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In this study, a new approach for rainfall spatial interpolation in the Luxembourgian case study is introduced. The method used here is based on a Fuzzy C-Means (FCM) clustering method. In a typical FCM procedure, there are a lot of available data and each data point belongs to a cluster, with a membership degree [0 1]. On the other hand, in our methodology, the center of clusters is determined first and then random data are generated around cluster centers. Therefore, this approach is called inverse FCM (i-FCM). In order to calibrate and validate the new spatial interpolation method, seven rain gauges in Luxembourg, Germany and France (three for calibration and four for validation) with more than 10 years of measured data were used and consequently, the rainfall for ungauged locations was estimated. The results show that the i-FCM method can be applied with acceptable accuracy in validation rain gauges with values for R2 and RMSE of (0.94–0.98) and (9–14 mm), respectively, on a monthly time scale and (0.86–0.89) and (1.67–2 mm) on a daily time scale. In the following, the maximum daily rainfall return periods (10, 25, 50 and 100 years) were calculated using a two-parameter Weibull distribution. Finally, the LISFLOOD FP flood model was used to generate flood hazard maps in Dudelange, Luxembourg with the aim to demonstrate a practical application of the estimated local rainfall return periods in an urban area.

We have reconstructed integrated water vapor (IWV) using the zenith wet delays to track the properties of hurricanes and explore their spatial and temporal distributions estimated from 922 GPS stations. Our results show that a surge in GPS-derived IWV occurred at least six hours prior to the landfall of two major hurricanes (Harvey and Irma) that struck the Gulf and East Coasts of the USA in 2017. We observed enhanced IWV, in particular, for the two hurricanes landfall locations. The observed variations exhibit a correlation with the precipitation value constructed from GPM/IMERG satellite mission coinciding with hurricane storm front passage. We used GPS-IWV data as inputs for spaghetti line plots for our path predictions, helping us predict the paths of Hurricanes Harvey and Irma. Hence, a directly estimable zenith wet delay sourced from GPS that has not been previously reported can serve as an additional resource for improving the monitoring of hurricane paths.

The conventional Global Navigation Satellite System (GNSS) processing is typically contaminated with errors due to atmospheric variabilities, such as those associated with the mesoscale phenomena. These errors are manifested in the parameter estimates, including station coordinates and atmospheric products. To enhance the accuracy of these GNSS products further, a better understanding of the local-scale atmospheric variability is necessary. As part of multi-GNSS processing, station coordinates, carrier phase ambiguities, orbits, zenith total delay (ZTD) and horizontal gradients are the main parameters of interest. Here, ZTD is estimated as the average zenith delay along the line-of-sight to every observed GNSS satellite mapped to the vertical while the horizontal gradients are estimated in NS and EW directions and provide a means to partly account for the azimuthally inhomogeneous atmosphere. However, a better atmospheric description is possible by evaluating the slant path delay (SPD) or slant wet delay (SWD) along GNSS ray paths, which are not resolved by ordinary ZTD and gradient analysis. SWD is expected to provide better information about the inhomogeneous distribution of water vapour that is disregarded when retrieving ZTD and horizontal gradients. Usually, SWD cannot be estimated directly from GNSS processing as the number of unknown parameters exceeds the number of observations. Thus, SWD is generally calculated from ZTD for each satellite and may be dominated by un-modelled atmospheric delays, clock errors, unresolved carrier-phase ambiguities and near-surface multipath scattering. In this work, we have computed multipath maps by stacking individual post-fit carrier residuals incorporating the signals from four GNSS constellations, i.e. BeiDou, Galileo, Glonass and GPS. We have selected a subset of global International GNSS Service (IGS) stations capable of multi-GNSS observables located in different climatic zones. The multipath effects are reduced by subtracting the stacked multipath maps from the raw post-fit carrier phase residuals. We demonstrate that the multipath stacking technique results in significantly reduced variations in the one-way post-fit carrier phase residuals. This is particularly evident for lower elevation angles, thus, producing a retrieval method for SWD that is less affected by site-specific multipath effects. We show a positive impact on SWD estimation using our multipath maps during increased atmospheric inhomogeneity as induced by severe weather events.

As one of the most important components of the global hydrologic cycle, atmospheric water vapor shows significant variability in both space and time over a large range of scales. This variability results from the interactions of many different factors, including topography and the presence of specific atmospheric processes. One of the key regions for affecting global climatic variations lies in the sub-Antarctic zone over the Southern Ocean with its Antarctic Circumpolar Current and the associated Antarctic Convergence. There, in this cold and maritime region, lies South Georgia Island with its weather and climate being largely affected by both the dominating ocean currents and the westerly winds in this zone. While the island forms an important outpost for various surface observations in this largely under sampled and extremely remote region, it also forms a barrier for these winds due to its high topography. This, in turn, leads to various local meteorological phenomena, such as warm Foehn winds, which have a significant impact on the near-surface meteorology and contribute to the accelerated glacier retreat observed for the northeast of the island.Surface meteorological data have been available for several stations near King Edward Point (KEP) in South Georgia for much of the 20th century. Since 2013 and 2014, Global Navigation Satellite System (GNSS) data have been available at five locations around the periphery of the island. In this study, we investigate the consistency between the different surface meteorological data sets and along with GNSS Precipitable Water Vapour we use these to analyse historic Foehn events.

Very high-resolution (VHR) optical Earth observation (EO) satellites as well as low-altitude and easy-to-use unmanned aerial systems (UAS/drones) provide ever-improving data sources for the generation of detailed 3-dimensional (3D) data using digital photogrammetric methods with dense image matching. Today both data sources represent cost-effective alternatives to dedicated airborne sensors, especially for remote regions. The latest generation of EO satellites can collect VHR imagery up to 0.30 m ground sample distance (GSD) of even the most remote location from different viewing angles many times per year. Consequently, well-chosen scenes from growing image archives enable the generation of high-resolution digital elevation models (DEMs). Furthermore, low-cost and easy to use drones can be quickly deployed in remote regions to capture blocks of images of local areas. Dense point clouds derived from these methods provide an invaluable data source to fill the gap between globally available low-resolution DEMs and highly accurate terrestrial surveys. Here we investigate the use of archived VHR satellite imagery with approx. 0.5 m GSD as well as low-altitude drone-based imagery with average GSD of better than 0.03 m to generate high-quality DEMs using photogrammetric tools over Tristan da Cunha, a remote island in the South Atlantic Ocean which lies beyond the reach of current commercial manned airborne mapping platforms. This study explores the potentials and limitations to combine this heterogeneous data sources to generate improved DEMs in terms of accuracy and resolution. A cross-validation between low-altitude airborne and spaceborne data sets describes the fit between both optical data sets. No co-registration error, scale difference or distortions were detected, and a quantitative cloud-to-cloud comparison showed an average distance of 0.26 m between both point clouds. Both point clouds were merged applying a conventional georeferenced approach. The merged DEM preserves the rich detail from the drone-based survey and provides an accurate 3D representation of the entire study area. It provides the most detailed model of the island to date, suitable to support practical and scientific applications. This study demonstrates that combination archived VHR satellite and low-altitude drone-based imagery provide inexpensive alternatives to generate high-quality DEMs.

