Correction to: Performance assessment of the relative gravimeter Scintrex CG-6

in Journal of Geodesy (2022), 96(1), 1-1

Seasonal low-degree changes in terrestrial water mass load from global GNSS measurements

in Journal of Geodesy (2017), 91(11), 1329-1350

Large-scale mass redistribution in the terrestrial water storage (TWS) leads to changes in the low-degree spherical harmonic coefficients of the Earth's surface mass density field. Studying these low ... [more ▼]

Large-scale mass redistribution in the terrestrial water storage (TWS) leads to changes in the low-degree spherical harmonic coefficients of the Earth's surface mass density field. Studying these low-degree fluctuations is an important task that contributes to our understanding of continental hydrology. In this study, we use global GNSS measurements of vertical and horizontal crustal displacements that we correct for atmospheric and oceanic effects, and use a set of modified basis functions similar to Clarke et al. (2007) to perform an inversion of the corrected measurements in order to recover changes in the coefficients of degree-0 (hydrological mass change), degree-1 (center of mass shift) and degree-2 (flattening of the Earth) caused by variations in the TWS over the period January 2003 - January 2015. We infer from the GNSS-derived degree-0 estimate an annual variation in total continental water mass with an amplitude of $(3.49 \pm 0.19) \times 10^{3}$ Gt and a phase of $70 \pm 3^{\circ}$ (implying a peak in early March), in excellent agreement with corresponding values derived from the Global Land Data Assimilation System (GLDAS) water storage model that amount to $(3.39 \pm 0.10) \times 10^{3}$ Gt and $71 \pm 2^{\circ}$, respectively. The degree-1 coefficients we recover from GNSS predict annual geocentre motion (i.e. the offset change between the center of common mass and the center of figure) caused by changes in TWS with amplitudes of $0.69 \pm 0.07$ mm for GX, $1.31 \pm 0.08$ mm for GY and $2.60 \pm 0.13$ mm for GZ. These values agree with GLDAS and estimates obtained from the combination of GRACE and the output of an ocean model using the approach of Swenson et al. (2008) at the level of about 0.5, 0.3 and 0.9 mm for GX, GY and GZ, respectively. Corresponding degree-1 coefficients from SLR, however, generally show higher variability and predict larger amplitudes for GX and GZ. The results we obtain for the degree-2 coefficients from GNSS are slightly mixed, and the level of agreement with the other sources heavily depends on the individual coefficient being investigated. The best agreement is observed for $T_{20}^C$ and $T_{22}^S$, which contain the most prominent annual signals among the degree-2 coefficients, with amplitudes amounting to $(5.47 \pm 0.44) \times 10^{-3}$ and $(4.52 \pm 0.31) \times 10^{-3}$ m of equivalent water height (EWH), respectively, as inferred from GNSS. Corresponding agreement with values from SLR and GRACE is at the level of or better than $0.4 \times 10^{-3}$ and $0.9 \times 10^{-3}$ m of EWH for $T_{20}^C$ and $T_{22}^S$, respectively, while for both coefficients, GLDAS predicts smaller amplitudes. Somewhat lower agreement is obtained for the order-1 coefficients, $T_{21}^C$ and $T_{21}^S$, while our GNSS inversion seems unable to reliably recover $T_{22}^C$. For all the coefficients we consider, the GNSS-derived estimates from the modified inversion approach are more consistent with the solutions from the other sources than corresponding estimates obtained from an unconstrained standard inversion. [less ▲]

An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit

in Journal of Geodesy (2013), 87(2), 127-142

One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial ... [more ▼]

One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo–Nyquist rule-of-thumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservative, and solutions with better spatial resolutions are possible. A new rule is introduced which limits the maximum achievable order (not degree!) to be smaller than the number of revolutions if the difference between the number of revolutions and the number of nodal days is of odd parity and to be smaller than half the number of revolutions if the difference is of even parity. The dependence on the parity is reflected in the eigenvalue spectrum of the normal matrix and becomes especially important in the presence of noise. The rule is based on applying the Nyquist sampling theorem separately in North–South and East–West direction. This is only possible for satellites in highly inclined orbits like champ and grace. Tables for these two satellite missions are also provided which indicate the passed and (in case of grace) expected repeat cycles and possible degradations in the quality of the gravity field solutions. [less ▲]

