Keywords

1 Introduction

Among the space geodetic techniques, Very Long Baseline Interferometry (VLBI) is able to provide the most accurate and unbiased estimates of the angle of the Earth’s orientation with respect to the rotation axis, expressed via UT1-UTC. Since 1984, regular observing campaigns have been launched for monitoring Earth orientation parameters (EOP) including UT1-UTC. They are now coordinated by the International VLBI Service for Geodesy and Astrometry (IVS) (Nothnagel et al 2017). Most sessions of the IVS observing campaigns for EOP determination either run for 24 h to determine the full set of EOP, or for 1 h to determine solely UT1-UTC. The 24-h programs run 2–3 times a week with latency between observations and delivery of EOP estimates of about 15–20 days. The 1-h programs on average run 2–3 times a day and the latency between observations and delivery of UT1-UTC estimates is 1–3 days. For that reason, these campaigns are called Intensives. Nowadays, a number of VLBI Intensive programs dedicated to the estimation of UT1-UTC run in parallel.

VLBI observations commenced in 1967. Since then, the VLBI technique went through a number of upgrades. The most recent upgrade is called the VLBI Global Observing System (VGOS) (Niell et al 2018). The changes in that upgrade, relevant to the present study, are faster slewing speeds of \(12^\circ \) over azimuth and \(6^\circ \) over elevation, combined with an increased data rate of currently 8 Gbps distributed among four bands. The fast slewing rates reduce the time when the antenna is slewing and thus not recording signals. The higher data rate allows for shorter observation times to reach the desired signal-to-noise ratio (SNR). Combined, this leads to a significantly increased number of scans per hour, up to 100, allowing for faster sampling of the atmosphere, which is considered one of the major error sources in VLBI.

There are around 200 extragalactic radio sources with sufficient brightness and compactness that are currently observed by VGOS radio telescopes and up to 100 sources can be observed in 1 h. Thus, the number of combinations of sources that can be selected for observations is extremely large. We are interested in developing new techniques for the generation of optimal observing plans, the so-called schedules, which provide UT1-UTC with minimum errors. The theoretical basis of the development of an optimal schedule was described in Schartner (2019).

In order to verify the optimized scheduling algorithm, we launched a research and development Intensive VLBI observing program, named VGOS-INT-S, on the 8418 km long baseline between macgo12m and wettz13s in 2021. Station macgo12m, also known as Mg, is located in Western Texas, USA, and station wettz13s, known as Ws, is located in Northeast Bavaria, Germany. Here, we outline the design of the observing program and discuss preliminary results.

2 Methods

The major error source in geodetic VLBI is mismodeling of the path delay in the neutral atmosphere. The a priori atmospheric path delay can be computed either using a regression model of surface atmospheric pressure and air temperature or by direct integration of equations of wave propagation through an inhomogeneous refractivity field derived from the output of numerical weather models. In both cases, the accuracy of the a priori path delay is still insufficient and we have to estimate the residual path delay in the zenith direction from the VLBI data themselves.

During the analysis, atmospheric delays are commonly divided into a hydrostatic and a non-hydrostatic (wet) part. While the hydrostatic part can be modeled with sufficient accuracy of around 1–2 mm if accurate ground pressure measurements are available, the wet part has to be estimated due to its higher variability. Historically, one zenith wet path delay (ZWD) per 1-h observing session was estimated. With the fast slewing VGOS antennas, we can develop a scheduling strategy that would allow us to estimate atmospheric path delay with segments as short as 5 min. To enable a more frequent estimation of ZWD, special emphasis has to be laid on providing observations at different elevation angles within the estimation interval.

Following this idea, a new VLBI observation strategy has been developed for VGOS-INT-S and applied using VieSched++ (Schartner and Böhm 2019). Due to the special geometry of the Mg/Ws baseline with its baseline length of 8418 km, observations at high elevation on one station naturally result in low elevation at the other station as depicted in Fig. 1. Although longer baselines are potentially more sensitive to UT1-UTC, they also have a limited mutually visible sky. For example, the frequently observed kokee/wettzell baseline has a length of 10358 km, resulting in a maximum observable elevation of only \(\sim 65^{\circ }\). This can potentially result in a worse determination of the ZWD and thus UT1-UTC.