This article is the second part of a two-part study, which explored the extent to which Building Information Modelling (BIM) is used for End-of-Lifecycle (EoL) scenario selection to minimise the Construction and Demolition Waste (CDW). The conventional literature review presented here is based on the conceptual landscape that was obtained from the bibliometric and scientometric analysis in the first part of the study. Seven main academic research directions concerning the BIM-based EoL domain were found, including social and cultural factors, BIM-based Design for Deconstruction (DfD), BIM-based deconstruction, BIM-based EoL within LCA, BIM-aided waste management, Material and Component Banks (M/C Banks), off-site construction, interoperability and Industry Foundation Classes (IFC). The analysis highlights research gaps in the path of raw materials to reusable materials, i.e., from the deconstruction to M/C banks to DfD-based designs and then again to deconstruction. BIM-based EoL is suffering from a lack of a global framework. The existing solutions are based on local waste management policies and case-specific sustainability criteria selection. Another drawback of these ad hoc but well-developed BIM-based EoL prototypes is their use of specific proprietary BIM tools to support their framework. This disconnection between BIM tools and EoL tools is reportedly hindering the BIM-based EoL, while no IFC classes support the EoL phase information exchange.

Multipath is a largely unmodelled source of error and causes large range errors in Global Navigation Satellite System (GNSS) observations. The effects have strong site-specific characteristics and impact each receiver differently. Multipath errors can propagate and can cause in-situ position and velocity biases and are also contributing to the pervasive draconitic harmonic signals. We employ an empirical approach to reducing the effects of multipath by stacking one-way post-fit carrier phase residual observations by applying an appropriate averaging scheme. Our processing is based on static multi-GNSS observations using various scientific GNSS software packages (Bernese GNSS Software, NAPEOS, GAMIT-GLOBK, PRIDE and GINS). Our multipath stacking (MPS ) uses the stacking of individual residuals generated by variable azimuth cell size (congruent cells) by allocating carrier phase residuals in each cell, unlike fixed azimuth cell resolution in the standard MPS approaches. This reduces the binning of fewer residuals at higher elevation angles. Before stacking, we also apply rigorous statistical outlier screening tests for each one-way post-fit carrier phase residual assigned to each of the congruent cells. We thus correct the multipath effects by subtracting the stacked multipath map from the post-fit carrier phase residual. Using this technique we produce a model available in the form of the Antenna Exchange (ANTEX) file format, that can potentially be implemented in routine GNSS analysis with no or little additional overhead for individual analysis centers (ACs).In this study, we assess the feasibility and applicability of the MPS maps as an International GNSS Service (IGS) product for routine GNSS analysis. We have selected a subset of IGS stations with and without known multipath issues in different climatic zones. We demonstrate the multipath stacking technique to result in a significant reduction of the variation in the one-way post-fit carrier phase residuals. For GPS-only solutions, the MPS technique shows a decrease of up to 30% in the RMS value of the one-way post-fit carrier phase residuals. We have also tested our MPS for other constellations such as GLONASS, Galileo and BeiDou, and combinations of these .

Flooding is the number one natural disaster in terms of insured and uninsured losses annually. The development of reliable methods for flood simulation have greatly improved our ability to predict floods thereby reducing damages and loss of life in flood-prone regions. However, there is still a lot of room for improvement and innovation to provide better predictions, especially for flash floods, particularly in urban areas This is addressed in the present study, the goal of which it is to improve simulation and prediction of flash floods and to develop a spatial decision-making model for implementing flood protection measures. In this regard, different approaches for flood simulation and flood protection should be applied. The proposed methodology links flood hazard modeling, remote sensing and machine learning methods. Combining these physical models and data driven methods will result in a more reliable hybrid model that can be employed for prediction of (flash) floods and event analysis. In order to achieve the research goal of present study we: i) add more functionality to a hydrodynamic model code; ii) complement the latter with data driven methods ;iii) develop a spatial decision-making model framework for defining flood protection measures, iv) validate process-based and data driven methods, and finally v) cross-evaluate Light Detection And Radar (LiDAR) topography with available local super-resolution drone data to assess the ability to incorporate local flood defenses into the models. The most important outcome is the creation of valuable flood maps in areas where it matters - while accounting for effects of land use and climate change. This will serve scientists as well as land and risk management authorities with better actionable flood risk information in locations where people and assets are located and in danger. It also develops innovative methodologies for estimating the changing risk from flash floods based on land use scenarios and climate change projections. Moreover, developing spatial multi-criteria decision making (SMCDM) can help decision makers to determine suitable locations and methods for flood protection measures. These methods will be particularly valuable in the context of solving current challenges of accounting for and mitigating flash floods and the effects of climate change.

Water vapor is an important medium for the transmission moisture and latent heat in the atmosphere. It is one of the most abundant and dominant greenhouse gases in the atmosphere, which is crucial for global warming. With higher temperatures, the specific humidity will also increase as predicted by the nonlinear Clausius-Clapeyron relationship, indicating a positive feedback loop. Hence, estimation of the trend of Integrated Water Vapor (IWV) in the atmosphere is of great importance for global warming research. However, previous studies have shown that the trends of IWV are usually rather small. Therefore, it is important to estimate the IWV trend and its associated uncertainty with a reasonable mathematical model for the homogenized time series from homogenously reprocessed GPS data sets. Since the 1990s, the Global Positioning System (GPS) has successfully been employed to retrieve IWV with a high temporal resolution, all-weather condition and with global coverage. In this work, we used the hourly GPS Zenith Total Delay (ZTD) time series for 1995.0-2017.0 at 21 European GPS stations derived from a homogeneous data reprocessing. For the conversion of ZTD to IWV, we employed the meteorological variables from ERA5, a state-of-the-art atmosphere reanalysis product newly released by the European Centre for Medium-Range Weather Forecasts (ECMWF). Then, we investigated the influence of noise model assumptions within the mathematical model on the uncertainties of IWV trend estimates. As expected, the results confirmed that the assumption of a white noise only model tends to underestimate the trend uncertainty. A first-order autoregressive process is the preferred mathematical model for a more realistic estimation of the IWV trend uncertainty.

