Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of $$3^{\circ }$$3∘. Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a $$5^{\circ }\times 5^{\circ }$$5∘×5∘ as well as a $$1^{\circ }\times 1^{\circ }$$1∘×1∘ global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.

中文翻译：

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VMF3/GPT3：改进的离散和经验对流层映射函数

对流层延迟的不正确建模是全球导航卫星系统 (GNSS) 或甚长基线干涉测量 (VLBI) 等空间大地测量技术的主要误差源之一。多年来，已经设计了许多方法，旨在将无线电波从天顶方向的延迟映射到观察到的仰角，即所谓的映射函数。本文包含了一种新方法，旨在改进当前最重要的离散映射函数，即 Vienna Mapping Functions 1 (VMF1)，随后称为 Vienna Mapping Functions 3 (VMF3)。它的设计方式是为了消除经验系数 b 和 c 以及调整特定仰角 $$3^{\circ }$$3∘ 的缺点。光线追踪器 RADIATE 的光线追踪延迟用作计算新映射函数系数的基础。模拟倾斜延迟的比较表明，VMF3 能够比 VMF1 更准确地近似潜在的光线追踪延迟，尤其是在低仰角时。换句话说，当需要最高精度时，VMF3 比 VMF1 更可取。除了修改映射函数的离散形式外，我们还在 $5^{\circ }\times 5^{\circ }$5∘×5∘ 上提出了一个新的经验模型，名为 Global Pressure and Temperature 3 (GPT3)以及 $$1^{\circ }\times 1^{\circ }$$1∘×1∘ 全局网格，一般基于相同的数据。它的主要组成部分是从各个（离散）VMF3 数据的特殊平均技术得出的静水和湿经验映射函数系数。此外，GPT3 还包含一组气象量，这些量是从它们的前身 Global Pressure and Temperature 2 中采用的。因此，GPT3 代表了一个非常全面的对流层模型，可用于一系列大地测量以及气象和气候目的，并且与 VMF3 完全一致。