We have analyzed recent gravity recovery and climate experiment (GRACE) RL04 monthly gravity solutions, using a new decorrelating post-processing approach. We find very good agreement with mass anomalies derived from a global hydrological model. The post-processed GRACE solutions exhibit only little amplitude damping and an almost negligible phase shift and period distortion for relevant hydrological basins. Furthermore, these post-processed GRACE solutions have been inspected in terms of data fit with respect to the original inter-satellite ranging and to SLR and GPS observations. This kind of comparison is new. We find variations of the data fit due to solution post-processing only within very narrow limits. This confirms our suspicion that GRACE data do not firmly 'pinpoint' the standard unconstrained solutions. Regarding the original Kusche (J Geod 81:733–749, 2007) decorrelation and smoothing method, a simplified (order-convolution) approach has been developed. This simplified approach allows to realize a higher resolution—as necessary, e.g., for generating computed GRACE observations—and needs far less coefficients to be stored.

Time-variable gravity data of the GRACE (Gravity Recovery And Climate Experiment) satellite mission provide global information on temporal variations of continental water storage. In this study, we incorporate GRACE data for the first time directly into the tuning process of a global hydrological model to improve simulations of the continental water cycle. For the WaterGAP Global Hydrology Model (WGHM), we adopt a multi-objective calibration framework to constrain model predictions by both measured river discharge and water storage variations from GRACE and illustrate it on the example of three large river basins: Amazon, Mississippi and Congo. The approach leads to improved simulation results with regard to both objectives. In case of monthly total water storage variations we obtained a RMSE reduction of about 25 mm for the Amazon, 6 mm for the Mississippi and 1 mm for the Congo river basin. The results highlight the valuable nature of GRACE data when merged into large-scale hydrological modeling. Furthermore, they reveal the utility of the multi-objective calibration framework for the integration of remote sensing data into hydrological models.

Approximately seven years of time-variable gravity data from the satellite mission Gravity Recovery and Climate Experiment (GRACE) are available to quantify present-day mass variations on and near the Earth's surface. Mass variations caused by the continental water cycle are the dominant signal component after subtracting contributions from atmosphere and oceans. This makes hydrology a primary area of application of GRACE data. To derive water storage variations at the scale of large river basins, appropriate filter techniques have to be applied to GRACE gravity fields given in a global spherical harmonic representation. A desirable filter technique minimises both GRACE data error and signal leakage across the border of the region of interest. This study evaluates the performance of six widely used filter methods (isotropic filters, anisotropic filters and decorrelation methods) and their parameter values to derive regionally averaged water mass variations from GRACE data. To this end, filtered time series from GRACE for 22 of the world's largest river basins were compared to continental water mass variations from a multimodel mean of three global hydrological models (WGHM, GLDAS and LaD). Filter-induced biases for seasonal amplitudes and phases of water storage variations, as well as satellite and leakage error budgets, were quantified for each river basin and explained in terms of storage variations in and around the basin. The optimum filter types and filter parameters were identified for each basin. The best results were provided by a decorrelation method that uses GRACE orbits for the filter design. Our ranking between all filter types and parameters depended on the geographical location, shape and signal characteristics of the specific river basin. Based on a multicriterial evaluation of satellite and leakage error, as well as an error assessment of the hydrological data, the filter selection and parameter optimisation results were shown to be reliable for 17 river basins. The results serve as a guideline for the optimal filtering of GRACE global spherical harmonic coefficients for hydrological applications.

