Determination of SLR station coordinates based on LEO, LARES, LAGEOS, and Galileo satellites

The number of satellites equipped with retroreflectors dedicated to Satellite Laser Ranging (SLR) increases simultaneously with the development and invention of the spherical geodetic satellites, low Earth orbiters (LEOs), Galileo and other components of the Global Navigational Satellite System (GNSS). SLR and GNSS techniques onboard LEO and GNSS satellites create the possibility of widening the use of SLR observations for deriving SLR station coordinates, which up to now have been typically based on spherical geodetic satellites. We determine SLR station coordinates based on integrated SLR observations to LEOs, spherical geodetic, and GNSS satellites orbiting the Earth at different altitudes, from 330 to 26,210 km. The combination of eight LEOs, LAGEOS-1/2, LARES, and 13 Galileo satellites increased the number of 7-day SLR solutions from 10–20% to even 50%. We discuss the issues of handling of range biases in multi-satellite combinations and the proper solution constraining and weighting. Weighted combination is characterized by a reduction of formal error medians of estimated station coordinates up to 50%, and the reduction of station coordinate residuals. The combination of all satellites with optimum weighting increases the consistency of station coordinates in terms of interquartile ranges by 10% of horizontal components for non-core stations w.r.t LAGEOS-only solutions.

On the geometry of baselines suitable for UT1 estimation with VLBI Intensive sessions

<p>One hour single baseline VLBI sessions, so-called Intensives, are routinely observed to derive UT1-UTC with a short latency. The selection of baselines for VLBI Intensive sessions and their application for the determination of UT1-UTC is a complex task. Thus far, it has been understood that long east-west extensions are critical for the accuracy of UT1-UTC. In this presentation, we show, that the answer is not as simple as that. </p><p>We run Monte-Carlo simulations for a global 10° grid of artificial station locations and discuss the suitability of the individual baselines for UT1-UTC estimation based on the formal error of dUT1. The antennas are located at latitudes of -80° to 80° and longitudes of 0° to 180° and are assumed to have the same properties than the WETTZ13S telescope. The nine stations at longitude 0° on the northern hemisphere are defined as reference stations. In total, 2898 possible baselines between the reference stations and other artificial stations are investigated over one year based on monthly schedules to minimize potential seasonal variations. Thus, with this study, it is possible to derive a complete picture of which baselines are most suitable for dUT1 estimates. </p><p>In general, the findings show optimal global geometries concerning Intensives. For example, we can confirm that the IVS-INT1 baseline including the stations Kokee and Wettzell is among the best ones available. Furthermore, we show that north-south baselines are also sensitive to dUT1 as long as their orientations are not parallel to the Earth rotation axis. Moreover, we highlight that east-west baselines on the equator are not suitable for estimating dUT1 due to the lack of variety in right-ascension of the visible sources. Additionally, we highlight, that very long baselines are problematic due to the highly restricted mutual visibility.</p>

Satellite Laser Ranging for Retrieval of the Local Values of the Love h2 and Shida l2 Numbers for the Australian ILRS Stations

This paper deals with the analysis of local Love and Shida numbers (parameters h2 and l2) values of the Australian Yarragadee and Mount Stromlo satellite laser ranging (SLR) stations. The research was conducted based on data from the Medium Earth Orbit (MEO) satellites, LAGEOS-1 and LAGEOS-2, and Low Earth Orbit (LEO) satellites, STELLA and STARLETTE. Data from a 60-month time interval, from 01.01.2014 to 01.01.2019, was used. In the first research stage, the Love and Shida numbers values were determined separately from observations of each satellite; the obtained values of h2, l2 exhibit a high degree of compliance, and the differences do not exceed formal error values. At this stage, we found that it was not possible to determine l2 from the data of STELLA and STARLETTE. In the second research stage, we combined the satellite observations of MEO (LAGEOS-1+LAGEOS-2) and LEO (STELLA+STARLETTE) and redefined the h2, l2 parameters. The final values were adopted, and further analyses were made based on the values obtained from the combined observations. For the Yarragadee station, local h2 = 0.5756 ± 0.0005 and l2 = 0.0751 ± 0.0002 values were obtained from LAGEOS-1 + LAGEOS-2 and h2 = 0.5742 ± 0.0015 were obtained from STELLA+STARLETTE data. For the Mount Stromlo station, we obtained the local h2 = 0.5601 ± 0.0006 and l2 = 0.0637 ± 0.0003 values from LAGEOS-1+LAGEOS-2 and h2 = 0.5618 ± 0.0017 from STELLA + STARLETTE. We found discrepancies between the local parameters determined for the Yarragadee and Mount Stromlo stations and the commonly used values of the h2, l2 parameters averaged for the whole Earth (so-called global nominal parameters). The sequential equalization method was used for the analysis, which allowed to determine the minimum time interval necessary to obtain stable h2, l2 values. It turned out to be about 50 months. Additionally, we investigated the impact of the use of local values of the Love/Shida numbers on the determination of the Yarragadee and Mount Stromlo station coordinates. We proposed to determine the stations (X, Y, Z) coordinates in International Terrestrial Reference Frame 2014 (ITRF2014) in two computational versions: using global nominal h2, l2 values and local h2, l2 values calculated during this research. We found that the use of the local values of the h2, l2 parameters in the process of determining the stations coordinates influences the result.