Tropical cyclones are one of the most powerful severe weather events that produce devastating socioeconomic and environmental impacts in the areas they strike. Therefore, monitoring and tracking of the arrival times and path of the tropical cyclones are extremely valuable in providing early warning to the public and governments. Hurricane Florence struck the East cost of USA in 2018 and offers an outstanding case study. We employed Global Positioning System (GPS) derived precipitable water vapor (PWV) data to track and investigate the characteristics of storm occurrences in their spatial and temporal distribution using a dense ground network of permanent GPS stations. Our findings indicate that a rise in GPS-derived PWV occurred several hours before Florence’s manifestation. Also, we compared the temporal distribution of the GPS-derived PWV content with the precipitation value for days when the storm appeared in the area under influence. The study will contribute to quantitative assessment of the complementary GPS tropospheric products in hurricane monitoring and tracking using GPS-derived water vapor evolution from a dense network of permanent GPS stations.

The time evolution of geophysical phenomena can be characterised by stochastic time series. The stochastic nature of the signal stems from the geophysical phenomena involved and any noise, which may be due to, e.g., un-modelled effects or measurement errors. Until the 1990s, it was usually assumed that white noise could fully characterise this noise. However, this was demonstrated to not be the case and it was proven that this assumption leads to underestimated uncertainties of the geophysical parameters inferred from the geodetic time series. Therefore, in order to fully quantify all the uncertainties as robustly as possible, it is imperative to estimate not only the deterministic but also the stochastic model parameters of the time series. In this regard, the Markov Chain Monte Carlo (MCMC) method can provide a sample of the distribution function of all parameters, including those regarding the noise, e.g., spectral index and amplitudes. After presenting the MCMC method and its implementation in our MCMC software we apply it to synthetic and real time series and perform a cross-evaluation using Maximum Likelihood Estimation (MLE) as implemented in the CATS software. Several examples as to how the MCMC method performs as a parameter estimation method for geodetic time series are given in this chapter. These include the applications to GPS position time series, superconducting gravity time series and monthly mean sea level (MSL) records, which all show very different stochastic properties. The impact of the estimated parameter uncertainties on sub-sequentially derived products is briefly demonstrated for the case of plate motion models. Finally, an evaluation of the MCMC method against the Hector method using weekly downsampled versions of the Benchmark Synthetic GNSS (BSG) time series as provided in Chap. 2 is presented separately in an appendix.

Although the statistical significances for the trends of integrated water vapor (IWV) are essential for a correct interpretation of climate change signals, obtaining accurate IWV trend estimates with realistic uncertainties remains a challenge. This study evaluates the feasibility of the IWV trends derived from the newly released fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA5) for climate change analysis in continental Europe. This is achieved by comparing the trends derived from in-situ ground-based Global Positioning System (GPS)’s daily IWV series from 1994 to 2019 at 109 stations. The realistic uncertainties and statistical significances of the IWV trends are evaluated with the time series analysis on their noise characteristics and proper noise models. Results show that autoregressive moving average ARMA(1,1) noise model is preferred rather than the commonly assumed white noise (WN) or first-order autoregressive AR(1) noise for about 68% of the ERA5 and GPS IWV series. An improper noise model would misevaluate the trend uncertainty of an IWV time series, compared with its specific preferred noise model. For example, ARMA(1,1) may misevaluate the standard deviations of their trend estimates (0.1–0.3 kg m−2 decade−1) by 10%. Nevertheless, ARMA(1,1) is recommended as the default noise model for the ERA5 and GPS IWV series. However, the preferred noise model for each ERA5 minus GPS (E-G) IWV series should be specifically determined, because the AR(1)-related models can result in an underestimation on its trend uncertainty by 90%. In contrast, power-law (PL) model can lead to an overestimation by up to nine times. The E-G IWV trends are within −0.2–0.4 kg m−2 decade−1, indicating that the ERA5 is a potential data source of IWV trends for climate change analysis in continental Europe. The ERA5 and GPS IWV trends are consistent in their magnitudes and geographical patterns, lower in Northwest Europe (0–0.4 kg m−2 decade−1) but higher around the Mediterranean Sea (0.6–1.4 kg m−2 decade−1).

It is anticipated that the performance of real-time (RT) GNSS meteorology can be further improved by incorporating observations from multiple Global Navigation Satellite System (GNSS), including GPS, GLONASS, Galileo and BeiDou. In this paper, an operational RT system for extracting zenith troposphere delay (ZTD) using a modified version of the Precise Point Positioning With Integer and Zero-difference Ambiguity Resolution Demonstrator (PPP-wizard) was established. GNSS, including GPS, GLONASS and Galileo, observation streams were processed using RT Precise Point Positioning (PPP) strategy based on RT satellite orbit/clock products from the Centre National d'Etudes Spatiales (CNES). An experiment covering 30 days was conducted, in which the observation streams of 20 globally distributed stations were processed. The initialization time and accuracy of the RT troposphere results using single- and multi-system observations were evaluated. The effect of PPP ambiguity resolution was also evaluated. Results reveal that RT troposphere estimates based on single system observations can both be applied in weather now-casting, in which the GPS-only solution is better than the GLONASS-only solution. The performance can also be improved by PPP ambiguity resolution and utilizing GNSS observations. Specifically, we notice that ambiguity resolution is more effective in improving the accuracy of ZTD, whereas the initialization process can be better accelerated by GNSS observations. Combining all techniques, the RT troposphere results with an average accuracy of about 8 mm in ZTD can be achieved after an initialization process of approximately 8.5 minutes, which demonstrates superior results for applying GNSS observations and ambiguity resolution for RT meteorological applications.

