Correction to "Topographically induced height errors in predicted atmospheric loading effects"

in Journal of Geophysical Research. Solid Earth (2011)

Figure 1 presented in the paper “Topographically induced height errors in predicted atmospheric loading effects” by van Dam et al., (Journal of Geophysical Research, VOL. 115, B07415, doi:10.1029 ... [more ▼]

Figure 1 presented in the paper “Topographically induced height errors in predicted atmospheric loading effects” by van Dam et al., (Journal of Geophysical Research, VOL. 115, B07415, doi:10.1029/2009JB006810) is incorrect. The correct image is presented here. The corrected image does not alter the conclusion presented in the original paper. [less ▲]

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 ▲]

Simulation of the time-variable gravity field by means of coupled geophysical models

in Earth System Science Data (2011), 3(1), 19-35

Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by ... [more ▼]

Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested. [less ▲]

Topographically corrected atmospheric loading effects

in Journal of Geophysical Research (2010), (115), 5-6

Atmospheric pressure variations are known to induce vertical displacements of the Earth’s surface with magnitudes large enough to be detected by geodetic observations. Estimates of these loading effects ... [more ▼]

Atmospheric pressure variations are known to induce vertical displacements of the Earth’s surface with magnitudes large enough to be detected by geodetic observations. Estimates of these loading effects are derived using global reanalysis fields of surface pressure as input. The input surface pressure has a minimum spatial sampling, which does not capture true surface pressure variations due to high topographic variability in some regions. In this paper, we investigate the effect that unmodeled topographic variability has on surface pressure estimates and subsequent estimates of vertical surface displacements. We find that the estimated height changes from the topographic surface pressure can be significant (2–4 mm) for sites in regions of high topographic variability. When we compare the estimated height changes to Global Positioning System residuals from the 2005 International Terrestrial Reference Frame Realization, we find that the heights derived from the topographic surface pressure, versus those from the normal surface pressure, perform better at reducing the scatter on the height coordinate time series. [less ▲]

Results of the European Comparison of Absolute Gravimeters in Walferdange (Luxembourg) of November 2007

in Gravity, Geoid and Earth Observation (2010)

The second international comparison of absolute gravimeters was held in Walferdange, Grand Duchy of Luxembourg, in November 2007, in which twenty absolute gravimeters took part. A short description of the ... [more ▼]

The second international comparison of absolute gravimeters was held in Walferdange, Grand Duchy of Luxembourg, in November 2007, in which twenty absolute gravimeters took part. A short description of the data processing and adjustments will be presented here and will be followed by the presentation of the results. Two different methods were applied to estimate the relative offsets between the gravimeters. We show that the results are equivalent as the uncertainties of both adjustments overlap. The absolute gravity meters agree with one another with a standard deviation of 2 μgal (1 gal = 1 cm/s2). [less ▲]

GPS Measurements of Crustal Uplift near Jakobshavn Isbrae due to Glacial Ice Mass Loss

in Journal of Geophysical Research (2010), 115

We analyze 2006–2009 data from four continuous Global Positioning System (GPS) receivers located between 5 and 150 km from the glacier Jakobshavn Isbræ, West Greenland. The GPS stations were established ... [more ▼]

We analyze 2006–2009 data from four continuous Global Positioning System (GPS) receivers located between 5 and 150 km from the glacier Jakobshavn Isbræ, West Greenland. The GPS stations were established on bedrock to determine the vertical crustal motion due to the unloading of ice from Jakobshavn Isbræ. All stations experienced uplift, but the uplift rate at Kangia North, only 5 km from the glacier front, was about 10 mm yr−1 larger than the rate at Ilulissat, located only "45 km further away. This suggests that most of the uplift is due to the unloading of the Earth’s surface as Jakobshavn thins and loses mass. Our estimate of Jakobshavn’s contribution to uplift rates at Kangia North and Ilulissat are 14.6 ± 1.7 mm yr−1 and 4.9 ± 1.1 mm yr−1, respectively. The observed rates are consistent with a glacier thinning model based on repeat altimeter surveys from NASA’s Airborne Topographic Mapper (ATM), which shows that Jakobshavn lost mass at an average rate of 22 ± 2 km3 yr−1 between 2006 and 2009. At Kangia North and Ilulissat, the predicted uplift rates computed using thinning estimates from the ATM laser altimetry are 12.1 ± 0.9 mm yr−1 and 3.2 ± 0.3 mm yr−1, respectively. The observed rates are slightly larger than the predicted rates. The fact that the GPS uplift rates are much larger closer to Jakobshavn than further away, and are consistent with rates inferred using the ATM!based glacier thinning model, shows that GPS measurements of crustal motion are a potentially useful method for assessing ice!mass change models. [less ▲]

