HOME DATA OVERVIEW - MONTHLY MASS - INTERACTIVE BROWSER - PGR & TRENDS - STERIC SEA LEVEL - DYNAMIC OCEAN TOPO PUBLICATIONS PEOPLE (OPEN IN NEW WINDOW OR TAB) MISSION STATUS UT.CSR GRACE GFZ GRACE PO.DAAC GRACE (OPEN IN NEW WINDOW OR TAB) GSFC GRACE CNES GRACE BONN GRACE ESIP FEDERATION

1. Amalvict, A; Hinderer, J; Rozsa, S , 2006 :
   Crustal vertical motion along a profile crossing the Rhine graben from the Vosges to the Black Forest Mountains: Results from absolute gravity, GPS and levelling observations .
   JOURNAL OF GEODYNAMICS 41 358 - 368

The Rhine plain is oriented north-south and limited by the Vosges Mountains (France) to the West and the Black Forest Mountains (Germany) to the East. The present-day tectonic evolution of this system is not well known and many questions are still pending: is the graben subsiding? Are the mountains uplifting? What is the relative behaviour of the three different geological components? In attempting to answer these questions, we compare for the first time in this region time series of absolute gravity (AG) measurements to the available GPS observations at three sites along a profile crossing the Rhine graben. Our reference station is the gravimetric observatory near Strasbourg (D), located in the Rhine plain where AG measurements are performed regularly since 1997 and where superconducting gravimeter (SG) observations are available almost continuously for 17 years. The secondary sites are the Welschbruch station in the Vosges Mountains where six AG measurements have been conducted since 1997 and the Black Forest Observatory (BFO) where three AG measurements are available. GPS permanent receivers are collocated at the Strasbourg-J9 site since 1999, at the WeIschbruch station since 2000, and at BFO since 2002. Levelling data are only available in the BFO region. We compare the long term content of two types of geodetic measurements with special emphasis on the trend despite the limited duration of our data sets. Assuming that the gravity changes are linear in time, we obtain k = 1.9 +/- 0.2 [mu Gal/yr at Strasbourg-J9, g = -0.96 +/- 0.2 mu Gal/yr at WeIschbruch site and g = 2.5 +/- 0.5 mu Gal/yr at BFO. The trends according to GPS observations are, respectively: - 1.51 +/- 0.07 and -0.74 +/- 0. 10 mm/yr at Strasbourg-J9 and Welschbruch site, respectively; there is no GPS result available at BFO. The AG results for BFO are very questionable, as well as the GPS observations at the Welschbruch station. Nonetheless, Strasbourg-J9 and Welschbruch AG measurements lead to subsidence and uplift, respectively, which are expected results in agreement with GPS at Strasbourg-J9. (c) 2005 Elsevier Ltd. All rights reserved.

2. Andersen, O; Berry, P; Freeman, J; Lemoine, FG; Lutsckhe, S; Jakobsen, F; Butts, M , 2008 :
   Satellite altimetry and GRACE gravimetry for studies of annual water storage variations in Bangladesh .
   TERRESTRIAL ATMOSPHERIC AND OCEANIC SCIENCES 19 47 - 52

Four different data sources have been compared with respect to observations of the annual water storage variations in the region of Bangladesh. Data from satellite altimeters and river gauges estimates the variation in surface water storage in the major rivers of Bangladesh. The GRACE satellites measure the integrated mass change and hence the terrestrial soil moisture variations, which can also be estimated by a hydrological model (GLDAS). These types of observations enable the derivation of the integrated water storage in the entire region of Bangladesh. For all data types, the annual signal has been estimated from a common dataset spanning the period 2003 and 2004. All four different data observe that water storage in Bangladesh is largely dominated by an annual signal with a phase peaking in early September. The annual variations in river level peaks roughly two weeks earlier than terrestrial soil moisture observations by GRACE observations and GLDAS model output.

3. Andersen, OB; Hinderer, J , 2005 :
   Global inter-annual gravity changes from GRACE: Early results .
   GEOPHYSICAL RESEARCH LETTERS 32 - L01402

Fifteen monthly gravity field solutions from the GRACE twin satellites launched more than two years ago have been studied to estimate gravity field changes between 2002 and 2003. The results demonstrate that GRACE is capable of capturing the changes in ground water on inter-annual scales with an accuracy of 0.4 muGal corresponding to 9 mm water thickness on spatial scales longer than 1300 km. Four of the most widely used global hydrological models have been investigated for their spatial comparison with GRACE observations of inter-annual gravity field variations due to changes in continental water storage. The Global Land Data Assimilation System model has a spatial correlation coefficient with GRACE observations of 0.65 over the northern hemisphere. This demonstrates that the observed gravity field changes on these scales are largely related to changes in continental water storage.

4. Andersen, OB; Seneviratne, SI; Hinderer, J; Viterbo, P , 2005 :
   GRACE-derived terrestrial water storage depletion associated with the 2003 European heat wave .
   GEOPHYSICAL RESEARCH LETTERS 32 - L18405

The GRACE twin satellites reveal large inter-annual terrestrial water-storage variations between 2002 and 2003 for central Europe. GRACE observes a negative trend in regional water storage from 2002 to 2003 peaking at -7.8 cm in central Europe with an accuracy of 1 cm. The 2003 excess terrestrial water storage depletion observed from GRACE can be related to the record-breaking heat wave that occurred in central Europe in 2003. We validate the measurements from GRACE using two independent hydrological estimates and direct gravity observations from superconducting gravimeters in Europe. All datasets agree well with the GRACE measurements despite the disparity of the employed information; the difference between datasets tends to be within GRACE margin of error. The April-to-August terrestrial water storage depletion is found to be significantly larger in 2003 than in 2002 from both models and observations.

5. Barletta, VR; Sabadini, R; Bordoni, A , 2008 :
   Isolating the PGR signal in the GRACE data: impact on mass balance estimates in Antarctica and Greenland .
   GEOPHYSICAL JOURNAL INTERNATIONAL 172 18 - 30

Redistribution of mass over the Earth and within the mantle changes the gravity field whose variations are monitored at high spatial resolution by the presently flying GRACE space gravity mission from NASA or, at longer wavelengths, by the Satellite Laser Ranging (SLR) constellation. In principle, GRACE data allow one to study the time evolution of various Earth phenomena through their gravitational effects. The correct identification of the gravitational spatial and temporal fingerprints of the individual hydrologic, atmospheric, oceanographic and solid Earth phenomena is thus extremely important, but also not trivial. In particular, it has been widely recognized that the gravitational estimates of present-day ice mass loss in Greenland and Antarctica, and the related effect on sea level changes, depend on an accurate determination of the Postglacial Rebound (PGR) after Pleistocene deglaciation, which in turn depends on the assumed solid Earth parameters and deglaciation model. Here we investigate the effect of the uncertainty of the solid Earth parameters (viscosity, litospheric thickness) and of different deglaciation processes on PGR in Greenland and Antarctica. We find that realistic constraints to the trend in ice mass loss derived from GRACE data determine a range of variation substantially wider than commonly stated, ranging from an important ice loss of -209 Gt yr(-1) to an accumulation of +88 Gt yr(-1) in Antarctica, and Greenland ablation at a rate between -122 and -50 Gt yr(-1). However, if we adopt the set of most probable Earth parameters, we infer a substantial mass loss in both regions, -171 +/- 39 and -101 +/- 22 Gt yr(-1) for Antarctica and Greenland, respectively.

6. Beutler, G; Drewes, H; Verdun, A , 2005 :
   The Integrated Global Geodetic Observing System (IGGOS) viewed from the perspective of history .
   JOURNAL OF GEODYNAMICS 40 414 - 431

Towards the end of the 19th century, geodetic observation techniques allowed it to create geodetic networks of continental size. The insight that big networks can only be set up through international collaboration led to the establishment of an international collaboration called "Central European Arc Measurement", the predecessor of the International Association of Geodesy (IAG), in 1864. The scope of IAG activities was extended already in the 19th century to include gravity. At the same time, astrometric, observations could be made with an accuracy of a few tenths of an arcsecond. The accuracy stayed roughly on this level, till the space age opened the door for milliarcsecond (mas) astrometry, Astrometric observations allowed it at the end of the 19th century to prove the existence of polar motion. The insight that polar motion is almost unpredictable led to the establishment of the International Latitude Service (ILS) in 1899. The IAG and the ILS were the tools (a) to establish and maintain the terrestrial and the celestial reference systems, including the transformation parameters between the two systems, and (b) to determine the Earth's gravity field. Satellite-geodetic techniques and astrometric radio-interferometric techniques revolutionized geodesy in the second half of the 20th century. Satellite Laser Ranging (SLR) and methods based on the interferometric exploitation of microwave signals (stemming from Quasars and/or from satellites) allow it to realize the celestial reference frame with (sub-)mas accuracy, the global terrestrial reference frame with (sub-)cm accuracy, and to monitor the transformation between the systems with a high time resolution and (sub-)mas accuracy. This development led to the replacement of the ILS through the IERS, the International Earth Rotation Service in 1989. In the pre-spacc era, the Earth's gravity field could "only" be established by terrestrial methods, The determination of the Earth's gravitational field was revolutionized twice in the space era, first by observing geodetic satellites with optical. Laser. and Doppler techniques, secondly by implementing a continuous tracking with spaceborne GPS receivers in connection with satellite gradiometry, The sequence of the satellite gravity missions CHAMP, GRACE, and GOCE allow it to name the first decade of the 21st century the "decade of gravity field determination". The techniques to establish and monitor the geometric and gravimetric reference frames are about to reach a mature state and will be the prevailing geodetic tools of the following decades. It is our duty to work in the spirit of our forefathers by creating similarly stable organizations within IAG with the declared goal to produce the geometric and gravimetric reference frames (including their time evolution) with the best available techniques and to make accurate and consistent products available to wider Earth sciences community as a basis for meaningful research in global change. IGGOS, the Integrated Global Geodetic Observing System, is TAG's attempt to achieve these goals. It is based on the well-functioning and well-established network of TAG services. (c) 2005 Elsevier Ltd. All rights reserved.

7. Beyerle, G; Schmidt, T; Michalak, G; Heise, S; Wickert, J; Reigber, C , 2005 :
   GPS radio occultation with GRACE: Atmospheric profiling utilizing the zero difference technique .
   GEOPHYSICAL RESEARCH LETTERS 32 - L13806

Radio occultation events recorded on 28 - 29 July 2004 by a GPS receiver aboard the GRACE-B satellite are analyzed. The stability of the receiver clock allows for the derivation of excess phase profiles using a zero difference technique, rendering the calibration procedure with concurrent observations of a reference GPS satellite obsolete. 101 refractivity profiles obtained by zero differencing and 96 profiles calculated with an improved single difference method are compared with co-located ECMWF meteorological analyses. Good agreement is found at altitudes between 5 and 30 km with an average fractional refractivity deviation below 1% and a standard deviation of 2 - 3%. Results from end-to-end simulations are consistent with these observations.