The main objective of the US-German twin-satellite mission GRACE (Gravity Recovery and Climate Experiment), launched in March 2002, is a precise survey of the Earth’s time-variable gravity field at unprecedented temporal and spatial scales. Temporal changes in the gravity field are related to continuous mass redistributions near the Earth’s surface which are caused by various geophysical and climatologically driven processes. Vice versa, transferring the GRACE-based gravity variations into time series of the spatial variability of surface mass anomalies, the mission allows for the first time for a quantification of the ongoing mass transport. Such data is of unique importance for a comprehensive modeling, understanding and interplay of these processes. In this contribution we give an overview of the basic features of the GRACE satellite mission, the gravity recovery process and the derived gravity products at GeoForschungsZentrum Potsdam (GFZ), as well as the interpretation of the GRACE gravity data with the focus on the detection of hydrological signals. This includes a description of the evolution and present status of the quality of GFZ’s GRACE-based global gravity models on the actual fourth model generation (called GFZ-RL04), and an overview of recent findings using GRACE data in hydrological applications.

Seasonal and inter-annual change in land water storage (expressed in terms of water volume change) over 27 large river basins worldwide are estimated from monthly GRACE geoids solutions computed at GFZ from February 2003 to February 2006. The largest annual water volume change is found in the Amazon basin, followed by the Parana, Ob, Orinoco, Tocantins, Niger, Congo, Ganges, Mekong, and Brahmaputra. In terms of trend over the 3-year period, positive and negative values are observed but in a number of cases computed trends are at the noise level. However significant negative trends are found in the Amazon, Ganges, Mississippi, Nile, Parana, and Zambezi basins, indicating water mass loss over that period. Positive trends (water mass gain) are marginally significant. We have computed the land water contribution to sea level change. On average over the 3-year time span, we find that the net effect is positive (net loss of water in terrestrial reservoirs), on the order of 0.19+/−0.06 mm/yr. If sustained over a longer time span than considered here, such a value may become comparable to the ice sheets contribution to sea level rise.

If we restrict the spatial resolution to a half-wavelength of about 1500 km and the temporal resolution to 1 month, GRACE-derived temporal gravity variations can be resolved within the μgal (10-8 m/s2) range. A comparison with ground gravity measurements from selected Superconducting Gravimeter (SG) stations forming the Global Geodynamics Project (GGP) provides an independent validation. For this study, five European SGstations were selected that both cover a large test field and allow closely located SG-stations to be studied. Prior to this comparison, GRACE and SG data sets have to be reduced for the same known gravity effects due to Earth and ocean tides, pole tide, and atmosphere. After these reductions, the remaining part can be mainly attributed to mass changes in terrestrial water storage. For this reason, gravity variations derived from global hydrological models are included in the comparison of SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. For most of the SG locations investigated here, the comparison based primarily on computed correlations shows quite a good agreement among the gravity variation derived from the three different kinds of data sets: SG, GRACE, and hydrology models. The variations in SG gravity (point measurements) prove to be representative for a large area within the μgal accuracy range, if local gravity effects are removed correctly. Additionally, a methodology for an analysis of dominant common features based on the EOF-technique is proposed and illustrated. The first principal component shows strong periodicity, and the search for arbitrary periods confirms a strong common annual component, which reduces the total signal content considerably. The first eigenvector reveals common features and differences between distinct SG stations. Discrepancies between SG, GRACE, and hydrology models at individual SG stations, detected by both methods, may provide valuable hints for further investigations of respective data series.

This study aims at the calibration of the formal variance covariance matrices of monthly GRACE-only gravity models that are known to give too optimistic accuracy measures for derived gravity functionals respectively surface mass anomalies. Based on 16 monthly solutions generated at GFZ Potsdam, a simple degree-dependent scaling of given variance-covariance matrices is considered, using difference degree amplitudes of monthly GRACE-only gravity field models that are separated by 12 months. It turns out that for the recent GFZ models the mean accuracy level of the monthly fields is about 20 - 40 times lower than the GRACE baseline accuracy. An observed scatter of the accuracy of the monthly models can be attributed to the amount of data used to generate the monthly model, but a more significant contribution arises from variations in the ground track coverage from month to month.Error propagation based on variance-covariance matrices calibrated with respect to 20 times the GRACE baseline, indicates that on global average the level of the model uncertainty is well reproduced when compared to residual surface mass variability in the space domain. Comparisons between time series of basin averages of surface mass variations from GRACE and state-of-the-art hydrology models seem to confirm this calibration factor for river basins with large annual mass variations. For basins with small variations the results suggest that a calibration with respect to 40 times the baseline may be a more representative value, however. As a general result it is observed that the formal respectively calibrated variance-covariance matrices of the monthly gravity models do not represent additional spurious gravity signals of significant amplitude caused by aliasing effects.

