Very Long Baseline Interferometry Data Research Articles

Combined Earth orientation parameters based on homogeneous and continuous VLBI and GPS data

The CONT02 campaign is of great interest for studies combining very long baseline interferometry (VLBI) with other space-geodetic techniques, because of the continuously available VLBI observations over 2 weeks in October 2002 from a homogeneous network. Especially, the combination with the Global Positioning System (GPS) offers a broad spectrum of common parameters. We combined station coordinates, Earth orientation parameters (EOPs) and troposphere parameters consistently in one solution using technique- specific datum-free normal equation systems. In this paper, we focus on the analyses concerning the EOPs, whereas the comparison and combination of the troposphere parameters and station coordinates are covered in a companion paper in Journal of Geodesy. In order to demonstrate the potential of the VLBI and GPS space-geodetic techniques, we chose a sub-daily resolution for polar motion (PM) and universal time (UT). A consequence of this solution set-up is the presence of a one-to-one correlation between the nutation angles and a retrograde diurnal signal in PM. The Bernese GPS Software used for the combination provides a constraining approach to handle this singularity. Simulation studies involving both nutation offsets and rates helped to get a deeper understanding of this singularity. With a rigorous combination of UT1–UTC and length of day (LOD) from VLBI and GPS, we showed that such a combination works very well and does not suffer from the systematic effects present in the GPS-derived LOD values. By means of wavelet analyses and the formal errors of the estimates, we explain this important result. The same holds for the combination of nutation offsets and rates. The local geodetic ties between GPS and VLBI antennas play an essential role within the inter-technique combination. Several studies already revealed non-negligible discrepancies between the terrestrial measurements and the space-geodetic solutions. We demonstrate to what extent these discrepancies propagate into the combined EOP solution.

Very long baseline interferometry as a tool to probe the ionosphere

In geodetic very long baseline interferometry (VLBI), the observations are performed at two distinct frequencies (2.3 and 8.4 GHz) in order to determine ionospheric delay corrections. This allows information to be obtained from the VLBI observables about the sum of electrons per area unit (total electron content) along the ray path through the ionosphere. Because of the fact that VLBI is a differential technique, the calculated ionospheric corrections depend on the differences of the propagation media over the stations. Additionally, an instrumental delay offset per station causes a bias of the ionospheric measurements. This paper presents a method to estimate ionospheric parameters, that is, values of vertical total electron content from VLBI data, and compares the outcomes to results from other space geodetic techniques. As VLBI observations cover more than two complete solar cycles, the relation to space weather indices on long‐term timescales can be shown.

Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium‐Range Weather Forecasts operational analysis data

In the analyses of geodetic very long baseline interferometry (VLBI) and GPS data the analytic form used for mapping of the atmosphere delay from zenith to the line of site is most often a three‐parameter continued fraction in 1/sin(elevation). Using the 40 years reanalysis (ERA‐40) data of the European Centre for Medium‐Range Weather Forecasts for the year 2001, the b and c coefficients of the continued fraction form for the hydrostatic mapping functions have been redetermined. Unlike previous mapping functions based on data from numerical weather models (isobaric mapping functions (Niell, 2000) and Vienna mapping functions (VMF) (Boehm and Schuh, 2004)), the new c coefficients are dependent on the day of the year, and unlike the Niell mapping functions (Niell, 1996) they are no longer symmetric with respect to the equator (apart from the opposite phase for the two hemispheres). Compared to VMF, this causes an effect on the VLBI or GPS station heights that is constant and as large as 2 mm at the equator and that varies seasonally between 4 mm and 0 mm at the poles. The updated VMF, based on these new coefficients and called VMF1 hereinafter, yields slightly better baseline length repeatabilities for VLBI data. The hydrostatic and wet mapping functions are applied in various combinations with different kinds of a priori zenith delays in the analyses of all VLBI International VLBI Service for Geodesy and Astrometry (IVS)‐R1 and IVS‐R4 24‐hour sessions of 2002 and 2003; the investigations concentrate on baseline length repeatabilities, as well as on absolute changes of station heights.

