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 \(3^{\circ }\). 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 \(5^{\circ }\times 5^{\circ }\) as well as a \(1^{\circ }\times 1^{\circ }\) 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.

Up to now, state‐of‐the‐art empirical slant delay modeling for processing observations from radio space geodetic techniques has been provided by a combination of two empirical models. These are GPT (Global Pressure and Temperature) and GMF (Global Mapping Function), both operating on the basis of long‐term averages of surface values from numerical weather models. Weaknesses in GPT/GMF, specifically their limited spatial and temporal variability, are largely eradicated by a new, combined model GPT2, which provides pressure, temperature, lapse rate, water vapor pressure, and mapping function coefficients at any site, resting upon a global 5° grid of mean values, annual, and semi‐annual variations in all parameters. Built on ERA‐Interim data, GPT2 brings forth improved empirical slant delays for geophysical studies. Compared to GPT/GMF, GPT2 yields a 40% reduction of annual and semi‐annual amplitude differences in station heights with respect to a solution based on instantaneous local pressure values and the Vienna mapping functions 1, as shown with a series of global VLBI (Very Long Baseline Interferometry) solutions.

Global pressure and temperature 2 wet (GPT2w) is an empirical troposphere delay model providing the mean values plus annual and semiannual amplitudes of pressure, temperature and its lapse rate, water vapor pressure and its decrease factor, weighted mean temperature, as well as hydrostatic and wet mapping function coefficients of the Vienna mapping function 1. All climatological parameters have been derived consistently from monthly mean pressure level data of ERA-Interim fields (European Centre for Medium-Range Weather Forecasts Re-Analysis) with a horizontal resolution of 1°, and the model is suitable to calculate slant hydrostatic and wet delays down to 3° elevation at sites in the vicinity of the earth surface using the date and approximate station coordinates as input. The wet delay estimation builds upon gridded values of the water vapor pressure, the weighted mean temperature, and the water vapor decrease factor, with the latter being tuned to ray-traced zenith wet delays. Comparisons with zenith delays at 341 globally distributed global navigation satellite systems stations show that the mean bias over all stations is below 1 mm and the mean standard deviation is about 3.6 cm. The GPT2w model with the gridded input file is provided at http://ggosatm.hg.tuwien.ac.at/DELAY/SOURCE/GPT2w/ .

A new realization of the International Celestial Reference Frame (ICRF) is presented based on the work achieved by a working group of the International Astronomical Union (IAU) mandated for this purpose. This new realization follows the initial realization of the ICRF completed in 1997 and its successor, ICRF2, adopted as a replacement in 2009. The new frame, referred to as ICRF3, is based on nearly 40 years of data acquired by very long baseline interferometry at the standard geodetic and astrometric radio frequencies (8.4 and 2.3 GHz), supplemented with data collected at higher radio frequencies (24 GHz and dual-frequency 32 and 8.4 GHz) over the past 15 years. State-of-the-art astronomical and geophysical modeling has been used to analyze these data and derive source positions. The modeling integrates, for the first time, the effect of the galactocentric acceleration of the solar system (directly estimated from the data) which, if not considered, induces significant deformation of the frame due to the data span. The new frame includes positions at 8.4 GHz for 4536 extragalactic sources. Of these, 303 sources, uniformly distributed on the sky, are identified as “defining sources” and as such serve to define the axes of the frame. Positions at 8.4 GHz are supplemented with positions at 24 GHz for 824 sources and at 32 GHz for 678 sources. In all, ICRF3 comprises 4588 sources, with three-frequency positions available for 600 of these. Source positions have been determined independently at each of the frequencies in order to preserve the underlying astrophysical content behind such positions. They are reported for epoch 2015.0 and must be propagated for observations at other epochs for the most accurate needs, accounting for the acceleration toward the Galactic center, which results in a dipolar proper motion field of amplitude 0.0058 milliarcsecond yr⁻¹(mas yr⁻¹). The frame is aligned onto the International Celestial Reference System to within the accuracy of ICRF2 and shows a median positional uncertainty of about 0.1 mas in right ascension and 0.2 mas in declination, with a noise floor of 0.03 mas in the individual source coordinates. A subset of 500 sources is found to have extremely accurate positions, in the range of 0.03–0.06 mas, at the traditional 8.4 GHz frequency. Comparing ICRF3 with the recently releasedGaiaCelestial Reference Frame 2 in the optical domain, there is no evidence for deformations larger than 0.03 mas between the two frames, in agreement with the ICRF3 noise level. Significant positional offsets between the three ICRF3 frequencies are detected for about 5% of the sources. Moreover, a notable fraction (22%) of the sources shows optical and radio positions that are significantly offset. There are indications that these positional offsets may be the manifestation of extended source structures. This third realization of the ICRF was adopted by the IAU at its 30th General Assembly in August 2018 and replaced the previous realization, ICRF2, on January 1, 2019.

In the past few years, numerical weather models (NWM) have been investigated to improve mapping functions which are used for tropospheric delay modeling in VLBI and GPS data analyses. The Vienna Mapping Functions VMF are based on direct raytracing through NWM, and so they are able to exploit the full information provided in the NWM. On the other hand, the Isobaric Mapping Functions IMF are using intermediate parameters calculated from the NWM. In this study, pressure level data from ECMWF (European Centre for Medium‐Range Weather Forecasts) are applied to determine the coefficients of the VMF and the IMF. Used for the analyses of IVS‐R1 and IVS‐R4 VLBI sessions, both mapping functions improve the repeatability of baseline lengths (by ∼10% for IVS‐R1 and ∼5% for IVS‐R4) compared to the Niell Mapping Functions NMF.