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Accurate modeling of tropospheric delays is crucial for the global navigation satellite system (GNSS), which finds extensive applications in early warning systems of natural hazards and extreme weather forecasting. Zenith tropospheric delay (ZTD) is estimated as a random walk process with a constraint in GNSS processing. The constraint, referred to as random walk process noise (RWPN), holds significant importance in real-time ZTD estimation and exhibits geographical and temporal specificity. Presently, RWPN is treated as either a constant value or derived from a numerical weather model (NWM). To address this, our study presents a global RWPN model (GRM) by parameterizing a decade of NWM-derived RWPN data. Taking into account its spatiotemporal nature, we formulate the RWPN equation for each station by employing trigonometric, exponential, and Legendre functions. The optimum RWPN value is determined by incorporating GRM using latitude, longitude, orthometric height, and time as inputs. To validate the efficacy of GRM, we compare its performance against RWPN values derived from both JRA-55 and ERA5 datasets for the year 2020. The results indicate that the GRM-derived values exhibit enhanced accuracy in comparison with the optimal fixed RWPN values, as well as the yearly and monthly mean RWPN values. Additionally, we assess the efficacy of the GRM model in real-time ZTD estimation across 20 globally distributed GNSS stations. The results reveal an improvement exceeding 10% when compared to the results of the best fixed RWPN values. The GRM model offers an effective solution for obtaining accurate RWPN values on a global level, all while minimizing computational demands and time constraints. This notable progress significantly bolsters the precision of real-time GNSS estimates, thus facilitating their application in time-sensitive geophysical and meteorological scenarios. Highlights: A global RWPN model is introduced for real-time GNSS tropospheric delay estimation. The model provides precise RWPN values while minimizing computation cost and time. The proposed model improves the accuracy of real-time ZTD estimation by over 10%. This model promotes GNSS in time-critical geophysical applications. [ABSTRACT FROM AUTHOR]

The correction of tropospheric influences via so-called path delays is critical for the analysis of observations from space geodetic techniques like the very long baseline interferometry (VLBI). In standard VLBI analysis, the a priori slant path delays are determined using the concept of zenith delays, mapping functions and gradients. The a priori use of ray-traced delays, i.e., tropospheric slant path delays determined with the technique of ray-tracing through the meteorological data of numerical weather models (NWM), serves as an alternative way of correcting the influences of the troposphere on the VLBI observations within the analysis. In the presented research, the application of ray-traced delays to the VLBI analysis of sessions in a time span of 16.5 years is investigated. Ray-traced delays have been determined with program RADIATE (see Hofmeister in Ph.D. thesis, Department of Geodesy and Geophysics, Faculty of Mathematics and Geoinformation, Technische Universität Wien. , 2016) utilizing meteorological data provided by NWM of the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with a standard VLBI analysis, which includes the tropospheric gradient estimation, the application of the ray-traced delays to an analysis, which uses the same parameterization except for the a priori slant path delay handling and the used wet mapping factors for the zenith wet delay (ZWD) estimation, improves the baseline length repeatability (BLR) at 55.9% of the baselines at sub-mm level. If no tropospheric gradients are estimated within the compared analyses, 90.6% of all baselines benefit from the application of the ray-traced delays, which leads to an average improvement of the BLR of 1 mm. The effects of the ray-traced delays on the terrestrial reference frame are also investigated. A separate assessment of the RADIATE ray-traced delays is carried out by comparison to the ray-traced delays from the National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Eriksson and MacMillan in , 2016) with respect to the analysis performances in terms of BLR results. If tropospheric gradient estimation is included in the analysis, 51.3% of the baselines benefit from the RADIATE ray-traced delays at sub-mm difference level. If no tropospheric gradients are estimated within the analysis, the RADIATE ray-traced delays deliver a better BLR at 63% of the baselines compared to the NASA GSFC ray-traced delays. [ABSTRACT FROM AUTHOR]

Precise global navigation satellite system (GNSS) positioning requires an accurate mapping function (MF) to model the tropospheric delay. To date, the most accurate MF is the Vienna mapping function 1 (VMF1). It utilizes data from a numerical weather model and therefore captures the short-term variability of the atmosphere. Still, the VMF1, or any other MF that is based on the VMF1 concept, is a parameterized mapping approach, and this means that it is tuned for specific elevation angles, station heights, and orbital altitudes. In this study, we analyze the systematic errors caused by such tuning on a global scale. We find that, in particular, the parameterization of the station height dependency is a major concern regarding the application in complex terrain or airborne applications. At this time, we do not provide an improved parameterized mapping approach to mitigate the systematic errors but instead we propose a (ultra-) rapid direct mapping approach, the so-called Potsdam mapping factors (PMFs). Since for any station-satellite link the ratio of the tropospheric delay in the slant and zenith direction is computed directly, the PMFs effectively eliminate the systematic errors. [ABSTRACT FROM AUTHOR]