Fig. 1
figure 1

Mutual visibility color-coded by the elevation of the partner telescope. The black lines represent the station horizon masks while the dashed gray line marks the theoretical horizon

Full size image

The new observation strategy is based on rapidly alternating between high and low-elevation scans to allow for an improved and potentially higher frequent ZWD determination. Therefore, the following scan sequence is repeated:

  • scan with high elevation at Mg (low elevation Wz)

  • scan without constraints

  • scan with high elevation at Wz (low elevation Mg)

  • scan without constraints

Thus, every other scan is especially dedicated to measuring ZWD. The remaining scans are selected in a way to increase the sensitivity towards UT1-UTC, e.g. by observing sources located at the corners of the mutually visible sky (Schartner et al 2021), or by reducing potential systematic errors caused by source-structure effects via observing a high number of different sources.

The effect of this special observing strategy is illustrated in Fig. 2, which depicts the distribution of observations in azimuth and elevation. While the distribution is more balanced using an old observing strategy, two clear clusters are visible with the new observing strategy, one at high elevation and one at low elevation. This confirms that the observing strategy is working as intended.

Fig. 2
figure 2

Scan distribution for station Ws. Left: new observation strategy. Right: old Intensive observing strategy. The darker the color, the higher the number of observations in this area. The black lines represent the station horizon mask while the dashed gray line marks the theoretical horizon

Full size image

3 Data

The VGOS-INT-S observing program started on December 7th, 2021 with session S21341. In the years 2021 and 2022, 27 sessions were observed successfully. Visibility data, geodetic databases, and results of the analysis are available at the IVS Data Centers.Footnote 1

Over time, the choice of the SNR target and integration time limit was iteratively adjusted based on station and correlator feedback. The first sessions S21341–S22011 were scheduled conservatively, using a fixed integration time of 30 s independent of the source brightness and thus mimicking the current 24-h operational VGOS (VGOS-OPS) mode to gather some experience on the new baseline. Afterward, the integration time was reduced to increase the number of observations per session, and an SNR-based observing time based on the source brightness and antenna sensitivity was utilized. For S22018–S22053 the minimum integration time was set to 15 s, while it was lowered to 12 s in the remaining sessions while the maximum allowed integration time (except for calibrator scans) was set to 30 s in all sessions. The target SNR per band was set to 15 for all sessions until S22053, while it was lowered to 10 between S22060–S22095, before being increased to 12 again for all sessions after S22109. In practice, the changes were very small and had little effect on the total number of scheduled observations (see Fig. 3), but they helped during the correlation process to recover most observations, especially in cases of reduced antenna sensitivity as discussed later.

Fig. 3
figure 3

Number of scheduled observations (blue bars), analyzed observations (blue hatched), and percentage of analyzed observations (orange)

Full size image

To troubleshoot existing hardware-related problems at the stations, two special sessions have been designed. First, S22277 was split into two sections. The first 30 min were observed regularly with an SNR-based integration time and a minimum of 12 s while the second 30 min were scheduled using a fixed 30-s long integration time. Second, S22284 was scheduled including onsa13ne (Oe; Sweden) to provide the independent baseline Mg/Oe.

Figure 3 depicts the number of scheduled and successful (defined as analyzed by the NASA analysis center) observations per session. Some sessions suffered from a significant number of non-detections, mostly explained by hardware failures. For S22067, 23 scans were not recorded at station Mg (from 19:45 until 20:00 UTC). For S22074, 12 observations were rejected during analysis due to large residuals. Similarly, 22 observations were rejected for S22214 and 12 observations for S22263. Furthermore, two sessions, namely S22213 and S22215, were scheduled using a different scheduling software instead of VieSched++, explaining the lower number of observations.

A list of the most important technical problems affecting VGOS-INT-S is provided in Table 1. Please note that the dates listed in this table are approximations. In some cases, it is not possible to find out exactly when a problem occurred. For some of the listed problems, it is also unclear how much they affected the performance of VGOS-INT-S. We expect that the LNA failure, first noticed in May 2022, had the most severe effect on the performance of the Intensive sessions due to decreased sensitivity of station wettz13s. This corresponds to the decrease of UT1-UTC precision for session S22158 onward as further discussed in Sect. 4.