Is there utility in rigorous combinations of VLBI and GPS Earth orientation parameters?

Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame, the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local ties (including internal systematic effects within the techniques) will be critically important in such an effort.

Simulation of precise orbit determination of lunar orbiters

Based on the ongoing Chinese lunar exploration mission, i.e. the “Chang'e 1” project, precise orbit determination of lunar orbiters is analyzed for the actual geographical distribution and observational accuracy of the Chinese united S-band (USB) observation and control network as well as the very long baseline interferometry (VLBI) tracking network. The observed data are first simulated, then solutions are found after including the effects of various error sources and finally compared. We use the space data analysis software package, GEODYN, developed at Goddard Space Flight Center, NASA, USA. The primary error source of the flight orbiting the moon is the lunar gravity field. Therefore, the (formal) error of JGL165P1, i.e. the model of the lunar gravity field with the highest accuracy at present, is first discussed. After simulating the data of ranging and velocity measurement as well as the VLBI data of the time delay and time delay rate, precise orbit determination is carried out when the error of the lunar gravity field is added in. When the orbit is determined, the method of reduced dynamics is adopted with the selection of appropriate empirical acceleration parameters to absorb the effect of errors in the lunar gravity field on the orbit determination. The results show that for lunar missions like the “Chang'e 1” project, that do not take the lunar gravity field as their main scientific objective, the method of reduced dynamics is a simple and effective means of improving the accuracy of the orbit determination of the lunar orbiters.

Results of the VLBI experiments conducted with Syowa Station, Antarctica

The first successful geodetic Very Long Baseline Interferometry (VLBI) observations to Antarctica were made on baselines from Syowa Station (Antarctica) to Tidbinbilla (Australia) and to Kashima (Japan) in January 1990. Regular geodetic experiments started in 1998 with the installation of a permanent VLBI terminal at Syowa Station. These observations are conducted at the standard geodetic VLBI frequencies of 2.3 and 8.4 GHz, S- and X-Bands. In the first year, the 11-m multipurpose antenna at Syowa Station observed together with the 26-m radio telescope of the University of Tasmania in Australia and the 26-m radio telescope of the Hartebeesthoek Radio Astronomy Observatory in South Africa. From 1999, the experiments were expanded to also include the O’Higgins Station in Antarctica, Fortaleza in Brazil and Kokee on Hawaii. From 1999 until the end of 2003, 25 observing sessions have been reduced and analyzed using the CALC/SOLVE geodetic VLBI data reduction package. The results show that the horizontal baseline of Syowa-Hobart is increasing at the rate of 57.0±1.9 mm/year. The baseline Syowa-Hartebeesthoek is also increasing, but at the lower rate of 9.8±1.9 mm/year. The VLBI result of 2.0±3.1 mm/year and the GPS result of −1.9±0.7 mm/year for the Syowa-O’Higgins horizontal baseline support the hypothesis of one rigid Antarctic plate without intra-plate deformation, which is consistent with the NNR-NUVEL-1A global plate motion model. The location of the Euler pole of the Antarctic plate by VLBI is estimated as 59.7°S and 62.6°E with a rotation rate of 0.190 deg/Myr, while that by GPS in our study is estimated as 60.6°S and 42.2°E with a rotation rate of 0.221 deg/Myr. These pole positions are slightly different to that implied by the NNR-NUVEL-1A model of 63.0°S and 64.2°E with a rotation rate of 0.238 deg/Myr. VLBI observations over a longer time span may resolve small discrepancy of current plate motion from the NNR-NUVEL-1A model. The consistency of the VLBI coordinates with the GPS coordinates at Syowa Station, after correction for the local tie vector components between the two reference markers, is also discussed.