8. Bingham, RJ; Haines, K , 2006 :
   Mean dynamic topography: intercomparisons and errors .
   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 364 903 - 916

Knowledge of the ocean dynamic topography, defined as the height of the sea surface above its rest-state (the geoid), would allow oceanographers to study the absolute circulation of the ocean and determine the associated geostrophic surface currents that help to regulate the Earth's climate. Here a novel approach to computing a mean dynamic topography (MDT), together with an error field, is presented for the northern North Atlantic. The method uses an ensemble of MDTs, each of which has been produced by the assimilation of hydrographic data into a numerical ocean model, to form a composite MDT, and uses the spread within the ensemble as a measure of the error on this MDT. The r.m.s. error for the composite MDT is 3.2 cm, and for the associated geostrophic currents the r.m.s. error is 2.5 cm s(-1). Taylor diagrams me used to compare the composite MDT with several MDTs produced by a variety of alternative methods. Of these, the composite MDT is found to agree remarkably well with an MDT based on the GRACE geoid GCM01C. It is shown how the composite MDT and its error field are useful validation products against which other MDTs and their error fields can be compared.

9. Bingham, RJ; Hughes, CW , 2006 :
   Observing seasonal bottom pressure variability in the North Pacific with GRACE .
   GEOPHYSICAL RESEARCH LETTERS 33 - L08607

Using monthly gravity field solutions from GRACE together with output from an ocean model we assess the ability of GRACE to observe seasonal ocean bottom pressure variability in the North Pacific. First, the spatial structure and temporal evolution of the long-term mean seasonal bottom pressure cycle in the North Pacific is characterised in the context of the ocean model. It is then shown that a mean seasonal cycle based on a limited subset of the model output corresponding to the intervals over which the GRACE monthly solutions were formed is representative of this long-term seasonal cycle. It is therefore concluded that the significant features of the seasonal cycle should be present in the GRACE data. Agreement is found between the ocean model and GRACE estimates of the bottom pressure seasonal cycle, thus demonstrating the worth of GRACE as a tool for studying ocean dynamics.

10. Birol, F; Brankart, JM; Lemoine, JM; Brasseur, P; Verron, J , 2005 :
    Assimilation of satellite altimetry referenced to the new GRACE geoid estimate .
    GEOPHYSICAL RESEARCH LETTERS 32 - L06601

[1] Currently, two satellite gravimetric missions (CHAMP, GRACE) are dedicated to the improvement of our knowledge of the geoid, and one (GOCE) is planned in the near future. This will allow the absolute altimeter ocean height measurements to be exploited, instead of only sea level variations. In this paper, we evaluate the impact of the GRACE mission on ocean data assimilation. The new approach is to directly assimilate the full altimetric signal relative to the first release of a GRACE geoid. The response of an eddy-permitting ocean model of the North Atlantic to the assimilation of this altimetric signal is analysed. The results are compared to that obtained using the usual approach, i.e., the assimilation of the dynamic topography derived from the addition of altimetric sea level anomalies and a mean dynamic topography estimate. Even if the GRACE mission resolution (333 km) is not yet compatible with oceanographic studies at mid latitude, we show that the geoid estimate can already be used with success in basin scale altimetric data assimilation problems.

11. Bock, H; Jaggi, A; Svehla, D; Beutler, G; Hugentobler, U; Visser, P , 2007 :
    Precise orbit determination for the GOCE satellite using GPS .
    ADVANCES IN SPACE RESEARCH 39 1638 - 1647

Apart from the gradiometer as the core instrument, the first ESA Earth Explorer Core Mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) will carry a 12-channel GPS receiver dedicated for precise orbit determination (POD) of the satellite. The EGG-C (European GOCE Gravity-Consortium), led by the Technical University in Munich, is building the GOCE HPF (High-level Processing Facility) dedicated to the Level 1b to Level 2 data processing. One of the tasks of this facility is the computation of the Precise Science Orbit (PSO) for GOCE. The PSO includes a reduced-dynamic and a kinematic orbit solution. The baseline for the PSO is a zero-difference procedure using GPS satellite orbits, clocks, and Earth Rotation Parameters (ERPs) from CODE (Center for Orbit Determination in Europe), one of the IGS (International GNSS Service) Analysis Centers. The scheme for reduced-dynamic and kinematic orbit determination is based on experiences gained from CHAMP and GRACE POD and is realized in one processing flow. Particular emphasis is. put on maximum consistency in the analysis of day boundary overlapping orbital arcs, as well as on the higher data sampling rate with respect to CHAMP and GRACE and on differences originating from different GPS antenna configurations. We focus on the description of the procedure used for the two different orbit determinations and on the validation of the procedure using real data from the two GRACE satellites as well as simulated GOCE data. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

12. Borghi, A; Carrion, D; Sona, G , 2007 :
    Validation and fusion of different databases in preparation of high-resolution geoid determination .
    GEOPHYSICAL JOURNAL INTERNATIONAL 171 539 - 549

An up to date determination of a high-resolution geoid requires the use of best available databases concerning digital terrain model (DTM), bathymetry, global geopotential model and gravity field. The occasion to revisit methods to validate and merge different data sets has been created by a new project for the determination of a new European Geoid. Since the computation of the latest European geoid and quasi-geoid model (EGG97), significant new or improved data sets have become available, such as new global geopotential models from CHAMP and GRACE missions, new national and global DTMs and new or upgraded gravity data sets. In the context of the new European Gravity and Geoid Project (EGGP), within the IAG Commission 2, some data validation tests have been performed in the Italian zone. In the area 19 degrees x 17 degrees wide, covering Italy, three kinds of tests have been performed: comparison among different DTMs in order to choose the best one to be used; comparisons in terms of geoid computation in some coastal areas, to evaluate bathymetry effects, and the validation of the EIGEN-CG01C and EIGEN-CG03C new global models up to degree and order 360. These preliminary tests lead to the choice of SRTM DTM (integrated in no-data holes), with an added bathymetry derived by the Italian 1:25 000 official cartography near the coasts and the NOAA bathymetry in high seas. The validation of the new global models and the comparison with EGM96 model show that, in terms of geoid computation, the EGM96 yields better results. Moreover, the validation of new available land gravity data and the cross-validation of two sets of gravity data on sea have been completed.

13. Bourda, G , 2008 :
    Length-of-day and space-geodetic determination of the Earth's variable gravity field .
    JOURNAL OF GEODESY 82 295 - 305

The temporal variations of the Earth's gravity field, nowadays routinely determined from satellite laser ranging (SLR) and GRACE (Gravity Recovery And Climate Experiment), are related to changes in the Earth's rotation rate through the Earth's inertia tensor. We study this connection from actual data by comparing the traditional length-of-day (LOD) measurements provided by the International Earth Rotation and Reference Systems Service (IERS) to the variations of the degree-2 and order-0 Stokes coefficient of the gravity field determined from fitting the orbits of the LAGEOS-1 and -2 satellites since 1985. The two series show a good correlation (0.62) and similar annual and semi-annual signals, indicating that the gravity-field-derived LOD is valuable. Our analysis also provides evidence for additional signals common to both series, especially at a period near 120 days, which could be due to hydrological effects.

14. Boy, JP; Chao, BF , 2005 :
    Precise evaluation of atmospheric loading effects on Earth's time-variable gravity field .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 110 - B08412

New space gravity missions will provide gravity measurements with unprecedented accuracy and high spatial resolution. To reveal the oceanic and hydrologic signals in monthly time-variable gravity field from the Gravity Recovery and Climate Experiment (GRACE) satellite (Tapley et al., 2004) entails the removal of the atmospheric contribution, which in turn requires a precise knowledge of the atmospheric mass redistribution. We reconstruct the three-dimensional (3-D) variations of air-density from vertical profiles of pressure, temperature, and specific humidity provided by the National Centers for Environmental Prediction (NCEP) atmospheric model of a realistic topography. We compare our results with those from the classical thin layer (2-D) approximation and show that the differences between the complete 3-D and the 2-D computations are often nonnegligible in the presence of the expected GRACE sensitivity up to harmonic degrees of 15-20, corresponding to wavelengths of 2000-2500 km. For actual computation, we recommend the use of the sigma level atmospheric data with special attention to the latitude and altitude dependence of the Earth's gravity. We also examine and conclude the importance of the differences with previous study which assumed a constant surface gravity acceleration without a latitudinal dependence.

15. Bruinsma, S; Forbes, JM; Nerem, RS; Zhang, XL , 2006 :
    Thermosphere density response to the 20-21 November 2003 solar and geomagnetic storm from CHAMP and GRACE accelerometer data .
    JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 111 - A06303

[ 1] Densities in the 400 - 500 km height region inferred from accelerometer measurements on the CHAMP and GRACE satellites are utilized to study the response to the isolated and severe geomagnetic storm of 20 - 21 November 2003. The CHAMP and GRACE satellites provide data at approximate local times of 1110/2310 and 1430/ 0230 hours, respectively. In a global sense, density increases of order 300 - 800% occur during this storm, with relatively little time delay at high latitudes and with about 4-hour delay at the equator. Significant latitudinal asymmetries in the response are discussed in the context of neutral wind patterns and enhanced summer versus winter Joule heating rates at high latitudes. Comparisons with the NRLMSISE-00 empirical model densities during this period show marked differences in amplitude of the response, as well as latitudinal and temporal structures. Evidence for a tight coupling between solar wind and neutral density variability is found for the high-latitude summer hemisphere near noon, in that densities near 410 km are very responsive to increases in solar wind dynamic pressure, even during periods when both B-z and B-y are near zero or positive. Filtering of the data reveals regional-scale ( similar to 1000 - 2000 km) density anomalies that are common between the CHAMP and GRACE measurements. During the geomagnetic disturbance, alternating regions of density enhancements ( similar to 50%) and depressions ( similar to 50%) exist between the pole and low to middle latitudes that have the appearance of a standing wave pattern. During magnetically quiet intervals before and after the storm, daytime density depressions ( similar to 4 - 8%) are seen that track the magnetic equator, while density enhancements ( similar to 10%) track the latitudes of the ionospheric Appleton anomaly peaks. Large-scale ( >= 1000 km) wave-like structures are also prevalent during both day and night during the magnetic disturbance and extend throughout both hemispheres, consistent with the concept that these are associated with the so-called "direct'' gravity waves forced in the auroral regions and propagating far from the source. Substantial variability is also present at medium scales ( similar to 300 - 500 km), but these structures are confined mainly to middle to high latitudes, in accord with theoretical expectations. GRACE-A and GRACE-B data are used in a feasibility study of the detection of small-scale wave activity by taking advantage of the 30-s separation of the satellites in the same orbital plane. Despite the large amount of maneuvers, which are not always recorded, this first analysis is promising. Amplitude variations of order 10 - 20% and wave speeds of 1000 - 1500 m s(-1) are observed.