The EUMETNET EIG GNSS Water Vapour Programme (E-GVAP) is responsible for the coordination of near real time GPS Zenith Total Delay (ZTD) production in Europe and for aiding the development of ZTD assimilation into Numerical Weather Prediction (NWP) models. Since 2000, the Geodetic Observatory Pecný (GOP) has been routinely estimating regional ZTDs in near real time. In 2010, GOP developed a modified processing system in order to provide the first optimal and robust ZTD solution with a global scope and hourly upgrade, fulfilling the requirements for assimilation into operational NWP models. Since July 2010, the GOP global tropospheric product has consisted of about 90 sites and has contributed routinely in a testing mode into the E-GVAP database. Global near real time ZTDs generated over ten months have been evaluated with respect to IGS and EUREF routine post-processed ZTD products, ZTDs integrated from radiosonde profiles, and ZTDs calculated from the Met Office global NWP model. Comparison with the GNSS post-processed solutions gives standard deviations of 3-6 mm in ZTD and biases of 1-2 mm, which is comparable to GOP regional near real time solution, however, for some isolated or low data quality stations up to 20 % quality decrease can be found. Comparison with NWP shows a latitudinal trend in the standard deviation with values as low as 4 mm at high latitudes, increasing to almost 20 mm in the tropics, and a lack of variability in the model background ZTD in the tropics. The evaluation with global radiosondes gives ZTD standard deviation of 5-16 mm, which is comparable with previous studies in European scope. Since the 10-month comparison gave satisfactory results, GOP was asked by UK Met Office to disseminate the global product to the end users via the Global Telecommunications System. Since 10 October 2011, the GOP global ZTD product configuration has been extended to about 164 global stations and still processed within 10 min. However, in GOP routine contribution to E-GVAP, about 124 stations are available in general due to hourly data latency above 30 min or data gaps. [ABSTRACT FROM AUTHOR]

Interferometric synthetic aperture radar phase data include not only signals due to crustal movements, but also those associated with microwave propagation delay through the atmosphere. In particular, the effect of water vapor can generate apparent signals in the order of a few centimeters or more, and prevent us from detecting such geophysical signals as those due to secular crustal deformation. To examine if and to what extent numerical weather model (NWM) outputs are helpful to reduce the tropospheric delay signals at spatial scales of 5-50 km wavelengths, we compared three approaches of tropospheric signal reduction, using 54 interferograms in central Hokkaido, Japan. The first approach is the conventional topography-correlated delay correction that is based on the regional digital elevation model (DEM). The second approach is based on the Japan Meteorological Agency's operational meso-scale analysis model (MSM) data, where we compute tropospheric delays and subtract them from the interferogram. However, the MSM data are available at predefined epochs and their spatial resolution is about 10 km; therefore, we need to interpolate both temporally and spatially to match with interferograms. Expecting to obtain a more physically plausible reduction of the tropospheric effects, we ran a 1-km mesh high-resolution numerical weather model WRF (Weather Research and Forecasting model) by ourselves, using the MSM data as the initial and boundary conditions. The third approach is similar to the second approach, except that we make use of the WRF-based tropospheric data. Results show that if the topography-correlated phases are significant, both the conventional DEM-based approach and the MSM-based approach reveal comparable performances. However, when the topography-correlated phases are insignificant, none of the approaches can efficiently reduce the tropospheric phases. Although it could reduce the tropospheric signals in a local area, in none of the case studies did the WRF model produce the 'best' performance. Whereas the global atmospheric model outputs are shown to be effective in reducing long-wavelength tropospheric signals, we consider that further improvements are needed for the initial and boundary condition data for high-resolution NWM, so that the NWM-based approach will become more reliable even in the case of a non-stratified troposphere. [ABSTRACT FROM AUTHOR]

Numerical weather models offer the possibility to compute corrections for a variety of space geodetic applications, including remote sensing techniques like interferometric SAR. Due to the computational complexity, exact ray-tracing is avoided in many cases and mapping approaches are applied to transform vertically integrated delay corrections into slant direction. Such an approach works well as long as lateral atmospheric gradients are small enough to be neglected. But since such an approximation holds only for very rare cases it is investigated how horizontal gradients of different atmospheric constituents can evoke errors caused by the mapping strategy. Moreover, it is discussed how sudden changes of wet refractivity can easily lead to millimeter order biases when simplified methods are applied instead of ray-tracing. By an example, based on real InSAR data, the differences of the various troposphere correction schemes are evaluated and it is shown how the interpretation of the geophysical signals can be affected. In addition, it is studied to which extend troposphere noise can be reduced by applying the exact ray-tracing solution. [ABSTRACT FROM AUTHOR]