Non-tidal Atmospheric Loading Research Articles

Application of Sntinel-1 radar interferometric images for the monitoring of vertical displacements of the earth’s surface affected by non-tidal atmospheric loading

The vertical movements of the Earth’s surface affected by non-tidal atmospheric loading (NTAL) are analyzed using satellite radar interferometry data. A clear relationship between deformation maps data derived from radar interferometry data and the GNSS time series of permanent stations has been established. The object of the study was the areas around the GNSS stations BYCH (Buchach), GORD (Horodok), CRNT (Chernivtsi). The input data were four pairs of radar interferometric images for the specified areas.Radar satellite images were obtained from the Sentinel-1A spacecraft. Data type — SLC (Single Look Complex) with vertical polarization. Acquisition mode — wideband interferometric IW (Interferometric Wide Swath). Data were processed using SNAP (Sentinel Application Platform) software. The processing yileded maps of vertical displacement of the specified territories where the earth’s surface displacement caused by influence of non-tidal atmospheric loading had taken place. The values obtained on the basis of vertical displacement maps have a high agreement with the results of time series of changes in the altitude position of permanent GNSS stations. The results obtained in the article are of both scientific and practical importance for studying the impact of non-tidal atmospheric loading in large areas. The practical significance is in improving the accuracy of terrestrial geodetic measurements’ processing, in particular high-precision levelling. The research data allow to make corrections of the results of levelling for short-period displacements affected by the influence of non-tidal atmospheric loading (NTAL).

The ULR-repro3 GPS data reanalysis and its estimates of vertical land motion at tide gauges for sea level science

Abstract. A new reanalysis of Global Navigation Satellite System (GNSS) data at or near tide gauges worldwide was produced by the University of La Rochelle (ULR) group within the third International GNSS Service (IGS) reprocessing campaign (repro3). The new solution, called ULR-repro3, complies with the IGS standards adopted for repro3, implementing advances in data modelling and corrections since the previous reanalysis campaign and extending the average record length by about 7 years. The results presented here focus on the main products of interest for sea level science: the station position time series and associated velocities on the vertical component at tide gauges. These products are useful to estimate accurate vertical land motion at the coast and supplement data from satellite altimetry or tide gauges for an improved understanding of sea level changes and their impacts along coastal areas. To provide realistic velocity uncertainty estimates, the noise content in the position time series was investigated considering the impact of non-tidal atmospheric loading. Overall, the ULR-repro3 position time series show reduced white noise and power-law amplitudes and lower station velocity uncertainties compared with the previous reanalysis. The products are available via SONEL (https://doi.org/10.26166/sonel_ulr7a; Gravelle et al., 2022).

Investigating temporal and spatial patterns in the stochastic component of ZTD time series over Europe

The EUREF Permanent GNSS Network (EPN) provides a unique atmospheric dataset over Europe in the form of Zenith Total Delay (ZTD) time series. These ZTD time series are estimated independently by different analysis centers, but a combined solution is also provided. Previous studies showed that changes in the processing strategy do not affect trends and seasonal amplitudes. However, its effect on the temporal and spatial variations of the stochastic component of ZTD time series has not yet been investigated. This study analyses the temporal and spatial correlations of the ZTD residuals obtained from four different datasets: one solution provided by ASI (Agenzia Spaziale Italiana Centro di Geodesia Spaziale, Italy), two solutions provided by GOP (Geodetic Observatory Pecny, Czech Republic), and one combined solution resulting from the EPN’s second reprocessing campaign. We find that the ZTD residuals obtained from the three individual solutions can be modeled using a first-order autoregressive stochastic process, which is less significant and must be completed by an additional white noise process in the combined solution. Although the combination procedure changes the temporal correlation in the ZTD residuals, it neither affects its spatial correlation structure nor its time-variability, for which an annual modulation is observed for stations up to 1,000 km apart. The main spatial patterns in the ZTD residuals also remain identical. Finally, we compare two GOP solutions, one of which only differs in the modeling of non-tidal atmospheric loading at the observation level, and conclude that its modeling has a negligible effect on ZTD values.

