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.

Water Vapor Tomography of the Lower Atmosphere from Multiparametric Inversion: the Mt. Etna Volcano Test Case

Space techniques based on GPS and SAR interferometry allow measuring millimetric ground deformations. Achieving such accuracy means removing atmospheric anomalies that frequently affect volcanic areas by modeling the tropospheric delays. Due to the prominent orography and the high spatial and temporal variability of weather conditions, the active volcano Mt. Etna (Italy) is particularly suitable to carry out research aimed at estimating and filtering atmospheric effects on GPS and DInSAR ground deformation measurements. The aim of this work is to improve the accuracy of the ground deformation measurements by modeling the tropospheric delays at Mt. Etna volcano. To this end, data from the monitoring network of 29 GPS permanent stations and MODIS multispectral satellite data series are used to reproduce the tropospheric delays affecting interferograms. A tomography algorithm has been developed to reproduce the wet refractivity field over Mt. Etna in 3D, starting from the slant tropospheric delays calculated by GPS in all the stations of the network. The developed algorithm has been tested on a synthetic atmospheric anomaly. The test confirms the capability of the software to faithfully reconstruct the simulated anomaly. With the aim of applying this algorithm to real cases, we introduce the water vapor content measured by the MODIS instrument on board Terra and Aqua satellites. The use of such data, although limited by cloud cover, provides a two-fold benefit: it improves the tomographic resolution and adds feedback for the GPS wet delay measurements. A cross-comparison between GPS and MODIS water vapor measurements for the first time shows a fair agreement between those indirect measurements on an entire year of data (2015). The tomography algorithm was applied on selected real cases to correct the Sentinel-1 DInSAR interferograms acquired over Mt. Etna during 2015. Indeed, the corrected interferograms show that the differential path delay reaches 0.1 m (i.e. 3 C-band fringes) in ground deformation, demonstrating how the atmospheric anomaly affects precision and reliability of DInSAR space-based techniques. The real cases show that the tomography is often able to capture the atmospheric effect at the large scale and correct interferograms, although in limited areas. Furthermore, the introduction of MODIS data significantly improves by ∼80% voxel resolution at the critical layer (1,000 m). Further improvements will be suitable for monitoring active volcanoes worldwide.

Calibrating the Tropospheric Delays of VLBI Observations using Numerical Weather Prediction Models

<p>The observations of geodetic Very Long Baseline Interferometry (VLBI) are affected by the troposphere, and this effect needs to be considered in the VLBI data analysis. The normal way of doing this is to estimate the zenith tropospheric delays and tropospheric gradients as additional parameter in the analysis. However, due to the poor geometric distributions of the observations in some VLBI sessions, like the Intensives, the tropospheric parameters cannot be estimated with a high accuracy. An alternative is to use external information on the tropospheric delay from Numerical Weather Prediction Models (NWM). Due to the increasing accuracy of the NWM, this alternative is becoming more and more interesting. In this work, we use tropospheric delays from the fifth ECMWF reanalysis, ERA5, in the analysis of VLBI data and evaluate the impacts on the results. We study the impact of different types of VLBI sessions, like Intensives, local networks, and global networks. The results of this study will show to what extent ERA5 data can be used to correct the tropospheric delays in geodetic VLBI. Furthermore, the results also give information on the accuracy of the tropospheric delays from NMW.</p>

Tropospheric products as a signal of interest – overview of troposphere sensing techniques

<p>The microwave signals passing through the troposphere are delayed by refraction. Its high variations, both in time and space, are caused mainly by water vapor. The tropospheric delay used to be considered only as a source of error that needed to be removed. Nowadays, these delays are also a source of interest. The tropospheric delays or integrated water vapor are being assimilated into nowcasting or numerical weather prediction (NWP) models. Moreover, long time series of tropospheric observations have become an important source of information for climate studies. On the other hand, the meteorological data support the space-geodetic community by providing models that can be used to reduce the troposphere impact on the signal propagation. Furthermore, the delays calculated by one microwave technique can be used to mitigate the errors in others.</p><p>There are several ways of observing the troposphere, especially considering water vapor. The classical meteorological are: in-situ measurements, radiosondes or radiometers, which allow to sense the amount of water vapor directly. Another, indirect way of observing the water vapor distribution is by using the Global Navigation Satellite Systems (GNSS). This method is called GNSS meteorology. Other microwave techniques such as Very Long Baseline Interferometry (VLBI) or Interferometric Synthetic Aperture Radar (InSAR) are also capable to retrieve the atmospheric information from their signals.</p><p>This contribution shows an overview of the troposphere sensing techniques and their applications. We present multi-comparisons of the tropospheric parameters, i.e. refractivity, tropospheric delays in zenith and slant directions and integrated water vapor. The integration of the different data sources often leads to an improved accuracy of the tropospheric products but requires a careful preparation of data. The combination of the data sources allows for using the techniques of complementary properties, for example InSAR with very high spatial resolution with GNSS observations of high temporal resolution. With the emergence of new technologies, some traditional ways of tropospheric measurements can be augmented with the new methods. For example, we have tested meteo-drones as an alternative to radiosondes. The comparisons with GNSS data shows a good agreement of the drone and microwave data, even better than with radiosonde. Moreover, we present the results of the GNSS data assimilation into NWP models and the developments towards multi-GNSS, real-time assimilation of advanced products such as slant delays and horizontal tropospheric gradients.</p>

A comparative study of different tropospheric delay solutions applied to GNSS observations of the MOSAiC expedition.

