GRACE Gravity Field Solutions Research Articles

A decorrelation filter based on the full error covariance of GRACE gravity field solutions

A decorrelation filter based on the full error covariance of GRACE gravity field solutions

Daily GRACE gravity field solutions track major flood events in the Ganges–Brahmaputra Delta

Abstract. Two daily gravity field solutions based on observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are evaluated against daily river runoff data for major flood events in the Ganges–Brahmaputra Delta (GBD) in 2004 and 2007. The trends over periods of a few days of the daily GRACE data reflect temporal variations in daily river runoff during major flood events. This is especially true for the larger flood in 2007, which featured two distinct periods of critical flood level exceedance in the Brahmaputra River. This first hydrological evaluation of daily GRACE gravity field solutions based on a Kalman filter approach confirms their potential for gravity-based large-scale flood monitoring. This particularly applies to short-lived, high-volume floods, as they occur in the GBD with a 4–5-year return period. The release of daily GRACE gravity field solutions in near-real time may enable flood monitoring for large events.

Improved daily GRACE gravity field solutions using a Kalman smoother

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure.The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations.From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.

Non-tidal atmospheric and oceanic mass variations and their impact on GRACE data analysis

Short term mass variations cannot be measured adequately by GRACE due to undersampling. Therefore, they are removed from the measurements beforehand using geophysical models (de-aliasing). As GRACE data analysis has not yet reached ultimate accuracy, one presumes that inadequate de-aliasing and geophysical model uncertainties are one possible reason for this. The standard GRACE de-aliasing procedure disregards geophysical model (atmospheric and oceanic) errors, therefore a procedure has been developed to take atmospheric and oceanic uncertainties into account. Thereby, we expect to improve the de-aliasing product and the resulting GRACE gravity field models. As the GRACE results are used for geophysical interpretations, any increase in accuracy will lead to a better understanding of geophysical processes. The paper summarizes the results of this work. First, the standard de-aliasing process as well as the new procedure, which is able to take geophysical model uncertainties into account, is summarized. After the definition of the performed error scenarios, an overview and discussion of the applied atmospheric and oceanic error maps is given. Finally, the impact of the previously defined error scenarios on the de-aliasing coefficients as well as on a GRACE gravity field solution is investigated. K-band range-rate satellite-to-satellite tracking (KBRR) residuals, as an intermediate gravity field result and gravity field solutions based on the applied error scenarios are analyzed. From the results obtained so far it can be concluded that GRACE results or rather KBRR residuals are sensitive to atmospheric and oceanic model errors. Depending on the error structure of the introduced model uncertainties, KBRR residuals could have been reduced. However, it has to be stated that with respect to the current GRACE error budget, atmospheric and oceanic model uncertainties seem not to play a prominent role in the accuracy of current GRACE gravity field solutions. Nevertheless, further and deeper analysis of the KBRR residuals is needed, as (positive) effects of model uncertainties are visible here.

Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons

Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved.

Ocean contribution to co-seismic crustal deformation and geoid anomalies: Application to the 2004 December 26 Sumatra–Andaman earthquake

Large earthquakes do not only heavily deform the crust in the vicinity of the fault, they also change the gravity field of the area affected by the earthquake due to mass redistribution in the upper layers of the Earth. Besides that, for sub-oceanic earthquakes deformation of the ocean floor causes relative sea level changes and mass redistribution of water that have again a significant effect on the gravity field. To model these deformations, sea level changes and gravity field perturbations self-consistently we use an adapted version of the sea level equation (SLE) that has been used for glacial isostatic adjustment studies. The sea level equation, next to our normal mode model for seismic solid earth modeling, allows us to compute a gravitationally self-consistent solution for the co-seismic relative sea level, surface deformation and geoid height changes. We apply our geographically detailed models to the case of the 2004 December 26 Sumatra–Andaman earthquake. Recent studies that have modeled the ocean mass effect on co-seismic gravity change for this specific earthquake show model results that indicate a broad negative change in geoid height around the fault due to ocean water redistribution (de Linage et al., 2009; Melini et al., 2010). Our model results for the ocean contribution to geoid height differ from these studies in the sense that we find a pattern similar to the elongated dipole pattern of the solid earth model outputs for gravity and vertical deformation, together with a relatively small broad negative geoid height change. We explain the relation between outcomes for geoid height, relative sea level and vertical deformation of the ocean floor and we confront our model results with a least squares estimation of the co-seismic discontinuity in GRACE-derived gravity field time series. We show that taking into account the contribution of ocean water redistribution to the co-seismic geoid height change next to a compressible solid earth model is essential to explain the predominant negative co-seismic geoid anomalies from the GRACE gravity field solutions. Besides, we introduce a detailed approach to modeling an earthquake in a normal mode model that better approximates realistic continuous slip on the fault plane than models that do not distribute slip with depth. To demonstrate the importance of the slip distribution we show the differences in outcomes for modeled geoid height and vertical deformation.