16. Bruinsma, SL; Forbes, JM , 2007 :
    Storm-time equatorial density enhancements observed by CHAMP and GRACE .
    JOURNAL OF SPACECRAFT AND ROCKETS 44 1154 - 1159

Total atmospheric densities have been simultaneously acquired from accelerometer measurements on the CHAMP (challenging minisatellite payload) and GRACE (gravity recovery and climate experiment) satellites over the past years. Both satellites have observed a large number of geomagnetic storms, most of them simultaneously, offering unique opportunities to study the temporal and latitudinal responses of the thermosphere to geomagnetic disturbances. The equatorial density enhancements observed during fast and significant increases in geomagnetic activity are calculated. The relationship between the density enhancements and local time, and the increase and maximum value of the geomagnetic activity are analyzed. The enhancements top 100% only if geomagnetic activity exceeds a minimum value, are larger on the nightside than on the dayside, and increase with attitude. The largest enhancement observed was 800%. The day-to-night density ratios become smaller during storm periods and are closest to unity for a local time of 0800/2000. The relative delay of the equatorial enhancement with respect to the ones observed at 60 degrees S and 60 degrees N is a function of geomagnetic activity, and it is shorter in the night sector than in the daylight sector. Equatorial propagation speeds of the density disturbance that are derived from the delay are of the order 400-1200 ms(-1).

17. Burke, WJ; Huang, CY; Marcos, FA; Wise, JO , 2007 :
    Interplanetary control of thermospheric densities during large magnetic storms .
    JOURNAL OF ATMOSPHERIC AND SOLAR-TERRESTRIAL PHYSICS 69 279 - 287

During the main phase of large magnetic storms significant energy can be deposited in the ionosphere but produce no commensurate magnetic perturbations on the ground. Consequently, models designed to predict and specify thermospheric energy budgets based on ground magnetic data are negatively impacted. To quantify these effects we compare thermospheric densities predicted by the MSIS model with those inferred from accelerometer measurements by the Gravity Recovery and Climate Experiment (GRACE) satellites during two magnetic storm periods in 2004. Although predictions and measurements are in substantial agreement during quiet times, the model significantly underpredicts densities during storms. Also, the model's maxima occur several hours after observed stormtime peaks. We show that polar cap potentials and magnetospheric electric fields derived from interplanetary parameters measured by the Advanced Composition Explorer satellite are roughly proportional to neutral densities observed by GRACE with lead times of similar to 4h. Finally, ion drift meter data from Defense Meteorological Satellite Program spacecraft suggest that unpredicted positive and negative spikes found in high latitude accelerometer data reflect encounters with strong head and tail thermospheric winds driven by anti-sunward convecting plasma. (c) 2006 Elsevier Ltd. All rights reserved.

18. Castruccio, F; Verron, J; Gourdeau, L; Brankart, JM; Brasseur, P , 2008 :
    Joint altimetric and in-situ data assimilation using the GRACE mean dynamic topography: a 1993-1998 hindcast experiment in the Tropical Pacific Ocean .
    OCEAN DYNAMICS 58 43 - 63

The altimetric satellite signal is the sum of the geoid and the dynamic topography, but only the latter is relevant to oceanographic applications. Poor knowledge of the geoid has prevented oceanographers from fully exploiting altimetric measurements through its absolute component, and applications have concentrated on ocean variability through analyses of sea level anomalies. Recent geodetic missions like CHAMP, GRACE and the forthcoming GOCE are changing this perspective. In this study, data assimilation is used to reconstruct the Tropical Pacific Ocean circulation during the 1993-1996 period. Multivariate observations are assimilated into a primitive equation ocean model (OPA) using a reduced order Kalman filter (the Singular Evolutive Extended Kalman filter). A 6-year (1993-1998) hindcast experiment is analyzed and validated by comparison with observations. In this experiment, the new capability offered by an observed absolute dynamic topography (built using the GRACE geoid to reference the altimetric data) is used to assimilate, in an efficient way, the in-situ temperature profiles from the TAO/TRITON moorings together with the T/P and ERS1&2 altimetric signal. GRACE data improves compatibility between both observation data sets. The difficulties encountered in this regard in previous studies such as Parent et al. (J Mar Syst 40-41:381-401, 2003) are now circumvented. This improvement helps provide more efficient data assimilation, as evidenced, by assessing the results against independent data. This leads in particular to significantly more realistic currents and vertical thermal structures.

19. Castruccio, F; Verron, J; Gourdeau, L; Brankart, JM; Brasseur, P , 2006 :
    On the role of the GRACE mission in the joint assimilation of altimetric and TAO data in a tropical Pacific Ocean model .
    GEOPHYSICAL RESEARCH LETTERS 33 - L14616

Recent advances in our knowledge of the earth geoid have made it possible to exploit absolute sea surface height measurements in realistic numerical modelling studies of the ocean. This letter provides evidence of the benefit of the GRACE referenced mean dynamic topography (MDT) for the simulation of the tropical Pacific ocean through the joint assimilation of altimetric data and of vertical temperature profiles from the TAO/TRITON array. Results are considered in relation to those obtained using a classical model MDT, based on the model itself, and are validated against independent XBT data. The use of the GRACE MDT leads to significantly improved results with respect to these independent data. If the compatibility between the altimetric sea surface height and the TAO/TRITON temperature improves the model simulation, some limitations exist, especially in the Warm Pool where a part of the sea surface height signature is associated to a salinity signal.

20. Chambers, DP , 2006 :
    Evaluation of new GRACE time-variable gravity data over the ocean .
    GEOPHYSICAL RESEARCH LETTERS 33 - L17603

Monthly GRACE gravity field models from the three science processing centers (CSR, GFZ, and JPL) are analyzed for the period from February 2003 to April 2005 over the ocean. The data are used to estimate maps of the mass component of sea level at smoothing radii of 500 km and 750 km. In addition to using new gravity field models, a filter has been applied to estimate and remove systematic errors in the coefficients that cause erroneous patterns in the maps of equivalent water level. The filter is described and its effects are discussed. The GRACE maps have been evaluated using a residual analysis with maps of altimeter sea level from Jason-1 corrected for steric variations using the World Ocean Atlas 2001 monthly climatology. The mean uncertainty of GRACE maps determined from an average of data from all 3 processing centers is estimated to be less than 1.8 cm RMS at 750 km smoothing and 2.4 cm at 500 km smoothing, which is better than was found previously using the first generation GRACE gravity fields.

21. Chambers, DP , 2006 :
    Observing seasonal steric sea level variations with GRACE and satellite altimetry .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 111 - C03010

[1] Sea level rises and falls as the temperature and salinity of the water column varies, which is known as steric sea level. Sea level also changes as water mass is redistributed within the ocean or is added or removed. Satellite radar altimeters measure the combination of both effects, while the Gravity Recovery and Climate Experiment ( GRACE) was designed to measure time variable gravity caused by movement of water mass. Theoretically, altimetry and GRACE data can be combined in order to compute the steric sea level variations. We test this by combining current GRACE and Jason 1 altimeter data and comparing against steric sea level observations. We will describe how to properly combine the altimetry and GRACE data, commenting on important corrections that need to be applied to each data type. Using empirical orthogonal function (EOF) analysis, we examine the leading modes of seasonal variability and find that using GRACE improves the ability to recover the dominant mode of steric sea level variability over using altimetry alone. The RMS error of the GRACE ocean mass variations is estimated to be about 2 cm of sea level at a 1000 km smoothing radius. Although this is larger than initially predicted from the GRACE mission, it is still significantly smaller than the recovered signal in several regions of the ocean.

22. Chambers, DP; Tamisiea, ME; Nerem, RS; Ries, JC , 2007 :
    Effects of ice melting on GRACE observations of ocean mass trends .
    GEOPHYSICAL RESEARCH LETTERS 34 - L05610

The Gravity Recovery and Climate Experiment (GRACE) was designed to measure variations in the Earth's gravity field from space at monthly intervals. Researchers have used these data to measure changes in water mass over various regions, including the global oceans and continental ice sheets covering Greenland and Antarctica. However, GRACE data must be smoothed in these analyses and the effects of geocenter motions are not included. In this study, we examine what effect each of these has in the computation of ocean mass trends using a simulation of ice melting on Greenland, Antarctica, and mountain glaciers. We find that the recovered sea level change is systematically lower when coefficients are smoothed and geocenter terms are not included. Assuming current estimates of ice melting, the combined error can be as large as 30-50% of the simulated sea level rise. This is a significant portion of the long-term sea level change signal, and needs to be considered in any application of GRACE data to estimating long-term trends in sea level due to gain of water mass from melting ice.

23. Chambers, DP; Wahr, J; Nerem, RS , 2004 :
    Preliminary observations of global ocean mass variations with GRACE .
    GEOPHYSICAL RESEARCH LETTERS 31 - L13310

Monthly estimates of the Earth's gravitational field from the GRACE mission are used to construct a time-series of global mean ocean mass variations between August 2002 and December 2003. This time-series is compared to a mean climatology determined from satellite altimeter measurements of global mean sea level corrected for the steric variation. The GRACE observations show a seasonal exchange of water mass with the continents of the same magnitude ( similar to8.5 mm) and phase ( maximum in early-to mid-October) as the steric-corrected altimetry. This is one of the first direct validations over the ocean of the primary GRACE science mission to measure time-variable transports of water mass in the Earth system, and it suggests that GRACE data can be used to measure non-steric mean sea level variations which is important for climate change studies.

24. Chao, BF , 2005 :
    On inversion for mass distribution from global (time-variable) gravity field .
    JOURNAL OF GEODYNAMICS 39 223 - 230

The well-known non-uniqueness of the gravitational inverse problem states that the external gravity field, even if completely and exactly known, cannot uniquely determine the density distribution of the body that produces the gravity field. In this paper, we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-D the degree of knowledge deficiency in trying to inversely recover the density distribution from an external gravity field solution is (n + 1)(n + 2)/2 - (2n + 1) = n(n - 1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources largely come from the Earth's surface over a wide range of timescales. (c) 2005 Elsevier Ltd. All rights reserved.

25. Chen, JL; Rodell, M; Wilson, CR; Famiglietti, JS , 2005 :
    Low degree spherical harmonic influences on Gravity Recovery and Climate Experiment (GRACE) water storage estimates .
    GEOPHYSICAL RESEARCH LETTERS 32 - L14405

We estimate terrestrial water storage variations using time variable gravity changes observed by the Gravity Recovery and Climate Experiment ( GRACE) satellites during the first 2 years of the mission. We examine how treatment of low-degree gravitational changes and geocenter variations affect GRACE based estimates of basin-scale water storage changes, using independently derived low-degree harmonics from Earth rotation (EOP) and satellite laser ranging (SLR) observations. GRACE based water storage changes are compared with estimates from NASA's Global Land Data Assimilation System (GLDAS). Results from the 22 GRACE monthly gravity solutions, covering the period April 2002 to July 2004, show remarkably good agreement with GLDAS in the Mississippi, Amazon, Ganges, Ob, Zambezi, and Victoria basins. Combining GRACE observations with EOP and SLR degree-2 spherical harmonic coefficient changes and SLR observed geocenter variations significantly affects and apparently improves the estimates, especially in the Mississippi, Ob, and Victoria basins.

26. Chen, JL; Tapley, BD; Wilson, CR , 2006 :
    Alaskan mountain glacial melting observed by satellite gravimetry .
    EARTH AND PLANETARY SCIENCE LETTERS 248 368 - 378

We use satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) as an indication of mass change to study potential long-term mountain glacial melting in southern Alaska and West Canada. The first 3.5 yr of GRACE monthly gravity data, spanning April 2002-November 2005, show a prominent glacial melting trend in the mountain regions around the Gulf of Alaska (GOA). GRACE-observed surface mass changes correlate remarkably well with available mass balance data at Gulkana and Wolverine, two benchmark glaciers of the U.S. Geological Survey (USGS), although the GRACE signals are smaller in magnitude. In addition, terrestrial water storage (TWS) changes estimated from an advanced land surface model show significant mass loss in this region during the same period. After correcting for the leakage errors and removing TWS contributions using model estimates, we conclude that GRACE-observed glacial melting in the GOA mountain region is equivalent to similar to -101 +/- 22 km(3)/yr, which agrees quite well with the assessment of similar to-96 +/- 35 km(3)/yr based on airborne laser altimetry data, and is consistent with an earlier estimate based on the first 2 yr of GRACE data. This study demonstrates the significant potentials of satellite gravity measurements for monitoring mountain glacial melting and regional climate change. (c) 2006 Elsevier B.V All rights reserved.

27. Chen, JL; Wilson, CR; Blankenship, DD; Tapley, BD , 2006 :
    Antarctic mass rates from GRACE .
    GEOPHYSICAL RESEARCH LETTERS 33 - L11502

We estimate mass trends over Antarctica using gravity variations observed by the Gravity Recovery and Climate Experiment ( GRACE) satellite mission during its first 3.5 years ( April 2002 - November 2005). An image of surface mass trends is constructed from 1 degrees x 1 degrees pixels over the entire continent, and shows two prominent features, a region of mass loss along the coast of West Antarctica, and one of accumulation in East Antarctica. After adjusting for bias due to smoothing and to GRACE's limited spatial resolution, and removing post glacial rebound (PGR) effects, the rate in West Antarctica is - 77 +/- 14 km(3)/year, similar to a recent estimate of ice mass loss from satellite altimetry and remote sensing data. The prominent East Antarctic feature in the Enderby Land region has a rate of + 80 +/- 16 km(3)/year. Published snow/ice mass rates from remote sensing measurements indicate approximate ice mass balance in this region, suggesting that this feature is either from unquantified snow accumulation in this region or more likely due to unmodeled PGR.

28. Chen, JL; Wilson, CR; Famiglietti, JS; Rodell, M , 2007 :
    Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity .
    JOURNAL OF GEODESY 81 237 - 245

In order to effectively recover surface mass or geoid height changes from the gravity recovery and climate experiment (GRACE) time-variable gravity models, spatial smoothing is required to minimize errors from noise. Spatial smoothing, such as Gaussian smoothing, not only reduces the noise but also attenuates the real signals. Here we investigate possible amplitude attenuations and phase changes of seasonal water storage variations in four drainage basins (Amazon, Mississippi, Ganges and Zambezi) using an advanced global land data assimilation system. It appears that Gaussian smoothing significantly affects GRACE-estimated basin-scale seasonal water storage changes, e.g., in the case of 800 km smoothing, annual amplitudes are reduced by about 25-40%, while annual phases are shifted by up to 10 degrees. With these effects restored, GRACE-estimated water storage changes are consistently larger than model estimates, indicating that the land surface model appears to underestimate terrestrial water storage change. Our analysis based on simulation suggests that normalized attenuation effects (from Gaussian smoothing) on seasonal water storage change are relatively insensitive to the magnitude of the true signal. This study provides a numerical approach that can be used to restore seasonal water storage change in the basins from spatially smoothed GRACE data.

29. Chen, JL; Wilson, CR; Famiglietti, JS; Rodell, M , 2005 :
    Spatial sensitivity of the Gravity Recovery and Climate Experiment (GRACE) time-variable gravity observations .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 110 - B08408

We analyze the spatial sensitivities of terrestrial water storage and geoid height changes determined from the time- variable gravity observed by the Gravity Recovery and Climate Experiment ( GRACE) twin satellite mission. On the basis of 15 GRACE monthly gravity solutions, covering the period April 2002 to December 2003, we examine the effects of spatial smoothing at radii varying from 400 to 2000 km and conclude that a 800 km Gaussian smoothing radius is effective for GRACE- derived terrestrial water storage and produces the minimum RMS residuals over the land of the differences between GRACE results and estimated water storage change from a global land data assimilation system. For GRACE estimated geoid height change, the effective smoothing radius can go down to 600 km. When the annual ( e. g., the sine and cosine) components are the primary concern, the effective spatial resolution can reach 600 and 400 km for GRACE estimated terrestrial water storage or geoid height change, respectively.

30. Chen, JL; Wilson, CR; Seo, KW , 2006 :
    Optimized smoothing of gravity recovery and climate experiment (GRACE) time-variable gravity observations .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 111 - B06408

[ 1] High-degree and high-order spherical harmonics of time-variable gravity fields observed by the Gravity Recovery and Climate Experiment ( GRACE) gravity mission are dominated by noise. We develop two smoothing methods that suppress these high-degree and high-order errors with results superior to more commonly used Gaussian smoothing. These optimized smoothing methods considerably improve signal-to-noise levels of GRACE terrestrial water storage estimates relative to residual signal and noise over the oceans and show significantly better spatial resolution and lower leakage error. On the basis of analysis using an advanced land surface model, the equivalent spatial resolution from these optimized smoothing estimates is about 500 km, compared to the roughly 800 1000 km Gaussian smoothing that is required to suppress high-degree noise in the GRACE fields.

31. Chen, JL; Wilson, CR; Tapley, BD , 2006 :
    Satellite gravity measurements confirm accelerated melting of Greenland ice sheet .
    SCIENCE 313 1958 - 1960

Using time-variable gravity measurements from the Gravity Recovery and Climate Experiment ( GRACE) satellite mission, we estimate ice mass changes over Greenland during the period April 2002 to November 2005. After correcting for the effects of spatial filtering and limited resolution of GRACE data, the estimated total ice melting rate over Greenland is - 239 +/- 23 cubic kilometers per year, mostly from East Greenland. This estimate agrees remarkably well with a recent assessment of - 224 +/- 41 cubic kilometers per year, based on satellite radar interferometry data. GRACE estimates in southeast Greenland suggest accelerated melting since the summer of 2004, consistent with the latest remote sensing measurements.

32. Chen, JL; Wilson, CR; Tapley, BD; Blankenship, D; Young, D , 2008 :
    Antarctic regional ice loss rates from GRACE .
    EARTH AND PLANETARY SCIENCE LETTERS 266 140 - 148

Using recent improved time-variable gravity solutions from the Gravity Recovery and Climate Experiment (GRACE), we estimate rates of Antarctic ice mass change for the period January 2003 through September 2006. Combined improvements in data and filtering techniques allow observation of ice loss in the northern Antarctic Peninsula (AP) and along the coast of the west and central Amundsen Sea Embayment (ASE) in West Antarctica. There is also evidence of ice loss along the coast near the Stancomb-Wills (STA) and Jutulstraumen (JUT) glaciers in Queen Maud Land. Apparent rates are adjusted for influences of limited spatial resolution, filtering, and estimated postglacial rebound (PGR) to obtain ice loss rates for the northern AP, coastal ASE, and STA/JUT of -28.8 +/- 7.9, -81 +/- 17, and -16.7 +/- 9.7 km(3)/yr, respectively. This is the first estimate for the northern AP from satellite gravity data. The ASE estimate (-81 +/- 17km(3)/yr) is consistent with a previous value (-77 +/- 14 km(3)/yr) using an earlier GRACE data release. These results indicate significant improvement in GRACE data quality, increased spatial resolution, and applicability of GRACE data to a wider class of problems than previously possible. (c) 2007 Elsevier B.V. All rights reserved.

33. Chen, JL; Wilson, CR; Tapley, BD; Blankenship, DD; Ivins, ER , 2007 :
    Patagonia icefield melting observed by gravity recovery and climate experiment (GRACE) .
    GEOPHYSICAL RESEARCH LETTERS 34 - L22501

Using recently released reprocessed gravity solutions from the Gravity Recovery and Climate Experiment (GRACE), we estimate the ice loss rate for the Patagonia Icefield (PIF) of South America, for the period April 2002 through December 2006. After postglacial rebound and hydrological effects are corrected, the estimated rate is -27.9 +/- 11 km(3)/year, equivalent to an average loss of similar to-1.6 m/year ice thickness change if evenly distributed over the entire PIF area. The estimated contribution to global sea level rise is 0.078 +/- 0.031 mm/year. This is an independent confirmation of relatively large melting rate estimates from earlier studies employing topographic and cartographic data.

34. Chen, JL; Wilson, CR; Tapley, BD; Famiglietti, JS; Rodell, M , 2005 :
    Seasonal global mean sea level change from satellite altimeter, GRACE, and geophysical models .
    JOURNAL OF GEODESY 79 532 - 539

We estimate seasonal global mean sea level changes using different data resources, including sea level anomalies from satellite radar altimetry, ocean temperature and salinity from the World Ocean Atlas 2001, time-variable gravity observations from the Gravity Recovery and Climate Experiment (GRACE) mission, and terrestrial water storage and atmospheric water vapor changes from the NASA global land data assimilation system and National Centers for Environmental Prediction reanalysis atmospheric model. The results from all estimates are consistent in amplitude and phase at the annual period, in some cases with remarkably good agreement. The results provide a good measure of average annual variation of water stored within atmospheric, land, and ocean reservoirs. We examine how varied treatments of degree-2 and degree-1 spherical harmonics from GRACE, laser ranging, and Earth rotation variations affect GRACE mean sea level change estimates. We also show that correcting the standard equilibrium ocean pole tide correction for mass conservation is needed when using satellite altimeter data in global mean sea level studies. These encouraging results indicate that is reasonable to consider estimating longer-term time series of water storage in these reservoirs, as a way of tracking climate change.