In Global Navigation Satellite System (GNSS) coordinate time-series unrecognized errors and unmodelled (periodic) effects may bias nonlinear motions induced by geophysical signals. Hence, understanding and mitigating these errors is vital to reducing biases and on revealing subtle geophysical signals. To assess the nature of periodic signals in coordinate time-series Precise Point Positioning (PPP) solutions for the period 2008–2015 are generated. The solutions consider Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) or combined GPS+GLONASS (GNSS) observations. We assess the periodic signals of station coordinates computed using the combined International GNSS Service (IGS) and four of its Analysis Centers (ACs) products. Furthermore, we make use of different filtering methods to investigate the sources of the periodic signals. A faint fortnightly signal in our PPP solution based on Jet Propulsion Laboratory (JPL) products and the existence of an 8 d period for those ACs generating combined GPS+GLONASS products are the main features in the GPS-only solutions. The existence of the 8 d period in the GPS-only solution indicates that GPS orbits computed in a combined GNSS solution contain GLONASS-specific signals. The GLONASS-only solution shows highly elevated powers at the third draconitic harmonic (∼120 d period), at the 8 d period and its harmonics (4 d, 2.67 d) besides the well-known annual, semi-annual and other draconitic harmonics. We show that the GLONASS constellation gaps before December 2011 contribute to the power at some of the frequencies. However, the well-known fortnightly signal in GPS-only solutions is not discernible in the GLONASS-only solution. The combined GNSS solution contains periodic signals from both systems, with most of the powers being reduced when compared to the single-GNSS solutions. A 52 per cent reduction for the horizontal components and a 36 per cent reduction for the vertical component are achieved for the fortnightly signal from the GNSS solution compared to the GPS-only solution. Comparing the results of the employed filtering methods reveals that the source of most of the powers of draconitic and fortnightly signals are satellite-induced with a non-zero contribution of site-specific errors.

Over the last decade, near real-time analysis of GPS data has become a well-established atmospheric observing tool, primarily coordinated by the EIG EUMETNET GPS Water Vapour Programme (E-GVAP) in Europe. In the near future, four operational GNSS will be available for commercial and scientific applications with atmospheric science benefiting from new signals from up to 60 satellites observed at any one place and time, however, many challenges remain regarding their optimal combined utilization. Besides raw data streaming, recent availability of precise real-time orbit and clock corrections enable wide utilization of autonomous Precise Point Positioning (PPP), which is particularly efficient for high-rate, real-time and multi-GNSS analyses.

In this section a summary of the national progress reports is given. GNSS4SWEC Management Committee (MC) members provided outline of the work conducted in their countries combining input from different partners involved. In the COST Action paticipated member from 32 COST countries, 1 Near Neighbour Country and 8 Intrantional Partners from Australia, Canada, Hong Kong and USA. The text reflects the state as of 1 January 2018.

Several research projects on condition assessment of bridges have proven that structural responses from dynamic excitation or static loading are influenced by local damages and thus, could be used for the detection and localisation of damages. Particularly, the curvature of structures is directly depending on their stiffness. In order to localise the discontinuities in curvature lines resulting from damage, this paper uses the so-called Deformation Area Difference Method (DAD), which is based on static load deflection tests on bridge structures. The DAD-method for damage localisation is presented within the paper using a theoretical example, which is then verified by two laboratory experiments. The first experiment consists of a reinforced concrete beam, which is loaded stepwise until failure of the concrete in the compression zone. Due to the load increase, the tensile zone of the beam starts cracking, leading to a stiffness reduction. The application of the DAD-method allows identifying the cracked area from the measurement of the deflection line. However, a challenge and a prerequisite for the applicability of the DAD-method is the highly accurate measurement of the deflection line. Therefore, one of the most modern measurement techniques such as digital photogrammetry is applied. Nonetheless, the accuracy of each measurement technique is limited. The second laboratory experiment consists of a steel beam, which is locally damaged at three positions. The degree of the damage is stepwise increased in order to identify at which degree of damage the applied DAD-method is still able to identify and localise damage. In this work, the focus lies on the minimisation of the effect of noise resulting from the limited measurement precision. Possible solutions were examined and proposed based on methods such as data smoothing using polynomial regression, consideration of standard deviation and measurement point variation. The reduction of the noise effect leads to an increase in the sensitivity of the damage localisation. The DAD-method has proven its potential for practical application through the successful localisation of cracking in the concrete beam.

Today Global Navigation Satellite Systems (GNSS) tropospheric products, such as zenith total delays (ZTD) and zenith wet delays (ZWD), are widely used as complementary data sets in numerical weather prediction models. In particular, the wet delays are treated as unknown parameters in GNSS processing and are estimated with other parameters such as station coordinates. In this study, we investigate the effects of Phase Center Correction (PCC) models on ZWD, integrated water vapor (IWV) and horizontal gradients derived from Global Positioning System (GPS) observations. Two solutions were generated using the GAMIT software over the European Reference Frame (EUREF) Permanent GNSS Network (EPN). The first (reference) solution was derived by applying the International GNSS Service (IGS) type-mean PCC models, while for the second solution PCC models from individual calibrations were used. The solutions were generated identically, except for the PCC model differences. The tropospheric products from the two solutions were then compared, with the assumption that common signals would be differenced out. The comparison of the two solutions clearly shows a bias in all tropospheric products, which can be attributed to PCC model deficiencies. Overall, mean biases of 1.8, 0.3, 0.14 and 0.19 mm are evident in ZWD, IWV, North–South and East–West gradients, respectively. Moreover, the differences between the two solutions show seasonal variations. For all antenna types, the ZWD and IWV differences are dominated by white plus power-law noise, with the latter characterizing the low-frequency spectrum. On the other hand, the horizontal gradients exhibit a white plus first-order autoregressive noise characteristic with less than 1% white noise. The individual PCC model provides a better fit to an external independent model in terms of gradient estimates and also provides up to 3% more carrier phase integer ambiguity resolution.

Long series of Zenith Wet Delay (ZWD) obtained as part of a homogeneous re-processing of Global Positioning System solutions constitute a reliable set of data to be assimilated into climate models. The correct stochastic properties, i.e. the noise model of these data, have to be identified to assess the real value of ZWD trend uncertainties since assuming an inappropriate noise model may lead to over- or underestimated error bounds leading to statistically insignificant trends. We present the ZWD time series for 1995–2017 for 120 selected globally distributed stations. The deterministic model in the form of a trend and significant seasonal signals were removed prior to the noise analysis. We examined different stochastic models and compared them to widely assumed white noise (WN). A combination of the autoregressive process of first-order plus WN (AR(1) + WN) was proven to be the preferred stochastic representation of the ZWD time series over the generally assumed white-noise-only approach. We found that for 103 out of 120 considered stations, the AR(1) process contributed to the AR(1) + WN model in more than 50% with noise amplitudes between 9 and 68 mm. As soon as the AR(1) + WN model was employed, 43 trend estimates became statistically insignificant, compared to 5 insignificant trend estimates for a white-noise-only model. We also found that the ZWD trend uncertainty may be underestimated by 5–14 times with median value of 8 using the white-noise-only assumption. Therefore, we recommend that AR(1) + WN model is employed before tropospheric trends are to be determined with the greatest reliability.

