Impact of atmospheric turbulence on geodetic very long baseline interferometry

We assess the impact of atmospheric turbulence on geodetic very long baseline interferometry (VLBI) through simulations of atmospheric delays. VLBI observations are simulated for the two best existing VLBI data sets: The continuous VLBI campaigns CONT05 and CONT08. We test different methods to determine the magnitude of the turbulence above each VLBI station, i.e., the refractive index structure constant C-n(2). The results from the analysis of the simulated data and the actually observed VLBI data are compared. We find that atmospheric turbulence today is the largest error source for geodetic VLBI. Accurate modeling of atmospheric turbulence is necessary to reach the highest accuracy with geodetic VLBI

High temporal resolution wet delay gradients estimated from multi-GNSS and microwave radiometer observations

We have used 1 year of multi-GNSS observations at the Onsala Space Observatory on the Swedish west coast to estimate the linear horizontal gradients in the wet propagation delay. The estimated gradients are compared to the corresponding ones from a microwave radiometer. We have investigated different temporal resolutions from 5 min to 1 d. Relative to the GPS-only solution and using an elevation cutoff angle of 10 and a temporal resolution of 5 min, the improvement obtained for the solution using GPS, Glonass, and Galileo data is an increase in the correlation coefficient of 11 % for the east gradient and 20 % for the north gradient. Out of all the different GNSS solutions, the highest correlation is obtained for the east gradients and a resolution of 2 h, while the best agreement for the north gradients is obtained for 6 h. The choice of temporal resolution is a compromise between getting a high correlation and the possibility of detecting rapid changes in the gradient. Due to the differences in geometry of the observations, gradients which happen suddenly are either not captured at all or captured but with much less amplitude by the GNSS data. When a weak constraint is applied in the estimation of process, the GNSS data have an improved ability to track large gradients, however, at the cost of increased formal errors

GPS tropospheric modelling: new developments and insights

GPS is widely used to monitor temporal and spatial variations of Earth’s crust, oceans and atmosphere. Of particular interest to this research is the use of GPS for studying variations in the Earth’s lower atmosphere. While there have been significant advances in the techniques and models used in GPS analyses over the past two decades, there is still room for improvement. In particular, observations at very low elevation angles still suffer greatly from modelling errors. These low-elevation observations provide useful information about the moisture content of the atmosphere and its variability around a GPS station, and are thus valuable data for meteorological studies if properly modelled. The main focus of this thesis is on optimization of the techniques and models used in GPS analysis for more accurate estimates of the tropospheric delays. Particular attention is paid to modelling low-elevation observations and challenging weather conditions. Throughout the thesis, we investigate several different aspects of modelling techniques and how each of them affect the tropospheric estimates. By applying a previously developed empirical model [Moore, 2015], the site-specific errors are shown to have large impacts on the tropospheric delay estimates: empirical mitigation of site-specific errors leads to improved repeatabilities of heights and tropospheric zenith delays for the majority of the stations in our analysis. The empirical site-specific model also significantly reduces the sensitivity of tropospheric zenith delay estimates to the choice of elevation cut-off. Another important potential source of error, the GPS estimates of tropospheric horizontal gradients are shown to be more accurate than the model values currently available. However, the conventional two-axis planar model of gradients does not accurately represent the actual gradients of the refractivity under weather conditions with asymmetric horizontal changes of refractivity. Such abnormal conditions may occur due to topography-driven gravity waves in the troposphere, and the mismodelled tropospheric horizontal gradients induce errors in the parameter estimates, sometimes leading to skewed position time series and inaccurate tropospheric zenith delays. A new parametrization of tropospheric gradients whereby an arbitrary number of gradients are estimated as discrete directional wedges is shown via both simulations and real case studies to largely improve the accuracy of recovered tropospheric zenith delays in asymmetric gradient scenarios. The new directional model significantly improves the repeatabilities of the station height time series in asymmetric gradient situations while causing slightly degraded repeatabilities for the stations in normal symmetric gradient conditions. The constraints on the temporal variations of the tropospheric delays are also investigated. It is shown via simulations and real experiments that it is generally preferable to avoid constraints on both tropospheric zenith delays and horizontal gradients. However, since the conventional model of horizontal gradients oversimplifies the horizontal variations of the refractivity in asymmetric gradient conditions, it is important to use a more complete model of gradients like the directional gradient model introduced in this thesis in conjunction with the relaxed constraints to avoid errors caused by the simplifying assumption of symmetric gradients by the conventional model