Relativistic jet motion in the core of the radio-loud quasar J1101+7225

Multi-epoch GHz Very Long Baseline Interferometry (VLBI) data of the radio-loud quasar J1101+7225 were analyzed to estimate the proper motion of extended optically thin jet components. Two components separated from the core could be mapped at 1.66 GHz, which is consistent with earlier observations. In one case we found evidence of high apparent superluminal motion (beta_app= 22.5+/-4) at large (deprojected) distances to the core (22 mas ~ 4 kpc at z= 1.46). Typically in other quasars such high separation velocities are only found much closer to the core component. Furthermore the Doppler factor, the magnetic field strength, and the angular size of the optically thick core were derived using published X-ray data. Analysis of 5 GHz VLBI data reveals the existence of further jet components within the central 5 mas. Additionally the data published so far on the GHz-spectrum were discussed at all angular resolutions. J1101+7225 turns out to be a standard quasar for studying different aspects of radio jet kinematics out to kpc-scales.

Deep VLBI Imaging of Faint Radio Sources in the NOAO Bootes Field

We have conducted a deep, very long baseline interferometry (VLBI) observation at 1.4 GHz of an area of sky located within the NOAO Bootes field, using the NRAO Very Long Baseline Array and 100 m Green Bank Telescope. Applying wide-field VLBI techniques, a total of 61 sources, selected from a Westerbork Synthesis Radio Telescope (WSRT) image, were surveyed simultaneously with a range of different sensitivities and resolutions. The survey covered a total of 1017 arcmin2 = 0.28 deg2 divided into annular fields centered on α = 14h29m270, δ = +35°28'3000 (J2000.0). The inner 0-2' of the field reached an unprecedented 1 σ rms noise level of 9 μJy beam-1 and yielded two detections. VLBI J142923.6466 and VLBI J142934.7033 have brightness temperatures in excess of 106 K, and we locate the active nuclei of their host galaxies (NDWFS J142923.6+352851 and NDWFS J142934.7+352859, with I ~ 16.3 and 19.6 mag, respectively). Further deep surveys of the inner 2'-4' and 4'-6' of the field, with 1 σ rms noise levels of 11-19 μJy beam-1, detected a previously known source, VLBI J142910.2224, a quasar with a brightness temperature in excess of 109 K, that was also used during these observations as an in-beam phase calibrator. The deep VLBI survey between 0' and 6' thus detected three radio sources, drawn from a total of 24 targets. A shallower VLBI survey, conducted between 6' and 18' of the field center, and with 1 σ rms noise levels of 37-55 μJy beam-1, detected a further six radio sources, drawn from 37 additional targets. Each of those six VLBI detections has a brightness temperature in excess of 105 K; this hints that those six are accretion-powered, a suggestion reinforced by the double structure of three of them. Combining the deep and shallow VLBI surveys, optical identifications are available for eight of the nine VLBI detections. Only VLBI J142906.6095 remains unidentified (I > 25.6 mag), quite unusually, as its integrated WSRT flux density is 20 mJy. Two other sources are not detected in the K-band (K > 18.5 mag), suggesting that some significant fraction of these compact radio sources may be located at z > 1. The VLBI detection rate for sub-mJy WSRT radio sources is 8%. The VLBI detection rate for mJy WSRT sources is higher, 29%. This observational trend is expected from a rapidly evolving radio source population. Moreover, this trend supports deep radio surveys, at lower resolution, which have suggested that the radio emission associated with fainter sub-mJy and μJy sources arises via processes associated with extended regions of star formation. The nine VLBI detections reported here pinpoint the precise location of active nuclei or candidate active nuclei, and their VLBI positions can help to anchor the NOAO Bootes field to the International Celestial Reference Frame. The simultaneous detection of several sub-mJy and mJy radio sources, in a single observation, suggest that their combined response may be used to self-calibrate wide-field VLBI data. There is every prospect that future deep VLBI observations will be able to take advantage of this wide-field technique, in any random direction on the sky, thereby generating large-area, unbiased surveys of the faint radio source population.