The performance of real-time (RT) precise positioning can be improved by utilizing observations from multiple Global Navigation Satellite Systems (GNSS) instead of one particular system. Since the end of 2012, BeiDou, independently established by China, began to provide operational services for users in the Asia-Pacific regions. In this study, a regional RT precise positioning system is developed to evaluate the performance of GPS/BeiDou observations in Australia in providing high precision positioning services for users. Fixing three hourly updated satellite orbits, RT correction messages are generated and broadcasted by processing RT observation/navigation data streams from the national network of GNSS Continuously Operating Reference Stations in Australia (AUSCORS) at the server side. At the user side, RT PPP is realized by processing RT data streams and the RT correction messages received. RT clock offsets, for which the accuracy reached 0.07 and 0.28 ns for GPS and BeiDou, respectively, can be determined. Based on these corrections, an accuracy of 12.2, 30.0 and 45.6 cm in the North, East and Up directions was achieved for the BeiDou-only solution after 30 min while the GPS-only solution reached 5.1, 15.3 and 15.5 cm for the same components at the same time. A further improvement of 43.7, 36.9 and 45.0 percent in the three directions, respectively, was achieved for the combined GPS/BeiDou solution. After the initialization process, the North, East and Up positioning accuracies were 5.2, 8.1 and 17.8 cm, respectively, for the BeiDou-only solution, while 1.5, 3.0, and 4.7 cm for the GPS-only solution. However, we only noticed a 20.9% improvement in the East direction was obtained for the GPS/BeiDou solution, while no improvements in the other directions were detected. It is expected that such improvements may become bigger with the increasing accuracy of the BeiDou-only solution.

This study demonstrates the effect of unmodelled (sub-)daily tidal displacement on GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) coordinate time series in comparison with GPS (Global Positioning System). More than two propagated periodic signals appear in GPS and GLONASS coordinate time series in the presence of an unmodelled M2 /O1 tidal displacements. The propagation mechanism of Stewart et al. (2005) explains well most of the periodic signals. At a fortnightly period, an unmodeled M2 tidal displacement propagates into two long-period signals at 13.6x (x is a positive integer) and 14.76 days for GPS, while only a significant propagated periodic signal at 14.76-day is discernible for GLONASS. Similarly, significant propagated periodic signals at 13.6x and 14.19 days for GPS and only at 14.19-day for GLONASS are evident as a result of an unmodeled O1 tidal displacement. However, an unmodeled Mf (long-period) results in a strong power of similar magnitude at 13.6x-day (∼13.66-day) for both GPS and GLONASS solutions. The appearance of different periodic signals but as a result of the same unmodelled tidal displacement is attributed to the different ground repeat periods of the constellations, which is one of the factors of the propagation mechanism from Stewart et al. (2005). The latter explains the reason why the 13.6x-day fortnightly is present only for GPS solutions. Comparing the powers of the M2 aliased periodic signals at 13.6x-day and 14.76-day from a stacked spectra over all stations, the amplitude of the former is larger than the latter by an order of magnitude. The results of this study may infer that the 13.6x-day periodic signal in GPS/GNSS (Global Navigation Satellite System) derived products of the IGS (International GNSS Service) is a joint contribution of the propagation of unmodelled (sub-)daily tidal displacements and errors at longer periods with the former appearing to contribute more. We also demonstrated that significant reduction of the propagated periodic signals can be achieved from combined-system solutions.

The velocity estimates and their uncertainties derived from position time series of Global Navigation Satellite System stations are affected by seasonal signals and their harmonics, and the statistical properties, i.e., the stochastic noise, contained in the series. If the deterministic model in the form of linear trend and periodic terms is not accurate enough to describe the time series, it will alter the stochastic model, and the resulting effect on the velocity uncertainties can be perceived as a result of a misfit of the deterministic model. The effects of insufficiently modeled seasonal signals will propagate into the stochastic model and falsify the results of the noise analysis, in addition to velocity estimates and their uncertainties. We provide the general dilution of precision (GDP) of velocity uncertainties as the ratio of uncertainties of velocities determined from to two different deterministic models while accounting for stochastic noise at the same time. In this newly defined GDP, the first deterministic model includes a linear trend, while the second one includes a linear trend and seasonal signals. These two are tested with the assumption of white noise only as well as the combinations of power-law and white noise in the data. The more seasonal terms are added to the series, the more biased the velocity uncertainties become. With increasing time span of observations, the assumption of seasonal signals becomes less important, and the power-law character of the residuals starts to play a crucial role in the determined velocity uncertainties. With reference frame and sea level applications in mind, we argue that 7 and 9 years of continuous observations is the threshold for white and flicker noise, respectively, while 17 years are required for random-walk to decrease GDP below 5% and to omit periodic oscillations in the GNSS-derived time series taking only the noise model into consideration.

The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction (NWP) models, which assimilate GNSS-derived zenith total delay (ZTD) estimates. The development of NWP models with faster assimilation cycles, e.g., 1-h assimilation cycle in the rapid update cycle NWP model, has increased the interest of the meteorological community toward sub-hour ZTD estimates. The suitability of real-time ZTD estimates obtained from three different precise point positioning software packages has been assessed by comparing them with the state-of-the-art IGS final troposphere product as well as collocated radiosonde (RS) observations. The ZTD estimates obtained by BNC2.7 show a mean bias of 0.21 cm, and those obtained by the G-Nut/Tefnut software library show a mean bias of 1.09 cm to the IGS final troposphere product. In comparison with the RS-based ZTD, the BNC2.7 solutions show mean biases between 1 and 2 cm, whereas the G-Nut/Tefnut solutions show mean biases between 2 and 3 cm with the RS-based ZTD, and the ambiguity float and ambiguity fixed solutions obtained by PPP-Wizard have mean biases between 6 and 7 cm with the references. The large biases in the time series from PPP-Wizard are due to the fact that this software has been developed for kinematic applications and hence does not apply receiver antenna eccentricity and phase center offset (PCO) corrections on the observations. Application of the eccentricity and PCO corrections to the a priori coordinates has resulted in a 66 % reduction of bias in the PPP-Wizard solutions. The biases are found to be stable over the whole period of the comparison, which are criteria (rather than the magnitude of the bias) for the suitability of ZTD estimates for use in NWP nowcasting. A millimeter-level impact on the ZTD estimates has also been observed in relation to ambiguity resolution. As a result of a comparison with the established user requirements for NWP nowcasting, it was found that both the G-Nut/Tefnut solutions and one of the BNC2.7 solutions meet the threshold requirements, whereas one of the BNC2.7 solution and both the PPP-Wizard solutions currently exceed this threshold.