35. Chen, JL; Wilson, CR; Tapley, BD; Grand, S , 2007 :
    GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake .
    GEOPHYSICAL RESEARCH LETTERS 34 - L13302

[1] We show that spherical harmonic (SH) solutions of the Gravity Recovery and Climate Experiment (GRACE) are now of sufficient quality to observe effects of co-seismic and post-seismic deformation due to the rupture from the Mw = 9.3 Sumatra-Andaman earthquake on December 26, 2004, and its companion Nias earthquake (Mw = 8.7) on March 28, 2005. The improved GGM 03 SH (Level 2) solutions, and improved filtering methods provide estimates with spatial resolution comparable to earlier estimates from range-rate (Level 1) GRACE data. The gravity field disturbance extends over 1800 km along Andaman and Sunda subduction zones, and changes with time following events. Gravity changes may be due to afterslip, viscoelastic relaxation, or other processes associated with dilatation. Satellite gravity measurements from GRACE provide a unique new measure of deformation and post-seismic processes associated with major earthquakes, especially in areas which are primarily oceanic.

36. Chen, JL; Wilson, CR; Tapley, BD; Ries, JC , 2004 :
    Low degree gravitational changes from GRACE: Validation and interpretation .
    GEOPHYSICAL RESEARCH LETTERS 31 - L22607

We examine low degree gravitational variations DeltaC(21), DeltaS(21), and DeltaC(20) observed by the Gravity Recovery and Climate Experiment (GRACE) satellites during the first 2 years of this gravity mission. The GRACE observations are compared with independent estimates from accurately measured Earth rotational changes and predictions from atmospheric, oceanic, and hydrological models. The 18 GRACE monthly gravity solutions, covering the period April 2002 to March 2004, show strong seasonal variability in the DeltaC(21), DeltaS(21), and DeltaC(20) time series, and generally agree with Earth rotation-derived changes and geophysical model estimates, in particular for DeltaS(21) and DeltaC(20). The reason for the poorer agreement between the GRACE results and the Earth rotation-derived estimates for DeltaC(21) is unclear. We demonstrate that the omission of the ocean pole tide in the GRACE data processing does have significant effects on the estimated DeltaC(21) and DeltaS(21).

37. Cheng, LY; Xsu, HZ , 2006 :
    The rotation of the gravity potential on the Earth's gravity field recovery .
    CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 49 93 - 98

We analyze the effect of approximate velocity in the formula of the rotation of the gravity potential, which is caused by the Earth rotation. We compute the difference between the satellite ephemeris's velocity and numerical integral's velocity. The ephemeris data come from GFZ's Rapid Science Orbit, TUM's Reduced-Dynamic Orbit, and GFZ's Post-processed Science Orbit respectively. The integral data are obtained based on the reference gravity Field models EGM96, EIGEN2, and EIGEN-CGO1C, respectively. The fitting between ephemeris velocity and integral velocity depended on EIGEN2 reference gravity field model is better than the EGM96 and EIGEN-CGO1C model. The variations of velocity difference have obvious periodicity, which coincides with the satellite orbit period. When the disturbing potential of 1m(2)/s(2) accuracy, or the approximate velocity of accuracy less 2mm/s in the formula of the rotation of the gravity potential is required, the satellite orbit data not satisfied the potential rotation computing demand are rejected from the GFZ's Rapid Science Orbit and TUM's Reduced-Dynamic Orbit. If the disturbing potential is desired 0.5m(2)/s(2) at satellite track, the satellite velocity required in formula of the rotation of the gravity potential should be re-computed or the GFZ's Post-processed Science Orbit is adopted.

38. Choi, S; Oh, CW; Luehr, H , 2006 :
    Tectonic relation between northeastern China and the Korean peninsula evealed by interpretation of GRACE satellite gravity data .
    GONDWANA RESEARCH 9 62 - 67

The major continental blocks in northeastern Asia are the North China block and the South China block, which have collided starting from the Korean peninsula. Geologic and geophysical interpretations reveal a well defined suture zone in northeastern China from Qinling through Dabie to Jiaodong. The discovery of high-pressure metamorphic rocks in the Hongseong area of the Korean peninsula, prominent evidence for the collision zone, indicates extension of the collision zone in northeastern China into the Korean peninsula. Interpretation of the GRACE satellite gravity dataset shows two prominent structural boundaries in the Yellow Sea. One extends from the Jiaodong Belt in eastern China to the Imjingang Belt in the Korean peninsula. The other extends from near Nanjing, eastern China, to Hongseong. Tectonic movement in or near the suture zone may be responsible for seismic activity in the western Korean peninsula and the development of the Yellow Sea sedimentary basin. (c) 2005 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

39. Ciufolini, I; Pavlis, E , 2005 :
    On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio .
    NEW ASTRONOMY 10 636 - 651

In this paper, we provide a detailed description of our recent analysis and determination of the frame-dragging effect obtained using the nodes of the satellites LAGEOS and LAGEOS 2, in reply to the paper "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio (doi: 10.1016/j.newast.2005.01.001). First, we discuss the impact of the (J)over dot(2n) uncertainties on our measurement and we show that the corresponding error is of the order of 1% of frame-dragging only. We report the result of the orbital simulations and analyses obtained with and without (J)over dot(4) and with a 4 equal to its EIGEN-GRACE02S value plus 12 times its published error, i.e., a (J)ovr dot(4) equal to about 611% of the value adopted in EIGEN-GRACE02S, that is (J)over dot(4) = 6.11 x (-1.41 x 10(-11)) -8.61 x 10(-11). In all these three cases, by also fitting the final combined residuals with a quadratic, we obtain the same value of the measured Lense-Thirring effect. This value differs by only 1% with respect to our recent measurement of the Lense-Thirring effect. Therefore, the error due to the uncertainties in the (J)over dot(2n) in our measurement of the gravitomagnetic effect can at most reach 1%, in complete agreement with our previously published error budget. Our total error budget in the measurement of frame-dragging is about 5% of the Lense-Thirring effect, alternatively even by simply considering the published errors in the (J)over dot(2n) and their recent determinations we get a total error budget of the order of 10%, in complete agreement with our previously published error budget. Furthermore, weexplicitly give the results and plot of a simulation clearly showing that the claim of Iorio's paper that the (J)over dot(2n) uncertainty may contribute to up a 45% error error in our measurement is clearly unsubstantiated. We then present a rigorous proof that any "imprint" or "memory" effect of the Lense-Thirring effect is completely negligible on the even zonal harmonics produced using the GRACE satellites only and used on the orbits of the LAGEOS satellites to measure the frame-dragging effect. In this paper we do not discuss the problem of the correlation of the Earth's even zonal harmonics since it only refers to our previous, 1998, analysis with EGM96 and it will be the subject of a different paper; nevertheless, we stress that in the present analysis with EIGENGRACE02S the total error due to the static Earth gravity field has been calculated by pessimistically summing up the absolute values of the errors due to each Earth's even zonal harmonic uncertainty, i.e., we have not used any covariance matrix to calculate the total error but we have just considered the worst possible contribution of each even zonal harmonic uncertainty to the total error budget. We also present and explain our past work on the technique of measuring the Lense-Thirring effect using the LAGEOS nodes and give its main references. Finally we discuss some other minor points and misunderstandings of the paper by Iorio, including some obvious mistakes contained both in this paper and in some other previous papers of Iorio. In conclusion, the criticisms in Iorio's paper are completely unfounded and misdirected: the uncertainties arising from the possible variations of the (J)over dot(2n) are fully accounted for in the error budget that we have published. (C) 2005 Elsevier B.V. All rights reserved.

40. Ciufolini, I; Pavlis, EC; Peron, R , 2006 :
    Determination of frame-dragging using Earth gravity models from CHAMP and GRACE .
    NEW ASTRONOMY 11 527 - 550

Using the new generation Earth's gravity field models EIGEN-2S, GGM01S and EIGEN-GRACE02S generated by the space missions CHAMP and GRACE, we have obtained an accurate measurement of the Lense-Thirring effect with the LAGEOS and LAGEOS 11 satellites analyzing about 10 years of data with the EIGEN-2S and GGM01S models and about I I years of data with EIGEN-GRACE02S. This new analysis is in agreement with our previous measurements of the Lense-Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth's models. However, the new determinations are more accurate and, especially, more robust than our previous measurements. In the present analysis we are only using the nodal rates of the two satellites, making no use of the perigee rate, as in our previous analyses. The perigee is affected by a number of non-gravitational perturbations difficult to be modelled and whose impact in the total error budget is not easy to assess. Using the EIGEN-2S model, we obtain a total error budget between 18% and 36%, of the Lense-Thirring effect due to all the error sources. Specifically, by using EIGEN-2S, we obtain: mu = 0.85, with a total error between 0.18 and 0.36, with GGM01S we get p = 1.06 with a total error between 0.19 and 0.24 and with EIGEN-GRACE02S we obtain p = 0.99, with a total error between 0.05 and 0.1, i.e., between 5% and 10% of the general relativistic predicted value of the Lense-Thirring effect. In addition to the analyses using EIGEN-2S, GGM01S and EIGEN-GRACE02S without the use of the perigee, we have also performed an analysis using the older model EGM96 with our previous method of combining the nodes of the LAGEOS satellites with the perigee of LAGEOS II. However, this analysis was performed over a period of about 10 years, i.e. about 2.5 times longer than any our previous analysis. The result using EGM96 over this longer period of observation agrees with our previous results over much shorter periods and with the EIGEN-2S, GGM01S and EIGEN-GRACE02S measurements of it. In addition to the accurate determination of frame-dragging and in agreement with our previous analyses of the orbits of the LAGEOS satellites, we have observed, since 1998, an anomalous change in the Earth quadrupole Coefficient, J(2) which agrees with recent findings of other authors. This anomalous variation of J(2) is accurately observed both on the node of LAGEOS and LAGEOS 11 and it is independent of the model used, i.e., it is observed by using the model EGM96 or by using EIGEN-2S, GGM01S or EIGEN-GRACE02S. However, this anomalous variation of the Earth quadrupole coefficient does not affect at all our determination of the Lense-Thirring effect thanks to the total elimination of the J(2)-induced errors with our especially devised estimation technique. (c) 2006 Elsevier B.V. All rights reserved.

41. Clarke, PJ; Lavallee, DA; Blewitt, G; van Dam, T , 2007 :
    Basis functions for the consistent and accurate representation of surface mass loading .
    GEOPHYSICAL JOURNAL INTERNATIONAL 171 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, 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 of GRACE gravity 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.

42. Cromwell, D; Shaw, AGP; Challenor, P; Houseago-Stokes, R; Tokmakian, R , 2006 :
    Towards measuring the meridional overturning circulation from space .
    OCEAN SCIENCE DISCUSSIONS 3 1623 - 1635

We present a step towards measuring the meridional overturning circulation (MOC), i.e. the full-depth water mass transport, in the North Atlantic using satellite data. Using the Parallel Ocean Climate Model, we simulate satellite observations of ocean bottom pressure and sea surface height (SSH) over the 20-year period from 1979–1998, and use a linear model to estimate the MOC. As much as 93.5% of the variability in the smoothed transport is thereby explained. This increases to 98% when SSH and bottom pressure are first smoothed. We present initial studies of predicting the time evolution of the MOC, with promising results. It should be stressed that this is an initial step only, and that to produce an actual working system for measuring the MOC from space would require considerable future work.

43. Crossley, D; Hinderer, J; Boy, JP , 2004 :
    Regional gravity variations in Europe from superconducting gravimeters .
    JOURNAL OF GEODYNAMICS 38 325 - 342

Recent satellite missions (CHAMP, GRACE) are now returning data on the time variation of the gravity field with harmonic coefficients computed every 4 weeks. The promise is to achieve a sub-microgal accuracy that will define continental mass variations involving large-scale hydrology. With this in mind, we examine the time varying gravity field over central Europe using a limited number of high quality ground-based superconducting gravimeter stations within the Global Geodynamics Project (GGP). Our purpose is to see whether there are coherent signals between the individual stations and to compare the regional component with that predicted from models of continental hydrology. The results are encouraging. We have found, using empirical orthogonal eigenfunctions of the gravity data that a clear annual signal is present that is consistent in phase (low amplitudes in summer) and amplitude (1-3 microgal) with that determined from a large-scale model of land water in connection with global climate modeling. More work is required to define how the gravity field is related to large-scale soil moisture and other mass variations, and we have yet to compare our results to the latest satellite-derived data. (C) 2004 Elsevier Ltd. All rights reserved.

44. Crossley, D; Hinderer, J; Boy, JP; Pierce, DW , 2005 :
    Empirical orthogonal function (EOF) software .
    GEOPHYSICAL JOURNAL INTERNATIONAL 161 257 - 264

Ground-based gravity observations have the potential to add useful information to the interpretation of data from the new satellite gravity missions (CHAMP, GRACE, GOCE). We examine 4.5 yr of data from eight superconducting gravimeters (SGs) associated with the Global Geodynamics Project (GGP), from 1997 to 2001, and simulate the time variations that might be seen by a satellite. Signals that are removed from the gravity data before spatial averaging are the solid Earth and ocean tides, a global atmospheric loading using a vertical perfect gas law for the atmosphere, International Earth Rotation Service (IERS) polar motion and instrument drift. The 1-d gravity residuals form the basis of an interpolated minimum curvature grid that we spatially average and analyse using both surface polynomials and empirical orthogonal functions (EOFs). A clear annual component is present that, if truly regional, should be easily detectable by a satellite such as GRACE. The signal is consistent with expected continental water storage, which provides some interest for the future comparison of ground and satellite data.

45. Crowley, JW; Mitrovica, JX; Bailey, RC; Tamisiea, ME; Davis, JL , 2008 :
    Annual variations in water storage and precipitation in the Amazon Basin .
    JOURNAL OF GEODESY 82 9 - 13

We combine satellite gravity data from the gravity recovery and climate experiment (GRACE) and precipitation measurements from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center's (CPC) Merged Analysis of Precipitation (CMAP) and the Tropical Rainfall Measuring Mission (TRMM), over the period from mid-2002 to mid-2006, to investigate the relative importance of sink (runoff and evaporation) and source (precipitation) terms in the hydrological balance of the Amazon Basin. When linear and quadratic terms are removed, the time-series of land water storage variations estimated from GRACE exhibits a dominant annual signal of 250 mm peak-to-peak, which is equivalent to a water volume change of similar to 1,800 km(3). A comparison of this trend with accumulated (i.e., integrated) precipitation shows excellent agreement and no evidence of basin saturation. The agreement indicates that the net runoff and evaporation contributes significantly less than precipitation to the annual hydrological mass balance. Indeed, raw residuals between the de-trended water storage and precipitation anomalies range from +/- 40 mm. This range is consistent with stream-flow measurements from the region, although the latter are characterized by a stronger annual signal than our residuals, suggesting that runoff and evaporation may act to partially cancel each other.

46. Crowley, JW; Mitrovica, JX; Bailey, RC; Tamisiea, ME; Davis, JL , 2006 :
    Land water storage within the Congo Basin inferred from GRACE satellite gravity data .
    GEOPHYSICAL RESEARCH LETTERS 33 - L19402

GRACE satellite gravity data is used to estimate terrestrial (surface plus ground) water storage within the Congo Basin in Africa for the period of April, 2002-May, 2006. These estimates exhibit significant seasonal (30 +/- 6 mm of equivalent water thickness) and long-term trends, the latter yielding a total loss of similar to 280 km(3) of water over the 50-month span of data. We also combine GRACE and precipitation data sets (CMAP, TRMM) to explore the relative contributions of the source term to the seasonal hydrological balance within the Congo Basin. We find that the seasonal water storage tends to saturate for anomalies greater than 30-40 mm of equivalent water thickness. Furthermore, precipitation contributed roughly three times the peak water storage after anomalously rainy seasons, in early 2003 and 2005, implying a similar to 60-70% loss from runoff and evapotranspiration. Finally, a comparison of residual land water storage (monthly estimates minus best-fitting trends) in the Congo and Amazon Basins shows an anti-correlation, in agreement with the "see-saw" variability inferred by others from runoff data.

47. Daho, SAB; Fairhead, JD; Zeggai, A; Ghezali, B; Derkaoui, A; Gourine, B; Khelifa, S , 2008 :
    New investigation on the choice of the tailored geopotential model for Algeria .
    JOURNAL OF GEODYNAMICS 45 154 - 162

The choice of the best geopotential model to reduce geodetic data is one of the critical steps in computing the geoid. Several studies have shown that the geopotential models tailored to regional or local gravity data are best suited for high precision geoid computations. Since 2000 a number of geoid models for Algeria have been produced by Geodetic Laboratory of the National Centre of Space Techniques. In particular 5 ' x 5 ' geoid models were generated in 2000, [Benahmed Daho, S. A., 2000. The new gravimetric geoid in Algeria. IGeS Bulletin No. 10 of the International Geoid Service (IGeS). ISSN 1128-3955. pp. 78-84.] and in 2004 [Benahmed Daho, S.A., Fairhead, J.D., 2004. A new quasigeoid computation from gravity and GPS data in Algeria. Newton's Bulletin No. 2. A Joint Bulletin of the Bureau Gravimetrique International and of the International Geoid Service. ISSN 1810-8547. pp. 52-59.] using different data sets and techniques. Although these results were satisfactory and internally consistent they do no have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height. During the same time and with the recent satellite missions CHAMP and GRACE several new global gravity models were released. These lead to substantial improvements of our knowledge of the long-wavelength part of the Earth's gravity field, and thereby of the long-wavelengths of the geoid. For the computation of a new gravimetric geoid model for Algeria we need a new investigation on the choice of the best and optimal geopotential model for the combined solution with local gravimetric and topographic data using the remove-restore technique. In this paper, an analysis was carried out to define the geopotential model, which fits best the local gravity field in Algeria. Six global geopotential models are used in this study: The new GRACE satellite-only and combined models EIGEN-GRACE02S and GGM02C, combined CHAMP and GRACE model EIGEN-CG01C, combined CHAMP and LAGEOS model EIGEN-GL04C, OSU91A and EGM96. The test of the fitting of these high order geopotential models to the gravity field in Algeria is based on the gravity data supplied by the B.G.I. and GETECH, and some of the precise GPS data collected from the international TYRGEONET (TYRhenian GEOdynamical NETWork), ALGEONET (ALGerian GEOdynamical NETWork) projects with baseline length ranging from about 1 to 1000 km. The comparisons were made at all gravity and GPS levelled data by computation of the residual data (i.e. observed data minus model). The geopotential model that provides the closest statistical fit to these data can be assumed to be the most suitable model to adopt for the determination of the new Algerian gravitnetric geoid. The study shows that the newly released combined model (EIGEN-GL04C) is consistently superior to other models in the Algerian region. Its standard deviation fit with GPS/levelling data is 30 cm and 27.5 cm before and after fitting. Hence, we strongly recommend the use of this new model in the computation of the new gravimetric geoid model for Algeria. (c) 2007 Elsevier Ltd. All rights reserved.

48. Davis, JL; Elosequi, P; Mitrovica, JX; Tamisiea, ME , 2004 :
    Climate-driven deformation of the solid Earth from GRACE and GPS .
    GEOPHYSICAL RESEARCH LETTERS 31 - L24605

GRACE data indicate large seasonal variations in gravity that are assumed to be related to climate-driven fluxes of surface water. Seasonal redistribution of surface mass should deform the Earth, and our calculations using GRACE data suggest vertical deformations of similar to13 mm in the region of greatest flux, the Amazon River Basin. To test the GRACE gravity-hydrology connection, we analyzed GPS data acquired from sites in this region. After accounting for degree 1 variations not observable with GRACE, we find that annual deformation measured with GPS correlates highly with predictions calculated from GRACE measurements. These results confirm the variations in surface water sensed by GRACE, which are significantly larger than those predicted by some hydrology models. The results also demonstrate that GRACE can be an important tool for monitoring deformation of the Earth, and suggest that combined analysis of GRACE and GPS may be a useful approach for estimation of geocenter variations.

49. Davis, JL; Tamisiea, ME; Elosegui, P; Mitrovica, JX; Hill, EM , 2008 :
    A statistical filtering approach for Gravity Recovery and Climate Experiment (GRACE) gravity data .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 113 - B04410

We describe and analyze a statistical filtering approach for Gravity Recovery and Climate Experiment (GRACE) data that uses a parameterized model for the temporal evolution of the GRACE coefficients. After least squares adjustment, a statistical test is performed to assess the significance of the estimated parameters. If the test is passed, the parameters are used by the filter in the reconstruction of the field; otherwise, they are rejected. The test is performed, and the filter is formed, separately for annual components of the model and the trend. This new approach is distinct from Gaussian smoothing since it uses the data themselves to test for specific components of the time-varying gravity field. The statistical filter appears inherently to remove most of the "stripes'' present in the GRACE fields, although destriping the fields prior to filtering seems to help the trend recovery. We demonstrate that the statistical filter produces reasonable maps for the annual components and trend. We furthermore assess the statistical filter for the annual components using ground-based GPS data in South America by assuming that the annual component of the gravity signal is associated only with groundwater storage. The undestriped, statistically filtered field has a chi(2) value relative to the GPS data consistent with the best result from smoothing. In the space domain, the statistical filters are qualitatively similar to Gaussian smoothing. Unlike Gaussian smoothing, however, the statistical filter has significant sidelobes, including large negative sidelobes on the north-south axis, potentially revealing information on the errors, and the correlations among the errors, for the GRACE coefficients.