Sensing atmospheric water vapour using the global positioning system

Includes bibliographical references .Atmospheric water vapour measurements are of importance to meteorologists, radio astronomers and geodesists. Precipitable water vapour (PWV) is a greenhouse gas to be reckoned with in numerical weather models and climate change studies, it is a nuisance in centimetre-wavelength radio astronomy and introduces range errors in space geodetic techniques. The propagation time of electromagnetic waves is the principal observable in the Global Positioning System (GPS). Accurate estimates of the delays experienced by the radio signals travelling from the satellites to ground-based receivers are made during the post-processing of GPS observations. In combination with meteorological observations made at the receiver, the estimated delays can be used to determine the amount of integrated precipitable water vapour along the signal path. In this thesis an overview of the basic GPS principles and components is provided, as well as a derivation, from first physical principles, of the mechanisms contributing to the delay experienced by a radio signal traversing the ionosphere and troposphere. Implementing this theoretical background, PWV and tropospheric delays are estimated and compared to measurements made by other techniques, namely radiosondes, water vapour radiometry and very long baseline interferometry (VLBI). A high degree of correlation is observed in all instances of inter-technique comparison. The usefulness of GPS-derived slant delays is demonstrated by their ability to reduce VLBI inter-station baseline repeatabilities when they are included in the VLBI analysis. However, this contributed to a higher mean formal baseline error. Furthermore, it shown that GPS-derived slant delay accuracies, when compared to radiometry, can be improved through the stacking of GPS processing residuals to make corrections for the effects of multi path and antenna phase centre variations. A modified residual stacking (MRS) method is proposed, in which data weighting is based on a measured autocorrelation function; however, in most instances the more complex MRS failed to significantly improve on the corrections made by normal residual stacking. GPS-derived PWV time-series from thirty South African stations for a four-year period are presented. A four-parameter model was fitted to the time-series to correct for seasonal effects and detect linear trends. It is shown that an autoregressive moving average (ARMA) model is required to estimate realistic trend uncertainties, rather than the white-noise model implicit in standard least-squares analyses. Furthermore, significant trends in PWV were observed in South Africa with the central parts showing a decrease in PWV during the study period, while an increase is observed over the southwest and northeast. These trends coincide with a temperature increase observed over the whole of South Africa for the study period. A hypothesis is presented to explain the different trends, based on the different sources of PWV in different climate areas. Lastly, vertical earth tide displacements (VETD) measured by gravimetry are compared to the modelled VETD applied during GPS processing. It is shown that rnismodelled VETD can contribute significant errors to GPS-derived PWV. A number of methods to mitigate this error are proposed and compared to each other, including a novel technique to accurately measure VETD by GPS

Using ground-based GPS to characterize atmospheric turbulence

A new method for measuring and studying atmospheric turbulence is presented. The method uses data from a local network of GPS receivers. The GPS data are processed in a way that assures that the estimated zenith total delays (ZTD) contain the effects of atmospheric turbulence present in the GPS observations. The turbulence is characterized using the spatial structure function for the atmospheric zenith total delay. The structure function is modeled by an expression with unknown parameters which contains information about the turbulence. The unknown parameters are solved by a fit to the observed ZTD variations. We apply the method to GPS data from the Yucca Mountain network, Nevada, USA. The results show that the magnitude of the turbulent variations in that region have a strong seasonal dependence, with much larger variations in summer compared to winter