Impact of loading effects on determination of the International Terrestrial Reference Frame

in Advances in Space Research (2010), 45(1), 144-154

The International Terrestrial Reference Frame (ITRF), as a realization of the International Terrestrial Reference System (ITRS), is represented by a set of station positions and linear velocities. They ... [more ▼]

The International Terrestrial Reference Frame (ITRF), as a realization of the International Terrestrial Reference System (ITRS), is represented by a set of station positions and linear velocities. They are intended to be used as regularized coordinates to which some corrections should be added to access instantaneous coordinates. The latest ITRS realization is the ITRF2005, which has integrated time series of station positions to form long-term solutions for the four space geodetic techniques. Currently, a purely linear model is used to parameterize station displacements in the estimation process, plus occasional discontinuities in case of earthquakes or equipment changes. However the input data have been derived without applying surface loading models and so surface loading effects are supposed to be embedded in the coordinates as measured quantities. We evaluate the effect of applying a posteriori loading corrections, which include the effect of atmospheric, non-tidal ocean, and continental water loading, to time series of positions estimated from Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), and Global Positioning System (GPS) data. We notice that they reduce about 50% or more of the annual signals in the translation and scale parameter time series of the SLR and VLBI techniques, except in SLR Z translation. In general, the estimated secular frame definition is negligibly affected and estimated positions and velocities are not significantly modified for stations that have accumulated a large number of observations. A multi-technique combination of such derived frames allows concluding that, for some cases, loading model corrections might degrade co-located station coordinates almost as much as they benefit them. However, most significant improvement of the estimated secular coordinates is observed for stations with less than 100 estimated positions as demonstrated with a multi-technique combination. [less ▲]

Anomalous harmonics in the spectra of GPS position estimates

in GPS Solutions (2008), 12(1), 55-64

Prior studies of the power spectra of GPS position time series have found pervasive seasonal signals against a power-law background of flicker noise plus white noise. Dong et al. (2002) estimated that ... [more ▼]

Prior studies of the power spectra of GPS position time series have found pervasive seasonal signals against a power-law background of flicker noise plus white noise. Dong et al. (2002) estimated that less than half the observed GPS seasonal power can be explained by redistributions of geophysical fluid mass loads. Much of the residual variation is probably caused by unidentified GPS technique errors and analysis artifacts. Among possible mechanisms, Penna and Stewart (2003) have shown how unmodeled analysis errors at tidal frequencies (near 12- and 24-hour periods) can be aliased to longer periods very efficiently. Signals near fortnightly, semiannual, and annual periods are expected to be most seriously affected. We have examined spectra for the 167 sites of the International GNSS (Global Navigation Satellite Systems) Service (IGS) network having more than 200 weekly measurements during 1996.0–2006.0. The non-linear residuals of the weekly IGS solutions that were included in ITRF2005, the latest version of the International Terrestrial Reference Frame(ITRF), have been used. To improve the detection of common-mode signals, the normalized spectra of all sites have been stacked, then boxcar smoothed for each local north (N), east (E), and height (H) component. The stacked, smoothed spectra are very similar for all three components. Peaks are evident at harmonics of about 1 cycle per year (cpy) up to at least 6 cpy, but the peaks are not all at strictly 1.0 cpy intervals. Based on the 6th harmonic of the N spectrum, which is among the sharpest and largest, and assuming a linear overtone model, then a common fundamental of 1.040 ± 0.008 cpy can explain all peaks well, together with the expected annual and semiannual signals. A flicker noise power-law continuum describes the background spectrum down to periods of a few months, after which the residuals become whiter. Similar sub-seasonal tones are not apparent in the residuals of available satellite laser ranging (SLR) and very long baseline interferometry (VLBI) sites, which are both an order of magnitude less numerous and dominated by white noise. There is weak evidence for a few isolated peaks near 1 cpy harmonics in the spectra of geophysical loadings, but these are much noisier than for GPS positions. Alternative explanations related to the GPS technique are suggested by the close coincidence of the period of the 1.040 cpy frequency, about 351.2 days, to the ‘‘GPS year’’; i.e., the interval required for the constellation to repeat its inertial orientation with respect to the sun. This could indicate that the harmonics are a type of systematic error related to the satellite orbits. Mechanisms could involve orbit modeling defects or aliasing of site-dependent positioning biases modulated by the varying satellite geometry. [less ▲]