50. de Viron, O; Schwarzbaum, G; Lott, F; Dehant, V , 2005 :
    Diurnal and subdiurnal effects of the atmosphere on the Earth rotation and geocenter motion .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 110 - B11404

[1] The diurnal cycle in the atmospheric angular momentum (AAM) and in the wind and surface pressure fields is studied with a realistic atmospheric general circulation model (GCM) in which the AAM budget is very well closed. For this, we used a 1 year simulation. From a geodetic point of view, we find that this model predicts AAM variations at diurnal timescale which produce a polar motion near 0.2 milliarc second. Additionally, at the same period, the model predicts a geocenter motion of the order of a millimeter. These results are compared with those obtained with the National Centers for Environmental Prediction/ National Center for Atmospheric Research and the European Centre for Medium-Range Weather Forecasts operational analysis data sets. As the AAM budget is not exactly closed in those two data sets, large quantitative differences with the GCM are found. These results witness that there are problems in using AAM values from the major weather prediction center to estimate the AAM and torques variation at diurnal and subdiurnal timescales. We have also computed, for the three models, the spherical harmonics decomposition of the diurnal and semidiurnal surface pressure signals. The results show large differences from one model to another, which advices carefulness when correcting gravity missions ( as Gravity Recovery and Climate Experiment ( GRACE), for instance) from the high-frequency effect of the atmosphere on the orbit, using operational analysis.

51. Desai, SD; Yuan, DN , 2006 :
    Application of the convolution formalism to the ocean tide potential: Results from the Gravity Recovery and Climate Experiment (GRACE) .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 111 - C06023

[ 1] A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment ( GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright ( 1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4 - 5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

52. Ditmar, P; Klees, R; Liu, X , 2007 :
    Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise .
    JOURNAL OF GEODESY 81 81 - 96

Satellite data that are used to model the global gravity field of the Earth are typically corrupted by correlated noise, which can be related to a frequency dependence of the data accuracy. We show an opportunity to take such noise into account by using a proper noise covariance matrix in the estimation procedure. If the dependence of noise on frequency is not known a priori, it can be estimated on the basis of a posteriori residuals. The methodology can be applied to data with gaps. Non-stationarity of noise can also be dealt with, provided that the necessary a priori information exists. The proposed methodology is illustrated with CHAllenging Mini-satellite Payload (CHAMP) data processing. It is shown, in particular, that the usage of a proper noise model can make the measurements of non-gravitational satellite accelerations unnecessarily. This opens the door for high-quality modeling of the Earth's gravity field on the basis of observed orbits of non-dedicated satellites (i.e., satellites without an on-board accelerometer). Furthermore, the processing of data from dedicated satellite missions - GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Explorer) - may also benefit from the proposed methodology.

53. Ditmar, P; Liu, XL , 2007 :
    Dependence of the Earth's gravity model derived from satellite accelerations on a priori information .
    JOURNAL OF GEODYNAMICS 43 189 - 199

Computation of a new Earth's gravity field model is difficult or even impossible if without a priori information about the gravity field. It is important to understand how incorporation of this information at different stages of gravity field modeling could influence the final results. The focus of the paper is on a technique based on satellite accelerations; a version of this technique was used earlier to derive the gravity field model DEOS_CHAMP-01C-70 from a 1-year set of CHAMP data. The technique makes use of both the original kinematic satellite orbit to derive the observed accelerations, and a smoothed orbit to compute the reference accelerations and to detect outliers. Now, using the same data set, we have analyzed how sensitive the obtained results are on the utilization of the a priori knowledge of the Earth's gravity field at different data processing steps. We have found that the final model is not very sensitive on how the smoothed satellite orbit is obtained, though it is advisable that this orbit accounts for a realistic gravity field model. On the contrary, it is crucial that the orbit used to derive the observed satellite accelerations should not be smoothed. Furthermore, it is important to built an accurate stochastic model of data noise. A reasonable way to do so is to analyze the posterior residuals, which are obtained as the difference between the observations and simulations based on a certain gravity field model. The quality of this model is not crucial; it can be obtained from the same data at the stage of trial data processing, i.e. without an accurate stochastic model (at least, if the number of data substantially exceeds the number of unknown parameters). Finally, the quality of gravity field model significantly depends on the reference gravity field. In particular, the EGM96 model noticeably improves the results of CHAMP data processing both at low and at high spherical harmonic degrees. (c) 2006 Elsevier Ltd. All rights reserved.

54. Dobslaw, H; Thomas, M , 2005 :
    Atmospheric induced oceanic tides from ECMWF forecasts .
    GEOPHYSICAL RESEARCH LETTERS 32 - L10615

The usability of ECMWF's forecasts for the determination of diurnal and semidiurnal mass variations in the atmosphere-ocean system due to atmospheric pressure tides is examined and contrasted to corresponding variabilities deduced from ECMWF's analyses. While the diurnal pressure tide and the oceanic response simulated with a baroclinic ocean model are well resolved from both analyses and forecasts, the semidiurnal tide can be recovered from 3 hourly forecasts only. In terms of rms values of geoid height anomalies, forecast errors cause 0.18 mm, different wind representations 0.09 mm, and the doubled temporal resolution 0.20 mm of deviations between forecasts and analyses. Since atmospheric tides are highly variable, a time-invariant harmonic approach might not meet high precision requirements as for the GRACE mission and for high-resolution Earth rotation parameters. Considering these forecast errors, forecasts allow to account for atmospheric variability and corresponding oceanic responses down to semidiurnal timescales, dispensing with any additional model of atmospheric tides.

55. Dobslaw, H; Thomas, M , 2007 :
    Impact of river run-off on global ocean mass redistribution .
    GEOPHYSICAL JOURNAL INTERNATIONAL 168 527 - 532

The impact of river run-off on global ocean mass redistribution is analysed by means of simulations with the baroclinic general circulation model OMCT driven by real-time atmospheric forcing fields from the European Centre for Medium Range Weather Forecasts (ECMWF). River run-off data have been deduced from a Hydrological Discharge Model (HDM) forced with ECMWF data as well. While submonthly mass variability is generally insignificant for GRACE de-aliasing purposes in most oceanic regions, monthly mean mass signals of up to 2 hPa occur in the Arctic Ocean during the melt season. Additionally, from freshwater fluxes due to precipitation, evaporation and river run-off the seasonal variations of total ocean mass are calculated. Correspondence with observed mass variations deduced from monthly GRACE gravity solutions indicates that a combination of ECMWF, HDM and OMCT allows a consistent prognostic simulation of mass exchanges among the atmosphere, ocean and continental hydrosphere. Thus, interpretations of GRACE based mass anomalies should account for both regional and global river run-off effects.

56. Dobslaw, H; Thomas, M , 2007 :
    Simulation and observation of global ocean mass anomalies .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 112 - C05040

[1] Recently reprocessed GRACE gravity fields are found to provide reliable ocean mass anomalies down to 500 km regional averages when comparing them to mass observations obtained from sterically corrected Jason 1 altimetry and simulated mass anomalies derived from the Ocean Model for Circulation and Tides (OMCT). Beside the assessment of systematic shortcomings of GRACE, Jason 1 and OMCT estimates, robust signals of mass anomalies in the North Pacific and in various regions of the Southern Ocean are identified in all three independent data sets. Correlations of up to 0.8 and rms values of differences of around 2 hPa indicate that uncertainties are well below the expected monthly mean mass signals of up to 6 hPa rms in these regions. By means of output of the numerical ocean model, mass anomalies are related to changes in barotropic ocean currents, providing in turn the opportunity to infer barotropic current anomalies from GRACE observations, and therefore principally allowing to monitor climate relevant changes of ocean currents from satellite observations.

57. Dumberry, M , 2008 :
    Decadal variations in gravity caused by a tilt of the inner core .
    GEOPHYSICAL JOURNAL INTERNATIONAL 172 921 - 933

A tilt of the geometric figure of the inner core with respect to the mantle results in a global internal mass displacement. This comprises two parts: the redistribution of mass from the rigid equatorial rotation of the elliptical inner core; and that from global elastic deformations that occur to maintain the mechanical equilibrium. This global mass reorganization leads to changes in the moment of inertia tensor and, equivalently, to changes in the degree 2 component of the gravitational field. In this work, we compute the predicted changes in both gravity and in the moment of inertia tensor as a function of inner core tilt. We show that the inclusion of elastic deformations increases the amplitude of the gravity change at the surface by a factor 1.97. The Stokes coefficients that are the most affected are C-21, S-21: a tilt angle of 0.05 degrees leads to a change in these coefficients of similar to 4 x 10(-11), while leading to changes in other coefficients of degree 2 that are three orders of magnitude smaller. Observed changes in C-21, S-21 and in polar motion contain decadal variations of undetermined origin; in an effort to determine whether these could be caused by temporal changes in inner core tilt, we compute the changes in C-21, S-21 based on the observed polar motion and compare this prediction against observed variations as determined by satellite laser ranging (SLR) between 1985 and 2005. We show that observed decadal changes in C-21, S-21 and in polar motion suggest that both are predominantly driven by variations in the moment of inertia tensor. The source of these variations cannot be unambiguously determined, nor can we confirm whether they are of internal or surficial origin. Changes in inner core tilt are then not necessarily the cause of these variations, though if they are, our results show that motion in the fluid core must not play a significant role in the global angular momentum balance.

58. Ellmann, A , 2005 :
    Two deterministic and three stochastic modifications of Stokes's formula: a case study for the Baltic countries .
    JOURNAL OF GEODESY 79 11 - 23

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8-5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.

59. Ellmann, A; Vanicek, P , 2007 :
    UNB application of Stokes-Helmert's approach to geoid computation .
    JOURNAL OF GEODYNAMICS 43 200 - 213

Over the past two decades the so-called Stokes-Helmert method has been used for regional geoid determination at the University of New Brunswick (UNB). The present contribution summarizes the main principles of the UNB approach and successive theoretical developments. A two-space set-up is used for formulating the boundary value problem and defining gravity quantities, which would be appropriate for downward continuation from the Earth's surface to the geoid level. Focus of this paper is given on the topographical effects, which are formulated in their spherical form. UNB's solution of the Stokes boundary value problem employs a modified Stokes's formula in conjunction of the low-degree contribution of a global geopotential model (GGM). Various aspects at the regional geoid computations in the context of UNB's principles are illustrated by employing a new GRACE satellite mission based geopotential model for the numerical study. The new gravimetric geoid model is compared with local GPS-levelling data. Possible reasons of the detected discrepancies between the gravimetric geoid model and the control points are discussed. (c) 2006 Elsevier Ltd. All rights reserved.

