Three Geoid Slope Validation Surveys were planned by the National Geodetic Survey for validating geoid improvement gained by incorporating airborne gravity data collected by the “Gravity for the Redefinition of the American Vertical Datum” (GRAV-D) project in flat, medium and rough topographic areas, respectively. The first survey GSVS11 over a flat topographic area in Texas confirmed that a 1-cm differential accuracy geoid over baseline lengths between 0.4 and 320 km is achievable with GRAV-D data included (Smith et al. in J Geod 87:885–907, 2013). The second survey, Geoid Slope Validation Survey 2014 (GSVS14) took place in Iowa in an area with moderate topography but significant gravity variation. Two sets of geoidal heights were computed from GPS/leveling data and observed astrogeodetic deflections of the vertical at 204 GSVS14 official marks. They agree with each other at a \({\pm }1.2\,\, \hbox {cm}\) level, which attests to the high quality of the GSVS14 data. In total, four geoid models were computed. Three models combined the GOCO03/5S satellite gravity model with terrestrial and GRAV-D gravity with different strategies. The fourth model, called xGEOID15A, had no airborne gravity data and served as the benchmark to quantify the contribution of GRAV-D to the geoid improvement. The comparisons show that each model agrees with the GPS/leveling geoid height by 1.5 cm in mark-by-mark comparisons. In differential comparisons, all geoid models have a predicted accuracy of 1–2 cm at baseline lengths from 1.6 to 247 km. The contribution of GRAV-D is not apparent due to a 9-cm slope in the western 50-km section of the traverse for all gravimetric geoid models, and it was determined that the slopes have been caused by a 5 mGal bias in the terrestrial gravity data. If that western 50-km section of the testing line is excluded in the comparisons, then the improvement with GRAV-D is clearly evident. In that case, 1-cm differential accuracy on baselines of any length is achieved with the GRAV-D-enhanced geoid models and exhibits a clear improvement over the geoid models without GRAV-D data. GSVS14 confirmed that the geoid differential accuracies are in the 1–2 cm range at various baseline lengths. The accuracy increases to 1 cm with GRAV-D gravity when the west 50 km line is not included. The data collected by the surveys have high accuracy and have the potential to be used for validation of other geodetic techniques, e.g., the chronometric leveling. To reach the 1-cm height differences of the GSVS data, a clock with frequency accuracy of \(10^{-18}\) is required. Using the GSVS data, the accuracy of ellipsoidal height differences can also be estimated.

The monitoring of rigid structures of modal frequencies greater than 5 Hz and sub-mm displacement is mainly based so far on relative quantities from accelerometers, strain gauges, etc. Additionally, geodetic techniques such as GPS and robotic total stations (RTS) are constrained by their low accuracy (few mm) and their low sampling rates. In this study, the application of QDaedalus is presented, which constitutes a measuring system developed at the Geodesy and Geodynamics Lab, ETH Zurich and consists of a small CCD camera and total station, for the monitoring of the oscillations of a rigid structure. In collaboration with the Institute of Structural Engineering of ETH Zurich and EMPA, the QDaedalus system was used for monitoring of the sub-mm displacement of a rigid prototype beam and the estimation of its modal frequencies up to 30 Hz. The results of the QDaedalus data analysis were compared to those of accelerometers and proved to hold sufficient accuracy and suitably supplementing the existing monitoring techniques.

