地确定大地水准面和似大地水准面高度参考面是可行的，即使在极端地形的地区，也可以在这种精度水平下一致地实现和使用正高和正常高的概念。
The separation between the reference surfaces for orthometric heights and normal heights-the geoid and the quasigeoid-is typically in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid-quasigeoid separation with centimeter accuracy or better, is essential for the realization of national and international height reference frames, and for precision height determination in geodetic engineering. The largest contribution to the geoid-quasigeoid separation is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic masses and apply it to determine the geoid-quasigeoid separation for two test areas in the Alps with very rough topography, using a very fine grid resolution of 100 m. The magnitude of the geoid-quasigeoid separation and its accuracy, its slopes, roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a rather small geoid-quasigeoid separation-only 30 cm at the highest summit-while results based on approximations are often larger by several decimeters. The accuracy of the topographic contribution to the geoid-quasigeoid separation is estimated to be 2-3 cm for areas with extreme topography. Analysis of roughness of the geoid-quasigeoid separation shows that a resolution of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for the determination of the geoid-quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy.