Gravity Field And Steady-state Ocean Circulation Explorer Observations Research Articles

GOCE-Derived Coseismic Gravity Gradient Changes Caused by the 2011 Tohoku-Oki Earthquake

In contrast to most of the coseismic gravity change studies, which are generally based on data from the Gravity field Recovery and Climate Experiment (GRACE) satellite mission, we use observations from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) Satellite Gravity Gradient (SGG) mission to estimate the coseismic gravity and gravity gradient changes caused by the 2011 Tohoku-Oki Mw 9.0 earthquake. We first construct two global gravity field models up to degree and order 220, before and after the earthquake, based on the least-squares method, with a bandpass Auto Regression Moving Average (ARMA) filter applied to the SGG data along the orbit. In addition, to reduce the influences of colored noise in the SGG data and the polar gap problem on the recovered model, we propose a tailored spherical harmonic (TSH) approach, which only uses the spherical harmonic (SH) coefficients with the degree range 30–95 to compute the coseismic gravity changes in the spatial domain. Then, both the results from the GOCE observations and the GRACE temporal gravity field models (with the same TSH degrees and orders) are simultaneously compared with the forward-modeled signals that are estimated based on the fault slip model of the earthquake event. Although there are considerable misfits between GOCE-derived and modeled gravity gradient changes (ΔVxx, ΔVyy, ΔVzz, and ΔVxz), we find analogous spatial patterns and a significant change (greater than 3σ) in gravity gradients before and after the earthquake. Moreover, we estimate the radial gravity gradient changes from the GOCE-derived monthly time-variable gravity field models before and after the earthquake, whose amplitudes are at a level over three times that of their corresponding uncertainties, and are thus significant. Additionally, the results show that the recovered coseismic gravity signals in the west-to-east direction from GOCE are closer to the modeled signals than those from GRACE in the TSH degree range 30–95. This indicates that the GOCE-derived gravity models might be used as additional observations to infer/explain some time-variable geophysical signals of interest.

Seasonal variations of thermospheric mass density at dawn/dusk from GOCE observations

Abstract. Thermospheric mass densities from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite for Sun-synchronous orbits between 83.5∘ S and 83.5∘ N, normalized to 270 km during 2009–2013, have been used to develop an empirical mass density model at dawn/dusk local solar time (LST) sectors based on the empirical orthogonal function (EOF) method. The main results of this study are that (1) the dawn densities peak in the polar regions, but the dusk densities maximize in the equatorial regions; (2) the relative seasonal variations to the annual mean have similar patterns across all latitudes regardless of solar activity conditions; (3) the seasonal density variations show obvious hemispheric asymmetry, with large amplitudes in the Southern Hemisphere; (4) both amplitude and phase of the seasonal variations have strong latitudinal and solar activity dependences, with high amplitude for the annual variation at higher latitudes and semiannual variation at lower latitudes; (5) the annual asymmetry and effect of the Sun–Earth distance vary with latitude and solar activity. Keywords. Atmospheric composition and structure (pressure, density, and temperature)

Distributed fault slip model for the 2011 Tohoku‐Oki earthquake from GNSS and GRACE/GOCE satellite gravimetry

AbstractThe Gravity Recovery and Climate Experiment (GRACE) mission (launched 2002) and the Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) mission (March 2009 to November 2013) collected spaceborne gravity data for the preseismic and postseismic periods of the 2011 Tohoku‐Oki earthquake. In addition, the dense Japan GeoNet Global Navigation Satellite Systems (GNSS) network measured with approximately 1050 stations the coseismic and postseismic surface displacements. We use a novel combination of GNSS, GRACE, and GOCE observations for a distributed fault slip model addressing the issues with gravimetric and geometric change over consistent time windows. Our model integrates the coseismic and postseismic effects as we include GOCE observations averaged over a 2 year interval, but their inclusion reveals the gravity change with unprecedented spatial accuracy. The gravity gradient grid, evaluated at GOCE orbit height of 265 km, has an estimated formal error of 0.20 mE which provides sensitivity to the mainly coseismic and integrated postseismic‐induced gravity gradient signal of −1.03 mE. We show that an increased resolution of the gravity change provides valuable information, with GOCE gravity gradient observations sensitive to a more focused slip distribution in contrast to the filtered GRACE equivalent. The 2 year averaging window of the observations makes it important to incorporate estimates of the variance/covariance of unmodeled processes in the inversion. The GNSS and GRACE/GOCE combined model shows a slip pattern with 20 m peak slip at the trench. The total gravity change (≈200 μGal) and the spatial mapping accuracy would have been considerably lower by omitting the GOCE‐derived fine‐scale gravity field information.

EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission

AbstractAfter more than 4.5 years in orbit, the Gravity field and steady‐state Ocean Circulation Explorer (GOCE) mission ended with the reentry of the satellite on 11 November 2013. This publication serves as a reference for the fifth gravity field model based on the time‐wise approach (EGM_TIM_RL05), a global model only determined from GOCE observations. Due to its independence of any other gravity data, a consistent and homogeneous set of spherical harmonic coefficients up to degree and order 280 (corresponding to spatial resolution of 71.5 km on ground) is provided including a full covariance matrix characterizing the uncertainties of the model. The associated covariance matrix realistically describes the model quality. It is the first model which is purely based on GOCE including all observations collected during the entire mission. The achieved mean global accuracy is 2.4 cm in terms of geoid heights and 0.7 mGal for gravity anomalies at a spatial resolution of 100 km.

Comparison of GGMs based on one year GOCE observations with the EGM08 and terrestrial data over the area of Sudan

Since 2010, a series of Global Geopotential Models (GGMs) based on Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravimetry mission have been released. In this study, the GGMs based on approximately 12 months of GOCE satellite gravity gradiometry (SGG) data have been compared over the area of Sudan with the EGM08 and terrestrial data. Geoid heights and free-air gravity anomalies from four GOCE/GRACE satellite-only GGMs, and one GOCE/GRACE GGM combined with terrestrial/altimetric gravity data were compared with the corresponding ones obtained from the EGM08, terrestrial free-air gravity anomalies and GNSS/levelling data.The results reveal that geoid heights and free-air gravity anomalies obtained from the GOCE-based GGMs agree with the corresponding ones from the EGM08 truncated to d/o 200 with standard deviation of 18–20cm, and 3.4–4.2mGal, respectively. Their agreement with the terrestrial free-air gravity anomalies and the GNSS/levelling geoid heights, in terms of standard deviation is about 5.5mGal, and about 50cm, respectively.

Global gravity field modeling based on GOCE and complementary gravity data

A combined high-resolution global gravity field model up to degree/order (d/o) 720, including error estimates in terms of a full variance–covariance matrix, is determined from GOCE (Gravity field and steady-state Ocean Circulation Explorer) and complementary gravity field data. GOCE observations, highly accurate in the low to medium wavelength part (∼d/o 40–220), are supplemented by GRACE (Gravity Recovery and Climate Experiment) with high accuracy in the low wavelength part (∼d/o 2–150), and altimetric and terrestrial gravity field observations to enhance the spectral resolution of the combined gravity field model. The theory of combining different data sets by least-squares techniques, applying optimum weighting strategies, is illustrated. Full normal equation systems are used to enable stochastic modeling of all individual observations. High performance computing techniques are applied in order to handle normal equations of enormous size (about 2TB). The quality of the resulting gravity field solution is analyzed by comparisons with independent gravity field models and GPS/leveling observations, and also in the frame of the computation of a mean dynamic topography. The validation shows that the new combined model TUM2013C achieves the quality level of established high-resolution models. Compared to EGM2008, the improvements due to the inclusion of GOCE are clearly visible.

Antarctic circumpolar current from satellite gravimetric models ITG-GRACE2010, GOCE-TIM3 and satellite altimetry

The Antarctic circumpolar current (ACC) is a clockwise ocean flow from west to east around Antarctica, connecting the Pacific, Indian and Atlantic oceans, and plays a key role in the heat transport and climate change. The geostrophic surface currents can be derived from the ocean dynamic height as the deviation of the actual sea level from satellite altimetry and the Earth's geoid. Although the gravity recovery and climate experiment (GRACE) and gravity field and steady-state ocean circulation explorer (GOCE) mission provided an initial estimate of global geostrophic currents, a more detailed Antarctic circumpolar current is still not well estimated. In this paper, the detailed ACC is estimated from the newest ITG-Grace2010 gravity model based on 7-years of GRACE data, and GO_CONS_GCF_2_TIM_R3 gravity model (hereafter referred to GOCE-TIM3) based on 12 months of GOCE data, with the mean sea surface height model MSS_CNES_CLS_11 from satellite altimetry, respectively. The evaluation and comparisons are performed with oceanographic models, the GOCO03S gravity model as well as in situ drifter's measurements. Results show that the Antarctic circumpolar current based on GOCE gravity field model depicts more details and transport characteristics with high accuracy and spatial resolution, e.g., Agulhas currents and Brazil-Malvinas Confluence regions, which are more consistent with the in situ drifter's results. The ACC based on ITG-Grace2010 model is similar with the result of the GOCE-TIM3 model with RMS of 8.39cm/s and 7.85cm/s, respectively, while the accuracy of GOCE-TIM3 is still higher. The correlation coefficients of the estimated velocities, compared to drifter results, are 0.70 and 0.76 for ITG-Grace2010 and GOCE-TIM3. ITG-Grace2010 model has more noise in the higher spherical harmonic coefficients and some better performances in the geostrophic currents are able to be obtained if the degrees are truncated to 160 for ITG-Grace2010, while the GOCE-TIM3 and GOCO03S model do not have this phenomenon. The gravity model GOCO03S with combined CHAMP, GRACE and GOCE observations almost have no improvement in ACC estimate when compared with GOCE-TIM3 results, while the RMS of GOCO03S is a little larger than the GOCE-TIM3 results.

