Recent applications in Earth sciences require geoid models to be determined with the sub-centimetre internal accuracy. Regional models of the geoid are usually determined using discrete gravity values measured at and/or outside the Earth, and global models of the Earth gravity field and topographic surface. In this article, we review the previous studies that (to some extent) discuss the estimation of the geoid internal error, and provide formulations and methodologies required for a comprehensive formal propagation of errors of gravity data and global models through a mathematical model used for regional geoid determination. The mathematical model is based on combining the inverse Poisson integral equation and the Hotine integral transform in the Helmert harmonic space; also called the one-step integration method. Calculations and tests are performed in one of the most challenging test areas (“the Colorado test area”) using ground and airborne gravity observations, a global digital terrain model (DTM) for topographic effects on gravity and the geoid, and a global Earth gravitational model (EGM) for the long-wavelength components of gravity and the geoid.

There are three main contributors to the total internal error of the geoid height, namely those associated with the EGM (for estimating the long-wavelength components of gravity and the geoid height), DTM heights (for evaluation of the topographic effects on observed gravity and the geoid height), and gravity observations (for determining the short-wavelength components of the geoid height). The geoid errors stemming from the EGM formal variances of its spherical harmonic coefficients amount to 7% (0.3 cm) of the total internal error budget of the geoid. The mean value of the standard deviation of the geoid height stemming from the topographic effects (due to uncertainties of DTM heights) is 1.05 cm which is 26% of the total internal error estimate. The observation errors and spatial distribution (resolution) of regional ground and airborne gravity observations, i.e., the design of the problem, are the dominant contributors to the internal error of the geoid height. The internal error estimate of the geoid model in the Colorado test area computed on the 1′ × 1′ grid is 2.74 cm which agrees with the differences between various geoid models that contributed to the Colorado-1 cm geoid experiment.

Determining a regional geoid model with sub-centimetre internal error in areas of rough topography, such as that of Colorado, requires high-accuracy and high-resolution gravity data. To assess the accuracy of regional gravity measurements required for sub-centimetre geoid models, we simulate airborne gravity measurements in the Colorado test area at a practically lower flight altitude; and improve the spatial distribution of existing ground gravity observations by filling in gaps using synthetic gravity disturbances. Results show that carrying out airborne gravity surveys with a gentle drape approach at an average flight altitude between 300 and 500 m above the Earth's surface provides airborne gravity measurements with a mean standard deviation of 0.75 mGal at 2.2 km spatial resolution. Thus, a sub-centimetre regional gravimetric geoid model in the Colorado test area would be achievable using the proposed configuration of the ground and airborne gravity observations and more accurate DTMs.

最近在地球科学中的应用需要以亚厘米的内部精度确定大地水准面模型。大地水准面的区域模型通常使用地球上和/或地球外测量的离散重力值以及地球重力场和地形表面的全球模型来确定。在本文中，我们回顾了（在某种程度上）讨论大地水准面内部误差估计的先前研究，并通过用于区域的数学模型提供了重力数据和全球模型误差的综合正式传播所需的公式和方法。大地水准面测定。数学模型基于Helmert调和空间中逆泊松积分方程和Hotine积分变换的结合；也称为一步积分法。

大地水准面高度的总内部误差有三个主要贡献者，即与 EGM 相关的那些（用于估计重力的长波长分量和大地水准面高度）、DTM 高度（用于评估地形对观测到的重力的影响和大地水准面高度）和重力观测（用于确定大地水准面高度的短波分量）。源自其球谐系数的 EGM 形式方差的大地水准面误差占大地水准面总内部误差预算的 7%（0.3 厘米）。由地形影响（由于 DTM 高度的不确定性）引起的大地水准面高度标准偏差的平均值为 1.05 厘米，占总内部误差估计值的 26%。区域地面和机载重力观测的观测误差和空间分布（分辨率），即问题的设计，是大地水准面高度内部误差的主要贡献者。在 1′×1′ 网格上计算的 Colorado 试验区大地水准面模型的内部误差估计为 2.74 cm，这与对 Colorado-1 cm 大地水准面实验有贡献的各种大地水准面模型之间的差异一致。

在科罗拉多州等崎岖地形地区确定具有亚厘米内部误差的区域大地水准面模型需要高精度和高分辨率的重力数据。为了评估亚厘米级大地水准面模型所需的区域重力测量的准确性，我们在科罗拉多测试区以实际较低的飞行高度模拟航空重力测量；通过使用合成重力扰动填补空白，改善现有地面重力观测的空间分布。结果表明，在地球表面上方 300 至 500 米的平均飞行高度上使用柔和悬垂法进行空中重力测量，可提供空间分辨率为 2.2 公里的平均标准偏差为 0.75 mGal 的空中重力测量。因此，