Monitoring the TOPEX and Jason-1 Microwave Radiometers with GPS and VLBI Wet Zenith Path Delays

Monitoring of altimeter microwave radiometer measurements is necessary in order to identify radiometer drifts or offsets that if uncorrected will introduce systematic errors into ocean height measurements. To examine TOPEX Microwave Radiometer (TMR) and Jason-1 Microwave Radiometer (JMR) behavior, we have used coincident wet zenith delay estimates from Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) geodetic sites near altimeter ground tracks. We derived a TMR path delay drift rate of −1.1 ± 0.1 mm/yr using GPS data for the period from 1993.0–1999.0 and −1.2 ± 0.5 mm/yr using VLBI data. Thereafter, the drift appears to have leveled off. Already after 2.3 years (82 cycles) of the Jason-1 mission, it is clear that there have been significant systematic errors in the JMR path delay measurements. From comparison with GPS wet delays, there is an offset of −5.2 ± 0.6 mm at about cycle 30 and a more abrupt offset of −11.5 ± 0.8 mm at cycle 69. If we look at the behavior of the JMR coldest brightness temperatures, we see that the offsets near cycle 30 and cycle 69 are mainly caused by corresponding offsets in the 23.8 GHz channel of −0.49 ± 0.12 K and −1.18 ± 0.13 K, although there is a small 34.0 GHz offset at cycle 69 of 0.75 ± 0.22 K. Drifts in the 18.0 and 34.0 GHz channels produce a small path delay drift of 0.3 ± 0.5 mm/yr.

Measurement of the Solar Gravitational Deflection of Radio Waves using Geodetic Very-Long-Baseline Interferometry Data, 1979–1999

We used very-long-baseline interferometry (VLBI) to measure the deflection by the Sun of radio waves emanating from distant compact radio sources. This bending is characterized in the parametrized post-Newtonian formalism by gamma, which is unity in general relativity. Using a large geodetic VLBI data set, we obtained gamma=0.9998(3)+/-0.0004(5) (estimated standard error). We found no systematic biases from our analysis of subgroups of data.

High data rate transmission in high resolution radio astronomy—vlbiGRID

Recent developments in Very Long Baseline Interferometry (VLBI) radio astronomy are aimed at improving reliability and reducing the cost of operations by moving from a custom made tape based system for using exchangeable disks in PCs. The advent of the iGRID2002 exhibition in September 2002 with the availability of high data rate international links gave us the opportunity to try transferring the data via the internet. This would not only test the capacity of the links but also prove the viability of the use of the internet for VLBI. This development would also eventually lead to instant turn-around of VLBI data, which currently stands at several weeks. The tests were successful achieving data rates from Manchester of 500 Mbps over the production network. This was the first demonstration of fibre-optic link connected international VLBI.

Recent crustal movements observed with the European VLBI network: geodetic analysis and results

Purely European geodetic Very Long Baseline Interferometry (VLBI) has been performed at regular intervals since January 1990. Meanwhile 10 VLBI sites in Europe from Sicily to Spitzbergen and the Iberian pensinsula to the Crimean peninsula contribute to the observation series. The observations are used to determine recent crustal movements in these parts of Europe. Baseline measurements are achieved with an accuracy of 2.0 mm plus an additional term depending on the baseline length of less than 1 part-per-billion. Significant horizontal crustal movements are determined with relative accuracies in the range of 10–40%, significant vertical crustal movements are determined with relative accuracies in the range of 30–40%. The determined crustal movements form thus a sound basis for interpretations in a geophysical and geological context. This article concentrates on a description of the geodetic VLBI data analysis, the analysis models used and the results for crustal movements.

