Geodesy for a Sustainable Earth

The ITRF2020 is the upcoming official solution of the International Terrestrial Reference Frame and is the successor to the currently used ITRF2014. The global ITRF2020 solution is based on an inter-technique combination of the four space-geodetic techniques VLBI, GNSS, SLR, and DORIS. In this context, the Combination Centre of the IVS (International VLBI Service for Geodesy and Astrometry) operated by the Federal Agency for Cartography and Geodesy (BKG, Germany) in close cooperation with the Deutsches Geodätisches Forschungsinstitut at TUM (DGFI-TUM, Germany) generates the final VLBI contribution of the IVS. This is achieved by an intra-technique combination utilizing the individual contributions of multiple IVS Analysis Centres (ACs). For the IVS contribution to the ITRF2020, sessions containing 24 h VLBI observations from 1979 until the end of 2020 were re-processed by 11 different ACs and submitted to the IVS Combination Centre. As a result, datum-free normal equations containing station coordinates and source positions as well as full sets of Earth Orientation Parameters (EOP) are delivered. In order to ensure consistency of the combined solution, time series of EOP and station coordinates were generated and further investigated for validation. Finally, the IVS contribution to the ITRF2020 comprises session-wise normal equations including EOP and station coordinates provided in SINEX format. In order to assess the quality of the contributions by the individual IVS ACs, internal as well as external comparisons of the estimated EOP are carried out, with the combined solution as well as external time series (e.g., IERS Bulletin A) serving as a reference. Additionally, the scale of the IVS contribution is investigated as VLBI is one of the space geodetic techniques realizing the scale of the ITRF. The evaluation of the contributions by the ACs, the combination procedure, and the results of the combined solution for station coordinates and EOP will be presented.

Over the past years, the International GNSS Service (IGS) has put efforts into reprocessing campaigns, reanalyzing the entire data collected by the IGS network since 1994. Using state-of-the-art models and software, the goal is to provide a consistent set of orbits, station coordinates, and earth rotation parameters. Unlike the previous campaigns—namely: repro1 and repro2—, the repro3 includes not only GPS and GLONASS but also the Galileo constellation. The main repro3 objective is the contribution to the next realization of the International Terrestrial Reference Frame (ITRF2020). To achieve this goal, several Analysis Centers (AC) submitted their own products to the IGS, which are combined to provide the final solutions for each product type. In this contribution, we focus on the combination of the orbit products. We present a consistent orbit solution based on a newly developed combination strategy, where the weights are determined by a Least-Squares Variance Component Estimation (LSVCE). The orbits are intended to be combined in an iterative processing: firstly, by aligning all the products via a Helmert transformation, secondly by defining which satellites will be used in the LSVCE, and finally by normalizing the inverse of the variances as weights that are used to compute a weighted mean. The combination results show an agreement between the different AC’s input orbits around 10 mm for GPS, 30 mm for GLONASS. The combination also highlights the improvement of the Galileo orbit determination over the past decade, the internal precision decreasing from around 35 mm to 16 mm for the most recent weeks. We used Satellite Laser Ranging (SLR) observations for external validation. The combined orbit has one of the best RMS agreements with respect to the SLR measurements (9.1 mm for GLONASS, and 8.3 mm over the last five years of the processed period).

In the present study, we estimate the correlations of the Helmert transformation’s parameters for various Terrestrial Reference Frame realizations (TRFs). The correlations can be served as an auxiliary diagnostic tool on assessing the quality of the Helmert transformation parameters (origin, scale, orientation and associated rates, respectively). Possible high correlations between the pair of parameters are signs of strong dependency of each other, hence their estimation can lead to misinterpretations. We compute the Helmert correlation coefficients of global TRFs for the following cases: (a) the SLR and VLBI intra-technique combinations contributing to the DTRF2014 construction and the associated SLR and VLBI inter-technique combinations and (b) the DORIS-related TRFs computed by the International DORIS Service (IDS) and the ITRF2014 (International TRF 2014). The results verify the good quality of DTRF2014 (DGFI-TUM TRF 2014) in terms of the Helmert parameters quality, for both SLR- and VLBI-related TRFs. For the case of the DORIS solutions, we find that the correlations are severely increased for the solution that includes 5 more years of observations than the ITRF2014 one.

The Japan Coast Guard (JCG) operates Satellite Laser Ranging (SLR) and Global Navigation Satellite System (GNSS) instruments at the Shimosato Hydrographic Observatory (SHO) in Wakayama Prefecture located at the southernmost area of the main island of Japan. SHO is a co-location site where SLR and GNSS can be linked by precisely measuring the local tie vector (relative position) between these two space geodetic techniques. In November 2020, JCG collaborated with the Geospatial Information Authority of Japan (GSI) and performed a local tie survey to precisely determine the local tie vector between the stone marker of the GNSS station and the invariant point (IVP) of the SLR telescope. The IVP of the SLR telescope was determined by an indirect method, in which the reflector targets mounted on the SLR telescope were precisely observed from the surrounding temporary marks. The SLR telescope was rotated at a constant interval during the survey so that the observed target positions form arcs, from which we determined the azimuth and elevation axes; the orthogonal projection of the elevation axis onto the azimuth axis was determined as the IVP. The resulting local tie vector and its variance-covariance information were submitted for the development of the upcoming International Terrestrial Reference Frame 2020 (ITRF2020).

The SLR station Riga operates a SLR system within ILRS (Riga 18844401, DOMES number 12302S002) and a collocated GNSS system (RIGA00LVA, DOMES number 12302M002) within IGS and EUREF networks. The reference geodetic mark (DOMES number 12302M001) was used for the mobile SLR system MTLRS operation in 1991. Domes 12302M002 is situated on top of an historical time service building which sits directly on the bedrock. Both other points are placed on concrete foundations built more than 50 years ago. All these points are included in the ITRF database. The first full local ties set was determined in 1995 using a 6 h GPS session run using three GPS receivers. In 2018 three geodetic pillars were installed to improve the local geodetic network at the site. In January 2021, a multitechnique survey campaign produced a new set of local ties and reported to the ITRF and related services. The obtained results show that the local tie stability is at the subcentimeter level over a 25 years period. The true stability may be better, taking into account the measurement technology used in the first survey 25 years ago. But to verify it we need to do more surveys.