Hydrological Excitation of Polar Motion Derived from GRACE Gravity Field Solutions

The influence of the continental water storage on the polar motion is not well known. Different models have been developed to evaluate these effects and compared to geodetic observations. However, previous studies have shown large discrepancies mainly attributed to the lack of global measurements of related hydrological parameters. Now, from the observations of the GRACE mission, we can estimate the polar motion excitation due to the global hydrology. Data processing of GRACE data is carried out by several centers of analysis, we focus on the new solution computed by the Groupe de Recherche de Géodésie Spatiale. At annual scales, excitations derived from GRACE data are in better agreement with geodetic observations than models estimates. The main contribution to the hydrological excitation comes from the monsoon climates regions where GRACE and models estimates are in a very good agreement. Still, the effect of the north high latitudes regions, where the principal areas of snow cover are found, cannot be neglected. At these regions, GRACE and models estimated contributions to polar motion excitations show significant discrepancies. Finally, GRACE-based excitations reveal the possible influence of water storage variations in exciting polar motion around the frequency of 3 cycles per year.

Propagation of atmospheric model errors to gravity potential harmonics-impact on GRACE de-aliasing

SUMMARY High-frequency, time-varying mass redistributions in the ocean and atmosphere have an impact on GRACE gravity field solutions due to the space–time sampling characteristics of signal and orbit. Consequently, aliasing of these signals into the GRACE observations is present and needs to be taken into account during data analysis by applying atmospheric and oceanic model data (de-aliasing). As the accuracy predicted prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties are regarded as a potential error source in GRACE gravity field determination. Therefore, this study aims to improve the de-aliasing process in order to obtain a more accurate GRACE gravity field time-series. As these time-series provide estimates for the integrated mass transport in the Earth system, like the global water cycle and solid Earth geophysical processes, any increase in accuracy will lead to improvements in the geophysical interpretation of the results. So in conclusion, improving the de-aliasing is of relevance for a better understanding of geophysical processes. By no longer regarding the atmosphere and ocean model output as error-free, deeper insight into the impact of such uncertainties on the de-aliasing and on the resulting GRACE gravity field models can be obtained. For this purpose, in a first step, a full error propagation of the atmospheric and oceanic model parameters up to the de-aliasing gravity field coefficients is performed and the GRACE K-Band-Satellite-to-Satellite Tracking (KBR-SST) residuals, as an intermediate gravity field result, are analysed. The paper reviews the standard GRACE de-aliasing process and presents the mathematical model applied for the error propagation. Specifically, the effect of uncertainties in the atmospheric input parameters (temperature, surface pressure, specific humidity, geopotential) on the gravity field potential coefficients used for de-aliasing is shown in several scenarios. Finally, the impact of dealiasing products (with and without error propagation) on a GRACE gravity field solution is investigated on the level of observation residuals. From the results obtained in this study it can be concluded that with respect to the current GRACE error budget, atmospheric model uncertainties do not play a prominent role in the error budget of current GRACE gravity field solutions. Nevertheless, in order to fully exploit the GRACE measurements towards the baseline accuracy, an optimized de-aliasing is needed. In this case, GRACE gravity field solutions are sensitive to uncertainties in atmospheric and oceanic models. Thus, the associated geophysical model errors shall be taken into account in the de-aliasing process.

Time‐variable gravity from GRACE: First results

Eleven monthly GRACE gravity field solutions are now available for analyses. We show those fields can be used to recover monthly changes in water storage, both on land and in the ocean, to accuracies of 1.5 cm of water thickness when smoothed over 1000 km. The amplitude of the annually varying signal can be determined to 1.0 cm. Results are 30% better for a 1500 km smoothing radius, and 40% worse for a 750 km radius. We estimate the annually varying component of water storage for three large drainage basins (the Mississippi, the Amazon, and a region draining into the Bay of Bengal), to accuracies of 1.0–1.5 cm.