In order to determine scale factors or more complex calibration functions of relative gravimeters it is usually necessary to calibrate these instruments regularly on points with known gravity values. Especially well suited are points with absolute measurements and with large gravity differences. This implies that gravimetric calibration lines are usually implemented in north–south direction or on stations with big height differences. The latter has the advantage that traveling time can be kept rather short. In 2013 we established a calibration line in the Swiss Alps between Interlaken (altitude 570 m) and Jungfraujoch (altitude 3,500 m). This line consists of 7 absolute stations and several eccentric points. The total gravity difference is more than 600 mGal. All absolute stations are easily accessible by car or are located in immediate vicinity of a station of the Jungfrau railway. Therefore, it is possible to measure the whole line with relative instruments in a closed loop in 1 day. The absolute stations have been chosen in a way that they are accessible during the whole year and that the gravity difference between two neighboring stations does not exceed 150 mGal. So, it is possible to calibrate as well gravimeters with a limited measuring range or with a non-linear scale factor. The expanded uncertainties (k = 2) of the gravity values at the absolute stations are varying between 5 and 6 μGal. All vertical gravity gradients (VGGs) have been determined by relative measurements on three levels above the marker. The newly established calibration line is free to be used by the whole gravity community and we hope that many institutions will profit. It is to our knowledge worldwide the first traceable gravimetric calibration line satisfying the BIPM Mutual Recognition Arrangement (MRA).

The alignment challenge presented by the Compact Linear Collider (CLIC) project requires us to look closely at the ultra-high frequencies (< 1 km) of the gravity field and our ability to model or determine underground equipotential profiles at a very high level of precision. This is of particular importance in the context of an alignment system based on Hydrostatic Levelling System (HLS) and other instruments dependent on gravity. In the first part of this paper, the theoretical formulation of the gravity field, Astronomical Levelling and a misalignment operator are presented. Then, the error propagation model of Astronomical Levelling is revisited and adapted to the specifications of accelerator alignment. Afterwards, numerical gravity field simulations, based on sinusoidal anomalies of varying geometry and density, give the first orders of magnitude of the signals in the equipotential and in the observation space which can be expected at ultra-high frequencies. Finally, a measurement campaign based around a tunnel, 850 m in length, at a depth of 80 m, that include deflections of the vertical and gravimetric measurements is presented.

With the advent of the GPS navigation system, a promising ground based technique has been introduced which makes it possible to estimate the amount of water vapor in the troposphere from operational GPS networks at relatively low additional costs. While the estimation of the integrated amount is currently well established, the determination of the spatial water vapor distribution and its temporal variation are still a major challenge. To account for the vertical resolution, several tomographic approaches were pursued. We developed the software package AWATOS (atmospheric water vapor tomography software) which is based on the assimilation of double differenced GPS observations. Applying a least-squares inversion, the inhomogeneous spatial distribution of water vapor is determined. An extensive investigation has been carried out in Switzerland. GPS measurements are performed by the dense permanent Swiss national GPS network AGNES of the Swiss Federal Office of Topography (swisstopo). A total of 40 equally distributed water vapor profiles have been estimated on an hourly basis. For the purpose of validation, 22 radiosonde profiles were used at the GPS and meteorological station Payerne. Furthermore, data of the numerical weather model aLMo (alpine model in Switzerland, MeteoSwiss) were compared with the tomographic results. An overall good agreement of the three methods with an rms of better than 1.6 g/m3 absolute humidity was achieved. The results show that AGNES can be used as a dedicated network for the purpose of GPS-tomography, using a horizontal resolution of approximately 50 km and height layers of 300–500 m thickness in the lower troposphere.

A dense network of 17 dual frequency GPS receivers has been operated for two weeks during June 2001 within a 20 km×20 km area around Marseille, France, as part of the ESCOMPTE field campaign ([Cros et al., 2004. The ESCOMPTE program: an overview. Atmos. Res. 69, 241–279]; http://medias.obs-mip.fr/escompte). The goal of this GPS experiment was to provide GPS data allowing for tomographic inversions and their validation within a well-documented observing period (the ESCOMPTE campaign). Simultaneous water vapor radiometer, solar spectrometer, Raman lidar and radiosonde data are used for comparison and validation. In this paper, we highlight the motivation, issues and describe the GPS field experiment. Some first results of integrated water vapor retrievals from GPS and the other sensing techniques are presented. The strategies for GPS data processing and tomographic inversions are discussed.