The datum problem is a fundamental issue in the network adjustment when connecting a local measurement network to an external reference frame. Datum elements in 3D networks are scale, translation, and orientation. We consider here the local tie network at geodetic core stations, where the external reference frame is the latest ITRF realization, ITRF2014, in the mean epoch of terrestrial observations.Accurate distance measurements are used for the determination of the network scale. Thus the improvement of its accuracy and the inclusion of weather measurements to account for refraction errors are essential. For rotation and translation of the network, we need external information. Angle observations are related to the coordinate system of the instrument (e.g. a tachymeter) which is usually aligned to the plumb line. Instruments have different vertical orientation at every station point and the direction of the plumb line does not coincide with the normal vector of the reference ellipsoid. Horizontally the observed set of angles are oriented in arbitrary or approximately oriented directions.External information which is needed for solving the absolute orientation are datum points, providing the link to the global coordinate system, and correction terms for the vertical orientation (deflection of the vertical), which can be derived from combined terrestrial/GNSS observations, from a gravity based geoid model, or from astronomical observations.In this article, we present the solutions/options for the datum problem in the framework of the EMPIR GeoMetre project using the example of the ITRF core stations Metsähovi and Wettzell using transformation-free approaches. The inclusion of distant targets is promising, since in small networks even a millimeter change in the coordinates of a datum point can significantly affect a local tie vector. It is shown that at both stations the determination of the deflection of the vertical using different techniques yield the same results within the measurement error.

Local tie vectors are a crucial component within the combination of several space geodetic techniques. The vectors define the geometric relations between the space geodetic techniques, referring to the invariant reference points of such techniques. The Global Geodetic Observing System aims for an accuracy of 1 mm in the position on a global scale. In ITRF2014, about 50 % of the used local ties show discrepancies of more than 5 mm w.r.t. the global solution. In the framework of the IAG/IERS Working Group on Site Survey and Co-location or joint research projects like the international GeoMetre project strategies to improve the reference point determination and the local ties are developed. Strategies mainly comprise the development or the recommendation for surveying instruments, developing approaches for transforming local measurements to the global frame, and deriving innovative analysis procedures to derive the reference point of space geodetic techniques.In this contribution, we focus on the reference point determination. At the Geodetic Observatory Wettzell, a measurement campaign was carried out in September 2020 to evaluate the benefit of close range photogrammetry in the framework of reference point determination. For this purpose, the invariant reference point of a Satellite Laser Ranging telescope was derived several times using various configurations. The estimated reference point and the axis offset vary in a range of ±0.1 mm and ±0.02 mm, respectively. The resulting standard deviations of the coordinate components of the combined solution are less than 0.1 mm and impressively demonstrate the potential of the presented method.

The scope of this paper is to perform an internal quality assessment, at frame parameter level, on the combined EPN weekly coordinate solutions. Specifically, the weekly SINEX solution files from the EPN Analysis Combination Centre are analyzed in order to infer the internal accuracy of the origin, orientation and scale of the respective epoch solutions. Our investigation covers almost the entire operational period of EPN starting from 1999 up to present time, and it uses both the routine and re-processed (repro2) series of combined weekly solutions. Through the results of this study we are able to assess the impact of various changes or updates that have been applied into the routine GNSS data processing and combination strategies on the quality of the estimated EPN weekly frames.

This paper shows the current status of the Red Atlántica de Estaciones Geodinámicas y Espaciales (RAEGE), a joint Spanish-Portuguese infrastructure of geodetic stations. When complete, it will be composed of four VGOS (VLBI Global Observing System) radio-telescopes, two in Spain (Yebes and Gran Canaria) and two in Portugal (Santa María and Flores islands, Açores archipelago). The Yebes VGOS radio-telescope is fully operational and integrated in the VGOS core network since 2016. The Santa María VGOS radio-telescope has undergone major maintenance operations and has resume regular IVS observations with its tri-band S/X/Ka receiver since end of May 2021, until it becomes a VGOS station by the second half of 2022. Additionally, each station will include GNSS receivers, gravimeters and a local-tie network. In particular, the RAEGE-Yebes station will have a Satellite Laser Ranging (SLR) system, which is under construction. It can be said that RAEGE is the Spanish-Portuguese response to UN resolution 69/266 and GGOS (Global Geodetic Observing System). The current status of all the four RAEGE stations will be shown.

The aim of this paper is to present the results from the GNSS-based densification of the International Terrestrial Reference Frame (ITRF) in the region of Cyprus. The regional network used for this task consists of nine permanent GNSS Cypriot stations (eight stations of the existing CYPOS network plus the NICO station which belongs to the global IGS network) and 34 additional stations of the EUREF Permanent GNSS Network (EPN) which are mostly located in the continental part of Europe. The data used in this densification project include daily GNSS observations at the above stations within a period of 62 months (30/11/2011–28/01/2017). The present study was carried out using the resources of the CyCLOPS strategic research infrastructure unit. A robust procedure was designed for the daily data processing using the Bernese GNSS software v5.2 installed in the CyCLOPS operating center. The multi-year solution is computed by combining the constraint-free daily solutions using the normal equations stacking strategy. The reference frame of the multi-year solution is IGb08 and it was enforced through a no-net-translation condition on the positions and velocities of 24 EPN (Class A) stations. The quality of the computed solution is verified by comparing the estimated velocities with their official EPN_A_IGb08_C1934 values, and reveals minimal differences (<1 mm/year) in all EPN stations for both horizontal and up components.

The National Geographic Institute of Spain (IGN Spain) develops, operates, and exploits the Spanish national geodetic networks and their associated infrastructure. This includes the permanent networks of reference GNSS (Global Navigation Satellite System) receivers, VLBI (Very Long Baseline Interferometry) telescopes, and a new SLR (Satellite Laser Ranging) station under construction at the Yebes Observatory. In order to fully exploit the opportunities offered by the availability of these space geodetic techniques, IGN has been operating Analysis Centres of GNSS and VLBI for a number of years, with the recent addition of an Associated Analysis Centre of the International Laser Ranging Service.IGN Spain is a EUREF Analysis Centre since 2001, contributing with their weekly and daily coordinate solutions to the realisation of the European Terrestrial Reference System. The activities of the AC include projects such as IBERRED, for geodynamic purposes, and the participation in the European E-GVAP programme for meteorological applications. Over the last years, IGN Spain has expanded its contribution to geodetic VLBI analysis, starting in 2019 the operational analysis of VLBI sessions and the submission of the respective solutions (containing consistently estimated Earth Orientation Parameters, station coordinates and source positions) to the International VLBI Service for Geodesy and Astrometry (IVS). Additionally, the reprocessing of the historical VLBI data since 1979 is ongoing, which is the basis for future contributions to the IVS combination series that will be provided for future realisations of the international terrestrial reference frame (ITRF). The latest addition to IGN Spain analysis capabilities is the IGN-Yebes Associated Analysis Centre. Highlights of its activities are the participation in the ITRF2020 reprocessing in collaboration with the Analysis Centre NSGF in the UK, and the computation of SLR centre-of-mass corrections for spherical geodetic satellites.IGN strives to further exploit the synergies between these groups and work towards the combined analysis of the data. A description of the analysis activities of IGN Spain, along with its future prospects, is presented.

