珠峰峰顶大地水准面高的确定

Determination of Geoid Height at the Summit of Mount Qomolangma

  • 摘要: 大地水准面高是珠峰正高确定的前提,通过计算珠峰似大地水准面(高程异常)以及似大地水准面与大地水准面间的高差确定大地水准面高。首先,利用地形模型、地球重力场模型、地面和航空融合重力数据等资料,基于Molodensky原理及移去-恢复技术精化珠峰地区分辨率为1.5′×1.5′的重力似大地水准面模型;其次,利用珠峰地区GNSS水准点纠正重力似大地水准面模型,消除系统差,得到1985国家高程基准下珠峰区域的似大地水准面模型;最后,利用珠峰峰顶实测重力值,采用移去-恢复和重力归算方法计算似大地水准面与大地水准面间的高差,完成珠峰峰顶大地水准面高的计算。结果表明,基于EIGEN-6C4地球重力场模型,融合地面、航空重力获得的重力似大地水准面精度达4.8 cm,相较于单独利用地面重力资料获得模型精度提升约40%;在1985国家高程基准下,珠峰峰顶高程异常为-25.586 m,似大地水准面与大地水准面间的高差为-1.216 m,大地水准面高为(-26.802±0.06) m,计算结果较2005年更加可靠。

     

    Abstract:
    Objectives The determination of the orthometric height of Mount Qomolangma requires the prior calculation of geoid height, which is determinined by the quasi-geoid (height anomaly) and the height difference between the quasi-geoid and geoid.
    Methods First, based on Molodensky principle and remove-restore technology, a 1.5'×1.5' gravity quasi-geoid model in Mount Qomolangma region can be established by using a terrain model, an earth gravity field model, and the fusion data of ground and airborne gravity. Then, system errors can be eliminated by correcting the gravity quasi-geoid model with GNSS-leveling points. The quasi-geoid based on the National Vertical Datum 1985 can be obtained. Finally, the height difference between the quasi-geoid and geoid can be calculated by using the remove-restore method by gravity at the summit of Mount Qomolangma.
    Results The results show that the EIGEN-6C4 earth gravity field model performs best in the region of Mount Qomolangma compared to EGM2008 and XGM2019e_2159. The precision of the gravity geoid model is 7.8 cm based solely on the EIGEN-6C4 and ground gravity data, while it is 4.8 cm based on the EIGEN-6C4 and the fusion data of ground and airborne gravity. The accuracy of model is improved by approximately 40% than using ground gravity data only. At the summit of Mount Qomolangma, the height anomaly is -25.586 m, the height difference between the quasi-geoid and geoid is -1.216 m, and the geoid height is (-26.802±0.06) m in the National Height Datum 1985.
    Conclusions Airborne gravity can effectively provide data for the region where ground gravity data is sparse or non-existent. By incorporating airborne gravity, the density of gravity data at the summit of Mount Qomolangma has been greatly improved, leading to an increased accuracy of the quasi-geoid model. The availability of richer data, more accurate models, and more advanced calculation methods in 2020 resulted in more reliable results compared to the 2005 measurement.

     

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