A nanoradian differential VLBI tracking demonstration

The shift due to Jovian gravitational deflection in the apparent angular position of the radio source P 0201+113 was measured with very long baseline interferometry (VLBI) to demonstrate a differential angular tracking technique with nanoradian accuracy. The raypath of the radio source P 0201+113 passed within 1 mrad of Jupiter (approximately 10 Jovian radii) on 21 Mar. 1988. Its angular position was measured 10 times over 4 hours on that date, with a similar measurement set on 2 Apr. 1988, to track the differential angular gravitational deflection of the raypath. According to general relativity, the expected gravitational bend of the raypath averaged over the duration of the March experiment was approximately 1.45 nrad projected onto the two California-Australia baselines over which it was measured. Measurement accuracies on the order of 0.78 nrad were obtained for each of the ten differential measurements. The chi(exp 2) per degree of freedom of the data for the hypothesis of general relativity was 0.6, which suggests that the modeled dominant errors due to system noise and tropospheric fluctuations fully accounted for the scatter in the measured angular deflections. The chi(exp 2) per degree of freedom for the hypothesis of no gravitational deflection by Jupiter was 4.1, which rejects the no-deflection hypothesis with greater than 99.999 percent confidence. The system noise contributed about 0.34 nrad per combined-baseline differential measurement and tropospheric fluctuations contributed about 0.70 nrad. Unmodeled errors were assessed, which could potentially increase the 0.78 nrad error by about 8 percent. The above chi(exp 2) values, which result from the full accounting of errors, suggest that the nanoradian gravitational deflection signature was successfully tracked

The uncertainty of the atmospheric integrated water vapour estimated from GNSS observations

Within the Global Climate Observing System (GCOS) Reference Upper-Air Network (GRUAN) there is a need for an assessment of the uncertainty in the integrated water vapour (IWV) in the atmosphere estimated from ground-based global navigation satellite system (GNSS) observations. All relevant error sources in GNSS-derived IWV are therefore essential to be investigated. We present two approaches, a statistical and a theoretical analysis, for the assessment of the uncertainty of the IWV. The method is valuable for all applications of GNSS IWV data in atmospheric research and weather forecast. It will be implemented to the GNSS IWV data stream for GRUAN in order to assign a specific uncertainty to each data point. In addition, specific recommendations are made to GRUAN on hardware, software,and data processing practices to minimise the IWV uncertainty. By combining the uncertainties associated with the input variables in the estimations of the IWV, we calculated the IWV uncertainties for several GRUAN sites with different weather conditions. The results show a similar relative importance of all uncertainty contributions where the uncertainties in the zenith total delay (ZTD) dominate the error budget of the IWV, contributing over 75% of the total IWV uncertainty. The impact of the uncertainty associated with the conversion factor between the IWV and the zenith wet delay (ZWD) is proportional to the amount of water vapour and increases slightly for moist weather conditions. The GRUAN GNSS IWV uncertainty data will provide a quantified confidence to be used for the validation of other measurement techniques

Wet Path Delay Corrections from Line-of-Sight Observations of Effelsberg’s Water Vapour Radiometer for Geodetic VLBI Sessions