In a joint effort, experts from measurement science and space-geodesy develop instrumentation and methods to further strengthen traceability to the SI definition of the metre for geodetic reference frames (GRF). GRFs are based on space-geodetic observations. Local-tie surveys at co-location sites play an important role for their computation. Novel tools are hence developed for reference point monitoring, but also for local tie vector determination and ground truth provision. This contribution reports on the instrumental approaches and achievements after 24 months project duration and discusses the remaining work in the project.

The Bureau of Products and Standards (BPS) is a key component of the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG). It supports GGOS in its goal to provide consistent geodetic products needed to monitor, map, and understand changes in the Earth’s shape, rotation, and gravity field. In its present structure, the two Committees “Earth System Modeling” and “Essential Geodetic Variables” as well as the Working Group “Towards a consistent set of parameters for the definition of a new Geodetic Reference System (GRS)” are associated to the BPS. This paper presents the structure and role of the BPS and it highlights some of the recent activities. A major focus is on the classification and description of geodetic products and their representation at the renewed GGOS website ( http://www.ggos.org ). This website serves as an “entrance door” to geodetic products to satisfy different user needs and communities (e.g., geodesists, geophysicists, other geosciences and further customers) in order to make geodesy more visible to other disciplines and to society.

In this study, we evaluate the suitability of recent Earth Gravitational Models (EGMs) for the realization of the International Height Reference System (IHRS) in Canada. Topographic gravity field models have been used to augment EGMs to spatial resolution reaching 2′ (about 4 km), which is comparable to regional geoid models. The advantages of using an EGM over a regional approach for the IHRS are its uniform representation of the Earth’s gravity field and its conformance to international standards and conventions. The main challenge is access to, and best use of knowledge of the regional gravity and topographic data. On the one hand, we determine that two recent hybrid models (EIGEN-6C4 and XGM2019) augmented by topographic signals give geopotential values (Wp) with accuracy of ~0.3 m2 s−2, which is close to those estimated by the Canadian regional geoid models at the 11 International Height Reference Frame sites in Canada. On the other hand, two recent augmented satellite-only models (DIR-R6 and GOCO06s) give Wp with accuracies between 1.5 and 1.7 m2 s−2 in Canada.

This paper is written as a progression of the ongoing discussion in geodesy about the merits of the Molodensky height system versus the classical height system. It is a rebuttal of a publication in the Proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy by Victor Popadyev titled “On the Advantage of Normal Heights: Once More on the Shape of Quasigeoid.” Even though Popadyev’s paper was not presented at the symposium it was published in the proceedings regardless. It purports to address a presentation from the symposium titled “The shape of the quasigeoid”, that applied a set of criteria to judge the suitability of the quasigeoid as a vertical reference surface, ultimately finding it inferior due to its edges and folds. The proceedings paper acknowledges these irregularities in the quasigeoid, but instead argues that the Molodensky system, apart from any vertical reference surface, should be evaluated on two different and more favorable criteria, and finds it superior on that basis. Herein, we continue the ongoing discussion by clarifying some of the misunderstandings in the Popadyev paper and explaining that even on the favourable criteria proposed the Molodensky system holds no advantages over the classical system.

Local geoid models presenting higher resolution than global ones are generally derived by a combination of different datasets, integrating individual pure astrogeodetic, gravimetric and GNSS/levelling solutions. To define local geoid, different interpolators may be applied starting from dataset of geoid height values. It is well known that the accuracy of the resulting models depends not only by interpolation method, but also by points numerosity and distribution. This article aims to analyse the performance of Kriging approaches in dependence of the density of the dataset. The experiments are carried out on geoid heights extracted in random way from an already existing local geoid model: different subsets are organized containing an increasing number of points in the same area and each of them is submitted to Kriging interpolations (Universal Kriging and Ordinary Kriging). The resulting models are compared with the original one and residuals are calculated to evaluate the accuracy in dependence of point density. The results demonstrate the efficiency of the Kriging methods, highlighting the possibility to achieve higher accuracy (a few centimetres) using a point density of 1 point/100 sqkm, in absence of gravity anomalies. Ordinary Kriging provides better results than Universal Kriging but the undulations between the resulting models are minimal (a few millimetres) when a high number of points is involved. Furthermore, the results highlight the limit of the leave one out Cross validation since it supplies higher residuals than direct comparison for both Universal Kriging and Ordinary Kriging, when few points are used.

Since the last decade, Indonesia has continuously improved the accuracy of the national geoid model by conducting rapid gravity acquisition using airborne and terrestrial gravimetry. As gravity data have been collected thoroughly in all regions, the time has come to carry out Indonesia’s geoid modeling. We started our study by employing the Stokes and Second Helmert’s condensation method to our terrestrial gravity data in Yogyakarta, Indonesia, with a target area of 1∘× 1∘. The computation was based on the commonly applied remove-compute-restore process. We used a satellite-only geopotential model of GO_CONS_GCF_2_TIM_R6 up to degree 300 to remove and restore the long-wavelength part of the gravity field within the modeling process. Numerical results show that few cm of geoid model accuracy was achieved when we compared it to the validation points. Also, our best performance geoid is estimated to be better than the Earth Gravitational Model 2008 (EGM2008) geoid model by up to 2.8 cm in terms of standard deviation.

Recent advances in the developments of optical atomic clocks have enabled 10−18-level frequency comparisons between fibre-linked clocks. Therefore, chronometric leveling with an uncertainty on the order of 1 cm has become possible, based on the general theory of relativity. Since measurement uncertainty does not deteriorate with increasing fibre length, applications of chronometric leveling in geodesy, particularly unification of height reference systems, have been actively studied. In Japan, a frequency comparison is under experimentation using a fibre link connecting two optical lattice clocks approximately 100 km apart. This study estimates both the potential difference between these two clock sites with a geodetic method and its uncertainty to verify the results of chronometric leveling, which will be obtained in the near future. We use orthometric heights derived from leveling surveys repeated for monitoring crustal deformation. When discussing an uncertainty at the 1-cm level in height, the effects of temporal variations in the gravitational potential on the height measurement need to be considered due to various geophysical phenomena, including tides. Our results show that the uncertainty in the height measurements by geodetic leveling is the largest and that tidal potential changes during the height measurements can cause systematic errors of a few mm. The effects due to variations in the nontidal ocean bottom pressure and atmospheric pressure are more than an order of magnitude smaller than the tidal effects at this spatial scale. An upper limit of groundwater effects is also estimated. In a future comparison with clocks with an uncertainty on the order of 10−19, tidal potential changes and groundwater effects must be more rigorously evaluated.