Determination of precise Galileo orbits using combined GNSS and SLR observations

Galileo satellites are equipped with laser retroreflector arrays for satellite laser ranging (SLR). In this study, we develop a methodology for the GNSS-SLR combination at the normal equation level with three different weighting strategies and evaluate the impact of laser observations on the determined Galileo orbits. We provide the optimum weighting scheme for precise orbit determination employing the co-location onboard Galileo. The combined GNSS-SLR solution diminishes the semimajor axis formal error by up to 62%, as well as reduces the dependency between values of formal errors and the elevation of the Sun above the orbital plane—the β angle. In the combined solution, the standard deviation of the SLR residuals decreases from 36.1 to 29.6 mm for Galileo-IOV satellites and |β|> 60°, when compared to GNSS-only solutions. Moreover, the bias of the Length-of-Day parameter is 20% lower for the combined solution when compared to the microwave one. As a result, the combination of GNSS and SLR observations provides promising results for future co-locations onboard the Galileo satellites for the orbit determination, realization of the terrestrial reference frames, and deriving geodetic parameters.

The effects of a ‘study abroad’ programme on the development of verb morphology for the expression of past time by the advanced learner: a lexical approach

This article presents an investigation of the benefits of a period of residence in a francophone country for a group of Irish university learners of French in relation to their acquisition of verb morphology to express past time. The study makes a cross-sectional comparison between this group of learners with two other groups: one, a group of learners before they leave for a period of residence abroad, and the other consisting of learners who chose not to partake in such a programme, but who continued to have further access to the target language through classroom instruction. Whilst results suggest that ‘study abroad’ has a more important effect than instruction, as manifested by general increases in the frequency, as well as accuracy, of use of the past tenses; the increased range of lexical verbs marked for past time; and a reduction in formal error; there remain a number of lexical limitations on such marking, such that past time marking continues to be constrained by the lexical value of the verb. In particular, unlike the passé composé, the imparfait is used with a limited range of verbs, notably étre and avoir. The occurrence of verbs conjugated in both tenses also remains limited, whereby the learners tend not to alternate freely between both past time forms with individual lexical verbs, but rather to restrict individual lexical verbs to a single past time form.

A degree-100 lunar gravity model from the Chang’e 5T1 mission

Context. Chinese lunar missions have grown in number over the last ten years, with an increasing focus on radio science investigations. In previous work, we estimated two lunar gravity field models, CEGM01 and CEGM02. The recently lunar mission, Chang’e 5T1, which had an orbital inclination between 18 and 68 degrees, and collected orbital tracking data continually for two years, made an improved gravity field model possible. Aims. Our aim was to estimate a new lunar gravity field model up to degree and order 100, CEGM03, and a new tidal Love number based on the Chang’e 5T1 tracking data combined with the historical tracking data used in the solution of CEGM02. The new model makes use of tracking data with this particular inclination, which has not been used in previous gravity field modeling. Methods. The solution for this new model was based on our in-house software, LUGREAS. The gravity spectrum power, post-fit residuals after precision orbit determination (POD), lunar surface gravity anomalies, correlations between parameters, admittance and coherence with topography model, and accuracy of POD were analyzed to validate the new CEGM03 model. Results. We analyzed the tracking data of the Chang’e 5T1 mission and estimated the CEGM03 lunar gravity field model. We found that the two-way Doppler measurement accuracy reached 0.2 mm s−1 with 10 s integration time. The error spectrum shows that the formal error for CEGM03 was at least reduced by about 2 times below the harmonic degree of 20, when compared to the CEGM02 model. The admittance and correlation of gravity and topography was also improved when compared to the correlations for the CEGM02 model. The lunar potential Love number k2 was estimated to be 0.02430±0.0001 (ten times the formal error). Conclusions. From the model analysis and comparison of the various models, we identified improvements in the CEGM03 model after introducing Chang’e 5T1 tracking data. Moreover, this study illustrates how the low and middle inclination orbits could contribute better accuracy for a low degree of lunar gravity field.