We analyze spatiotemporal variations of surface mass anomalies induced by hydrological mass redistributions at the Earth's surface. To this end, we use a suite of global hydrological models as well as products from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. As a novelty we identify dominating periodic patterns that are not restricted to the fundamental annual frequency and its overtones, using a method that combines conventional empirical orthogonal functions (EOF) analysis with a determination of sine waves of arbitrary periods from the principal components. We assess the significance of the derived spectra in view of correlated errors of the GRACE data by means of a Monte Carlo technique. This allows us to create filtered GRACE time series including only the significant terms, which will serve for basin‐specific calibration of hydrological models with respect to the dominant periodic water storage variations. The study reveals that besides dominating annual signals, semiannual (found only in a few basins), and also long‐periodic waves in the range of 2.1 to 2.5 years contribute to periodic water storage variations. An interpretation and a preliminary explanation of these spectra is included. Comparisons of the spectra obtained from GRACE and global hydrological models exhibit in many river basins a systematic advance of the phases of annual terms of the hydrological models as compared to GRACE in the range of 1 to 6 weeks. This indicates deficiencies of the hydrological models with regard to runoff routing in the river network and/or water retention in lakes and wetlands.

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10 −8 m / s 2 ) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.

Signatures between monthly global Earth gravity field solutions obtained from GRACE satellite mission data are analyzed with respect to continental water storage variability. GRACE gravity field models are derived in terms of Stokes' coefficients of a spherical harmonic expansion of the gravitational potential from the analysis of gravitational orbit perturbations of the two GRACE satellites using GPS high–low and K-band low–low intersatellite tracking and on-board accelerometry. Comparing the GRACE observations, i.e., the mass variability extracted from temporal gravity variations, with the water mass redistribution predicted by hydrological models, it is found that, when filtering with an averaging radius of 750 km, the hydrological signals generated by the world's major river basins are clearly recovered by GRACE. The analyses are based on differences in gravity and continental water mass distribution over 3- and 6-month intervals during the period April 2002 to May 2003. A background model uncertainty of some 35 mm in equivalent water column height from one month to another is estimated to be inherent in the present GRACE solutions at the selected filter length. The differences over 3 and 6 months between the GRACE monthly solutions reveal a signal of some 75 mm scattering with peak values of 400 mm in equivalent water column height changes over the continents, which is far above the uncertainty level and about 50% larger than predicted by global hydrological models. The inversion method, combining GRACE results with the signal and stochastic properties of a hydrological model as ‘a priori’ in a statistical least squares adjustment, significantly reduces the overall power in the obtained water mass estimates due to error reduction, but also reflects the current limitations in the hydrological models to represent total continental water storage change in particular for the major river basins.

The Gravity Recovery and Climate Experiment ( GRACE) processing centers at the GeoForschungsZentrum Potsdam (GFZ) and the University of Texas Center for Space Research (UTCSR) provide time series of monthly gravity field solutions covering the period since mission launch in March 2002. Although the achieved accuracy still remains an order of magnitude below the mission's baseline goal, these time series have successfully been used to study terrestrial phenomena such as water storage variations. Over the oceans, the monthly gravity field solutions can be converted into estimates of the fluctuating ocean bottom pressure (OBP), which is the sum of atmospheric and oceanic mass variations. The GRACE products may be validated against in situ OBP observations which are available from a ground truth site in the tropical northwest Atlantic Ocean. Large differences are observed between the in situ and GRACE-derived OBP which are investigated by comparing the tidal and nontidal ocean models used at GFZ and UTCSR for dealiasing short-term (<2 months) mass variations from satellite measurements. Results show that the barotropic nontidal and tide models need improvement at periods shorter than 1 day and longer than 2 weeks. On a global scale the monthly OBP fields from GRACE generally overestimate the variability compared to ocean general circulation models, especially in tropical regions. This may be attributed to continuing deficiencies in GRACE data processing. Nevertheless, there is some initial evidence that GRACE possesses the potential to observe large-scale averages of bottom pressure fluctuations.