Water vapour induced excess path lengths in electromagnetic waves have been one of the most unmanageable errors in space geodesy, such as GPS and VLBI. The difficulty mainly comes from the highly variable distribution of atmospheric water vapour both in time and space. In general, these wet path delays cannot be estimated accurately by atmospheric models that are conventionally used in space geodetic applications. In the last few decades, water vapour radiometry has shown great potential for measuring atmospheric water vapour content. However, the wet path delay retrieval processes are strongly dependent on radiosonde data, although periodic radiosonde observations are rarely available in the vicinity of water vapour radiometers (WVRs). Radiosonde observations are weather profiles from balloon starts which are transmitted by radio signals. On the other hand, the possibility of using a numerical weather model (NWM) instead of a radiosonde has been on the increase in recent years. NWM can provide meteorological profiles for those places where radiosonde data is not available. The focus of this thesis is mainly on the improvement of the wet path delay corrections in geodetic VLBI sessions using the WVR observations at the 100m Effelsberg radio telescope. Compared to other WVRs, the Effelsberg one has a great advantage in terms of observation. It always points at the same direction as the VLBI antenna because it has been installed on the prime focus cabin of the telescope. However the Effelsberg station does not make periodic radiosonde observations. To overcome this weakness, the numerical weather model of the European Centre of Medium Range Weather Forecasts (ECMWF) was introduced. It provides meteorological profiles over Effelsberg such as atmospheric pressures, temperatures, and water vapour pressures. Those profiles were processed by a radiative transfer model, which calculates theoretical measurements of brightness temperature and converts them into wet path delays. These two models were combined to be compared with WVRobserved wet path delays. For a better comparison between wet path delays from the WVR and the models, zenith wet delays (ZWDs) were used. As the results of the comparison illustrate, ZWDs from the models showed higher values than the WVR-measured ones by roughly 30 mm. For comparison with GPS-derived values, average offsets and standard deviations of the models and the WVR were -4.3±11.0 mm and -44.8±24.0 mm, respectively. From these ZWD comparisons it was found that further corrections to the WVR ZWDs are necessary. In addition, the noisy behaviour of the raw WVR ZWD measurements should be smoothed by a running mean method before application. In addition, averaged offsets between the models and the WVR measurements should be determined for the correction of individual sessions. However, already at this step it became obvious that the instrumental calibrations of the radiometer are far from being mature resulting in erroneous absorption profiles. ZWDs from the WVR measurements with different levels of corrections were applied as corrections to the wet components of the atmospheric refraction in the five geodetic VLBI sessions. Impacts on baseline repeatability and height precision by these were investigated. As the results show, the baseline repeatability was improved in terms of Root Mean Squared Error (RMS) when the offset correction was applied. However, the improvement was less than one percent. Although the repeatability of the height component was improved in terms of Weighted RMS (WRMS) with respect to the short term mean height by a factor of 2, the height component itself showed a larger deviation from the original value than that expected from the ZWD corrections. A possible reason is that the estimation of the many parameters in the least squares adjustment can easily affected the height parameter. The conclusion of this study is that the Effelsberg WVR observations are not perfectly suited for wet path delay corrections yet. This is mainly due to the imperfectness of instrumental calibration. Further studies based on an increased number of WVR data with better internal calibrations seems to be necessary to make a final judgment regarding the usefulness of the WVR for wet path delay corrections in geodetic VLBI.Zur Korrektur von feuchtebedingten Laufzeitverzögerungen mit dem co-linearen Wasserdampfradiometer in Effelsberg für geodätische VLBI-Messungen Wasserdampfinduzierte Refraktionseffekte der elektromagnetischen Wellen stellen die zurzeit größte Fehlerquelle bei Messverfahren der Satellitengeodäsie, wie z.B. GPS und VLBI, dar. Die Problematik rührt hauptsächlich her von der stark variierenden Verteilung von atmosphärischem Wasserdampf sowohl in der Zeit als auch im Raum. Im