Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so.

Validation of tropospheric ties at the test setup GNSS co-location site Potsdam

Atmospheric ties are theoretically affected by the height differences between antennas at the same site and the meteorological conditions. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, potentially degrading a combined solution employing atmospheric ties. In order to investigate the possible effects on GNSS atmospheric delay, this study set up an experiment of four co-located GNSS stations of the same type, both antenna and receiver. Specific height differences for each antenna w.r.t the reference antenna are given. One antenna was equipped with a radome at the same height and type as a antenna close to the ground. In addition, a meteorological sensor was used for meteorological data recording. The results show that tropospheric ties from the analytical equation based on meteorological data from GPT3, Numerical Weather Model, and in-situ measurements, and ray-traced tropospheric ties, reduced the bias of zenith delay roughly by 72 %. However, the in-situ tropospheric ties yield the best precision in this study. These results demonstrate, that the instrument effects on GNSS zenith delays were mitigated by using the same instrument. In contrast, the radome causes unexpected bias of GNSS zenith delays in this study. Additionally, multipath effects at low-elevation observations degraded the tropospheric east gradients.

Validation of tropospheric ties at the test setup GNSS co-location site in Potsdam

<p>Atmospheric ties are induced by differences between the set-up of observing geodetic systems at co-location sites, are mainly attributed to frequency and position, and are usually quantified by zenith delay and gradient component offsets derived by weather models or in situ instuments.. Similar to local ties, they could be applied to combine datasets from several space geodetic techniques, thus contributing to the improvement of the realization of terrestrial reference frames (TRF). Theoretically, atmospheric ties are affected only by the height differences between antennas at the same site and meteorological conditions. Therefore, atmospheric ties could be determined analytically based on meteorological information from in situ measurements or weather models. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, potentially degrading a combined atmospheric ties solution should tight constraints be used. In this study, we set up a GNSS experiment campaign on the rooftop of a building in Telegrafernberg that offers unobscured data coverage for one month. We compared the estimated zenith delay and gradients from GNSS stations in this experiment, applying atmospheric ties from (1) meteorological data from the Global Pressure and Temperature model 3 (GPT3), (2) ERA5 reanalysis, and (3) in-situ measurements, as well as corrections derived from ray tracing (Potsdam Mapping Functions, PMF). The results show that atmospheric ties employing GPT3, ERA5, in-situ measurements, and ray tracing has an excellent and comparable performance in term of bias mitigation, but not in term of standard deviation, for zenith delay. Moreover, the unexpected bias in zenith delay was identified in the antenna with radome installation. A significantly large bias was identified in estimated gradients; the source of this discrepancy has been traced back to unmitigated multipath effects in this experiment.</p>

Assessment on atmospheric parameters at co-location sites

<p>Atmospheric ties are affected by the differences of atmospheric parameters of space geodetic techniques at co-location sites. Similar to local ties, they could be applied along with local ties for a combination of space geodetic techniques to improve the realization of terrestrial reference frames (TRF). Theoretically, atmospheric ties are affected by the height differences between antennas at the same site and meteorological conditions. Therefore, atmospheric ties could be determined by analytical equation based on meteorological information from in situ measurements or weather model. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, thus potentially degrading a combined atmospheric ties solution. In this study, we analyse the time series of zenith delays from co-located GNSS antennas at Wettzell (height differences below 3 meters), for 11 years (2008–2018). GNSS observations were analyzed with Bernese GNSS software version 5.2 with double-differencing technique and relative tropospheric delay and gradients were estimated with L1, L2, and the ionosphere-free (L3) linear combination thereof. Atmospheric ties were derived analytically employing meteorological data from Global Pressure and Temperature model 3 (GPT3) and ERA5 reanalysis, as well as corrections derived from ray tracing (Potsdam Mapping Functions, PMF). The comparison shows that zenith delay differences are dominated by equipment changes. The discrepancies between atmospheric ties and estimated zenith delay differences are frequency dependent, with the L1 solutions being the least biased. For these small vertical differences, seasonal signals are not significant for all frequencies.</p>