The South Scotia Ridge Transform (SSRT) plate boundary between the Scotia and Antarctic plates experienced large strike-slip earthquakes on August 4, 2003 (M w 7.6) and November 17, 2013 (M w 7.8). These events have overlapping aftershock zones, which is unusual. A 36°–45° southward dipping fault zone ruptured with left-lateral displacements in each event along the northern margin of the South Orkney micro-continent near 60°S. Slip distributions for the two events are determined using teleseismic body and surface wave recordings along with constraints from GPS ground motion recordings at station BORC on Laurie Island (South Orkney Islands), just south of the SSRT. The aftershock distributions, high-frequency back-projections, and unconstrained body wave finite-fault inversions permit significant overlap of the 2003 and 2013 slip zones; however, the GPS static displacements resolve differences in the large-slip regions of the two ruptures. The 2013 earthquake sequence along the SSRT initiated with M w 6.1 (November 13) and M w 6.8 (November 16) foreshocks located ∼ 50 km west of the mainshock hypocenter, and had aftershocks extending ∼ 250 km eastward. The rupture spread primarily eastward at ∼ 2.5 km / s with a total rupture duration of about 120 s, with two distinct patches of large-slip located northwest and northeast of the South Orkney Islands. The rupture swept past BORC, with high-rate GPS (HRGPS) ground motion recordings capturing the time-varying slip history of the faulting. Traditional GPS data require that the largest-slip region of the shorter rupture in 2003 is located in the gap NNE of BORC between the two patches that ruptured in 2013. There appears to be some overlap of lower slip regions. The complementary slip distributions comprise a relatively uniform offset along this portion of the SSRT, which is one of the most seismically active regions of the entire Antarctic plate boundary.

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations.

Zenith Total Delay (ZTD) time series, derived from the re-processing of Global Positioning System (GPS) data, provide valuable information for the evaluation of global atmospheric reanalysis products such as ERA-Interim. Identifying the correct noise characteristics in the ZTD time series is an important step to assess the "true" magnitude of ZTD trend uncertainties. The ZTD residual time series for 1995–2015 are generated from our homogeneously re-processed and homogenized GPS time series from over 700 globally distributed stations classified into five major climate zones. The annual peak of ZTD data ranges between 10 and 150 mm with the smallest values for the polar and Alpine zone. The amplitudes of daily curve fall between 0 and 12 mm with the greatest variations for the dry zone. The autoregressive process of fourth order plus white noise model were found to be optimal for ZTD series. The tropical zone has the largest amplitude of autoregressive noise (9.59 mm) and the greatest amplitudes of white noise (13.00 mm). All climate zones have similar median coefficients of AR(1) (0.80 ± 0.05) with a minimum for polar and Alpine, which has the highest coefficients of AR(2) (0.27 ± 0.01) and AR(3) (0.11 ± 0.01) and clearly different from the other zones considered. We show that 53 of 120 examined trends became insignificant, when the optimum noise model was employed, compared to 11 insignificant trends for pure white noise. The uncertainty of the ZTD trends may be underestimated by a factor of 3 to 12 compared to the white noise only assumption.

We present a Bayesian Monte Carlo Markov Chain method to simultaneously estimate the spectral index and power amplitude of a fractional differenced Gaussian process at low frequency, in presence of white noise, and a linear trend and periodic signals. This method provides a sample of the likelihood function and thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. We test this method with simulated and real Global Positioning System height time series and propose it as an alternative to optimization methods currently in use. Furthermore, without any mathematical proof, the results from the simulations suggest that this method is unaffected by the stationary regime and hence, can be used to check whether or not a time series is stationary.

[1] The accuracy of Global Positioning System (GPS) time series is degraded by the presence of offsets. To assess the effectiveness of methods that detect and remove these offsets, we designed and managed the Detection of Offsets in GPS Experiment. We simulated time series that mimicked realistic GPS data consisting of a velocity component, offsets, white and flicker noises (1/f spectrum noises) composed in an additive model. The data set was made available to the GPS analysis community without revealing the offsets, and several groups conducted blind tests with a range of detection approaches. The results show that, at present, manual methods (where offsets are hand picked) almost always give better results than automated or semi‒automated methods (two automated methods give quite similar velocity bias as the best manual solutions). For instance, the fifth percentile range (5% to 95%) in velocity bias for automated approaches is equal to 4.2 mm/year (most commonly ±0.4 mm/yr from the truth), whereas it is equal to 1.8 mm/yr for the manual solutions (most commonly 0.2 mm/yr from the truth). The magnitude of offsets detectable by manual solutions is smaller than for automated solutions, with the smallest detectable offset for the best manual and automatic solutions equal to 5 mm and 8 mm, respectively. Assuming the simulated time series noise levels are representative of real GPS time series, robust geophysical interpretation of individual site velocities lower than 0.2–0.4 mm/yr is therefore certainly not robust, although a limit of nearer 1 mm/yr would be a more conservative choice. Further work to improve offset detection in GPS coordinates time series is required before we can routinely interpret sub‒mm/yr velocities for single GPS stations.

A ZWD correction method is also presented and results are shown, which improve upon those without the correction. The ZWD estimates are produced using an undifferenced global navigation satellite system GNSS processing technique known as PPP. This, coupled with the chosen PSI method, provides a low noise solution when compared to similar experiments involving the integration of GNSS and interferometric synthetic aperture radar InSAR data. The results show that there is good temporal and spatial correlation between the PPP ZWD estimates and the PSI-derived atmospheric phase contributions. Noticeable improvements in the PSI solution when comparing before and after processing runs to precise levelling observations are shown.