In the frame of the “Modernization of the Hellenic Gravity Network - ModernGravNet” project, relative and absolute gravity measurements were carried out at selected 1st and 2nd order benchmarks of the Hellenic gravity network. These measurements are used first for the evaluation of the network. Then, as the official network gravity values are referenced to the Potsdam gravity system, transformation parameters are determined for converting official values to the new gravity system as it is defined by the absolute gravity measurements. A northeast to southwest trend is revealed from corrections computed from the parametric modeling. Moreover, global geopotential models are assessed at the network benchmarks as a first step towards the development of a new geoid model for Greece and successively the establishment of a national geoid-based vertical datum.

The recovery of Earth’s time variable gravity field from satellite data relied heavily on Satellite Laser Ranging (SLR) before the recent GRACE and GRACE Follow-On satellite gravity missions. Currently, the monthly gravity solutions from GRACE/GRACE-FO provide important global information about the temporal variations of gravity field. However, there are a few low-degree coefficients derived from GRACE/GRACE-FO that are not well determined, because of the satellite gravity mission configuration and issues with the accelerometer data. These low-degree coefficients can be determined reasonably well using SLR data from the dedicated SLR satellite configuration and can be used to replace the less well-determined values from GRACE/GRACE-FO. A more rigorous and consistent approach is to directly combine SLR and GRACE/GRACE-FO gravity solutions in a simultaneous solution. This paper presents a combination strategy for gravity field recovery from combined SLR and GRACE/GRACE-FO mission data. To correctly account for all correlations, the combination is performed at the information (normal) equation level. The coefficients C20 and C30 are determined mainly from SLR by renaming C20 and C30 parameters in GRACE/GRACE-FO information equations. The results show that the combined products are improved in comparison with the nominal GRACE/GRACE-FO gravity solutions. The gravity field products are evaluated by comparing different gravity solutions through coefficient-wise comparison, equivalent water height variations and mass changes over selected areas.

The Satellite Laser Ranging (SLR) processing at the Astronomical Institute of the University of Bern (AIUB) is currently extended from the geodetic satellites LAGEOS-1/2 and Etalon-1/2 to also include LARES. The orbits are determined in 7-day arcs together with station coordinates, low-degree spherical harmonic (SH) coefficients of the Earth’s gravity field, Earth Rotation Parameters (ERP), geocenter variations and range biases for selected stations. Due to the lower orbital altitude, LARES experiences a more variable environment such that the orbit parametrization has to be adapted. In this paper, we present SLR solutions for 5 years with different orbit parametrizations for LARES, i.e., LARES 7-day arcs are either determined from one set of orbit parameters and stochastic pulses at fixed time-intervals, or by stacking of seven daily arcs with continuity conditions at the day boundaries, so-called long-arcs. Including LARES does slightly improve the ERP and does not degrade the quality of the estimated SH coefficients and station coordinates. Additionally, it allows co-estimating the SH coefficient C30 and further low-degree SH coefficients.

Dedicated gravity field missions like GRACE and GRACE-FO use ultra-precise inter-satellite ranging observations to derive time series of monthly gravity field solutions. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite with a dual-frequency GNSS receiver may also serve as a gravity field sensor. To this end, GPS-derived kinematic LEO orbit positions are used as pseudo-observations for gravity field recovery. Although less sensitive, this technique can provide valuable information for the monitoring of large-scale time-variable gravity signals, particularly for those months where no inter-satellite ranging measurements are available. Due to a growing number of LEO satellites that collect continuous and mostly uninterrupted GPS data, the value of a combined multi-LEO gravity field time series is likely to increase in the near future.In this paper, we present monthly gravity field time series derived from GPS-based kinematic orbit positions of the GRACE, GRACE-FO and Swarm missions. We analyze their individual contribution as well as the additional benefit of their combination. For this purpose, two combination strategies at solution level are studied that are based on (i) least-squares variance component estimation, and (ii) stochastic properties of the gravity field solutions. By evaluating mass variations in Greenland and the Amazon river basin, the resulting gravity field time series are assessed with respect to superior solutions based on inter-satellite ranging.

The global gravitational potential generated by the attraction of the Earth’s topographic masses has been computed in spectral domain. The mass-source information is provided by the 1 arcmin resolution Earth2014 relief model and four averaged density values for rock, ocean, lake, and ice areas. The topography and bathymetry are split into confocal ellipsoidal shells of a defined thickness. Based on the provided mass-source information, the gravitational potential is expanded for each shell and then summed up to represent the complete gravitational potential of the topography (and bathymetry). In this contribution, we present the impact of different shell thicknesses to the model accuracy and computation time. Moreover, we expanded our topographic gravity field model up to spherical harmonic degree and order 5,494. Such short scale mass information represented by the topography can be used to complement high-resolution combined static gravity field models for the very high-frequency components of the gravity field. As an example, we enhanced (augmented) EIGEN-6C4 model with the high frequency components retrieved from the topographic model. The deflections of vertical values computed from the augmented model are compared w.r.t. ground truth observations in Germany, Southern Colorado and Iowa (USA) which suggest as expected a considerable improvement over rugged mountainous regions and comparable residuals in areas of moderate topography.

Satellite gravity missions, like GRACE and GRACE Follow-On, successfully map the Earth’s gravity field and its change over time. With the addition of the laser ranging interferometer (LRI) to GRACE-FO, a significant improvement over GRACE for inter-satellite ranging was achieved. One of the limiting factors is the accelerometer for measuring the non-gravitational forces acting on the satellite. The classical electrostatic accelerometers are affected by a drift at low frequencies. This drawback can be counterbalanced by adding an accelerometer based on cold atom interferometry (CAI) due to its high long-term stability. The CAI concept has already been successfully demonstrated in ground experiments and is expected to show an even higher sensitivity in space.In order to investigate the potential of the CAI concept for future satellite gravity missions, a closed-loop simulation is performed in the context of GRACE-FO like missions. The sensitivity of the CAI accelerometer is estimated based on state-of-the-art ground sensors and predictions for space applications. The sensor performance is tested for different scenarios and the benefits to the gravity field solutions are quantitatively evaluated. It is shown that a classical accelerometer aided by CAI technology improves the results of the gravity field recovery especially in reducing the striping effects. The non-gravitational accelerations are modelled using a detailed surface model of a GRACE-like satellite body. This is required for a realistic determination of the variations of the non-gravitational accelerations during one interferometer cycle. It is demonstrated that the estimated error due to this variation is significant. We consider different orbit altitudes and also analyze the effect of drag compensation.