60. Fan, Y; van den Dool, H , 2004 :
    Climate Prediction Center global monthly soil moisture data set at 0.5 degrees resolution for 1948 to present .
    JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES 109 - D10102

[ 1] We have produced a 0.5degrees x 0.5degrees monthly global soil moisture data set for the period from 1948 to the present. The land model is a one-layer "bucket'' water balance model, while the driving input fields are Climate Prediction Center monthly global precipitation over land, which uses over 17,000 gauges worldwide, and monthly global temperature from global Reanalysis. The output consists of global monthly soil moisture, evaporation, and runoff, starting from January 1948. A distinguishing feature of this data set is that all fields are updated monthly, which greatly enhances utility for near-real-time purposes. Data validation shows that the land model does well; both the simulated annual cycle and interannual variability of soil moisture are reasonably good against the limited observations in different regions. A data analysis reveals that, on average, the land surface water balance components have a stronger annual cycle in the Southern Hemisphere than those in the Northern Hemisphere. From the point of view of soil moisture, climates can be characterized into two types, monsoonal and midlatitude climates, with the monsoonal ones covering most of the low-latitude land areas and showing a more prominent annual variation. A global soil moisture empirical orthogonal function analysis and time series of hemisphere means reveal some interesting patterns ( like El Nino-Southern Oscillation) and long-term trends in both regional and global scales.

61. Featherstone, WE , 2007 :
    Augmentation of AUSGeoid98 with GRACE satellite gravity data .
    JOURNAL OF SPATIAL SCIENCE 52 75 - 86

The AUSGeoid98 gravimetric quasigeoid model of Australia is augmented in the medium- and long-wavelength bands by removing its EGM96 basis and replacing this with GGM02C and EIGEN-GL04C, whose long wavelengths are derived from Gravity Recovery And Climate Experiment (GRACE) satellite gravimetry. No significant improvement over AUSGeoid98 is seen: agreements with GPS-levelling change from +/-28 cm to +/-27 cm (acknowledging distortions in the levelling); agreements with astrogeodetic vertical deflections do not change, remaining at about +/-1 arc-second. While this remove-replace approach is not theoretically exact, it is likely that errors in the terrestrial gravity data are contaminating these combined GRACE solutions in the medium wavelengths over Australia.

62. Fengler, MJ; Freeden, W; Kohlhaas, A; Michel, V; Peters, T , 2007 :
    Wavelet modeling of regional and temporal variations of the earth's gravitational potential observed by GRACE .
    JOURNAL OF GEODESY 81 5 - 15

This work is dedicated to the wavelet modeling of regional and temporal variations of the Earth's gravitational potential observed by the GRACE (gravity recovery and climate experiment) satellite mission. In the first part, all required mathematical tools and methods involving spherical wavelets are provided. Then, we apply our method to monthly GRACE gravity fields. A strong seasonal signal can be identified which is restricted to areas where large-scale redistributions of continental water mass are expected. This assumption is analyzed and verified by comparing the time-series of regionally obtained wavelet coefficients of the gravitational signal originating from hydrology models and the gravitational potential observed by GRACE. The results are in good agreement with previous studies and illustrate that wavelets are an appropriate tool to investigate regional effects in the Earth's gravitational field.

63. Fengler, MJ; Michel, D; Michel, V , 2006 :
    Harmonic spline-wavelets on the 3-dimensional ball and their application to the reconstruction of the Earth's density distribution from gravitational data at arbitrarily shaped satellite orbits .
    ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 86 856 - 873

We introduce splines for the approximation of harmonic functions on a 3-dimensional ball. Those splines are combined with a multiresolution concept. More precisely, at each step of improving the approximation we add more data and, at the same time, reduce the hat-width of the used spline basis functions. Finally, a convergence theorem is proved. One possible application, that is discussed in detail, is the reconstruction of the Earth's density distribution from gravitational data obtained at a satellite orbit. This is an exponentially ill-posed problem where only the harmonic part of the density can be recovered since its orthogonal complement has the potential 0. Whereas classical approaches use a truncated singular value decomposition (TSVD) with the well-known disadvantages like the non-localizing character of the used spherical harmonics and the bandlimitedness of the solution, modem regularization techniques use wavelets allowing a localized reconstruction via convolutions with kernels that are only essentially large in the region of interest. The essential remaining drawback of a TSVD and the wavelet approaches is that the integrals (i.e. the inner product in case of a TSVD and the convolution in case of wavelets) are calculated on a spherical orbit, which is not given in reality. Thus, simplifying modelling assumptions, that certainly include a modelling error, have to be made. The splines introduced here have the important advantage, that the given data need not be located on a sphere but may be (almost) arbitrarily distributed in the outer space of the Earth. This includes, in particular, the possibility to mix data from different satellite missions (different orbits, different derivatives of the gravitational potential) in the calculation of the Earth's density distribution. Moreover, the approximating splines can be calculated at varying resolution scales, where the differences for increasing the resolution can be computed with the introduced spline-wavelet technique. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

64. Fenoglio-Marc, L; Kusche, J; Becker, M , 2006 :
    Mass variation in the Mediterranean Sea from GRACE and its validation by altimetry, steric and hydrologic fields .
    GEOPHYSICAL RESEARCH LETTERS 33 - L19606

The seasonal seawater mass variation in the Mediterranean Sea is estimated between April 2002 and July 2004 from GRACE and altimetry data and from hydrologic and oceanographic models. A smoothed spatial averaging kernel is applied to each field, in order to obtain comparable basin averages. The GRACE seawater mass corrected for the leakage of continental hydrology and the filtered steric-corrected altimeter sea level have similar annual amplitude and phase. To restore the magnitude of the GRACE-derived water mass signal we apply a scaling factor to the smoothed annual amplitude. The estimated scaled mass signal has an annual amplitude of 52 +/- 17 mm peaking in November. We combine the seawater mass variation with the Mediterranean freshwater deficit and obtain a net flow at the Strait of Gibraltar with annual amplitude of 60 +/- 25 mm/month (0.06 Sv) and maximum in September.

65. Fenoglio-Marc, L; Kusche, J; Becker, M; Fukumori, I , 2007 :
    Comment on "On the steric and mass-induced contributions to the annual sea level variations in the Mediterranean Sea'' by David Garcia et al. .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 112 - C12018
66. Fleming, K; Martinec, Z; Hagedoorn, J , 2004 :
    Geoid displacement about Greenland resulting from past and present-day mass changes in the Greenland Ice Sheet .
    GEOPHYSICAL RESEARCH LETTERS 31 - L06617

Predictions are presented of secular changes in the geoid arising from glacial-isostatic adjustment (GIA) following the Last Glacial Maximum and from present-day mass changes in the Greenland Ice Sheet (GIS). Geoid displacement from ongoing GIA is dominated by ice-load changes outside of Greenland at lower spherical-harmonic degrees (< 30), and modified at higher degrees by the recent ( last few thousand years) GIS history. Ice-margin mass changes dominate the present-day GIS geoid response, although comparable signals are obtained when considering the uncertainty range in the higher-elevation changes (> 2000 m). Spatial variability is noted when the present-day GIS response is expanded to degree and order 32. This is detectable by GRACE when assuming an optimistic accuracy, but is too small by a factor of ca. 3 for an alternate accuracy estimate. Present-day GIS geoid displacement rates are generally less than the equivalent response from ice-mass changes in Antarctica, Patagonia and Alaska.

67. Flury, J , 2004 :
    Ice mass balance and ice dynamics from satellite gravity missions .
    EARTH MOON AND PLANETS 94 83 - 91

An overview of advances in ice research which can be expected from future satellite gravity missions is given. We compare present and expected future accuracies of the ice mass balance of Antarctica which might be constrained to 0.1-0.3 mm/year of sea level equivalent by satellite gravity data. A key issue for the understanding of ice mass balance is the separation of secular and interannual variations. For this aim, one would strongly benefit from longer uninterrupted time series of gravity field variations (10 years or more). An accuracy of 0.01 mm/year for geoid time variability with a spatial resolution of 100 km would improve the separability of ice mass balance from mass change due to glacial isostatic adjustment and enable the determination of regional variations in ice mass balance within the ice sheets. Thereby the determination of ice compaction is critical for the exploitation of such high accuracy data. A further benefit of improved gravity field models from future satellite missions would be the improvement of the height reference in the polar areas, which is important for the study of coastal ice processes. Sea ice thickness determination and modelling of ice bottom topography could be improved as well.

68. Flury, J , 2006 :
    Short-wavelength spectral properties of the gravity field from a range of regional data sets .
    JOURNAL OF GEODESY 79 624 - 640

The GRACE (gravity recovery and climate experiment) and GOCE (gravity field and steady-state ocean circulation explorer) dedicated gravity satellite missions are expected to deliver the long-wavelength scales of the Earth's gravity field with extreme precision. For many applications in Earth sciences, future research activities will have to focus on a similar precision on shorter scales not recovered by satellite missions. Here, we investigate the signal power of gravity anomalies at such short scales. We derive an average degree variance and power spectral density model for topography-reduced gravity anomalies (residual terrain model anomalies and de-trended refined Bouguer anomalies), which is valid for wavelengths between 0.7 and 100 km. The model is based on the analysis of gravity anomalies from 13 test regions in various geographical areas and geophysical settings, using various power spectrum computation approaches. The power of the derived average topography-reduced model is considerably lower than the Tscherning-Rapp free air anomaly model. The signal power of the individual test regions deviates from the obtained average model by less than a factor of 4 in terms of square-root power spectral amplitudes. Despite the topographic reduction, the highest signal power is found in mountainous areas and the lowest signal power in flat terrain. For the derived average power spectral model, a validation procedure is developed based on least-squares prediction tests. The validation shows that the model leads to a good prediction quality and realistic error measures. Therefore, for least-squares prediction, the model could replace the use of autocovariance functions derived from local or regional data.

69. Flury, J; Rummel, R , 2004 :
    Future satellite gravimetry for geodesy .
    EARTH MOON AND PLANETS 94 13 - 29

After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is shown based on the analysis of spectral signal power of various gravity field components and on the comparison with current knowledge and expected performance of GRACE and GOCE. Both, accuracy and resolution can be improved by future dedicated gravity satellite missions. For applications in geodesy, the spectral omission error due to the limited spatial resolution of a gravity satellite mission is a limiting factor. The recommended strategy is to extend as far as possible the spatial resolution of future missions, and to improve at the same time the modelling of the very small scale components using terrestrial gravity information and topographic models.We discuss the geodetic needs in improved gravity models in the areas of precise height systems, GNSS levelling, inertial navigation and precise orbit determination. Today global height systems with a 1 cm accuracy are required for sea level and ocean circulation studies. This can be achieved by a future satellite mission with higher spatial resolution in