Mantle viscosity from Monte Carlo inversion of very long baseline interferometry data

Using a Monte Carlo approach, we determine the mantle viscosity profiles which best fit the currently observed very long baseline interferometry (VLBI) baseline lengths in North America. Our inversion, which is based on the deglaciation model ICE‐1 and on the most recent VLBI global solution (we employ the Goddard Space Flight Center VLBI solution 1102, which contains data through July 1998 (Ma and Ryan, 1998)), demonstrates that the observations are best fit for a shallow upper mantle with viscosity below the traditional reference value of 1021 Pa s. The lower mantle viscosity cannot be unequivocally determined by means of VLBI data alone. In fact, our inversion indicates that two distinct solutions are possible. The first is characterized by a lower mantle with viscosity of a few times 1021 Pa s, a value in agreement with that derived by the global set of relative sea level curves. The second admissible solution corresponds to a lower mantle with viscosity close to 1023 Pa s. We have found that the viscosity of the transition zone may vary between 5×1021 and 5×1022 Pa s, i.e., larger than the lowest admissible values found for the lower mantle viscosity. The results of the Monte Carlo inversion are essentially stable with respect to time, since similar viscosity profiles are suggested if the VLBI global solution 1014 is employed, which contained data through July 1995. However, the increased precision of VLBI data since that time has somewhat narrowed the set of admissible viscosity profiles above the 670‐km depth discontinuity. Choosing various subsets of solution 1102, we have also tested the robustness of the results presented, with reference to possible data contaminations due to tectonic deformations.

VLBI and VLA observations of intraday polarization variability in 0917+624 and 0954+658

ABSTRA C T Total intensity and polarization la 6 cm Very Large Array (VLA) and global very long baseline interferometry (VLBI) images of the quasar 09171624 and the BL Lacertae object 09541658 (both at epoch 1991.43) are analysed. Integrated measurements using the VLA during the VLBI observations indicated that, although there were no substantial total intensity variations, there were significant polarization variations for both sources during the 24-h VLBI experiment. The VLBI data were divided into 2‐3 h segments in order to try to identify corresponding rapid variability in the VLBI structure. This analysis revealed intraday variability (IDV) in the VLBI core of 09171624: both the polarized flux and the polarization position angle varied substantially on time-scales of ,5‐10 h. There is evidence that the VLA polarization variations for 09541658 occurred in an inner VLBI jet component, where the polarized flux varied by ,30‐40 per cent on time-scales of , 2h . 09171624 and 09541658 were observed together with 07161714, an object that also displayed IDV in the polarized flux density measured during our experiment (analysed in a separate paper). These three sources were targeted for the VLBI observations since they had been previously identified as intraday variables, but we had no way of knowing whether they would vary during our observations. The fact that all three exhibited IDV in polarization (but not in total intensity) during our experiment suggests that polarization IDV occurs frequently in at least some IDV sources.

Influence of Adopted Nutation Model on VLBI NEOS-Intensives Analysis

Very Long Baseline Interferometry (VLBI) provides information about the Earth’s rotation. Various observational programs have operated for different specific purposes since 1983. The purpose of the NEOS-Intensive program is to make observations of Universal Time (UT1–UTC). Short observational sessions (1-2 hours) include only the transcontinental baseline (Wettzell - NRAO20). 20–30 individual scans are performed during the observational time. Only five parameters, wet delay for the reference station, wet delay for the second station, clock offset for the second station, clock rate for the second station, and UT1–UTC are considered in the parametric model.The purpose of this paper is to investigate the influence of the adopted nutation model on the UT1–UTC estimates. VLBI data from the NEOS-Intensives have been analyzed using the OCCAM 3.4 software. All reduction calculations are in accordance with the IERS Conventions 1996 (McCarthy, 1996).

A vision towards automated real-time VLBI

The paper presents a general concept for very long baseline interferometry (VLBI) in near real-time and describes two important components of real-time VLBI: the direct transmission of the received signals from the radiotelescopes to the correlator or to a central computer for further processing and the automation of the VLBI data analysis by methods of artificial intelligence (AI). The concept of a knowledge-based system which supports the data analyst is presented and an example for automatic editing of the station log-files is given.