Proof-of-principle demonstrations have been made for cold atom interferometer (CAI) sensors. Using CAI-based accelerometers in the next generation of satellite gravimetry missions can provide long-term stability and precise measurements of the non-gravitational forces acting on the satellites. This would allow a better understanding of climate change processes and geophysical phenomena which require long-term monitoring of mass variations with sufficient spatial and temporal resolution. The proposed accuracy and long-term stability of CAI-based accelerometers appear promising, while there are some major drawbacks in the long dead times and the comparatively small dynamic range of the sensors. One interesting way to handle these limitations is to use a hybridization with a conventional navigation sensor. This study discusses one possible solution to employ measurements of a CAI accelerometer together with a conventional Inertial Measurement Unit (IMU) using a Kalman filter framework.A hybrid navigation solution of these two sensors for applications on ground has already been demonstrated in simulations. Here, we adapt this method to a space-based GRACE-like gravimetry mission. A simulation is performed, where the sensitivity of the CAI accelerometer is estimated based on state-of-the-art ground sensors and further published space scenarios. Our results show that the Kalman filter framework can be used to combine the measurements of conventional inertial measurement units with the CAI accelerometers measurements in a way to benefit from the high accuracy of the conventional IMU measurements in higher frequencies together with the high stability of CAI measurements in lower frequencies. We will discuss the challenges, potential solutions, and the possible performance limits of the proposed hybrid accelerometry scenario.

Here we present early results from lumped-element numerical simulations of a novel class of nano electromechanical systems (NEMS) presently being considered for ground-based gravimetry and future micro accelerometry applications in GPS-denied environments, including spacecraft. The strategy we discuss is based on measuring the effects of non-inertial or gravitational forces on the dynamics of a standard oscillator driven at its resonance frequency by a time-dependent electrostatic potential. In order to substantially enhance the sensitivity of the instrument, the oscillating mass is made to simultaneously interact with a nearby boundary so as to be affected by quantum electrodynamical Casimir forces. Furthermore, unlike previously published proposals, in the design presented herein the Casimir boundary does not oscillate but it is a fixed semiconducting layer. As already demonstrated experimentally, this arrangement enables Casimir force time-modulation by semiconductor back-illumination. Such a design strategy, first suggested by this author as a promising approach to gravitational wave detection in different nano-sensors, allows for the realization of a Casimir force-pumped mechanical parametric amplifier. Such devices can, in principle, yield gains of several orders of magnitude in the mechanical response amplitude over the response from standard unpumped oscillators. The numerical proof-of-concept first presented herein points to a potentially new class of gravimetry products based on exploiting appropriately engineered dispersion forces as an emerging enabling general purpose technology on the nanoscale.

The publicly available Earth Orientation Parameter (EOP) time series provided by the Earth Orientation Centre of the IERS (e.g., IERS Bulletin A, IERS 14 C04) result from the combination of individual space-geodetic solutions on a daily basis, i.e., a parameter-level combination. Current activities of the Federal Agency for Cartography and Geodesy (BKG) focus on the development of a combination strategy, the main objective of which is to improve the consistency between the space-geodetic techniques through common parameters, i.e., mainly EOP, but also station coordinates and tropospheric parameters using local ties and atmospheric ties, respectively. In this study, we present our combination strategy and the results of the combination of VLBI data available within approximately two weeks (i.e., Intensive and R1/R4 sessions) with data from the global GNSS network. The combination is done at the normal equation (NEQ) level on a daily and multi-day basis. We compare our EOP solutions with the respective daily and multi-day single-technique EOP solutions as well as with the low-latency inter-technique EOP time series (COMBI RAP) examined in previous studies, which is based on the combination of GNSS and VLBI Intensive data only. We found regarding the dUT1 solution, that the addition of the VLBI R1/R4 sessions to the VLBI Intensives and GNSS data has a positive impact on the entire 7-day solution, and especially stabilizes the dUT1 estimates of the boundary days of the multi-day continuous polygon. The dUT1 estimates of the left and right boundary day compared to IERS Bulletin A and COMBI RAP reveal an improvement in terms of WRMS of the residuals by 2.3 μs and 1.4 μs, respectively. For the pole coordinates, the consistency of the estimates with external reference series is almost at the same level as for the COMBI RAP solution.

The relationship between the length of day (LOD) and El-Niño Southern Oscillation (ENSO) has been well studied since the 1980s. LOD is the negative time-derivative of UT1-UTC, which is directly proportional to Earth Rotation Angle (ERA), one of the Earth Orientation Parameters (EOP). The EOP can be determined using Very Long Baseline Interferometry (VLBI), which is a space geodetic technique. In addition, satellite techniques such as the Global Navigation Satellite System (GNSS), Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) can provide Earth Rotation Parameters, i.e., polar motion and LOD. ENSO is a climate phenomenon occurring over the tropical eastern Pacific Ocean that mainly affects the tropics and the subtropics. Extreme ENSO events can cause extreme weather like flooding and droughts in many parts of the world. In this work, we investigated the effect of ENSO on the LOD from January 1979 to April 2022 using the wavelet coherence method. This method computes the coherence between the two non-stationary time-series in the time-frequency domain using the real-valued Morlet wavelet. We used the Multivariate ENSO index version 2 (MEI v.2) which is the most robust series as the climate index for the ENSO, and LOD time-series from IERS (EOP 14 C04 (IAU2000A)). We also used Oceanic Niño and Southern Oscillation index in this study for comparison. The results show strong coherence of 0.7 to 0.9 at major ENSO events for the periods 2–4 years between LOD and MEI.v2.

Since 1969 Lunar Laser Ranging (LLR) data have been collected by different observatories and analysed by various analysis groups. LLR is providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics. In recent years, observations have been carried out with larger telescopes and at infra-red (IR) wavelength, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. The increased number of high-accuracy observations allows for more accurate determination of Earth Orientation Parameters (EOPs) from LLR data compared to previous years. In this study we focus on ΔUT1 results from different constellations and compare our LLR solution to the IERS EOP C04 series.