The comparison of the integrated precipitable water vapor (IPWV) retrieved by GPS, microwave radiometer, solar spectrometer and radiosondes, operated within the French field campaign ESCOMPTE, shows an overall good agreement. The time dependent relative fluctuation as well as the absolute amount of water vapor match with high accuracy. The software package AWATOS (Atmospheric WAter vapor TOmography Software), developed at the Geodesy and Geodynamics Lab, ETH Zürich, is used to determine the spatial distribution and variation of water vapor in the troposphere by double differenced GPS measurements. The comparison with refractivity profiles derived from radiosonde data shows the success of this method.

During the last few years, new developments in the field of geodetic astronomy have been sparsely published. This might be due to the fact that the determination of deflections of the vertical still required relatively large efforts, both in time and in manpower, thus keeping the costs per point at a high level. Recently, the development of new high performance image sensors (CCD) at a reasonable price level enabled and initiated fundamental improvements in astrogeodetic observation instrumentations in terms of efficiency, automation, accuracy, and real-time capability. This promising development leads to a revitalization of astrogeodetic methods and offers very encouraging prospects for local high-precision astrogeodetic gravity field and geoid determinations. In this paper, two slightly different versions of the digital zenith camera, initially developed at the Institut für Erdmessung, University of Hannover, are presented as high-precision state-of-the-art instruments. Using modern CCD technology for imaging stars and a GPS receiver, these systems allow the direct determination of the direction of the plumb line and thus its deflection from the ellipsoidal normal within a fully automated procedure in real-time. In addition to a description of the system’s design and performance, the processing steps are presented: image data acquisition, data transfer and processing giving deflections of the vertical immediately after measurement.

GPS meteorology can be successfully used to model the tropospheric refraction effect on radiowave signals. We describe an approach to estimate and model the spatial distribution of the tropospheric water vapor. We refine the tomographic software package AWATOS which is based on the assimilation of GPS double difference observations. The observations are allocated to a voxel model, which is defined according to the distribution of the GPS stations. Performing a least‐squares adjustment, the refractivity of each voxel is determined. Tests of the software are performed, based on simulated and real data. The latter were obtained during a dedicated field campaign on the Big Island of Hawaii. The tomographic profiles are compared with radiosonde data. The results obtained for continuous atmospheric conditions fit well, whereas larger differences occur in discontinuous atmospheric weather conditions. Overall, an accuracy of 5–20 ppm (refractivity units) has been achieved.

The experiment GPS/H2O involving 17 GPS receivers has been operated for two weeks in June 2001 in a dense network around Marseille. This project was integrated into the ESCOMPTE campaign. This paper will focus on the GPS analysis in preparation of the tomographic inversion of GPS slant delays. As first results, GPS tropospheric parameters zenith delays and horizontal gradients have been extracted. For a first visualization of the humidity field overlying the network, zenith delays have been transformed into precipitable water. Successive humidity fields are presented for a period of sudden drop in humidity, indicating some spatial resolution in the small network. The time series of horizontal gradients evaluated at individual sites are compared to correlated zenith delay variations over the whole network (horizontal gradient of zenith delays), showing that in the small size network horizontal atmospheric structure is reflected by both types of parameters. To compare these two quantities, scaling of zenith delays due to different station altitudes was necessary. In this way, a GPS internal validation of the individual gradients by comparison with the horizontal gradient of zenith delays has been established. Differential features along transects across the network indicate a good spatial resolution of tropospheric phenomena, encouraging for the further tomographic exploitation of the data. Moreover, individual and zenith delay gradients weight differently atmospheric horizontal gradients occurring at different heights. This different sensitivity has been used for a first identification of a vertical atmospheric structure from GPS tropospheric delays, by observing an inclined frontal zone crossing the network.

