Classically, vertical reference frames were realized as national or continent-wide networks of geopotential differences derived from geodetic leveling, i.e., from the combination of spirit leveling and gravimetry. Those networks are affected by systematic errors in leveling, leading to tilts in the order of decimeter to meter in larger networks. Today, there opens the possibility to establish a worldwide unified vertical reference frame based on a conventional (quasi)geoid model. Such a frame would be accessible through GNSS measurements, i.e., physical heights would be derived by the method of GNSS-leveling. The question arises, whether existing geodetic leveling data are abolished completely for the realization of vertical reference frames, are used for validation purposes only, or whether existing or future geodetic leveling data can still be of use for the realization of vertical reference frames. The question is mainly driven by the high quality of leveled potential differences over short distances. In the following we investigate two approaches for the combination of geopotential numbers from GNSS-leveling and potential differences from geodetic leveling. In the first approach, both data sets are combined in a common network adjustment leading to potential values at the benchmarks of the leveling network. In the second approach, potential differences from geodetic leveling are used as observable for regional gravity field modeling. This leads to a grid of geoid heights based on classical observables like gravity anomalies and now also on leveled potential differences. Based on synthetic data and a realistic stochastic model, we show that incorporating leveled potential differences improves the quality of a continent-wide network of GNSS-heights (approach 1) by about 40% and that formal and empirical errors of a regional geoid model (approach 2) are reduced by about 20% at leveling benchmarks. While these numbers strongly depend on the chosen stochastic model, the results show the benefit of using leveled potential differences for the realization of a modern geoid-based reference frame. Independent of the specific numbers of the improvement, an additional benefit is the consistency (within the error bounds of each observation type) of leveling data with vertical coordinates from GNSS and a conventional geoid model. Even though we focus on geodetic leveling, the methods proposed are independent of the specific technique used to observe potential (or equivalently height) differences and can thus be applied also to other techniques like chronometric or hydrodynamic leveling.

传统上，垂直参考系被实现为国家或大陆范围内的位势差网络，该网络源自大地水准测量，即精神水准测量和重力测量的结合。这些网络受到水准测量系统误差的影响，导致较大网络中出现分米到米量级的倾斜。如今，基于传统（准）大地水准面模型建立全球统一垂直参考系成为可能。这样的框架可以通过 GNSS 测量来访问，即物理高度将通过 GNSS 水准测量方法得出。问题是，现有的大地水准测量数据是否完全废除以实现垂直参考系，仅用于验证目的，或者现有或未来的大地水准测量数据是否仍可用于实现垂直参考系。这个问题主要是由短距离内的高质量电位差引起的。在下文中，我们研究了两种将 GNSS 水准测量的位势数与大地测量水准测量的位差相结合的方法。在第一种方法中，两个数据集组合在一个共同的网络调整中，从而得出均衡网络基准的潜在值。在第二种方法中，大地水准面的潜在差异被用作区域重力场建模的可观测值。这导致基于重力异常等经典可观测值以及现在基于水平电位差的大地水准面高度网格。 基于合成数据和现实的随机模型，我们表明，纳入水平电位差可将全大陆 GNSS 高度网络（方法 1）的质量提高约 40%，并且区域大地水准面模型的形式和经验误差（方法 2) 在平整基准上减少了约 20%。虽然这些数字很大程度上取决于所选的随机模型，但结果显示了使用均衡电位差来实现现代基于大地水准面的参考系的好处。与改进的具体数字无关，另一个好处是水准测量数据与来自 GNSS 和传统大地水准面模型的垂直坐标的一致性（在每种观测类型的误差范围内）。尽管我们专注于大地测量，但所提出的方法独立于用于观察潜在（或等效高度）差异的特定技术，因此也可以应用于其他技术，例如计时或水动力水准测量。