Quantitative Evaluation of Environmental Loading Products and Thermal Expansion Effect for Correcting GNSS Vertical Coordinate Time Series in Taiwan

We explored the driving factors of nonlinear signals in vertical coordinate sequences of stations in a Taiwan global navigation satellite system (GNSS) network, including atmospheric loading (ATML), hydrological loading (HYDL), and non-tidal ocean loading (NTOL) effects. At the same time, we used the finite element analysis software MIDAS to quantify the vertical displacements of different types of monuments due to the thermal expansion effect, including deep drilled braced (DDB) and short drilled braced (SDB). By quantitatively comparing the correction results of GNSS time series with different single mass loading models, we found that there was little difference in the correction of different environmental loading products. We compared different combinations of each loading product to correct the GNSS time series, and finally selected the best combination suitable for Taiwan GNSS network, that is, ATML (GFZ_ECMWF IB) + HYDL (IMLS_MERRA2) + NTOL (IMLS_MPIOM06). We found that the spatial and temporal models of ATML and NTOL are very similar, with non-tidal atmospheric loading and non-tidal ocean loading working together, a pattern that may be related to tropical cyclones. Both models also showed good correction effect on GNSS stations in the western plain of Taiwan, but with limited correction effect in the eastern part of Taiwan. This may be due to the influence of the subtropical monsoon climate in Taiwan and the barrier of the central mountain range, resulting in obvious differences between eastern and western Taiwan. The hydrological loading was found to act in the opposite way to the thermal expansion effect in the temporal domain, indicating that some displacements in hydrological loading may cancel out displacements caused by the thermal expansion effect. This aspect of displacement is not included in the hydrological loading model but should be considered when accurately estimating the temporal and spatial variation of water storage capacity in Taiwan using GNSS observed displacements.

ГЕОДИНАМІКА

The paper analyzes the vertical displacements of the GNSS sites of civil engineering structures caused by non-tidal atmospheric loading (NTAL). The object of the study is the Dnister Hydroelectric Power Plant №1 (HPP-1) and its GNSS monitoring network. The initial data are the RINEX-files of 14 GNSS stations of the Dnister HPP-1 and 8 permanent GNSS stations within a radius of 100 km, the NTAL model downloaded from the repository of German Research Centre for Geosciences GFZ for 2019-2021, and materials on the geological structure of the object. Methods include comparison and analysis of the altitude component of GNSS time series with model values of NTAL as well as interpretation of the geodynamic vertical displacements, taking into account the analysis of the geological structure. As a result, it was found that the sites of the GNSS network of the Dnister HPP-1 undergo less vertical displacements than the permanent GNSS stations within a radius of 100 km. This corresponds to the difference in thickness and density of the rocks under the GNSS sites and stations, so they undergo different elastic deformations by the same NTAL. In addition, the research detected different dynamics of vertical displacements of GNSS sites on the dam and on the river banks. It leads to cracks and deformations of concrete structures in the dam-bank contact zones. During the anomalous impact of NTAL, the altitude of even nearby sites can change if the geological structure beneath them is different. The work shows that for civil engineering structures it is necessary to apply special models to take into account NTAL deformations for high-precision engineering and geodetic measurements.

Identifying the sensitivity of GPS to non-tidal loadings at various time resolutions: examining vertical displacements from continental Eurasia

We examine the sensitivity of the Global Positioning System (GPS) to non-tidal loading for a set of continental Eurasia permanent stations. We utilized daily vertical displacements available from the Nevada Geodetic Laboratory (NGL) at stations located at least 100 km away from the coast. Loading-induced predictions of displacements of earth’s crust are provided by the Earth-System-Modeling Group of the GFZ (ESMGFZ). We demonstrate that the hydrological loading, supported by barystatic sea-level changes to close the global mass budget (HYDL + SLEL), contributes to GPS displacements only in the seasonal band. Non-tidal atmospheric loading, supported by non-tidal oceanic loading (NTAL + NTOL), correlates positively with GPS displacements for almost all time resolutions, including non-seasonal changes from 2 days to 5 months, which are often considered as noise, intra-seasonal and seasonal changes with periods between 4 months and 1.4 years, and, also, inter-annual signals between 1.1 and 3.0 years. Correcting the GPS vertical displacements by NTAL leads to a reduction in the time series variances, evoking a whitening of the GPS stochastic character and a decrease in the standard deviation of noise. Both lead, on average, to an improvement in the uncertainty of the GPS vertical velocity by a factor of 2. To reduce its impact on the GPS displacement time series, we recommend that NTAL is applied at the observation level during the processing of GPS observations. HYDL might be corrected at the observation level or remain in the data and be applied at the stage of time series analysis.