Global Navigation Satellite Systems (GNSS) meteorology is an established operational service providing hourly updated GNSS tropospheric products to the National Meteorologic Services (NMS) in Europe. In the last decade through the ground-based GNSS network densification and new processing strategies like Precise Point Positioning (PPP) it has become possible to obtain sub-hourly tropospheric products for monitoring severe weather events. In this work one year (January–December 2013) of sub-hourly GNSS tropospheric products (Zenith Total Delay) are computed using the PPP strategy for seven stations in Bulgaria. In order to take advantage of the sub-hourly GNSS data to derive Integrated Water Vapour (IWV) surface pressure and temperature with similar temporal resolution is required. As the surface observations are on 3 hourly basis the first step is to compare the surface pressure and temperature from numerical weather prediction model Weather Forecasting and Research (WRF) with observations at three synoptic stations in Bulgaria. The mean difference between the two data-sets for 1) surface pressure is less than 0.5 hPa and the correlation is over 0.989, 2) temperature the largest mean difference is 1.1 °C and the correlation coefficient is over 0.957 and 3) IWV mean difference is in range 0.1–1.1 mm. The evaluation of WRF on annual bases shows IWV underestimation between 0.5 and 1.5 mm at five stations and overestimation at Varna and Rozhen. Varna and Rozhen have also much smaller correlation 0.9 and 0.76. The study of the monthly IWV variation shows that at those locations the GNSS IWV has unexpected drop in April and March respectively. The reason for this drop is likely problems with station raw data. At the remaining 5 stations a very good agreement between GNSS and WRF is observed with high correlation during the cold part of 2013 i.e. March, October and December (0.95) and low correlation during the warm part of 2013 i.e. April to August (below 0.9). The diurnal cycle of the WRF model shows a dry bias in the range of 0.5-1.5 mm. Between 00 and 01 UTC the GNSS IWV tends to be underestimate IWV which is likely due to the processing window used. The precipitation efficiency from GNSS and WRF show very good agreement on monthly bases with a maximum in May-June and minimum in August–September. The annual precipitation efficiency in 2013 at Lovech and Burgas is about 6 %.

In 2013 the International GNSS Service (IGS) Tide Gauge Benchmark Monitoring (TIGA) Working Group started their reprocessing campaign which proposes to re-analyse all relevant GPS observations from 1995 to the end of 2012 in order to provide high quality estimates of vertical land motion for monitoring of sea level changes. The TIGA Working Group will also produce a combined solution from the individual TIGA Analysis Centres (TAC) contributions. The consortium of British Isles continuous GNSS Facility (BIGF) and the University of Luxembourg TAC (BLT) will contribute weekly minimally constrained SINEX solutions from its reprocessing using the Bernese GNSS Software (BSW) version 5.2 and the University of Luxembourg will also act as a TIGA Combination Centre (TCC). The BLT will generate two solutions, one based on BSW5.2 using a network double difference (DD) strategy and a second one based on BSW5.2 using a Precise Point Positioning (PPP) strategy. In the DD strategy we have included all IGb08 core stations in order to achieve a consistent reference frame implementation. As an initial test for the TIGA combination, all TACs agreed to provide weekly SINEX solutions for a four-week period in December 2011. Taking these individual TAC solutions the TCC has computed a first combination using two independent combination software packages: CATREF and GLOBK. In this study we will present preliminary results from the BLT reprocessing and from the combination tests.

The number of Global Navigation Satellite System (GNSS) satellites and their geometry directly affect the quality of positioning and derived satellite products. Accordingly, the International GNSS Service (IGS) recommends GNSS antennas to be installed away from natural and man-made surfaces and structures, which may affect the incoming signals through severe multipath or obstructions. Following these recommendations, continuous GNSS (cGNSS) stations are generally located in low multipath environments with minimal signal obstructions. However, some applications require GNSS antennas to be installed at specific locations in order to measure local processes. In support of sea level studies, cGNSS stations are established at or close to tide gauges in order to accurately monitor the local vertical land movements experienced by the sea level sensors. However, the environment at the tide gauge might not be optimal for GNSS observations due to the aforementioned station-specific effects, which may degrade the quality of coordinate solutions. This study investigates the impact of severe signal obstructions on long-term position time series for some selected stations. A masking profile from an actually obstructed site is extracted, simulated and applied to unobstructed IGS sites. To investigate these effects, we implemented a new feature called azimuth-dependent elevation masking in the Bernese GNSS Software version 5.2. We present our preliminary results on the use of this new feature to study the impact of different obstruction scenarios on long-term GNSS position time series and vertical land movement estimates. The results show that a certain obstruction, with the effect being highly dependent on its severity and azimuthal direction, affects all coordinate components with the effect being more significant for the Up component. Moreover, it causes changes in the rate estimates and increases the rate uncertainty with the effect being site-specific.

SUMMARY A large storm surge event occurred on 2007 November 2009 in the southern North Sea where strong winds caused the sea level to rise drastically by up to 3 m within several hours. Based on the Proudman Oceanographic Laboratory storm surge model, the predicted loading displacements at coastal stations can reach a few centimetres in the vertical and several millimetres in the horizontal directions. In this study, we used two-hourly global positioning system (GPS) positions at 26 stations around the southern North Sea to identify the loading displacements caused by this storm surge event. We find that the mean rms of the differences between the estimated and predicted displacements are 4.9, 1.3 and 1.4 mm, which are insignificant compared to the one-sigma GPS positioning errors of 5.1, 2.0 and 2.4 mm for the Up, East and North components, respectively. More interestingly, in both vertical and horizontal directions, the estimated displacements successfully tracked the temporal evolution ofthestormsurgeloadingeffects.Inaddition,withinthewholeof2007November,weusedthe predicted displacements to correct the two-hourly GPS positions, and consequently reduced the rms of the estimated displacements on average from 9.3, 3.0 and 2.9 mm to 7.8, 2.8 and 2.8 mm for Up, East and North components, respectively. Therefore, subdaily loading effects due to storm surges should be paid attention to in the GPS positioning that contributes to crustal-motion studies around shallow seas such as the North Sea, the Baltic Sea and the Gulf of Mexico.

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (Real-Time Kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used seven days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 minutes of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 minutes to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g.

This paper presents estimates of rates of mean sea level (MSL) change around the UK based on a larger tide gauge data set and more accurate analysis methods than have been employed so far. The spatial variation of the trend in MSL is found to be similar to that inferred from geological information and from advanced geodetic techniques, which is a similar conclusion to that arrived at in previous, less precise and complete studies. The tide gauge MSL trends for 1901 onwards are estimated to be 1.4 +/- 0.2 mm/year larger than those inferred from geology or geodetic methods, suggesting a regional sea level rise of climate change origin several 1/10s mm/year lower than global estimates for the 20th century. However, UK MSL change cannot be described in terms of a simple linear increase alone but includes variations on interannual and decadal timescales. The possible sources of variation in a ‘UK sea level index’ are explored. Air pressure is clearly one such possible source but its direct local forcing through the ‘inverse barometer’ accounts for only one third of the observed variability. A number of larger scale atmospheric and ocean processes must also play important roles, but modelling them satisfactorily and separating the individual contributions presents a major challenge. As regards future regional UK sea level changes, one concludes that there is no basis for major modification to existing projections for the 2080s included in the 2002 UK Climate Impacts Programme studies.