Elastic uplift in southeast Greenland due to rapid ice mass lost

in Geophysical Research Letters (2007), 34(L21701), 1-6

The rapid unloading of ice from the southeastern sector of the Greenland ice sheet between 2001 and 2006 caused an elastic uplift of ~35 mm at a GPS site in Kulusuk. Most of the uplift results from ice ... [more ▼]

The rapid unloading of ice from the southeastern sector of the Greenland ice sheet between 2001 and 2006 caused an elastic uplift of ~35 mm at a GPS site in Kulusuk. Most of the uplift results from ice dynamic-induced volume losses on two nearby outlet glaciers. Volume loss from Helheim Glacier, calculated from sequential digital elevation models, contributes about ~16 mm of the observed uplift, with an additional ~5 mm from volume loss of Kangerdlugssuaq Glacier. The remaining uplift signal is attributed to significant melt-induced ice volume loss from the ice sheet margin along the southeast coast between 62°N and 66°N. [less ▲]

Basis functions for the consistent and accurate representation of surface mass loading

in Geophysical Journal International (2007), 171(1), 1-10

Inversion of geodetic site displacement data to infer surface mass loads has previously been demonstrated using a spherical harmonic representation of the load. This method suffers from the continent-rich ... [more ▼]

Inversion of geodetic site displacement data to infer surface mass loads has previously been demonstrated using a spherical harmonic representation of the load. This method suffers from the continent-rich, ocean-poor distribution of geodetic data, coupled with the predominance of the continental load (water storage and atmospheric pressure) compared with the ocean bottom pressure (including the inverse barometer response). Finer-scale inversion becomes unstable due to the rapidly increasing number of parameters which are poorly constrained by the data geometry. Several approaches have previously been tried to mitigate this, including the adoption of constraints over the oceanic domain derived from ocean circulation models, the use of smoothness constraints for the oceanic load, and the incorporation ofGRACEgravity field data. However, these methods do not provide appropriate treatment of mass conservation and of the ocean’s equilibrium-tide response to the total gravitational field. Instead,we propose a modified set of basis functions as an alternative to standard spherical harmonics. Our basis functions allow variability of the load over continental regions, but impose global mass conservation and equilibrium tidal behaviour of the oceans. We test our basis functions first for the efficiency of fitting to realistic modelled surface loads, and then for accuracy of the estimates of the inferred load compared with the known model load, using synthetic geodetic displacements with real GPS network geometry. Compared to standard spherical harmonics, our basis functions yield a better fit to the model loads over the period 1997–2005, for an equivalent number of parameters, and provide a more accurate and stable fit using the synthetic geodetic displacements. In particular, recovery of the low-degree coefficients is greatly improved. Using a nine-parameter fit we are able to model 58 per cent of the variance in the synthetic degree-1 zonal coefficient time-series, 38–41 per cent of the degree-1 non-zonal coefficients, and 80 per cent of the degree-2 zonal coefficient. An equivalent spherical harmonic estimate truncated at degree 2 is able to model the degree-1 zonal coefficient similarly (56 per cent of variance), but only models 59 per cent of the degree-2 zonal coefficient variance and is unable to model the degree-1 non-zonal coefficients. [less ▲]