Correcting for site displacements at different levels of the Gauss-Markov model – A case study for geodetic VLBI

In a previous paper, Glomsda et al. (2020) revisited the impact of distinct parts of non-tidal loading in the analysis of geodetic Very Long Baseline Interferometry (VLBI). The loading is represented by displacements of the reference positions of the observing VLBI antennas, which are variables of a corresponding Gauss-Markov model for estimating various geodetic target parameters. These displacements were applied at two different levels of the model, the observation and the normal equation level, and quite similar results were obtained for both cases. In this paper, the authors provide a more detailed theoretical discussion of the application of site displacements at the distinct levels, which also comprises the a posteriori application at the solution level. For each case, the respective formulas and implications for the Gauss-Markov model are derived, and equations for assessing the differences between the estimated parameters are established. In this way, the authors aim to create a deeper understanding of the results of the previous paper, which show the capability of the normal equation level to approximate the application of site displacements at the observation level with less effort and prerequisites, and to provide evidence for the claims made in that paper (for VLBI only): (i) the chosen reference frame of the site displacements is basically irrelevant except for the solution level; (ii) the Jacobi matrix does not change substantially; (iii) the loss of temporal resolution of the site displacements is more important than the linear approximation of the functional model at the normal equation level; and (iv) the station coordinate estimates for all three levels strongly depend on the regularizing (datum-) conditions of the model. The theoretical results are substantiated with numerical examples, which consider site displacements generated from non-tidal atmospheric loading by the Earth-System-Modelling group of the Deutsches GeoForschungsZentrum (GFZ). However, the results are valid for site displacements of any source.

Quantitative Evaluation of Environmental Loading Induced Displacement Products for Correcting GNSS Time Series in CMONOC

Mass redistribution within the Earth system deforms the surface elastically. Loading theory allows us to predict loading induced displacement anywhere on the Earth’s surface using environmental loading models, e.g., Global Land Data Assimilation System. In addition, different publicly available loading products are available. However, there are differences among those products and the differences among the combinations of loading models cannot be ignored when precisions of better than 1 cm are required. Many scholars have applied these loading corrections to Global Navigation Satellite System (GNSS) time series from mainland China without considering or discussing the differences between the available models. Evaluating the effects of different loading products over this region is of paramount importance for accurately removing the loading signal. In this study, we investigate the performance of these different publicly available loading products on the scatter of GNSS time series from the Crustal Movement Observation Network of China. We concentrate on five different continental water storage loading models, six different non-tidal atmospheric loading models, and five different non-tidal oceanic loading models. We also investigate all the different combinations of loading products. The results show that the difference in RMS reduction can reach 20% in the vertical component depending on the loading correction applied. We then discuss the performance of different loading combinations and their effects on the noise characteristics of GNSS height time series and horizontal velocities. The results show that the loading products from NASA may be the best choice for corrections in mainland China. This conclusion could serve as an important reference for loading products users in this region.

Influence of Geophysical Signals on Coordinate Variations GNSS Permanent Stations in Central Europe

Abstract This article presents an analysis of the extent of the impact of deformations of the earth’s crust resulting from geophysical models on changes in the coordinates of Global Navigation Satellite System (GNSS) stations. The author presents the results of analyses of the spatial correlation coefficient of deformation components for the non-tidal atmospheric loading (NTAL), non-tidal ocean loading (NTOL) and hydrological loading (HYDRO) models of geophysical deformation. In addition, the author calculated the correlation coefficients between station’s coordinate series to determine whether the deformations of the earth’s crust have a more global, large-area (regional scale) or local-range (local scale) impact, limited to the nearest of stations. In addition to correlation coefficients, the author analysed the similarity in periodic components between station coordinates by calculating the coherence between them. The results of the analysis showed that for the height components (Up), we observe the global range of deformation models, and the NTAL deformation has the greatest influence on the change in them. The lack of correlation between coordinate signals for horizontal components may result from specific local conditions in the place of the station, low-resolution of geophysical models and small amplitudes of these signals in relation to noise. An analysis of the coherence coefficients showed that each station coordinates shows completely different periodic components in the North, East and Up directions.

Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

We describe a comprehensive analysis of the 469 European Global Positioning System (GPS) vertical position time series. The assumptions we present should be employed to perform the post-glacial rebound (PGR)-oriented comparison. We prove that the proper treatment of either deterministic or stochastic components of the time series is indispensable to obtain reliable vertical velocities along with their uncertainties. The statistical significance of the vertical velocities is examined; due to their small vertical rates, 172 velocities from central and western Europe are found to fall below their uncertainties and excluded from analyses. The GPS vertical velocities reach the maximum values for Scandinavia with the maximal uplift equal to 11.0 mm/yr. Moreover, a comparison between the GPS-derived rates and the present-day motion predicted by the newest Glacial Isostatic Adjustment (GIA) ICE-6G_C (VM5a) model is provided. We prove that these rates agree at a 0.5 mm/yr level on average; the Sweden area with the most significant uplift observed agrees within 0.2 mm/yr. The largest discrepancies between GIA-predicted uplift and the GPS vertical rates are found for Svalbard; the difference is equal to 6.7 mm/yr and arises mainly from the present-day ice melting. The GPS-derived vertical rates estimated for the southern coast of the Baltic Sea are systematically underestimated by the GIA prediction by up to 2 mm/yr. The northern British Isles vertical rates are overestimated by the GIA model by about 0.5 mm/yr. The area of the Netherlands and the coastal area of Belgium are both subsiding faster than it is predicted by the GIA model of around 1 mm/yr. The inland part of Belgium, Luxemburg and the western part of Germany show strong positive velocities when compared to the GIA model. Most of these stations uplift of more than 1 mm/yr. It may be caused by present-day elastic deformation due to terrestrial hydrology, especially for Rhein basin, or non-tidal atmospheric loading, for Belgium and Luxembourg.

The International Terrestrial Reference Frame: lessons from ITRF2014

We review the progress and continuous improvements being made since more than 30 years in the determination and development of the International Terrestrial Reference Frame (ITRF). We present the modeling innovations introduced in the ITRF2014 elaboration, mainly (1) the estimation of the annual and semi-annual signals embedded in the time series of station coordinates provided by the four space geodesy techniques, and (2) the incorporation of post-seismic deformation (PSD) models for sites subject to major earthquakes. We recall the rank deficiency problem in the ITRF combination model that is related to the specification of the ITRF defining parameters. We evaluate the precision and accuracy of the main ITRF2014 geodetic and geophysical products using some key performance indicators. We address some scientific questions of space geodesy contribution, via ITRF2014 results, to understand geophysical processes that affect the Earth system, such as earthquake displacements, tectonic motions and loading effects. We evaluate in particular the performance of estimating periodic signals versus applying a non-tidal atmospheric loading model. A particular emphasis is devoted to the level of agreement between techniques in terms of seasonal signals, frame physical parameters (origin and scale) and consistency with terrestrial local ties at co-location sites. Main conclusions are then drawn to guide and improve our analysis and combination strategy for future ITRF developments.

Tropospheric products of the second GOP European GNSS reprocessing (1996–2014)