GNSS-based velocity fields are a key tool to assess the boundaries around major deforming areas, to explain the main patterns of surface motion and deformation, to analytically review existing kinematics models and finally, to study the underlying tectonic activities. Determination of a velocity field for Africa is of great importance in the determination of the African Reference Frame; this is essential for better understanding the African plate tectonics. Therefore, this study focusses on the determination of the African velocity fields using continuously operated GNSS stations. We processed and analyzed 11 years of data obtained from a total number of 145 GNSS site using GFZ’s EPOS.P8 software. The result shows that Africa moves in the North-East direction. The station coordinates derived with PPP show averaged RMS values of 2.9 mm, 9.9 mm and 8.5 mm for the north, east and up components with respect to the estimated trajectory models. Horizontal velocities at sites located on stable Nubia plate fit a single plate model with residual motion below 1 mm/year of RMS. We confirm significant southeast motion in Morocco and Zambia with residual velocities of 1.4 mm/year and 0.9 mm/year, respectively. We estimate the Euler Poles for Nubia and Somalia with 48.59°N, −78.64°E, 0.264°/Myr and 60.38°N, −83.33°E, 0.272°/Myr, respectively. Vertical velocities range from −2 to +2 mm/year, close to their uncertainties, with no distinct geographic pattern. The study also provides continental-wide position and velocity field solution for Africa, and can also be considered as a contribution to the upcoming AFREF, the African Geodetic Reference Frame.

Long-term tide gauge records provide valuable insights to sea level variations but interpretation requires an accurate determination of associated vertical land motion. Within the Tide Gauge Benchmark Monitoring Pilot Project of the International GNSS Service dedicated reprocessing campaigns are performed for GNSS stations co-located with tide gauges. Based on 341 stations the GFZ contribution to the third TIGA reprocessing provides vertical land motion rates for 230 stations at or close to recently active tide gauges. GNSS station coordinate time series determined by using a network approach and a conventional time series analysis show mean repeatabilities of 2.9, 3.3, and 5.6 mm for north, east, and up coordinates. The derived vertical velocity pattern is analyzed but also compared to the ALTIGAPS and the ULR6a solutions showing mean differences of 0.04 mm yr−1 and −0.1 mm yr−1, respectively. By correcting tide gauge records available via PSMSL for the individual vertical station velocity including eventually velocity changes geocentric sea level changes are determined. Compared to AVISO’s multi-mission altimetric trend map a difference of −0.7 mm yr−1 is determined.

The objective of this paper is to introduce CyCLOPS, a novel strategic research infrastructure unit, and present its current progress of implementation, and integration in the National geodetic, geophysical and geotechnical infrastructure of the government-controlled areas of the Republic of Cyprus. CyCLOPS is co-funded by the European Regional Development Fund and the Republic of Cyprus through the Research and Innovation Foundation under the grant agreement RIF/INFRASTRUCTURES/1216/0050. CyCLOPS is developed via the collaboration of the Cyprus University of Technology (CUT) and the German Aerospace Center (DLR), and supported by the Cyprus Geological Survey Department and the Department of Lands and Surveys. The main objective of CyCLOPS is to establish an integrated infrastructure for space-based monitoring of geohazards using the most prominent earth observation technologies (EO), such as GNSS and InSAR. Furthermore, the infrastructure will densify and form the backbone for the definition of the next generation national datum of the Republic of Cyprus. Eleven Tier-1/2 state-of-the-art GNSS CORS, precise weather stations, tiltmeters and specifically designed InSAR triangular trihedral corner reflectors will be deployed, in a collocated fashion, at selected locations throughout the government-controlled areas of Cyprus. The collocated configuration will be established and installed to be compliant with the most stringent CORS monumentation specifications, support all current GNSS constellations and SAR missions. Finally, one of CyCLOPS’ fundamental aims is to actively contribute to the on-going efforts and growing demand for more precise positioning services and high-quality modern reference frames, in conformity with the recommendations of the UN-GGIM (and its Subcommittee of Geodesy) to establish and enhance national geodetic infrastructures to support the sustainable management of geospatial information on the changing Earth.

Installing a VLBI transmitter on Galileo satellites will allow observing satellites in parallel to quasars with Very Long Baseline Interferometry (VLBI) telescopes. This offers a variety of new applications such as the direct determination of the absolute orientation of the satellite constellation with respect to the International Celestial Reference Frame (ICRF) and the improvement of the Terrestrial Reference Frame (TRF) exploiting the possibilities of direct high precision tying of the different space geodetic equipment. In preparation of these observations by enhancing the capabilities of the VLBI scheduling program VieSched++, we perform an evaluation study of observations of a Galileo satellite employing Dilution of Precision (DOP) factors. The idea is to introduce DOP factors in the decision process of VieSched++ after a thorough assessment of DOP factors for individual parameters. In our study, we choose an existing network of VLBI Global Observing System (VGOS) type telescopes for observing Galileo satellite GSAT0212 within a 24 h arbitrary session. Preparing the DOP factor analysis, we first carry out a theoretical study to investigate the VLBI sensitivity to satellite orbit displacements in the local orbital frame with normal (radial), tangential and cross-track direction. This analysis shows that the highest sensitivity of a satellite observation is that of the tangential component if the direction of the satellite track is parallel to the direction of the observing baseline. A satellite observation is most sensitive towards the cross-track component if these two directions are orthogonal to each other. The DOP factor analysis itself is performed separating the satellite position again into its three components and adding a separate DOP factor for the UT1-UTC (dUT1) parameter. The periods, where satellite observations are possible, were determined using VieSched++. At a later stage, these DOP factors will be used as an optimization criterion for the scheduling process. The DOP factors of potential observations from the chosen VGOS network to GSAT0212 reach minimum DOP values of 27.13 in normal, 1.49 in tangential, and 1.67 in cross-track direction and 0.45 for determining dUT1. With these results, which have confirmed intuitive considerations on the relative magnitudes, we have laid the groundwork for using DOP factors as driving criteria in the scheduling process of Galileo satellites embedded in regular VLBI observations of quasars.

GNSS frequency transfer (FT) based on precise point positioning delivers instability values down to sub-10−16 between two modern receivers. In the present study we investigate the technical limits such receivers impose on FT by means of a dedicated experiment at Germany’s national metrology institute (PTB). For this purpose, four geodetic receivers, two of the same type each, were all connected to one single antenna and fed by the highly stable UTC (PTB) frequency signal. Since all error sources affecting the satellite signals are the same for all receivers, they cancel out when forming receiver-to-receiver single differences (SDs). Due to the fact that the remaining SD carrier phase ambiguities can be easily fixed to integer values, only the relative receiver clock error remains in the SDs. We assess the instability of three different receiver combinations, two with the same receiver type (intra-receiver) and one with different types (inter-receiver). The intra-receiver pairs reach lower instability values faster than the inter-receiver combination, which is in part caused by the different signal tracking modes of the receivers. To be specific, the 10−18 instability range was only reached by the intra-receiver pairs, whereas the inter-receiver combination already hits its noise floor at about 1.5 ⋅ 10−17. In addition, our analysis of using different observation type combinations only shows small differences regarding the link instability.