In the framework of the European Union SEa Level Fluctuations (SELF) I and the SELF II Projects designed to study sea level variations around the Mediterranean and Black Seas, the Global Positioning System (GPS) technique was adopted to measure the ongoing crustal movements at tide gauge stations. Tide gauges measure sea-level variations with respect to a ground benchmark. In order to determine true sea-level variations of a few millimeters per year, it is necessary to estimate the ground vertical movement to a high degree of accuracy. Countries involved in the projects were Spain, France, Italy, Greece, Bulgaria and Russia. In the period from 1993 to 1998 repeated observations at more than 28 tide gauges and at a number of reference and intermediate stations were conducted. GPS measurements were complemented by Water Vapor Radiometers (WVR) at selected sites. Individual campaigns were evaluated and analyzed and showed height variations in the millimeter–centimeter range. All data were processed following common standards using the Bernese Software in a unified analysis to generate a combined solution. Based on the normal equations of all of the campaigns, a combined solution for the SELF Projects sites was generated. In the analysis of multi-technique anchor sites to the International Terrestrial Reference Frame ITRF97, it is shown that vertical rates of different techniques may be of different sign with respect to each other and also with respect to the ITRF97 combination. Vertical rates are not reliable in general and even the restriction to the use of long the long-time series sites KOSG, ONSA, WTZR, MADR, GRAZ and MATE did not ensure significant and unique vertical rates. Nevertheless, they had to be used for the reference frame definition. The results of repeated gravity observations and the continuous GPS observations at Porto Corsini and Medicina were compared to the epoch-wise GPS campaigns and revealed that the vertical rates are in conformance with each other if taken over the same period in time. The impact of the WVR observations on tide gauge position variation estimation is shown to improve the vertical component in the case of baseline-wise observations with two WVRs by up to 50%. It is shown, that the time span is too short for epoch-type observations to resolve significant height variations. The estimated rates of about 0–20 mm/year are most likely explained by systematic and random errors in the GPS observations. The absolute gravity observations at selected tide gauges are accurate to ±3 μGal and are in general agreement with the zero result from GPS. The main outcome of the SELF campaign observations therefore was the determination of a homogeneous zero-epoch data set and the creation of a database that includes the complete link from the GPS sites to the sea level in the five Mediterranean countries involved.

We have analyzed data from an experiment over the Madrid (Spain) area obtained from 5 GPS receivers and 3 Water Vapor Radiometers (WVR), in order to compare their retrievals of Tropospheric Slant Delays. For this purpose we have fitted a simple gradient model to both types of data, using a Kalman filter to account for the temporal variability of the zenith and gradient parameters. We show that the retrieved gradients with the two instruments are compatible, thus suggesting that the derived slant delays can be useful for tomographic analysis. We compare the estimates of ZWD obtained with the GIPSY and the Bernese software packages. Finally, we compare the estimated gradients with those obtained with HIRLAM, a Numerical Weather Prediction model.

Tropospheric water vapor is of central interest in a large variety of geoscientific fields, such as geodesy, geodynamics, climate research and meteorology. A new instrumental approach to ground-based mapping of tropospheric water vapor has been developed. It is based on high-resolution absorption measurements in the near infrared region by means of a solar spectrometer (SSM). To prove the feasability and accuracy potential of the new technique, a 30 day field experiment was carried out, performing SSM measurements simultaneously with two independent methods. One of them uses the Global Positioning System (GPS). This technique, called GPS meteorology, exploits the high sensitivity of the satellite signals to atmospheric delay for a determination of tropospheric parameters. As a third technique two ground-based microwave water vapor radiometers (WVR) were operated. A comparison of the three different techniques, exploiting absorption-, refraction-, and emission properties of water vapor, respectively, demonstrated the potential of solar spectrometry for precise and absolute determination of PW without meteorological a priori information.

Precise estimation of the vertical deformation is a challenge for understanding geodynamical processes. In mountainous areas, the main limitation of precise GAS vertical measurement lies in the difficulty of estimating tropospheric delay due to high differential elevation and large weather variability. We carried out two GPS campaigns in July 1994 (8 days) and March 1996 (11 days), during extreme weather conditions, on a 1 390 m height difference baseline. The zenith delay was calibrated with a standard atmospheric model (STD), Water Vapor Radiometric measurements (WVR) and surface pressure measurements, or computed through a least squares estimation (LSE). Half daily repeatability of the vertical LSE solutions has a precision of 11-14 mm with a small difference of 1 mm between the two expeditions.