Three-dimensional modelling of crustal motions caused by subduction and continental convergence in the central Mediterranean

Summary Crustal deformation in the central Mediterranean is modelled by means of 3-D finite element models assuming a viscoelastic rheology. The tectonic mechanisms under investigation are subduction of the Ionian oceanic lithosphere beneath the Calabrian arc and continental convergence between the African and Eurasian blocks. Very Long Baseline Interferometry (VLBI) data at the station Noto in Sicily and the results from global models of plate motions are taken as representative of the motion of the African plate with respect to Eurasia, while VLBI solutions at Matera and Medicina, in the southern and northern parts of the Italian peninsula, are geodetic observations that must be compared with modelling results. Vertical deformation rates are taken from geological and tide gauge records. The model that best fits the observations includes the effects of subduction in the southern Tyrrhenian and convergence between Africa and Europe. The overthrusting of the Tyrrhenian domain onto the Adriatic domain results in an eastward component of the velocity at the eastern border of the Tyrrhenian domain, in agreement with VLBI data from the Matera and Medicina stations and GPS data from northeastern Sicily and the Eolian Islands. The highest subsidence rates are obtainedinthe southern Tyrrhenian, and are of the order of 1.2–1.4 mm yr− 1. Along the whole Adriatic coast of the Italian peninsula, subsidence in the foredeeps is of the order of 0.2–0.5 mm yr− 1. The Apenninic chain is rising with rates of the order of 0.2–0.4 mm yr− 1. Subduction beneath the Calabrian arc is responsible for a roll-back velocity higher than in the northern areas. 2-D models, built for the geological past, indicate the possibility of roll-back velocities of several centimetres per year. In particular, active rifting in the Tyrrhenian and softening of the crust in the back-arc basin result in a trench retreat velocity in agreement with geological estimates. Our results show that numerical modelling can be used to estimate present-day deformation rates and the contribution of active tectonics to sea-level changes along coastal areas.

MINQUE for block diagonal bordered systems such as those encountered in VLBI data analysis

A sparse matrix method is developed for computing variance factors for block-diagonal, bordered systems of equations using MINQUE (Minimum Norm Quadratic Unbiased Estimation). This method greatly reduces the computational effort required to apply MINQUE, thus making it practical to compute variance factors for some very large systems of equations. The computer implementation of the method is described and applied to the computation of variance factors for a combination of 1609 VLBI (Very Long Baseline Interferometry) observing sessions. The purpose of this test was to compute a variance factor for each of the data sets and, perhaps, to obtain more realistic variance estimates to replace those in common use for the analysis of VLBI data. It was found that the method is satisfactory for use with such large problems, and the test served to verify that the variances in current use in VLBI data adjustments are adequate.

Astrometric Detection of a Low‐Mass Companion Orbiting the Star AB Doradus

We report submilliarcsecond--precise astrometric measurements for the late-type star AB Doradus via a combination of VLBI(very long baseline interferometry) and Hipparcos satellite data. Our astrometric analysis results in the precise determination of the kinematics of this star, that reveals an orbital motion readily explained as caused by the gravitational interaction with a low-mass companion.

Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data

We develop a formalism for parameterizing and evaluating the effects of lateral variations in the properties of Earth's atmosphere on the propagation of microwave signals. A parametric form is incorporated into our analysis of very long baseline interferometry (VLBI) data, and the estimated atmospheric delay gradients are compared with those calculated from three‐dimensional weather analysis fields from the National Center for Environmental Prediction (NCEP). For a 12‐day series of experiments in January 1994, the VLBI and the NCEP analyses show common atmospheric gradient delays with amplitudes of up to 30 mm at 10° elevation angle. Comparison of the characteristics over a longer period of time reveals common mean north‐south gradients with amplitudes up to ≈10 mm at 10° elevation at midlatitudes. No discernible mean east‐west gradients were found in either data set. The root‐mean‐square (RMS) variations of the gradient effects, determined from the NCEP analysis, are similar in the north‐south and east‐west directions, with a typical RMS scatter of 6–10 mm at 10° elevation. After accounting for gradients, detailed analysis of the January 1994 VLBI data shows clearly that the residual station height variations of ≈10 mm at Westford, Massachusetts, are almost totally explained by the effects of atmospheric pressure loading.