Nontidal ocean loading: amplitudes and potential effects in GPS height time series

in Journal of Geodesy (2012), 86(11), 1043-1057

Ocean bottom pressure (OBP) changes are caused by a redistribution of the ocean’s internal mass that are driven by atmospheric circulation, a change in the mass entering or leaving the ocean, and/or a ... [more ▼]

Ocean bottom pressure (OBP) changes are caused by a redistribution of the ocean’s internal mass that are driven by atmospheric circulation, a change in the mass entering or leaving the ocean, and/or a change in the integrated atmospheric mass over the ocean areas. The only previous global analysis investigating the magnitude of OBP surface displacements used older OBP data sets (van Dam et al. in J Geophys Res 129:507–517, 1997). Since then significant improvements in meteorological forcing models used to predict OBP have been made, augmented by observations from satellite altimetry and expendable bathythermograph profiles. Using more recent OBP estimates from the Estimating the Circulation and Climate of the Ocean (ECCO) project, we reassess the amplitude of the predicted effect of OBP on the height coordinate time series from a global distribution of GPS stations. OBP-predicted loading effects display an RMS scatter in the height of between 0.2 and 3.7 mm, larger than previously reported but still much smaller (by a factor of 2) than the scatter observed due to atmospheric pressure loading. Given the improvement in GPS hardware and data analysis techniques, the OBP signal is similar to the precision of weekly GPS height coordinates. We estimate the effect of OBP on GPS height coordinate time series using the MIT reprocessed solution, mi1. When we compare the predicted OBP height time series with mi1, we find that the scatter is reduced over all stations by 0.1 mm on average with reductions as high as 0.7 mm at some stations. More importantly we are able to reduce the scatter on 65 % of the stations investigated. The annual component of the OBP signal is responsible for 80 % of the reduction in scatter on average.We find that stations located close to semi-enclosed bays or seas are affected by OBP loading to a greater extent than other stations. [less ▲]

Results of the first North American comparison of absolute gravimeters, NACAG-2010

in Journal of Geodesy (2012), 86

The effect of using inconsistent ocean tidal loading models on GPS coordinate solutions

in Journal of Geodesy (2011)

We use up to a 6-year span of GPS data from 85 globally distributed stations to compare solutions using ocean tidal loading (OTL) corrections computed in differ- ent reference frames: center of mass of ... [more ▼]

We use up to a 6-year span of GPS data from 85 globally distributed stations to compare solutions using ocean tidal loading (OTL) corrections computed in differ- ent reference frames: center of mass of the solid Earth (CE), and center of mass of the Earth system (CM). We compare solution sets that differ only in the frame used for the OTL model computations, for three types of GPS solutions. In global solutions with all parameters including orbits estimated simultaneously, we find coordinate differences of ∼0.3mm between solutions using OTL computed in CM and OTL computed in CE. When orbits or orbits and clocks are fixed, larger biases appear if the user applies an OTL model inconsistent with that used to derive the orbit and clock products. Network solutions (orbits fixed, satellite clocks estimated) show differences smaller than 0.5 mm due to model inconsistency, but PPP solutions show distortions at the ∼1.3 mm level. The much larger effect on PPP solutions indicates that satellite clock estimates are sensitive to the OTL model applied. The time series of coordinate differences shows a strong spectral peak at a period of ∼14 days when inconsistent OTL models are applied and smaller peaks at ∼annual and ∼semi-annual periods, for both ambiguity-free and ambiguity-fixed solutions. These spurious coordinate variations disappear in solutions using consistent OTL mod- els. Users of orbit and clock products must ensure that they use OTL coefficients computed in the same reference frame as the OTL coefficients used by the analysis centers that produced the products they use; otherwise, systematic errors will be introduced into position solutions. All modern products should use loading models computed in the CM frame, but legacy products may require loading models computed in the CE frame. Analysts and authors need to document the frame used for all loading computations in product descriptions and papers. [less ▲]

Integer ambiguity resolution in precise point poistioning: method comparison

in Journal of Geodesy (2010), 84(9), 569-581

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a ... [more ▼]

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality. [less ▲]

A method of error adjustment for marine gravity with application to Mean Dynamic Topography in the northern North Atlantic

in Journal of Geodesy (2009), 83(2), 161-174