Allgemeinen können diese Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre nicht exakt genug durch atmosphärische Modelle berechnet werden, die herkömmlich in Satellitengeodäsieanwendungen genutzt werden. In den vergangenen Jahrzehnten hat die Wasserdampfradiometrie ein großes Potential entwickelt, um den atmosphärischen Wasserdampfbestandteil zu messen. Allerdings ist der Prozess der Umrechnung von gemessenen Helligkeitstemperaturen in Laufzeitverzögerungen stark von gleichzeitig durchgeführten Radiosondenmessungen abhängig. Dabei werden die Messergebnisse von an aufsteigenden Ballons befestigten Wettersensoren für verschiedene Druckstufen per Radiosignal ausgesendet. Leider werden periodische Radiosondenbeobachtungen aber nur selten in der Nähe des Wasserdampfradiometers (WVR) durchgeführt. Dem gegenüber besteht seit einigen Jahren die Möglichkeit, ein numerisches Wettermodell anstelle der Radiosondenergebnisse zu nutzen. Ein numerisches Wettermodell kann meteorologische Profile für solche Orte liefern, wo eine Radiosonde nicht verfügbar ist. Der Schwerpunkt dieser Dissertation liegt hauptsächlich auf der verbesserten Bestimmung der Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre in der geodätischen VLBI, wobei die Wasserdampfradiometerbeobachtungen am Radioteleskop in Effelsberg genutzt werden. Verglichen mit anderen Wasserdampfradiometern hat dieses Instrument große Vorteile hinsichtlich der Messwertgewinnung. Es zeigt immer in dieselbe Richtung wie die VLBI-Antenne, weil es im Primärfokus des Teleskopes installiert ist. In oder in der Nähe von Effelsberg werden jedoch keine Radiosondenbeobachtungen durchgeführt. Um diese Schwäche zu beheben, wurde ein numerisches Wettermodell des European Centre for Medium Range Weather Forecasts (ECMWF) für die Bestimmung von Kalibrierwerten herangezogen. Es liefert für das Radioteleskop in Effelsberg meteorologische Daten wie z.B. Druck, Temperatur und Wasserdampfdruck. Solche Profile wurden in einem Strahlungsübertragungsmodell verarbeitet, welches theoretische Messungen der Helligkeitstemperatur ermittelt und diese in Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre umwandelt. Um die Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre aus Wasserdampfradiometermessungen und die Modelle besser vergleichen zu können, wurden alle Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre auf die Zenitrichtung (Zenith Wet Delays, ZWD) bezogen. Der Vergleich hatte zum Ergebnis, dass die ZWDs der Modelle einen um ca. 30 mm höheren Wert zeigten als jene, die mit einem Wasserdampfradiometer gemessen wurden. Im Vergleich zu GPS-abgeleiteten ZWDs betrugen die durchschnittlichen Offsets der Modelle und des Wasserdampfradiometers -4.3±11.0 mm beziehungsweise -44.8±24.0 mm. Diese ZWDVergleiche haben gezeigt, dass eine Korrektur der WVR ZWDs erforderlich ist. Außerdem hatte es den Anschein, dass die rohen WVR-ZWD-Messungen geglättet werden sollten, um das Rauschen des Instruments zu reduzieren. Für die Fehlerkorrektur wurden außerdem in jeder einzelnen Session durchschnittliche Offsets zwischen den Modellen und den Wasserdampfradiometern berechnet und angesetzt. Allerdings zeigte sich schon hier, dass die interne Kalibrierung des Instruments einige Defizite aufwies und die Ergebnisse dadurch in ihrer Genauigkeit eingeschränkt waren. Die Korrekturen an den Laufzeitverzögerungen in Zenitrichtung aus verschiedenen Ansätzen wurden in fünf geodätischen VLBI-Sessionen verwendet und die Auswirkungen auf die Basislinienwiederholbarkeit und Höhengenauigkeit untersucht. Es stellte sich heraus, dass die Basislinienwiederholbarkeit bei manchen Basislinien verbessert werden konnte, wenn Offsets an den gemessenen WVR-Ergebnissen angebracht wurden. Die Verbesserung war jedoch kleiner als 1 Prozent. Obwohl die Höhengenauigkeit, ausgedrückt als Root Mean Squared Error (RMS) und Weighted RMS (WRMS), um den Faktor 2 verbessert werden konnte, zeigte die Höhenkomponente selbst eine größere Ablage von den Ursprungswerten als erwartet. Als Ursache dafür wurde die Vielzahl der zu schätzenden Parameter und ihre zum Teil hohen Korrelationen identifiziert. Die Schlussfolgerung dieser Untersuchung ist somit, dass die Waserdampfradiometerbeobachtungen in Effelsberg noch nicht gänzlich für die Fehlerbehebung der Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre geeignet sind, was hauptsächlich auf die Unvollkommenheit einer instrumentellen Kalibrierung zurückzuführen ist. Es werden weitere Studien mit einer größeren Zahl von WVR- Messwerten mit einer verbesserten Kalibrierung des WVR notwendig sein, um die Zweckmäßigkeit des Wasserdampfradiometers für die Fehlerbehebung der Laufzeitverzögerungen durch den feuchten Anteil der Atmosphäre in der geodätischen VLBI abschließend nachweisen zu können