Table 1 List of technical difficulties encountered during VGOS-INT-S sessions
Full size table

4 Results

Figure 4 depicts the VGOS-INT-S precision and accuracy, independently derived from the GSFC operational solutions produced with the Solve/\(\nu \)Solve software package. We use two measures of UT1-UTC errors: formal uncertainties derived from the observation SNR following the law of error propagation, called here precision, and the differences of the UT1-UTC estimates and the IERS C04 time series, called here accuracy. To interpolate the daily IERS C04 UT1-UTC values to the Intensive reference epoch, first, tidal effects with periods \(<35\) days were subtracted, followed by a Lagrangian interpolation of order four and re-adding the previously subtracted tidal effects. It is visible that the formal errors between S22025 and S22081 are significantly smaller compared to most of the remaining sessions. Within this period, eight sessions have been observed with an average formal error \(\sigma _{\text{UT1-UTC}}\) of 3.1 µs and an offset w.r.t. IERS C04 of 1.1 µs. The root mean square error (RMSE) during this period is 31.7 µs. For the remaining sessions, the average formal error is increased to 9.8 µs, the offset w.r.t. IERS C04 is increased to −2.1 µs, and the RMSE is increased to 80.7 µs. The increase in uncertainty might be explained by the technical problems encountered at the stations as listed in Table 1. Especially the LNA failure at station wettz13s, noticed on May 2022 (S22158) corresponds well to the decrease in precision depicted in Fig. 4. However, it does not explain why the previous session (S22109) also suffered decreased precision. This might be a simple coincidence, or it might be that the LNA failure already happened earlier and was only noticed in May 2022.

Fig. 4
figure 4

VGOS-INT-S accuracy (top) and precision (bottom) extracted from the GSFC analysis reports. Accuracy: UT1-UTC estimate w.r.t. IERS C04, the 3\(\sigma \) value is depicted in the error bars. Precision: UT1-UTC formal error \(\sigma \). The red background depicts sessions affected by decreased sensitivity due to the LNA failure. Note that the exact date of the LNA failure is unknown. It was first noticed in S22158 but might have already occurred before this session

Full size image

Still, the very small formal uncertainties and good agreement with IERS C04 between S22025 and S22081 suggest that superior precision in UT1-UTC determination at the Mg/Ws baseline can be achieved. For comparison, during the same time, the VGOS-INT-A sessions at the kokee12m/wettz13s baseline achieved an average formal error of 4.3 µs with an offset w.r.t. IERS C04 of −8.6 µs and a RMSE of 28.7 µs, although according to simulations, it is expected that based on the baseline geometry alone, VGOS-INT-A should be 40% more sensitive towards UT1-UTC compared to VGOS-INT-S (Schartner et al 2021). The obtained results are also comparable with the VGOS-INT-B sessions, observed between Japan and Sweden, that achieved an RMSE of 23.2 µs and a bias of −3.8 µs between December 2019 and February 2020 (Haas et al 2021).

Here, it is to note that the GSFC operational analysis presented above does not yet make use of a more frequent estimation of ZWD enabled by the observation strategy. Instead, ZWD is parameterized as a constant offset only. This highlights that the proposed scheduling strategy provides highly accurate UT1-UTC estimates even when a traditional parameterization is used.

To assess the impact of a reduced ZWD interval enabled by the new scheduling approach, the sessions have been analyzed with 60-min and with 10-min long ZWD intervals using two independent software packages, pSolve and VieVS. The mean of the differences in UT1 between the two pSolve solutions is 0.2 µs and the RMSE is 2.0 µs, which is insignificant. Using VieVS, similar results have been obtained. Compared to IERS C04, the improvement in terms of RMSE based on the new scheduling approach is 0.7 µs and, thus, insignificant. Considering hardware failure, an absence of evidence should not be construed as evidence of absence. We need more data with properly working hardware to assess the significance of the impact of scheduling and analysis approaches on UT1 determination. Therefore, the VGOS-INT-S program is continued in 2023 and even extended by 24-h sessions, alternating hourly between the standard and improved scheduling strategy, for improved comparability of the two approaches.

5 Summary

We presented a design of a research and development VLBI observing program for the determination of UT1-UTC at a single baseline between fast slewing radiotelescopes wettz13s (Germany) and macgo12m (Texas, USA).

Although the telescopes suffered a number of technical failures, the results are very encouraging. Despite the shorter baseline length compared to more typical Intensive sessions and the resulting theoretical lower sensitivity towards UT1-UTC, the VGOS-INT-S sessions performed exceptionally well during the first part of 2022. We plan to continue the campaign and investigate errors of UT1-UTC determination in detail.