The focus of this article is on the accelerometer on board the two GRACE (Gravity Recovery and Climate Experiment) satellites. In a first analysis the accelerometer system is studied. The behavior of the test mass and its capacitive feedback system is simulated in the time and the frequency domain for one degree of freedom. Only linear accelerations are considered so far. The second part of the analysis is about the practical implementation of the simulation model: Non-gravitational forces were derived from the GFZ (GeoForschungsZentrum) EPOS (Earth Parameter and Orbit System) software. In a closed loop the accelerometer measurements derived from these data in connection with simulated tracking data have been used for orbit recovery including the estimation of biases and scale factors for the accelerometer data. Details and results of this procedure are presented.Key words. GRACE – sensor analysis – accelerometer

A new model of the Earth's gravity field, called GRIM5‐S1, was prepared in a joint German‐French effort. The solution is based on satellite orbit perturbation analysis and exploits tracking data from 21 satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The satellite‐only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in satellite orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential satellite mission CHAMP and should provide new standards in computing orbits of next altimetric missions like Jason and ENVISAT. The GRIM5‐S1 normals also give the basis for the tracking/surface data combined solution GRIM5‐C1.

The striking improvements in long- to medium-wavelengths gravity field recovery achieved with GPS-CHAMP and GPS-GRACE high-low and GRACE K-band range low-low satellite-to-satellite tracking prompted us to combine the satellite data with surface data from altimetry over the oceans and gravimetry over the continents to generate a new, high resolution global gravity field model: EIGEN-CG01C. The model is complete to degree/order 360 in terms of spherical harmonics and resolves half-wavelengths of 55 km in the geoid and gravity anomaly fields. A special band-limited combination method has been applied in order to preserve the high accuracy from the satellite data in the lower frequency band of the geopotential and to allow for a smooth transition to the high- frequency band, dominated by the surface data. Compared to pre-CHAMP/GRACE global high- resolution gravity field models, the accuracy was improved by one order of magnitude to 4 cm and 0.5 mgal in terms of geoid heights and gravity anomalies, respectively, at a spatial resolution of 200 km half-wavelength. The overall accuracy at degree/order 360 is estimated to be 20 cm and 5 mgal, respectively, and benefits significantly from recently released new gravity anomaly compilations over the polar regions. In general, the accuracy over the oceans is better than over the continents reflecting the higher quality of the available surface data.

In order to exploit the GRACE- based time-variable gravity signals (e.g. in hy- drological modeling of the global water cycle) ap- propriate techniques to separate the relevant hy- drological signal from the integral satellite grav- ity data will be needed. Recent investigations focus on comparisons on the basis of time vari- ations of the Earth gravity field reconstructed from monthly GRACE-only gravity field solu- tions and global hydrological models. This shows both pronounced similarities and considerable dierences. On the other hand, since the same holds for comparisons between various state-of- the-art hydrology models, a more general view on the morphology of time-variable gravity sig- nals due to hydrological mass redistributions will be needed. In a preparatory study to this end we have investigated time-variable signals derived from three dieren t state-of-the-art global hy- drology models and from recent time series of monthly GRACE-only gravity models. In or- der to infer common characteristic features from the distinct data sources we use spectral coher- ence analysis and Empirical Orthogonal Func- tions analysis in the space domain. The contri- bution presents current results.