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Modeling the North American vertical datum of 1988 errors in the conterminous United States

机译：对美国本土1988年误差的北美垂直基准进行建模

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A large systematic difference (ranging from ?20 cm to +130 cm) was found between NAVD 88 (North AmericanVertical Datum of 1988) and the pure gravimetric geoid models. This difference not only makes it very difficult to augment the local geoid model by directly using the vast NAVD 88 network with state-of-the-art technologies recently developed in geodesy, but also limits the ability of researchers to effectively demonstrate the geoid model improvements on the NAVD 88 network. Here, both conventional regression analyses based on various predefined basis functions such as polynomials, B-splines, and Legendre functions and the Latent Variable Analysis (LVA) such as the Factor Analysis (FA) are used to analyze the systematic difference. Besides giving a mathematical model, the regression results do not reveal a great deal about the physical reasons that caused the large differences in NAVD 88, which may be of interest to various researchers. Furthermore, there is still a significant amount of no-Gaussian signals left in the residuals of the conventional regression models. On the other side, the FA method not only provides a better not of the data, but also offers possible explanations of the error sources. Without requiring extra hypothesis tests on the model coefficients, the results from FA are more efficient in terms of capturing the systematic difference. Furthermore, without using a covariance model, a novel interpolating method based on the relationship between the loading matrix and the factor scores is developed for predictive purposes. The prediction error analysis shows that about 3-7 cm precision is expected in NAVD 88 after removing the systematic difference.
机译：在NAVD 88（1988年北美垂直基准）和纯重力大地水准面模型之间发现了很大的系统差异（范围从20厘米到+130厘米）。这种差异不仅使直接使用庞大的NAVD 88网络和最新的大地测量学最新技术来增强本地大地水准面模型非常困难，而且还限制了研究人员有效证明大地水准面模型改进的能力在NAVD 88网络上。在这里，两种基于各种预定义基础函数（例如多项式，B样条和勒让德函数）的常规回归分析以及诸如变量分析（FA）的潜在变量分析（LVA）都用于分析系统差异。除了给出数学模型外，回归结果还没有揭示导致NAVD 88出现巨大差异的物理原因，这可能引起不同研究人员的兴趣。此外，传统回归模型的残差中仍然留有大量的非高斯信号。另一方面，FA方法不仅可以提供更好的数据，而且可以提供错误源的可能解释。不需要对模型系数进行额外的假设检验，FA的结果在捕获系统差异方面更为有效。此外，在不使用协方差模型的情况下，出于预测目的，开发了一种基于加载矩阵与因子得分之间关系的新颖内插方法。预测误差分析表明，除去系统差异后，NAVD 88的精度预计约为3-7 cm。

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