This paper addresses an approach to assess the impact of phase centre correction errors of selected receiving antennas in the Polish ASG-Eupos network using GNSS processing strategies such as zero differencing and double differencing. The objective is to characterise the nature of the error patterns of GNSS receiver antennas and to understand their impact on GNSS derived integrated water vapour and geodetic estimates. A semi-analytical approach for characterising variants of error patterns is applied. Differences of up to +12 mm between type-mean and individual receiver antenna calibrations of current antenna models on the ionosphere-free linear combination are identified for repeatable pattern deformations. The analyses show that repeatable effects on tropospheric estimates of up to 8 mm – which corresponds to approx. 1.2 kg/m2 – occur even though only 5 mm variations were applied to the pattern. The results of our analysis show a strong correlation with the type of error patterns that affect the estimates differently. Due to the complex relationship between datum settings, processing strategy, baseline orientation and satellite sky distribution, artefacts in GNSS processing models and their effects must to be modelled in order to achieve a better understanding in the context of GNSS networks and GNSS meteorology.

In high precision Global Navigation Satellite Systems (GNSS) applications, it is necessary to take phase center corrections (PCC) into account. Beside these corrections for carrier phase measurements, also corrections for the codephase are necessary, so called codephase center corrections (CPC). The CPC, also known as group delay variations, are antenna dependent delays of the received codephase, which are varying with azimuth and elevation of the incoming GNSS signal. A concept for estimating absolute CPC and PCC for multi GNSS signals has been established by the Institut für Erdmessung.In this paper, the standard calibration approach with a sampling rate of 1 Hz is briefly described, which works well for PCC estimation. The main challenge of this approach for estimating repeatable CPC patterns is the significantly higher noise to pattern ratio in the observations compared to PCC determination. Therefore, an alternative processing strategy is presented in this contribution. By increasing the sampling rate to 10 Hz, the empirical mode decomposition can be used to reduce the noise of the input observations by maintaining all pattern information. With this method, the calibration repeatability is improved by 46% to 60% for GPS and Galileo C1C signals for a geodetic antenna. Moreover, the estimated pattern is validated in the positioning domain with a single point positioning approach. By considering the estimated CPC the accuracy of the height component can be improved.

For highly precise and accurate positioning and navigation with Global Navigation Satellite Systems (GNSS), it is mandatory to take phase center corrections (PCC) into account. These corrections are provided by different calibration facilities and methods. Currently, discussions in the framework of the International GNSS Service (IGS) antenna working group (AWG) are ongoing on how to accept new calibration facilities as an official IGS calibration facility.In this paper, different image similarity measures and their potential for comparing PCC are presented. Currently used comparison strategies are discussed and their performance is illustrated with several geodetic antennas. We show that correlation coefficients are an appropriate measure to compare different sets of PCC since they perform independently of a constant part within the patterns. However, feature detection algorithms like the Speeded-Up Robust Features (SURF) mostly do not find distinctive structures within the PCC differences due to the smooth character of PCC. Therefore, they are inapplicable for comparing PCC. Singular Value Decomposition (SVD) of PCC differences (ΔPCC) can be used to analyse which structures ΔPCC are composed of. We show that characteristic structures can be found within ΔPCC. Therefore, the SVD is a promising tool to analyse the impact of PCC differences in the coordinate domain.

Multipath in urban environments still represents a great challenge for Global Navigation Satellite System (GNSS) positioning as it is a degrading factor which limits the attainable accuracy, precision and integrity. In an urban trench, the dense building structures in the vicinity of the antenna cause reflections of the satellite signals resulting in multipath errors. Various work has been presented for simulating reflections for stations under laboratory conditions, yet the simulative analysis of multipath propagation in urban environments is currently developing.In this contribution, we enhanced an existing Ray-Tracing algorithm which identifies potentially multipath affected satellite signals. So far, it calculates reflection points on a plane ground and estimates the resulting multipath error. We extended it for the urban area case by introducing a 3D city building model with possible reflections on all surfaces of the buildings. Based on the geometry between the antenna position, satellite position and the reflection surface, the extra path delays, the characteristics of the propagation channel and the signal amplitudes are calculated. The resulting multipath errors are then estimated from the discriminator function using state of the art correlator parameters and antenna models.For a validation, the simulation results are compared with code-minus-carrier combination from a real GNSS experiment in a dense urban area in Hannover. We find that the simulated multipath errors fit the observations in terms of the amplitude, but with uncertainties in the building model, the multipath wave length is too large. The distance to the reflection surface is a key factor which influences the multipath wavelength.

GNSS integrity monitoring requires proper bounding to characterize all ranging error sources. Unlike classical approaches based on probabilistic assumptions, our alternative integrity approach depends on deterministic interval bounds as inputs. The intrinsically linear uncertainty propagation with intervals is adequate to describe remaining systematic uncertainty, the so-called imprecision. In this contribution, we make a proposal on how to derive the required intervals in order to quantify and bound the residual error for empirical troposphere models, based on the refined sensitivity analysis via interval arithmetic. We evaluated experimentally the Saastamoinen model with (i) a priori ISO standard atmosphere, and (ii) on-site meteorological measurements from IGS and Deutscher Wetterdienst (DWD) stations as inputs. We obtain consistent and complete enclosure of residual ZPD errors w.r.t IGS ZPD products. Thanks to the DWD dense network, interval maps for meteorological parameters and residual ZPD errors are generated for Germany as by-products. These experimental results and products are finally validated, taking advantage of the high-quality tropospheric delays estimated by the Vienna Ray Tracer. Overall, the results indicate that our strategy based on interval analysis successfully bounds tropospheric model uncertainty. This will contribute to a realistic uncertainty assessment of GNSS-based single point positioning.