A Simulation Study on Triple Frequency Ambiguity Resolution for Reference Stations Using Different Strategy Regarding Elevation angles

This paper proposes an ambiguity resolution method using triple frequency for reference stations. Using the reference coordinate information, geometry based ambiguity resolution performance is analysed. Although orbit errors and tropospheric model errors still remain, wide lane ambiguity could be fixed in several epochs. However, the narrow lane wave length of about 10cm is too short to overcome error sources by simply combining the measurement. Therefore, we have divided the elevation angle into 5 degree intervals and investigated the measurement errors and the time to fix of each section. For high elevation satellites, it is possible to determine in several epochs by integer rounding. On the other hand, if the elevation is lower than 30 degrees, the tropospheric zenith delay must be estimated with ambiguities. The proposed algorithm estimates ambiguities and tropospheric zenith delay simultaneously utilizing ambiguity free observations of high elevation satellites. Ambiguities for high elevation satellites are resolved by integer rounding in several epochs. The algorithm has been verified by generating the simulated observation data for the ‘Cheon-an’ and ‘Boen’ reference stations in the Korea.

INVESTIGATION OF THE AIR QUALITY CHANGE EFFECT ON GNSS SIGNALS

Air pollution is the most important environmental problem in Zonguldak city center. Since bituminous coal is used for domestic heating in houses and generating electricity in thermal power plants, particulate matter (PM₁₀) is the leading air pollutant. Previous studies have shown that the water vapor in the troposphere is responsible for the tropospheric zenith delay in Global Navigation Satellite System (GNSS) measurements. In this study, data obtained from the ZONG GNSS station from Türkiye Ulusal Sabit GNSS Ağı (TUSAGA-Active network) in the central district of Zonguldak province, processed with GIPSY-OASIS II and GAMIT/GlobK software using the VMF1 mapping function, which is developed previously and considered to be the most accurate model. The resulting values were examined separately in terms of software. The meteorological parameters obtained from the Turkish State Meteorological Service and the air pollution values obtained from the Ministry of Environment and Urban Planning were analyzed and the zenith delay values were compared. When wet zenith delays of different days with different amounts of PM₁₀ concentrations were examined in succession and under the same meteorological conditions, differences in the range of 20–40 mm on ZTD were observed.

Assimilation Impact of Different GPS Analysis Methods on Precipitation Forecast: A Heavy Rainfall Case Study of Kani City, Gifu Prefecture on July 15, 2010

In this study, we examined variations in predicted precipitable water produced from different Global Positioning System (GPS) zenith delay methods, and assessed the corresponding difference in predicted rainfall after assimilating the obtained precipitable water data. Precipitable water data estimated from the GPS and three-dimensional horizontal wind velocity field derived from the X-band dual polarimetric radar were assimilated in CReSS and rainfall forecast experiments were conducted for the heavy rainfall system in Kani City, Gifu Prefecture on July 15, 2010. In the GPS analysis, a method to simultaneously estimate coordinates and zenith delay, i.e., the simultaneous estimation method, and a method to successively estimate coordinates and zenith delay, i.e., the successive estimation method, were used to estimate precipitable water. The differences generated from using predicted orbit data provided in pseudo-real time from the International GNSS (Global Navigation Satellite System) Service for geodynamics (IGS) versus precise orbit data released after a 10-day delay were examined. The change in precipitable water due to varying the analysis methods was larger than that due to the type of satellite orbit information. In the rainfall forecast experiments, those using the successive estimation method results had a better precision than those using the simultaneous estimation method results. Both methods that included data assimilation had higher rainfall forecast precisions than the forecast precision without precipitable water assimilation. Water vapor obtained from GPS analysis is accepted as important in rainfall forecasting, but the present study showed additional improvements can be attained from incorporating a zenith delay analysis method.