Methodological and numerical investigations for the establishment of a unified global vertical datum

与全球性的几何高度系统不同，大多数国家的物理高度系统都与一个单独的垂直基准面有关，由在特定验潮站观测到的当地平均海面确定。 由于海面地形的原因，全球范围内不同物理高度系统的参考高度不一致，约为1-2 m。然而，对于许多全球大地测量应用以及监测地球动力学和气候过程而言，统一的全球垂直基准是必不可少的。因此，本研究项目的主要目标是制定可用于全球连接国家高程系统的基准参数的确定方法。在该项目的第一阶段，已经开发了两种不同精度的方法，并通过在德国、巴西和澳大利亚的试验区进行方法学和数值研究来分析它们的性能。第一种方法是以卫星观测为基础的，因此在大地测量基础设施有限的国家看来特别有意义，厘米-分米精度已经得到验证。为了实现统一到亚厘米级，第二种方法的基础上的扩展的固定大地边值问题（GBVP）的解决方案已被提出，并使用闭环模拟验证。与第一种方法不同，还需要地面重力数据。在调查和取得的成果的基础上，扩展的固定GBVP的方法应在研究项目的第二阶段进一步发展和分析。主要目标是实际实现的方法，以便将其应用到真实的观测数据。在这种情况下，该方法必须考虑到全球分布的地球重力测量的有限可用性进行调整。因此，需要通过对积分核进行适当的修改，将全球积分区域限制在覆盖区域高分辨率重力数据的近区。此外，为了减少系统误差，应利用移除-计算-恢复方法实现地面重力数据与卫星观测和地形信息的结合。这两个程序，主要用于重力大地水准面确定的基础上标量自由GBVP，需要适应目前的问题。此外，第二个项目阶段也应该被用来分析所有近似误差的固定GRWP的球形解决方案，造成超过1毫米的影响。这些努力将导致一个完整的理论的非线性固定GBVP的地形边界表面，整合适当的校正项的线性化问题的解决方案，在球形和恒定半径近似。

In contrast to global, geometrically defined height systems, most national, physical height systems are related to an individual vertical datum, defined by the local mean sea surface observed at a specific tide gauge. Due to sea surface topography, the reference levels of different physical height systems are inconsistent by about 1-2 m at a global scale. However, for many global geodetic applications as well as the monitoring of geodynamic and climatological processes a unified global vertical datum is indispensable. Therefore, the primary objective of this research project is the development of methods for the determination of datum parameters that can be used to globally connect national height systems. In the first phase of the project, two methods of different accuracy have been developed and their performance was analyzed by conducting methodological and numerical investigations using test areas in Germany, Brazil, and Australia. For the first method, which is based on satellite observations and therefore particularly interesting from the view of countries with a limited geodetic infrastructure, cm-dm accuracy has been verified. To achieve a unification up to sub-cm level, a second method based on the solution of an extended fixed Geodetic Boundary Value Problem (GBVP) has been proposed and validated using a closed-loop simulation. In contrast to the first approach, terrestrial gravity data are additionally required. On the basis of the investigations and achieved results, the method of the extended fixed GBVP should be further developed and analyzed within the second phase of the research project. The main goal is the practical realization of the method in order to apply it to real observation data. In this context, the method has to be adapted considering the limited availability of globally distributed terrestrial gravity measurements. Thus, the global integration area needs to be restricted to a near zone covering regional high-resolution gravity data by applying a suitable modification of the integral kernel. Furthermore, in order to reduce systematic errors, a combination of terrestrial gravity data with satellite observations and topographic information should be realized by utilizing a remove-compute-restore approach. Both procedures, primarily used in gravimetric geoid determination based on the scalar free GBVP, need to be adapted to the present problem. Moreover, the second project phase should also be used to analyze all approximation errors in the spherical solution of the fixed GRWP that cause an impact of more than 1 mm. These efforts will result in a complete theory of the non-linear fixed GBVP for the topographical boundary surface, integrating suitable correction terms into the solution of the linearized problem in spherical and constant radius approximation.