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

与全球几何定义的高度系统不同，大多数国家的物理高度系统与单个垂直基准面有关，该垂直基准面由在特定验潮仪观测到的当地平均海面定义。由于海面地形的原因，不同物理高度系统的参考水平在全球范围内相差约1-2m。然而，对于许多全球大地测量应用以及对地球动力学和气候过程的监测来说，统一的全球垂直基准是必不可少的。因此，这一研究项目的主要目标是开发确定可用于全球连接国家高程系统的基准参数的方法。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调查来分析它们的性能。第一种方法以卫星观测为基础，因此在大地测量基础设施有限的国家看来特别令人感兴趣，厘米-分米的精确度已得到核实。为了实现亚厘米级的统一，提出了一种基于扩展固定大地边值问题(GBVP)求解的第二种方法，并用闭环系统仿真进行了验证。与第一种方法不同的是，还需要地球重力数据。在已有研究成果的基础上，在第二阶段的研究中，应进一步发展和分析扩展的固定边界条件法。主要目标是实现该方法，以便将其应用于实际观测数据。在这方面，考虑到全球分布的地球重力测量的可获得性有限，必须对该方法进行调整。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-恢复的方法，实现地面重力数据与卫星观测和地形信息的结合。这两种方法主要用于基于无标量GBVP的重力大地水准面确定，需要适应当前的问题。此外，第二个项目阶段还应用于分析固定GRWP的球解中造成超过1 mm影响的所有近似误差。将适当的修正项引入到球面和等半径近似下线性化问题的求解中，形成了一套完整的地形边界面固定边值问题的非线性理论。

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.