<p><span>The<em> Multidisciplinary Drifting Observatory for the Study of Arctic Climate </em>(MOSAiC) campaign was conducted from September 2019 to October 2020. It aimed to observe the Arctic region's environmental parameters, considered to be the epicenter of the effects of climate change. On this occasion, a multi-GNSS antenna was deployed on the<em> R/V Polarstern</em>. This installation aims mainly at estimating tropospheric delays, a proxy for the determination of atmospheric water vapor content. The number of observations of this type in the marine - and moreover polar - domain remains extremely limited so far. This experiment is also a good opportunity to carry out a comparative study of the tropospheric delay solutions that can be provided by different geodetic processing software. The underlying idea is to evaluate the repeatability of the different products and the overall state-of-the-art accuracy. We propose here to process the GNSS data acquired during the polar campaign with several packages (namely Bernese GNSS Software, GINS, TRACK, and CSRS-PPP) and compare the results and their agreement level. The data are also validated from observations made on land by GNSS stations at Bremerhaven (Germany), Tromsø (Norway) & Ny Ålesund (Svalbard), the VLBI station of Ny Ålesund, and the ECMWF ERA5 numerical model.</span></p>

Robust InSAR Tropospheric Delay Correction Using Global Atmospheric Models

<p>Tropospheric delays are the main source of error when measuring ground displacements using InSAR. Increasingly, global atmospheric models (GAMs), e.g., ERA5 and MERRA2 reanalysis data, are used to reduce tropospheric signals in InSAR deformation observations. However, due to the coarse spatial resolution of current GAMs (~10s of kilometers), it is still challenging to obtain tropospheric corrections for high-resolution InSAR data (~10s of meters). Here we present an advanced GAM-based correction method, aimed at improving InSAR geodesy, that incorporates spatial stochastic models of the troposphere in the corrections. We first estimate stochastic models of the tropospheric parameters (temperature, pressure, and partial pressure of water vapor) at different GAM altitude layers and we then interpolate the parameters according to the correlation between pixels of interest and the GAM grid locations (3D). The interpolation accounts for spatial variabilities of the tropospheric random field, instead of subjectively using an inverse distance method or using a local spline function, which are commonly used in current GAM-correction methods. We also estimate the integral of the tropospheric delays along the satellite line-of-sight (LOS) direction directly, instead of calculating the projected zenith-delays, because the troposphere is not purely stratified. Our new method can easily be applied using any of the present GAMs; here we implemented it with the latest ECMWF ERA5 reanalysis outputs. We validate the new method for both interferograms and time-series analysis products (deformation velocities and time-series solutions), using hundreds of the Sentinel-1 images over the island of Hawaii from 2015 to 2020. The results show that the average standard deviation of non-deforming interferograms reduces from 2.55 cm to 1.91 cm when applying the new method, compared with standard deviations of 2.47 cm (PyAPS), 2.44 cm (d-LOS), and 2.10 cm (GACOS), after using three common GAM correction methods. In addition, the new method improves most (87%, i.e., 243 out of 280) of the interferograms, while only about half (52%, 53%, and 66%) are improved by the earlier correction methods. The results demonstrate the importance of considering (1) tropospheric stochastic models in GAM-corrections, (2) horizontal heterogeneities when estimating the LOS delays, and (3) tropospheric delays when mapping long-wavelength or small-magnitude deformation using InSAR.</p>

Impact of the Galileo constellation on GNSS Tropospheric Tomography

<p>GNSS Tomography is a promising tool to reconstruct the wet refractivity field (Nw) related to water vapor due to the continuous pass of GNSS rays through the atmosphere. To improve observation geometry compared to a sole GPS/ Glonass system scenario, applying further multi-GNSS observations in GNSS Tomography has become an essential research point in the recent decade. Therefore, the aim of this presentation is to investigate the impact of different constellations to solve the ill-posed inverse problem to retrieve a wet refractivity field by focusing on Galileo's effect on the accuracy of the estimated refractivity. Regarding this, the designed models loosely constrained due to provide an optimum situation for assessing the influence of Galileo constellation in the tomography solution. Test computations are based on data from a regional RTK-GNSS network close to Vienna operated by the Austrian power-supply company EVN (EnergieVersorgung Niederösterreich) and mostly located in the west part of Austria. The span DoYs 233-246 in August 2019 was chosen as a period of interest due to the high precipitation during that time. Consequently, we have considered the following processing schemes: 1- GPS+ Glonass (GR), 2- GPS+ Galileo (GE), and 3- GPS + Glonass + Galileo (GRE) to generate the reconstructed Nw field by means of the in-house Tomography software TOMTRP. Furthermore, as the Slant Tropospheric Delays (SWDs) and corresponding residuals are used as input data for GNSS tomography, so the impact of the mentioned schemes to estimate SWDs has been investigated here. Finally, in order to analyze the efficiency of the three schemes, the reconstructed refractivity profiles are compared to radiosonde profiles available in that area.</p>