A review and framework for the evaluation of pixel-level uncertainty estimates in satellite aerosol remote sensing

Recent years have seen the increasing inclusion of per-retrieval prognostic (predictive) uncertainty estimates within satellite aerosol optical depth (AOD) data sets, providing users with quantitative tools to assist in the optimal use of these data. Prognostic estimates contrast with diagnostic (i.e. relative to some external truth) ones, which are typically obtained using sensitivity and/or validation analyses. Up to now, however, the quality of these uncertainty estimates has not been routinely assessed. This study presents a review of existing prognostic and diagnostic approaches for quantifying uncertainty in satellite AOD retrievals, and it presents a general framework to evaluate them based on the expected statistical properties of ensembles of estimated uncertainties and actual retrieval errors. It is hoped that this framework will be adopted as a complement to existing AOD validation exercises; it is not restricted to AOD and can in principle be applied to other quantities for which a reference validation data set is available. This framework is then applied to assess the uncertainties provided by several satellite data sets (seven over land, five over water), which draw on methods from the empirical to sensitivity analyses to formal error propagation, at 12 Aerosol Robotic Network (AERONET) sites. The AERONET sites are divided into those for which it is expected that the techniques will perform well and those for which some complexity about the site may provide a more severe test. Overall, all techniques show some skill in that larger estimated uncertainties are generally associated with larger observed errors, although they are sometimes poorly calibrated (i.e. too small or too large in magnitude). No technique uniformly performs best. For powerful formal uncertainty propagation approaches such as optimal estimation, the results illustrate some of the difficulties in appropriate population of the covariance matrices required by the technique. When the data sets are confronted by a situation strongly counter to the retrieval forward model (e.g. potentially mixed land–water surfaces or aerosol optical properties outside the family of assumptions), some algorithms fail to provide a retrieval, while others do but with a quantitatively unreliable uncertainty estimate. The discussion suggests paths forward for the refinement of these techniques.

A review and framework for the evaluation of pixel-level uncertainty estimates in satellite aerosol remote sensing

Recent years have seen the increasing inclusion of per-retrieval prognostic (predictive) uncertainty estimates within satellite aerosol optical depth (AOD) data sets, providing users with quantitative tools to assist in optimal use of these data. Prognostic estimates contrast with diagnostic (i.e. relative to some external truth) ones, which are typically obtained using sensitivity and/or validation analyses. Up to now, however, the quality of these uncertainty estimates has not been routinely assessed. This study presents a review of existing prognostic and diagnostic approaches for quantifying uncertainty in satellite AOD retrievals, and presents a general framework to evaluate them, based on the expected statistical properties of ensembles of estimated uncertainties and actual retrieval errors. It is hoped that this framework will be adopted as a complement to existing AOD validation exercises; it is not restricted to AOD and can in principle be applied to other quantities for which a reference validation data set is available. This framework is then applied to assess the uncertainties provided by several satellite data sets (seven over land, five over water), which draw on methods from the empirical to sensitivity analyses to formal error propagation, at 12 Aerosol Robotic Network (AERONET) sites. The AERONET sites are divided into those where it is expected that the techniques will perform well, and those for which some complexity about the site may provide a more severe test. Overall all techniques show some skill in that larger estimated uncertainties are generally associated with larger observed errors, although they are sometimes poorly calibrated (i.e. too small/large in magnitude). No technique uniformly performs best. For powerful formal uncertainty propagation approaches such as Optimal Estimation the results illustrate some of the difficulties in appropriate population of the covariance matrices required by the technique. When the data sets are confronted by a situation strongly counter to the retrieval forward model (e.g. potential mixed land/water surfaces, or aerosol optical properties outside of the family of assumptions), some algorithms fail to provide a retrieval, while others do but with a quantitatively unreliable uncertainty estimate. The discussion suggests paths forward for refinement of these techniques.