CubeSats can be used for many space missions and Earth science applications if their orbits can be determined precisely. The Precise Orbit Determination (POD) methods are well developed for large LEO satellites during the last two decades. However, CubeSats are built from Commercial Off-The-Shelf (COTS) components and have their own characteristics, which need more investigations. In this paper, precise orbits of 17 3U-CubeSats in the Spire Global constellation are determined using both the reduced-dynamic and the kinematic POD methods. The limitations in using elevation-dependent weighting models for CubeSats POD are also discussed and, as an alternative approach, a weighting model based on the Signal-to-Noise Ratio (SNR) has been proposed. One-month processing of these CubeSats revealed that around 40% of orbits can be determined at the decimeter accuracy, while 50% have accuracy at centimeters. Such precise orbits fulfil most mission requirements that require such POD accuracy. Internal validation methods confirmed the POD procedure and approved the distinction of weighting based on SNR values over the elevation angles.

Geomagnetic storms are one of the major factors causing Total Electron Content (TEC) anomalies. Analyses of TEC fluctuations also provide a valuable understanding of the mechanisms of earthquakes and tsunamis. However, there is no clear consistency in investigations of TEC disturbances that should be considered simultaneously in both solar and seismic activities. Therefore, based on Machine Learning (ML) and time series analysis techniques, we build TEC forecast models to study relationships among ionospheric anomalies, geomagnetic storms, and earthquakes. Robust statistical tests are used to select the optimal models and estimate forecast performance. Depending on the quality of input data and sampling rates, the forecast performance can get from ~2.0 to ~2.5 TECU for 3-day predictions using daily time series and reach up to ~1.3 TECU using one-minute time series. These models present significant relationships between the ionosphere, solar activity, and seismic events, which can be applied to hazard warning systems.

Water vapor is a key variable in meteorology and climate studies. Since the late 90s, Global Navigation Satellite System (GNSS) estimates from ground antennas are commonly used for its description. Indeed, propagation delays are due to the transit of the signal through the atmosphere. The correction of these delays is a crucial step that is needed for the precise GNSS positioning. Integrated Water Vapor (IWV) contents are derived from these delays and are used to describe the distribution of water vapour in the atmosphere.However, severe meteorological phenomena often originate over the oceans and could strongly affect coastal regions. These phenomena are less well described or forecasted because of the small number of observations available in these regions. In this context, the potential of shipborne GNSS measurements has already been highlighted.This work aims at investigating the impact of some GNSS processing parameters on IWV retrieval from a shipborne antenna in PPP mode. The studied parameters are cutoff angle, random walk of the estimated delays, and observation weighting. Data were collected for 2 months in 2018 by the GNSS antenna of a vessel operating in the Bay of Brest, France. The impact of the parameters is assessed by comparing the shipborne GNSS-derived IWV to the IWV estimated from a close GNSS ground station, and those computed by the ERA5 reanalysis and operational radiosonde profiles from the nearest Météo-France station. The most satisfying parameterization is shown to have Root Mean Squared (RMS) differences of 0.5 kg m−2, 0.9 kg m−2, and 1.2 kg m−2 compared to GNSS ground station, ERA5, and radiosonde respectively. These conclusive results are also confirmed by comparing the GNSS height estimates to the measurements from the Brest tide gauge, with an RMS difference of 4.9 cm.

GNSS tomography is an all-weather remote sensing technique to capture the spatiotemporal behavior of the atmospheric water vapor using the standing infrastructure of GNSS satellites and networks. In this method, the troposphere is discretized to a finite number of 3D elements (voxel) in horizontal and vertical directions. Then, the wet refractivity in these voxels is reconstructed using the Slant Wet Delay (SWD) observations in the desired tomography domain by means of the discrete inverse concept. Due to the insufficient spatial coverage of GNSS signals in the voxels within the given time window, some of the voxels are intersected by a few signals or plenty of signals, and others are not passed by any signals at all. Therefore, the design matrix is sparse, and the observation equation system of the tomography model is mixed-determined. Some constraints have to be applied or external data sources should be added to the tomography problem in order to reconstruct the wet refractivity field. Moreover, the GNSS tomography is a kind of discrete ill-posed problem, as all singular values of the structure matrix (A) in the tomography problem decay gradually to zero without any noticeable gap in the spectrum. Hence, slight changes in the measurements can lead to extremely unstable parameter solutions. In consequence, the regularization method should be applied to the inversion process and ensure a stable and unique solution for the tomography problem. In this research, the Total Variation (TV) method is suggested to retrieve a regularized solution. TV is a nonlinear technique, which resists noise and efficiently preserves discontinuities in the model. This method can also reconstruct the wet refractivity field without any initial field in a shorter time span. For this purpose, observation data from the EPOSA (Echtzeit Positionierung Austria) GNSS network located in the eastern part of Austria is processed within the period DoYs 232-245 in 2019. Then, the TV method is performed in six different tomography windows (10–60 min) with a time step of 10 min by focusing on near-real-time applications. Finally, radiosonde measurements in the area of interest are utilized to compare the estimated wet refractivity field in order to obtain the accuracy of the proposed method.

The effective isotropic radiated power (EIRP) is the measured radiated power of an antenna pointed in a specific direction. For the Global Positioning System (GPS), the EIRP is a function of the transmitted power and the gain of the transmitting antenna. It is a fundamental observation used for estimating surface reflectivity that can be used to estimate near-surface soil moisture. Most investigations of GPS EIRP for soil moisture used level 1 version 2.1 data from the eight satellites of the Cyclone Global Navigation Satellite System (CYGNSS) mission. The newer version 3.0 introduces a dynamic EIRP calibration algorithm with the variations in GPS transmit power being tracked using the direct signal power measured by the navigation receivers. In this paper we compare the estimated EIRP from versions 2.1 and 3.0 for the year of 2020. We correlate the estimated surface reflectivity with reference soil moisture observations from the Soil Moisture Active Passive (SMAP) mission provided on a 9x9 km grid using the bistatic radar equation for coherent reflections. The correlation of CYGNSS with SMAP is slightly improved using version 3.0 versus 2.1 with average of 0.10 and maximum of 0.30. The advantage of version 3.0 was most noticeable in areas where soil moisture retrieval is challenging, such as the arid and densely vegetated regions of the world.

The Global Navigation Satellite System – Interferometric Reflectometry (GNSS-IR) technique utilizes the GNSS Signal-to-Noise Ratio (SNR) data to retrieve soil moisture. In this study, the physical SNR model incorporating antenna’s cross-polarization component is re-derived to a more intuitive and straightforward degree, which is based on the work of V. U. Zavorotny et al. 2009. Then this model is used in combination with the signal reconstruction method we proposed before to correct the cross-polarization effect when retrieving soil moisture. Both simulation and experiment data were used for validation purpose. The results showed that the mean retrieval error could be reduced by about 0.16cm3⋅cm−3 after cross-polarization correction.