Abstract. In this paper, we present results of the second reprocessing of all data from 1996 to 2014 from all stations in International Association of Geodesy (IAG) Reference Frame Sub-Commission for Europe (EUREF) Permanent Network (EPN) as performed at the Geodetic Observatory Pecný (GOP). While the original goal of this research was to ultimately contribute to the realization of a new European Terrestrial Reference System (ETRS), we also aim to provide a new set of GNSS (Global Navigation Satellite System) tropospheric parameter time series with possible applications to climate research. To achieve these goals, we improved a strategy to guarantee the continuity of these tropospheric parameters and we prepared several variants of troposphere modelling. We then assessed all solutions in terms of the repeatability of coordinates as an internal evaluation of applied models and strategies and in terms of zenith tropospheric delays (ZTDs) and horizontal gradients with those of the ERA-Interim numerical weather model (NWM) reanalysis. When compared to the GOP Repro1 (first EUREF reprocessing) solution, the results of the GOP Repro2 (second EUREF reprocessing) yielded improvements of approximately 50 and 25 % in the repeatability of the horizontal and vertical components, respectively, and of approximately 9 % in tropospheric parameters. Vertical repeatability was reduced from 4.14 to 3.73 mm when using the VMF1 mapping function, a priori ZHD (zenith hydrostatic delay), and non-tidal atmospheric loading corrections from actual weather data. Raising the elevation cut-off angle from 3 to 7° and then to 10° increased RMS from coordinates' repeatability, which was then confirmed by independently comparing GNSS tropospheric parameters with the NWM reanalysis. The assessment of tropospheric horizontal gradients with respect to the ERA-Interim revealed a strong sensitivity of estimated gradients to the quality of GNSS antenna tracking performance. This impact was demonstrated at the Mallorca station, where gradients systematically grew up to 5 mm during the period between 2003 and 2008, before this behaviour disappeared when the antenna at the station was changed. The impact of processing variants on long-term ZTD trend estimates was assessed at 172 EUREF stations with time series longer than 10 years. The most significant site-specific impact was due to the non-tidal atmospheric loading followed by the impact of changing the elevation cut-off angle from 3 to 10°. The other processing strategy had a very small or negligible impact on estimated trends.

Monte Carlo SSA to detect time-variable seasonal oscillations from GPS-derived site position time series

We explore the capability of singular spectrum analysis (SSA) to extract time-variable seasonal oscillations from continual GPS observations and demonstrate the statistical assessment on the colored noise (in particular the first-order autoregressive AR(1) noise) using Monte Carlo SSA (MCSSA) methodology. We provide example applications to ~15-year vertical coordinate time series for 36 globally distributed International GNSS Service (IGS) sites. We find the SSA-filtered seasonal signals can easily pass the confidence interval and hypothesis tests of MCSSA. However, maximum likelihood estimate (MLE) results show that 72% of sites have their flicker noise amplitudes reduced after removing SSA-filtered annual signal, implying that the SSA-filtered seasonal signals may contain an artificial signal driven by colored noise. Therefore, the AR(1) null hypothesis noise model may be misleading in surrogate data tests for GPS seasonal signals. Moreover, comparison between SSA-filtered GPS annual signals and joint geophysical model predictions (non-tidal atmospheric loading+non-tidal ocean loading+hydrological loading) confirms that seasonal signals are resulting from a combination of mass loading and systematic error.

Impact of loading displacements on SLR-derived parameters and on the consistency between GNSS and SLR results

Displacements of the Earth’s surface caused by tidal and non-tidal loading forces are relevant in high-precision space geodesy. Some of the corrections are recommended by the international scientific community to be applied at the observation level, e.g., ocean tidal loading (OTL) and atmospheric tidal loading (ATL). Non-tidal displacement corrections are in general recommended not to be applied in the products of the International Earth Rotation and Reference Systems Service, in particular atmospheric non-tidal loading (ANTL), oceanic and hydrological non-tidal corrections. We assess and compare the impact of OTL, ATL and ANTL on SLR-derived parameters by reprocessing 12 years of SLR data considering and ignoring individual corrections. We show that loading displacements have an influence not only on station long-term stability, but also on geocenter coordinates, Earth Rotation Parameters, and satellite orbits. Applying the loading corrections reduces the amplitudes of annual signals in the time series of geocenter and station coordinates. The general improvement of the SLR station 3D coordinate repeatability when applying OTL, ATL and ANTL corrections are 19.5 %, 0.2 % and 3.3 % respectively, w.r.t. the solutions without loading corrections. ANTL corrections play a crucial role in the combination of optical (SLR) and microwave (GNSS, VLBI, DORIS) space geodetic observation techniques, because of the so-called Blue-Sky effect: SLR measurements can be carried out only under cloudless sky conditions—typically during high air pressure conditions, when the Earth’s crust is deformed, whereas microwave observations are weather-independent. Thus, applying the loading corrections at the observation level improves SLR-derived products as well as the consistency with microwave-based results. We assess the Blue-Sky effect on SLR stations and the consistency improvement between GNSS and SLR solutions when ANTL corrections are included. The omission of ANTL corrections may lead to inconsistencies between SLR and GNSS solutions of up to 2.5 mm for inland stations. As a result, the estimated GNSS–SLR coordinate differences correspond better to the local ties at the co-located stations when applying ANTL corrections.