Long-term planning for flood risk management in coastal and estuarine areas requires timely and reliable information on changes in land and sea levels. In this paper we describe how we have produced a detailed, high-resolution map of current changes in land levels for the Thames region, and carried out a new assessment of the changes in sea level relative to the land along the Thames Estuary over the past few decades/past century. We conclude the paper by considering the potential benefits of extended monitoring for the long-term planning of flood and coastal defences in that region.

CGPS coordinate time series analysis strategy was evaluated to determine highly accurate vertical station velocity estimates with realistic uncertainties. This strategy uses a combination of techniques to (1) obtain the most accurate parameter estimates of the station motion model, (2) infer the stochastic properties of the time series in order to compute more realistic error bounds for all parameter estimates, and (3) improve the understanding of apparent common systematic variations in the CGPS coordinate time series, which are believed to be of geophysical and/or technical origin. The strategy provided a pre-processing of the coordinate time series in which outliers and discontinuities were identified. Subsequent parameterization included a mean value, a constant rate, periodic terms with annual and semi-annual frequencies, and offset magnitudes for identified discontinuities. All parameters plus the magnitudes of different stochastic noise were determined using maximum likelihood estimation (MLE). Empirical orthogonal function (EOF) analysis was used to study both the temporal and spatial variability of the common modes determined by this technique. After outlining the CGPS coordinate time series analysis strategy this paper shows initial results for coordinate time series for a four year (2000–2003) period from a selection of CGPS stations in Europe that are part of the European Sea Level Service (ESEAS) CGPS network

We assess the use of precise point positioning (PPP) within the Bernese GPS software (BSW) Version 5.0 over the period from 2000 to 2005. In our strategy, we compute a set of daily PPP solutions for international GNSS service (IGS) reference frame (IGb00) sites by fixing IGS final satellite orbits and clock products, followed by a Helmert transformation of these solutions into ITRF2000, forming a set of continuous position time series over the entire time span. We assess BSW PPP by comparing our set of transformation parameters with those produced by the IGS analysis centre coordinator (ACC) and our position time series with those of the Jet Propulsion Laboratory (JPL) and the Scripps Orbit and Permanent Array Centre at the Scripps Institute of Oceanography (SIO). The distributions of the north (N), east (E) and up (U) daily position differences are characterized by means and SD of +2.2 ± 4.8, −0.6 ± 7.9 and +4.8 ± 17.3 mm with respect to JPL, and of +0.1 ± 4.4, −0.1 ± 7.4 and −0.1 ± 11.8 mm with respect to SIO. Similarly, we find sub-millimetre mean velocity differences and SD for the N, E and U components of 0.9, 1.5 and 2.2 mm/year with JPL, and of 1.2, 1.6 and 2.3 mm/year with SIO. A noise analysis using maximum likelihood estimation (MLE) shows that when estimating global site velocities from our position time series, the series need to be on average up to 1.3 times longer than those of JPL and SIO, before an uncertainty of less than 0.5 mm/year is obtained.

Modern Numerical Weather Prediction (NWP) models make use of the GNSS-derived Zenith Total Delay (ZTD) or Integrated Water Vapour (IWV) estimates to enhance the quality of their forecasts. Usually, the ZTD is assimilated into the NWP models on 3- hourly to 6-hourly intervals but with the advancement of NWP models towards higher update rates e.g. 1-hourly cycling in the Rapid Update Cycle (RUC) NWP, it has become of high interest to estimate ZTD on sub-hourly intervals. In turn, this imposes requirements related to the timeliness and accuracy of the ZTD estimates and has lead to a development of various strategies to process GNSS observations to obtain ZTD with different latencies and accuracies. Using present GNSS products and tools, ZTD can be estimated in real-time (RT), near real-time (NRT) and post-processing (PP) modes. The aim of this study is to provide an overview and accuracy assessment of various RT, NRT, and PP IWV estimation systems and comparing their achieved accuracy with the user requirements for GNSS meteorology. The NRT systems are based on Bernese GPS Software 5.0 and use a double-differencing strategy whereas the PP system is based on the Bernese GNSS Software 5.2 using the precise point positioning (PPP) strategy. The RT systems are based on the BKG Ntrip Client 2.7 and the PPPWizard both using PPP. The PPP-Wizard allows integer ambiguity resolution at a single station and therefore the effect of fixing integer ambiguities on ZTD estimates will also be presented.

Advances in GPS error modelling and the continued effort of re-processing have considerably decreased the scatter in position estimates over the last decade. The associated reduction of noise in derived position time series has revealed the presence of previously undetected periodic signals. It has been shown that these signals have frequencies related to the orbits of the GPS satellites. A number of potential sources for these periodicities at the draconitic frequency and its harmonics have already been suggested in the literature and include, e.g., errors in the sub-daily tidal models, multipath and unresolved integer ambiguities. Due to the geometrical relationship between the observing site and the orbiting satellite, deficiencies in the modelling of electromagnetic phase centres of receiving antennas have the potential to also contribute to the discovered periodic signals. The change from relative to absolute type mean antenna/radome calibrations within the International GNSS Service (IGS) led to a significant improvement, but the use of individual calibrations could possibly add further refinements to computed solutions. However, at this stage providing individual calibrations for all IGS stations is not feasible. Furthermore, antenna near-field electromagnetic effects might outweigh the benefits of individual calibrations once an antenna is permanently installed. In this study, we investigate the differences between position estimates obtained using individual and type mean antenna/radome calibrations as used by the IGS community. We employ position time series derived from precise point positioning (PPP) as implemented in two scientific GNSS software packages. Our results suggest that the calibration differences propagate directly into the position estimates, affecting both sub-daily and daily results and yielding periodic variations. The sub-daily variations have periods close to half a sidereal day and one sidereal day with peak-to-peak amplitudes of up to 10 mm in all position components. The stacked power spectra of the daily difference time series reveal peaks at the GPS draconitic frequency and its harmonics with peak-to-peak amplitudes of up to 1 mm. Although these results are still preliminary, they confirm that small differences between individual and type mean antenna/radome calibrations propagate into position time series and may be partly responsible for the spurious signals with draconitic frequency and its harmonics.