North American height datums and their offsets: Evaluation of the GOCE-based global geopotential models in Canada and the USA

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched on March 17, 2009. Three generations of global geopotential models have been computed and released based on the data collected by GOCE since then. The first generation of the models has been computed from the first two months of the data, and more observations, ranging from six to eight months, have been used in the computation of the second generation models. The third generation models are based on eighteen months of GOCE observations. The evaluation of these models is important in view of Canada’s and the USA’s decision to modernize and unify their vertical datums based on the geoid. In this paper, the released GOCE-based models are evaluated using 1315 and 18399 GNSS/levelling stations in Canada and the USA, respectively. In addition, three GRACE-based models and EGM2008 are included in the evaluation procedure as ’pre-GOCE era’ models to identify any improvements brought by the new GOCE-based models in the region. The results provide evidence that the third generation time-wise (go_cons_gcf_2_tim_r3) and direct approach (go_cons_gcf_2_dir_r3) GOCE models perform slightly better than the rest of the geopotential models in Canada and the USA

North American height datums and their offsets: Evaluation of the GOCE-based global geopotential models in Canada and the USA

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched on March 17, 2009. Three generations of global geopotential models have been computed and released based on the data collected by GOCE since then. The first generation of the models has been computed from the first two months of the data, and more observations, ranging from six to eight months, have been used in the computation of the second generation models. The third generation models are based on eighteen months of GOCE observations. The evaluation of these models is important in view of Canada’s and the USA’s decision to modernize and unify their vertical datums based on the geoid. In this paper, the released GOCE-based models are evaluated using 1315 and 18399 GNSS/levelling stations in Canada and the USA, respectively. In addition, three GRACE-based models and EGM2008 are included in the evaluation procedure as ’pre-GOCE era’ models to identify any improvements brought by the new GOCE-based models in the region. The results provide evidence that the third generation time-wise (go−cons−gcf−2−tim−r3) and direct approach (go−cons−gcf−2−dir−r3) GOCE models perform slightly better than the rest of the geopotential models in Canada and the USA.

Validation of GOCE global gravity field models using terrestrial gravity data in Norway

Validation of GOCE global gravity field models using terrestrial gravity data in NorwayThe GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gravity gradiometry mission maps the Earth's gravity field. Harmonic analysis of GOCE observations provides a global gravity field model (GGFM). Three theoretical strategies, namely the direct, the space-wise and the time-wise approach, have been proposed for GOCE harmonic analysis. Based on these three methods, several GGFMs have been provided to the user community by ESA. Thereby different releases are derived from different periods of GOCE observations and some of the models are based on combinations with other sources of gravity field information. Due to the multitude of GOCE GGFMs, validation against independent data is a crucial task for the quality description of the different models.In this study, GOCE GGFMs from three releases are validated with respect to terrestrial free-air gravity anomalies in Norway. The spectral enhancement method is applied to avoid spectral inconsistency between the terrestrial and the GOCE free-air gravity anomalies.The results indicate that the time-wise approach is a reliable harmonic analysis procedure in all three releases of GOCE models. The space-wise approach, available in two releases, provides similar results as the time-wise approach. The direct approach seems to be highly affected by a-priori information.

Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry, altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.

GOCE gradients in various reference frames and their accuracies

Abstract. The objective of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) is the determination of the Earth’s gravity field with high spatial resolution. The main science sensor (the gradiometer) measures differential accelerations, from which the gravitational gradients, i.e. the matrix of the second derivatives of the gravitational potential, are derived. Some of them (the diagonal components of the gravitational tensor) are observed with highest accuracy, 4 mE/√Hz in a frequency range from 5 mHz to 100 mHz, whereas the off-diagonals are obtained less accurately. The gradients will be observed in the instrument frame, which approximates the along-track oriented, local orbital frame. For the transformation of the gradients in other frames (e.g. in the strictly earth-pointing frame or a local geodetic frame), the transformation parameters (orientation angles) and all components of the gravity tensor have to be known with sufficient accuracy. We show how the elements of the gravitational tensor and their accuracies look like in the various frames as well as their spectral behaviour, if only the GOCE observations are used for the transformation. Only V'zz keeps approximately its original accuracy in all frames discussed, except in the earth-fixed frame ITRF (International Terrestrial Reference Frame). Therefore we recommend to analyse the gradients as ‘close’ as possible in the observation frame.Key words. Satellite gradiometry, GOCE mission, reference frames, transformation errors