Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489–20502, 1997. https://doi.org/10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017. https://doi.org/10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.

中文翻译：

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VLBI 分析中精致的离散和经验水平梯度

在全球导航卫星系统 (GNSS) 或甚长基线干涉测量 (VLBI) 等空间大地测量技术中，对对流层延迟的方位不对称性的缺失或不正确考虑是一个相当大的误差源。所谓的水平对流层梯度通常用于对这种方位角变化进行建模，并且对于低仰角的观测特别需要。除了在数据分析中估计梯度（这已成为空间大地测量技术中的常见做法）之外，还可以根据与实际观测不同的数据源预先确定梯度。通过数值天气模型 (NWM) 使用射线追踪，我们根据 Chen 和 Herring 的标准梯度模型确定了 VLBI 观测的离散梯度值（称为 GRAD）（J Geophys Res 102(B9):20489–20502, 1997。 https://doi.org/10.1029/97JB01739）以及新的高阶梯度模型。这些梯度是在与维也纳映射函数 3 (VMF3) 相同的数据基础上生成的（Landskron 和 Böhm，J Geod，2017 年。https://doi.org/10.1007/s00190-017-1066-2），因此它们可以也可以被视为 VMF3 梯度，因为它们彼此完全一致。从维也纳 VLBI 和卫星软件 (VieVS) 的 VLBI 分析中可以看出，当使用先验梯度 GRAD 而不是估计梯度时，基线长度重复性 (BLR) 平均提高了 5%。这种改进的原因是梯度估计对于具有少量观测值的 VLBI 会话产生较差的结果，而 GRAD 先验梯度不受此影响。我们还开发了一种适用于地球上任何时间和地点的新经验梯度模型，该模型包含在全球压力和温度 3 (GPT3) 模型中。尽管只能描述方位角不对称的系统组成部分并且根本没有短期变化，但即使是这些经验先验梯度也会稍微减少（改善）关于梯度估计的 BLR。总的来说，本文指出先验水平梯度对于 VLBI 分析实际上比之前假设的更重要，特别是离散模型 GRAD 以及经验模型 GPT3 确实能够细化和改进结果。